Physical Properties of Seawater … · Physical Properties of Seawater 3.1. MOLECULAR PROPERTIES OF WATER Many of the unique characteristics of the ocean can be ascribed to the nature

C H A P T E R

3

Physical Properties of Seawater

3.1. MOLECULAR PROPERTIESOF WATER

Many of the unique characteristics of theocean can be ascribed to the nature of wateritself. Consisting of two positively chargedhydrogen ions and a single negatively chargedoxygen ion, water is arranged as a polar mole-cule having positive and negative sides. Thismolecular polarity leads to water’s high dielec-tric constant (ability to withstand or balance anelectric field). Water is able to dissolve manysubstances because the polar water moleculesalign to shield each ion, resisting the recombina-tion of the ions. The ocean’s salty character isdue to the abundance of dissolved ions.

The polar nature of the water moleculecauses it to form polymer-like chains of up toeight molecules. Approximately 90% of thewater molecules are found in these chains.Energy is required to produce these chains,which is related to water’s heat capacity. Waterhas the highest heat capacity of all liquidsexcept ammonia. This high heat capacity is theprimary reason the ocean is so important inthe world climate system. Unlike the land andatmosphere, the ocean stores large amounts ofheat energy it receives from the sun. This heatis carried by ocean currents, exporting orimporting heat to various regions. Approxi-mately 90% of the anthropogenic heatingassociated with global climate change is stored

in the oceans, because water is such an effectiveheat reservoir (see Section S15.6 located on thetextbook Web site

; “S” denotes supplementalmaterial).

As seawater is heated, molecular activityincreases and thermal expansion occurs,reducing the density. In freshwater, as tempera-ture increases from the freezing point up to about4�C, the added heat energy forms molecularchains whose alignment causes the water toshrink, increasing the density. As temperatureincreases above this point, the chains breakdown and thermal expansion takes over; thisexplainswhy freshwater has a densitymaximumat about 4�C rather than at its freezing point. Inseawater, these molecular effects are combinedwith the influence of salt, which inhibits theformation of the chains. For the normal range ofsalinity in the ocean, the maximum densityoccurs at the freezing point, which is depressedto well below 0�C (Figure 3.1).

Water has a very high heat of evaporation (orheat of vaporization) and a very high heat offusion. The heat of vaporization is the amountof energy required to changewater from a liquidto a gas; the heat of fusion is the amount ofenergy required to change water from a solidto a liquid. These quantities are relevant forour climate as water changes state from a liquidin the ocean to water vapor in the atmosphereand to ice at polar latitudes. The heat energy

29Descriptive Physical Oceanography

� 2011. Lynne Talley, George Pickard, William Emery and James Swift.

Published by Elsevier Ltd. All rights reserved.

involved in these state changes is a factor inweather and in the global climate system.

Water’s chain-like molecular structure alsoproduces its high surface tension. The chainsresist shear, giving water a high viscosity forits atomic weight. This high viscosity permitsformation of surface capillary waves, with wave-lengths on the order of centimeters; the restoringforces for these waves include surface tension aswell as gravity. Despite their small size, capil-lary waves are important in determining thefrictional stress between wind and water. Thisstress generates larger waves and propels thefrictionally driven circulation of the ocean’ssurface layer.

3.2. PRESSURE

Pressure is the normal force per unit areaexerted by water (or air in the atmosphere) onboth sides of the unit area. The units of forceare (mass� length/time2). The units of pressureare (force/length2) or (mass/[length � time2]).Pressure units in centimeters-gram-second (cgs)are dynes/cm2 and in meter-kilogram-second(mks) they are Newtons/m2. A special unit for

pressure is the Pascal, where 1 Pa ¼ 1 N/m2.Atmospheric pressure is usually measured inbars where 1 bar ¼ 106 dynes/cm2 ¼ 105 Pa.Ocean pressure is usually reported in decibarswhere 1 dbar ¼ 0.1 bar ¼ 105 dyne/cm2 ¼104 Pa.

The force due to pressure arises when there isa difference in pressure between two points. Theforce is directed from high to low pressure.Hence we say the force is oriented “down thepressure gradient” since the gradient is directedfrom low to high pressure. In the ocean, thedownward force of gravity is mostly balancedby an upward pressure gradient force; that is,the water is not accelerating downward.Instead, it is kept from collapsing by the upwardpressure gradient force. Therefore pressureincreases with increasing depth. This balanceof downward gravity force and upward pres-sure gradient force, with no motion, is calledhydrostatic balance (Section 7.6.1).

The pressure at a given depth depends on themass ofwater lying above that depth. A pressurechange of 1 dbar occurs over a depth change ofslightly less than 1 m (Figure 3.2 and Table 3.1).Pressure in the ocean thus varies from nearzero (surface) to 10,000 dbar (deepest). Pressure

0

10

20

30

Tem

peratu

re (°C

)

0 10 20 30 40Salinity

0 5 10 15 20 25

30

–2

Freezing point

Temp. of max. density

90% of ocean

Mean T&SMost

abundant

FIGURE 3.1 Values of density st

(curved lines) and the loci of maximumdensity and freezing point (at atmosphericpressure) for seawater as functions oftemperature and salinity. The full density r

is 1000 þ st with units of kg/m3.

3. PHYSICAL PROPERTIES OF SEAWATER30

is usually measured in conjunction with otherseawater properties such as temperature,salinity, and current speeds. The properties areoften presented as a function of pressure ratherthan depth.

Horizontal pressure gradients drive the hori-zontal flows in the ocean. For large-scalecurrents (of horizontal scale greater than a kilo-meter), the horizontal flows are much strongerthan their associated vertical flows and areusually geostrophic (Chapter 7). The horizontalpressure differences that drive the oceancurrents are on the order of one decibar overhundreds or thousands of kilometers. This ismuch smaller than the vertical pressuregradient, but the latter is balanced by the down-ward force of gravity and does not drive a flow.Horizontal variations in mass distributioncreate the horizontal variation in pressure inthe ocean. The pressure is greater where thewater column above a given depth is heaviereither because it is higher density or because itis thicker or both.

Pressure is usually measured with an elec-tronic instrument called a transducer. The accu-racy and precision of pressure measurementsis high enough that other properties such astemperature, salinity, current speeds, and soforth can be displayed as a function of pressure.However, the accuracy, about 3 dbar at depth, isnot sufficient to measure the horizontal pressuregradients. Therefore other methods, such as thegeostrophic method, or direct velocity measure-ments, must be used to determine the actualflow. Prior to the 1960s and 1970s, pressurewas measured using a pair of mercury ther-mometers, one of which was in a vacuum(“protected” by a glass case) and not affectedby pressure while the other was exposed to thewater (“unprotected”) and affected by pressure,as described in the following section. Moreinformation about these instruments andmethods is provided in Section S6.3 of thesupplementary materials on the textbook Website.

TABLE 3.1 Comparison of Pressure (dbar) and Depth(m) at Standard Oceanographic DepthsUsing the UNESCO (1983) Algorithms

Pressure (dbar) Depth (m) Difference (%)

0 0 0

100 99 1

200 198 1

300 297 1

500 495 1

1000 990 1

1500 1453 1.1

2000 1975 1.3

3000 2956 1.5

4000 3932 1.7

5000 4904 1.9

6000 5872 2.1

Percent difference ¼ (pressure � depth)/pressure � 100%.

0

2000

4000

6000D

epth

(m

)

0 2000 4000 6000

Pressure (dbar)

FIGURE 3.2 The relation between depth and pressure,using a station in the northwest Pacific at 41� 53’N, 146�18’W.

PRESSURE 31

3.3. THERMAL PROPERTIES OFSEAWATER: TEMPERATURE,

HEAT, AND POTENTIALTEMPERATURE

One of the most important physical charac-teristics of seawater is its temperature. Temper-ature was one of the first ocean parameters to bemeasured and remains the most widelyobserved. In most of the ocean, temperature isthe primary determinant of density; salinity isof primary importance mainly in high latituderegions of excess rainfall or sea ice processes(Section 5.4). In the mid-latitude upper ocean(between the surface and 500 m), temperatureis the primary parameter determining soundspeed. (Temperature measurement techniquesare described in Section S6.4.2 of the supple-mentary materials on the textbook Web site.)

The relation between temperature andheat content is described in Section 3.3.2. Asa parcel of water is compressed or expanded,its temperature changes. The concept of “poten-tial temperature” (Section 3.3.3) takes thesepressure effects into account.

3.3.1. Temperature

Temperature is a thermodynamic property ofa fluid, due to the activity or energy of mole-cules and atoms in the fluid. Temperature ishigher for higher energy or heat content. Heatand temperature are related through the specificheat (Section 3.3.2).

Temperature (T) in oceanography is usuallyexpressed using the Celsius scale (�C), exceptin calculations of heat content, when tempera-ture is expressed in degrees Kelvin (K). Whenthe heat content is zero (no molecular activity),the temperature is absolute zero on the Kelvinscale. (The usual convention for meteorology isdegrees Kelvin, except in weather reporting,since atmospheric temperature decreases tovery low values in the stratosphere and above.)

A change of 1�C is the same as a change of 1 K. Atemperature of 0�C is equal to 273.16 K. Therange of temperature in the ocean is from thefreezing point, which is around �1.7�C (depen-ding on salinity), to a maximum of around 30�Cin the tropical oceans. This range is considerablysmaller than the range of air temperatures. Asfor all other physical properties, the tempera-ture scale has been refined by internationalagreement. The temperature scale used mostoften is the International Practical TemperatureScale of 1968 (IPTS-68). It has been supersededby the 1990 International Temperature Scale(ITS-90). Temperatures should be reported inITS-90, but all of the computer algorithmsrelated to the equation of state that date from1980 predate ITS-90. Therefore, ITS-90 tempera-tures should be converted to IPTS-68 by multi-plying ITS-90 by 0.99976 before using the 1980equation of state subroutines.

The ease with which temperature can bemeasured has led to a wide variety of oceanicand satellite instrumentation to measure oceantemperatures (see supplementary material inSection S6.4.2 on the textbook Web site).Mercury thermometers were in common usefrom the late 1700s through the 1980s. Reversing(mercury) thermometers, invented by Negrettiand Zamba in 1874, were used on water samplebottles through the mid-1980s. These thermom-eters have ingenious glasswork that cuts off themercury column when the thermometers areflipped upside down by the shipboard observer,thus recording the temperature at depth. Theaccuracy and precision of reversing thermome-ters is 0.004 and 0.002�C. Thermistors are nowused for most in situ measurements. The bestthermistors used most often in oceanographicinstruments have an accuracy of 0.002�C andprecision of 0.0005e0.001�C.

Satellites detect thermal infrared electromag-netic radiation from the sea surface; this radia-tion is related to temperature. Satellite seasurface temperature (SST) accuracy is about0.5e0.8 K, plus an additional error due to the


presence or absence of a very thin (10 mm) skinlayer that can reduce the desired bulk (1e2 m)observation of SST by about 0.3 K.

3.3.2. Heat

The heat content of seawater is its thermody-namic energy. It is calculated using themeasured temperature, measured density, andthe specific heat of seawater. The specific heatis a thermodynamic property of seawaterexpressing how heat content changes withtemperature. Specific heat depends on tempera-ture, pressure, and salinity. It is obtained fromformulas that were derived from laboratorymeasurements of seawater. Tables of values orcomputer subroutines supplied by UNESCO(1983) are available for calculating specificheat. The heat content per unit volume, Q, iscomputed from the measured temperatureusing

Q ¼ rcpT (3.1)

where T is temperature in degrees Kelvin, r isthe seawater density, and cp is the specific heatof seawater. The mks units of heat are Joules,that is, units of energy. The rate of time changeof heat is expressed in Watts, where 1 W ¼ 1J/sec. The classical determinations of thespecific heat of seawater were reported byThoulet and Chevallier (1889). In 1959, Coxand Smith (1959) reported new measurementsestimated to be accurate to 0.05%, with values1 to 2% higher than the old ones. A further study(Millero, Perron, & Desnoyers, 1973) yieldedvalues in close agreement with those of Coxand Smith.

The flux of heat through a surface is definedas the amount of energy that goes through thesurface per unit time, so the mks units of heatflux are W/m2. The heat flux between the atmo-sphere and ocean depends in part on thetemperature of the ocean and atmosphere.

Maps of heat flux are based on measurementsof the conditions that cause heat exchange(Section 5.4). As a simple example, what heatloss from a 100 m thick layer of the ocean isneeded to change the temperature by 1�C in 30days? The required heat flux is rcpDT V/Dt.Typical values of seawater density and specificheat are about 1025 kg/m3 and 3850 J/(kg �C).V is the volume of the 100 m thick layer, whichis 1 m2 across, and Dt is the amount of time(sec). The calculated heat change is 152 W. Theheat flux through the surface area of 1 m2 isthus about 152 W/m2. In Chapter 5 all ofthe components of ocean heat flux and theirgeographic distributions are described.

3.3.3. Potential Temperature

Seawater is almost, but not quite, incom-pressible. A pressure increase causes a waterparcel to compress slightly. This increases thetemperature in the water parcel if it occurswithout exchange of heat with the surroundingwater (adiabatic compression). Conversely ifa water parcel is moved from a higher to a lowerpressure, it expands and its temperaturedecreases. These changes in temperature areunrelated to surface or deep sources of heat. Itis often desirable to compare the temperaturesof two parcels of water that are found atdifferent pressures. Potential temperature isdefined as the temperature that a water parcelwould have if moved adiabatically to anotherpressure. This effect has to be consideredwhen water parcels change depth.

