metrologia

The leap second its history and possible future

R A Nelson D D McCarthy S MalysJ Levine B Guinot H F FliegelR L Beard and T R Bartholomew

Abstract This paper reviews the theoretical motivation for the leap second in the context of the historical evolutionof time measurement The periodic insertion of a leap second step into the scale of Coordinated Universal Time(UTC) necessitates frequent changes in complex timekeeping systems and is currently the subject of discussion inworking groups of various international scienti c organizations UTC is an atomic time scale that agrees in ratewith International Atomic Time (TAI) but differs by an integral number of seconds and is the basis of civil timeIn contrast Universal Time (UT1) is an astronomical time scale de ned by the Earthrsquos rotation and is used incelestial navigation UTC is presently maintained to within 09 s of UT1 As the needs of celestial navigation thatdepend on UT1 can now be met by satellite systems such as the Global Positioning System (GPS) options forrevising the de nition of UTC and the possible role of leap seconds in the future are considered

1 Introduction why we have leap seconds

Approximately once a year a leap second is introducedinto UTC the worldrsquos atomic time scale for civil timein order to keep it in phase with the rotation of theEarth Leap seconds ensure that on average the Suncontinues to be overhead on the Greenwich meridian atnoon to within about 1 s When the atomic de nitionof the International System of Units (SI) second wasintroduced in 1967 it was effectively made equivalentto an astronomical second based on a mean solar day of86 400 s in about 1820 However over approximatelythe past 1000 years the Earthrsquos rotation has beenslowing at an average rate of 14 ms per century so thatthe day is now about 25 ms longer than it was in 1820A difference of 25 ms per day amounts to about 1 s per

R A Nelson Satellite Engineering Research Corporation7701 Woodmont Avenue Suite 208 Bethesda MD 20814USA

D D McCarthy US Naval Observatory 3450 MassachusettsAvenue NW Washington DC 20392 USA

S Malys National Imagery and Mapping Agency Research andTechnology Of ce ATTR (MS D-82) 4600 Sangamore RoadBethesda MD 20816 USA

J Levine National Institute of Standards and TechnologyDepartment of Commerce MS 847 325 Broadway BoulderCO 80303 USA

B Guinot Observatoire de Paris D Acircepartement drsquoAstronomieFondamentale 61 avenue de lrsquoObservatoire F-75014 ParisFrance

H F Fliegel The Aerospace Corporation 2350 E El SegundoBlvd El Segundo CA 90245 USA

R L Beard Naval Research Laboratory 4555 Overlook AvenueSW Code 8150 Washington DC 20375 USA

T R Bartholomew Litton TASC Inc 131 National BusinessParkway Annapolis Junction MD 20701 USA

year and this is the reason for the more or less regularinsertion of leap seconds Superimposed on this veryslowly increasing difference are shorter-term variationsin the length of the day Periods between leap secondsare not therefore constant and in fact over the pastthirty years there have been several years in which leapseconds have been omitted

The primary reason for introducing the concept ofthe leap second was to meet the requirement of celestialnavigation to keep the difference between solar timeand atomic time small However the motivation forthe leap second has diminished because of the wideavailability of satellite navigation systems such asGPS while the operational complexities of maintainingprecise timekeeping systems have made the insertionof leap second adjustments increasingly dif cult andcostly

The question currently being debated in recentlycreated working groups of various internationalscienti c organizations is whether there continues tobe a need for the leap second with its many technicalinconveniences or whether it would be better simply tolet atomic time run freely and accept that the worldrsquoscivil time scale will slowly diverge from the rotationof the Earth This article gives the history and detailedtechnical background to the current practice and outlinesvarious solutions

2 Measurement of time

21 Clocks

Two elements are needed to measure the passage oftime (a) a time ldquoreckonerrdquo which is a repeatable

Metrologia 2001 38 509-529 509

R A Nelson et al

phenomenon whose motion or change of state isobservable and obeys a de nite law and (b) a timereference with respect to which the position or state ofthe time reckoner can be determined These elementscorrespond to the two properties of time measurementinterval and epoch Together the time reckoner and thetime reference constitute a clock

From remote antiquity the celestial bodies ndash theSun Moon and stars ndash have been the fundamentalreckoners of time The rising and setting of the Sunand the stars determine the day and night the phases ofthe Moon determine the month and the positions of theSun and stars along the horizon determine the seasons

Sundials were among the rst instruments used tomeasure the time of day The Egyptians divided the dayand night into 12 h each which varied with the seasonsWhile the notion of 24 equal hours was applied intheoretical works of Hellenistic astronomy the unequalldquoseasonal hourrdquo was used by the general public [1]When the rst reliable water clocks were constructedgreat care was taken to re ect the behaviour of a sundialinstead of the apparent motion of the heavens [2] Itwas not until the fourteenth century that an hour ofuniform length became customary due to the inventionof mechanical clocks These clocks were signi cantnot only because they were masterpieces of mechanicalingenuity but also because they altered the publicrsquosperception of time [3 4]

In the era of telescopic observations pendulumclocks served as the standard means of keeping timeuntil the introduction of modern electronics Quartz-crystal clocks were developed as an outgrowth of radiotechnology in the 1920s and 1930s [5] Harold Lyons[6] at the National Bureau of Standards in WashingtonDC (now the National Institute of Standards andTechnology Gaithersburg Md) constructed the rstatomic clock in 1948 using the microwave absorptionline of ammonia to stabilize a quartz oscillator LouisEssen and J V L Parry [7] at the National PhysicalLaboratory in Teddington UK constructed a practicalcaesium beam atomic clock in 1955 Commercialcaesium frequency standards appeared a year laterNorman Ramsey developed the hydrogen maser atHarvard University in 1960 [8]

Once practical atomic clocks became operationalthe Bureau International de lrsquoHeure (BIH) and severalnational laboratories began to establish atomic timescales [9] The responsibility for the maintenance ofthe international standard is now given to the BureauInternational des Poids et Mesures (BIPM) Some formof atomic time has been maintained continuously since1955 [10]

22 Time scales

Three primary methods of measuring time have beenin common use for modern applications in astronomyphysics and engineering These methods have evolved

as the design and construction of clocks have advancedin precision and sophistication The rst is UniversalTime (UT) the time scale based on the rotation of theEarth on its axis The second is Ephemeris Time (ET)the time scale based on the revolution of the Earthin its orbit around the Sun The third is Atomic Time(AT) the time scale based on the quantum mechanicsof the atom Each of these measures of time has had avariety of re nements and modi cations for particularapplications

The true measure of the Earthrsquos rotation is UT1which is the form of Universal Time corrected forpolar motion and used in celestial navigation Howeverowing to irregularities in the Earthrsquos rotation UT1 isnot uniform UT2 is UT1 corrected for the seasonalvariation

Ephemeris Time (ET) is a theoretically uniformtime scale de ned by the Newtonian dynamical laws ofmotion of the Earth Moon and planets This measureof time has been succeeded by several new time scalesthat are consistent with the general theory of relativity

The scale of International Atomic Time (TAI)is maintained by the BIPM with contributions fromnational timekeeping institutions TAI is a practicalrealization of a uniform time scale

The basis of civil time is Coordinated UniversalTime (UTC) an atomic time scale that correspondsexactly in rate with TAI but is kept within 09 s ofUT1 by the occasional insertion or deletion of a 1 sstep The decision to insert this leap second is madeby the International Earth Rotation Service (IERS)Since 1972 when UTC was introduced there havebeen twenty-two leap seconds all of which have beenpositive

3 Time measured by the rotation of the Earth

31 Universal Time

Universal Time (UT1) is the measure of astronomicaltime de ned by the rotation of the Earth on its axiswith respect to the Sun It is nominally equivalent tomean solar time referred to the meridian of Greenwichand reckoned from midnight The mean solar day istraditionally described as the time interval betweensuccessive transits of the ctitious mean Sun over agiven meridian Historically the unit of time the meansolar second was de ned as 186 400 of a mean solarday [11 12]

The ecliptic is the apparent annual path of theSun against the background of stars The intersectionof the ecliptic with the celestial equator provides afundamental reference point called the vernal equinoxIn practice Universal Time is determined not bythe meridian transit of the mean Sun but by thediurnal motion of the vernal equinox in accordancewith a conventional formula specifying UT1 in termsof Greenwich Mean Sidereal Time (GMST) The

510 Metrologia 2001 38 509-529

The leap second its history and possible future

current de ning relation for UT1 with respect to theastronomical reference system of the Fifth FundamentalKatalog (FK5) [13] is given in [14]

UT0 a designation no longer in common use isUT1 corrupted by the torque-free precessional motionof the Earthrsquos axis of rotation with respect to theEarthrsquos surface [15] This effect called variation oflatitude was predicted by Leonhard Euler [16] in 1765as a property of rigid body motion and was identi edobservationally by Seth Chandler [17] in 1891 Thedifference [UT0 ndash UT1] has a maximum value of about20 ms at mean latitude [18]

Apparent solar time as read directly by a sundialor more precisely determined by the altitude of theSun is the local time de ned by the actual diurnalmotion of the Sun However because of the tilt ofthe Earthrsquos axis and the elliptical shape of the Earthrsquosorbit the time interval between successive passages ofthe Sun over a given meridian is not constant Thedifference between mean and apparent solar time iscalled the equation of time The maximum amountby which apparent noon precedes mean noon is about165 min around 3 November while the maximumamount by which mean noon precedes apparent noonis about 145 min around 12 February Until the earlynineteenth century apparent solar time was used asthe argument for astronomical ephemerides Howeveras clocks improved and their use by ships at sea andby railroads grew apparent solar time was graduallyreplaced by mean solar time

32 Sidereal Time

Local Sidereal Time (LST) is the measure ofastronomical time de ned by the rotation of the Earthwith respect to the stars LST may be de ned as theright ascension of the local meridian which is the anglebetween the vernal equinox and the local meridianmeasured along the celestial equator In particularGreenwich sidereal time is the right ascension of theGreenwich meridian

The sidereal day is the time interval betweensuccessive transits of the vernal equinox It representsthe Earthrsquos period of rotation relative to the stars and isapproximately 86 1640905 mean solar seconds Owingto precession of the Earthrsquos axis with respect to thecelestial reference system the sidereal day is about00084 s shorter than the actual period of rotationin inertial space Thus the true rotational period ofthe Earth is approximately 86 1640989 mean solarseconds However the mean solar day presently exceedsa day of exactly 8 400 SI seconds by about 25 msTherefore the Earthrsquos period of rotation is currentlyabout 86 1641014 SI seconds

Even LST is not a uniform measure of astronomicaltime In the early twentieth century the inherentaccuracy of the Shortt free-pendulum clocks rst

revealed the periodic effects of nutation The principalterm consists of an eighteen-year oscillation with anamplitude of about 1 s These effects cannot beneglected and it became necessary to introduce theconcept of mean sidereal time which is affected onlyby precession

Greenwich Mean Sidereal Time (GMST) is meansidereal time with respect to the Greenwich meridianfrom which Universal Time (UT1) is derived Inthe past UT1 was determined using a worldwidenetwork of visual transit telescopes photographiczenith tubes and impersonal (prismatic) astrolabesThree basic techniques are now used to estimateUT1 (a) Very Long Baseline Interferometry (VLBI)measurements of selected radio point sources mostlyquasars (b) satellite laser ranging and (c) tracking ofGPS satellites Strictly speaking because of the motionof satellite orbital nodes in space VLBI providesthe only rigorous determination of UT1 A revisedconventional celestial reference frame based on theobserved positions of extragalactic objects is beingdeveloped that changes the basis for UT1 removes theneed for the equinox and changes the use of precessionand nutation

33 Variations in the Earthrsquos rotation

Three types of variation in the Earthrsquos rotationhave been identi ed a steady deceleration random uctuations and periodic changes [19]

As early as 1695 Sir Edmond Halley [20] wasled to suspect an acceleration in the mean motionof the Moon from a study of ancient eclipses of theSun recorded by Claudius Ptolemy and the medievalArabian astronomer Muhammed al-Batt AringanAring otilde By themid-eighteenth century the lunar acceleration was fullyestablished In 1754 Immanuel Kant [21] suggestedthat this acceleration might be an apparent phenomenoncaused by a steady deceleration in the Earthrsquos rotationdue to tidal friction Part of the effect was laterattributed to the variation in the solar perturbation on theMoonrsquos orbit As shown by Pierre-Simon Laplace andJohn Couch Adams the planetary perturbations causethe Earthrsquos orbital eccentricity to diminish and as aconsequence the Sunrsquos mean action on the Moon alsodiminishes In addition the observed lunar accelerationis affected by the recession of the Moon from the Earthin order to compensate the decrease in the Earthrsquosrate of spin by conservation of angular momentum Itwas not until the twentieth century that an apparentacceleration of the Sun was also identi ed [22-24]

Recent studies of eclipses by F R Stephensonand L V Morrison [25 26] suggest that the long-termaverage rate of increase in the length of the day is about17 ms per century (ndash45 10ndash22 rads2) Although theincrease in the length of day seems miniscule it has acumulative effect on a time scale based on the Earthrsquos

Metrologia 2001 38 509-529 511

R A Nelson et al

rotation In the past 2000 years the Earth acting as aclock has lost over 3 h For example the calculated pathof the total eclipse of the Sun witnessed in Babylon in136 BC would be in error by 488 corresponding toa time difference of 11 700 s assuming a uniform rateof rotation [27]

Sir Harold Jeffreys made the rst quantitativeestimate of global tidal friction in 1920 [28 29] Hefound that the energy dissipation in the shallow seasappeared to be of the correct order of magnitude toaccount for the apparent lunar and solar accelerationsThe rate of energy dissipation by tidal friction isnow considered to correspond to a rate of increasein the length of day of 23 ms per century (ndash6110ndash22 rads2) To account for the observed decelerationthere must also be a component in the opposite directionof about 06 ms per century (+16 10ndash22 rads2)which is possibly associated with changes in the Earthoblateness parameter caused by post-glacial rebound[30] or with deep ocean dissipation [31]

Evidence for a long-term deceleration in the Earthrsquosrotation extending over millions of years also exists incoral fossils that exhibit both daily and annual growthrings [32] For example several corals dating from themiddle of the Devonian Period some 370 million yearsago indicate that the number of days in the year wasbetween 385 and 410 The evidence suggests that therate of deceleration was substantially the same then asit is now [33]

Besides a steady decrease the Earthrsquos rotation issubject to frequent small changes that are random andcumulative [34 35] This variation was inferred fromstudies of statistical irregularities in the displacementsof the Moon Sun Mercury and Venus in proportionto their mean motions Random uctuations were rstobserved directly by atomic clocks in the mid-1950s[36]

There is also a periodic seasonal variation causedprincipally by meteorological effects The seasonalvariation was rst reported in 1936 by A Scheibeand U Adelsberger [37] who performed measurementsof the Earthrsquos rotation with excellent quartz-crystalclocks at the Physikalische-Technische Bundesanstalt(Germany) N Stoyko [38] at the BIH in 1937 foundthat the length of the day in January exceeded thatin July by 2 ms based on the performance of Shorttpendulum clocks and by comparison of the rates ofquartz-crystal clocks at the national time services Theseasonal variation in the length of the day is now knownto be of the order of 05 ms about the mean [39] Therotation of the Earth runs slow by about 30 ms inMay and runs fast by a similar amount in NovemberBy international agreement an empirical correction forthe seasonal variation has been applied since 1 January1956 resulting in the time scale UT2 The differencebetween UT2 and UT1 as currently applied is givenin [40] UT2 has a peak-to-peak amplitude of about60 ms

4 Time measured by the orbital motionsof the celestial bodies

The need for more uniform measures of astronomicaltime resulted in the de nition of time scales determinedfrom the motions of the celestial bodies in the solarsystem Originally based on Newtonian mechanics theyhave been re ned to take into account the effects ofgeneral relativity

In addition the unit of time previously withinthe exclusive domain of astronomy was incorporatedinto the creation of the SI In 1948 at the request ofthe International Union of Pure and Applied Physics(IUPAP) the 9th General Conference on Weights andMeasures (CGPM) resolved to adopt for internationaluse a practical system of units covering all branchesof metrology A limited set of base units including thesecond was selected by the 10th CGPM in 1954 anda representative list of derived units was compiled bythe International Committee for Weights and Measures(CIPM) in 1956 The SI was of cially established bythe 11th CGPM in 1960 [41]

41 Ephemeris Time

Because the variations in the Earthrsquos rotationare complex the CIPM referred the study of anew de nition of the second to the InternationalAstronomical Union (IAU) in 1948 At the suggestionof G M Clemence [42] the Conference on theFundamental Constants of Astronomy held in Paris in1950 recommended to the IAU that instead of theperiod of rotation of the Earth on its axis the newstandard of time ought to be based on the period ofrevolution of the Earth around the Sun as representedby Newcombrsquos Tables of the Sun published in 1895The measure of astronomical time de ned in this waywas given the name Ephemeris Time (ET)

The working de nition of Ephemeris Time wasthrough Newcombrsquos formula for the geometric meanlongitude of the Sun for an epoch of January 0 190012h UT [43]

L = 279 41 48 04 + 129 602 768 13 T + 1 089 T2

where is the time reckoned in Julian centuries of36 525 days The linear coef cient determines the unitof time while the constant determines the epoch TheIAU adopted this proposal in 1952 at its 8th GeneralAssembly in Rome [44]

Initially the period of revolution of the Earth wasunderstood to be the sidereal year However it wassubsequently pointed out by Andr Acirce Danjon that thetropical year is more fundamental than the sidereal yearas the length of the tropical year (equinox to equinox)is derived directly from Newcombrsquos formula whereasthe length of the sidereal year ( xed star to xed star)depends on the adopted value of the precession [45]

From the value of the linear coef cient inNewcombrsquos formula the tropical year of 1900 contains

512 Metrologia 2001 38 509-529

The leap second its history and possible future

[(360 60 60)129 602 76813] 36 525 86 400= 31 556 9259747 s Therefore at the recommendationof the CIPM the 10th CGPM in 1954 proposed thefollowing de nition of the second

ldquoThe second is the fraction 131 556 925975 of thelength of the tropical year for 19000rdquo

But although the IAU approved this de nition atits General Assembly in 1955 Danjon commented thatthe fraction ought to have a slightly more precisevalue to bring about exact numerical agreement withNewcombrsquos formula [46] Consequently the CIPM in1956 under the authority given by the 10th CGPM in1954 de ned the second of ephemeris time to be

ldquothe fraction 131 556 9259747 of the tropical year for1900 January 0 at 12 hours ephemeris timerdquo

This de nition was rati ed by the 11th CGPM in 1960[47] Reference to the year 1900 does not imply that thisis the epoch of a mean solar day of 86 400 s Rather itis the epoch of the tropical year of 31 556 9259747 s

Although ET was de ned in terms of the longitudeof the Sun in practice it was realized indirectly bycomparison of observations of lunar positions withlunar ephemerides Thus a set of secondary time scales(denoted by ET0 ET1 and ET2) were de ned thatdiffered because of subsequent improvements to theconventional ephemerides [48]

In 1958 the IAU General Assembly adopted aresolution that de ned the epoch of Ephemeris Time tocoincide with Newcombrsquos formula as follows [49]

ldquoEphemeris Time (ET) or Temps des Eph Acircem Acircerides(TE) is reckoned from the instant near the beginningof the calendar year AD 1900 when the geometricmean longitude of the Sun was 279 41 48 04 atwhich instant the measure of Ephemeris Time was1900 January 0d 12h preciselyrdquo

The resolution also included the de nition of the secondgiven by the CIPM in 1956 In a separate resolution theepoch for Universal Time was chosen as 1900 January0d 12h UT based on the Fourth Fundamental Katalog(FK4) [50] However the equinox of Newcombrsquos Sunthe lunar theory and the FK4 did not agree preciselyand they were moving with respect to one another Thusthe actual instant in time corresponding to the epochof ET was approximately 4 s later than the epoch ofUT [51]

Ephemeris Time (ET) is a dynamical timedetermined by the theory of celestial mechanics andis theoretically uniform [52] ET may be characterizedas the independent variable that brings the observedpositions of the celestial bodies into accord with theircalculated positions constructed from the Newtonianlaws of motion Therefore in effect it is de ned bythese laws [53]

42 Relativistic time scales

In 1960 ET replaced UT1 as the independent variableof astronomical ephemerides However ET did notinclude relativistic effects and did not distinguishbetween proper time and coordinate time Accordinglyat the 16th General Assembly in Grenoble in 1976the IAU de ned time-like arguments that distinguishcoordinate systems with origins at the centre of theEarth and the centre of the solar system respectivelyand are consistent with the general theory of relativity[54] In 1979 these time scales received the namesTerrestrial Dynamical Time (TDT) and BarycentricDynamical Time (TDB) [55]

TDT replaced ET in 1984 as the tabular argumentof the fundamental geocentric ephemerides TDT hasan origin of 1 January 1977 0 h TAI with a unit intervalequal to the SI second and maintains continuity withET At this epoch a rate correction of ndash10 10ndash13

was applied to TAI to bring the unit of TAI moreclosely into accord with the SI second [56] In 1991the IAU renamed TDT simply Terrestrial Time (TT) Apractical realization of TT is [57]

[TT] = [TAI] + 32184 s

The constant offset represents the difference betweenET and UT1 at the de ning epoch of TAI on 1 January1958

The relationship between TT and TAI is notstrictly rigorous for two fundamental reasons [58]First TAI is a statistically formed time scale based oncontributions from the major timing centres whereasTT is theoretically uniform Second a scale oftime based on the laws of gravitation may not bephilosophically equivalent to one based on the quantummechanics of the atom

For ephemerides referred to the barycentre ofthe solar system the argument is TDB Through anappropriately chosen scaling factor TDB varies fromTT or TDT by only periodic variations with amplitudesless than 0002 s

From the deliberations of the IAU Working Groupon Reference Systems formed in 1988 there arose ninerecommendations that were contained in Resolution A4adopted by the 21st IAU General Assembly in 1991[59] The general theory of relativity was explicitlyintroduced as the theoretical basis for the celestialreference frame and the form of the space-time metricto post-Newtonian order was speci ed The IAUalso clari ed the de nition of Terrestrial Time (TT)and adopted two additional time scales GeocentricCoordinate Time (TCG) and Barycentric CoordinateTime (TCB) [60] The ldquocoordinaterdquo time scales TCGand TCB are complementary to the ldquodynamicalrdquo timescales TT (or TDT) and TDB They differ in ratefrom TT and are related by four-dimensional space-timecoordinate transformations [61] These de nitions were

Metrologia 2001 38 509-529 513

R A Nelson et al

further clari ed by resolutions adopted at the 24th IAUGeneral Assembly held in Manchester in 2000 [62]

5 International Atomic Time

Although ET was a uniform time scale it was noteasily realized or disseminated The rapid developmentof atomic clocks permitted yet another de nition oftime [63]

51 Experimental atomic time scales

The rst operational caesium beam frequency standardappeared in 1955 at the National Physical Laboratory(NPL UK) [64] The Royal Greenwich Observatory(RGO) established a time scale known as GreenwichAtomic (GA) using free-running quartz-crystal clocksperiodically calibrated in terms of this standard

A commercial caesium frequency standard theldquoAtomichronrdquo was developed in 1956 [65] The USNaval Observatory (USNO) inaugurated its A1 atomictime scale on 13 September 1956 initially based on acaesium clock at the Naval Research Laboratory (NRL)consisting of an Atomichron caesium standard and aquartz-crystal clock The frequency of the crystal wasmatched daily to the caesium standard which was notoperated continuously [66] The National Bureau ofStandards (NBS) in Boulder Colo also maintained anatomic time scale NBS-A starting 9 October 1957The epochs of A1 and NBS-A were made coincidentand set equal to UT2 on 1 January 1958 [67]

The A1 time scale was introduced for world use on1 January 1959 By 1961 A1 was based on atomic os-cillators at the USNO NRL NBS USNO Time ServiceSub-Station (Richmond Florida) Harvard UniversityNational Research Council (Ottawa) NPL CentreNational drsquo AcircEtudes des T Acircel Acircecommunications (Bagneux)and Observatoire de Neuch Atildeatel (Switzerland) [68 69]

Once continuous atomic time became establishedat various laboratories the BIH began a mean atomictime scale based on frequency comparisons by means ofVLF carriers at 3 kHz to 30 kHz used for long-distancecommunications and radio navigation [70] Initially itwas designated AM and then A3 representing anaverage of the three best scales In 1960 the BIHbegan publication of the differences between UT2 andvarious individual atomic times obtained by integrationof accurate frequency comparisons By 1969 the BIHhad rede ned A3 to be an averaged atomic time scale(TA) based on several primary laboratory standardsIn 1971 this scale became the scale of InternationalAtomic Time (TAI) [71]

52 Atomic de nition of the second

In June 1955 Louis Essen and J V L Parry of the NPLmeasured the operational resonance frequency of thelaboratoryrsquos caesium standard with respect to the second

of UT2 as (9 192 631 830 plusmn 10) Hz by comparison withthe adopted frequency of a quartz standard which wascalibrated from astronomical measurements performedat the RGO [72] Over the following three years incooperation with William Markowitz and R G Hall atthe USNO they determined its value in terms of thesecond of Ephemeris Time Photographs of the Moonand surrounding stars were taken by the USNO dual-rate Moon camera over the period 195550 to 195825to determine the Ephemeris Time from the positionof the Moon at a known UT2 The UT2 scale basedon observations made with photographic zenith tubes(PZTs) at the USNO was calibrated with the caesium-beam atomic clock in Teddington via simultaneousobservations of the intervals between time pulsesbroadcast by radio stations WWV (then in GreenbeltMd) and GBR (Rugby UK) The measured caesiumfrequency was 9 192 631 770 Hz with a probable errorof plusmn 20 Hz [73] The principal uncertainty arose fromthe astronomical measurements themselves

Only seven years after the de nition of theephemeris second as an SI unit in 1960 the 13thCGPM in October 1967 adopted the atomic secondas the fundamental unit of time in the InternationalSystem of Units The second was de ned as [74]

ldquothe duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the twohyper ne levels of the ground state of the caesium133 atomrdquo

The second of atomic time is in principleequivalent to the second of Ephemeris Time Howeverthis decision did not consider a recommendation ofCommissions 4 (Ephemerides) and 31 (Time) of theIAU in 1967 in Prague which requested the CGPMto recognize the ephemeris second as a part of theIAU system of astronomical constants thus causingobjections from some astronomers [75]

53 Establishment of TAI

A prevalent opinion among astronomers in the mid-1960s had been that the atomic standards could providethe unit of time but not the continuous scale of timethat they needed [76] But on the contrary the BIHwas convinced that an atomic standard was the bestreference for time and devoted its resources to theestablishment of a practical international scale of atomictime [77]

In 1967 IAU Commissions 4 and 31 [78]recommended that the BIH compute an internationalscale of atomic time comprising independent timescales of the major national time services based onexperience gained from the experimental scale A3 Italso suggested that this scale be published in the form ofcorrections to the contributing time scales with respectto the international scale Similar recommendationsfollowed from the International Union of Radio Science

514 Metrologia 2001 38 509-529

The leap second its history and possible future

(URSI) in 1969 and the International Radio ConsultativeCommittee (CCIR) in 1970

The Comit Acirce Consultatif pour la D Acirce nition de laSeconde (CCDS) of the CIPM recommended guidelinesfor the establishment of International Atomic Time(TAI) in 1970 The CCDS stated [79]

ldquoInternational Atomic Time (TAI) is the time referencecoordinate established by the Bureau International delrsquoHeure on the basis of readings of atomic clocksoperating in various establishments in accordance withthe de nition of the second the unit of time of theInternational System of Unitsrdquo

In conformity with the recommendations of IAUCommissions 4 and 31 in 1967 the CCDS [80]de ned the origin so that TAI would be in approximateagreement with UT2 on 1 January 1958 0 h UT2 The14th CGPM approved the establishment of TAI in 1971

Yet an important task remained To de ne the scaleof atomic time completely one must de ne where in theuniverse the SI second is to be realized In recognitionof the framework of general relativity the de nitionwas completed in 1980 by the statement [81]

ldquoTAI is a coordinate time scale de ned in a geocentricreference frame with the SI second as realized on therotating geoid as the scale unitrdquo

Thus relativistic corrections are required for the primarylaboratory realizations of the SI second used in thecalibration of TAI to compensate the frequency shiftsbetween their individual locations and a point xed onthe surface of the rotating geoid

TAI when formally adopted in 1971 was anextension of the BIH atomic time scale that had beencontinuous back to 1955 In 1988 responsibility formaintaining TAI was transferred from the BIH to theBIPM A distribution of approximately two hundredclocks maintained in fty laboratories contribute to TAIusing an optimized weighting algorithm

6 Coordinated Universal Time

There were two communities of users Some suchas astronomers geodesists and navigators wanted abroadcast time connected with the angle of the Earthrsquosrotation in space Others such as physicists andengineers at time and frequency laboratories wantedit to be perfectly uniform to agree with the best clocksAttempts to meet the needs of both communities led tothe creation of Coordinated Universal Time (UTC)

