J Geod (2009) 83:537–545DOI 10.1007/s00190-008-0264-3

ORIGINAL ARTICLE

Characterization of diurnal cycles in ZTD from a decade of globalGPS observations

Shuanggen Jin · O. F. Luo · S. Gleason

Received: 26 March 2008 / Accepted: 22 August 2008 / Published online: 20 September 2008© Springer-Verlag 2008

Abstract The diurnal cycle of the tropospheric zenith totaldelay (ZTD) is one of the most obvious signals for the variousphysical processes relating to climate change on a short timescale. However, the observation of such ZTD oscillations ona global scale with traditional techniques (e.g. radiosondes)is restricted due to limitations in spatial and temporal resolu-tion. Nowadays, the International GNSS Service (IGS) pro-vides an important data source for investigating the diurnaland semidiurnal cycles of ZTD and related climatic signals.In this paper, 10 years of ZTD data from 1997 to 2007 with a2-hour temporal resolution are derived from global positio-ning system (GPS) observations taken at 151 globally distri-buted IGS reference stations. These time series are used toinvestigate diurnal and semidiurnal oscillations. Significantdiurnal and semidiurnal oscillations of ZTD are found for allGPS stations used in this study. The diurnal cycles (24 hoursperiod) have amplitudes between 0.2 and 10.9 mm with anuncertainty of about 0.5 mm and the semidiurnal cycles (12 hperiod) have amplitudes between 0.1 and 4.3 mm with anuncertainty of about 0.2 mm. The larger amplitudes of thediurnal and semidiurnal ZTD cycles are observed in the low-latitude equatorial areas. The peak times of the diurnal cyclesspread over the whole day, while the peak value of the semi-diurnal cycles occurs typically about local noon. These GPS-derived diurnal and semidiurnal ZTD signals are similar with

S.G. Jin (B) · O. F. LuoKorea Astronomy and Space Science Institute, 61-1, Whaam-dong,Yuseong-gu, Daejeon 305-348, South Koreae-mail: sgjin@kasi.re.kr; sg.jin@yahoo.com

S.G. JinCenter for Space Research, University of Texas at Austin,Austin, TX, USA

S. GleasonNational Oceanography Centre, Southampton, UK

the surface pressure tides derived from surface synoptic pres-sure observations, indicating that atmospheric tides are themain driver of the diurnal and semidiurnal ZTD variations.

Keywords Zenith tropospheric delay · Diurnal cycle ·Atmospheric tide · IGS

1 Introduction

The tropospheric zenith total delay (ZTD) is the integratedrefractivity along a vertical path through the neutral atmos-phere:

ZTD = cτ = 10−6

∞∫

0

N (s)ds (1)

where c is the speed of light in a vacuum, τ is the delaymeasured in units of time and N is the neutral atmosphe-ric refractivity. The refractivity N is empirically related tostandard meteorological variables (Davis et al. 1985), inclu-ding the hydrostatic component (Nh) and the wet component(Nw). Thus, ZTD is the sum of the hydrostatic or dry delay(ZHD) and non-hydrostatic or wet delay (ZWD) due to theeffects of dry gases and water vapor. The dry componentis related to the atmospheric pressure at the surface, whilethe wet component can be transformed into the precipitablewater vapor (PWV) and plays an important role in energytransfer and climatic changes (Bevis et al. 1994; Duan et al.1996; Tregoning et al. 1998; Hernandez-Pajares et al. 2001).Therefore, ZTD is an important parameter of the atmosphere,which is closely related to weather and climate phenomena onvarious temporal and spatial scales. The diurnal cycle of ZTDis one of the most obvious climate signals, which reflectsmost physical processes (such as convection, radiation and

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atmospheric tides) on a short time scale. For example, thevariations of the atmospheric tides at the solar day (diurnal)and half solar day (semidiurnal) periods due to thermal andgravitational excitation from the Sun may cause oscillationsin ZTD at these tidal frequencies. However, the observationof such ZTD oscillations on a global scale with traditionaltechniques (e.g. radiosondes) is restricted due to limitationsin spatial and temporal resolution.