The adiabatic lapse rate or adiabatic temperaturegradient is the change in temperature per unitchange in pressure for an adiabatic displace-ment of a water parcel. The expression for thelapse rate is

GðS;T;pÞ ¼ vT

vp

��heat

(3.2)

where S, T, and p are the measured salinity,temperature, and pressure and the derivative

THERMAL PROPERTIES OF SEAWATER: TEMPERATURE, HEAT, AND POTENTIAL TEMPERATURE 33

is taken holding heat content constant. Note thatboth the compressibility and the adiabatic lapserate of seawater are functions of temperature,salinity, and pressure. The adiabatic lapse ratewas determined for seawater through labora-tory measurements. Since the full equation ofstate of seawater is a complicated function ofthese quantities, the adiabatic lapse rate is alsoa complicated polynomial function of tempera-ture, salinity, and pressure. In contrast, the lapserate for ideal gases can be derived from basicphysical principles; in a dry atmosphere thelapse rate is approximately 9.8�C/km. The lapserate in the ocean, about 0.1 to 0.2�C/km, is muchsmaller since seawater is much less compress-ible than air. The lapse rate is calculated usingcomputer subroutines based on UNESCO(1983).

The potential temperature is (Fofonoff, 1985):

qðS;T;pÞ ¼ TþZ pr

pGðS;T;pÞdp (3.3)

where S, T, and p are the measured (in situ)salinity, temperature, and pressure, G is theadiabatic lapse rate, and q is the temperaturethat a water parcel of properties (S, T, p) wouldhave if moved adiabatically and withoutchange of salinity from an initial pressure pto a reference pressure pr where pr may begreater or less than p. The integration abovecan be carried out in a single step (Fofonoff,1977). An algorithm for calculating q is givenby UNESCO (1983), using the UNESCO adia-batic lapse rate (Eq. 3.2); computer subroutinesin a variety of different programminglanguages are readily available. The usualconvention for oceanographic studies is toreference potential temperature to the seasurface. When defined relative to the seasurface, potential temperature is always lowerthan the actual measured temperature, andonly equal to temperature at the sea surface.(On the other hand, when calculating potentialdensity referenced to a pressure other than sea

surface pressure, potential temperature mustalso be referenced to the same pressure; seeSection 3.5.)

As an example, if a water parcel of temper-ature 5�C and salinity 35.00 were lowered adia-batically from the surface to a depth of 4000 m,its temperature would increase to 5.45�C dueto compression. The potential temperaturerelative to the sea surface of this parcel isalways 5�C, while its measured, or in situ,temperature at 4000 m is 5.45�C. Conversely,if its temperature was 5�C at 4000 m depthand it was raised adiabatically to the surface,its temperature would change to 4.56�C dueto expansion. The potential temperature ofthis parcel relative to the sea surface is thus4.56�C. Temperature and potential temperaturereferenced to the sea surface from a profile inthe northeastern North Pacific are shown inFigure 3.3. Compressibility itself depends ontemperature (and salinity), as discussed inSection 3.5.4.

3.4. SALINITY ANDCONDUCTIVITY

Seawater is a complicated solution contain-ing the majority of the known elements. Someof the more abundant components, as percentof total mass of dissolved material, are chlorineion (55.0%), sulfate ion (7.7%), sodium ion(30.7%), magnesium ion (3.6%), calcium ion(1.2%), and potassium ion (1.1%) (Millero, Feis-tel, Wright, & McDougall, 2008). While the totalconcentration of dissolved matter varies fromplace to place, the ratios of the more abundantcomponents remain almost constant. This “law”of constant proportions was first proposedby Dittmar (1884), based on 77 samples ofseawater collected from around the worldduring the Challenger Expedition (see ChapterS1, Section S1.2, on the textbook Web site),confirming a hypothesis from Forchhammer(1865).


The dominant source of the salts in the oceanis river runoff fromweathering of the continents(see Section 5.2). Weathering occurs very slowlyover millions of years, and so the dissolvedelements become equally distributed in theocean as a result of mixing. (The total time forwater to circulate through the oceans is, atmost, thousands of years, which is much shorterthan the geologic weathering time.) However,there are significant differences in total concen-tration of the dissolved salts from place to place.These differences result from evaporation andfrom dilution by freshwater from rain and riverrunoff. Evaporation and dilution processesoccur only at the sea surface.

Salinity was originally defined as the mass ingrams of solid material in a kilogram ofseawater after evaporating the water away;this is the absolute salinity as described inMillero et al. (2008). For example, the average

salinity of ocean water is about 35 grams of saltsper kilogram of seawater (g/kg), written as“S ¼ 35 &” or as “S ¼ 35 ppt” and read as“thirty-five parts per thousand.” Because evap-oration measurements are cumbersome, thisdefinition was quickly superseded in practice.In the late 1800s, Forch, Knudsen, and Sorensen(1902) introduced a more chemically based defi-nition: “Salinity is the total amount of solidmaterials in grams contained in one kilogramof seawater when all the carbonate has beenconverted to oxide, the bromine and iodinereplaced by chlorine, and all organic mattercompletely oxidized.”

This chemical determination of salinity wasalso difficult to carry out routinely. The methodused throughout most of the twentieth centurywas to determine the amount of chlorine ion(plus the chlorine equivalent of the bromineand iodine) referred to as chlorinity, by titration

0

1000

2000

3000

4000

5000

Pre

ssu

re (

dec

ibar

)

0 5 10 15 20

Temperature/potential temperature (°C)

0 5 10 15 20

T

θ

T

0

1000

2000

3000

4000

5000

30 35 40

Conductivity (mmho)

30 35 40

(a) (b) (c)0

1000

2000

3000

4000

5000

33.5 34.0 34.5

Salinity

33.5 34.0 34.5

0

1000

2000

3000

4000

5000

0 1 2 3

θ

FIGURE 3.3 (a) Potential temperature (q) and temperature (T) (�C), (b) conductivity (mmho), and (c) salinity in thenortheastern North Pacific (36� 30’N, 135�W).

SALINITY AND CONDUCTIVITY 35

with silver nitrate, and then to calculate salinityby a relation based on the measured ratio ofchlorinity to total dissolved substances. (SeeWallace, 1974, Wilson, 1975, or Millero et al.,2008 for a full account.) The current definitionof salinity, denoted by S&, is “the mass of silverrequired to precipitate completely the halogensin 0.3285234 kg of the seawater sample.” Thecurrent relation between salinity and chlorinitywas determined in the early 1960s:

Salinity ¼ 1:80655� Chlorinity (3.4)

These definitions of salinity based on chemi-cal analyses were replaced by a definition basedon seawater’s electrical conductivity, whichdepends on salinity and temperature (see Lewis &Perkin, 1978; Lewis & Fofonoff, 1979; Figure 3.3).This conductivity-based quantity is called prac-tical salinity, sometimes using the symbol psufor practical salinity units, although the preferredinternational convention has been to use no unitsfor salinity. Salinity is now written as, say,S ¼ 35.00 or S ¼ 35.00 psu. The algorithm that iswidely used to calculate salinity from conduc-tivity and temperature is called the practicalsalinity scale 1978 (PSS 78). Electrical conduc-tivity methods were first introduced in the1930s (see Sverdrup, Johnson, & Fleming, 1942for a review). Electrical conductivity dependsstrongly on temperature, but with a smallresidual due to the ion content or salinity. There-fore temperature must be controlled ormeasured very accurately during the conduc-tivity measurement to determine the practicalsalinity. Advances in the electrical circuits andsensor systems permitted accurate compensa-tion for temperature, making conductivity-based salinity measurements feasible (seesupplemental materials in Chapter S6, SectionS6.4.3 on the textbook Web site).

Standard seawater solutions of accuratelyknown salinity and conductivity are requiredfor accurate salinity measurement. The practicalsalinity (SP) of a seawater sample is now given

in terms of the ratio of the electrical conductivityof the sample at 15�C and a pressure of one stan-dard atmosphere to that of a potassium chloridesolution in which the mass fraction of KCl is32.4356 � 10�3 at the same temperature andpressure. The potassium chloride solutionsused as standards are now prepared in a singlelaboratory in the UK. PSS 78 is valid for therange S ¼ 2 to 42, T ¼ �2.0 to 35.0�C and pres-sures equivalent to depths from 0 to 10,000 m.

The accuracy of salinity determined fromconductivity is �0.001 if temperature is veryaccurately measured and standard seawater isused for calibration. This is a major improve-ment on the accuracy of the older titrationmethod, which was about �0.02. In archiveddata sets, salinities that are reported to threedecimal places of accuracy are derived fromconductivity, while those reported to two placesare from titration and usually predate 1960.

The conversion from conductivity ratio topractical salinity is carried out using a computersubroutine based on the formula from Lewis(1980). The subroutine is part of the UNESCO(1983) routines for seawater calculations.

In the 1960s, the pairing of conductivitysensors with accurate thermistors made itpossible to collect continuous profiles of salinityin the ocean. Because the geometry of theconductivity sensors used on these instrumentschange with pressure and temperature, calibra-tion with water samples collected at the sametime is required to achieve the highest possibleaccuracies of 0.001.

An example of the relationship betweenconductivity, temperature, and salinity profilesin the northeastern North Pacific is shown inFigure 3.3. Deriving salinity from conductivityrequires accurate temperature measurementbecause the conductivity profile closely trackstemperature.

The concept of salinity assumes negligiblevariations in the composition of seawater.However, a study of chlorinity, density relativeto pure water, and conductivity of seawater


carried out in England on samples from theworld oceans (Cox, McCartney, & Culkin,1970) revealed that the ionic composition ofseawater does exhibit small variations fromplace to place and from the surface to deepwater. It was found that the relationshipbetween density and conductivity was a littlecloser than between density and chlorinity.This means that the proportion of one ion toanother may change; that is, the chemicalcomposition may change, but as long as the totalweight of dissolved substances is the same, theconductivity and the density will be unchanged.

Moreover, there are geographic variations inthe dissolved substances not measured by theconductivity method that affect seawaterdensity and hence should be included in abso-lute salinity. The geostrophic currents computedlocally from density (Section 7.6.2), based on theuse of salinity PSS 78, are highly accurate.However, it is common practice to map proper-ties on surfaces of constant potential density orrelated surfaces that are closest to isentropic(Section 3.5). On a global scale, these dissolvedconstituents can affect the definition of thesesurfaces.

The definition of salinity is therefore under-going another change equivalent to that of1978. The absolute salinity recommended by theIOC, SCOR, and IAPSO (2010) is a return tothe original definition of “salinity,” which isrequired for the most accurate calculation ofdensity; that is, the ratio of the mass of all dis-solved substances in seawater to the mass ofthe seawater, expressed in either kg/kg or g/kg(Millero et al., 2008). The new estimate for abso-lute salinity incorporates two corrections overPSS 78: (1) representation of improved informa-tion about the composition of the Atlanticsurface seawater used to define PSS 78 andincorporation of 2005 atomic weights, and (2)corrections for the geographic dependence ofthe dissolved matter that is not sensed byconductivity. To maintain a consistent globalsalinity data set, the IOC, SCOR, and IAPSO

(2010) manual strongly recommends that obser-vations continue to be made based on conduc-tivity and PSS 78, and reported to nationalarchives in those practical salinity units. Forcalculations involving salinity, the manual indi-cates two corrections for calculating the absolutesalinity SA from the practical salinity SP:

SA ¼ SR þ dSA ¼ ð35:16504gkg�1=35ÞSP þ dSA

(3.5)

The factor multiplying SP yields the“reference salinity” SR, which is presently themost accurate estimate of the absolute salinityof reference Atlantic surface seawater. Ageographically dependent anomaly, dSA, isthen added that corrects for the dissolvedsubstances that do not affect conductivity; thiscorrection, as currently implemented, dependson dissolved silica, nitrate, and alkalinity. Themean absolute value of the correction globallyis 0.0107 g/kg, and it ranges up to 0.025 g/kgin the northern North Pacific, so it is significant.If nutrients and carbon parameters are notmeasured along with salinity (which is byfar the most common circumstance), thena geographic lookup table based on archivedmeasurements is used to estimate the anomaly(McDougall, Jackett, & Millero, 2010). It isunderstood that the estimate (Eq. 3.5) of abso-lute salinity could evolve as additional measure-ments are made.

All of the work that appears in this bookpredates the adoption of the new salinity scale,and all salinities are reported as PSS 78 and alldensities are calculated according to the 1980equation of state using PSS 78.

3.5. DENSITY OF SEAWATER

Seawater density is important because itdetermines the depth to which a water parcelwill settle in equilibrium d the least dense ontop and the densest at the bottom. The distribu-tion of density is also related to the large-scale

DENSITY OF SEAWATER 37

circulation of the oceans through thegeostrophic/thermal wind relationship (seeChapter 7). Mixing is most efficient betweenwaters of the same density because adiabaticstirring, which precedes mixing, conservespotential temperature and salinity and conse-quently, density. More energy is required tomix through stratification. Thus, property distri-butions in the ocean are effectively depicted bymaps on density (isopycnal) surfaces, whenproperly constructed to be closest to isentropic.(See the discussion of potential and neutraldensity in Section 3.5.4.)