61 Original UTC system

Originally radio time signals controlled from the RoyalGreenwich Observatory were kept closely in phasewith the Earthrsquos rotation using direct astronomicalobservations resulting in a nominal time interval of

a second that could vary slightly from day to dayBeginning in 1944 the time signals were generatedby quartz-crystal clocks at a uniform rate with stepcorrections introduced when necessary to maintainagreement with astronomical time When an atomicstandard became available at the NPL in 1955 theMSF time and frequency broadcast service of theUK based its signal on the provisional frequencyof 9 192 631 830 Hz for caesium In 1958 the NPLadopted the frequency 9 192 631 770 Hz but announcedthat the MSF service would have an annual rate offsetof a stated amount in addition to step corrections tokeep the disseminated time signals close to the scaleof UT2 [82]

Following the creation of their atomic time scalesin the period 1956-57 the USNO and the NBS eachmaintained two systems of atomic clock time TheUSNO system of uniform time A1 was related toEphemeris Time while the USNO Master Clock wasadjusted daily to UT2 from PZT observations Similarlythe NBS time scale NBS-A had a uniform ratesynchronized with A1 while NBS-UA was derived byapplying rate offsets and small steps to follow UT2 andwas disseminated by radio station WWV A summaryof the corrections utilized by WWV is given in [83]

At rst time signals broadcast from variouscountries were so loosely controlled that a listenermonitoring several stations could hear the pulsesarriving at different times To reduce the disparitiesthe World Administrative Radio Conference (Geneva)in 1959 requested the CCIR to study the questionof establishing and operating a worldwide standardfrequency and time signal service

The nautical almanacs of the UK and the USAwere combined in 1957 beginning with the editions for1960 In August 1959 it was also agreed to coordinatetheir time and frequency transmissions Coordinationbegan 1 January 1960 The participating observatoriesand laboratories were the USNO RGO NBS NRLand NPL Gradually other countries joined the systemwhich was entrusted to the BIH in 1961 In January1965 the BIH decided to attach UTC to its atomic timeA3 (which became TAI) by a mathematical relationship[84] This was the origin of the link between TAI andUTC The name ldquoCoordinated Universal Time (UTC)rdquowas approved by a resolution of IAU Commissions 4and 31 at the 13th General Assembly in 1967 [85]

62 Revised UTC system

Details of the UTC system were formalized by CCIRStudy Group 7 in Geneva in 1962 and were adoptedby the CCIR in its Recommendation 374 [86] of 1963The frequency offset was announced by the BIH afterconsultation with the observatories concerned to matchas nearly as practical the rotational speed of the Earthand remained constant for each year while steps of100 ms were inserted periodically at the beginning of

Metrologia 2001 38 509-529 515

R A Nelson et al

the month on dates determined by the BIH to maintainthe time signals to within about 01 s of UT2

As UTC included rate offsets to reduce the need forstep adjustments the broadcast time signals indicatedneither the SI second nor the mean solar secondbut rather variable intervals to stay in step withUT2 from which the SI second could be obtainedby applying a known correction Attempts to followthese uctuations necessitated revisions in complexequipment on a frequent basis and risked temporaryinterruptions of service At an interim session in MonteCarlo during March 1965 Study Group 7 suggested thatexperimental broadcasts and studies should be made toinvestigate how to provide both the epoch of UniversalTime and the international unit of time interval in thesame emission [87]

The revised CCIR Recommendation 374-1 [88]of 1966 allowed for the limited and provisional useof an experimental ldquoStepped Atomic Time (SAT)rdquo inwhich the broadcast time rate was the atomic timerate with no carrier deviation but in which frequentstep adjustments of 200 ms were applied to match UT2to within 01 s The existence of two parallel systemsUTC and SAT was regarded as a phase in the evolutionand adoption of a single practical and internationallyacceptable system [89]

63 Present UTC system

At the 15th General Assembly of the URSI in Munichin 1966 Commission 1 expressed the opinion thatall proposed methods of operating standard time andfrequency services contained defects and that theseservices must inevitably develop towards a system ofuniform atomic time and constant frequency For thoserequiring astronomical time some form of correctionwould be necessary [90 91] In 1967 at a meeting heldin Brussels under the auspices of the URSI to considerfrequency coordination in Europe it was unanimouslyagreed that both rate offsets and step adjustments shouldbe discontinued It was suggested that the deviations ofUTC from UT2 would have no signi cance for civilpurposes but could be disseminated to navigators intables or in the transmissions themselves [92]

Dissatisfaction with the existing form of UTC andthe need to study the implications of the new de nitionof the second adopted in 1967 prompted discussions bythe CIPM and the CCIR Following a recommendationof the CCDS the CIPM formed a preparatorycommission for the international coordination of timescales The concept of the leap second analogous to theleap day in the calendar was proposed independentlyby G M R Winkler [93] and Louis Essen [94] at ameeting of the commission held at the BIPM in May1968 [95 96] It was proposed that integer steps ofseconds replace the steps of 100 ms or 200 ms thenbeing used because they were too frequent and toosmall Consideration of possible modi cations to UTC

was also given by CCIR Study Group 7 in Boulderin August 1968 [97] The view was expressed that thebest system would be one with 1 s steps without rateoffsets so that equipment generating a pulse train wouldnot require a change in frequency To meet the needsof navigators it was suggested that coded informationmight be incorporated in the emission to indicate thedifference between UTC and UT2 to higher resolutionAn Interim Working Party IWP 71 was formed toinvestigate requirements submit proposals and x adate for the introduction of the new system The optionsunder consideration at this time were summarized asfollows [98]

ldquoDiscarding the suggestion (for practical reasons and toavoid confusions) of two time scales one approachingUT (the present UTC) and the other without offsetsand adjustments only three alternatives remain (a) stepadjustment of 01 s or 02 s to maintain the UTCsuf ciently near to UT2 to permit to ignore thedifference in most of the applications (b) completedisuse of UTC system replacing it with a coordinateduniform time scale without offsets and steps andtherefore not approaching UT (c) step adjustment of1 s exactlyrdquo

Speci c proposals were made by Study Group 7 inGeneva in October 1969 which were approved by theCCIR XIIth Plenary Assembly in New Delhi in January1970 In its Recommendation 460 [99] the CCIRstated that (a) carrier frequencies and time intervalsshould be maintained constant and should correspondto the de nition of the SI second (b) step adjustmentswhen necessary should be exactly 1 s to maintainapproximate agreement with Universal Time (UT) and(c) standard signals should contain information onthe difference between UTC and UT The CCIR alsodecided to begin the new UTC system on 1 January1972

At the IAUrsquos 14th General Assembly in BrightonUK in August 1970 the chairman of CCIR IWP 71H M Smith sought the views of Commissions 4(Ephemerides) and 31 (Time) The appropriate methodof providing both precise Earth orientation to navigatorsand uniform time to time and frequency laboratorieswas discussed As the navigator requires knowledgeof UT1 rather than UT2 it was recommended thatradio time signals should disseminate differences in theform of [UT1 ndash UTC] Several astronomers emphasizedthat visual observers in astronomical and related eldsrequire UT1 to a precision of 01 s as this is aboutthe limit of human time discrimination In addition thealmanacs were designed to permit a determination ofposition to 01 minute of arc and for this a comparableprecision in time of 025 s was required At BrightonCommission 31 adopted recommendations similar tothose of the CCIR Also the IAU General Assemblyresolved that adequate means should be provided toensure that the difference [UT1 ndash UTC] would be

516 Metrologia 2001 38 509-529

The leap second its history and possible future

available before permitting UTC to depart from UT1by more than about 01 s [100]

Detailed instructions for the implementation ofCCIR Recommendation 460 were drafted at a furthermeeting of Study Group 7 that was held in February1971 [101] The de ning epoch of 1 January 19720 h 0 m 0 s UTC was set 10 s behind TAI whichwas the approximate accumulated difference betweenTAI and UT1 since the inception of TAI in 1958and a unique fraction of a second adjustment wasapplied so that UTC would differ from TAI byan integral number of seconds The recommendedmaximum departure of UTC from UT1 was 07 sThe term ldquoleap secondrdquo was introduced for the steppedsecond An additional correction DUT1 was introducedhaving integral multiples of 01 s to be embodied in thetime signals such that when added to UTC they wouldyield a better approximation to UT1 For examplethis second level of correction was achieved by NBSradio stations WWV and WWVH by using double ticksor pulses after the start of each minute in its UTCbroadcasts [102]

The recommendations of the IAU were formalizedby resolutions of Commissions 4 and 31 at the15th General Assembly in Sydney in 1973 and afterfurther discussion the name UTC was retained [103]UTC was recommended as the basis of standardtime in all countries the time in common (civil)use as disseminated by radio signals The limit of[UT1 ndash UTC] was set at plusmn0950 s as this is themaximum difference that can be accommodated by thecode format The maximum deviation of UT1 from[UTC + DUT1] was set at plusmn0100 s In 1974 the CCIRincreased the tolerance for [UT1 ndash UTC] from 07 sto 09 s

The present UTC system is de ned by ITU-R(formerly CCIR) Recommendation ITU-R TF460-5[104]

ldquoUTC is the time scale maintained by the BIPM withassistance from the IERS which forms the basis of acoordinated dissemination of standard frequencies andtime signals It corresponds exactly in rate with TAIbut differs from it by an integral number of secondsThe UTC scale is adjusted by the insertion or deletionof seconds (positive or negative leap seconds) to ensureapproximate agreement with UT1rdquo

The interval between time signals of UTC is thusexactly equal to the SI second A history of rate offsetsand step adjustments in UTC is given in [105]

7 The leap second

71 Rate of increase in length of day

Because the Earthrsquos rotation is gradually slowingdown and in addition has both random and periodic uctuations it is not a uniform measure of time The

time difference T [ET ndash UT1] [TT ndash UT1]represents the difference between the uniform scale ofEphemeris Time or Terrestrial Time and the variablescale of Universal Time Values of T are summarizedin [106] Before 1955 the values are given by T[ET ndash UT1] based on observations of the Moon After1955 values are given by T [TT ndash UT1] [TAI +32184 s ndash UT1] from measurements by atomic clocksas published by the BIH and the BIPM

According to Stephenson and Morrison [107] overthe past 2700 years can be represented by aparabola of approximately the form

T = (31 scy2) (T ndash 1820)2(100)2 ndash 20 s

where T is expressed in seconds and T is the yearFigure 1 plots this equation together with observationssince 1620 The curve has a minimum at the year 1820and passes through 0 at the year 1900 Actual values of

T based on astronomical data may differ somewhatfrom this smoothed t For example the value of Tis 32184 s at 19580 the origin of TAI However nosingle parabola can satisfactorily represent all modernand historical data

The derivative of T is

Lday (00017 sdcy) (T ndash 1820)100

Figure 1 Observations and parabolic t of T versus timesince 1620 (after Stephenson and Morrison [26])

Figure 2 Change in the length of day with respect to areference day of 86 400 s versus time (after Stephensonand Morrison [26])

Metrologia 2001 38 509-529 517

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

R A Nelson et al

phenomenon whose motion or change of state isobservable and obeys a de nite law and (b) a timereference with respect to which the position or state ofthe time reckoner can be determined These elementscorrespond to the two properties of time measurementinterval and epoch Together the time reckoner and thetime reference constitute a clock

From remote antiquity the celestial bodies ndash theSun Moon and stars ndash have been the fundamentalreckoners of time The rising and setting of the Sunand the stars determine the day and night the phases ofthe Moon determine the month and the positions of theSun and stars along the horizon determine the seasons

Sundials were among the rst instruments used tomeasure the time of day The Egyptians divided the dayand night into 12 h each which varied with the seasonsWhile the notion of 24 equal hours was applied intheoretical works of Hellenistic astronomy the unequalldquoseasonal hourrdquo was used by the general public [1]When the rst reliable water clocks were constructedgreat care was taken to re ect the behaviour of a sundialinstead of the apparent motion of the heavens [2] Itwas not until the fourteenth century that an hour ofuniform length became customary due to the inventionof mechanical clocks These clocks were signi cantnot only because they were masterpieces of mechanicalingenuity but also because they altered the publicrsquosperception of time [3 4]

In the era of telescopic observations pendulumclocks served as the standard means of keeping timeuntil the introduction of modern electronics Quartz-crystal clocks were developed as an outgrowth of radiotechnology in the 1920s and 1930s [5] Harold Lyons[6] at the National Bureau of Standards in WashingtonDC (now the National Institute of Standards andTechnology Gaithersburg Md) constructed the rstatomic clock in 1948 using the microwave absorptionline of ammonia to stabilize a quartz oscillator LouisEssen and J V L Parry [7] at the National PhysicalLaboratory in Teddington UK constructed a practicalcaesium beam atomic clock in 1955 Commercialcaesium frequency standards appeared a year laterNorman Ramsey developed the hydrogen maser atHarvard University in 1960 [8]

Once practical atomic clocks became operationalthe Bureau International de lrsquoHeure (BIH) and severalnational laboratories began to establish atomic timescales [9] The responsibility for the maintenance ofthe international standard is now given to the BureauInternational des Poids et Mesures (BIPM) Some formof atomic time has been maintained continuously since1955 [10]

22 Time scales

Three primary methods of measuring time have beenin common use for modern applications in astronomyphysics and engineering These methods have evolved

as the design and construction of clocks have advancedin precision and sophistication The rst is UniversalTime (UT) the time scale based on the rotation of theEarth on its axis The second is Ephemeris Time (ET)the time scale based on the revolution of the Earthin its orbit around the Sun The third is Atomic Time(AT) the time scale based on the quantum mechanicsof the atom Each of these measures of time has had avariety of re nements and modi cations for particularapplications

The true measure of the Earthrsquos rotation is UT1which is the form of Universal Time corrected forpolar motion and used in celestial navigation Howeverowing to irregularities in the Earthrsquos rotation UT1 isnot uniform UT2 is UT1 corrected for the seasonalvariation

Ephemeris Time (ET) is a theoretically uniformtime scale de ned by the Newtonian dynamical laws ofmotion of the Earth Moon and planets This measureof time has been succeeded by several new time scalesthat are consistent with the general theory of relativity

The scale of International Atomic Time (TAI)is maintained by the BIPM with contributions fromnational timekeeping institutions TAI is a practicalrealization of a uniform time scale

The basis of civil time is Coordinated UniversalTime (UTC) an atomic time scale that correspondsexactly in rate with TAI but is kept within 09 s ofUT1 by the occasional insertion or deletion of a 1 sstep The decision to insert this leap second is madeby the International Earth Rotation Service (IERS)Since 1972 when UTC was introduced there havebeen twenty-two leap seconds all of which have beenpositive

3 Time measured by the rotation of the Earth

31 Universal Time

Universal Time (UT1) is the measure of astronomicaltime de ned by the rotation of the Earth on its axiswith respect to the Sun It is nominally equivalent tomean solar time referred to the meridian of Greenwichand reckoned from midnight The mean solar day istraditionally described as the time interval betweensuccessive transits of the ctitious mean Sun over agiven meridian Historically the unit of time the meansolar second was de ned as 186 400 of a mean solarday [11 12]

The ecliptic is the apparent annual path of theSun against the background of stars The intersectionof the ecliptic with the celestial equator provides afundamental reference point called the vernal equinoxIn practice Universal Time is determined not bythe meridian transit of the mean Sun but by thediurnal motion of the vernal equinox in accordancewith a conventional formula specifying UT1 in termsof Greenwich Mean Sidereal Time (GMST) The

510 Metrologia 2001 38 509-529

The leap second its history and possible future

current de ning relation for UT1 with respect to theastronomical reference system of the Fifth FundamentalKatalog (FK5) [13] is given in [14]

UT0 a designation no longer in common use isUT1 corrupted by the torque-free precessional motionof the Earthrsquos axis of rotation with respect to theEarthrsquos surface [15] This effect called variation oflatitude was predicted by Leonhard Euler [16] in 1765as a property of rigid body motion and was identi edobservationally by Seth Chandler [17] in 1891 Thedifference [UT0 ndash UT1] has a maximum value of about20 ms at mean latitude [18]

Apparent solar time as read directly by a sundialor more precisely determined by the altitude of theSun is the local time de ned by the actual diurnalmotion of the Sun However because of the tilt ofthe Earthrsquos axis and the elliptical shape of the Earthrsquosorbit the time interval between successive passages ofthe Sun over a given meridian is not constant Thedifference between mean and apparent solar time iscalled the equation of time The maximum amountby which apparent noon precedes mean noon is about165 min around 3 November while the maximumamount by which mean noon precedes apparent noonis about 145 min around 12 February Until the earlynineteenth century apparent solar time was used asthe argument for astronomical ephemerides Howeveras clocks improved and their use by ships at sea andby railroads grew apparent solar time was graduallyreplaced by mean solar time

32 Sidereal Time

Local Sidereal Time (LST) is the measure ofastronomical time de ned by the rotation of the Earthwith respect to the stars LST may be de ned as theright ascension of the local meridian which is the anglebetween the vernal equinox and the local meridianmeasured along the celestial equator In particularGreenwich sidereal time is the right ascension of theGreenwich meridian

The sidereal day is the time interval betweensuccessive transits of the vernal equinox It representsthe Earthrsquos period of rotation relative to the stars and isapproximately 86 1640905 mean solar seconds Owingto precession of the Earthrsquos axis with respect to thecelestial reference system the sidereal day is about00084 s shorter than the actual period of rotationin inertial space Thus the true rotational period ofthe Earth is approximately 86 1640989 mean solarseconds However the mean solar day presently exceedsa day of exactly 8 400 SI seconds by about 25 msTherefore the Earthrsquos period of rotation is currentlyabout 86 1641014 SI seconds

Even LST is not a uniform measure of astronomicaltime In the early twentieth century the inherentaccuracy of the Shortt free-pendulum clocks rst

revealed the periodic effects of nutation The principalterm consists of an eighteen-year oscillation with anamplitude of about 1 s These effects cannot beneglected and it became necessary to introduce theconcept of mean sidereal time which is affected onlyby precession

Greenwich Mean Sidereal Time (GMST) is meansidereal time with respect to the Greenwich meridianfrom which Universal Time (UT1) is derived Inthe past UT1 was determined using a worldwidenetwork of visual transit telescopes photographiczenith tubes and impersonal (prismatic) astrolabesThree basic techniques are now used to estimateUT1 (a) Very Long Baseline Interferometry (VLBI)measurements of selected radio point sources mostlyquasars (b) satellite laser ranging and (c) tracking ofGPS satellites Strictly speaking because of the motionof satellite orbital nodes in space VLBI providesthe only rigorous determination of UT1 A revisedconventional celestial reference frame based on theobserved positions of extragalactic objects is beingdeveloped that changes the basis for UT1 removes theneed for the equinox and changes the use of precessionand nutation

33 Variations in the Earthrsquos rotation

Three types of variation in the Earthrsquos rotationhave been identi ed a steady deceleration random uctuations and periodic changes [19]

As early as 1695 Sir Edmond Halley [20] wasled to suspect an acceleration in the mean motionof the Moon from a study of ancient eclipses of theSun recorded by Claudius Ptolemy and the medievalArabian astronomer Muhammed al-Batt AringanAring otilde By themid-eighteenth century the lunar acceleration was fullyestablished In 1754 Immanuel Kant [21] suggestedthat this acceleration might be an apparent phenomenoncaused by a steady deceleration in the Earthrsquos rotationdue to tidal friction Part of the effect was laterattributed to the variation in the solar perturbation on theMoonrsquos orbit As shown by Pierre-Simon Laplace andJohn Couch Adams the planetary perturbations causethe Earthrsquos orbital eccentricity to diminish and as aconsequence the Sunrsquos mean action on the Moon alsodiminishes In addition the observed lunar accelerationis affected by the recession of the Moon from the Earthin order to compensate the decrease in the Earthrsquosrate of spin by conservation of angular momentum Itwas not until the twentieth century that an apparentacceleration of the Sun was also identi ed [22-24]

Recent studies of eclipses by F R Stephensonand L V Morrison [25 26] suggest that the long-termaverage rate of increase in the length of the day is about17 ms per century (ndash45 10ndash22 rads2) Although theincrease in the length of day seems miniscule it has acumulative effect on a time scale based on the Earthrsquos

Metrologia 2001 38 509-529 511

R A Nelson et al

rotation In the past 2000 years the Earth acting as aclock has lost over 3 h For example the calculated pathof the total eclipse of the Sun witnessed in Babylon in136 BC would be in error by 488 corresponding toa time difference of 11 700 s assuming a uniform rateof rotation [27]

Sir Harold Jeffreys made the rst quantitativeestimate of global tidal friction in 1920 [28 29] Hefound that the energy dissipation in the shallow seasappeared to be of the correct order of magnitude toaccount for the apparent lunar and solar accelerationsThe rate of energy dissipation by tidal friction isnow considered to correspond to a rate of increasein the length of day of 23 ms per century (ndash6110ndash22 rads2) To account for the observed decelerationthere must also be a component in the opposite directionof about 06 ms per century (+16 10ndash22 rads2)which is possibly associated with changes in the Earthoblateness parameter caused by post-glacial rebound[30] or with deep ocean dissipation [31]

Evidence for a long-term deceleration in the Earthrsquosrotation extending over millions of years also exists incoral fossils that exhibit both daily and annual growthrings [32] For example several corals dating from themiddle of the Devonian Period some 370 million yearsago indicate that the number of days in the year wasbetween 385 and 410 The evidence suggests that therate of deceleration was substantially the same then asit is now [33]

Besides a steady decrease the Earthrsquos rotation issubject to frequent small changes that are random andcumulative [34 35] This variation was inferred fromstudies of statistical irregularities in the displacementsof the Moon Sun Mercury and Venus in proportionto their mean motions Random uctuations were rstobserved directly by atomic clocks in the mid-1950s[36]

There is also a periodic seasonal variation causedprincipally by meteorological effects The seasonalvariation was rst reported in 1936 by A Scheibeand U Adelsberger [37] who performed measurementsof the Earthrsquos rotation with excellent quartz-crystalclocks at the Physikalische-Technische Bundesanstalt(Germany) N Stoyko [38] at the BIH in 1937 foundthat the length of the day in January exceeded thatin July by 2 ms based on the performance of Shorttpendulum clocks and by comparison of the rates ofquartz-crystal clocks at the national time services Theseasonal variation in the length of the day is now knownto be of the order of 05 ms about the mean [39] Therotation of the Earth runs slow by about 30 ms inMay and runs fast by a similar amount in NovemberBy international agreement an empirical correction forthe seasonal variation has been applied since 1 January1956 resulting in the time scale UT2 The differencebetween UT2 and UT1 as currently applied is givenin [40] UT2 has a peak-to-peak amplitude of about60 ms

4 Time measured by the orbital motionsof the celestial bodies

The need for more uniform measures of astronomicaltime resulted in the de nition of time scales determinedfrom the motions of the celestial bodies in the solarsystem Originally based on Newtonian mechanics theyhave been re ned to take into account the effects ofgeneral relativity

In addition the unit of time previously withinthe exclusive domain of astronomy was incorporatedinto the creation of the SI In 1948 at the request ofthe International Union of Pure and Applied Physics(IUPAP) the 9th General Conference on Weights andMeasures (CGPM) resolved to adopt for internationaluse a practical system of units covering all branchesof metrology A limited set of base units including thesecond was selected by the 10th CGPM in 1954 anda representative list of derived units was compiled bythe International Committee for Weights and Measures(CIPM) in 1956 The SI was of cially established bythe 11th CGPM in 1960 [41]

41 Ephemeris Time

Because the variations in the Earthrsquos rotationare complex the CIPM referred the study of anew de nition of the second to the InternationalAstronomical Union (IAU) in 1948 At the suggestionof G M Clemence [42] the Conference on theFundamental Constants of Astronomy held in Paris in1950 recommended to the IAU that instead of theperiod of rotation of the Earth on its axis the newstandard of time ought to be based on the period ofrevolution of the Earth around the Sun as representedby Newcombrsquos Tables of the Sun published in 1895The measure of astronomical time de ned in this waywas given the name Ephemeris Time (ET)

The working de nition of Ephemeris Time wasthrough Newcombrsquos formula for the geometric meanlongitude of the Sun for an epoch of January 0 190012h UT [43]

L = 279 41 48 04 + 129 602 768 13 T + 1 089 T2

where is the time reckoned in Julian centuries of36 525 days The linear coef cient determines the unitof time while the constant determines the epoch TheIAU adopted this proposal in 1952 at its 8th GeneralAssembly in Rome [44]

Initially the period of revolution of the Earth wasunderstood to be the sidereal year However it wassubsequently pointed out by Andr Acirce Danjon that thetropical year is more fundamental than the sidereal yearas the length of the tropical year (equinox to equinox)is derived directly from Newcombrsquos formula whereasthe length of the sidereal year ( xed star to xed star)depends on the adopted value of the precession [45]

From the value of the linear coef cient inNewcombrsquos formula the tropical year of 1900 contains

512 Metrologia 2001 38 509-529

The leap second its history and possible future

[(360 60 60)129 602 76813] 36 525 86 400= 31 556 9259747 s Therefore at the recommendationof the CIPM the 10th CGPM in 1954 proposed thefollowing de nition of the second

ldquoThe second is the fraction 131 556 925975 of thelength of the tropical year for 19000rdquo

But although the IAU approved this de nition atits General Assembly in 1955 Danjon commented thatthe fraction ought to have a slightly more precisevalue to bring about exact numerical agreement withNewcombrsquos formula [46] Consequently the CIPM in1956 under the authority given by the 10th CGPM in1954 de ned the second of ephemeris time to be

ldquothe fraction 131 556 9259747 of the tropical year for1900 January 0 at 12 hours ephemeris timerdquo

This de nition was rati ed by the 11th CGPM in 1960[47] Reference to the year 1900 does not imply that thisis the epoch of a mean solar day of 86 400 s Rather itis the epoch of the tropical year of 31 556 9259747 s

Although ET was de ned in terms of the longitudeof the Sun in practice it was realized indirectly bycomparison of observations of lunar positions withlunar ephemerides Thus a set of secondary time scales(denoted by ET0 ET1 and ET2) were de ned thatdiffered because of subsequent improvements to theconventional ephemerides [48]

In 1958 the IAU General Assembly adopted aresolution that de ned the epoch of Ephemeris Time tocoincide with Newcombrsquos formula as follows [49]

ldquoEphemeris Time (ET) or Temps des Eph Acircem Acircerides(TE) is reckoned from the instant near the beginningof the calendar year AD 1900 when the geometricmean longitude of the Sun was 279 41 48 04 atwhich instant the measure of Ephemeris Time was1900 January 0d 12h preciselyrdquo

The resolution also included the de nition of the secondgiven by the CIPM in 1956 In a separate resolution theepoch for Universal Time was chosen as 1900 January0d 12h UT based on the Fourth Fundamental Katalog(FK4) [50] However the equinox of Newcombrsquos Sunthe lunar theory and the FK4 did not agree preciselyand they were moving with respect to one another Thusthe actual instant in time corresponding to the epochof ET was approximately 4 s later than the epoch ofUT [51]

Ephemeris Time (ET) is a dynamical timedetermined by the theory of celestial mechanics andis theoretically uniform [52] ET may be characterizedas the independent variable that brings the observedpositions of the celestial bodies into accord with theircalculated positions constructed from the Newtonianlaws of motion Therefore in effect it is de ned bythese laws [53]

42 Relativistic time scales

In 1960 ET replaced UT1 as the independent variableof astronomical ephemerides However ET did notinclude relativistic effects and did not distinguishbetween proper time and coordinate time Accordinglyat the 16th General Assembly in Grenoble in 1976the IAU de ned time-like arguments that distinguishcoordinate systems with origins at the centre of theEarth and the centre of the solar system respectivelyand are consistent with the general theory of relativity[54] In 1979 these time scales received the namesTerrestrial Dynamical Time (TDT) and BarycentricDynamical Time (TDB) [55]

TDT replaced ET in 1984 as the tabular argumentof the fundamental geocentric ephemerides TDT hasan origin of 1 January 1977 0 h TAI with a unit intervalequal to the SI second and maintains continuity withET At this epoch a rate correction of ndash10 10ndash13

was applied to TAI to bring the unit of TAI moreclosely into accord with the SI second [56] In 1991the IAU renamed TDT simply Terrestrial Time (TT) Apractical realization of TT is [57]

[TT] = [TAI] + 32184 s

The constant offset represents the difference betweenET and UT1 at the de ning epoch of TAI on 1 January1958

The relationship between TT and TAI is notstrictly rigorous for two fundamental reasons [58]First TAI is a statistically formed time scale based oncontributions from the major timing centres whereasTT is theoretically uniform Second a scale oftime based on the laws of gravitation may not bephilosophically equivalent to one based on the quantummechanics of the atom

For ephemerides referred to the barycentre ofthe solar system the argument is TDB Through anappropriately chosen scaling factor TDB varies fromTT or TDT by only periodic variations with amplitudesless than 0002 s

From the deliberations of the IAU Working Groupon Reference Systems formed in 1988 there arose ninerecommendations that were contained in Resolution A4adopted by the 21st IAU General Assembly in 1991[59] The general theory of relativity was explicitlyintroduced as the theoretical basis for the celestialreference frame and the form of the space-time metricto post-Newtonian order was speci ed The IAUalso clari ed the de nition of Terrestrial Time (TT)and adopted two additional time scales GeocentricCoordinate Time (TCG) and Barycentric CoordinateTime (TCB) [60] The ldquocoordinaterdquo time scales TCGand TCB are complementary to the ldquodynamicalrdquo timescales TT (or TDT) and TDB They differ in ratefrom TT and are related by four-dimensional space-timecoordinate transformations [61] These de nitions were