Nowadays, the global positioning system (GPS) has beenwidely used to determine ZTD with a high temporal-resolution (Emardson et al. 1998; Jin et al. 2007). TheGPS-derived ZTD data have several advantages, such ascontinuity, availability under all weather conditions, highresolution, long-term stability and low cost (Ware et al. 2000).Moreover, the GPS-derived ZTDs are highly accurate andhave proven consistent with other observation techniques,e.g., the very long baseline interferometry (VLBI) and radio-sondes (Elgered et al. 1997; Bevis et al. 1994; Rocken et al.1993; Duan et al. 1996; Emardson et al. 1998; Behrend et al.2000; Snajdrova et al. 2005). Therefore, the GPS-derivedZTDs have been widely applied in meteorology and clima-tology on various time scales, e.g., numeric weather predic-tion using wet delay derived PWV estimates (e.g., Kuo et al.1993; Gendt et al. 2004) and studying diurnal variations ofPWV (Dai et al. 2002; Wu et al. 2003). Although there havebeen many regional applications of ground-based GPS data(e.g., Dai et al. 2002), only a few studies have been conductedto take advantage of the growing global International GNSSService (IGS) network (Beutler et al. 1999; Hagemann et al.2003; Deblonde et al. 2005). For example, Humphreys et al.(2005) investigated semidiurnal variation in ZTD, but theyonly used surface pressure data at 13 sites and several years ofIGS-supplied ZTD. In this paper, a global 10-year ZTD dataset at over 151 sites is generated from the currently existingglobal IGS network for 1997–2007 with various geophysi-cal models’ corrections. These data are used to study diurnaland semidiurnal oscillations of ZTD on a global scale. Thepossible reasons of GPS-derived subdiurnal signals in ZTDare further discussed by comparing with three-hourly surfacesynoptic pressure data from more than global 8000 land andocean weather stations.

2 GPS data analysis and post-processing

The International GNSS (Global Navigation SatelliteSystems) Service (IGS) was formally established in 1993 bythe International Association of Geodesy (IAG), and beganroutine operations on 1 January 1994 (Beutler et al. 1999).The IGS coordinates a worldwide network of permanent tra-cking stations with about 350 GPS stations, which are finan-ced and operated by numerous organizations, providing thehigh quality data products for use in GNSS related Earth

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Fig. 1 GPS-sites used in this study

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Fig. 2 Number of IGS stations since 1997. The solid triangles are theall IGS stations and the circles are IGS stations used in this study

science research, navigation application and educationaloutreach. Since 1998, the IGS has regularly generated acombined tropospheric product in the form of weekly filescontaining ZTD in 2-h time intervals using its network of tra-cking stations (ftp://cddis.gsfc.nasa.gov/gps/products/trop_new). However, the IGS did not provide the ZTD productsbefore 1998, and furthermore, Humphreys et al. (2004)demonstrated a drastically attenuated oscillation in the IGS-provided ZTD products between during 1997–2000 and2000–2004, which was probably due to the used algorithmand ongoing changes in the network operations.

For this study we selected a set of 151 globally distributedIGS sites with continuous observations spanning at least fiveyears (Fig. 1). About 80 sites have 10 years of continuousdata and about 80% of all sites have 8 years of continuousobservations from 1999 to 2007 (see Fig. 2). The GAMITsoftware package (King and Bock 2005) was used for thedata processing to estimate station positions, satellite orbitsand the 2-hourly ZTD and atmospheric gradients. Here theIGS final satellite orbits, IGS Earth orientation parameters,

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Diurnal ZTD cycles from GPS observations 539

0 2 4 6 8 100.0

1.0

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Uncertainty of ZTD (mm)

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TD

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Fig. 3 Histogram of uncertainty of ZTD at all GPS sites