Density, usually denoted r, is the amount ofmass per unit volume and is expressed in kilo-grams per cubic meter (kg/m3). A directlyrelated quantity is the specific volume anomaly,usually denoted a, where a ¼ 1/r. The densityof pure water, with no salt, at 0�C, is 1000 kg/m3

at atmospheric pressure. In the open ocean,density ranges from about 1021 kg/m3 (at thesea surface) to about 1070 kg/m3 (at a pressureof 10,000 dbar). As a matter of convenience, itis usual in oceanography to leave out the firsttwo digits and use the quantity

sstp ¼ rðS;T;pÞ � 1000 kg=m3 (3.6)

where S ¼ salinity, T ¼ temperature (�C), andp ¼ pressure. This is referred to as the in situdensity. In earlier literature, ss,t,0 was commonlyused, abbreviated as st. st is the density of thewater sample when the total pressure on it hasbeen reduced to atmospheric (i.e., the waterpressure p ¼ 0 dbar) but the salinity andtemperature are as measured. Unless the anal-ysis is limited to the sea surface, st is not thebest quantity to calculate. If there is range ofpressures, the effects of adiabatic compressionshould be included when comparing waterparcels. A more appropriate quantity is potentialdensity, which is the same as st but with temper-ature replaced by potential temperature andpressure replaced by a single reference pressurethat is not necessarily 0 dbar. Potential density isdescribed in Section 3.5.2.

The relationship between the density ofseawater and temperature, salinity, and pres-sure is the equation of state for seawater. Theequation of state

rðS;T;pÞ ¼ rðS;T; 0Þ=½l� p=KðS;T;pÞ� (3.7)

was determined through meticulous laboratorymeasurements at atmospheric pressure. Thepolynomial expressions for the equation of stater(S, T, 0) and the bulk modulus K(S, T, p) contain15 and 27 terms, respectively. The pressuredependence enters through the bulk modulus.The largest terms are those that are linear in S,T, and p, with smaller terms that are propor-tional to all of the different products of these.Thus, the equation of state is weakly nonlinear.

Today, the most common version of Eq. (3.7) is“EOS 80” (Millero & Poisson, 1980; Fofonoff,1985). EOS 80 uses the practical salinity scalePSS 78 (Section 3.4). The formulae may be foundin UNESCO (1983), which provides practicalcomputer subroutines and are included invarious texts such as Pond and Pickard (1983)and Gill (1982). EOS 80 is valid for T ¼ �2 to40�C, S ¼ 0 to 40, and pressures from 0 to 10,000dbar, and is accurate to 9� 10�3 kg/m3 or better.A new version of the equation of state has beenintroduced (IOC, SCOR, and IAPSO, 2010), basedon a new definition of salinity and is termedTEOS-10. Only EOS 80 is used in this book.

Historically, density was calculated fromtables giving the dependence of the densityon salinity, temperature, and pressure. Earlierdeterminations of density were based onmeasurements by Forch, Jacobsen, Knudsen,and Sorensen and were presented in the Hydro-graphical Tables (Knudsen, 1901). Cox et al.(1970) found that the s0 values (at T ¼ 0�C) in“Knudsen’s Tables” were low by about 0.01 (onaverage) in the salinity range from 15 e 40, andbyup to 0.06 at lower salinities and temperatures.

To determine seawater density over a rangeof salinities in the laboratory, Millero (1967)used a magnetic float densimeter. A Pyrex glassfloat containing a permanent magnet floats in a


250 ml cell that contains the seawater and is sur-rounded by a solenoid, with the entire apparatussitting in a constant temperature bath. The float isslightly less dense than the densest seawater andis loadedwith small platinumweights until it justsinks to the bottom of the cell. A current throughthe solenoid is then slowly increased until thefloat just lifts off the bottom of the cell. Thedensity of the seawater is then related to thecurrent through the solenoid. The relationbetween current and density is determined bycarrying out a similar experiment with purewater in the cell. The accuracy of the relativedensity determined this way is claimed tobe �2 � 10�6 (at atmospheric pressure). But asthe absolute density of pure water is known tobe only�4� 10�6, the actual accuracyof seawaterdensity is more limited. The influence ofpressure was determined using a high pressureversion of the previously mentioned densimetertomeasure the bulkmodulus (K). Khas also beendetermined from measurements of sound speedin seawater because sound speed depends onthe bulk modulus and seawater compressibility.

The following subsections explore howseawater density depends on temperature,salinity, and pressure, and discusses concepts(such as potential and neutral density) thatreduce, as much as possible, the effects ofcompressibility on a given analysis.

3.5.1. Effects of Temperature andSalinity on Density

Density values evaluated at the ocean’ssurface pressure are shown in Figure 3.1 (curvedcontours) for the whole range of salinities andtemperatures found anywhere in the oceans.The shaded bar in the figure shows that mostof the ocean lies within a relatively narrowsalinity range. More extreme values occur onlyat or near the sea surface, with fresher watersoutside this range (mainly in areas of runoff orice melt) and the most saline waters in relativelyconfined areas of high evaporation (such as

marginal seas). The ocean’s temperature rangeproduces more of the ocean’s density variationthan does its salinity range. In other words,temperature dominates oceanic density varia-tions for the most part. (As noted previously,an important exception is where surface watersare relatively fresh due to large precipitation orice melt; that is, at high latitudes and also in thetropics beneath the rainy Intertropical Conver-gence Zone of the atmosphere.) The curvatureof the density contours in Figure 3.1 is due tothe nonlinearity of the equation of state. Thecurvature means that the density change fora given temperature or salinity change isdifferent at different temperatures or salinities.

To emphasize this point, Table 3.2 shows thechange of density (Dst) for a temperaturechange (DT) of þ1 K (left columns) and thevalue of Dst for a salinity change (DS) of þ0.5(right columns). These are arbitrary choices forchanges in temperature and salinity. The mostimportant thing to notice in the table is howdensity varies at different temperatures andsalinities for given changes in each. At hightemperatures, st varies significantly with T atall salinities. As temperature decreases, therate of variation with T decreases, particularlyat low salinities (as found at high latitudes orin estuaries). The change of st with DS is aboutthe same at all temperatures and salinities, butis slightly greater at low temperature.

3.5.2. Effect of Pressure on Density:Potential Density

Seawater is compressible, although notnearly as compressible as a gas. As a waterparcel is compressed, the molecules are pushedcloser together and the density increases. Atthe same time, and for a completely differentphysical reason, adiabatic compression causesthe temperature to increase, which slightlyoffsets the density increase due to compression.(See discussion of potential temperature inSection 3.3.)


Density is primarily a function of pressure(Figure 3.4) because of this compressibility. Pres-sure effects on density have little to do with theinitial temperature and salinity of the waterparcel. To trace a water parcel from one placeto another, the dependence of density on pres-sure should be removed. An early attempt wasto use st, defined earlier, in which the pressureeffect was removed from density but not fromtemperature. It is now standard practice to usepotential density, in which density is calculatedusing potential temperature instead of tempera-ture. (The measured salinity is used.) Potential

density is the density that a parcel would haveif it were moved adiabatically to a chosen refer-ence pressure. If the reference pressure is the seasurface, then we first compute the potentialtemperature of the parcel relative to surfacepressure, then evaluate the density at pressure0 dbar.1 We refer to potential density referencedto the sea surface (0 dbar) as sq, which signifiesthat potential temperature and surface pressurehave been used.

The reference pressure for potential densitycan be any pressure, not just the pressure atthe sea surface. For these potential densities,potential temperature is calculated relative tothe chosen reference pressure and then thepotential density is calculated relative to thesame reference pressure. It is common to referto potential density referenced to 1000 dbar ass1, referenced to 2000 dbar as s2, to 3000 dbaras s3 and so on, following Lynn and Reid (1968).

3.5.3. Specific Volume and SpecificVolume Anomaly

The specific volume (a) is the reciprocal ofdensity so it has units of m3/kg. For somepurposes it is more useful than density. The insitu specific volume is written as as,t,p. The

TABLE 3.2 Variation of Density (Dst) with Variations of Temperature (DT) and of Salinity (DS) as Functions ofTemperature and Salinity

Salinity 0 20 35 40 0 20 35 40

Temperature (�C) Dst for DT [ D1�C Dst for DS [ D0.5

30 �0.31 �0.33 �0.34 �0.35 0.38 0.37 0.37 0.38

20 �0.21 �0.24 �0.27 �0.27 0.38 0.38 0.38 0.38

10 �0.09 �0.14 �0.18 �0.18 0.39 0.39 0.39 0.39

0 þ0.06 �0.01 �0.06 �0.07 0.41 0.40 0.40 0.40

0

1000

2000

3000

4000

5000

Pre

ssu

re (

db

ar)

1030 1035 1040 1045 1050

Density (kg m–3)

FIGURE 3.4 Increase in density with pressure fora water parcel of temperature 0�C and salinity 35.0 at thesea surface.

1 The actual pressure at the sea surface is the atmospheric pressure, but we do not include atmospheric pressure in many

applications since pressure ranges within the ocean are so much larger.


specific volume anomaly (d) is also sometimesconvenient. It is defined as:

d ¼ as;t;p � a35;0;p (3.8)

The anomaly is calculated relative to a35,0,p,which is the specific volume of seawater ofsalinity 35 and temperature 0�C at pressure p.With this standard d is usually positive. Theequation of state relates a (and d) to salinity,temperature, and pressure. Originally all calcu-lations of geostrophic currents from the distri-bution of mass were done by hand usingtabulations of the component terms of d,described in previous editions of this book.With modern computer methods, tabulationsare not necessary. The computer algorithms fordynamic calculations (Section 7.5.1) still usespecific volume anomaly d, computed usingsubroutines, rather than the actual density r,to increase the calculation precision.

3.5.4. Effect of Temperature andSalinity on Compressibility: IsentropicSurfaces and Neutral Density

Cold water is more compressible than warmwater; it is easier to deform a cold parcel thana warm parcel. When two water parcels withthe same density but different temperature andsalinity characteristics (one warm/salty, theother cold/fresh) are submerged to the samepressure, the colder parcel will be denser. Ifthere were no salt in seawater, so that densitydepended only on temperature and pressure,then potential density as defined earlier, usingany single pressure for a reference, would beadequate for defining a unique isentropic surface.An isentropic surface is one along which waterparcels can move adiabatically, that is, withoutexternal input of heat or salt.

When analyzing properties within the oceanto determine where water parcels originate, itis assumed that motion and mixing is mostlyalong a quasi-isentropic surface and that mixing

across such a surface (quasi-vertical mixing)is much less important (Montgomery, 1938).However, because seawater density dependson both salinity and temperature, the actualsurface that a water parcel moves along in theabsence of external sources of heat or freshwaterdepends on how the parcel mixes along thatsurface since its temperature and salinity willbe altered as it mixes with adjacent waterparcels on that surface. This quasi-lateral mix-ing alters the temperature (and salinity) andtherefore, the compressibility of the mixture.As a result, when it moves laterally, the parcelwill equilibrate at a different pressure than ifthere had been no mixing. This means that thereare no closed, unique isentropic surfaces in theocean, since if our water parcel were to returnto its original latitude and longitude, it willhave moved to a different density and hencepressure because its temperature and salinitywill have changed due to mixing along thatsurface. Note that these effects are importanteven without diapycnal mixing between waterparcels on different isentropic surfaces (quasi-vertical mixing), which also can change temper-ature, salinity, and compressibility.

The density differences associated with thesedifferences in compressibility can be substantial(Figure 3.5). For instance, water spilling out ofthe Mediterranean Sea through the Strait ofGibraltar is saline and rather warm comparedwith water spilling into the Atlantic from theNordic Seas over the Greenland-Iceland ridge(Chapter 9). The Mediterranean Water (MW)density is actually higher than the Nordic SeaOverflow Water (NSOW) density where theyflow over their respective sills, which are at aboutthe same depth. However, the warm, saline MW(13.4�C, 37.8 psu) is not as compressible as themuch colder NSOW (about 1�C, 34.9 psu; Price &Baringer, 1994). The potential density relative to4000 dbar of MW is lower than that of the morecompressible NSOW. The NSOW reaches thebottom of the North Atlantic, while the MWdoes not. (As both types of water plunge


downward, they entrain or mix with the watersthat they pass through. This also has an effecton how deep they fall, so the difference incompressibility is not the only cause for differentoutcomes.)

Restating this more generally, changing thereference pressure for potential density altersthe density difference between twowater parcels(Figure 3.5). For the pair labeled 1, the densitiesare the same at the sea surface (upper panel).Because the cold parcel compresses more thanthe warm one with increasing pressure, the

cold parcel is denser than thewarmone at higherpressure (lower panel). The pair labeled 2 illus-trates the MW (warm, salty) and NSOW (cold,fresh) pair with their properties at the sills wherethey enter the North Atlantic. At the sea surface,whichneither parcel ever reaches, theMediterra-nean parcel would actually be denser than theNordic Seas parcel. Near the ocean bottom, repre-sented by 4000 dbar (Figure 3.5b), the colderNordic Seas parcel is markedly denser than theMediterranean parcel. Therefore, if both parcelsdropped to the ocean bottom from their respectivesills, without any mixing, the Nordic Seas parcelwould lie under the Mediterranean parcel. (Inactuality, as already mentioned, there is a largeamount of entrainment mixing as these parcelsdrop down into the North Atlantic.)