Metrologia 2001 38 509-529 513

R A Nelson et al

further clari ed by resolutions adopted at the 24th IAUGeneral Assembly held in Manchester in 2000 [62]

5 International Atomic Time

Although ET was a uniform time scale it was noteasily realized or disseminated The rapid developmentof atomic clocks permitted yet another de nition oftime [63]

51 Experimental atomic time scales

The rst operational caesium beam frequency standardappeared in 1955 at the National Physical Laboratory(NPL UK) [64] The Royal Greenwich Observatory(RGO) established a time scale known as GreenwichAtomic (GA) using free-running quartz-crystal clocksperiodically calibrated in terms of this standard

A commercial caesium frequency standard theldquoAtomichronrdquo was developed in 1956 [65] The USNaval Observatory (USNO) inaugurated its A1 atomictime scale on 13 September 1956 initially based on acaesium clock at the Naval Research Laboratory (NRL)consisting of an Atomichron caesium standard and aquartz-crystal clock The frequency of the crystal wasmatched daily to the caesium standard which was notoperated continuously [66] The National Bureau ofStandards (NBS) in Boulder Colo also maintained anatomic time scale NBS-A starting 9 October 1957The epochs of A1 and NBS-A were made coincidentand set equal to UT2 on 1 January 1958 [67]

The A1 time scale was introduced for world use on1 January 1959 By 1961 A1 was based on atomic os-cillators at the USNO NRL NBS USNO Time ServiceSub-Station (Richmond Florida) Harvard UniversityNational Research Council (Ottawa) NPL CentreNational drsquo AcircEtudes des T Acircel Acircecommunications (Bagneux)and Observatoire de Neuch Atildeatel (Switzerland) [68 69]

Once continuous atomic time became establishedat various laboratories the BIH began a mean atomictime scale based on frequency comparisons by means ofVLF carriers at 3 kHz to 30 kHz used for long-distancecommunications and radio navigation [70] Initially itwas designated AM and then A3 representing anaverage of the three best scales In 1960 the BIHbegan publication of the differences between UT2 andvarious individual atomic times obtained by integrationof accurate frequency comparisons By 1969 the BIHhad rede ned A3 to be an averaged atomic time scale(TA) based on several primary laboratory standardsIn 1971 this scale became the scale of InternationalAtomic Time (TAI) [71]

52 Atomic de nition of the second

In June 1955 Louis Essen and J V L Parry of the NPLmeasured the operational resonance frequency of thelaboratoryrsquos caesium standard with respect to the second

of UT2 as (9 192 631 830 plusmn 10) Hz by comparison withthe adopted frequency of a quartz standard which wascalibrated from astronomical measurements performedat the RGO [72] Over the following three years incooperation with William Markowitz and R G Hall atthe USNO they determined its value in terms of thesecond of Ephemeris Time Photographs of the Moonand surrounding stars were taken by the USNO dual-rate Moon camera over the period 195550 to 195825to determine the Ephemeris Time from the positionof the Moon at a known UT2 The UT2 scale basedon observations made with photographic zenith tubes(PZTs) at the USNO was calibrated with the caesium-beam atomic clock in Teddington via simultaneousobservations of the intervals between time pulsesbroadcast by radio stations WWV (then in GreenbeltMd) and GBR (Rugby UK) The measured caesiumfrequency was 9 192 631 770 Hz with a probable errorof plusmn 20 Hz [73] The principal uncertainty arose fromthe astronomical measurements themselves

Only seven years after the de nition of theephemeris second as an SI unit in 1960 the 13thCGPM in October 1967 adopted the atomic secondas the fundamental unit of time in the InternationalSystem of Units The second was de ned as [74]

ldquothe duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the twohyper ne levels of the ground state of the caesium133 atomrdquo

The second of atomic time is in principleequivalent to the second of Ephemeris Time Howeverthis decision did not consider a recommendation ofCommissions 4 (Ephemerides) and 31 (Time) of theIAU in 1967 in Prague which requested the CGPMto recognize the ephemeris second as a part of theIAU system of astronomical constants thus causingobjections from some astronomers [75]

53 Establishment of TAI

A prevalent opinion among astronomers in the mid-1960s had been that the atomic standards could providethe unit of time but not the continuous scale of timethat they needed [76] But on the contrary the BIHwas convinced that an atomic standard was the bestreference for time and devoted its resources to theestablishment of a practical international scale of atomictime [77]

In 1967 IAU Commissions 4 and 31 [78]recommended that the BIH compute an internationalscale of atomic time comprising independent timescales of the major national time services based onexperience gained from the experimental scale A3 Italso suggested that this scale be published in the form ofcorrections to the contributing time scales with respectto the international scale Similar recommendationsfollowed from the International Union of Radio Science

514 Metrologia 2001 38 509-529

The leap second its history and possible future

(URSI) in 1969 and the International Radio ConsultativeCommittee (CCIR) in 1970

The Comit Acirce Consultatif pour la D Acirce nition de laSeconde (CCDS) of the CIPM recommended guidelinesfor the establishment of International Atomic Time(TAI) in 1970 The CCDS stated [79]

ldquoInternational Atomic Time (TAI) is the time referencecoordinate established by the Bureau International delrsquoHeure on the basis of readings of atomic clocksoperating in various establishments in accordance withthe de nition of the second the unit of time of theInternational System of Unitsrdquo

In conformity with the recommendations of IAUCommissions 4 and 31 in 1967 the CCDS [80]de ned the origin so that TAI would be in approximateagreement with UT2 on 1 January 1958 0 h UT2 The14th CGPM approved the establishment of TAI in 1971

Yet an important task remained To de ne the scaleof atomic time completely one must de ne where in theuniverse the SI second is to be realized In recognitionof the framework of general relativity the de nitionwas completed in 1980 by the statement [81]

ldquoTAI is a coordinate time scale de ned in a geocentricreference frame with the SI second as realized on therotating geoid as the scale unitrdquo

Thus relativistic corrections are required for the primarylaboratory realizations of the SI second used in thecalibration of TAI to compensate the frequency shiftsbetween their individual locations and a point xed onthe surface of the rotating geoid

TAI when formally adopted in 1971 was anextension of the BIH atomic time scale that had beencontinuous back to 1955 In 1988 responsibility formaintaining TAI was transferred from the BIH to theBIPM A distribution of approximately two hundredclocks maintained in fty laboratories contribute to TAIusing an optimized weighting algorithm

6 Coordinated Universal Time

There were two communities of users Some suchas astronomers geodesists and navigators wanted abroadcast time connected with the angle of the Earthrsquosrotation in space Others such as physicists andengineers at time and frequency laboratories wantedit to be perfectly uniform to agree with the best clocksAttempts to meet the needs of both communities led tothe creation of Coordinated Universal Time (UTC)

61 Original UTC system

Originally radio time signals controlled from the RoyalGreenwich Observatory were kept closely in phasewith the Earthrsquos rotation using direct astronomicalobservations resulting in a nominal time interval of

a second that could vary slightly from day to dayBeginning in 1944 the time signals were generatedby quartz-crystal clocks at a uniform rate with stepcorrections introduced when necessary to maintainagreement with astronomical time When an atomicstandard became available at the NPL in 1955 theMSF time and frequency broadcast service of theUK based its signal on the provisional frequencyof 9 192 631 830 Hz for caesium In 1958 the NPLadopted the frequency 9 192 631 770 Hz but announcedthat the MSF service would have an annual rate offsetof a stated amount in addition to step corrections tokeep the disseminated time signals close to the scaleof UT2 [82]

Following the creation of their atomic time scalesin the period 1956-57 the USNO and the NBS eachmaintained two systems of atomic clock time TheUSNO system of uniform time A1 was related toEphemeris Time while the USNO Master Clock wasadjusted daily to UT2 from PZT observations Similarlythe NBS time scale NBS-A had a uniform ratesynchronized with A1 while NBS-UA was derived byapplying rate offsets and small steps to follow UT2 andwas disseminated by radio station WWV A summaryof the corrections utilized by WWV is given in [83]

At rst time signals broadcast from variouscountries were so loosely controlled that a listenermonitoring several stations could hear the pulsesarriving at different times To reduce the disparitiesthe World Administrative Radio Conference (Geneva)in 1959 requested the CCIR to study the questionof establishing and operating a worldwide standardfrequency and time signal service

The nautical almanacs of the UK and the USAwere combined in 1957 beginning with the editions for1960 In August 1959 it was also agreed to coordinatetheir time and frequency transmissions Coordinationbegan 1 January 1960 The participating observatoriesand laboratories were the USNO RGO NBS NRLand NPL Gradually other countries joined the systemwhich was entrusted to the BIH in 1961 In January1965 the BIH decided to attach UTC to its atomic timeA3 (which became TAI) by a mathematical relationship[84] This was the origin of the link between TAI andUTC The name ldquoCoordinated Universal Time (UTC)rdquowas approved by a resolution of IAU Commissions 4and 31 at the 13th General Assembly in 1967 [85]

62 Revised UTC system

Details of the UTC system were formalized by CCIRStudy Group 7 in Geneva in 1962 and were adoptedby the CCIR in its Recommendation 374 [86] of 1963The frequency offset was announced by the BIH afterconsultation with the observatories concerned to matchas nearly as practical the rotational speed of the Earthand remained constant for each year while steps of100 ms were inserted periodically at the beginning of

Metrologia 2001 38 509-529 515

R A Nelson et al

the month on dates determined by the BIH to maintainthe time signals to within about 01 s of UT2

As UTC included rate offsets to reduce the need forstep adjustments the broadcast time signals indicatedneither the SI second nor the mean solar secondbut rather variable intervals to stay in step withUT2 from which the SI second could be obtainedby applying a known correction Attempts to followthese uctuations necessitated revisions in complexequipment on a frequent basis and risked temporaryinterruptions of service At an interim session in MonteCarlo during March 1965 Study Group 7 suggested thatexperimental broadcasts and studies should be made toinvestigate how to provide both the epoch of UniversalTime and the international unit of time interval in thesame emission [87]

The revised CCIR Recommendation 374-1 [88]of 1966 allowed for the limited and provisional useof an experimental ldquoStepped Atomic Time (SAT)rdquo inwhich the broadcast time rate was the atomic timerate with no carrier deviation but in which frequentstep adjustments of 200 ms were applied to match UT2to within 01 s The existence of two parallel systemsUTC and SAT was regarded as a phase in the evolutionand adoption of a single practical and internationallyacceptable system [89]

63 Present UTC system

At the 15th General Assembly of the URSI in Munichin 1966 Commission 1 expressed the opinion thatall proposed methods of operating standard time andfrequency services contained defects and that theseservices must inevitably develop towards a system ofuniform atomic time and constant frequency For thoserequiring astronomical time some form of correctionwould be necessary [90 91] In 1967 at a meeting heldin Brussels under the auspices of the URSI to considerfrequency coordination in Europe it was unanimouslyagreed that both rate offsets and step adjustments shouldbe discontinued It was suggested that the deviations ofUTC from UT2 would have no signi cance for civilpurposes but could be disseminated to navigators intables or in the transmissions themselves [92]

Dissatisfaction with the existing form of UTC andthe need to study the implications of the new de nitionof the second adopted in 1967 prompted discussions bythe CIPM and the CCIR Following a recommendationof the CCDS the CIPM formed a preparatorycommission for the international coordination of timescales The concept of the leap second analogous to theleap day in the calendar was proposed independentlyby G M R Winkler [93] and Louis Essen [94] at ameeting of the commission held at the BIPM in May1968 [95 96] It was proposed that integer steps ofseconds replace the steps of 100 ms or 200 ms thenbeing used because they were too frequent and toosmall Consideration of possible modi cations to UTC

was also given by CCIR Study Group 7 in Boulderin August 1968 [97] The view was expressed that thebest system would be one with 1 s steps without rateoffsets so that equipment generating a pulse train wouldnot require a change in frequency To meet the needsof navigators it was suggested that coded informationmight be incorporated in the emission to indicate thedifference between UTC and UT2 to higher resolutionAn Interim Working Party IWP 71 was formed toinvestigate requirements submit proposals and x adate for the introduction of the new system The optionsunder consideration at this time were summarized asfollows [98]

ldquoDiscarding the suggestion (for practical reasons and toavoid confusions) of two time scales one approachingUT (the present UTC) and the other without offsetsand adjustments only three alternatives remain (a) stepadjustment of 01 s or 02 s to maintain the UTCsuf ciently near to UT2 to permit to ignore thedifference in most of the applications (b) completedisuse of UTC system replacing it with a coordinateduniform time scale without offsets and steps andtherefore not approaching UT (c) step adjustment of1 s exactlyrdquo

Speci c proposals were made by Study Group 7 inGeneva in October 1969 which were approved by theCCIR XIIth Plenary Assembly in New Delhi in January1970 In its Recommendation 460 [99] the CCIRstated that (a) carrier frequencies and time intervalsshould be maintained constant and should correspondto the de nition of the SI second (b) step adjustmentswhen necessary should be exactly 1 s to maintainapproximate agreement with Universal Time (UT) and(c) standard signals should contain information onthe difference between UTC and UT The CCIR alsodecided to begin the new UTC system on 1 January1972

At the IAUrsquos 14th General Assembly in BrightonUK in August 1970 the chairman of CCIR IWP 71H M Smith sought the views of Commissions 4(Ephemerides) and 31 (Time) The appropriate methodof providing both precise Earth orientation to navigatorsand uniform time to time and frequency laboratorieswas discussed As the navigator requires knowledgeof UT1 rather than UT2 it was recommended thatradio time signals should disseminate differences in theform of [UT1 ndash UTC] Several astronomers emphasizedthat visual observers in astronomical and related eldsrequire UT1 to a precision of 01 s as this is aboutthe limit of human time discrimination In addition thealmanacs were designed to permit a determination ofposition to 01 minute of arc and for this a comparableprecision in time of 025 s was required At BrightonCommission 31 adopted recommendations similar tothose of the CCIR Also the IAU General Assemblyresolved that adequate means should be provided toensure that the difference [UT1 ndash UTC] would be

516 Metrologia 2001 38 509-529

The leap second its history and possible future

available before permitting UTC to depart from UT1by more than about 01 s [100]

Detailed instructions for the implementation ofCCIR Recommendation 460 were drafted at a furthermeeting of Study Group 7 that was held in February1971 [101] The de ning epoch of 1 January 19720 h 0 m 0 s UTC was set 10 s behind TAI whichwas the approximate accumulated difference betweenTAI and UT1 since the inception of TAI in 1958and a unique fraction of a second adjustment wasapplied so that UTC would differ from TAI byan integral number of seconds The recommendedmaximum departure of UTC from UT1 was 07 sThe term ldquoleap secondrdquo was introduced for the steppedsecond An additional correction DUT1 was introducedhaving integral multiples of 01 s to be embodied in thetime signals such that when added to UTC they wouldyield a better approximation to UT1 For examplethis second level of correction was achieved by NBSradio stations WWV and WWVH by using double ticksor pulses after the start of each minute in its UTCbroadcasts [102]

The recommendations of the IAU were formalizedby resolutions of Commissions 4 and 31 at the15th General Assembly in Sydney in 1973 and afterfurther discussion the name UTC was retained [103]UTC was recommended as the basis of standardtime in all countries the time in common (civil)use as disseminated by radio signals The limit of[UT1 ndash UTC] was set at plusmn0950 s as this is themaximum difference that can be accommodated by thecode format The maximum deviation of UT1 from[UTC + DUT1] was set at plusmn0100 s In 1974 the CCIRincreased the tolerance for [UT1 ndash UTC] from 07 sto 09 s

The present UTC system is de ned by ITU-R(formerly CCIR) Recommendation ITU-R TF460-5[104]

ldquoUTC is the time scale maintained by the BIPM withassistance from the IERS which forms the basis of acoordinated dissemination of standard frequencies andtime signals It corresponds exactly in rate with TAIbut differs from it by an integral number of secondsThe UTC scale is adjusted by the insertion or deletionof seconds (positive or negative leap seconds) to ensureapproximate agreement with UT1rdquo

The interval between time signals of UTC is thusexactly equal to the SI second A history of rate offsetsand step adjustments in UTC is given in [105]

7 The leap second

71 Rate of increase in length of day

Because the Earthrsquos rotation is gradually slowingdown and in addition has both random and periodic uctuations it is not a uniform measure of time The

time difference T [ET ndash UT1] [TT ndash UT1]represents the difference between the uniform scale ofEphemeris Time or Terrestrial Time and the variablescale of Universal Time Values of T are summarizedin [106] Before 1955 the values are given by T[ET ndash UT1] based on observations of the Moon After1955 values are given by T [TT ndash UT1] [TAI +32184 s ndash UT1] from measurements by atomic clocksas published by the BIH and the BIPM

According to Stephenson and Morrison [107] overthe past 2700 years can be represented by aparabola of approximately the form

T = (31 scy2) (T ndash 1820)2(100)2 ndash 20 s

where T is expressed in seconds and T is the yearFigure 1 plots this equation together with observationssince 1620 The curve has a minimum at the year 1820and passes through 0 at the year 1900 Actual values of

T based on astronomical data may differ somewhatfrom this smoothed t For example the value of Tis 32184 s at 19580 the origin of TAI However nosingle parabola can satisfactorily represent all modernand historical data

The derivative of T is

Lday (00017 sdcy) (T ndash 1820)100

Figure 1 Observations and parabolic t of T versus timesince 1620 (after Stephenson and Morrison [26])

Figure 2 Change in the length of day with respect to areference day of 86 400 s versus time (after Stephensonand Morrison [26])

Metrologia 2001 38 509-529 517

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

The leap second its history and possible future

current de ning relation for UT1 with respect to theastronomical reference system of the Fifth FundamentalKatalog (FK5) [13] is given in [14]

UT0 a designation no longer in common use isUT1 corrupted by the torque-free precessional motionof the Earthrsquos axis of rotation with respect to theEarthrsquos surface [15] This effect called variation oflatitude was predicted by Leonhard Euler [16] in 1765as a property of rigid body motion and was identi edobservationally by Seth Chandler [17] in 1891 Thedifference [UT0 ndash UT1] has a maximum value of about20 ms at mean latitude [18]

Apparent solar time as read directly by a sundialor more precisely determined by the altitude of theSun is the local time de ned by the actual diurnalmotion of the Sun However because of the tilt ofthe Earthrsquos axis and the elliptical shape of the Earthrsquosorbit the time interval between successive passages ofthe Sun over a given meridian is not constant Thedifference between mean and apparent solar time iscalled the equation of time The maximum amountby which apparent noon precedes mean noon is about165 min around 3 November while the maximumamount by which mean noon precedes apparent noonis about 145 min around 12 February Until the earlynineteenth century apparent solar time was used asthe argument for astronomical ephemerides Howeveras clocks improved and their use by ships at sea andby railroads grew apparent solar time was graduallyreplaced by mean solar time

32 Sidereal Time

Local Sidereal Time (LST) is the measure ofastronomical time de ned by the rotation of the Earthwith respect to the stars LST may be de ned as theright ascension of the local meridian which is the anglebetween the vernal equinox and the local meridianmeasured along the celestial equator In particularGreenwich sidereal time is the right ascension of theGreenwich meridian

The sidereal day is the time interval betweensuccessive transits of the vernal equinox It representsthe Earthrsquos period of rotation relative to the stars and isapproximately 86 1640905 mean solar seconds Owingto precession of the Earthrsquos axis with respect to thecelestial reference system the sidereal day is about00084 s shorter than the actual period of rotationin inertial space Thus the true rotational period ofthe Earth is approximately 86 1640989 mean solarseconds However the mean solar day presently exceedsa day of exactly 8 400 SI seconds by about 25 msTherefore the Earthrsquos period of rotation is currentlyabout 86 1641014 SI seconds

Even LST is not a uniform measure of astronomicaltime In the early twentieth century the inherentaccuracy of the Shortt free-pendulum clocks rst

revealed the periodic effects of nutation The principalterm consists of an eighteen-year oscillation with anamplitude of about 1 s These effects cannot beneglected and it became necessary to introduce theconcept of mean sidereal time which is affected onlyby precession

Greenwich Mean Sidereal Time (GMST) is meansidereal time with respect to the Greenwich meridianfrom which Universal Time (UT1) is derived Inthe past UT1 was determined using a worldwidenetwork of visual transit telescopes photographiczenith tubes and impersonal (prismatic) astrolabesThree basic techniques are now used to estimateUT1 (a) Very Long Baseline Interferometry (VLBI)measurements of selected radio point sources mostlyquasars (b) satellite laser ranging and (c) tracking ofGPS satellites Strictly speaking because of the motionof satellite orbital nodes in space VLBI providesthe only rigorous determination of UT1 A revisedconventional celestial reference frame based on theobserved positions of extragalactic objects is beingdeveloped that changes the basis for UT1 removes theneed for the equinox and changes the use of precessionand nutation

33 Variations in the Earthrsquos rotation

Three types of variation in the Earthrsquos rotationhave been identi ed a steady deceleration random uctuations and periodic changes [19]

As early as 1695 Sir Edmond Halley [20] wasled to suspect an acceleration in the mean motionof the Moon from a study of ancient eclipses of theSun recorded by Claudius Ptolemy and the medievalArabian astronomer Muhammed al-Batt AringanAring otilde By themid-eighteenth century the lunar acceleration was fullyestablished In 1754 Immanuel Kant [21] suggestedthat this acceleration might be an apparent phenomenoncaused by a steady deceleration in the Earthrsquos rotationdue to tidal friction Part of the effect was laterattributed to the variation in the solar perturbation on theMoonrsquos orbit As shown by Pierre-Simon Laplace andJohn Couch Adams the planetary perturbations causethe Earthrsquos orbital eccentricity to diminish and as aconsequence the Sunrsquos mean action on the Moon alsodiminishes In addition the observed lunar accelerationis affected by the recession of the Moon from the Earthin order to compensate the decrease in the Earthrsquosrate of spin by conservation of angular momentum Itwas not until the twentieth century that an apparentacceleration of the Sun was also identi ed [22-24]

Recent studies of eclipses by F R Stephensonand L V Morrison [25 26] suggest that the long-termaverage rate of increase in the length of the day is about17 ms per century (ndash45 10ndash22 rads2) Although theincrease in the length of day seems miniscule it has acumulative effect on a time scale based on the Earthrsquos

Metrologia 2001 38 509-529 511

R A Nelson et al

rotation In the past 2000 years the Earth acting as aclock has lost over 3 h For example the calculated pathof the total eclipse of the Sun witnessed in Babylon in136 BC would be in error by 488 corresponding toa time difference of 11 700 s assuming a uniform rateof rotation [27]

Sir Harold Jeffreys made the rst quantitativeestimate of global tidal friction in 1920 [28 29] Hefound that the energy dissipation in the shallow seasappeared to be of the correct order of magnitude toaccount for the apparent lunar and solar accelerationsThe rate of energy dissipation by tidal friction isnow considered to correspond to a rate of increasein the length of day of 23 ms per century (ndash6110ndash22 rads2) To account for the observed decelerationthere must also be a component in the opposite directionof about 06 ms per century (+16 10ndash22 rads2)which is possibly associated with changes in the Earthoblateness parameter caused by post-glacial rebound[30] or with deep ocean dissipation [31]

Evidence for a long-term deceleration in the Earthrsquosrotation extending over millions of years also exists incoral fossils that exhibit both daily and annual growthrings [32] For example several corals dating from themiddle of the Devonian Period some 370 million yearsago indicate that the number of days in the year wasbetween 385 and 410 The evidence suggests that therate of deceleration was substantially the same then asit is now [33]

Besides a steady decrease the Earthrsquos rotation issubject to frequent small changes that are random andcumulative [34 35] This variation was inferred fromstudies of statistical irregularities in the displacementsof the Moon Sun Mercury and Venus in proportionto their mean motions Random uctuations were rstobserved directly by atomic clocks in the mid-1950s[36]

There is also a periodic seasonal variation causedprincipally by meteorological effects The seasonalvariation was rst reported in 1936 by A Scheibeand U Adelsberger [37] who performed measurementsof the Earthrsquos rotation with excellent quartz-crystalclocks at the Physikalische-Technische Bundesanstalt(Germany) N Stoyko [38] at the BIH in 1937 foundthat the length of the day in January exceeded thatin July by 2 ms based on the performance of Shorttpendulum clocks and by comparison of the rates ofquartz-crystal clocks at the national time services Theseasonal variation in the length of the day is now knownto be of the order of 05 ms about the mean [39] Therotation of the Earth runs slow by about 30 ms inMay and runs fast by a similar amount in NovemberBy international agreement an empirical correction forthe seasonal variation has been applied since 1 January1956 resulting in the time scale UT2 The differencebetween UT2 and UT1 as currently applied is givenin [40] UT2 has a peak-to-peak amplitude of about60 ms

4 Time measured by the orbital motionsof the celestial bodies

The need for more uniform measures of astronomicaltime resulted in the de nition of time scales determinedfrom the motions of the celestial bodies in the solarsystem Originally based on Newtonian mechanics theyhave been re ned to take into account the effects ofgeneral relativity

In addition the unit of time previously withinthe exclusive domain of astronomy was incorporatedinto the creation of the SI In 1948 at the request ofthe International Union of Pure and Applied Physics(IUPAP) the 9th General Conference on Weights andMeasures (CGPM) resolved to adopt for internationaluse a practical system of units covering all branchesof metrology A limited set of base units including thesecond was selected by the 10th CGPM in 1954 anda representative list of derived units was compiled bythe International Committee for Weights and Measures(CIPM) in 1956 The SI was of cially established bythe 11th CGPM in 1960 [41]

41 Ephemeris Time

Because the variations in the Earthrsquos rotationare complex the CIPM referred the study of anew de nition of the second to the InternationalAstronomical Union (IAU) in 1948 At the suggestionof G M Clemence [42] the Conference on theFundamental Constants of Astronomy held in Paris in1950 recommended to the IAU that instead of theperiod of rotation of the Earth on its axis the newstandard of time ought to be based on the period ofrevolution of the Earth around the Sun as representedby Newcombrsquos Tables of the Sun published in 1895The measure of astronomical time de ned in this waywas given the name Ephemeris Time (ET)

The working de nition of Ephemeris Time wasthrough Newcombrsquos formula for the geometric meanlongitude of the Sun for an epoch of January 0 190012h UT [43]

L = 279 41 48 04 + 129 602 768 13 T + 1 089 T2

where is the time reckoned in Julian centuries of36 525 days The linear coef cient determines the unitof time while the constant determines the epoch TheIAU adopted this proposal in 1952 at its 8th GeneralAssembly in Rome [44]

Initially the period of revolution of the Earth wasunderstood to be the sidereal year However it wassubsequently pointed out by Andr Acirce Danjon that thetropical year is more fundamental than the sidereal yearas the length of the tropical year (equinox to equinox)is derived directly from Newcombrsquos formula whereasthe length of the sidereal year ( xed star to xed star)depends on the adopted value of the precession [45]

From the value of the linear coef cient inNewcombrsquos formula the tropical year of 1900 contains

512 Metrologia 2001 38 509-529

The leap second its history and possible future

[(360 60 60)129 602 76813] 36 525 86 400= 31 556 9259747 s Therefore at the recommendationof the CIPM the 10th CGPM in 1954 proposed thefollowing de nition of the second

ldquoThe second is the fraction 131 556 925975 of thelength of the tropical year for 19000rdquo

But although the IAU approved this de nition atits General Assembly in 1955 Danjon commented thatthe fraction ought to have a slightly more precisevalue to bring about exact numerical agreement withNewcombrsquos formula [46] Consequently the CIPM in1956 under the authority given by the 10th CGPM in1954 de ned the second of ephemeris time to be

ldquothe fraction 131 556 9259747 of the tropical year for1900 January 0 at 12 hours ephemeris timerdquo

This de nition was rati ed by the 11th CGPM in 1960[47] Reference to the year 1900 does not imply that thisis the epoch of a mean solar day of 86 400 s Rather itis the epoch of the tropical year of 31 556 9259747 s

Although ET was de ned in terms of the longitudeof the Sun in practice it was realized indirectly bycomparison of observations of lunar positions withlunar ephemerides Thus a set of secondary time scales(denoted by ET0 ET1 and ET2) were de ned thatdiffered because of subsequent improvements to theconventional ephemerides [48]

In 1958 the IAU General Assembly adopted aresolution that de ned the epoch of Ephemeris Time tocoincide with Newcombrsquos formula as follows [49]

ldquoEphemeris Time (ET) or Temps des Eph Acircem Acircerides(TE) is reckoned from the instant near the beginningof the calendar year AD 1900 when the geometricmean longitude of the Sun was 279 41 48 04 atwhich instant the measure of Ephemeris Time was1900 January 0d 12h preciselyrdquo

The resolution also included the de nition of the secondgiven by the CIPM in 1956 In a separate resolution theepoch for Universal Time was chosen as 1900 January0d 12h UT based on the Fourth Fundamental Katalog(FK4) [50] However the equinox of Newcombrsquos Sunthe lunar theory and the FK4 did not agree preciselyand they were moving with respect to one another Thusthe actual instant in time corresponding to the epochof ET was approximately 4 s later than the epoch ofUT [51]