1997 1999 2001 2003 2005 20072300

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D (

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TD

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Fig. 4 Times series of zenith total delay (ZTD) (upper), power spec-trum (middle) and mean diurnal ZTD values at each of local time(LT = 1, 3, 5, . . . , 23) over the entire period with error bars (bottom)at Wuhan (WUHN), China

azimuth- and elevation-dependent antenna phase centermodels, an elevation angle cutoff of 7◦ and a mapping func-tion (hydrostatic and wet) (Niell 1996) as recommendedby Byun et al. (2005) were used in the data processing.Meanwhile, the IERS03 solid Earth tide model (McCarthy

and Petit 2004) and ocean tide model FES2004 (Lyard et al.2006) were used. The output of the data processing consists ofa 10-year continuous ZTD time series with a temporal resolu-tion of 2 h and their uncertainties from the GAMIT softwareas shown in Fig. 3. The mean uncertainty of the resulting ZTDestimations is about 1.8 mm. Figure 4 shows a case of the 10-year ZTD time series (upper), power spectrum (middle) andthe mean diurnal ZTD values (bottom) at local times (LT)in two hour increments (LT = 1, 3, 5, . . . , 23) at Wuhan(WUHN), China, where the mean diurnal ZTD values arecalculated from the 2-h ZTD time series over 10 years.Significant annual variations (upper panel) and subdiurnalvariations with obvious 12 and 24 h periods are observed. Tobetter demonstrate the short time scale variation, the diur-nal component (24 h period, S1) and semidiurnal component(12 h period, S2) of the generated ZTD time series are ana-lyzed using the harmonic function shown below

ZTDt = a +4∑

k=1

[Sk sin(2π(t − t0)/pk + ϕk)] + εt (2)

where a is the constant term, Sk and ϕk are the amplitude andphase at periods pk(=1 year, 0.5 year, 1 day and 0.5 day), res-pectively, and εt is the residual. Through the method of leastsquares we can determine the unknown parameters in Eq. 2for each station using the whole 10-year data set with 2-hsampling as well as their formal uncertainties, e.g., ampli-tudes and phases of ZTD variations at annual, semiannual,diurnal and semidiurnal time scales. Here the diurnal andsemidiurnal variations are analyzed and discussed in thefollowing sections.

3 Results and discussion

3.1 Diurnal and semidiurnal ZTD cycles

The 10-year GPS-derived ZTD time series has been used toanalyze the diurnal and semidiurnal ZTD cycles and theirfeatures. Figure 5a shows a colour coded map of diurnalZTD amplitudes derived from the GPS data. The diurnalcycle (S1) has amplitudes between 0.2 and 10.9 mm withan uncertainty of about 0.5 mm. As illustrated in Fig. 6, thediurnal ZTD amplitudes reduce with increasing latitude withthe largest amplitudes appearing in the low-latitude equa-torial areas, in particular in tropical Asia and the Gulf ofMexico. At these low latitudes, amplitudes of up to 10.9 mmare observed, while the high latitude areas reveal generallylower diurnal ZTD amplitudes. The peak values of the diur-nal cycles occur spreading over the whole day (Fig. 7a). Forthe European stations there appears to be a preference forthe second half of the day. At the semidiurnal cycle (S2),

amplitudes between 0.1 and 4.3 mm with an uncertainty of

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Fig. 5 Diurnal variation amplitudes (mm). a from GPS-derived ZTDand b from COADS surface pressure data adjusted by a scale factor(2.28 mm/hPa)

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Fig. 6 Diurnal ZTD amplitudes as a function of station latitude

about 0.2 mm are observed (Fig. 8). Similar to the diurnalresults mentioned above, the largest semidiurnal amplitudesare also found in low-latitude equatorial areas (see Fig. 9).The first peak of the semidiurnal cycle occurs typically aro-und local noon (see Fig. 10). These diurnal and semidiurnal

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ruoH

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Fig. 7 Time of diurnal peak values at local time (LT: hour) where ateach GPS sites longitude the Sun is at its highest elevation at 12:00LT. a from global IGS GPS observations and b from COADS surfacepressure data

cycles of ZTD may be due to certain short time scalephysical processes such as diurnal convection, atmospherictides, general circulation and the coupling between the lowerand the middle and upper atmosphere.