The surfaces that we use to map and tracewater parcels should approximate isentropicsurfaces. Early choices, that were an improve-ment over constant depth surfaces, includedsigma-t surfaces (Montgomery, 1938) and evenpotential temperature surfaces (Worthingtonand Wright, 1970). A method, introduced byLynn and Reid (1968), that produces surfacesthat are closer to isentropic uses isopycnalswith a reference pressure for the potentialdensity that is within 500 m of the pressure ofinterest. Therefore when working in the top500 m, a surface reference pressure is used.When working at 500 to 1500 m, a referencepressure of 1000 dbar is used, and so forth.Experience has shown this pressure discretiza-tion is sufficient to remove most of the problemsassociated with the effect of pressure on density.When isopycnals mapped in this fashion moveinto a different pressure range, they must bepatched onto densities at the reference pressurein the new range. Reid (1989, 1994, 1997, 2003)followed this practice in his monographs onPacific, Atlantic, and Indian Ocean circulations.

It is less complicated to use a continuouslyvarying surface rather than one patched fromdifferent reference pressures, although in prac-tice there is little difference between them.

0

10

20

30

32 34 36 38 40Salinity

3840 42

44

46

48

0 dbar

4000 dbar

(1)

(1)

(2)

(2)

0

10

20

30

Po

ten

tial

tem

per

atu

re32 34 36 38 40

Salinity

22 24

26 28

30

Po

ten

tial

tem

per

atu

re(a)

(b)

FIGURE 3.5 Potential density relative to (a) 0 dbar and(b) 4000 dbar as a function of potential temperature (relativeto 0 dbar) and salinity. Parcels labeled 1 have the samedensity at the sea surface. The parcels labeled 2 representsMediterranean (saltier) and Nordic Seas (fresher) sourcewaters at their sills.


“Neutral surfaces,” introduced by Ivers (1975),a student working with J.L. Reid, use a nearlycontinuously varying reference pressure. Ifa parcel is followed along its path from oneobservation station to the next, assuming thepath is known, then it is possible to track its pres-sure and adjust its reference pressure and densityat each station. McDougall (1987a) refined thisneutral surface concept and introduced it widely.Jackett andMcDougall (1997) created a computerprogram for computing their version of thisneutral density, based on a standard climatology(average temperature and salinity on a grid forthe whole globe, derived from all available obser-vations; Section 6.6.2), marching away froma single location in the middle of the Pacific.The Jackett and McDougall neutral density isdenoted gN with numerical values that aresimilar to those of potential density (with unitsof kg/m3). Neutral density depends on latitude,longitude, and pressure, and is defined only forranges of temperature and salinity that occur inthe open ocean. This differs from potentialdensity, which is defined for all values of temper-ature and salinity through a well-defined equa-tion of state that has been determined in thelaboratory and is independent of location.Neutral density cannot be contoured as a functionof potential temperature and salinity analo-gously to Figure 3.5 for density or potentialdensity.

The advantage of neutral density formapping quasi-isentropic surfaces is that itremoves the need to continuously vary the refer-ence pressure along surfaces that have depthvariation (since this is already done in anapproximate manner within the provided soft-ware and database). Neutral density is a conve-nient tool. Both potential and neutral densitysurfaces are approximations to isentropicsurfaces. Ideas and literature on how to bestapproximate isentropic surfaces continue to bedeveloped; neutral density is currently themost popular and commonly used approxima-tion for mapping isentropes over large distances

that include vertical excursions of more thanseveral hundred meters.

3.5.5. Linearity and Nonlinearityin the Equation of State

As described earlier, the equation of state(3.6) is somewhat nonlinear in temperature,salinity, and pressure; that is, it includes prod-ucts of salinity, temperature, and pressure. Forpractical purposes, in theoretical and simplenumerical models, the equation of state is some-times approximated as linear and its pressuredependence is ignored:

rzr0 þ aðT� T0Þ þ bðS� S0Þ;a ¼ vr=vT and b ¼ vr=vS

(3.9)

where r0, T0,, and S0 are arbitrary constantvalues of r, T, and S; they are usually chosenas the mean values for the region beingmodeled. Here a is the thermal expansion coeffi-cient, which expresses the change in densityfor a given change in temperature (and shouldnot be confused with specific volume, definedwith the same symbol in Section 3.5.3), andb is the haline contraction coefficient, which isthe change in density for a given change insalinity. The terms a and b are nonlinear func-tions of salinity, temperature, and pressure;their mean values are chosen for linear models.Full tables of values are given in UNESCO(1987). The value of ar (at the sea surface and ata salinity of 35 psu) ranges from 53� 10�6 K�1 ata temperature of 0�C to 257 � 10�6 K�1 at atemperature of 20�C. The value of br (at thesea surface and at a salinity of 35 psu) rangesfrom 785 � 10�6 psu�1 (at a temperature of 0�C)to 744 � 10�6 psu�1 (at a temperature of 20�C).

Nonlinearity in the equation of state leads tothe curvature of the density contours in Figures3.1 and 3.5. Mixing between two water parcelsmust occur along straight lines in the tempera-ture/salinity planes of Figures 3.1 and 3.5.Because of the concave curvature of the density


contours, when two parcels of the same densitybut different temperature and salinity aremixed together, the mixture has higher densitythan the original water parcels. Thus theconcavity of the density contours means thatthere is a contraction in volume as waterparcels mix. This effect is called cabbeling(Witte, 1902). In practice, cabbeling may be oflimited importance, having demonstrableimportance only where water parcels of verydifferent initial properties mix together. Exam-ples of problems where cabbeling has beena factor are in the formation of dense water inthe Antarctic (Foster, 1972) and in the modifica-tion of intermediate water in the North Pacific(Talley & Yun, 2001).

There are two other important mixing effectsassociated with the physical properties ofseawater: thermobaricity and double diffusion.Thermobaricity (McDougall, 1987b) is bestexplained by the rotation with depth ofpotential density contours in the potentialtemperatureesalinity plane (Section 3.5.4). Asin Figure 3.5, consider two water parcels ofdifferent potential temperature and salinity inwhich the warmer, saltier parcel is slightlydenser than the colder, fresher one. (This isa common occurrence in subpolar regionssuch as the Arctic and the Antarctic.) If thesetwo water parcels are suddenly brought toa greater pressure, it is possible for them toreverse their relative stratification, with thecolder, fresher one compressing more thanthe warmer one, and therefore becoming thedenser of the two parcels. The parcels wouldnow be vertically stable if the colder, fresherone were beneath the warmer, saltier one. Ther-mobaricity is an important effect in the Arctic,defining the relative vertical juxtaposition ofthe Canadian and Eurasian Basin Deep Waters(Section 12.2).

Double diffusion results from a difference indiffusivities for heat and salt, therefore, it isnot a matter of linearity or nonlinearity. At themolecular level, these diffusivities clearly differ.

Because double diffusive effects are apparent inthe ocean’s temperatureesalinity properties, thedifference in diffusivities scales up in some wayto the eddy diffusivity. Diffusivity and mixingare discussed in Chapter 7, and double diffusionin Section 7.4.3.2.

3.5.6. Static Stability and Brunt-VaisalaFrequency

Static stability, denoted by E, is a formalmeasure of the tendency of a water column tooverturn. It is related to the density stratifica-tion, with higher stability where the watercolumn is more stratified. A water column isstatically stable if a parcel of water that ismoved adiabatically (with no heat or saltexchange) up or down a short distance returnsto its original position. The vigor with whichthe parcel returns to its original positiondepends on the density difference betweenthe parcel and the surrounding water columnat the displaced position. Therefore the rate ofchange of density of the water column withdepth determines a water column’s staticstability. The actual density of the parcelincreases or decreases as it is moved down orup because the pressure on it increases ordecreases, respectively. This adiabatic changein density must be accounted for in the defini-tion of static stability.

The mathematical derivation of the staticstability of a water column is presented in detailin Pond and Pickard (1983) and other texts. Thefull expression for E is complicated. For verysmall vertical displacements, static stabilitymight be approximated as

Ez� ðl=rÞ ðvr=vzÞ (3.10a)

where r is in situ density. The water column isstable, neutral, or unstable depending onwhether E is positive, zero, or negative, respec-tively. Thus, if the density gradient is positivedownwards, the water column is stable andthere is no tendency for vertical overturn.


For larger vertical displacements, a muchbetter approximation uses local potentialdensity, sn:

E ¼ �ðl=rÞðvsn=vzÞ (3.10b)

Here the potential density anomaly sn iscomputed relative to the pressure at the centerof the interval used to compute the verticalgradient. This local pressure reference approxi-mately removes the adiabatic pressure effect.Many computer subroutines for seawater prop-erties use this standard definition. An equiva-lent expression for stability is

E ¼ �ðl=rÞðvr=vzÞ � ðg=C2Þ (3.10c)

where r is in situ density, g ¼ acceleration dueto gravity, and C ¼ in situ sound speed. Theaddition of the term g/C2 allows for thecompressibility of seawater. (Sound waves arecompression waves; Section 3.7.)

A typical density profile from top to bottomof the ocean has a surface mixed layer withlow stratification, an upper ocean layer withan intermediate amount of stratification, anintermediate layer of high stratification (pycno-cline), and a deep layer of low stratification(Section 4.2). The water in the pycnocline isvery stable; it takes much more energy todisplace a particle of water up or downthan in a region of lesser stability. Thereforeturbulence, which causes most of the mixingbetween different water bodies, is less able topenetrate through the stable pycnocline thanthrough less stable layers. Consequently, thepycnocline is a barrier to the vertical transportof water and water properties. The stability ofthese layers is measured by E. In the upper1000 m in the open ocean, values of E rangefrom 1000 � 10�8 m�1 to 100 � 10�8 m�1, withlarger values in the pycnocline. Below 1000 m,E decreases; in abyssal trenches E may be aslow as 1 � 10�8 m�1.

Static instabilitiesmay be found near the inter-faces between different waters in the process ofmixing.Because these instabilities occur at a small

vertical scale, on the order of meters, they requirecontinuous profilers for detection. Unstableconditions with vertical extents greater than tensof meters are uncommon below the surface layer.

The buoyancy (Brunt-Vaisala) frequency associ-ated with internal gravity waves (Chapter 8) isan intrinsic frequency associated with staticstability. If a water parcel is displaced upwardin a statically stable water column, it will sinkand overshoot the original position. The denserwater beneath its original position will force itback up into lighter water, and it will continueoscillating. The frequency of the oscillationdepends on the static stability: the more strati-fied the water column, the higher the staticstability and the higher the buoyancy frequency.The Brunt-Vaisala frequency, N, is an intrinsicfrequency of internal waves:

N2 ¼ gEzg½�ðl=rÞðvsn=vzÞ� (3.11)

The frequency in cycles/sec (hertz) isf ¼ N/2p and the period is s ¼ 2p/N. In theupper ocean, where E typically ranges from1000 � 10�8 to 100 � 10�8 m�1, periods ares¼ 10 to 33 min (Figure 3.6). For the deep ocean,E ¼ 1 � 10�8 m�1 and s z 6 h.

The final quantity that we define based onvertical density stratification is the “stretching”part of the potential vorticity (Section 7.6). Poten-tial vorticity is a dynamical property of a fluidanalogous to angular momentum. Potentialvorticity has three parts: rotation due to Earth’srotation (planetary vorticity), rotation due torelative motions in the fluid (relative vorticity,for instance, in an eddy), and a stretchingcomponent proportional to the vertical changein density, which is analogous to layer thickness(Eq. 7.41). In regions where currents are weak,relative vorticity is small and the potentialvorticity can be approximated as

Qz� ðf=rÞðvr=vzÞ (3.12a)

This is sometimes called “isopycnic potentialvorticity.” The vertical density derivative is


calculated from locally referenced potentialdensity, so it can be expressed in terms ofBrunt-Vaisala frequency:

Q ¼ ðf=gÞN2 (3.12b)

3.5.7. Freezing Point of Seawater

The salt in seawater depresses the freezingpoint below 0�C (Figure 3.1). An algorithm forcalculating the freezing point of seawater isgiven by Millero (1978). Depression of thefreezing point is why a mixture of salt waterand ice is used to make ice cream; as the icemelts, it cools the water (and ice cream) below0�C. At low salinities, below the salinity ofmost seawater, cooling water reaches itsmaximum density before freezing and sinkswhile still fluid. The water column then over-turns and mixes until the whole water columnreaches the temperature of maximum density.

On further cooling the surface water becomeslighter and the overturning stops. The watercolumn freezes from the surface down, withthe deeper water remaining unfrozen.However, at salinities greater than 24.7 psu,maximum density is achieved at the freezingpoint. Therefore more of the water columnmust be cooled before freezing can begin, sofreezing is delayed compared with the fresh-water case.

3.6. TRACERS

Dissolved matter in seawater can help intracing specific water masses and pathways offlow. Some of these properties can be used fordating seawater (determine the length of timesince the water was last at the sea surface;Section 4.7). Most of these constituents occur insuch small concentrations that their variations

0

1000

2000

3000

4000

5000

Pre

ssu

re (

db

ar)

24 26 28

Potential density

0

1000

2000

3000

4000

5000

0 2 4 6

Brunt−Väisälä Frequency(cycles per hour)

30 15

Period (minutes) 10

North Pacific24.258°N, 147.697°W

FIGURE 3.6 (a) Potentialdensity and (b) Brunt-Vaisalafrequency (cycles/h) andperiod (minutes) for a profilein the western North Pacific.


do not significantly affect density variations orthe relationship between chlorinity, salinity,and conductivity. (See Section 3.5 for commentson this.) These additional properties of seawatercan be: conservative or non-conservative;natural or anthropogenic (man-made); stableor radioactive; transient or non-transient. Thetext by Broecker and Peng (1982) describes thesources and chemistry of many tracers in detail.