Ephemeris Time (ET) is a dynamical timedetermined by the theory of celestial mechanics andis theoretically uniform [52] ET may be characterizedas the independent variable that brings the observedpositions of the celestial bodies into accord with theircalculated positions constructed from the Newtonianlaws of motion Therefore in effect it is de ned bythese laws [53]

42 Relativistic time scales

In 1960 ET replaced UT1 as the independent variableof astronomical ephemerides However ET did notinclude relativistic effects and did not distinguishbetween proper time and coordinate time Accordinglyat the 16th General Assembly in Grenoble in 1976the IAU de ned time-like arguments that distinguishcoordinate systems with origins at the centre of theEarth and the centre of the solar system respectivelyand are consistent with the general theory of relativity[54] In 1979 these time scales received the namesTerrestrial Dynamical Time (TDT) and BarycentricDynamical Time (TDB) [55]

TDT replaced ET in 1984 as the tabular argumentof the fundamental geocentric ephemerides TDT hasan origin of 1 January 1977 0 h TAI with a unit intervalequal to the SI second and maintains continuity withET At this epoch a rate correction of ndash10 10ndash13

was applied to TAI to bring the unit of TAI moreclosely into accord with the SI second [56] In 1991the IAU renamed TDT simply Terrestrial Time (TT) Apractical realization of TT is [57]

[TT] = [TAI] + 32184 s

The constant offset represents the difference betweenET and UT1 at the de ning epoch of TAI on 1 January1958

The relationship between TT and TAI is notstrictly rigorous for two fundamental reasons [58]First TAI is a statistically formed time scale based oncontributions from the major timing centres whereasTT is theoretically uniform Second a scale oftime based on the laws of gravitation may not bephilosophically equivalent to one based on the quantummechanics of the atom

For ephemerides referred to the barycentre ofthe solar system the argument is TDB Through anappropriately chosen scaling factor TDB varies fromTT or TDT by only periodic variations with amplitudesless than 0002 s

From the deliberations of the IAU Working Groupon Reference Systems formed in 1988 there arose ninerecommendations that were contained in Resolution A4adopted by the 21st IAU General Assembly in 1991[59] The general theory of relativity was explicitlyintroduced as the theoretical basis for the celestialreference frame and the form of the space-time metricto post-Newtonian order was speci ed The IAUalso clari ed the de nition of Terrestrial Time (TT)and adopted two additional time scales GeocentricCoordinate Time (TCG) and Barycentric CoordinateTime (TCB) [60] The ldquocoordinaterdquo time scales TCGand TCB are complementary to the ldquodynamicalrdquo timescales TT (or TDT) and TDB They differ in ratefrom TT and are related by four-dimensional space-timecoordinate transformations [61] These de nitions were

Metrologia 2001 38 509-529 513

R A Nelson et al

further clari ed by resolutions adopted at the 24th IAUGeneral Assembly held in Manchester in 2000 [62]

5 International Atomic Time

Although ET was a uniform time scale it was noteasily realized or disseminated The rapid developmentof atomic clocks permitted yet another de nition oftime [63]

51 Experimental atomic time scales

The rst operational caesium beam frequency standardappeared in 1955 at the National Physical Laboratory(NPL UK) [64] The Royal Greenwich Observatory(RGO) established a time scale known as GreenwichAtomic (GA) using free-running quartz-crystal clocksperiodically calibrated in terms of this standard

A commercial caesium frequency standard theldquoAtomichronrdquo was developed in 1956 [65] The USNaval Observatory (USNO) inaugurated its A1 atomictime scale on 13 September 1956 initially based on acaesium clock at the Naval Research Laboratory (NRL)consisting of an Atomichron caesium standard and aquartz-crystal clock The frequency of the crystal wasmatched daily to the caesium standard which was notoperated continuously [66] The National Bureau ofStandards (NBS) in Boulder Colo also maintained anatomic time scale NBS-A starting 9 October 1957The epochs of A1 and NBS-A were made coincidentand set equal to UT2 on 1 January 1958 [67]

The A1 time scale was introduced for world use on1 January 1959 By 1961 A1 was based on atomic os-cillators at the USNO NRL NBS USNO Time ServiceSub-Station (Richmond Florida) Harvard UniversityNational Research Council (Ottawa) NPL CentreNational drsquo AcircEtudes des T Acircel Acircecommunications (Bagneux)and Observatoire de Neuch Atildeatel (Switzerland) [68 69]

Once continuous atomic time became establishedat various laboratories the BIH began a mean atomictime scale based on frequency comparisons by means ofVLF carriers at 3 kHz to 30 kHz used for long-distancecommunications and radio navigation [70] Initially itwas designated AM and then A3 representing anaverage of the three best scales In 1960 the BIHbegan publication of the differences between UT2 andvarious individual atomic times obtained by integrationof accurate frequency comparisons By 1969 the BIHhad rede ned A3 to be an averaged atomic time scale(TA) based on several primary laboratory standardsIn 1971 this scale became the scale of InternationalAtomic Time (TAI) [71]

52 Atomic de nition of the second

In June 1955 Louis Essen and J V L Parry of the NPLmeasured the operational resonance frequency of thelaboratoryrsquos caesium standard with respect to the second

of UT2 as (9 192 631 830 plusmn 10) Hz by comparison withthe adopted frequency of a quartz standard which wascalibrated from astronomical measurements performedat the RGO [72] Over the following three years incooperation with William Markowitz and R G Hall atthe USNO they determined its value in terms of thesecond of Ephemeris Time Photographs of the Moonand surrounding stars were taken by the USNO dual-rate Moon camera over the period 195550 to 195825to determine the Ephemeris Time from the positionof the Moon at a known UT2 The UT2 scale basedon observations made with photographic zenith tubes(PZTs) at the USNO was calibrated with the caesium-beam atomic clock in Teddington via simultaneousobservations of the intervals between time pulsesbroadcast by radio stations WWV (then in GreenbeltMd) and GBR (Rugby UK) The measured caesiumfrequency was 9 192 631 770 Hz with a probable errorof plusmn 20 Hz [73] The principal uncertainty arose fromthe astronomical measurements themselves

Only seven years after the de nition of theephemeris second as an SI unit in 1960 the 13thCGPM in October 1967 adopted the atomic secondas the fundamental unit of time in the InternationalSystem of Units The second was de ned as [74]

ldquothe duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the twohyper ne levels of the ground state of the caesium133 atomrdquo

The second of atomic time is in principleequivalent to the second of Ephemeris Time Howeverthis decision did not consider a recommendation ofCommissions 4 (Ephemerides) and 31 (Time) of theIAU in 1967 in Prague which requested the CGPMto recognize the ephemeris second as a part of theIAU system of astronomical constants thus causingobjections from some astronomers [75]

53 Establishment of TAI

A prevalent opinion among astronomers in the mid-1960s had been that the atomic standards could providethe unit of time but not the continuous scale of timethat they needed [76] But on the contrary the BIHwas convinced that an atomic standard was the bestreference for time and devoted its resources to theestablishment of a practical international scale of atomictime [77]

In 1967 IAU Commissions 4 and 31 [78]recommended that the BIH compute an internationalscale of atomic time comprising independent timescales of the major national time services based onexperience gained from the experimental scale A3 Italso suggested that this scale be published in the form ofcorrections to the contributing time scales with respectto the international scale Similar recommendationsfollowed from the International Union of Radio Science

514 Metrologia 2001 38 509-529

The leap second its history and possible future

(URSI) in 1969 and the International Radio ConsultativeCommittee (CCIR) in 1970

The Comit Acirce Consultatif pour la D Acirce nition de laSeconde (CCDS) of the CIPM recommended guidelinesfor the establishment of International Atomic Time(TAI) in 1970 The CCDS stated [79]

ldquoInternational Atomic Time (TAI) is the time referencecoordinate established by the Bureau International delrsquoHeure on the basis of readings of atomic clocksoperating in various establishments in accordance withthe de nition of the second the unit of time of theInternational System of Unitsrdquo

In conformity with the recommendations of IAUCommissions 4 and 31 in 1967 the CCDS [80]de ned the origin so that TAI would be in approximateagreement with UT2 on 1 January 1958 0 h UT2 The14th CGPM approved the establishment of TAI in 1971

Yet an important task remained To de ne the scaleof atomic time completely one must de ne where in theuniverse the SI second is to be realized In recognitionof the framework of general relativity the de nitionwas completed in 1980 by the statement [81]

ldquoTAI is a coordinate time scale de ned in a geocentricreference frame with the SI second as realized on therotating geoid as the scale unitrdquo

Thus relativistic corrections are required for the primarylaboratory realizations of the SI second used in thecalibration of TAI to compensate the frequency shiftsbetween their individual locations and a point xed onthe surface of the rotating geoid

TAI when formally adopted in 1971 was anextension of the BIH atomic time scale that had beencontinuous back to 1955 In 1988 responsibility formaintaining TAI was transferred from the BIH to theBIPM A distribution of approximately two hundredclocks maintained in fty laboratories contribute to TAIusing an optimized weighting algorithm

6 Coordinated Universal Time

There were two communities of users Some suchas astronomers geodesists and navigators wanted abroadcast time connected with the angle of the Earthrsquosrotation in space Others such as physicists andengineers at time and frequency laboratories wantedit to be perfectly uniform to agree with the best clocksAttempts to meet the needs of both communities led tothe creation of Coordinated Universal Time (UTC)

61 Original UTC system

Originally radio time signals controlled from the RoyalGreenwich Observatory were kept closely in phasewith the Earthrsquos rotation using direct astronomicalobservations resulting in a nominal time interval of

a second that could vary slightly from day to dayBeginning in 1944 the time signals were generatedby quartz-crystal clocks at a uniform rate with stepcorrections introduced when necessary to maintainagreement with astronomical time When an atomicstandard became available at the NPL in 1955 theMSF time and frequency broadcast service of theUK based its signal on the provisional frequencyof 9 192 631 830 Hz for caesium In 1958 the NPLadopted the frequency 9 192 631 770 Hz but announcedthat the MSF service would have an annual rate offsetof a stated amount in addition to step corrections tokeep the disseminated time signals close to the scaleof UT2 [82]

Following the creation of their atomic time scalesin the period 1956-57 the USNO and the NBS eachmaintained two systems of atomic clock time TheUSNO system of uniform time A1 was related toEphemeris Time while the USNO Master Clock wasadjusted daily to UT2 from PZT observations Similarlythe NBS time scale NBS-A had a uniform ratesynchronized with A1 while NBS-UA was derived byapplying rate offsets and small steps to follow UT2 andwas disseminated by radio station WWV A summaryof the corrections utilized by WWV is given in [83]

At rst time signals broadcast from variouscountries were so loosely controlled that a listenermonitoring several stations could hear the pulsesarriving at different times To reduce the disparitiesthe World Administrative Radio Conference (Geneva)in 1959 requested the CCIR to study the questionof establishing and operating a worldwide standardfrequency and time signal service

The nautical almanacs of the UK and the USAwere combined in 1957 beginning with the editions for1960 In August 1959 it was also agreed to coordinatetheir time and frequency transmissions Coordinationbegan 1 January 1960 The participating observatoriesand laboratories were the USNO RGO NBS NRLand NPL Gradually other countries joined the systemwhich was entrusted to the BIH in 1961 In January1965 the BIH decided to attach UTC to its atomic timeA3 (which became TAI) by a mathematical relationship[84] This was the origin of the link between TAI andUTC The name ldquoCoordinated Universal Time (UTC)rdquowas approved by a resolution of IAU Commissions 4and 31 at the 13th General Assembly in 1967 [85]

62 Revised UTC system

Details of the UTC system were formalized by CCIRStudy Group 7 in Geneva in 1962 and were adoptedby the CCIR in its Recommendation 374 [86] of 1963The frequency offset was announced by the BIH afterconsultation with the observatories concerned to matchas nearly as practical the rotational speed of the Earthand remained constant for each year while steps of100 ms were inserted periodically at the beginning of

Metrologia 2001 38 509-529 515

R A Nelson et al

the month on dates determined by the BIH to maintainthe time signals to within about 01 s of UT2

As UTC included rate offsets to reduce the need forstep adjustments the broadcast time signals indicatedneither the SI second nor the mean solar secondbut rather variable intervals to stay in step withUT2 from which the SI second could be obtainedby applying a known correction Attempts to followthese uctuations necessitated revisions in complexequipment on a frequent basis and risked temporaryinterruptions of service At an interim session in MonteCarlo during March 1965 Study Group 7 suggested thatexperimental broadcasts and studies should be made toinvestigate how to provide both the epoch of UniversalTime and the international unit of time interval in thesame emission [87]

The revised CCIR Recommendation 374-1 [88]of 1966 allowed for the limited and provisional useof an experimental ldquoStepped Atomic Time (SAT)rdquo inwhich the broadcast time rate was the atomic timerate with no carrier deviation but in which frequentstep adjustments of 200 ms were applied to match UT2to within 01 s The existence of two parallel systemsUTC and SAT was regarded as a phase in the evolutionand adoption of a single practical and internationallyacceptable system [89]

63 Present UTC system

At the 15th General Assembly of the URSI in Munichin 1966 Commission 1 expressed the opinion thatall proposed methods of operating standard time andfrequency services contained defects and that theseservices must inevitably develop towards a system ofuniform atomic time and constant frequency For thoserequiring astronomical time some form of correctionwould be necessary [90 91] In 1967 at a meeting heldin Brussels under the auspices of the URSI to considerfrequency coordination in Europe it was unanimouslyagreed that both rate offsets and step adjustments shouldbe discontinued It was suggested that the deviations ofUTC from UT2 would have no signi cance for civilpurposes but could be disseminated to navigators intables or in the transmissions themselves [92]

Dissatisfaction with the existing form of UTC andthe need to study the implications of the new de nitionof the second adopted in 1967 prompted discussions bythe CIPM and the CCIR Following a recommendationof the CCDS the CIPM formed a preparatorycommission for the international coordination of timescales The concept of the leap second analogous to theleap day in the calendar was proposed independentlyby G M R Winkler [93] and Louis Essen [94] at ameeting of the commission held at the BIPM in May1968 [95 96] It was proposed that integer steps ofseconds replace the steps of 100 ms or 200 ms thenbeing used because they were too frequent and toosmall Consideration of possible modi cations to UTC

was also given by CCIR Study Group 7 in Boulderin August 1968 [97] The view was expressed that thebest system would be one with 1 s steps without rateoffsets so that equipment generating a pulse train wouldnot require a change in frequency To meet the needsof navigators it was suggested that coded informationmight be incorporated in the emission to indicate thedifference between UTC and UT2 to higher resolutionAn Interim Working Party IWP 71 was formed toinvestigate requirements submit proposals and x adate for the introduction of the new system The optionsunder consideration at this time were summarized asfollows [98]

ldquoDiscarding the suggestion (for practical reasons and toavoid confusions) of two time scales one approachingUT (the present UTC) and the other without offsetsand adjustments only three alternatives remain (a) stepadjustment of 01 s or 02 s to maintain the UTCsuf ciently near to UT2 to permit to ignore thedifference in most of the applications (b) completedisuse of UTC system replacing it with a coordinateduniform time scale without offsets and steps andtherefore not approaching UT (c) step adjustment of1 s exactlyrdquo

Speci c proposals were made by Study Group 7 inGeneva in October 1969 which were approved by theCCIR XIIth Plenary Assembly in New Delhi in January1970 In its Recommendation 460 [99] the CCIRstated that (a) carrier frequencies and time intervalsshould be maintained constant and should correspondto the de nition of the SI second (b) step adjustmentswhen necessary should be exactly 1 s to maintainapproximate agreement with Universal Time (UT) and(c) standard signals should contain information onthe difference between UTC and UT The CCIR alsodecided to begin the new UTC system on 1 January1972

At the IAUrsquos 14th General Assembly in BrightonUK in August 1970 the chairman of CCIR IWP 71H M Smith sought the views of Commissions 4(Ephemerides) and 31 (Time) The appropriate methodof providing both precise Earth orientation to navigatorsand uniform time to time and frequency laboratorieswas discussed As the navigator requires knowledgeof UT1 rather than UT2 it was recommended thatradio time signals should disseminate differences in theform of [UT1 ndash UTC] Several astronomers emphasizedthat visual observers in astronomical and related eldsrequire UT1 to a precision of 01 s as this is aboutthe limit of human time discrimination In addition thealmanacs were designed to permit a determination ofposition to 01 minute of arc and for this a comparableprecision in time of 025 s was required At BrightonCommission 31 adopted recommendations similar tothose of the CCIR Also the IAU General Assemblyresolved that adequate means should be provided toensure that the difference [UT1 ndash UTC] would be

516 Metrologia 2001 38 509-529

The leap second its history and possible future

available before permitting UTC to depart from UT1by more than about 01 s [100]

Detailed instructions for the implementation ofCCIR Recommendation 460 were drafted at a furthermeeting of Study Group 7 that was held in February1971 [101] The de ning epoch of 1 January 19720 h 0 m 0 s UTC was set 10 s behind TAI whichwas the approximate accumulated difference betweenTAI and UT1 since the inception of TAI in 1958and a unique fraction of a second adjustment wasapplied so that UTC would differ from TAI byan integral number of seconds The recommendedmaximum departure of UTC from UT1 was 07 sThe term ldquoleap secondrdquo was introduced for the steppedsecond An additional correction DUT1 was introducedhaving integral multiples of 01 s to be embodied in thetime signals such that when added to UTC they wouldyield a better approximation to UT1 For examplethis second level of correction was achieved by NBSradio stations WWV and WWVH by using double ticksor pulses after the start of each minute in its UTCbroadcasts [102]

The recommendations of the IAU were formalizedby resolutions of Commissions 4 and 31 at the15th General Assembly in Sydney in 1973 and afterfurther discussion the name UTC was retained [103]UTC was recommended as the basis of standardtime in all countries the time in common (civil)use as disseminated by radio signals The limit of[UT1 ndash UTC] was set at plusmn0950 s as this is themaximum difference that can be accommodated by thecode format The maximum deviation of UT1 from[UTC + DUT1] was set at plusmn0100 s In 1974 the CCIRincreased the tolerance for [UT1 ndash UTC] from 07 sto 09 s

The present UTC system is de ned by ITU-R(formerly CCIR) Recommendation ITU-R TF460-5[104]

ldquoUTC is the time scale maintained by the BIPM withassistance from the IERS which forms the basis of acoordinated dissemination of standard frequencies andtime signals It corresponds exactly in rate with TAIbut differs from it by an integral number of secondsThe UTC scale is adjusted by the insertion or deletionof seconds (positive or negative leap seconds) to ensureapproximate agreement with UT1rdquo

The interval between time signals of UTC is thusexactly equal to the SI second A history of rate offsetsand step adjustments in UTC is given in [105]

7 The leap second

71 Rate of increase in length of day

Because the Earthrsquos rotation is gradually slowingdown and in addition has both random and periodic uctuations it is not a uniform measure of time The

time difference T [ET ndash UT1] [TT ndash UT1]represents the difference between the uniform scale ofEphemeris Time or Terrestrial Time and the variablescale of Universal Time Values of T are summarizedin [106] Before 1955 the values are given by T[ET ndash UT1] based on observations of the Moon After1955 values are given by T [TT ndash UT1] [TAI +32184 s ndash UT1] from measurements by atomic clocksas published by the BIH and the BIPM

According to Stephenson and Morrison [107] overthe past 2700 years can be represented by aparabola of approximately the form

T = (31 scy2) (T ndash 1820)2(100)2 ndash 20 s

where T is expressed in seconds and T is the yearFigure 1 plots this equation together with observationssince 1620 The curve has a minimum at the year 1820and passes through 0 at the year 1900 Actual values of

T based on astronomical data may differ somewhatfrom this smoothed t For example the value of Tis 32184 s at 19580 the origin of TAI However nosingle parabola can satisfactorily represent all modernand historical data

The derivative of T is

Lday (00017 sdcy) (T ndash 1820)100

Figure 1 Observations and parabolic t of T versus timesince 1620 (after Stephenson and Morrison [26])

Figure 2 Change in the length of day with respect to areference day of 86 400 s versus time (after Stephensonand Morrison [26])

Metrologia 2001 38 509-529 517

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

R A Nelson et al

rotation In the past 2000 years the Earth acting as aclock has lost over 3 h For example the calculated pathof the total eclipse of the Sun witnessed in Babylon in136 BC would be in error by 488 corresponding toa time difference of 11 700 s assuming a uniform rateof rotation [27]

Sir Harold Jeffreys made the rst quantitativeestimate of global tidal friction in 1920 [28 29] Hefound that the energy dissipation in the shallow seasappeared to be of the correct order of magnitude toaccount for the apparent lunar and solar accelerationsThe rate of energy dissipation by tidal friction isnow considered to correspond to a rate of increasein the length of day of 23 ms per century (ndash6110ndash22 rads2) To account for the observed decelerationthere must also be a component in the opposite directionof about 06 ms per century (+16 10ndash22 rads2)which is possibly associated with changes in the Earthoblateness parameter caused by post-glacial rebound[30] or with deep ocean dissipation [31]

Evidence for a long-term deceleration in the Earthrsquosrotation extending over millions of years also exists incoral fossils that exhibit both daily and annual growthrings [32] For example several corals dating from themiddle of the Devonian Period some 370 million yearsago indicate that the number of days in the year wasbetween 385 and 410 The evidence suggests that therate of deceleration was substantially the same then asit is now [33]

Besides a steady decrease the Earthrsquos rotation issubject to frequent small changes that are random andcumulative [34 35] This variation was inferred fromstudies of statistical irregularities in the displacementsof the Moon Sun Mercury and Venus in proportionto their mean motions Random uctuations were rstobserved directly by atomic clocks in the mid-1950s[36]

There is also a periodic seasonal variation causedprincipally by meteorological effects The seasonalvariation was rst reported in 1936 by A Scheibeand U Adelsberger [37] who performed measurementsof the Earthrsquos rotation with excellent quartz-crystalclocks at the Physikalische-Technische Bundesanstalt(Germany) N Stoyko [38] at the BIH in 1937 foundthat the length of the day in January exceeded thatin July by 2 ms based on the performance of Shorttpendulum clocks and by comparison of the rates ofquartz-crystal clocks at the national time services Theseasonal variation in the length of the day is now knownto be of the order of 05 ms about the mean [39] Therotation of the Earth runs slow by about 30 ms inMay and runs fast by a similar amount in NovemberBy international agreement an empirical correction forthe seasonal variation has been applied since 1 January1956 resulting in the time scale UT2 The differencebetween UT2 and UT1 as currently applied is givenin [40] UT2 has a peak-to-peak amplitude of about60 ms

4 Time measured by the orbital motionsof the celestial bodies

The need for more uniform measures of astronomicaltime resulted in the de nition of time scales determinedfrom the motions of the celestial bodies in the solarsystem Originally based on Newtonian mechanics theyhave been re ned to take into account the effects ofgeneral relativity

In addition the unit of time previously withinthe exclusive domain of astronomy was incorporatedinto the creation of the SI In 1948 at the request ofthe International Union of Pure and Applied Physics(IUPAP) the 9th General Conference on Weights andMeasures (CGPM) resolved to adopt for internationaluse a practical system of units covering all branchesof metrology A limited set of base units including thesecond was selected by the 10th CGPM in 1954 anda representative list of derived units was compiled bythe International Committee for Weights and Measures(CIPM) in 1956 The SI was of cially established bythe 11th CGPM in 1960 [41]

41 Ephemeris Time

Because the variations in the Earthrsquos rotationare complex the CIPM referred the study of anew de nition of the second to the InternationalAstronomical Union (IAU) in 1948 At the suggestionof G M Clemence [42] the Conference on theFundamental Constants of Astronomy held in Paris in1950 recommended to the IAU that instead of theperiod of rotation of the Earth on its axis the newstandard of time ought to be based on the period ofrevolution of the Earth around the Sun as representedby Newcombrsquos Tables of the Sun published in 1895The measure of astronomical time de ned in this waywas given the name Ephemeris Time (ET)

The working de nition of Ephemeris Time wasthrough Newcombrsquos formula for the geometric meanlongitude of the Sun for an epoch of January 0 190012h UT [43]

L = 279 41 48 04 + 129 602 768 13 T + 1 089 T2

where is the time reckoned in Julian centuries of36 525 days The linear coef cient determines the unitof time while the constant determines the epoch TheIAU adopted this proposal in 1952 at its 8th GeneralAssembly in Rome [44]

Initially the period of revolution of the Earth wasunderstood to be the sidereal year However it wassubsequently pointed out by Andr Acirce Danjon that thetropical year is more fundamental than the sidereal yearas the length of the tropical year (equinox to equinox)is derived directly from Newcombrsquos formula whereasthe length of the sidereal year ( xed star to xed star)depends on the adopted value of the precession [45]

From the value of the linear coef cient inNewcombrsquos formula the tropical year of 1900 contains

512 Metrologia 2001 38 509-529

The leap second its history and possible future

[(360 60 60)129 602 76813] 36 525 86 400= 31 556 9259747 s Therefore at the recommendationof the CIPM the 10th CGPM in 1954 proposed thefollowing de nition of the second

ldquoThe second is the fraction 131 556 925975 of thelength of the tropical year for 19000rdquo

But although the IAU approved this de nition atits General Assembly in 1955 Danjon commented thatthe fraction ought to have a slightly more precisevalue to bring about exact numerical agreement withNewcombrsquos formula [46] Consequently the CIPM in1956 under the authority given by the 10th CGPM in1954 de ned the second of ephemeris time to be

ldquothe fraction 131 556 9259747 of the tropical year for1900 January 0 at 12 hours ephemeris timerdquo

This de nition was rati ed by the 11th CGPM in 1960[47] Reference to the year 1900 does not imply that thisis the epoch of a mean solar day of 86 400 s Rather itis the epoch of the tropical year of 31 556 9259747 s

Although ET was de ned in terms of the longitudeof the Sun in practice it was realized indirectly bycomparison of observations of lunar positions withlunar ephemerides Thus a set of secondary time scales(denoted by ET0 ET1 and ET2) were de ned thatdiffered because of subsequent improvements to theconventional ephemerides [48]

In 1958 the IAU General Assembly adopted aresolution that de ned the epoch of Ephemeris Time tocoincide with Newcombrsquos formula as follows [49]

ldquoEphemeris Time (ET) or Temps des Eph Acircem Acircerides(TE) is reckoned from the instant near the beginningof the calendar year AD 1900 when the geometricmean longitude of the Sun was 279 41 48 04 atwhich instant the measure of Ephemeris Time was1900 January 0d 12h preciselyrdquo

The resolution also included the de nition of the secondgiven by the CIPM in 1956 In a separate resolution theepoch for Universal Time was chosen as 1900 January0d 12h UT based on the Fourth Fundamental Katalog(FK4) [50] However the equinox of Newcombrsquos Sunthe lunar theory and the FK4 did not agree preciselyand they were moving with respect to one another Thusthe actual instant in time corresponding to the epochof ET was approximately 4 s later than the epoch ofUT [51]

Ephemeris Time (ET) is a dynamical timedetermined by the theory of celestial mechanics andis theoretically uniform [52] ET may be characterizedas the independent variable that brings the observedpositions of the celestial bodies into accord with theircalculated positions constructed from the Newtonianlaws of motion Therefore in effect it is de ned bythese laws [53]

42 Relativistic time scales

In 1960 ET replaced UT1 as the independent variableof astronomical ephemerides However ET did notinclude relativistic effects and did not distinguishbetween proper time and coordinate time Accordinglyat the 16th General Assembly in Grenoble in 1976the IAU de ned time-like arguments that distinguishcoordinate systems with origins at the centre of theEarth and the centre of the solar system respectivelyand are consistent with the general theory of relativity[54] In 1979 these time scales received the namesTerrestrial Dynamical Time (TDT) and BarycentricDynamical Time (TDB) [55]

TDT replaced ET in 1984 as the tabular argumentof the fundamental geocentric ephemerides TDT hasan origin of 1 January 1977 0 h TAI with a unit intervalequal to the SI second and maintains continuity withET At this epoch a rate correction of ndash10 10ndash13

was applied to TAI to bring the unit of TAI moreclosely into accord with the SI second [56] In 1991the IAU renamed TDT simply Terrestrial Time (TT) Apractical realization of TT is [57]

[TT] = [TAI] + 32184 s

The constant offset represents the difference betweenET and UT1 at the de ning epoch of TAI on 1 January1958

The relationship between TT and TAI is notstrictly rigorous for two fundamental reasons [58]First TAI is a statistically formed time scale based oncontributions from the major timing centres whereasTT is theoretically uniform Second a scale oftime based on the laws of gravitation may not bephilosophically equivalent to one based on the quantummechanics of the atom

For ephemerides referred to the barycentre ofthe solar system the argument is TDB Through anappropriately chosen scaling factor TDB varies fromTT or TDT by only periodic variations with amplitudesless than 0002 s

From the deliberations of the IAU Working Groupon Reference Systems formed in 1988 there arose ninerecommendations that were contained in Resolution A4adopted by the 21st IAU General Assembly in 1991[59] The general theory of relativity was explicitlyintroduced as the theoretical basis for the celestialreference frame and the form of the space-time metricto post-Newtonian order was speci ed The IAUalso clari ed the de nition of Terrestrial Time (TT)and adopted two additional time scales GeocentricCoordinate Time (TCG) and Barycentric CoordinateTime (TCB) [60] The ldquocoordinaterdquo time scales TCGand TCB are complementary to the ldquodynamicalrdquo timescales TT (or TDT) and TDB They differ in ratefrom TT and are related by four-dimensional space-timecoordinate transformations [61] These de nitions were