For a tracer to be conservative there are nosignificant processes other than mixing bywhich the tracer is changed below the surface.Even salinity, potential temperature, and hencedensity, can be used as conservative tracerssince they have extremely weak sources withinthe ocean. This near absence of in situ sourcesand sinks means that the spreading of watermasses in the ocean can be approximately tracedfrom their origin at the sea surface by their char-acteristic temperature/salinity values. Near thesurface, evaporation, precipitation, runoff, andice processes change salinity, and many surfaceheat-transfer processes change the temperature(Section 5.4). Absolute salinity can be changedonly very slightly within the ocean due tochanges in dissolved nutrients and carbon(end of Section 3.4). Temperature can be raisedvery slightly by geothermal heating at the oceanbottom. Even though water coming out ofbottom vents at some mid-ocean ridges can beextremely hot (up to 400�C), the total amountof water streaming out of the vents is tiny, andthe high temperature quickly mixes away,leaving a miniscule large-scale temperatureincrease.

Non-conservative properties are changed bychemical reactions or biological processeswithin the water column. Dissolved oxygen isan example. Oxygen enters the ocean from theatmosphere at the sea surface. It is alsoproduced through photosynthesis by phyto-plankton in the sunlit upper ocean (photiczone or euphotic zone) and consumed by respi-ration by zooplankton, bacteria, and other crea-tures. Equilibration with the atmosphere keeps

ocean mixed layer waters at close to 100% satu-ration. Below the surface layer, oxygen contentdrops rapidly. This is not a function of thetemperature of the water, which generally islower at depth, since cold water can hold moredissolved oxygen than warm water. (Forexample, for a salinity of 35: at 30�C, 100%oxygen saturation occurs at 190 mmol/kg; at10�C it is 275 mmol/kg; and at 0�C it is 350mmol/kg.) The drop in oxygen content and satu-ration with depth is due to respiration withinthe water column, mainly by bacteria feedingon organic matter (mostly dead plankton andfecal pellets) sinking from the photic zone. Sincethere is no source of oxygen below the mixedlayer and photic zone, oxygen decreases withincreasing age of the subsurface water parcels.Oxygen is also used by nitrifying bacteria,which convert the nitrogen in ammonium(NH4) to nitrate (NO3).

The rate at which oxygen is consumed iscalled the oxygen utilization rate. This ratedepends on local biological productivity so itis not uniform in space. Therefore the decreasein oxygen from a saturated surface value is nota perfect indication of age of the water parcel,especially in the biologically active upper oceanand continental shelves. However, below thethermocline, the utilization rate is more uniformand changes in oxygen following a water parcelcorrespond relatively well to age.

Nutrients are another set of natural, non-conservative, commonly observed properties.These include dissolved silica, phosphate, andthe nitrogen compounds (ammonium, nitrite,and nitrate). Nutrients are essential to oceanlife so they are consumed in the ocean’s surfacelayer where life is abundant; consequently,concentrations there are low. Nutrient contentincreases with depth and age, as almost a mirrorimage of the oxygen decrease. Silica is used bysome organisms to form protective shells. Silicare-enters the water column when the hard partsof these organisms dissolve as they fall to theocean floor. Some of this material reaches the

TRACERS 47

seafloor and accumulates, creating a silica sourceon the ocean bottom as well. Some silica alsoenters the water column through venting atmid-ocean ridges. The other nutrients (nitrate,nitrite, ammonium, and phosphate) re-enterthe water column as biological (bacterial)activity decays the soft parts of the fallingdetritus. Ammonium and phosphate are imme-diate products of the decay. Nitrifying bacteria,which are present through the water column,then convert ammonium to nitrite and finallynitrate; this process also, in addition to respira-tion, consumes oxygen. Because oxygen isconsumed and nutrients are produced, the ratiosof nitrate to oxygen and of phosphate to oxygenare nearly constant throughout the oceans. Theseproportions are known as “Redfield ratios,” afterRedfield (1934) who demonstrated the near-constancy of these proportions. Nutrients arediscussed further in Section 4.6.

Other non-conservative properties related tothe ocean’s carbon system, including dissolvedinorganic carbon, dissolved organic carbon,alkalinity, and pH, have been widely measuredover the past several decades. These have bothnatural and anthropogenic sources and areuseful tracers of water masses.

Isotopes that occur in trace quantities are alsouseful. Two have been widely measured: 14Cand 3He. 14C is radioactive andnon-conservative.3He is conservative. Both have predominantlynatural sources but both also have anthropogenicsources in the upper ocean. Isotope concentra-tions are usuallymeasured and reported in termsof ratios to the more abundant isotopes. For 14C,the reported unit is based on the ratio of 14C to12C. For 3He, the reported unit is based on theratio of 3He to 4He.Moreover, the values are oftenreported in terms of the normalized differencebetween this ratio and a standard value, usuallytaken to be the average atmospheric value (seeBroecker & Peng, 1982).

Most of the 14C in the ocean is natural. It iscreated continuously in the atmosphere bycosmic ray bombardment of nitrogen, and enters

the ocean through gas exchange. “Bomb” radio-carbon is an anthropogenic tracer that enteredthe upper ocean as a result of atomic bomb testsbetween 1945 and 1963 (Key, 2001). In the ocean,14C and 12C are incorporated by phytoplanktonin nearly the same ratio as they appear in theatmosphere. After the organic material diesand leaves the photic zone, the 14C decays radio-actively,with a half-life of 5730 years. The ratio of14C to 12C decreases. Since values are reported asanomalies, as the difference from the atmo-spheric ratio, the reported oceanic quantitiesare generally negative (Section 4.7 andFigure 4.24). The more negative the anomaly,the older the water. Positive anomaliesthroughout the upper ocean originated fromthe anthropogenic bomb release of 14C.

The natural, conservative isotope 3He origi-nates in Earth’s mantle and is outgassed at ventsin the ocean floor. It is usually reported in termsof its ratio to the much more abundant 4Hecompared with this ratio in the atmosphere. Itis an excellent tracer of mid-depth circulation,since its sources tend to be the tops of mid-oceanridges, which occur at about 2000 m. Theanthropogenic component of 3He is describedin the last paragraph of this Section.

Another conservative isotope that is oftenmeasured in seawater is the stable (heavy)isotope of oxygen, 18O. Measurements are againreported relative to the most common isotope16O. Rainwater is depleted in this heavy isotopeof oxygen (compared with seawater) because itis easier for the lighter, more common isotopeof oxygen, 16O, to evaporate from the sea andland. A second step of reduction of 18O in atmo-spheric water vapor relative to seawater occurswhen rain first forms, mostly at warmer atmo-spheric temperatures, since the heavier isotopefalls out preferentially. Thus rainwater isdepleted in 18O relative to seawater, and rainformed at lower temperatures is more depletedthan at higher temperatures. For physical ocean-ographers, 18O content can be a useful indicatorin a high latitude region of whether the source of


freshwater at the sea surface is rain/runoff/glacial melt (lower 18O content), or melted seaice (higher content). In paleoclimate records, itreflects the temperature of the precipitation(higher 18O in warmer rain); ice formed duringthe (cold) glacial periods is more depleted in18O than ice formed in the warm interglacialsand hence 18O content is an indicator of relativeglobal temperature.

Transient tracers are chemicals that have beenintroduced by human activity; hence they areanthropogenic. They are gradually invadingthe ocean, marking the progress of water fromthe surface to depth. They can be either stableor radioactive. They can be either conservativeor non-conservative. Commonly measuredtransient tracers include chlorofluorocarbons,tritium, and much of the upper ocean 3He and14C. Chlorofluorocarbons (CFCs) were intro-duced as refrigerants and for industrial use.They are extremely stable (conservative) inseawater. Their usage peaked in 1994, whenrecognition of their role in expanding the ozonehole in the atmosphere finally led to interna-tional conventions to phase out their use.Because different types of CFCs were usedover the years, the ratio of different types ina water parcel can yield approximate dates forwhen the water was at the sea surface. Tritiumis a radioactive isotope of hydrogen that hasalso been measured globally; it was releasedinto the atmosphere through atomic bombtesting in the 1960s and then entered the ocean,primarily in the Northern Hemisphere. Tritiumdecays to 3Hewith a half-life of 12.4 years, whichis comparable to the circulation time of theupper ocean gyres.When 3He is measured alongwith tritium, the time since the water was at thesea surface can be estimated (Jenkins, 1998).

3.7. SOUND IN THE SEA

In the atmosphere, we receive much of ourinformation about the material world by means

of wave energy, either electromagnetic (light) ormechanical (sound). In the atmosphere, light inthe visible part of the spectrum is attenuatedless than sound; we can see much fartheraway than we can hear. In the sea the reverseis true. In clear ocean water, sunlight may bedetectable (with instruments) down to 1000 m,but the range at which humans can see detailsof objects is rarely more than 50 m, and usuallyless. On the other hand, sound waves can bedetected over vast distances and are a muchbetter vehicle for undersea information thanlight.

The ratio of the speed of sound in air to thatin water is small (about 1:4.5), so only a smallamount of sound energy starting in onemediumcan penetrate into the other. This contrasts withthe relatively efficient passage of light energythrough the air/water interface (speed ratioonly about 1.33:1). This is why a personstanding on the shore can see into the waterbut cannot hear any noises in the sea. Likewise,divers cannot converse underwater becausetheir sounds are generated in the air in thethroat and little of the sound energy is trans-mitted into the water. Sound sources used inthe sea generate sound energy in solid bodies(transducers), for example, electromagnetically,in which the speed of sound is similar to thatin water. Thus the two are acoustically“matched” and the transducer energy is trans-mitted efficiently into the sea.

Sound is a wave. All waves are characterizedby amplitude, frequency, and wavelength(Section 8.2). Sound speed (C), frequency (n),and wavelength (l) are connected by the waveequation C ¼ nl. The speed does not dependon frequency, so the wavelength depends onsound speed and frequency. The frequencies ofsounds range from 1 Hz or less (1 Hz ¼ 1 vibra-tion per second) to thousands of kilohertz(1 kHz ¼ 1000 cycles/sec). The wavelengths ofsounds in the sea cover a vast range, from about1500 m for n ¼ 1 Hz to 7 cm for n ¼ 200 kHz.Most underwater sound instruments use

SOUND IN THE SEA 49

a more restricted range from 10 to 100 kHz, forwhich the wavelengths are 14 to 1.4 cm.

There are many sources of sound in the sea.A hydrophone listening to the ambient soundin the sea will record a wide range of frequen-cies and types of sounds, from low rumbles tohigh-frequency hisses. Some sources of under-sea sounds are microseisms (10 e 100 Hz); ships(50 e 1500 Hz); the action of wind, waves, andrain at the surface (1 e 20 kHz); cavitation ofair bubbles and animal noises (10 e 400 Hz);and fish and crustaceans (1 e 10 kHz). Noisesassociated with sea ice range from 1 e 10 kHz.

Sound is a compressional wave; water mole-cules move closer together and farther apart asthe wave passes. Therefore sound speeddepends on the medium’s compressibility.The more compressible a medium is for a givendensity, the slower the wave since moreactivity is required to move the molecules.The speed of sound waves in the sea, C, isgiven by

C ¼ ðbrÞ�1=2 where b ¼ r�1ðvr=vpÞq;S:(3.13)

b is the adiabatic compressibility of seawater(with potential temperature and salinityconstant), r is the density, p is the pressure, qis the potential temperature, and S is thesalinity. Since b and r depend (nonlinearly)on temperature and pressure, and to a lesserextent, salinity, so does the speed of soundwaves. There are various formulae for thedependence of Eq. (3.13) on T, S, and p; allderived from experimental measurements.The two most accepted are those of Del Grosso(1974) and of Chen and Millero (1977); DelGrosso’s equation is apparently more accurate,based on results from acoustic tomography andinverted echo sounder experiments (e.g.,Meinen & Watts, 1997). Both are long andnonlinear polynomials, as is the equation ofstate. We present a simpler formula, whichitself is simplified from Mackenzie (1981) and

is similar to Del Grosso (1974), to illustratefeatures of the relationship:

C ¼ 1448:96þ 4:59T� 0:053T2

þ 1:34ðS� 35Þ þ 0:016p(3.14)

in which T, S, and p are temperature, salinity,and depth, and the constants have the correctunits to yield C in m/s. The sound speed is1449 m/s at T ¼ 0�C, S ¼ 35, and p ¼ 0. Thesound speed increases by 4.5 m/s for DT ¼ þ1 K, by 1.3 m/s for DS ¼ þ 1, and by 16 m/sfor Dp ¼ 1000 dbar.

Sound speed is higher where the medium isless compressible. Seawater is less compressiblewhen it is warm, as noted in the previous poten-tial density discussion and apparent from thesimplified equation (3.14). Seawater is also lesscompressible at high pressure, where the fluidis effectively more rigid because the moleculesare pushed together. Salinity variations havea negligible effect in most locations. In theupper layers, where temperature is high, soundspeed is high, and decreases downward withdecreasing temperature (Figure 3.7). However,pressure increases with depth, so that at mid-depth, the decrease in sound speed due tocooler water is overcome by an increase insound speed due to higher pressure. In mostareas of the ocean, the warmwater at the surfaceand the high pressure at the bottom producemaximum sound speeds at the surface andbottom and a minimum in between. Thesound-speed minimum is referred to as theSOund Fixing And Ranging (SOFAR) channel.In Figure 3.6, the sound-speed minimum is atabout 700 m depth. In regions where tempera-ture is low near the sea surface, for instance athigh latitudes, there is no surface maximum insound speed, and the sound channel is foundat the sea surface.