Metrologia 2001 38 509-529 513

R A Nelson et al

further clari ed by resolutions adopted at the 24th IAUGeneral Assembly held in Manchester in 2000 [62]

5 International Atomic Time

Although ET was a uniform time scale it was noteasily realized or disseminated The rapid developmentof atomic clocks permitted yet another de nition oftime [63]

51 Experimental atomic time scales

The rst operational caesium beam frequency standardappeared in 1955 at the National Physical Laboratory(NPL UK) [64] The Royal Greenwich Observatory(RGO) established a time scale known as GreenwichAtomic (GA) using free-running quartz-crystal clocksperiodically calibrated in terms of this standard

A commercial caesium frequency standard theldquoAtomichronrdquo was developed in 1956 [65] The USNaval Observatory (USNO) inaugurated its A1 atomictime scale on 13 September 1956 initially based on acaesium clock at the Naval Research Laboratory (NRL)consisting of an Atomichron caesium standard and aquartz-crystal clock The frequency of the crystal wasmatched daily to the caesium standard which was notoperated continuously [66] The National Bureau ofStandards (NBS) in Boulder Colo also maintained anatomic time scale NBS-A starting 9 October 1957The epochs of A1 and NBS-A were made coincidentand set equal to UT2 on 1 January 1958 [67]

The A1 time scale was introduced for world use on1 January 1959 By 1961 A1 was based on atomic os-cillators at the USNO NRL NBS USNO Time ServiceSub-Station (Richmond Florida) Harvard UniversityNational Research Council (Ottawa) NPL CentreNational drsquo AcircEtudes des T Acircel Acircecommunications (Bagneux)and Observatoire de Neuch Atildeatel (Switzerland) [68 69]

Once continuous atomic time became establishedat various laboratories the BIH began a mean atomictime scale based on frequency comparisons by means ofVLF carriers at 3 kHz to 30 kHz used for long-distancecommunications and radio navigation [70] Initially itwas designated AM and then A3 representing anaverage of the three best scales In 1960 the BIHbegan publication of the differences between UT2 andvarious individual atomic times obtained by integrationof accurate frequency comparisons By 1969 the BIHhad rede ned A3 to be an averaged atomic time scale(TA) based on several primary laboratory standardsIn 1971 this scale became the scale of InternationalAtomic Time (TAI) [71]

52 Atomic de nition of the second

In June 1955 Louis Essen and J V L Parry of the NPLmeasured the operational resonance frequency of thelaboratoryrsquos caesium standard with respect to the second

of UT2 as (9 192 631 830 plusmn 10) Hz by comparison withthe adopted frequency of a quartz standard which wascalibrated from astronomical measurements performedat the RGO [72] Over the following three years incooperation with William Markowitz and R G Hall atthe USNO they determined its value in terms of thesecond of Ephemeris Time Photographs of the Moonand surrounding stars were taken by the USNO dual-rate Moon camera over the period 195550 to 195825to determine the Ephemeris Time from the positionof the Moon at a known UT2 The UT2 scale basedon observations made with photographic zenith tubes(PZTs) at the USNO was calibrated with the caesium-beam atomic clock in Teddington via simultaneousobservations of the intervals between time pulsesbroadcast by radio stations WWV (then in GreenbeltMd) and GBR (Rugby UK) The measured caesiumfrequency was 9 192 631 770 Hz with a probable errorof plusmn 20 Hz [73] The principal uncertainty arose fromthe astronomical measurements themselves

Only seven years after the de nition of theephemeris second as an SI unit in 1960 the 13thCGPM in October 1967 adopted the atomic secondas the fundamental unit of time in the InternationalSystem of Units The second was de ned as [74]

ldquothe duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the twohyper ne levels of the ground state of the caesium133 atomrdquo

The second of atomic time is in principleequivalent to the second of Ephemeris Time Howeverthis decision did not consider a recommendation ofCommissions 4 (Ephemerides) and 31 (Time) of theIAU in 1967 in Prague which requested the CGPMto recognize the ephemeris second as a part of theIAU system of astronomical constants thus causingobjections from some astronomers [75]

53 Establishment of TAI

A prevalent opinion among astronomers in the mid-1960s had been that the atomic standards could providethe unit of time but not the continuous scale of timethat they needed [76] But on the contrary the BIHwas convinced that an atomic standard was the bestreference for time and devoted its resources to theestablishment of a practical international scale of atomictime [77]

In 1967 IAU Commissions 4 and 31 [78]recommended that the BIH compute an internationalscale of atomic time comprising independent timescales of the major national time services based onexperience gained from the experimental scale A3 Italso suggested that this scale be published in the form ofcorrections to the contributing time scales with respectto the international scale Similar recommendationsfollowed from the International Union of Radio Science

514 Metrologia 2001 38 509-529

The leap second its history and possible future

(URSI) in 1969 and the International Radio ConsultativeCommittee (CCIR) in 1970

The Comit Acirce Consultatif pour la D Acirce nition de laSeconde (CCDS) of the CIPM recommended guidelinesfor the establishment of International Atomic Time(TAI) in 1970 The CCDS stated [79]

ldquoInternational Atomic Time (TAI) is the time referencecoordinate established by the Bureau International delrsquoHeure on the basis of readings of atomic clocksoperating in various establishments in accordance withthe de nition of the second the unit of time of theInternational System of Unitsrdquo

In conformity with the recommendations of IAUCommissions 4 and 31 in 1967 the CCDS [80]de ned the origin so that TAI would be in approximateagreement with UT2 on 1 January 1958 0 h UT2 The14th CGPM approved the establishment of TAI in 1971

Yet an important task remained To de ne the scaleof atomic time completely one must de ne where in theuniverse the SI second is to be realized In recognitionof the framework of general relativity the de nitionwas completed in 1980 by the statement [81]

ldquoTAI is a coordinate time scale de ned in a geocentricreference frame with the SI second as realized on therotating geoid as the scale unitrdquo

Thus relativistic corrections are required for the primarylaboratory realizations of the SI second used in thecalibration of TAI to compensate the frequency shiftsbetween their individual locations and a point xed onthe surface of the rotating geoid

TAI when formally adopted in 1971 was anextension of the BIH atomic time scale that had beencontinuous back to 1955 In 1988 responsibility formaintaining TAI was transferred from the BIH to theBIPM A distribution of approximately two hundredclocks maintained in fty laboratories contribute to TAIusing an optimized weighting algorithm

6 Coordinated Universal Time

There were two communities of users Some suchas astronomers geodesists and navigators wanted abroadcast time connected with the angle of the Earthrsquosrotation in space Others such as physicists andengineers at time and frequency laboratories wantedit to be perfectly uniform to agree with the best clocksAttempts to meet the needs of both communities led tothe creation of Coordinated Universal Time (UTC)

61 Original UTC system

Originally radio time signals controlled from the RoyalGreenwich Observatory were kept closely in phasewith the Earthrsquos rotation using direct astronomicalobservations resulting in a nominal time interval of

a second that could vary slightly from day to dayBeginning in 1944 the time signals were generatedby quartz-crystal clocks at a uniform rate with stepcorrections introduced when necessary to maintainagreement with astronomical time When an atomicstandard became available at the NPL in 1955 theMSF time and frequency broadcast service of theUK based its signal on the provisional frequencyof 9 192 631 830 Hz for caesium In 1958 the NPLadopted the frequency 9 192 631 770 Hz but announcedthat the MSF service would have an annual rate offsetof a stated amount in addition to step corrections tokeep the disseminated time signals close to the scaleof UT2 [82]

Following the creation of their atomic time scalesin the period 1956-57 the USNO and the NBS eachmaintained two systems of atomic clock time TheUSNO system of uniform time A1 was related toEphemeris Time while the USNO Master Clock wasadjusted daily to UT2 from PZT observations Similarlythe NBS time scale NBS-A had a uniform ratesynchronized with A1 while NBS-UA was derived byapplying rate offsets and small steps to follow UT2 andwas disseminated by radio station WWV A summaryof the corrections utilized by WWV is given in [83]

At rst time signals broadcast from variouscountries were so loosely controlled that a listenermonitoring several stations could hear the pulsesarriving at different times To reduce the disparitiesthe World Administrative Radio Conference (Geneva)in 1959 requested the CCIR to study the questionof establishing and operating a worldwide standardfrequency and time signal service

The nautical almanacs of the UK and the USAwere combined in 1957 beginning with the editions for1960 In August 1959 it was also agreed to coordinatetheir time and frequency transmissions Coordinationbegan 1 January 1960 The participating observatoriesand laboratories were the USNO RGO NBS NRLand NPL Gradually other countries joined the systemwhich was entrusted to the BIH in 1961 In January1965 the BIH decided to attach UTC to its atomic timeA3 (which became TAI) by a mathematical relationship[84] This was the origin of the link between TAI andUTC The name ldquoCoordinated Universal Time (UTC)rdquowas approved by a resolution of IAU Commissions 4and 31 at the 13th General Assembly in 1967 [85]

62 Revised UTC system

Details of the UTC system were formalized by CCIRStudy Group 7 in Geneva in 1962 and were adoptedby the CCIR in its Recommendation 374 [86] of 1963The frequency offset was announced by the BIH afterconsultation with the observatories concerned to matchas nearly as practical the rotational speed of the Earthand remained constant for each year while steps of100 ms were inserted periodically at the beginning of

Metrologia 2001 38 509-529 515

R A Nelson et al

the month on dates determined by the BIH to maintainthe time signals to within about 01 s of UT2

As UTC included rate offsets to reduce the need forstep adjustments the broadcast time signals indicatedneither the SI second nor the mean solar secondbut rather variable intervals to stay in step withUT2 from which the SI second could be obtainedby applying a known correction Attempts to followthese uctuations necessitated revisions in complexequipment on a frequent basis and risked temporaryinterruptions of service At an interim session in MonteCarlo during March 1965 Study Group 7 suggested thatexperimental broadcasts and studies should be made toinvestigate how to provide both the epoch of UniversalTime and the international unit of time interval in thesame emission [87]

The revised CCIR Recommendation 374-1 [88]of 1966 allowed for the limited and provisional useof an experimental ldquoStepped Atomic Time (SAT)rdquo inwhich the broadcast time rate was the atomic timerate with no carrier deviation but in which frequentstep adjustments of 200 ms were applied to match UT2to within 01 s The existence of two parallel systemsUTC and SAT was regarded as a phase in the evolutionand adoption of a single practical and internationallyacceptable system [89]

63 Present UTC system

At the 15th General Assembly of the URSI in Munichin 1966 Commission 1 expressed the opinion thatall proposed methods of operating standard time andfrequency services contained defects and that theseservices must inevitably develop towards a system ofuniform atomic time and constant frequency For thoserequiring astronomical time some form of correctionwould be necessary [90 91] In 1967 at a meeting heldin Brussels under the auspices of the URSI to considerfrequency coordination in Europe it was unanimouslyagreed that both rate offsets and step adjustments shouldbe discontinued It was suggested that the deviations ofUTC from UT2 would have no signi cance for civilpurposes but could be disseminated to navigators intables or in the transmissions themselves [92]

Dissatisfaction with the existing form of UTC andthe need to study the implications of the new de nitionof the second adopted in 1967 prompted discussions bythe CIPM and the CCIR Following a recommendationof the CCDS the CIPM formed a preparatorycommission for the international coordination of timescales The concept of the leap second analogous to theleap day in the calendar was proposed independentlyby G M R Winkler [93] and Louis Essen [94] at ameeting of the commission held at the BIPM in May1968 [95 96] It was proposed that integer steps ofseconds replace the steps of 100 ms or 200 ms thenbeing used because they were too frequent and toosmall Consideration of possible modi cations to UTC

was also given by CCIR Study Group 7 in Boulderin August 1968 [97] The view was expressed that thebest system would be one with 1 s steps without rateoffsets so that equipment generating a pulse train wouldnot require a change in frequency To meet the needsof navigators it was suggested that coded informationmight be incorporated in the emission to indicate thedifference between UTC and UT2 to higher resolutionAn Interim Working Party IWP 71 was formed toinvestigate requirements submit proposals and x adate for the introduction of the new system The optionsunder consideration at this time were summarized asfollows [98]

ldquoDiscarding the suggestion (for practical reasons and toavoid confusions) of two time scales one approachingUT (the present UTC) and the other without offsetsand adjustments only three alternatives remain (a) stepadjustment of 01 s or 02 s to maintain the UTCsuf ciently near to UT2 to permit to ignore thedifference in most of the applications (b) completedisuse of UTC system replacing it with a coordinateduniform time scale without offsets and steps andtherefore not approaching UT (c) step adjustment of1 s exactlyrdquo

Speci c proposals were made by Study Group 7 inGeneva in October 1969 which were approved by theCCIR XIIth Plenary Assembly in New Delhi in January1970 In its Recommendation 460 [99] the CCIRstated that (a) carrier frequencies and time intervalsshould be maintained constant and should correspondto the de nition of the SI second (b) step adjustmentswhen necessary should be exactly 1 s to maintainapproximate agreement with Universal Time (UT) and(c) standard signals should contain information onthe difference between UTC and UT The CCIR alsodecided to begin the new UTC system on 1 January1972

At the IAUrsquos 14th General Assembly in BrightonUK in August 1970 the chairman of CCIR IWP 71H M Smith sought the views of Commissions 4(Ephemerides) and 31 (Time) The appropriate methodof providing both precise Earth orientation to navigatorsand uniform time to time and frequency laboratorieswas discussed As the navigator requires knowledgeof UT1 rather than UT2 it was recommended thatradio time signals should disseminate differences in theform of [UT1 ndash UTC] Several astronomers emphasizedthat visual observers in astronomical and related eldsrequire UT1 to a precision of 01 s as this is aboutthe limit of human time discrimination In addition thealmanacs were designed to permit a determination ofposition to 01 minute of arc and for this a comparableprecision in time of 025 s was required At BrightonCommission 31 adopted recommendations similar tothose of the CCIR Also the IAU General Assemblyresolved that adequate means should be provided toensure that the difference [UT1 ndash UTC] would be

516 Metrologia 2001 38 509-529

The leap second its history and possible future

available before permitting UTC to depart from UT1by more than about 01 s [100]

Detailed instructions for the implementation ofCCIR Recommendation 460 were drafted at a furthermeeting of Study Group 7 that was held in February1971 [101] The de ning epoch of 1 January 19720 h 0 m 0 s UTC was set 10 s behind TAI whichwas the approximate accumulated difference betweenTAI and UT1 since the inception of TAI in 1958and a unique fraction of a second adjustment wasapplied so that UTC would differ from TAI byan integral number of seconds The recommendedmaximum departure of UTC from UT1 was 07 sThe term ldquoleap secondrdquo was introduced for the steppedsecond An additional correction DUT1 was introducedhaving integral multiples of 01 s to be embodied in thetime signals such that when added to UTC they wouldyield a better approximation to UT1 For examplethis second level of correction was achieved by NBSradio stations WWV and WWVH by using double ticksor pulses after the start of each minute in its UTCbroadcasts [102]

The recommendations of the IAU were formalizedby resolutions of Commissions 4 and 31 at the15th General Assembly in Sydney in 1973 and afterfurther discussion the name UTC was retained [103]UTC was recommended as the basis of standardtime in all countries the time in common (civil)use as disseminated by radio signals The limit of[UT1 ndash UTC] was set at plusmn0950 s as this is themaximum difference that can be accommodated by thecode format The maximum deviation of UT1 from[UTC + DUT1] was set at plusmn0100 s In 1974 the CCIRincreased the tolerance for [UT1 ndash UTC] from 07 sto 09 s

The present UTC system is de ned by ITU-R(formerly CCIR) Recommendation ITU-R TF460-5[104]

ldquoUTC is the time scale maintained by the BIPM withassistance from the IERS which forms the basis of acoordinated dissemination of standard frequencies andtime signals It corresponds exactly in rate with TAIbut differs from it by an integral number of secondsThe UTC scale is adjusted by the insertion or deletionof seconds (positive or negative leap seconds) to ensureapproximate agreement with UT1rdquo

The interval between time signals of UTC is thusexactly equal to the SI second A history of rate offsetsand step adjustments in UTC is given in [105]

7 The leap second

71 Rate of increase in length of day

Because the Earthrsquos rotation is gradually slowingdown and in addition has both random and periodic uctuations it is not a uniform measure of time The

time difference T [ET ndash UT1] [TT ndash UT1]represents the difference between the uniform scale ofEphemeris Time or Terrestrial Time and the variablescale of Universal Time Values of T are summarizedin [106] Before 1955 the values are given by T[ET ndash UT1] based on observations of the Moon After1955 values are given by T [TT ndash UT1] [TAI +32184 s ndash UT1] from measurements by atomic clocksas published by the BIH and the BIPM

According to Stephenson and Morrison [107] overthe past 2700 years can be represented by aparabola of approximately the form

T = (31 scy2) (T ndash 1820)2(100)2 ndash 20 s

where T is expressed in seconds and T is the yearFigure 1 plots this equation together with observationssince 1620 The curve has a minimum at the year 1820and passes through 0 at the year 1900 Actual values of

T based on astronomical data may differ somewhatfrom this smoothed t For example the value of Tis 32184 s at 19580 the origin of TAI However nosingle parabola can satisfactorily represent all modernand historical data

The derivative of T is

Lday (00017 sdcy) (T ndash 1820)100

Figure 1 Observations and parabolic t of T versus timesince 1620 (after Stephenson and Morrison [26])

Figure 2 Change in the length of day with respect to areference day of 86 400 s versus time (after Stephensonand Morrison [26])

Metrologia 2001 38 509-529 517

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

The leap second its history and possible future

[(360 60 60)129 602 76813] 36 525 86 400= 31 556 9259747 s Therefore at the recommendationof the CIPM the 10th CGPM in 1954 proposed thefollowing de nition of the second

ldquoThe second is the fraction 131 556 925975 of thelength of the tropical year for 19000rdquo

But although the IAU approved this de nition atits General Assembly in 1955 Danjon commented thatthe fraction ought to have a slightly more precisevalue to bring about exact numerical agreement withNewcombrsquos formula [46] Consequently the CIPM in1956 under the authority given by the 10th CGPM in1954 de ned the second of ephemeris time to be

ldquothe fraction 131 556 9259747 of the tropical year for1900 January 0 at 12 hours ephemeris timerdquo

This de nition was rati ed by the 11th CGPM in 1960[47] Reference to the year 1900 does not imply that thisis the epoch of a mean solar day of 86 400 s Rather itis the epoch of the tropical year of 31 556 9259747 s

Although ET was de ned in terms of the longitudeof the Sun in practice it was realized indirectly bycomparison of observations of lunar positions withlunar ephemerides Thus a set of secondary time scales(denoted by ET0 ET1 and ET2) were de ned thatdiffered because of subsequent improvements to theconventional ephemerides [48]

In 1958 the IAU General Assembly adopted aresolution that de ned the epoch of Ephemeris Time tocoincide with Newcombrsquos formula as follows [49]

ldquoEphemeris Time (ET) or Temps des Eph Acircem Acircerides(TE) is reckoned from the instant near the beginningof the calendar year AD 1900 when the geometricmean longitude of the Sun was 279 41 48 04 atwhich instant the measure of Ephemeris Time was1900 January 0d 12h preciselyrdquo

The resolution also included the de nition of the secondgiven by the CIPM in 1956 In a separate resolution theepoch for Universal Time was chosen as 1900 January0d 12h UT based on the Fourth Fundamental Katalog(FK4) [50] However the equinox of Newcombrsquos Sunthe lunar theory and the FK4 did not agree preciselyand they were moving with respect to one another Thusthe actual instant in time corresponding to the epochof ET was approximately 4 s later than the epoch ofUT [51]

Ephemeris Time (ET) is a dynamical timedetermined by the theory of celestial mechanics andis theoretically uniform [52] ET may be characterizedas the independent variable that brings the observedpositions of the celestial bodies into accord with theircalculated positions constructed from the Newtonianlaws of motion Therefore in effect it is de ned bythese laws [53]

42 Relativistic time scales

In 1960 ET replaced UT1 as the independent variableof astronomical ephemerides However ET did notinclude relativistic effects and did not distinguishbetween proper time and coordinate time Accordinglyat the 16th General Assembly in Grenoble in 1976the IAU de ned time-like arguments that distinguishcoordinate systems with origins at the centre of theEarth and the centre of the solar system respectivelyand are consistent with the general theory of relativity[54] In 1979 these time scales received the namesTerrestrial Dynamical Time (TDT) and BarycentricDynamical Time (TDB) [55]

TDT replaced ET in 1984 as the tabular argumentof the fundamental geocentric ephemerides TDT hasan origin of 1 January 1977 0 h TAI with a unit intervalequal to the SI second and maintains continuity withET At this epoch a rate correction of ndash10 10ndash13

was applied to TAI to bring the unit of TAI moreclosely into accord with the SI second [56] In 1991the IAU renamed TDT simply Terrestrial Time (TT) Apractical realization of TT is [57]

[TT] = [TAI] + 32184 s

The constant offset represents the difference betweenET and UT1 at the de ning epoch of TAI on 1 January1958

The relationship between TT and TAI is notstrictly rigorous for two fundamental reasons [58]First TAI is a statistically formed time scale based oncontributions from the major timing centres whereasTT is theoretically uniform Second a scale oftime based on the laws of gravitation may not bephilosophically equivalent to one based on the quantummechanics of the atom

For ephemerides referred to the barycentre ofthe solar system the argument is TDB Through anappropriately chosen scaling factor TDB varies fromTT or TDT by only periodic variations with amplitudesless than 0002 s

From the deliberations of the IAU Working Groupon Reference Systems formed in 1988 there arose ninerecommendations that were contained in Resolution A4adopted by the 21st IAU General Assembly in 1991[59] The general theory of relativity was explicitlyintroduced as the theoretical basis for the celestialreference frame and the form of the space-time metricto post-Newtonian order was speci ed The IAUalso clari ed the de nition of Terrestrial Time (TT)and adopted two additional time scales GeocentricCoordinate Time (TCG) and Barycentric CoordinateTime (TCB) [60] The ldquocoordinaterdquo time scales TCGand TCB are complementary to the ldquodynamicalrdquo timescales TT (or TDT) and TDB They differ in ratefrom TT and are related by four-dimensional space-timecoordinate transformations [61] These de nitions were

Metrologia 2001 38 509-529 513

R A Nelson et al

further clari ed by resolutions adopted at the 24th IAUGeneral Assembly held in Manchester in 2000 [62]

5 International Atomic Time

Although ET was a uniform time scale it was noteasily realized or disseminated The rapid developmentof atomic clocks permitted yet another de nition oftime [63]

51 Experimental atomic time scales

The rst operational caesium beam frequency standardappeared in 1955 at the National Physical Laboratory(NPL UK) [64] The Royal Greenwich Observatory(RGO) established a time scale known as GreenwichAtomic (GA) using free-running quartz-crystal clocksperiodically calibrated in terms of this standard

A commercial caesium frequency standard theldquoAtomichronrdquo was developed in 1956 [65] The USNaval Observatory (USNO) inaugurated its A1 atomictime scale on 13 September 1956 initially based on acaesium clock at the Naval Research Laboratory (NRL)consisting of an Atomichron caesium standard and aquartz-crystal clock The frequency of the crystal wasmatched daily to the caesium standard which was notoperated continuously [66] The National Bureau ofStandards (NBS) in Boulder Colo also maintained anatomic time scale NBS-A starting 9 October 1957The epochs of A1 and NBS-A were made coincidentand set equal to UT2 on 1 January 1958 [67]

The A1 time scale was introduced for world use on1 January 1959 By 1961 A1 was based on atomic os-cillators at the USNO NRL NBS USNO Time ServiceSub-Station (Richmond Florida) Harvard UniversityNational Research Council (Ottawa) NPL CentreNational drsquo AcircEtudes des T Acircel Acircecommunications (Bagneux)and Observatoire de Neuch Atildeatel (Switzerland) [68 69]

Once continuous atomic time became establishedat various laboratories the BIH began a mean atomictime scale based on frequency comparisons by means ofVLF carriers at 3 kHz to 30 kHz used for long-distancecommunications and radio navigation [70] Initially itwas designated AM and then A3 representing anaverage of the three best scales In 1960 the BIHbegan publication of the differences between UT2 andvarious individual atomic times obtained by integrationof accurate frequency comparisons By 1969 the BIHhad rede ned A3 to be an averaged atomic time scale(TA) based on several primary laboratory standardsIn 1971 this scale became the scale of InternationalAtomic Time (TAI) [71]

52 Atomic de nition of the second

In June 1955 Louis Essen and J V L Parry of the NPLmeasured the operational resonance frequency of thelaboratoryrsquos caesium standard with respect to the second

of UT2 as (9 192 631 830 plusmn 10) Hz by comparison withthe adopted frequency of a quartz standard which wascalibrated from astronomical measurements performedat the RGO [72] Over the following three years incooperation with William Markowitz and R G Hall atthe USNO they determined its value in terms of thesecond of Ephemeris Time Photographs of the Moonand surrounding stars were taken by the USNO dual-rate Moon camera over the period 195550 to 195825to determine the Ephemeris Time from the positionof the Moon at a known UT2 The UT2 scale basedon observations made with photographic zenith tubes(PZTs) at the USNO was calibrated with the caesium-beam atomic clock in Teddington via simultaneousobservations of the intervals between time pulsesbroadcast by radio stations WWV (then in GreenbeltMd) and GBR (Rugby UK) The measured caesiumfrequency was 9 192 631 770 Hz with a probable errorof plusmn 20 Hz [73] The principal uncertainty arose fromthe astronomical measurements themselves

Only seven years after the de nition of theephemeris second as an SI unit in 1960 the 13thCGPM in October 1967 adopted the atomic secondas the fundamental unit of time in the InternationalSystem of Units The second was de ned as [74]

ldquothe duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the twohyper ne levels of the ground state of the caesium133 atomrdquo

The second of atomic time is in principleequivalent to the second of Ephemeris Time Howeverthis decision did not consider a recommendation ofCommissions 4 (Ephemerides) and 31 (Time) of theIAU in 1967 in Prague which requested the CGPMto recognize the ephemeris second as a part of theIAU system of astronomical constants thus causingobjections from some astronomers [75]

53 Establishment of TAI

A prevalent opinion among astronomers in the mid-1960s had been that the atomic standards could providethe unit of time but not the continuous scale of timethat they needed [76] But on the contrary the BIHwas convinced that an atomic standard was the bestreference for time and devoted its resources to theestablishment of a practical international scale of atomictime [77]

In 1967 IAU Commissions 4 and 31 [78]recommended that the BIH compute an internationalscale of atomic time comprising independent timescales of the major national time services based onexperience gained from the experimental scale A3 Italso suggested that this scale be published in the form ofcorrections to the contributing time scales with respectto the international scale Similar recommendationsfollowed from the International Union of Radio Science

514 Metrologia 2001 38 509-529

The leap second its history and possible future

(URSI) in 1969 and the International Radio ConsultativeCommittee (CCIR) in 1970

The Comit Acirce Consultatif pour la D Acirce nition de laSeconde (CCDS) of the CIPM recommended guidelinesfor the establishment of International Atomic Time(TAI) in 1970 The CCDS stated [79]

ldquoInternational Atomic Time (TAI) is the time referencecoordinate established by the Bureau International delrsquoHeure on the basis of readings of atomic clocksoperating in various establishments in accordance withthe de nition of the second the unit of time of theInternational System of Unitsrdquo

In conformity with the recommendations of IAUCommissions 4 and 31 in 1967 the CCDS [80]de ned the origin so that TAI would be in approximateagreement with UT2 on 1 January 1958 0 h UT2 The14th CGPM approved the establishment of TAI in 1971

Yet an important task remained To de ne the scaleof atomic time completely one must de ne where in theuniverse the SI second is to be realized In recognitionof the framework of general relativity the de nitionwas completed in 1980 by the statement [81]

ldquoTAI is a coordinate time scale de ned in a geocentricreference frame with the SI second as realized on therotating geoid as the scale unitrdquo

Thus relativistic corrections are required for the primarylaboratory realizations of the SI second used in thecalibration of TAI to compensate the frequency shiftsbetween their individual locations and a point xed onthe surface of the rotating geoid

TAI when formally adopted in 1971 was anextension of the BIH atomic time scale that had beencontinuous back to 1955 In 1988 responsibility formaintaining TAI was transferred from the BIH to theBIPM A distribution of approximately two hundredclocks maintained in fty laboratories contribute to TAIusing an optimized weighting algorithm

6 Coordinated Universal Time

There were two communities of users Some suchas astronomers geodesists and navigators wanted abroadcast time connected with the angle of the Earthrsquosrotation in space Others such as physicists andengineers at time and frequency laboratories wantedit to be perfectly uniform to agree with the best clocksAttempts to meet the needs of both communities led tothe creation of Coordinated Universal Time (UTC)

61 Original UTC system

Originally radio time signals controlled from the RoyalGreenwich Observatory were kept closely in phasewith the Earthrsquos rotation using direct astronomicalobservations resulting in a nominal time interval of

a second that could vary slightly from day to dayBeginning in 1944 the time signals were generatedby quartz-crystal clocks at a uniform rate with stepcorrections introduced when necessary to maintainagreement with astronomical time When an atomicstandard became available at the NPL in 1955 theMSF time and frequency broadcast service of theUK based its signal on the provisional frequencyof 9 192 631 830 Hz for caesium In 1958 the NPLadopted the frequency 9 192 631 770 Hz but announcedthat the MSF service would have an annual rate offsetof a stated amount in addition to step corrections tokeep the disseminated time signals close to the scaleof UT2 [82]

Following the creation of their atomic time scalesin the period 1956-57 the USNO and the NBS eachmaintained two systems of atomic clock time TheUSNO system of uniform time A1 was related toEphemeris Time while the USNO Master Clock wasadjusted daily to UT2 from PZT observations Similarlythe NBS time scale NBS-A had a uniform ratesynchronized with A1 while NBS-UA was derived byapplying rate offsets and small steps to follow UT2 andwas disseminated by radio station WWV A summaryof the corrections utilized by WWV is given in [83]

At rst time signals broadcast from variouscountries were so loosely controlled that a listenermonitoring several stations could hear the pulsesarriving at different times To reduce the disparitiesthe World Administrative Radio Conference (Geneva)in 1959 requested the CCIR to study the questionof establishing and operating a worldwide standardfrequency and time signal service

The nautical almanacs of the UK and the USAwere combined in 1957 beginning with the editions for1960 In August 1959 it was also agreed to coordinatetheir time and frequency transmissions Coordinationbegan 1 January 1960 The participating observatoriesand laboratories were the USNO RGO NBS NRLand NPL Gradually other countries joined the systemwhich was entrusted to the BIH in 1961 In January1965 the BIH decided to attach UTC to its atomic timeA3 (which became TAI) by a mathematical relationship[84] This was the origin of the link between TAI andUTC The name ldquoCoordinated Universal Time (UTC)rdquowas approved by a resolution of IAU Commissions 4and 31 at the 13th General Assembly in 1967 [85]

62 Revised UTC system

Details of the UTC system were formalized by CCIRStudy Group 7 in Geneva in 1962 and were adoptedby the CCIR in its Recommendation 374 [86] of 1963The frequency offset was announced by the BIH afterconsultation with the observatories concerned to matchas nearly as practical the rotational speed of the Earthand remained constant for each year while steps of100 ms were inserted periodically at the beginning of

Metrologia 2001 38 509-529 515

R A Nelson et al

the month on dates determined by the BIH to maintainthe time signals to within about 01 s of UT2

As UTC included rate offsets to reduce the need forstep adjustments the broadcast time signals indicatedneither the SI second nor the mean solar secondbut rather variable intervals to stay in step withUT2 from which the SI second could be obtainedby applying a known correction Attempts to followthese uctuations necessitated revisions in complexequipment on a frequent basis and risked temporaryinterruptions of service At an interim session in MonteCarlo during March 1965 Study Group 7 suggested thatexperimental broadcasts and studies should be made toinvestigate how to provide both the epoch of UniversalTime and the international unit of time interval in thesame emission [87]

The revised CCIR Recommendation 374-1 [88]of 1966 allowed for the limited and provisional useof an experimental ldquoStepped Atomic Time (SAT)rdquo inwhich the broadcast time rate was the atomic timerate with no carrier deviation but in which frequentstep adjustments of 200 ms were applied to match UT2to within 01 s The existence of two parallel systemsUTC and SAT was regarded as a phase in the evolutionand adoption of a single practical and internationallyacceptable system [89]

63 Present UTC system

At the 15th General Assembly of the URSI in Munichin 1966 Commission 1 expressed the opinion thatall proposed methods of operating standard time andfrequency services contained defects and that theseservices must inevitably develop towards a system ofuniform atomic time and constant frequency For thoserequiring astronomical time some form of correctionwould be necessary [90 91] In 1967 at a meeting heldin Brussels under the auspices of the URSI to considerfrequency coordination in Europe it was unanimouslyagreed that both rate offsets and step adjustments shouldbe discontinued It was suggested that the deviations ofUTC from UT2 would have no signi cance for civilpurposes but could be disseminated to navigators intables or in the transmissions themselves [92]

Dissatisfaction with the existing form of UTC andthe need to study the implications of the new de nitionof the second adopted in 1967 prompted discussions bythe CIPM and the CCIR Following a recommendationof the CCDS the CIPM formed a preparatorycommission for the international coordination of timescales The concept of the leap second analogous to theleap day in the calendar was proposed independentlyby G M R Winkler [93] and Louis Essen [94] at ameeting of the commission held at the BIPM in May1968 [95 96] It was proposed that integer steps ofseconds replace the steps of 100 ms or 200 ms thenbeing used because they were too frequent and toosmall Consideration of possible modi cations to UTC

was also given by CCIR Study Group 7 in Boulderin August 1968 [97] The view was expressed that thebest system would be one with 1 s steps without rateoffsets so that equipment generating a pulse train wouldnot require a change in frequency To meet the needsof navigators it was suggested that coded informationmight be incorporated in the emission to indicate thedifference between UTC and UT2 to higher resolutionAn Interim Working Party IWP 71 was formed toinvestigate requirements submit proposals and x adate for the introduction of the new system The optionsunder consideration at this time were summarized asfollows [98]

ldquoDiscarding the suggestion (for practical reasons and toavoid confusions) of two time scales one approachingUT (the present UTC) and the other without offsetsand adjustments only three alternatives remain (a) stepadjustment of 01 s or 02 s to maintain the UTCsuf ciently near to UT2 to permit to ignore thedifference in most of the applications (b) completedisuse of UTC system replacing it with a coordinateduniform time scale without offsets and steps andtherefore not approaching UT (c) step adjustment of1 s exactlyrdquo

Speci c proposals were made by Study Group 7 inGeneva in October 1969 which were approved by theCCIR XIIth Plenary Assembly in New Delhi in January1970 In its Recommendation 460 [99] the CCIRstated that (a) carrier frequencies and time intervalsshould be maintained constant and should correspondto the de nition of the SI second (b) step adjustmentswhen necessary should be exactly 1 s to maintainapproximate agreement with Universal Time (UT) and(c) standard signals should contain information onthe difference between UTC and UT The CCIR alsodecided to begin the new UTC system on 1 January1972

At the IAUrsquos 14th General Assembly in BrightonUK in August 1970 the chairman of CCIR IWP 71H M Smith sought the views of Commissions 4(Ephemerides) and 31 (Time) The appropriate methodof providing both precise Earth orientation to navigatorsand uniform time to time and frequency laboratorieswas discussed As the navigator requires knowledgeof UT1 rather than UT2 it was recommended thatradio time signals should disseminate differences in theform of [UT1 ndash UTC] Several astronomers emphasizedthat visual observers in astronomical and related eldsrequire UT1 to a precision of 01 s as this is aboutthe limit of human time discrimination In addition thealmanacs were designed to permit a determination ofposition to 01 minute of arc and for this a comparableprecision in time of 025 s was required At BrightonCommission 31 adopted recommendations similar tothose of the CCIR Also the IAU General Assemblyresolved that adequate means should be provided toensure that the difference [UT1 ndash UTC] would be

516 Metrologia 2001 38 509-529

The leap second its history and possible future

available before permitting UTC to depart from UT1by more than about 01 s [100]

Detailed instructions for the implementation ofCCIR Recommendation 460 were drafted at a furthermeeting of Study Group 7 that was held in February1971 [101] The de ning epoch of 1 January 19720 h 0 m 0 s UTC was set 10 s behind TAI whichwas the approximate accumulated difference betweenTAI and UT1 since the inception of TAI in 1958and a unique fraction of a second adjustment wasapplied so that UTC would differ from TAI byan integral number of seconds The recommendedmaximum departure of UTC from UT1 was 07 sThe term ldquoleap secondrdquo was introduced for the steppedsecond An additional correction DUT1 was introducedhaving integral multiples of 01 s to be embodied in thetime signals such that when added to UTC they wouldyield a better approximation to UT1 For examplethis second level of correction was achieved by NBSradio stations WWV and WWVH by using double ticksor pulses after the start of each minute in its UTCbroadcasts [102]

The recommendations of the IAU were formalizedby resolutions of Commissions 4 and 31 at the15th General Assembly in Sydney in 1973 and afterfurther discussion the name UTC was retained [103]UTC was recommended as the basis of standardtime in all countries the time in common (civil)use as disseminated by radio signals The limit of[UT1 ndash UTC] was set at plusmn0950 s as this is themaximum difference that can be accommodated by thecode format The maximum deviation of UT1 from[UTC + DUT1] was set at plusmn0100 s In 1974 the CCIRincreased the tolerance for [UT1 ndash UTC] from 07 sto 09 s

The present UTC system is de ned by ITU-R(formerly CCIR) Recommendation ITU-R TF460-5[104]

ldquoUTC is the time scale maintained by the BIPM withassistance from the IERS which forms the basis of acoordinated dissemination of standard frequencies andtime signals It corresponds exactly in rate with TAIbut differs from it by an integral number of secondsThe UTC scale is adjusted by the insertion or deletionof seconds (positive or negative leap seconds) to ensureapproximate agreement with UT1rdquo

The interval between time signals of UTC is thusexactly equal to the SI second A history of rate offsetsand step adjustments in UTC is given in [105]

7 The leap second

71 Rate of increase in length of day

Because the Earthrsquos rotation is gradually slowingdown and in addition has both random and periodic uctuations it is not a uniform measure of time The

time difference T [ET ndash UT1] [TT ndash UT1]represents the difference between the uniform scale ofEphemeris Time or Terrestrial Time and the variablescale of Universal Time Values of T are summarizedin [106] Before 1955 the values are given by T[ET ndash UT1] based on observations of the Moon After1955 values are given by T [TT ndash UT1] [TAI +32184 s ndash UT1] from measurements by atomic clocksas published by the BIH and the BIPM

According to Stephenson and Morrison [107] overthe past 2700 years can be represented by aparabola of approximately the form

T = (31 scy2) (T ndash 1820)2(100)2 ndash 20 s

where T is expressed in seconds and T is the yearFigure 1 plots this equation together with observationssince 1620 The curve has a minimum at the year 1820and passes through 0 at the year 1900 Actual values of

T based on astronomical data may differ somewhatfrom this smoothed t For example the value of Tis 32184 s at 19580 the origin of TAI However nosingle parabola can satisfactorily represent all modernand historical data

The derivative of T is

Lday (00017 sdcy) (T ndash 1820)100

Figure 1 Observations and parabolic t of T versus timesince 1620 (after Stephenson and Morrison [26])

Figure 2 Change in the length of day with respect to areference day of 86 400 s versus time (after Stephensonand Morrison [26])

Metrologia 2001 38 509-529 517

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

R A Nelson et al

further clari ed by resolutions adopted at the 24th IAUGeneral Assembly held in Manchester in 2000 [62]

5 International Atomic Time

Although ET was a uniform time scale it was noteasily realized or disseminated The rapid developmentof atomic clocks permitted yet another de nition oftime [63]

51 Experimental atomic time scales

The rst operational caesium beam frequency standardappeared in 1955 at the National Physical Laboratory(NPL UK) [64] The Royal Greenwich Observatory(RGO) established a time scale known as GreenwichAtomic (GA) using free-running quartz-crystal clocksperiodically calibrated in terms of this standard

A commercial caesium frequency standard theldquoAtomichronrdquo was developed in 1956 [65] The USNaval Observatory (USNO) inaugurated its A1 atomictime scale on 13 September 1956 initially based on acaesium clock at the Naval Research Laboratory (NRL)consisting of an Atomichron caesium standard and aquartz-crystal clock The frequency of the crystal wasmatched daily to the caesium standard which was notoperated continuously [66] The National Bureau ofStandards (NBS) in Boulder Colo also maintained anatomic time scale NBS-A starting 9 October 1957The epochs of A1 and NBS-A were made coincidentand set equal to UT2 on 1 January 1958 [67]

The A1 time scale was introduced for world use on1 January 1959 By 1961 A1 was based on atomic os-cillators at the USNO NRL NBS USNO Time ServiceSub-Station (Richmond Florida) Harvard UniversityNational Research Council (Ottawa) NPL CentreNational drsquo AcircEtudes des T Acircel Acircecommunications (Bagneux)and Observatoire de Neuch Atildeatel (Switzerland) [68 69]

Once continuous atomic time became establishedat various laboratories the BIH began a mean atomictime scale based on frequency comparisons by means ofVLF carriers at 3 kHz to 30 kHz used for long-distancecommunications and radio navigation [70] Initially itwas designated AM and then A3 representing anaverage of the three best scales In 1960 the BIHbegan publication of the differences between UT2 andvarious individual atomic times obtained by integrationof accurate frequency comparisons By 1969 the BIHhad rede ned A3 to be an averaged atomic time scale(TA) based on several primary laboratory standardsIn 1971 this scale became the scale of InternationalAtomic Time (TAI) [71]

52 Atomic de nition of the second

In June 1955 Louis Essen and J V L Parry of the NPLmeasured the operational resonance frequency of thelaboratoryrsquos caesium standard with respect to the second

of UT2 as (9 192 631 830 plusmn 10) Hz by comparison withthe adopted frequency of a quartz standard which wascalibrated from astronomical measurements performedat the RGO [72] Over the following three years incooperation with William Markowitz and R G Hall atthe USNO they determined its value in terms of thesecond of Ephemeris Time Photographs of the Moonand surrounding stars were taken by the USNO dual-rate Moon camera over the period 195550 to 195825to determine the Ephemeris Time from the positionof the Moon at a known UT2 The UT2 scale basedon observations made with photographic zenith tubes(PZTs) at the USNO was calibrated with the caesium-beam atomic clock in Teddington via simultaneousobservations of the intervals between time pulsesbroadcast by radio stations WWV (then in GreenbeltMd) and GBR (Rugby UK) The measured caesiumfrequency was 9 192 631 770 Hz with a probable errorof plusmn 20 Hz [73] The principal uncertainty arose fromthe astronomical measurements themselves

Only seven years after the de nition of theephemeris second as an SI unit in 1960 the 13thCGPM in October 1967 adopted the atomic secondas the fundamental unit of time in the InternationalSystem of Units The second was de ned as [74]

ldquothe duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the twohyper ne levels of the ground state of the caesium133 atomrdquo

The second of atomic time is in principleequivalent to the second of Ephemeris Time Howeverthis decision did not consider a recommendation ofCommissions 4 (Ephemerides) and 31 (Time) of theIAU in 1967 in Prague which requested the CGPMto recognize the ephemeris second as a part of theIAU system of astronomical constants thus causingobjections from some astronomers [75]

53 Establishment of TAI

A prevalent opinion among astronomers in the mid-1960s had been that the atomic standards could providethe unit of time but not the continuous scale of timethat they needed [76] But on the contrary the BIHwas convinced that an atomic standard was the bestreference for time and devoted its resources to theestablishment of a practical international scale of atomictime [77]

In 1967 IAU Commissions 4 and 31 [78]recommended that the BIH compute an internationalscale of atomic time comprising independent timescales of the major national time services based onexperience gained from the experimental scale A3 Italso suggested that this scale be published in the form ofcorrections to the contributing time scales with respectto the international scale Similar recommendationsfollowed from the International Union of Radio Science

514 Metrologia 2001 38 509-529

The leap second its history and possible future

(URSI) in 1969 and the International Radio ConsultativeCommittee (CCIR) in 1970

The Comit Acirce Consultatif pour la D Acirce nition de laSeconde (CCDS) of the CIPM recommended guidelinesfor the establishment of International Atomic Time(TAI) in 1970 The CCDS stated [79]

ldquoInternational Atomic Time (TAI) is the time referencecoordinate established by the Bureau International delrsquoHeure on the basis of readings of atomic clocksoperating in various establishments in accordance withthe de nition of the second the unit of time of theInternational System of Unitsrdquo

In conformity with the recommendations of IAUCommissions 4 and 31 in 1967 the CCDS [80]de ned the origin so that TAI would be in approximateagreement with UT2 on 1 January 1958 0 h UT2 The14th CGPM approved the establishment of TAI in 1971

Yet an important task remained To de ne the scaleof atomic time completely one must de ne where in theuniverse the SI second is to be realized In recognitionof the framework of general relativity the de nitionwas completed in 1980 by the statement [81]

ldquoTAI is a coordinate time scale de ned in a geocentricreference frame with the SI second as realized on therotating geoid as the scale unitrdquo

Thus relativistic corrections are required for the primarylaboratory realizations of the SI second used in thecalibration of TAI to compensate the frequency shiftsbetween their individual locations and a point xed onthe surface of the rotating geoid

TAI when formally adopted in 1971 was anextension of the BIH atomic time scale that had beencontinuous back to 1955 In 1988 responsibility formaintaining TAI was transferred from the BIH to theBIPM A distribution of approximately two hundredclocks maintained in fty laboratories contribute to TAIusing an optimized weighting algorithm

6 Coordinated Universal Time

There were two communities of users Some suchas astronomers geodesists and navigators wanted abroadcast time connected with the angle of the Earthrsquosrotation in space Others such as physicists andengineers at time and frequency laboratories wantedit to be perfectly uniform to agree with the best clocksAttempts to meet the needs of both communities led tothe creation of Coordinated Universal Time (UTC)

61 Original UTC system

Originally radio time signals controlled from the RoyalGreenwich Observatory were kept closely in phasewith the Earthrsquos rotation using direct astronomicalobservations resulting in a nominal time interval of

a second that could vary slightly from day to dayBeginning in 1944 the time signals were generatedby quartz-crystal clocks at a uniform rate with stepcorrections introduced when necessary to maintainagreement with astronomical time When an atomicstandard became available at the NPL in 1955 theMSF time and frequency broadcast service of theUK based its signal on the provisional frequencyof 9 192 631 830 Hz for caesium In 1958 the NPLadopted the frequency 9 192 631 770 Hz but announcedthat the MSF service would have an annual rate offsetof a stated amount in addition to step corrections tokeep the disseminated time signals close to the scaleof UT2 [82]

Following the creation of their atomic time scalesin the period 1956-57 the USNO and the NBS eachmaintained two systems of atomic clock time TheUSNO system of uniform time A1 was related toEphemeris Time while the USNO Master Clock wasadjusted daily to UT2 from PZT observations Similarlythe NBS time scale NBS-A had a uniform ratesynchronized with A1 while NBS-UA was derived byapplying rate offsets and small steps to follow UT2 andwas disseminated by radio station WWV A summaryof the corrections utilized by WWV is given in [83]

At rst time signals broadcast from variouscountries were so loosely controlled that a listenermonitoring several stations could hear the pulsesarriving at different times To reduce the disparitiesthe World Administrative Radio Conference (Geneva)in 1959 requested the CCIR to study the questionof establishing and operating a worldwide standardfrequency and time signal service

The nautical almanacs of the UK and the USAwere combined in 1957 beginning with the editions for1960 In August 1959 it was also agreed to coordinatetheir time and frequency transmissions Coordinationbegan 1 January 1960 The participating observatoriesand laboratories were the USNO RGO NBS NRLand NPL Gradually other countries joined the systemwhich was entrusted to the BIH in 1961 In January1965 the BIH decided to attach UTC to its atomic timeA3 (which became TAI) by a mathematical relationship[84] This was the origin of the link between TAI andUTC The name ldquoCoordinated Universal Time (UTC)rdquowas approved by a resolution of IAU Commissions 4and 31 at the 13th General Assembly in 1967 [85]

62 Revised UTC system

Details of the UTC system were formalized by CCIRStudy Group 7 in Geneva in 1962 and were adoptedby the CCIR in its Recommendation 374 [86] of 1963The frequency offset was announced by the BIH afterconsultation with the observatories concerned to matchas nearly as practical the rotational speed of the Earthand remained constant for each year while steps of100 ms were inserted periodically at the beginning of

Metrologia 2001 38 509-529 515

R A Nelson et al

the month on dates determined by the BIH to maintainthe time signals to within about 01 s of UT2

As UTC included rate offsets to reduce the need forstep adjustments the broadcast time signals indicatedneither the SI second nor the mean solar secondbut rather variable intervals to stay in step withUT2 from which the SI second could be obtainedby applying a known correction Attempts to followthese uctuations necessitated revisions in complexequipment on a frequent basis and risked temporaryinterruptions of service At an interim session in MonteCarlo during March 1965 Study Group 7 suggested thatexperimental broadcasts and studies should be made toinvestigate how to provide both the epoch of UniversalTime and the international unit of time interval in thesame emission [87]

The revised CCIR Recommendation 374-1 [88]of 1966 allowed for the limited and provisional useof an experimental ldquoStepped Atomic Time (SAT)rdquo inwhich the broadcast time rate was the atomic timerate with no carrier deviation but in which frequentstep adjustments of 200 ms were applied to match UT2to within 01 s The existence of two parallel systemsUTC and SAT was regarded as a phase in the evolutionand adoption of a single practical and internationallyacceptable system [89]

63 Present UTC system

At the 15th General Assembly of the URSI in Munichin 1966 Commission 1 expressed the opinion thatall proposed methods of operating standard time andfrequency services contained defects and that theseservices must inevitably develop towards a system ofuniform atomic time and constant frequency For thoserequiring astronomical time some form of correctionwould be necessary [90 91] In 1967 at a meeting heldin Brussels under the auspices of the URSI to considerfrequency coordination in Europe it was unanimouslyagreed that both rate offsets and step adjustments shouldbe discontinued It was suggested that the deviations ofUTC from UT2 would have no signi cance for civilpurposes but could be disseminated to navigators intables or in the transmissions themselves [92]

Dissatisfaction with the existing form of UTC andthe need to study the implications of the new de nitionof the second adopted in 1967 prompted discussions bythe CIPM and the CCIR Following a recommendationof the CCDS the CIPM formed a preparatorycommission for the international coordination of timescales The concept of the leap second analogous to theleap day in the calendar was proposed independentlyby G M R Winkler [93] and Louis Essen [94] at ameeting of the commission held at the BIPM in May1968 [95 96] It was proposed that integer steps ofseconds replace the steps of 100 ms or 200 ms thenbeing used because they were too frequent and toosmall Consideration of possible modi cations to UTC

was also given by CCIR Study Group 7 in Boulderin August 1968 [97] The view was expressed that thebest system would be one with 1 s steps without rateoffsets so that equipment generating a pulse train wouldnot require a change in frequency To meet the needsof navigators it was suggested that coded informationmight be incorporated in the emission to indicate thedifference between UTC and UT2 to higher resolutionAn Interim Working Party IWP 71 was formed toinvestigate requirements submit proposals and x adate for the introduction of the new system The optionsunder consideration at this time were summarized asfollows [98]

ldquoDiscarding the suggestion (for practical reasons and toavoid confusions) of two time scales one approachingUT (the present UTC) and the other without offsetsand adjustments only three alternatives remain (a) stepadjustment of 01 s or 02 s to maintain the UTCsuf ciently near to UT2 to permit to ignore thedifference in most of the applications (b) completedisuse of UTC system replacing it with a coordinateduniform time scale without offsets and steps andtherefore not approaching UT (c) step adjustment of1 s exactlyrdquo

Speci c proposals were made by Study Group 7 inGeneva in October 1969 which were approved by theCCIR XIIth Plenary Assembly in New Delhi in January1970 In its Recommendation 460 [99] the CCIRstated that (a) carrier frequencies and time intervalsshould be maintained constant and should correspondto the de nition of the SI second (b) step adjustmentswhen necessary should be exactly 1 s to maintainapproximate agreement with Universal Time (UT) and(c) standard signals should contain information onthe difference between UTC and UT The CCIR alsodecided to begin the new UTC system on 1 January1972

At the IAUrsquos 14th General Assembly in BrightonUK in August 1970 the chairman of CCIR IWP 71H M Smith sought the views of Commissions 4(Ephemerides) and 31 (Time) The appropriate methodof providing both precise Earth orientation to navigatorsand uniform time to time and frequency laboratorieswas discussed As the navigator requires knowledgeof UT1 rather than UT2 it was recommended thatradio time signals should disseminate differences in theform of [UT1 ndash UTC] Several astronomers emphasizedthat visual observers in astronomical and related eldsrequire UT1 to a precision of 01 s as this is aboutthe limit of human time discrimination In addition thealmanacs were designed to permit a determination ofposition to 01 minute of arc and for this a comparableprecision in time of 025 s was required At BrightonCommission 31 adopted recommendations similar tothose of the CCIR Also the IAU General Assemblyresolved that adequate means should be provided toensure that the difference [UT1 ndash UTC] would be

516 Metrologia 2001 38 509-529

The leap second its history and possible future

available before permitting UTC to depart from UT1by more than about 01 s [100]

Detailed instructions for the implementation ofCCIR Recommendation 460 were drafted at a furthermeeting of Study Group 7 that was held in February1971 [101] The de ning epoch of 1 January 19720 h 0 m 0 s UTC was set 10 s behind TAI whichwas the approximate accumulated difference betweenTAI and UT1 since the inception of TAI in 1958and a unique fraction of a second adjustment wasapplied so that UTC would differ from TAI byan integral number of seconds The recommendedmaximum departure of UTC from UT1 was 07 sThe term ldquoleap secondrdquo was introduced for the steppedsecond An additional correction DUT1 was introducedhaving integral multiples of 01 s to be embodied in thetime signals such that when added to UTC they wouldyield a better approximation to UT1 For examplethis second level of correction was achieved by NBSradio stations WWV and WWVH by using double ticksor pulses after the start of each minute in its UTCbroadcasts [102]

The recommendations of the IAU were formalizedby resolutions of Commissions 4 and 31 at the15th General Assembly in Sydney in 1973 and afterfurther discussion the name UTC was retained [103]UTC was recommended as the basis of standardtime in all countries the time in common (civil)use as disseminated by radio signals The limit of[UT1 ndash UTC] was set at plusmn0950 s as this is themaximum difference that can be accommodated by thecode format The maximum deviation of UT1 from[UTC + DUT1] was set at plusmn0100 s In 1974 the CCIRincreased the tolerance for [UT1 ndash UTC] from 07 sto 09 s

The present UTC system is de ned by ITU-R(formerly CCIR) Recommendation ITU-R TF460-5[104]

ldquoUTC is the time scale maintained by the BIPM withassistance from the IERS which forms the basis of acoordinated dissemination of standard frequencies andtime signals It corresponds exactly in rate with TAIbut differs from it by an integral number of secondsThe UTC scale is adjusted by the insertion or deletionof seconds (positive or negative leap seconds) to ensureapproximate agreement with UT1rdquo

The interval between time signals of UTC is thusexactly equal to the SI second A history of rate offsetsand step adjustments in UTC is given in [105]

7 The leap second

71 Rate of increase in length of day

Because the Earthrsquos rotation is gradually slowingdown and in addition has both random and periodic uctuations it is not a uniform measure of time The

time difference T [ET ndash UT1] [TT ndash UT1]represents the difference between the uniform scale ofEphemeris Time or Terrestrial Time and the variablescale of Universal Time Values of T are summarizedin [106] Before 1955 the values are given by T[ET ndash UT1] based on observations of the Moon After1955 values are given by T [TT ndash UT1] [TAI +32184 s ndash UT1] from measurements by atomic clocksas published by the BIH and the BIPM

According to Stephenson and Morrison [107] overthe past 2700 years can be represented by aparabola of approximately the form

T = (31 scy2) (T ndash 1820)2(100)2 ndash 20 s

where T is expressed in seconds and T is the yearFigure 1 plots this equation together with observationssince 1620 The curve has a minimum at the year 1820and passes through 0 at the year 1900 Actual values of

T based on astronomical data may differ somewhatfrom this smoothed t For example the value of Tis 32184 s at 19580 the origin of TAI However nosingle parabola can satisfactorily represent all modernand historical data

The derivative of T is

Lday (00017 sdcy) (T ndash 1820)100

Figure 1 Observations and parabolic t of T versus timesince 1620 (after Stephenson and Morrison [26])

Figure 2 Change in the length of day with respect to areference day of 86 400 s versus time (after Stephensonand Morrison [26])

Metrologia 2001 38 509-529 517

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

The leap second its history and possible future

(URSI) in 1969 and the International Radio ConsultativeCommittee (CCIR) in 1970

The Comit Acirce Consultatif pour la D Acirce nition de laSeconde (CCDS) of the CIPM recommended guidelinesfor the establishment of International Atomic Time(TAI) in 1970 The CCDS stated [79]

ldquoInternational Atomic Time (TAI) is the time referencecoordinate established by the Bureau International delrsquoHeure on the basis of readings of atomic clocksoperating in various establishments in accordance withthe de nition of the second the unit of time of theInternational System of Unitsrdquo

In conformity with the recommendations of IAUCommissions 4 and 31 in 1967 the CCDS [80]de ned the origin so that TAI would be in approximateagreement with UT2 on 1 January 1958 0 h UT2 The14th CGPM approved the establishment of TAI in 1971

Yet an important task remained To de ne the scaleof atomic time completely one must de ne where in theuniverse the SI second is to be realized In recognitionof the framework of general relativity the de nitionwas completed in 1980 by the statement [81]

ldquoTAI is a coordinate time scale de ned in a geocentricreference frame with the SI second as realized on therotating geoid as the scale unitrdquo

Thus relativistic corrections are required for the primarylaboratory realizations of the SI second used in thecalibration of TAI to compensate the frequency shiftsbetween their individual locations and a point xed onthe surface of the rotating geoid