Sound propagation can be represented interms of rays that trace the path of the sound(Figure 3.8). In the SOFAR channel, at about1100 m in Figure 3.8, sound waves directed at


moderate angles above the horizontal arerefracted downward, across the depth of thesound-speed minimum, and then refractedupward; they continue to oscillate about thesound-speed minimum depth. (Rays that travelsteeply up or down from the source will not bechanneled but may travel to the surface orbottom and be reflected there.) Low frequencysound waves (hundreds of hertz) can travelconsiderable distances (thousands of kilome-ters) along the SOFAR channel. This permitsdetection of submarines at long ranges and hasbeen used for locating lifeboats at sea. Usingthe SOFAR channel to track drifting subsurfacefloats to determine deep currents is describedin Chapter S6, Section S6.5.2 of the supple-mental materials located on the textbookWeb site.

The deep SOFAR channel of Figure 3.8b ischaracteristic of middle and low latitudes,

where the temperature decreases substantiallyas depth increases. At high latitudes where thetemperatures near the surface may be constantor even decrease toward the surface, the soundspeed can have a surfaceminimum (Figure 3.8a).The much shallower sound channel, calleda surface duct, may even be in the surface layer.In this case, downward directed sound raysfrom a shallow source are refracted upwardwhile upward rays from the subsurface sourceare reflected downward from the surface andthen refracted upward again. In this situation,detection of deep submarines from a surfaceship using sonar equipment mounted in thehull may not be possible and deep-towed sonarequipment may be needed. In shallow water(e.g., bottom depth<200m), reflection can occurboth from the surface and from the bottom.

A pulse transmitted from a source near theSOFAR channel axis does not appear to

FIGURE 3.7 For station Papa in the Pacific Ocean at 39�N, 146�W, August, 1959: (a) temperature (�C) and salinity (psu)profiles, (b) corrections to sound speed due to salinity, temperature, and pressure, (c) resultant in situ sound-speed profileshowing sound-speed minimum (SOFAR channel).

SOUND IN THE SEA 51

distant receivers as a sharp pulse but asa drawn-out signal rising slowly to a peak fol-lowed by a sharp cutoff. The peak before thecutoff is the arrival of the sound energy alongthe sound channel axis (direct signal), whilethe earlier arrivals are from sound that trav-eled along the refracted ray routes. It mightappear in Figure 3.8b that the refracted rayshave to travel a greater distance than thedirect ray and would thus be delayed, butthis is an illusion. Figure 3.8b is drawn withgross vertical exaggeration to enable the raysto be shown clearly, but the differences indistances traveled by refracted rays and thedirect rays are very small; the greater speed

in the refracted ray paths compensates forthe greater distance they travel, so the directray arrives last.

Sound is used widely to locate and observesolid objects in the water. Echo sounders areused to measure bottom depths to the ocean’smaximum depth of more than 11,000 m. SONAR(SOund Navigation And Ranging) can deter-mine the direction and distance to a submarineat ranges of hundreds of meters and to schoolsof fish at somewhat lesser ranges. Sidescansonars determine the structure of the oceanbottom and can be used to locate shipwrecks.Acoustically tracked Swallow floats (seeChapter S6, Section S6.5.2 of the supplemental

FIGURE 3.8 Sound raydiagrams: (a) from a shallowsource for a sound-speedprofile initially increasingwith depth in upper mixedlayer to a shallow minimumand then decreasing, and (b)from a sound source nearthe speed minimum in thesound channel for a typicalopen ocean sound-speedprofile.


material on the textbook Web site) providedsome of the first direct observations of deepcurrents. Current speeds (or the speed ofa ship relative to the water) are often measuredusing the reflection of sound waves from smallparticles moving with the water, applying theprinciple of Doppler shift. Because temperatureand density affect the sound velocity, sound canbe used to infer ocean water characteristics andtheir variations. Sound is used to measuresurface processes such as precipitation, ameasure-ment that is otherwise nearly impossible todetermine.

In echo sounding, short pulses of soundenergy are directed vertically downward wherethey reflect off of the bottom and return to theship. (Echo sounders are also used to detectshoals of fish,whose air bladders are good reflec-tors of sound energy. Modern “fish finders” aresimply low-cost echo sounders designed torespond to the fish beneath the vessel.) Theacoustic travel time, t, yields the depth D ¼Cot/2, where Co is the mean sound speedbetween the surface and the bottom. Trans-ducers in ordinary echo sounders are not muchlarger than the wavelength of the sound, so theangular width of the sound beam is large. Widebeams cannot distinguish the details of bottomtopography. For special sounding applications,much larger sound sources that form a narrowerbeam are used. It is also possible to improve theresolution by using higher frequencies (up to 100kHz or even 200 kHz), but the absorption ofsound energy by seawater increases roughly asthe square of the frequency, so higher frequencyecho sounders cannot penetrate as deeply.

Inhomogeneities distort an initial sharpsound pulse so that the signal received ata hydrophone is likely to have an irregular tailof later arrival sounds. This is referred to asreverberation. One source of reverberation is the“deep scattering layer,” which is biological innature. This layer is characterized by diel(day/night) vertical migrations of severalhundreds of meters; the organisms migrate

toward the sea surface at dusk to feed andback down at dawn. This layer was first identi-fied because of the scattering produced by theplankton and (gas-filled) fish bladders.

Sound is used to determine the speed ofocean currents and of ships, using a techniquecalled acoustic Doppler profiling (see ChapterS6, Section S6.5.5.1 of the supplemental materiallocated on the textbook Web site). Sound istransmitted from a source and reflects off theparticles (mainly plankton) in the water andreturns back to a receiver. If the source is movingrelative to the particles, then the received soundwave has a different frequency from the trans-mitted wave, a phenomenon called Dopplershifting. Doppler shift is familiar to anyonewho has listened to the sound of a siren whenan emergency vehicle first approaches (Dopplershifting the sound to a higher frequency and,therefore, a higher pitch) and then retreatsaway (Doppler shifting the sound to a lowerfrequency and lower pitch). Acoustic Dopplerspeed logs are common on ships and give a rela-tively accurate measure of the speed of the shipthrough the water. If the ship’s speed is trackedvery precisely using, for instance, GPS naviga-tion, then the ship speed can be subtractedfrom the speed of the ship relative to the waterto yield the speed of the water relative to theGPS navigation, providing a measure of currentspeeds. Acoustic Doppler current profilers arealso moored in the ocean to provide long-termrecords of current speeds.

Sound can be used to map the ocean’stemperature structure and its changes, througha technique called acoustic tomography (seeChapter S6, Section S6.6.1 of the supplementalmaterial located on the textbook Web site). Sincesound speed depends on temperature, temp-erature changes along a ray path result in traveltime changes. With extremely accurate clocks,these changes can be detected. If multiple raypaths crisscross a region, the travel time changescan be combined using sophisticated data anal-ysis techniques to map temperature changes in

SOUND IN THE SEA 53

the region. This technique has been especiallyuseful in studying the three-dimensional struc-ture of deep convection in regions and seasonsthat are virtually impossible to study fromresearch ships. Similar techniques have beenapplied to very long distance monitoring ofbasin-average ocean temperature, which ispossible because of the lack of attenuation ofsound waves over extremely long distances(Munk & Wunsch, 1982). However, large-scalemonitoring of ocean temperature changesusing sound has been eclipsed by the globaltemperatureesalinity profiling float array, Argo,which provides local as well as basin-averageinformation.

Muchmore information about ocean acousticscan be found in textbooks such as Urick (1983).

3.8. LIGHT AND THE SEA

This is a very brief introduction to a complexsubject. Full treatments are available in varioussources; some suggestions are Mobley (1995)and Robinson (2004).

Sunlight with a range of wavelengths entersthe sea after passing through the atmosphere.Within the upper layer of the ocean, up to 100m depth or more, the visible light interactswith the water molecules and the substancesthat are dissolved or suspended in the water.The light provides energy for photosynthesisand also heats the upper layer. Processes of back-scattering, absorption, and re-emission result inthe visible light (ocean color) that emerges backfrom the ocean surface into the atmosphere.This emerging radiation is then measured withinstruments above the sea surface, includingsatellites. For satellite observations, the atmo-sphere again affects the signal from the sea.Observations of ocean color by satellites canthen be related to the processes within the oceanthat affect the emerging light, including an abun-dance of phytoplankton, particulate organiccarbon, suspended sediment, and so forth.

Absorption (attenuation) of the sun’s energyin the upper layer depends on the materialswithin the water; therefore these materials affecthow heating is distributed in the surface layerand affects mixed layer processes. Generalcirculation models that are run with observedforcing sometimes use information about lightattenuation, affecting mixed layer formationand, consequently, sea surface temperature inthe model.

Section 3.8.1 describes the optical propertiesof seawater and Section 3.8.2 describes thequantity that is observed as ocean color. Exam-ples of observations are shown in Chapter 4.

3.8.1. Optical Properties

The sun irradiates the earth with a peak in thevisible spectrum (wavelengths from about 400to 700 nm, from violet to red, where 1 nm ¼10�9 m). Sunlight behaves differently in waterand air. The ocean absorbs light in much shorterdistances than the atmosphere. When this short-wave energy penetrates the sea, some of it isscattered, but much is absorbed, almost allwithin the top 100 m. The energy is attenuatedapproximately exponentially. This is the photic(euphotic) zone, where photosynthesis occurs.This penetration of solar energy into the ocean’supper layer is also important in the ocean’s heatbudget (Chapter 5).

A schematic overview of the ocean’s opticalprocesses is shown in Figure 3.9, after Mobley(1995), who provides much greater detail andprecise expressions for each of the quantitiesin the diagram. Each of the quantities can beobserved, with greater or lesser difficulty. Atthe top of the diagram, the external environ-mental quantities that determine the amountof radiation entering the ocean are the sun’sradiance distribution, which depends on itsposition and on sky conditions; the sea state,since this determines how much radiation isreflected without entering the sea; and the oceanbottom, if it is shallow enough to intercept the


light. The inherent optical properties of theseawater determine how it absorbs and scattersradiation, as a function of wavelength; thisdepends on the matter that is dissolved, sus-pended, or active (in the case of phytoplankton).

The environmental conditions and inherentoptical properties work together through a radi-ative transfer equation to set the radiometricquantities of the medium. Here it is useful toprovide some definitions of the radiometricquantities listed in the middle box of Figure 3.9.First, we note that light from a source, whichcould be at any point in a medium in which lightis diffused or scattered, illuminates a completesphere around the source. Therefore the solidangle, measured in “steradians” (sr), is a usefulmeasure, similar to area. Next, the flux of energyfrom the light is measured in Watts (J/sec). Theradiance is the flux of energy per unit area andper unit steradian; it is measured in units ofW/(sr m2). If the radiance is measured as a func-tion of wavelength of the light (i.e., spectralradiance), then its units are W/(sr m2 nm) ifwavelength is measured in nanometers.

The irradiance is the total amount of radiancethat reaches a given point (i.e., where youroptical measurement is made), so it is the sumof radiance coming in from all directions to the

observation point; therefore it is the integral ofradiance over all solid angles, and has units ofW/m2 for total irradiance, or W/(m2 nm) forspectral irradiance (which is a function of wave-length). Next, upwelling irradiance is defined asthe irradiance from all solid angles below theobservation point; downwelling irradiancewould come from all angles above that point.

Reflectance is the ratio of upwelling irradianceto downwelling irradiance, defined at a point;reflectance defined this way has no units. It isnot the same as actual reflected light from thesea surface. Rather, reflectance is the lightemerging from the ocean. For remote sensing,in which the radiation from the ocean’s surfaceis being measured from a specified location,rather than from all directions, reflectance canbe defined alternatively as the ratio of upwellingradiance to downwelling irradiance; in this case,reflectance has units of (sr�1).

Finally, the amount of radiation available forphotosynthesis (photosynthetically availableradiation; PAR) is measured in photons s�1 m�2.

Returning to Figure 3.9, the rightmost bottombox lists the apparent optical properties of theseawater. These include the rate at which lightis attenuated within the water column, andhow much light returns back out through the

Inherent opticalproperties of seawater

AbsorptionScattering

EnvironmentIncident radiance (sun

position and sky conditions)

Sea State Bottom condition

Radiometric quantities

Downwelling and upwellingirradiance

Photosynthetically availableradiation (PAR)

Apparent opticalproperties of the ocean

ReflectanceDownwelling and upwelling

irradiance attenuationPAR attenuation

Reflectance(ocean color)

Upper layer heating Photosynthesis

FIGURE 3.9 Schematicof optical processes inseawater. Adapted andsimplified from Mobley(1995), with added indi-cators of seawater heatingand photosynthesis, aswell as satellite observa-tion of ocean color.

LIGHT AND THE SEA 55

sea surface (indicated as reflectance). The irradi-ance and PAR are attenuated with increasingdepth as the radiation is absorbed, scattered,and used for photosynthesis by phytoplankton.Attenuation is often approximately exponential.If attenuation were exactly exponential, of theform I(z) ¼ Io e�Kz, where Io is the radiationintensity at the sea surface, I the intensity ata depth z meters below the surface, and K thevertical attenuation coefficient of the water,then the apparent optical properties would beexpressed in terms of the e-folding depth, K.The actual attenuation is not exponential, sothe attenuation coefficient, K, is proportionalto the depth derivative of the radiation intensity(and would be equal to the e-folding depth if thedependence were exponential).

The effects of depth and constant attenuationcoefficient on light intensity are illustrated inTable 3.3, from Jerlov (1976). The coefficient Kdepends mainly on factors affecting absorptionof light in the water and to a lesser extent onscattering. The last two columns of Table 3.3indicate the range of penetrations found inactual seawater.