TAI when formally adopted in 1971 was anextension of the BIH atomic time scale that had beencontinuous back to 1955 In 1988 responsibility formaintaining TAI was transferred from the BIH to theBIPM A distribution of approximately two hundredclocks maintained in fty laboratories contribute to TAIusing an optimized weighting algorithm

6 Coordinated Universal Time

There were two communities of users Some suchas astronomers geodesists and navigators wanted abroadcast time connected with the angle of the Earthrsquosrotation in space Others such as physicists andengineers at time and frequency laboratories wantedit to be perfectly uniform to agree with the best clocksAttempts to meet the needs of both communities led tothe creation of Coordinated Universal Time (UTC)

61 Original UTC system

Originally radio time signals controlled from the RoyalGreenwich Observatory were kept closely in phasewith the Earthrsquos rotation using direct astronomicalobservations resulting in a nominal time interval of

a second that could vary slightly from day to dayBeginning in 1944 the time signals were generatedby quartz-crystal clocks at a uniform rate with stepcorrections introduced when necessary to maintainagreement with astronomical time When an atomicstandard became available at the NPL in 1955 theMSF time and frequency broadcast service of theUK based its signal on the provisional frequencyof 9 192 631 830 Hz for caesium In 1958 the NPLadopted the frequency 9 192 631 770 Hz but announcedthat the MSF service would have an annual rate offsetof a stated amount in addition to step corrections tokeep the disseminated time signals close to the scaleof UT2 [82]

Following the creation of their atomic time scalesin the period 1956-57 the USNO and the NBS eachmaintained two systems of atomic clock time TheUSNO system of uniform time A1 was related toEphemeris Time while the USNO Master Clock wasadjusted daily to UT2 from PZT observations Similarlythe NBS time scale NBS-A had a uniform ratesynchronized with A1 while NBS-UA was derived byapplying rate offsets and small steps to follow UT2 andwas disseminated by radio station WWV A summaryof the corrections utilized by WWV is given in [83]

At rst time signals broadcast from variouscountries were so loosely controlled that a listenermonitoring several stations could hear the pulsesarriving at different times To reduce the disparitiesthe World Administrative Radio Conference (Geneva)in 1959 requested the CCIR to study the questionof establishing and operating a worldwide standardfrequency and time signal service

The nautical almanacs of the UK and the USAwere combined in 1957 beginning with the editions for1960 In August 1959 it was also agreed to coordinatetheir time and frequency transmissions Coordinationbegan 1 January 1960 The participating observatoriesand laboratories were the USNO RGO NBS NRLand NPL Gradually other countries joined the systemwhich was entrusted to the BIH in 1961 In January1965 the BIH decided to attach UTC to its atomic timeA3 (which became TAI) by a mathematical relationship[84] This was the origin of the link between TAI andUTC The name ldquoCoordinated Universal Time (UTC)rdquowas approved by a resolution of IAU Commissions 4and 31 at the 13th General Assembly in 1967 [85]

62 Revised UTC system

Details of the UTC system were formalized by CCIRStudy Group 7 in Geneva in 1962 and were adoptedby the CCIR in its Recommendation 374 [86] of 1963The frequency offset was announced by the BIH afterconsultation with the observatories concerned to matchas nearly as practical the rotational speed of the Earthand remained constant for each year while steps of100 ms were inserted periodically at the beginning of

Metrologia 2001 38 509-529 515

R A Nelson et al

the month on dates determined by the BIH to maintainthe time signals to within about 01 s of UT2

As UTC included rate offsets to reduce the need forstep adjustments the broadcast time signals indicatedneither the SI second nor the mean solar secondbut rather variable intervals to stay in step withUT2 from which the SI second could be obtainedby applying a known correction Attempts to followthese uctuations necessitated revisions in complexequipment on a frequent basis and risked temporaryinterruptions of service At an interim session in MonteCarlo during March 1965 Study Group 7 suggested thatexperimental broadcasts and studies should be made toinvestigate how to provide both the epoch of UniversalTime and the international unit of time interval in thesame emission [87]

The revised CCIR Recommendation 374-1 [88]of 1966 allowed for the limited and provisional useof an experimental ldquoStepped Atomic Time (SAT)rdquo inwhich the broadcast time rate was the atomic timerate with no carrier deviation but in which frequentstep adjustments of 200 ms were applied to match UT2to within 01 s The existence of two parallel systemsUTC and SAT was regarded as a phase in the evolutionand adoption of a single practical and internationallyacceptable system [89]

63 Present UTC system

At the 15th General Assembly of the URSI in Munichin 1966 Commission 1 expressed the opinion thatall proposed methods of operating standard time andfrequency services contained defects and that theseservices must inevitably develop towards a system ofuniform atomic time and constant frequency For thoserequiring astronomical time some form of correctionwould be necessary [90 91] In 1967 at a meeting heldin Brussels under the auspices of the URSI to considerfrequency coordination in Europe it was unanimouslyagreed that both rate offsets and step adjustments shouldbe discontinued It was suggested that the deviations ofUTC from UT2 would have no signi cance for civilpurposes but could be disseminated to navigators intables or in the transmissions themselves [92]

Dissatisfaction with the existing form of UTC andthe need to study the implications of the new de nitionof the second adopted in 1967 prompted discussions bythe CIPM and the CCIR Following a recommendationof the CCDS the CIPM formed a preparatorycommission for the international coordination of timescales The concept of the leap second analogous to theleap day in the calendar was proposed independentlyby G M R Winkler [93] and Louis Essen [94] at ameeting of the commission held at the BIPM in May1968 [95 96] It was proposed that integer steps ofseconds replace the steps of 100 ms or 200 ms thenbeing used because they were too frequent and toosmall Consideration of possible modi cations to UTC

was also given by CCIR Study Group 7 in Boulderin August 1968 [97] The view was expressed that thebest system would be one with 1 s steps without rateoffsets so that equipment generating a pulse train wouldnot require a change in frequency To meet the needsof navigators it was suggested that coded informationmight be incorporated in the emission to indicate thedifference between UTC and UT2 to higher resolutionAn Interim Working Party IWP 71 was formed toinvestigate requirements submit proposals and x adate for the introduction of the new system The optionsunder consideration at this time were summarized asfollows [98]

ldquoDiscarding the suggestion (for practical reasons and toavoid confusions) of two time scales one approachingUT (the present UTC) and the other without offsetsand adjustments only three alternatives remain (a) stepadjustment of 01 s or 02 s to maintain the UTCsuf ciently near to UT2 to permit to ignore thedifference in most of the applications (b) completedisuse of UTC system replacing it with a coordinateduniform time scale without offsets and steps andtherefore not approaching UT (c) step adjustment of1 s exactlyrdquo

Speci c proposals were made by Study Group 7 inGeneva in October 1969 which were approved by theCCIR XIIth Plenary Assembly in New Delhi in January1970 In its Recommendation 460 [99] the CCIRstated that (a) carrier frequencies and time intervalsshould be maintained constant and should correspondto the de nition of the SI second (b) step adjustmentswhen necessary should be exactly 1 s to maintainapproximate agreement with Universal Time (UT) and(c) standard signals should contain information onthe difference between UTC and UT The CCIR alsodecided to begin the new UTC system on 1 January1972

At the IAUrsquos 14th General Assembly in BrightonUK in August 1970 the chairman of CCIR IWP 71H M Smith sought the views of Commissions 4(Ephemerides) and 31 (Time) The appropriate methodof providing both precise Earth orientation to navigatorsand uniform time to time and frequency laboratorieswas discussed As the navigator requires knowledgeof UT1 rather than UT2 it was recommended thatradio time signals should disseminate differences in theform of [UT1 ndash UTC] Several astronomers emphasizedthat visual observers in astronomical and related eldsrequire UT1 to a precision of 01 s as this is aboutthe limit of human time discrimination In addition thealmanacs were designed to permit a determination ofposition to 01 minute of arc and for this a comparableprecision in time of 025 s was required At BrightonCommission 31 adopted recommendations similar tothose of the CCIR Also the IAU General Assemblyresolved that adequate means should be provided toensure that the difference [UT1 ndash UTC] would be

516 Metrologia 2001 38 509-529

The leap second its history and possible future

available before permitting UTC to depart from UT1by more than about 01 s [100]

Detailed instructions for the implementation ofCCIR Recommendation 460 were drafted at a furthermeeting of Study Group 7 that was held in February1971 [101] The de ning epoch of 1 January 19720 h 0 m 0 s UTC was set 10 s behind TAI whichwas the approximate accumulated difference betweenTAI and UT1 since the inception of TAI in 1958and a unique fraction of a second adjustment wasapplied so that UTC would differ from TAI byan integral number of seconds The recommendedmaximum departure of UTC from UT1 was 07 sThe term ldquoleap secondrdquo was introduced for the steppedsecond An additional correction DUT1 was introducedhaving integral multiples of 01 s to be embodied in thetime signals such that when added to UTC they wouldyield a better approximation to UT1 For examplethis second level of correction was achieved by NBSradio stations WWV and WWVH by using double ticksor pulses after the start of each minute in its UTCbroadcasts [102]

The recommendations of the IAU were formalizedby resolutions of Commissions 4 and 31 at the15th General Assembly in Sydney in 1973 and afterfurther discussion the name UTC was retained [103]UTC was recommended as the basis of standardtime in all countries the time in common (civil)use as disseminated by radio signals The limit of[UT1 ndash UTC] was set at plusmn0950 s as this is themaximum difference that can be accommodated by thecode format The maximum deviation of UT1 from[UTC + DUT1] was set at plusmn0100 s In 1974 the CCIRincreased the tolerance for [UT1 ndash UTC] from 07 sto 09 s

The present UTC system is de ned by ITU-R(formerly CCIR) Recommendation ITU-R TF460-5[104]

ldquoUTC is the time scale maintained by the BIPM withassistance from the IERS which forms the basis of acoordinated dissemination of standard frequencies andtime signals It corresponds exactly in rate with TAIbut differs from it by an integral number of secondsThe UTC scale is adjusted by the insertion or deletionof seconds (positive or negative leap seconds) to ensureapproximate agreement with UT1rdquo

The interval between time signals of UTC is thusexactly equal to the SI second A history of rate offsetsand step adjustments in UTC is given in [105]

7 The leap second

71 Rate of increase in length of day

Because the Earthrsquos rotation is gradually slowingdown and in addition has both random and periodic uctuations it is not a uniform measure of time The

time difference T [ET ndash UT1] [TT ndash UT1]represents the difference between the uniform scale ofEphemeris Time or Terrestrial Time and the variablescale of Universal Time Values of T are summarizedin [106] Before 1955 the values are given by T[ET ndash UT1] based on observations of the Moon After1955 values are given by T [TT ndash UT1] [TAI +32184 s ndash UT1] from measurements by atomic clocksas published by the BIH and the BIPM

According to Stephenson and Morrison [107] overthe past 2700 years can be represented by aparabola of approximately the form

T = (31 scy2) (T ndash 1820)2(100)2 ndash 20 s

where T is expressed in seconds and T is the yearFigure 1 plots this equation together with observationssince 1620 The curve has a minimum at the year 1820and passes through 0 at the year 1900 Actual values of

T based on astronomical data may differ somewhatfrom this smoothed t For example the value of Tis 32184 s at 19580 the origin of TAI However nosingle parabola can satisfactorily represent all modernand historical data

The derivative of T is

Lday (00017 sdcy) (T ndash 1820)100

Figure 1 Observations and parabolic t of T versus timesince 1620 (after Stephenson and Morrison [26])

Figure 2 Change in the length of day with respect to areference day of 86 400 s versus time (after Stephensonand Morrison [26])

Metrologia 2001 38 509-529 517

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

R A Nelson et al

the month on dates determined by the BIH to maintainthe time signals to within about 01 s of UT2

As UTC included rate offsets to reduce the need forstep adjustments the broadcast time signals indicatedneither the SI second nor the mean solar secondbut rather variable intervals to stay in step withUT2 from which the SI second could be obtainedby applying a known correction Attempts to followthese uctuations necessitated revisions in complexequipment on a frequent basis and risked temporaryinterruptions of service At an interim session in MonteCarlo during March 1965 Study Group 7 suggested thatexperimental broadcasts and studies should be made toinvestigate how to provide both the epoch of UniversalTime and the international unit of time interval in thesame emission [87]

The revised CCIR Recommendation 374-1 [88]of 1966 allowed for the limited and provisional useof an experimental ldquoStepped Atomic Time (SAT)rdquo inwhich the broadcast time rate was the atomic timerate with no carrier deviation but in which frequentstep adjustments of 200 ms were applied to match UT2to within 01 s The existence of two parallel systemsUTC and SAT was regarded as a phase in the evolutionand adoption of a single practical and internationallyacceptable system [89]

63 Present UTC system

At the 15th General Assembly of the URSI in Munichin 1966 Commission 1 expressed the opinion thatall proposed methods of operating standard time andfrequency services contained defects and that theseservices must inevitably develop towards a system ofuniform atomic time and constant frequency For thoserequiring astronomical time some form of correctionwould be necessary [90 91] In 1967 at a meeting heldin Brussels under the auspices of the URSI to considerfrequency coordination in Europe it was unanimouslyagreed that both rate offsets and step adjustments shouldbe discontinued It was suggested that the deviations ofUTC from UT2 would have no signi cance for civilpurposes but could be disseminated to navigators intables or in the transmissions themselves [92]

Dissatisfaction with the existing form of UTC andthe need to study the implications of the new de nitionof the second adopted in 1967 prompted discussions bythe CIPM and the CCIR Following a recommendationof the CCDS the CIPM formed a preparatorycommission for the international coordination of timescales The concept of the leap second analogous to theleap day in the calendar was proposed independentlyby G M R Winkler [93] and Louis Essen [94] at ameeting of the commission held at the BIPM in May1968 [95 96] It was proposed that integer steps ofseconds replace the steps of 100 ms or 200 ms thenbeing used because they were too frequent and toosmall Consideration of possible modi cations to UTC

was also given by CCIR Study Group 7 in Boulderin August 1968 [97] The view was expressed that thebest system would be one with 1 s steps without rateoffsets so that equipment generating a pulse train wouldnot require a change in frequency To meet the needsof navigators it was suggested that coded informationmight be incorporated in the emission to indicate thedifference between UTC and UT2 to higher resolutionAn Interim Working Party IWP 71 was formed toinvestigate requirements submit proposals and x adate for the introduction of the new system The optionsunder consideration at this time were summarized asfollows [98]

ldquoDiscarding the suggestion (for practical reasons and toavoid confusions) of two time scales one approachingUT (the present UTC) and the other without offsetsand adjustments only three alternatives remain (a) stepadjustment of 01 s or 02 s to maintain the UTCsuf ciently near to UT2 to permit to ignore thedifference in most of the applications (b) completedisuse of UTC system replacing it with a coordinateduniform time scale without offsets and steps andtherefore not approaching UT (c) step adjustment of1 s exactlyrdquo

Speci c proposals were made by Study Group 7 inGeneva in October 1969 which were approved by theCCIR XIIth Plenary Assembly in New Delhi in January1970 In its Recommendation 460 [99] the CCIRstated that (a) carrier frequencies and time intervalsshould be maintained constant and should correspondto the de nition of the SI second (b) step adjustmentswhen necessary should be exactly 1 s to maintainapproximate agreement with Universal Time (UT) and(c) standard signals should contain information onthe difference between UTC and UT The CCIR alsodecided to begin the new UTC system on 1 January1972

At the IAUrsquos 14th General Assembly in BrightonUK in August 1970 the chairman of CCIR IWP 71H M Smith sought the views of Commissions 4(Ephemerides) and 31 (Time) The appropriate methodof providing both precise Earth orientation to navigatorsand uniform time to time and frequency laboratorieswas discussed As the navigator requires knowledgeof UT1 rather than UT2 it was recommended thatradio time signals should disseminate differences in theform of [UT1 ndash UTC] Several astronomers emphasizedthat visual observers in astronomical and related eldsrequire UT1 to a precision of 01 s as this is aboutthe limit of human time discrimination In addition thealmanacs were designed to permit a determination ofposition to 01 minute of arc and for this a comparableprecision in time of 025 s was required At BrightonCommission 31 adopted recommendations similar tothose of the CCIR Also the IAU General Assemblyresolved that adequate means should be provided toensure that the difference [UT1 ndash UTC] would be

516 Metrologia 2001 38 509-529

The leap second its history and possible future

available before permitting UTC to depart from UT1by more than about 01 s [100]

Detailed instructions for the implementation ofCCIR Recommendation 460 were drafted at a furthermeeting of Study Group 7 that was held in February1971 [101] The de ning epoch of 1 January 19720 h 0 m 0 s UTC was set 10 s behind TAI whichwas the approximate accumulated difference betweenTAI and UT1 since the inception of TAI in 1958and a unique fraction of a second adjustment wasapplied so that UTC would differ from TAI byan integral number of seconds The recommendedmaximum departure of UTC from UT1 was 07 sThe term ldquoleap secondrdquo was introduced for the steppedsecond An additional correction DUT1 was introducedhaving integral multiples of 01 s to be embodied in thetime signals such that when added to UTC they wouldyield a better approximation to UT1 For examplethis second level of correction was achieved by NBSradio stations WWV and WWVH by using double ticksor pulses after the start of each minute in its UTCbroadcasts [102]

The recommendations of the IAU were formalizedby resolutions of Commissions 4 and 31 at the15th General Assembly in Sydney in 1973 and afterfurther discussion the name UTC was retained [103]UTC was recommended as the basis of standardtime in all countries the time in common (civil)use as disseminated by radio signals The limit of[UT1 ndash UTC] was set at plusmn0950 s as this is themaximum difference that can be accommodated by thecode format The maximum deviation of UT1 from[UTC + DUT1] was set at plusmn0100 s In 1974 the CCIRincreased the tolerance for [UT1 ndash UTC] from 07 sto 09 s

The present UTC system is de ned by ITU-R(formerly CCIR) Recommendation ITU-R TF460-5[104]

ldquoUTC is the time scale maintained by the BIPM withassistance from the IERS which forms the basis of acoordinated dissemination of standard frequencies andtime signals It corresponds exactly in rate with TAIbut differs from it by an integral number of secondsThe UTC scale is adjusted by the insertion or deletionof seconds (positive or negative leap seconds) to ensureapproximate agreement with UT1rdquo

The interval between time signals of UTC is thusexactly equal to the SI second A history of rate offsetsand step adjustments in UTC is given in [105]

7 The leap second

71 Rate of increase in length of day

Because the Earthrsquos rotation is gradually slowingdown and in addition has both random and periodic uctuations it is not a uniform measure of time The

time difference T [ET ndash UT1] [TT ndash UT1]represents the difference between the uniform scale ofEphemeris Time or Terrestrial Time and the variablescale of Universal Time Values of T are summarizedin [106] Before 1955 the values are given by T[ET ndash UT1] based on observations of the Moon After1955 values are given by T [TT ndash UT1] [TAI +32184 s ndash UT1] from measurements by atomic clocksas published by the BIH and the BIPM

According to Stephenson and Morrison [107] overthe past 2700 years can be represented by aparabola of approximately the form

T = (31 scy2) (T ndash 1820)2(100)2 ndash 20 s

where T is expressed in seconds and T is the yearFigure 1 plots this equation together with observationssince 1620 The curve has a minimum at the year 1820and passes through 0 at the year 1900 Actual values of

T based on astronomical data may differ somewhatfrom this smoothed t For example the value of Tis 32184 s at 19580 the origin of TAI However nosingle parabola can satisfactorily represent all modernand historical data

The derivative of T is

Lday (00017 sdcy) (T ndash 1820)100

Figure 1 Observations and parabolic t of T versus timesince 1620 (after Stephenson and Morrison [26])

Figure 2 Change in the length of day with respect to areference day of 86 400 s versus time (after Stephensonand Morrison [26])

Metrologia 2001 38 509-529 517

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

The leap second its history and possible future

available before permitting UTC to depart from UT1by more than about 01 s [100]

Detailed instructions for the implementation ofCCIR Recommendation 460 were drafted at a furthermeeting of Study Group 7 that was held in February1971 [101] The de ning epoch of 1 January 19720 h 0 m 0 s UTC was set 10 s behind TAI whichwas the approximate accumulated difference betweenTAI and UT1 since the inception of TAI in 1958and a unique fraction of a second adjustment wasapplied so that UTC would differ from TAI byan integral number of seconds The recommendedmaximum departure of UTC from UT1 was 07 sThe term ldquoleap secondrdquo was introduced for the steppedsecond An additional correction DUT1 was introducedhaving integral multiples of 01 s to be embodied in thetime signals such that when added to UTC they wouldyield a better approximation to UT1 For examplethis second level of correction was achieved by NBSradio stations WWV and WWVH by using double ticksor pulses after the start of each minute in its UTCbroadcasts [102]

The recommendations of the IAU were formalizedby resolutions of Commissions 4 and 31 at the15th General Assembly in Sydney in 1973 and afterfurther discussion the name UTC was retained [103]UTC was recommended as the basis of standardtime in all countries the time in common (civil)use as disseminated by radio signals The limit of[UT1 ndash UTC] was set at plusmn0950 s as this is themaximum difference that can be accommodated by thecode format The maximum deviation of UT1 from[UTC + DUT1] was set at plusmn0100 s In 1974 the CCIRincreased the tolerance for [UT1 ndash UTC] from 07 sto 09 s

The present UTC system is de ned by ITU-R(formerly CCIR) Recommendation ITU-R TF460-5[104]

ldquoUTC is the time scale maintained by the BIPM withassistance from the IERS which forms the basis of acoordinated dissemination of standard frequencies andtime signals It corresponds exactly in rate with TAIbut differs from it by an integral number of secondsThe UTC scale is adjusted by the insertion or deletionof seconds (positive or negative leap seconds) to ensureapproximate agreement with UT1rdquo

The interval between time signals of UTC is thusexactly equal to the SI second A history of rate offsetsand step adjustments in UTC is given in [105]

7 The leap second

71 Rate of increase in length of day

Because the Earthrsquos rotation is gradually slowingdown and in addition has both random and periodic uctuations it is not a uniform measure of time The

time difference T [ET ndash UT1] [TT ndash UT1]represents the difference between the uniform scale ofEphemeris Time or Terrestrial Time and the variablescale of Universal Time Values of T are summarizedin [106] Before 1955 the values are given by T[ET ndash UT1] based on observations of the Moon After1955 values are given by T [TT ndash UT1] [TAI +32184 s ndash UT1] from measurements by atomic clocksas published by the BIH and the BIPM

According to Stephenson and Morrison [107] overthe past 2700 years can be represented by aparabola of approximately the form

T = (31 scy2) (T ndash 1820)2(100)2 ndash 20 s

where T is expressed in seconds and T is the yearFigure 1 plots this equation together with observationssince 1620 The curve has a minimum at the year 1820and passes through 0 at the year 1900 Actual values of

T based on astronomical data may differ somewhatfrom this smoothed t For example the value of Tis 32184 s at 19580 the origin of TAI However nosingle parabola can satisfactorily represent all modernand historical data

The derivative of T is

Lday (00017 sdcy) (T ndash 1820)100

Figure 1 Observations and parabolic t of T versus timesince 1620 (after Stephenson and Morrison [26])

Figure 2 Change in the length of day with respect to areference day of 86 400 s versus time (after Stephensonand Morrison [26])

Metrologia 2001 38 509-529 517

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

R A Nelson et al

Figure 3 Change in the length of day since 1620 (afterStephenson and Morrison [25])

which represents the change in the length of day (LOD)in SI seconds relative to the standard reference day ofexactly 86 400 SI seconds This equation is plotted inFigure 2 According to this long-term trend the rateof increase in the length of the day is about 17 msper century

Figure 3 illustrates observations of changes in thelength of day during the era of telescopic observationsfrom 1620 onwards Over this modern period the LODhas been increasing at about 14 ms per century [108]That is today is approximately 14 ms longer than aday a century ago Other studies imply slightly differentvalues [109 110] The actual value of the LOD willdepart from any long-term trend due to short-term uctuations of between ndash3 ms and +4 ms on a timescale of decades The epoch at which the mean solarday was exactly 86 400 SI seconds was approximately1820 This is also the approximate mean epoch of theobservations analysed by Newcomb ranging in datefrom 1750 to 1892 that resulted in the de nition of thesecond of Ephemeris Time from which the SI secondwas derived [111]

72 Motivation for the leap second

UTC is kept within 09 s of UT1 by the occasionalinsertion of a leap second adjustment When thepresent UTC system was established in 1972 the timedifference T [TT ndash UT1] = [TAI + 32184 s ndash UT1]was equal to 4223 s Thus the difference between TAIand UT1 in 1972 was approximately 10 s To maintaincontinuity with UT1 UTC was initially set behind TAIby this amount As of 1 January 2001 22 positiveleap seconds have been added Thus UTC is presentlybehind TAI by 32 s Figure 4 illustrates the relationshipsbetween TAI UTC and UT1

The 1 s increments are indications of theaccumulated difference in time between a uniformtime and a time measured by the Earthrsquos rotationBy analogy if a watch that loses 2 s per day weresynchronized with a perfect clock at the beginning of acertain day then after one day the watch would be inerror by 2 s At the end of a month the watch would bein error by roughly 1 min It would then be convenientto reset the watch by inserting 1 min of time

Figure 4 Difference between TAI and UT1 since 1955(from Quinn [70])

Figure 5 Difference between TAI and UTC due to leapseconds since 1972

Similarly the insertion of leap seconds is dueto the fact that the present length of the mean solarday is about 25 ms longer than a day of precisely86 400 SI seconds as a consequence of the long-termtrend so that the Earthrsquos rotation runs slow with respectto atomic time The SI second is equivalent to thesecond of Ephemeris Time which in turn is equal tothe mean solar second of the early nineteenth centuryThe length of the day was exactly 86 400 SI seconds inabout 1820 Before then the mean solar day was lessthan 86 400 s and since then it has been greater than86 400 s At the rate of about 14 ms per century overthe past 180 years the length of the day has increasedby roughly 25 ms so that today the length of the day isabout 86 4000025 SI seconds The difference of 25 msper day accumulates to nearly 1 s over an entire yearIt is this accumulated difference that is compensated bythe occasional insertion of a leap second to make thelength of the year 1 s longer A change in the frequencyof occurrence of leap seconds is an indication of theslowing down or acceleration of the Earthrsquos rotation

A least-squares t of the difference [TAI ndash UTC]since 1972 shown in Figure 5 implies a nearly linear

518 Metrologia 2001 38 509-529

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

The leap second its history and possible future

increase with a slope of (210 plusmn 005) ms per day Thisvalue represents the average excess in the length of dayduring the past three decades and is in approximateagreement with the value computed on the basis of thelong-term trend Recent global weather conditions havecontributed to a short-term change in the length of dayDecade uctuations due to the interaction between theEarthrsquos core and mantle and global ocean circulationmay also contribute Thus at present the day is actuallycloser to 86 400 SI seconds and leap seconds have notbeen required However this condition cannot persistand the long-term trend will be eventually restored

The motivation for the leap second therefore is dueto the fact that the second as presently de ned is ldquotooshortrdquo to keep in step with the Earth However had thesecond been de ned to be exactly equal to a mean solarsecond at the origin of TAI in 1958 the discrepancywould not have been removed the agreement betweenthe SI second and the mean solar second would haveonly been temporary and their difference would simplyhave become gradually more apparent over the nextcentury

73 Operational dif culties of preservingthe leap second

Modern commercial transport systems depend almostentirely on satellite navigation systems Future systemsare likely to rely on these systems and theiraugmentation systems to improve navigation accuracyreliability integrity and availability beyond currentcapabilities Increasing worldwide reliance on satellitenavigation for air transport is likely to demand systemsfree of any unpredictable changes in epoch

Many telecommunications systems rely on precisetime synchronization For example spread-spectrumcommunications are not possible without a coherenttime reference Thus during the introduction ofa leap second communications can be lost untilsynchronization is re-established However onlysystems that depend speci cally on time are affectedby the introduction of leap seconds systems dependingon frequency have little or no sensitivity to epoch

Another important consideration is the growinguse of computers In todayrsquos world of high-speed intercomputer communications that time stampmessages at the sub-second level 1 s can be a signi cantlength of time In addition clocks normally count from59 s to 0 s of the next minute Leap seconds requirea count sequence of 59 s 60 s and then 0 s of thenext minute Many computer systems have a problemintroducing the second labelled ldquo60rdquo A similar concernis that when dating events using the Julian Day (JD) orModi ed Julian Day (MJD) including fractions of a daya positive leap second would create a situation wheretwo events 1 s apart can receive identical dates whenthose dates are expressed with a numerical precisionequivalent to 1 s

In global synchronization operations involvingmultiple locations one frequently deals with differinghardware and software systems based on differentstandards and operating practices The possibleintroduction of one or two 61 s minutes per yearinto continuous site processes would directly affectsynchronization if the leap seconds were not treatedidentically at the same instant at all cooperating sites

The real-world operation of timing systems isconfronted by equipment upgrades and personnelchanges The possible effects of maintenance proce-dures and human factors in accommodating leap secondsteps should be given consideration in assessing thereliability of such systems

Stand-alone data-gathering systems isolated byspeci c specialized technical applications are nowextremely rare Modern data systems rely on continu-ous highly accurate time The possibility of disruptionsto continuous service would have a major impact ontheir interactive operation In some cases the need toavoid disruptions has led to considerations of using non-traditional timekeeping systems such as GPS Time ora time scale maintained by an individual governmentcontractor as a means of serving this purpose

Continuing use of a non-uniform time scale in-cluding leap seconds in the face of these considerationscould lead to the proliferation of independent uniformtimes adopted to be convenient for particular objectivesIf that happens UTC would receive less acceptance asan international standard

74 Operational dif culties of eliminatingthe leap second

Many astronomers and satellite ground-station operatorswould prefer that leap seconds should not be eliminatedThere is a signi cant amount of operational software atastronomical observatories and satellite ground stationsthat assumes implicitly that DUT1 will always be asmall number less than 1 s This assumption would nolonger be true if leap seconds were eliminated Fixingtesting and documenting all the computer codes couldbe an enormous task

The current transmission formats for radio andtelephone broadcasts of time signals depend on the factthat DUT1 is less than 1 s It may be dif cult to changethese formats due to the prevalence of legacy hardware

In commercial industry there are certain clocks thatreceive radio broadcast time signals to automaticallydisplay accurate time These and similar devices mightbe affected adversely by a change in the broadcastformat

8 Satellite navigation systems

Historically the rationale behind the de nition of UTCwas for its application to celestial navigation whileproviding a precise standard for time and frequency

Metrologia 2001 38 509-529 519

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

R A Nelson et al

Celestial navigation using stellar observations requiresknowledge of UT1 at the time of the observationsWhen it was introduced UTC was still the mostreadily available worldwide system for independentdetermination of position But as the formation ofUTC progressed the ability to track satellites on aworldwide basis and the growing global communicationand positioning capabilities they could provide becamemajor considerations

Today with GPS [112] and GLONASS [113]complemented by LORAN and other radionavigationsystems celestial position determination is not ascommon These systems and the augmentation systemsthey have fostered have been incorporated into virtuallyevery facet of international telecommunication militaryand commercial technology With extremely highaccuracy and global coverage satellite navigationsystems have collectively become a new public utilityknown by the general designation of Global NavigationSatellite System (GNSS)

81 GPS

The Global Positioning System (GPS) is a satellitenavigation system developed by the US Departmentof Defense The programme evolved from earliersystems and was formally chartered in 1973 [114]The GPS comprises a nominal constellation of twenty-four satellites with an orbital radius of 26 560 kmcorresponding to a period of revolution of 12 siderealhours (11 h 58 min) There are six orbital planesinclined at 55 with four satellites per plane Theconstellation geometry ensures that between four andeleven satellites are simultaneously visible at all timesfrom any point on the Earth Block I developmentalprototype satellites were launched between 1978and 1985 while Block II production satellites werelaunched beginning in 1989 The system was declaredfully operational in 1995 The current GPS constellationconsists of twenty-eight Block IIIIAIIR satellites

Each satellite carries multiple caesium andrubidium atomic clocks The fundamental clockfrequency is 1023 MHz The satellite and globaltracking network atomic clocks are used to generate thecontinuous system time known as GPS Time whichis speci ed to be within 1 m s of UTC as maintainedby USNO except leap seconds are not inserted Thealgorithm de ning the relationship between GPS Timeand UTC thus includes a correction for leap secondsThe origin of GPS Time is midnight of 56 January1980 with the consequence that TAI is ahead of GPSTime by 19 s a constant value As of 1 January 2001GPS Time is ahead of UTC by 13 s With appropriatecorrections for signal propagation relativity and othereffects GPS provides a reference for time with aprecision of 10 ns or better

The GPS satellites transmit signals at two carrierfrequencies in L-band the L1 component with a centre

frequency of 157542 MHz and the L2 component witha centre frequency of 122760 MHz The precision Pcode (or the encrypted Y code used in place of theP code) is a spread-spectrum pseudo-random noise(PRN) code with a bit rate (ldquochip raterdquo) of 1023 MHzThe P(Y) code has a period of 38058 weeks butit is truncated into one-week segments to distinguishindividual satellites The coarseacquisition CA code isa PRN code with a bit rate of 1023 MHz that repeatsitself every 1 ms [115 116]

GPS provides two levels of service The PrecisePositioning Service intended for authorized usersemploys the P(Y) code which is transmitted on boththe L1 and L2 frequencies The Standard PositioningService intended for civil users employs the CA codewhich is transmitted on only the L1 frequency The CAcode is also used for satellite acquisition by all users

The determination of position may be characterizedas the process of triangulation using pseudo-rangemeasurements from four or more satellites The militaryP(Y) code receiver has a 95 horizontal positionaccuracy of about 5 m Until recently the civil CAcode was intentionally degraded by a technique calledSelective Availability (SA) which introduced positionerrors of 50 m to 100 m by dithering the satelliteclock data This technique also restricted time transferto about 300 ns in real time However on 2 May 2000under a US presidential directive the SA feature ofthe CA code was set to zero Consequently the civilGPS accuracy is now about 10 m to 30 m in positionand 10 ns to 30 ns in time Differential correctionsystems where they are available can permit positiondetermination to an accuracy of less than a metre

A variety of GPS modernization initiatives areunder way With the addition of a new L2 civil(L2C) signal on GPS Block IIR-M satellites in 2003the civil 95 horizontal position accuracy willbecome about 5 m to 10 m Also in 2000 the WorldRadiocommunication Conference (Istanbul) approved athird civil frequency known as L5 to be centred at117645 MHz in the Aeronautical Radio NavigationServices (ARNS) band This third frequency to beavailable on GPS Block IIF satellites in 2005 wouldpermit the creation of two beat frequencies that wouldyield sub-metre positioning accuracy in real time [117]A new generation of GPS with enhanced capabilitiesGPS III is to be implemented beginning in 2010

The orbit determination process for GPS likevirtually all other Earth-orbiting satellites requiresprecise knowledge of [UT1 ndash UTC] The commonprocedure involves integration of the equations ofmotion in an Earth-Centred Inertial (ECI) referenceframe The tracking stations however are located inthe Earth-Centred Earth-Fixed (ECEF) reference frameof the rotating Earth The usual choice of the inertialcoordinate system is the J20000 reference frame basedon the FK5 star catalogue while the physical model ofthe Earth is the World Geodetic System 1984 (WGS 84)

520 Metrologia 2001 38 509-529

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

The leap second its history and possible future

[118 119] The data from the tracking stations aretypically time-tagged with a particular realization ofUTC Moreover the Earthrsquos gravitational eld is alsorotating with the Earth and the perturbing gravitationalforces must be transformed via four rotation matricesfrom the ECEF frame into the ECI frame as part of theorbit determination process The matrices account forthe Earthrsquos polar motion variable rotation nutation andprecession Near real-time orbit determination must usepredictions of [UT1 ndash UTC] Today these predictionsare expressed in the form of a polynomial model thatis updated weekly [120]

As GPS Time does not include leap secondsthe introduction of a leap second into UTC does notaffect GPS users The GPS operational control segmenthowever must carefully account for the leap secondstep in [UT1 ndash UTC] Prior to a leap second event twosets of ldquoEarth Orientation Parametersrdquo are provided tothe GPS control segment One set is used up to thetime a leap second is inserted and a second set whichcontains the new 1 s step in [UT1 ndash UTC] is used afterthe leap second is inserted

82 GLONASS

The Russian Global Navigation Satellite System(GLONASS) has many features in common withGPS [121 122] The nominal constellation consistsof twenty-four satellites in three planes inclined at648 The orbital radius is 25 510 km and the period is817 sidereal day (11 h 15 min) The rst satellite waslaunched in 1982 The system was fully deployed inearly 1996 but currently there are only nine operationalsatellites However there is a commitment to restore thecomplete twenty-four satellite constellation by 2004

In contrast to GPS the GLONASS satellites alltransmit the same codes and are distinguished byindividual L-band carrier frequencies Thus while GPSuses the spread-spectrum technique of Code DivisionMultiple Access (CDMA) GLONASS uses FrequencyDivision Multiple Access (FDMA) The GLONASSdesign uses Moscow Time [UTC + 3 h] as its timereference instead of its own internal time Thus usersof this system are directly affected by leap secondsDuring the process of resetting the time to account fora leap second the system is unavailable for navigationservice because the clocks are not synchronized

83 Utilization of satellite systems

Current CGPM ITU-R and IAU recommendationsaddress the use of satellites for space servicesfrequencies and time transfer The growing utilizationof satellite systems and their internal time scales maygradually become the primary source of time formany practical applications Laboratories separated byseveral thousand kilometres can routinely perform timecomparisons using GPS common-view techniques with

a precision of a few nanoseconds GLONASS canprovide continental time transfer with somewhat lessprecision Another technique coming into wider useis Two-Way Satellite Time Transfer (TWSTT) usinggeostationary communications satellites This techniqueutilizes the wideband communications capability totransmit bidirectional spread-spectrum ranging codesthat permit time comparisons at the sub-nanosecondlevel

In comparison the DUT1 code available interrestrial radio signals that disseminate UTC has aresolution of 01 s The corresponding position error onthe equator is about 50 m A 1 s resolution betweenUT1 and UTC corresponds to a position error usingcelestial measurements of 05 km As a result satellitesystems are superseding UTC radio signals as a meansof time determination for navigation

9 International agreements on time

No single international agency by itself could assumecomplete responsibility for the de nition and rulesfor the dissemination of time Many internationalscienti c organizations listed below have combinedtheir efforts in the development realization anddissemination of International Atomic Time (TAI) andCoordinated Universal Time (UTC) Their work hasestablished the link between the traditional astronomicaldetermination of time and that based on fundamentalatomic phenomena This essential cooperation wasrequired to support the necessary scienti c foundation

(1) The General Conference on Weights and Measures(Conf Acircerence G Acircen Acircerale des Poids et MesuresCGPM) which has responsibility for the Inter-national System of Units (Syst Aacuteeme InternationaldrsquoUnit Acirces SI) was established by the Conventionof the Metre (Convention du M Aacuteetre) signed inParis by representatives of seventeen countriesin 1875 and amended in 1921 The Conventionnow has fty-one signatories Under the termsof the Convention the Bureau International desPoids et Mesures (BIPM) operates under thesupervision of the International Committee forWeights and Measures (Comit Acirce International desPoids et Mesures CIPM) which itself comesunder the authority of the CGPM [123 124]During the period when TAI and UTC weredeveloped the CIPM received guidance from theComit Acirce Consultatif pour la D Acirce nition de la Seconde(CCDS) set up in 1956 This committee wasrenamed the Consultative Committee for Timeand Frequency (Comit Acirce Consultatif du Tempset des Fr Acircequences CCTF) in 1997 The BIPMorganizes the time links used for computing anddisseminating TAI and UTC It issues a monthlyCircular T that contains the information neededto obtain these time scales at the best level ofaccuracy

Metrologia 2001 38 509-529 521

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

R A Nelson et al

(2) The International Radio Consultative Committee(CCIR) of the International TelecommunicationUnion (ITU) was established in 1927 to coordinatetechnical studies tests and measurements inthe various elds of telecommunications and toestablish international standards Recommendationsfor standardization of international broadcast timewere drafted at the CCIR Xth Plenary Assemblyin Geneva in 1963 and XIth Plenary Assemblyin Oslo in 1966 Study Group 7 was formed in1959 to include space radiocommunication andfrequencies and was responsible for the de nitionof UTC as the standard for frequency and timedissemination The ITU Plenipotentiary Conferenceof 1992 reorganized the CCIR into the ITU-R(Radiocommunication Sector) Working Party 7Acontinues as the responsible body for StandardFrequency and Time Signals

(3) The International Astronomical Union (IAU) wasestablished during the Constitutive Assembly ofthe International Research Council (IRC) heldin Brussels in 1919 The IRC was succeededby the International Council of Scienti c Unions(ICSU) in 1931 (renamed the International Councilfor Science in 1998) [125 126] Through itsCommissions 4 (Ephemerides) 19 (Rotation of theEarth) and 31 (Time) the IAU standardized thede nitions of Universal Time Ephemeris Time andthe various relativistic time scales and determinedtheir relationships to International Atomic Time

(4) The International Union of Geodesy and Geo-physics (IUGG) is a member of the ICSU andwas established by the IRC in 1919 The IUGG isdedicated to the scienti c study of the Earth and itsenvironment in space and includes the InternationalAssociation of Geodesy (IAG)

(5) The International Union of Radio Science (URSI)is a member of the ICSU and was established bythe IRC in 1919 to encourage scienti c studies ofradiotelegraphy and promote international cooper-ation Its present charter includes intercomparisonand standardization of the measuring instrumentsused in scienti c work and scienti c aspectsof telecommunications URSI made the originalrecommendation for the worldwide broadcast ofoffset atomic time

(6) The Bureau International de lrsquoHeure (BIH) wasestablished at the Paris Observatory in 1919by the IRC Constitutive Assembly to coordinateinternational radio time signals Originally the BIHwas under the direction of IAU Commission 31but in 1956 it became a service of the Federationof Astronomical and Geophysical Data AnalysisServices (FAGS) with the IAU IUGG and URSIas parent unions The BIH was requested by theCCIR in 1963 to determine the proper offsets

between UT2 and broadcast atomic time and tocoordinate the worldwide standard frequency andtime signal service prescribed by the CCIR TheBIH transferred this function as well as theestablishment of International Atomic Time tothe BIPM on 1 January 1988 while its activitieson the rotation of the Earth were taken over bya new service the International Earth RotationService

(7) The International Earth Rotation Service (IERS)was established in 1987 by the IAU and theIUGG and began operation on 1 January 1988Its structure was reorganized commencing in2001 The IERS is an international consortiumof national laboratories and observatories thatprovides operational data related to the orientationof the Earth in space It has the responsibilityfor decisions regarding changes to UTC based onobservations of the Earthrsquos rotation and determineswhen leap seconds should be applied The IERSpublishes four bulletins Bulletin A (daily andsemiweekly) is issued by the Sub-Bureau forRapid Service and Predictions at USNO andcontains rapid determinations for Earth OrientationParameters Bulletin B contains monthly EarthOrientation Parameters Bulletin C containingannouncements of the leap seconds in UTC andBulletin D containing announcements of the valueof DUT1 are distributed as required

Merely to enumerate these agencies and theircommissions study groups and sub-committees is torealize the complexity of the international establishmentin charge of time and the dif culty of makingfundamental changes The present de nition of UTCis the result of far-reaching compromises among thecommunities that these agencies represent

Todayrsquos user communities have changed signi -cantly in the few ensuing decades just as the usesof time have changed The traditional radio broadcastof time signals is being overtaken by satellite signalslinked directly to atomic standards Ensembles ofatomic standards in individual laboratories and high-speed computer networks are synchronized to thesesame standards The many and diverse purposes thatan international time scale must serve are now partof an international telecommunication and commercialinfrastructure involving signi cant economic interests inwhich changes represent a major nancial investmentThis new relationship could make change more dif cultIf a new or revised international standard is to representall the legitimate interests coordination with non-traditional agencies and groups may be necessary

10 Legal time

An important consideration with the current de nitionof UTC is the legal de nition of time implied within

522 Metrologia 2001 38 509-529

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

The leap second its history and possible future

the domestic laws of individual countries [127] Thepurpose of statutes governing legal time is to promotecommerce and the public interest

101 Standard Time

The advent of the railroads in the second quarter ofthe nineteenth century introduced an era of high-speedtransport and mobility Efforts to coordinate schedulesculminated in the adoption of regional zones of StandardTime and the choice of Greenwich as the internationalreference for the prime meridian

Greenwich Mean Time (GMT) has been the legaltime in the UK since 1880 In the USA the StandardTime Act of 19 March 1918 as amended by theUniform Time Act of 1966 established eight timezones that are based on mean solar time and arenominally separated in longitude by intervals of 15(1 h) with respect to the Greenwich meridian [128 129]It also authorized the Interstate Commerce Commissionto modify the time zone boundaries In 1983 thisresponsibility was transferred to the Department ofTransportation

The publication of the British Nautical Almanacbeginning with the year 1767 by the Astronomer RoyalNevil Maskelyne which enabled the determinationof longitude at sea using observations of theMoonrsquos position with respect to the stars andthe contemporaneous development of the marinechronometer by John Harrison had establishedGreenwich as the de facto fundamental reference forlongitude and time for over a century [130 131]The Greenwich meridian was formally recommendedas a worldwide standard reference for longitude andtime at the International Meridian Conference held inWashington DC in October 1884 at the invitation ofthe United States Government as a result of discussionsthat had taken place at several scienti c conferencesover the previous decade By then nearly three-quartersof the worldrsquos commercial ships used charts basedon the Greenwich meridian The Conference alsorecommended the adoption of a Universal Day de nedas a mean solar day counted from 0 up to 24 hoursthat would begin at midnight at the prime meridian[132 133]

The idea of time zones was rst proposed in1870 by Charles F Dowd [134] an American collegeprofessor as a method of regulating time for therailroads In Dowdrsquos plan standard time would beused by the railroads while each city and town wouldpreserve its own local time A similar proposal butone that recommended adjusting local time to railroadtime was later successfully promoted by William FAllen [135] editor of a prominent railroad periodicaland Secretary of the American Railway AssociationImportant contributions were also made by ClevelandAbbe [136] of the US Signal Service and SandfordFleming [137] of the Canadian Paci c Railway To

permit a more convenient location of time zoneboundaries the Greenwich meridian was chosen asthe primary reference rather than Washington DCldquoStandard Railway Timerdquo was adopted throughoutNorth America at noon on Sunday 18 November 1883reducing the number of railroad times from forty-nineto ve and was soon extended to civil time [138]

The rapid growth of the railroads created a demandfor time synchronization across large distances andthe continuing expansion of the network of telegraphwires along their rights of way provided the means forachieving it Towards the end of the nineteenth centurythe US Naval Observatory was disseminating a dailytime signal via the Western Union Telegraph Companyto cities throughout the East South and Midwest ofthe USA [139]

Daylight Saving Time was conceived by WilliamWillett a successful London builder in 1907 [140]it was rst introduced in Europe and North Americaduring the First World War as a means of conservingenergy [141] In the USA the Standard Time Act of1918 required the observance of Daylight Saving Timewhich is advanced 1 h ahead of Standard Time overseven months of the year in addition to providing alegal basis for ve time zones (extended to eight in1966 to cover all US territories)

102 Greenwich Mean Time

Originally Greenwich Mean Time (GMT) was de nedas mean solar time on the meridian of Greenwichreckoned from mean noon In 1919 the BIH undertookto coordinate the emission of radio time signals onthe basis of Greenwich Civil Time (ie GMT plus12 h) as recommended by the International MeridianConference

The astronomical almanacs kept GMT as thetime argument until 1925 Beginning in 1925 theBritish Nautical Almanac and many other nationalephemerides reckoned GMT from midnight to coincidewith the civil day rather than noon as had been thetraditional astronomical practice The rede ned GMTwas designated Universal Time (UT) by the IAU in1928 [142] However the term GMT persisted inalmanacs and navigation publications and the ambiguityin its intended meaning was the cause of some confusion[143]

103 Coordinated Universal Time

The terms ldquomean solar timerdquo and ldquoGMTrdquo have cometo be recognized as being synonymous with UTC inordinary language In 1970 Commission 31 of theIAU recommended that clocks in common use wouldindicate minutes seconds and fractions of UTC andthat the term ldquoGMTrdquo would be accepted as the generalequivalent of UTC in navigation and communications[144] The 15th CGPM in 1975 adopted the followingresolution [145]

Metrologia 2001 38 509-529 523

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

R A Nelson et al

ldquoThe 15th Conf Acircerence G Acircen Acircerale des Poids et Mesuresconsidering that the system called ldquoCoordinated

Universal Timerdquo (UTC) is widely used that itis broadcast in most radio transmissions of timesignals that this wide diffusion makes availableto the users not only frequency standards but alsoInternational Atomic Time and an approximationto Universal Time (or if one prefers mean solartime)

notes that this Coordinated Universal Time providesthe basis of civil time the use of which is legalin most countries

judges that this usage is strongly endorsedrdquo

The international diplomatic authority for the decisionsof the CGPM and its organs is conveyed throughthe Convention of the Metre of 1875 The CCIR in1978 and the World Administrative Radio Conference(Geneva) in 1979 recommended that UTC shouldbe used to designate the time in all internationaltelecommunication activities [146]

The ITU Radio Regulations de ne UTC as thetime scale based on the SI second as speci ed inRecommendation ITU-R TF460-5 The de nition isaccompanied by the following Note [147]

ldquoFor most practical purposes associated with the RadioRegulations UTC is equivalent to mean solar time atthe prime meridian (0 longitude) formerly expressedin GMTrdquo

This de nition is cited in the Code of FederalRegulations Title 47 that speci es the rules of the USFederal Communications Commission (FCC) [148]

The role that UTC plays in national andinternational monetary exchange telecommunicationsand related forms of commerce is not clear Should thede nition of UTC be revised the effect on legal codesmay need to be investigated

11 Future developments

111 Options for UTC

There exist a variety of options for the future of UTCSome of these options are identi ed and discussedbelow

(1) Maintain the status quo The advantage ofmaintaining the present form of UTC is thatestablished timekeeping practices will not requiremodi cation On the other hand if leap secondswere continued the required number and frequencycan only increase as shown in Figure 6 By2100 there would be a need for nearly two leapseconds per year The current emerging problemsand the resulting dissatisfaction with leap secondswill only continue to grow The operational impactand associated cost of maintaining leap seconds in

Figure 6 Projected increase in leap seconds versus time(after McCarthy and Klepczynski [149])

complex timekeeping systems must be consideredin evaluating their continued use in the future

(2) Increase the tolerance between UT1 and UTC Asmall increment of several leap seconds could beinserted into UTC every few years or alternativelya ldquoleap minuterdquo in about fty years The advantageof this approach is that it would be relatively easyto adopt However due to the parabolic rate ofdeparture between solar time and atomic time thetolerance would have to be continually increasedand eventually larger time steps would be required

(3) Periodic insertion of leap seconds A time stepcould be inserted into UTC at a well-de nedinterval such as on 29 February every four yearsThe advantage is that the date would be predictableHowever the number of leap seconds would notbe predictable and large time steps would still berequired

(4) Variable adjustments in frequency This alternativeis similar to the original form of UTC thatwas abandoned Introducing a variable atomicscale in step with solar time would causesigni cant disruptions to equipment and would notdisseminate the unit of time the SI second

(5) Rede ne the second This option would appearto be the most fundamental solution Howeverit would be inconsistent with the usual practicein metrology which is to adopt a new de nitionof a unit only when its realization under theold de nition becomes the limiting source ofexperimental uncertainty and to maintain continuitybetween the old and new realizations Changing thede nition of the second to be closer to the currentrotational second would alter the value of everyphysical measurement and render obsolete everyinstrument related to time Moreover the solutionwould be only temporary as the Earth continuesto decelerate

524 Metrologia 2001 38 509-529

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

The leap second its history and possible future

(6) Substitute TAI for UTC TAI is the fundamentalatomic time scale ldquoin the backgroundrdquo from whichother scales of uniform time are derived TAI isrelated to UTC by the relation [TAI] [UTC +

AT] where AT is the increment to be appliedto UTC to give TAI and is equal to the total numberof leap seconds plus 10 s In 2001 the value of

AT was +32 s The advantage of TAI is that itis a continuous atomic time scale without stepsHowever TAI is currently not easily available tothe precise time user and as TAI is currentlyahead of UTC by an offset of 32 s a worldwideadjustment of clocks would be required if it wereadopted as the scale of civil time Promotion oftwo parallel time scales for civil timekeepingone with leap seconds and one without wouldbe potentially confusing In addition as UTC isrecognized as the primary basis of civil timein resolutions of various international treaty andscienti c organizations and by many conformingnational legal codes a worldwide change in thelegal de nition of time would be required if UTCwere replaced by TAI

(7) Discontinue leap seconds in UTC This optionwould permit continuity with the existing UTCtime scale and would eliminate the need for futureadjustments to complex timekeeping systemsFigure 7 shows the projected difference betweenUTC without leap seconds and UT1 If the currentrate of deceleration of the Earthrsquos rotation were topersist and no leap seconds were added by 2050 thedifference between UTC and UT1 would be about1 min By the end of the twenty- rst century theexpected difference would be about 25 min [149]However these differences are minor comparedwith the difference between apparent solar timeand mean solar time (up to 165 min) mean solartime and clock time within a given time zone(nominally up to 30 min) or Daylight Saving

Figure 7 Projected difference between UTC and UT1if leap seconds were discontinued (after McCarthy andKlepczynski [149])

Time and Standard Time (1 h) It is thus unlikelythat the growing difference between clock timeand levels of daylight would be noticeable for theforeseeable future Also certain religious customsdepend on the actual observation of the Sun or theMoon and do not depend on clock time Thereforethe elimination of leap seconds would have nopractical effect on the correspondence betweencivil time and solar time or on contemporarysocial conventions The use of UTC without leapseconds would retain all the advantages of TAI Thetransition to a continuous UTC system might beplanned for a future date suf ciently far in advancethat changes to existing hardware and softwarewhere necessary could be accommodated withinthe normal maintenance and replacement schedules

112 Requirements of celestial navigation

There remains the need to meet the requirementsof celestial navigation Three possible options foraddressing this need if the current UTC system wererevised are considered Additional alternatives may beidenti ed as the issue is debated

(1) Alternative time scale for navigation A newbroadcast scale of time possibly designatedldquoUT1Crdquo might be disseminated by supplementarycoded signals that provide the approximatedifference between the newly de ned UTC andUT1 just as DUT1 codes currently give thedifference between the presently de ned UTCand UT1 to the nearest 01 s However mosttime code formats would have to be modi ed toaccommodate a difference in time greater than 1s As a bene cial trade-off the resolution mightbe increased in the process for example to 0001s The time difference [UTC ndash UT1C] might alsobe conveniently disseminated in satellite navigationmessages possibly as a commercial service

(2) Greater emphasis on UT1 predictions These re-quirements might also be met by published predic-tions of [UT1 ndash UTC] The IERSUSNO providesdaily and semiweekly predictions in Bulletin Aavailable on the Internet at httpwwwiersorg Theestimated accuracies are 00017 s at 10 days and00039 s at 30 days For example the NationalImagery and Mapping Agency (NIMA) providesEarth Orientation Parameter Prediction coef cientsbased on IERSUSNO weekly post- t values thatare used to generate [UT1 ndash UTC] predictionsfor GPS orbit determination In addition long-term projections might be included in the nauticalephemerides with less precision With the usualyearly schedule of publication the extrapolationshould not bring errors exceeding 1 s (leadingto a position error of 05 km at most) Throughboth short-term and long-term UT1 predictions it

Metrologia 2001 38 509-529 525

R A Nelson et al

would be possible to complement the informationto navigators by disseminating a correction to theargument of the ephemerides as is done currentlywith DUT1

(3) Greater emphasis on satellite navigation systemsDue to the availability of the GPS and GLONASSsatellite navigation systems and the possibility ofsimilar future systems such as Galileo the needfor coded terrestrial radio time signals is lessthan it once was Existing international agreementsmight be recast to redirect the focus of thoseagreements towards increased use of modernsatellite navigational aids

12 Conclusions

The transition from solar time to atomic timemade possible by the development of atomic clocksrepresents a paradigm shift in the way time itself isperceived that is not unlike the transition from theunequal hour to the equal hour ve hundred yearsago brought about by the invention of mechanicalclocks or the transition from apparent time to meansolar time some two hundred years ago that was madepossible by improvements to pendulum clocks Themost basic issue in the future of UTC is the nature ofthe social requirement to adjust an extremely preciseuniform time scale to the time determined using thevariable rotation of the Earth Common practice todayhas already compromised this requirement to the pointthat we are content with conventional constructionssuch as mean solar time zone time and DaylightSaving Time We should realize that as a result ofthe change from apparent to mean time the local meannoon of our clocks can sometimes be about 15 minbefore or after the apparent noon of the Sun thus theafternoons in November are half an hour shorter thanthe mornings while in February the mornings are halfan hour shorter than the afternoons This change waseven more fundamental than that from local mean timeto zone time [150]

All these conventions introduce substantial differ-ences between the commonly accepted time and solartime that are orders of magnitude larger than thedifference between a uniform time scale and a solartime scale We anticipate that this difference will growby an additional 2 min over the next century Will webe willing to neglect this difference in civil time scalesThe astronomically determined rotation angle will bemeasured with improving accuracy during that periodand will be made available to users sooner Will thisbe able to satisfy user needs

In each stage of the evolution of timekeeping therehas been an incremental step away from the Sun as themeasure of time in favour of a more uniform accessibleor convenient standard The next stage in the evolutionof UTC may be a de nition of civil time in terms ofa continuous scale of atomic time and a disassociation

of civil time from solar time altogether accompaniedby the adoption of a representation of UT1 for thoseusers who need it

Throughout the history of time measurement fromsundials to atomic clocks time scales have always beenestablished by taking into account prevailing technologyand needs Since the UTC system of leap secondswas introduced thirty years ago both of these factorshave changed Therefore we should perhaps not be toohesitant in adapting to modern technology and modernneeds

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5 Gerber E A Sykes R A Proc IEEE 1966 54103-116 reprinted in Time and Frequency Theory andFundamentals Natl Bur Stand (US) Monograph 140(Edited by B E Blair) Washington DC US GovtPrinting Of ce 1974 41-56

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Received on 9 July 2001 and in revised formon 5 September 2001

Metrologia 2001 38 509-529 529