The smallest attenuation coefficient in Table3.3 (K ¼ 0.02 m�1) represents the clearest oceanwater and deepest penetration of light energy.Energy penetrates coastal waters less readily

because of the extra attenuation due to sus-pended particulate matter and dissolved mate-rials. The largest attenuation coefficient listedin the table, K ¼ 2 m�1, represents very turbidwater with many suspended particles.

In seawater, the attenuation coefficient Kalso varies considerably with wavelength.Figure 3.10b shows the relative amounts ofenergy penetrating clear ocean water to 1, 10,and 50 m as a function of wavelength (solidcurves). Light with blue wavelengths penetratesdeepest; penetration by yellow and red is muchless. That is, blue light, with wavelength ofabout 450 nm, has the least attenuation in clearocean water. At shorter and longer wavelengths(in the ultraviolet and red), the attenuation ismuch greater. The increased attenuation in theultraviolet is not important to the ocean’s heatbudget, because the amount of energy reachingsea level at such short wavelengths is small.Much more solar energy is contained in andbeyond the red end of the spectrum. Virtuallyall of the energy at wavelengths shorter thanthe visible is absorbed in the top meter of water,while the energy at long wavelengths (1500 nmor greater) is absorbed in the top fewcentimeters.

All wavelengths are attenuated more inturbid water than in clear water. In clear ocean

TABLE 3.3 Amount of Light Penetrating to Specified Depths in Seawater as a Percentage of that Entering Throughthe Surface

Vertical Attenuation Coefficient K (mL1) Clearest Ocean Water Turbid Coastal Water

Depth (m) K ¼ 0.02 K ¼ 0.2 K ¼ 2

0 100% 100% 100% 100% 100%

1 98 82 14 45 18

2 96 67 2 39 8

10 82 14 0 22 0

50 37 0 0 5 0

100 14 0 0 0.5 0

Jerlov, 1976.


water, there is enough light at 50 to 100 m topermit a diver to work, but in turbid coastalwaters almost all of the energy may have beenabsorbed by a depth of 10 m. K is larger forturbid water than clear (Figure 3.10a), and theleast attenuation is in the yellow part of thespectrum. In turbid water, less energy pene-trates to 1 m and 10 m, and the maximum pene-tration is shifted to the yellow (Figure 3.10b).(The energy reaching 50 m in this turbidwater is too small to show on the scale of thisgraph.)

In clear ocean water, the superior penetra-tion of blue and green light is evident bothvisually when diving and also in color photo-graphs taken underwater by natural light.

Red or yellow objects appear darker in coloror even black as they are viewed at increasingdepths because the light at the red end of thespectrum has been absorbed in the upperlayers and little is left to be reflected by theobjects. Blue or green objects retain their colorsto greater depths.

The presence of plankton in seawater alsochanges the penetration depth of solar radia-tion, and hence the depth at which the sun’sheat is absorbed. This changes the way thesurface mixed layer develops, which can inturn impact the plankton, leading to a feedback.There are significant and permanent geograph-ical variations in this vertical distribution ofabsorption, since some regions of the world

FIGURE 3.10 (a) Attenuationcoefficient kl, as a function ofwavelength l (mm) for clearestocean water (solid line) and turbidcoastal water (dashed line). (b)Relative energy reaching 1, 10, and50 m depth for clearest ocean waterand reaching 1 and 10 m for turbidcoastal waters.


ocean have much higher biological productivitythan others.

3.8.2. Ocean Color

To the eye, the color of the sea ranges fromdeep blue to green to greenish yellow (Jerlov,1976). Broadly speaking, deep or indigo bluecolor is characteristic of tropical and equatorialseas, particularly where there is little biologicalproduction. At higher latitudes, the colorchanges through green-blue to green in polarregions. Coastal waters are generally greenish.

Two factors contribute to the blue color ofopen ocean waters at low latitudes. Becausewater molecules scatter the short-wave (blue)light much more than the long-wave (red) light,the color seen is selectively blue. In addition,because the red and yellow components ofsunlight are rapidly absorbed in the upper fewmeters, the only light remaining to be scatteredby the bulk of the water is blue. Looking at thesea from above, sky light reflected from thesurface is added to the blue light scatteredfrom the body of the water. If the sky is blue,the sea will still appear deep blue, but if thereare clouds, the white light reflected from thesea surface dilutes the blue scattered lightfrom the water and the sea appears lessintensely blue.

If there are phytoplankton in the water, theirchlorophyll absorbs blue light and also red light,which shifts the water color to green. (This isalso why plants are green.) The organic prod-ucts from plants may also add yellow dyes tothe water; these will absorb blue and shift theapparent color toward the green. These shiftsin color generally occur in the more productivehigh-latitude and coastal waters. In somecoastal regions, rivers carry dissolved organicsubstances that emphasize the yellowish greencolor. The red color that occurs sporadically insome coastal areas, the so-called red tide, iscaused by blooms of reddish brown phyto-plankton. Mud, silt, and other finely divided

inorganic materials carried into the ocean byrivers can impart their own color to the water.In some fjords, the low-salinity surface layermay be milky white from the finely divided“rock flour” produced by abrasion in theglaciers and carried down by the melt water.The sediment can be kept in suspension byturbulence in the upper layer for a time, butwhen it sinks into the saline water, it flocculates(forms lumps) and sinks more rapidly. Whendiving in such a region the diver may be ableto see only a fraction of a meter in the upperlayer but be able to see several meters in thesaline water below.

The color of seawater and depth of penetra-tion of light were traditionally judged usinga white Secchi disk (see Chapter S6, SectionS6.8 of the supplemental materials located onthe textbook Web site) lowered from the ship.This method has been superseded by a suite ofinstruments that measure light penetration atdifferent wavelengths, transparency of thewater at various wavelengths, and fluorescence.Most important, color observations are nowmade continuously and globally by colorsensors on satellites.

Ocean color is a well-defined quantity, relatedto reflectance (Figure 3.9 and definition inSection 3.8.1). Reflectance, or ocean color, canbe measured directly above the ocean’s surface.Observations of ocean color since the 1980shave been made from satellites, and must becorrected for changes as the light passesupward through the atmosphere. Ocean colorobservations are then converted, throughcomplex algorithms, to physically useful quan-tities such as the amount of chlorophyllpresent, or the amount of particulate organiccarbon, or the amount of “yellow substance”(gelbstoff) that is created by decaying vegeta-tion. With global satellite coverage, these quan-tities can be observed nearly continuously andin all regions.

Robinson (2004) provided a complete treat-ment of the optical pathways involved in ocean


color remote sensing, starting with consider-ation of the total radiance observed by the satel-lite sensor. Many pathways contribute to theobserved radiance. These can be grouped intoan atmospheric path radiance (Lp), a “water-leaving radiance” from just below the seasurface (Lw), and a radiance due to all surfacereflections (Lr) within the instantaneous fieldof view of the satellite sensor. The radiance Ls

received at the satellite sensor is

Ls ¼ Lp þ TLw þ TLr (3.15)

T is the transmittance, which gives theproportion of radiance that reaches the sensorwithout being scattered out of the field of view.

The water-leaving radiance provides theinformation about ocean color, so it is thedesired observed quantity. It is closely relatedto the reflectance; the ratio of water-leavingradiance just above the sea surface to downwel-ling irradiance incident on the sea surface is the“remote sensing reflectance,” or “normalizedwater-leaving radiance.” The three net radianceterms depend on the wavelength and on theturbidity of the seawater. The largest

contribution is from the atmospheric pathwayLp. The water-leaving and reflected radiancesare much smaller. Because of the weak signalstrength for the ocean pathways (water-leavingradiance), ocean color remote sensing requiresvery precise atmospheric correction of thevisible light sensed by the satellite. Complexradiative transfer models are invoked to carryout this correction and often the accuracy ofthe chlorophyll estimates depends critically onthis atmospheric correction. After correction,the resultant radiances are analyzed for variouscomponents related to biological activity, partic-ularly chlorophyll.

The biggest effect of chlorophyll on the spec-trum of reflectance (normalized water-leavingradiance) is to reduce the energy at the blueend of the spectrum compared with the spec-trum for clear water. This is demonstrated inFigure 3.11 (H. Gordon, personal communica-tion, 2009). Here the spectrum of radiance isshown with and without correction for theatmosphere. When the atmosphere is notremoved, there is virtually no differencebetween the spectra for low and high chloro-phyll waters. When the atmospheric signal is

FIGURE 3.11 Example of observationsof water-leaving radiance observed by theMulti-angle Imaging SpectroRadiometer(MISR), with bands observed by satellitecolor sensors indicated. Solid curves: lowchlorophyll water (0.01 mg/m3). Dottedcurves: high chlorophyll water (10.0 mg/m3).The two lower curves have the atmosphericsignal removed. (H. Gordon, personalcommunication, 2009.)


removed, the desired difference emerges. Thehigh chlorophyll spectrum is depressed atthe blue end of the spectrum and elevated atthe green and red.

Ocean color observations from satellites canalso be used as a proxy for the attenuation prop-erties of seawater, which can be used in mixedlayer models that are set up to be run withobserved atmospheric forcing. Absorption ofsolar radiation in the ocean heats the upperlayer. The time and space distribution of absorp-tion is directly related to the substances in thewater column, and this affects ocean color. Inpractice, at present most mixed layer modelsin ocean general circulation models use a sumof two exponentially decaying functions thatare proxies for attenuation of red light (quicklyabsorbed) and blue-green light (penetratingmuch deeper), with coefficients based onassumption of a particular Jerlov (1976) watertype (Paulson & Simpson, 1977). However,explicit incorporation of biological effects onattenuation (incorporation of ocean color obser-vations and of bio-optical models along withmixed layer models) is being tested widelyand is a likely direction for the future, sincethe effects on modeled mixed layer temperatureare clear (Wu, Tang, Sathyendranath, & Platt,2007) and can in fact affect the temperatureof the overlying atmosphere (Shell, Frouin,Nakamoto, & Somerville, 2003).

3.9. ICE IN THE SEA

Ice in the sea has two origins: the freezing ofseawater and the ice broken off from glaciers.The majority of ice comes from the first of thesesources and is referred to as sea ice; the glacierssupply “pinnacle” icebergs in the NorthernHemisphere and flat "tabular" icebergs in theSouthern Hemisphere. Sea ice alters the heatand momentum transfers between the atmo-sphere and the ocean, is a thermal insulator,damps surface waves, changes the temperature

and salinity structure in the upper layer bymelting and freezing, and is a major hindranceto navigation. Ice cover is an important part ofEarth’s climate feedbacks because of its highreflectivity, that is, its high albedo (Section5.4.3). The iceealbedo feedback, which affectsclimate, is described in Section 5.4.5, and is espe-cially important in the Arctic (Section 12.8).

3.9.1. Freezing Process

When water loses sufficient heat (by radia-tion, conduction to the atmosphere, convection,or evaporation) it freezes to ice, in other words,it changes to the solid state. Initial freezingoccurs at the surface and then the ice thickensby freezing at its lower surface as heat is con-ducted away from the underlying waterthrough the ice to the air.

The initial freezing process is different forfresh and low-salinity water than for moresaline water because the temperature at whichwater reaches its maximum density varieswith salinity. Table 3.4 gives the values of thefreezing point and temperature of maximumdensity for water of various salinities. (Notethat the values are for freezing, etc., at atmo-spheric pressure. Increased pressure lowersthe freezing point, which decreases by about0.08 K per 100 m increase in depth in the sea.)

To contrast the freezing process for fresh-water and seawater, first imagine a freshwaterlake where the temperature initially decreasesfrom about 10�C at the surface to about 5�C

TABLE 3.4 Temperatures of the Freezing Point (tf) andof Maximum Density (trmax) for Fresh andSalt Water

S 0 10 20 24.7 30 35 psu

tf 0 �0.5 �1.08 �1.33 �1.63 �1.91�C

trmax þ3.98 þ1.83 �0.32 �1.33 d ��C

Note that the values for freezing and so forth are at atmospheric

pressure. Increased pressure lowers the freezing point, which

decreases by about 0.08 K per 100 m increase in depth in the sea.


at about 30 m depth. As heat is lost through thesurface, the density of the water increases andvertical convective mixing (overturn) occurswith the temperature of the surface water layergradually decreasing. This continues until theupper mixed layer cools to 3.98�C and thenfurther cooling of the surface water causes itsdensity to decrease and it stays near the top.The result is a rapid loss of heat from a thinsurface layer, which soon freezes. For seawaterof salinity ¼ 35 psu of the same initial temper-ature distribution, surface cooling first resultsin a density increase and vertical mixing byconvention currents occurs through a graduallyincreasing depth, but it is not until thewhole column reaches �1.91�C that freezingcommences. As a much greater volume ofwater has to be cooled through a greatertemperature range than in the freshwatercase, it takes longer for freezing to start insalt water than in freshwater. A simple calcula-tion for a column of freshwater of 100 cm depthand 1 cm2 cross-section initially at 10�C showsthat it takes a heat loss of l63 J to freeze the top1 cm layer, whereas for a similar column ofseawater of S ¼ 35 psu it takes a loss of 305 Jto freeze the top 1 cm because the wholecolumn has to be cooled to �1.91�C ratherthan just the top 1 cm to 0�C for the freshwater.

Note that as seawater of salinity <24.7 psuhas a higher temperature of maximum densitythan its freezing point, it will behave in amannersimilar to freshwater, although with a lowerfreezing point. For seawater of salinity >24.7psu, (in high latitudes) the salinity generallyincreases with depth, and the stability of thewater column usually limits the depth ofconvection currents to 30e50 m. Therefore icestarts to form at the surface before the deepwater reaches the freezing point.

Generally, sea ice forms first in shallow waternear the coast, particularly where the salinity isreduced by river runoff and where currents areminimal. When fully formed, this sea ice con-nected to the shore is known as “fast ice.” The

first process is the formation of needle-likecrystals of pure ice, which impart an “oily”appearance to the sea surface (grease or frazilice). The crystals increase in number and forma slush, which then thickens and breaks upinto pancakes of approximately one meteracross. With continued cooling, these pancakesgrow in thickness and lateral extent, eventuallyforming a continuous sheet of floe or sheet ice.

Once ice has formed at the sea surface, whenthe air is colder than the water below, freezingcontinues at the lower surface of the ice andthe rate of increase of ice thickness depends onthe rate of heat loss upward through the ice(and any snow cover). This loss is directlyproportional to the temperature differencebetween top and bottom surfaces and inverselyproportional to the thickness of the ice and snowcover.

With very cold air, a sheet of sea ice of up to10 cm in thickness can form in 24 hours, therate of growth then decreasing with increasingice thickness. Snow on the top surface insulatesit and reduces the heat loss markedly, depend-ing on its degree of compaction. For instance,5 cm of new powder snow may have insulationequivalent to 250e350 cm of ice, while 5 cm ofsettled snow can be equivalent to only 60e100cm of ice, and 5 cm of hard-packed snow canbe equivalent to only 20e30 cm of ice.

As an example of the annual cycle of thedevelopment of an ice sheet at a location in theCanadian Arctic, ice was observed to start toform in September, was about 0.5 m thick inOctober, 1 m in December, 1.5 m in February,and reached its maximum thickness of 2 m inMaydafter which it started to melt.

3.9.2. Brine Rejection

In the initial stage of ice-crystal formation, saltis rejected and increases the density of the neigh-boring seawater, some of which then tends tosink and some of which is trapped among theice crystals forming pockets called “brine cells.”

ICE IN THE SEA 61

The faster the freezing, the more brine is trapped.Sea ice in bulk is therefore not pure water-ice buthas a salinity of as much as 15 psu for new ice(and less for old ice because gravity causes thebrine cells to migrate downward in time). Withcontinued freezing, more ice freezes out withinthe brine cells leaving the brine more saline, ina process called brine rejection. Some of the saltsmay even crystallize out.

Because of brine rejection, the salinity of first-year ice is generally 4e10 psu, for second-yearice (ice that has remained frozen beyond the firstyear) salinity decreases to 1e3 psu, and formultiyear ice salinity may be less than 1 psu. Ifsea ice is lifted above sea level, as happenswhen ice becomes thicker or rafting occurs, thebrine gradually trickles down through it andeventually leaves almost salt-free, clear old ice.Such ice may be melted and used for drinkingwhereas melted new ice is not potable. Sea ice,therefore, is considered a material of variablecomposition and properties that depends verymuch on its history. (For more detail seeDoronin & Kheisin, 1975.)

As a result of brine rejection, the salinity ofthe unfrozen waters beneath the forming seaice increases. When this occurs in shallowregions, such as over continental shelves, theincrease in salinity can be marked and can resultin formation of very dense waters. This is thedominant mechanism for formation of thedeep and bottom waters in the Antarctic(Chapter 13), and for formation of the densestpart of the North Pacific Intermediate Waterin the Pacific (Chapter 10). Brine rejection isa central process for modification of watermasses in the Arctic as well (Chapter 12).

3.9.3. Density and Thermodynamicsof Sea Ice

The density of pure water at 0�C is 999.9kg/m3 and that of pure ice is 916.8 kg/m3.However the density of sea ice may be greaterthan this last figure (if brine is trapped among

the ice crystals) or less (if the brine has escapedand gas bubbles are present.) Values from 924 to857 kg/m3 were recorded on the NorwegianMaud Expedition (Malmgren, 1927).

The amount of heat required to melt sea icevaries considerably with its salinity. For S ¼ 0psu (freshwater ice) it requires 19.3 kJ/kg from�2�C and 21.4 kJ/kg from �20�C, while for seaice of S ¼ 15 psu, it requires only 11.2 kJ/kgfrom�2�C but 20.0 kJ/kg from�20�C. The smalldifference of heat (2.1 kJ/kg) needed to raise thetemperature of freshwater ice from �20�C to�2�C is because no melting takes place; that is,it is a true measure of the specific heat of pureice. However, for sea ice of S ¼ 15 psu, moreheat (8.8 kJ/kg) is required to raise its tempera-ture through the same range, because some icenear brine cells melts and thus requires latentheat of melting as well as heat to raise its temper-ature. Note also that less heat is needed to meltnew ice (S ¼ 15 psu) than old ice, which hasa lower salinity.

3.9.4. Mechanical Properties of Sea Ice

Because of the spongy nature of first-year seaice (crystals þ brine cells) it has much lessstrength than freshwater ice. Also, as fast freezingresults in more brine cells, the strength of iceformed thisway is less thanwhen freezing occursslowly; in other words, sea ice formed in verycold weather is initially weaker than ice formedin less cold weather. As the temperature of icedecreases, its hardness and strength increase,and ice becomes stronger with age as the brinecells migrate downward. When ice forms incalmwater, the crystals tend to lineup inapatternand such ice tends to fracture along cleavageplanes more easily than ice formed in roughwater where the crystals are more randomlyarranged and cleavage planes are not formed.

The mechanical behavior of sea ice iscomplex when temperature changes. As the icetemperature decreases below its freezing point,the ice expands initially, reaches a maximum


expansion, and then contracts. For instance, anice floe of S ¼ 4 psu will expand by 1 m per1 km length between �2 and �3�C, reaches itsmaximum expansion at �10�C, and thereaftercontracts slightly. Ice of S ¼ 10 psu expands4 m per 1 km length from �2 to �3�C, andreaches its maximum expansion at �18�C. Theexpansion on cooling can cause an ice sheet tobuckle and “pressure ridges” to form, whilecontraction on further cooling after maximumexpansion results in cracks, sometimes wide,in the ice sheet.

Pressure ridges can also develop as a result ofwind stress on the surface driving ice sheetstogether. The ridges on top are accompaniedby a thickening of the lower surface of the iceby four to five times the height of the surfaceridges. Sea ice generally floats with about five-sixths of its thickness below the surface andone-sixth above, so relatively small surfaceridges can be accompanied by deep ridgesunderneath d depths of 25 to 50 m below thesea surface have been recorded. Thickening ofan ice sheet may also result from rafting whenwind or tide forces one ice sheet on top ofanother or when two sheets, in compression,crumble and pile up ice at their contact. Oldridges, including piled up snow, are referredto as hummocks. As they are less saline thannewer pressure ridges, they are stronger andmore of an impediment to surface travels thanthe younger ridges.

3.9.5. Types of Sea Ice and its Motion

Sea ice can be categorized as fast ice (attachedto the shore), pack ice (seasonal to multiyear icewith few gaps), and cap ice (thick, mostly multi-year ice), as described in Section 12.7.1. Severalforces determine the motion of sea ice if it isnot landfast:

(a) Wind stress at the top surface (themagnitude depending on the wind speedand the roughness of the ice surface as

ridges increase the wind stress). Typical icespeeds are 1 to 2% of the wind speed.

(b) Frictional drag on the bottom of an ice sheetmoving over still water tends to slow itdown, while water currents (ocean andtidal) exert a force on the bottom of the ice inthe direction of the current. Because currentspeeds generally decrease with increase indepth, the net force on deep ice and icebergswill be less than on thin ice, and pack ice willmove past icebergs when there is significantwind stress.

(c) In the cases of (a) and (b), the effect of theCoriolis force (Section 7.2.3) is to divertthe ice motion by 15e20 degrees to theright of the wind or current stress in theNorthern Hemisphere (to the left in theSouthern Hemisphere). (It was theobservation of the relation between winddirection and ice movement by Nansen,and communicated by him to Ekman, thatcaused the latter to develop his well-known theory of wind-driven currents.)It is convenient to note that as surfacefriction causes the surface wind to blow atabout 15 degrees to the left of the surfaceisobars, the direction of the latter isapproximately that in which the ice islikely to drift (Northern Hemisphere).

(d) If the ice sheet is not continuous, collisionsbetween individual floes may occur witha transfer of momentum (i.e., decrease ofspeed of the faster floe and increase ofspeed of the slower). Energy may go intoice deformation and building up ridgesat impact. This is referred to as internalice resistance and increases with iceconcentration, that is, the proportion of areacovered by ice. The effect of upper surfaceroughness (R on a scale of 1 to 9) and iceconcentration (C on a scale of 1 to 9) on thespeed of the ice V (expressed as a percentageof the wind speed) is given by: V ¼ R(1 �0.08�C) (taken to only one decimal place),so that the speed of the ice increases with

ICE IN THE SEA 63

roughness but decreases with increasedice concentration. Note that for very closepack ice, stresses of wind or current areintegrated over quite large areas and thelocal motion may not relate well to the localwind.

3.9.6. Polynyas and Leads

Regions of nearly open water within the icepack are often found where one might expectto find ice. These open water areas are criticalfor airesea heat exchange, since ice is a rela-tively good insulator. Small breaks between icefloes are called leads; these are created by motionof the ice pack and have random locations.Larger recurrent open water areas are calledpolynyas. There are two types of polynyas,depending on the mechanism maintainingthe open water (Figure 3.12; see also Barber &Massom, 2007):

1. Latent heat polynyas are forced open by winds,often along coasts or ice shelf edges. New icesoon forms; latent heat from the forming seaice is discharged to the atmosphere at a rateof as much as 200e500 W/m2.

2. Sensible heat polynyas result from relativelywarm water upwelling to the surfaceand melting the ice there. Another termoften encountered is flaw polynya, whichmeans that the polynya occurs at theboundary between fast ice and pack ice.Because most polynyas include a mixtureof these forcings, nomenclature is tendingtoward being more specific about theforcing (mechanicalewind; convectiveemelting: Williams, Carmack, & Ingram,2007).

Wind-forced polynyas are usually near coast-lines or the edges of ice shelves or fast ice, wherewinds can be very strong, often forced by stronglandesea temperature differences (katabaticwinds). The open water is often continuallyfreezing in these polynyas since they are keptopen through mechanical forcing. These wind-forced polynyas act as ice factories, producinglarger amounts of new ice than regions wherethe ice is thicker and airesea fluxes are mini-mized by the ice cover. If these polynyas occurover shallow continental shelves, the brinerejected in the ongoing sea ice formationprocess, together with temperatures at the

Wind-forced (latent heat) polynya

Melting (sensible heat) polynya, driven by mixing

Wind

Sea ice

Brine rejection

Heat loss

Polynya

Dense shelf water

Warm, saltier

Cold, fresher

Sea ice

Vertic

al

excu

rsion

Tidal mixing Melting

Cold, fresher

Cold, saltier

(b)(a)

Polynya

Heat loss

FIGURE 3.12 Schematics of polynya formation: (a) latent heat polynya kept open by winds and (b) sensible heat polynyakept open by tidal mixing with warmer subsurface waters (after Hannah et al., 2009).


freezing point, can produce especially denseshelf waters. This is one of the major mecha-nisms for creating very dense waters in theglobal ocean (Section 7.11), particularly aroundthe coastlines of Antarctica (Chapter 13) andthe Arctic (Chapter 12), as well as the densest(intermediate) water formed in the North Pacificin the Okhotsk Sea (Chapter 10).

Polynyas that are maintained by meltingwithin the ice pack result from mixing of thecold, fresh surface layer with underlyingwarmer, saltier water. These polynyas mightalso produce sea ice along their peripherysince the airesea fluxes will be larger thanthrough the ice cover, but the upward heatflux from the underlying warmer water meansthat they produce new ice much less efficientlythan wind-forced polynyas. The vertical mixingcan result from convection within the polynya,which can occur in deep water formation sitessuch as the Odden-Nordbukta in the GreenlandSea (Section 12.2.3). In shallow regions, the mix-ing process can be greatly enhanced by tidesmoving the waters over undersea banks(Figure 3.12b). A number of the well-knownpolynyas in the Canadian Archipelago inthe Arctic Ocean are tidally maintained(Figure 12.23 from Hannah, Dupont, & Dunphy,

2009), as is a recurrent polynya over KashevarovBank in the Okhotsk Sea (Figure 10.29).

3.9.7. Ice Break-up

Ice break-up is caused by wave action, tidalcurrents, and melting. Melting of ice occurswhen it gains enough heat by absorption ofsolar radiation and by conduction from theair and from nearby seawater to raise itstemperature above the melting point. Theabsorption of radiation depends on the albedoof the surface (proportion of radiationreflected), which varies considerably; forexample, the albedo for seawater is from 0.05to 0.10 (it is a very good absorber of radiation),for snow-free sea ice it is from 0.3 to 0.4, whilefor fresh snow it is 0.8 to 0.9. Dark materials,like dirt and dust, have a low albedo of 0.1to 0.25 and absorb radiation well. Such mate-rial on ice can form a center for the absorptionof radiation and consequent melting of icearound it, so puddles can form. These canabsorb heat because of the low albedo ofwater and may even melt right through anice sheet. When any open water forms, itabsorbs heat and causes rapid melting of icefloating in it.

ICE IN THE SEA 65

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