3.2 Seasonal variability of the diurnal and semidiurnal ZTDcycles

The diurnal and semidiurnal ZTD is expected to vary undervarious climate conditions, such as the season, temperature,solar radiation, etc. In the following, the diurnal and semi-diurnal variability of ZTD is investigated in different sea-sons. The averaged diurnal ZTD variations on a global scalefor March–April–May (MAM), June–July–August (JJA),September–October–November (SON) and December–January–February (DJF), have been considered individually.These represent the spring, summer, autumn and winter inthe Northern Hemisphere and the autumn, winter, spring andsummer in the Southern Hemisphere. Figure 11 shows themonthly diurnal ZTD variation anomalies (mm) at Wuhan(WUHN), China, namely the monthly diurnal ZTD meanat each of local times (LT= 1, 3, 5, . . . , 23) minus the total

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Diurnal ZTD cycles from GPS observations 541

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mm

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(a)

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Fig. 8 Semidiurnal variation amplitudes (mm). a from GPS-derivedZTD and b from COADS surface pressure data adjusted by a scalefactor (2.28 mm/hPa)

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iatio

n am

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de (

mm

)

Fig. 9 Semidiurnal ZTD amplitudes as a function of station latitude

average for each month over the whole period. It has revealeda significant seasonal dependence of the subdiurnal ZTDoscillations. For example, the diurnal ZTD variation has asignificant peak around noon, but in summer there is a second

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Time (LT: hour)

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Fig. 11 Mean diurnal ZTD variation anomalies (mm) for each monthat Wuhan (WUHN), China

marked peak around midnight, indicating a significantsemidiurnal cycle in summer (Fig. 12). The diurnal andsemidiurnal ZTD signals for each season are extractedfrom GPS-derived ZTDs using the same harmonic analysis

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Time (LT: hour)

Seaso

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TD

anom

aly

(m

m)

SpringSummerAutumnWinter

Fig. 12 Mean diurnal ZTD cycle anomalies for each season at Wuhan(WUHN), China

as described by Eq. 2. The results are further analyzed toexplore possible seasonal dependence of the diurnal andsemidiurnal oscillations. Generally the largest diurnal ZTDamplitudes are observed mainly in the low- and mid-latituderegions for all seasons (Fig. 13). The diurnal ZTD amplitudesare generally larger during summer than during winter. Forexample, for December-January-February (DJF), the diurnalZTD amplitudes are consistently larger in the Southernhemisphere (summer) than in the Northern hemisphere(winter). In contrast, the semidiurnal ZTD amplitudes arerelatively weaker than the diurnal ones in their correspon-ding seasons and moreover is the seasonal variability notobvious (see Fig. 14).

3.3 Discussion

The atmospheric density changes the refractive index of thezenith column of air under the influence of the atmospherictides, which causes oscillations in the ZTD at tidal frequen-cies. Thus, the oscillations in ZTD within periods of a solarday (diurnal) and half a solar day (semidiurnal) may reflectthe diurnal and semidiurnal tides induced on the atmosphereby thermal and gravitational excitation from the Sun. Underthe assumption of hydrostatic equilibrium, the change inpressure with height is related to total density at altitude hthrough the approximate relationship with hydrostatic equi-librium approximation as

d p = −ρ(h)g(h)dh (3)

where ρ(h)and g(h) are the density and gravity at the altitudeh, respectively. Disregarding the change in the accelerationof gravity g with respect to height, the zenith hydrostaticdelay (ZHD) can be further deduced as (Saastamoinen 1973)

ZHD = kp0 (4)

where k is a scale factor (2.28 mm/hPa) and p0 is the pressureat height h0 (Davis et al. 1985), namely ZHD = 2.28 p0. Thescale factor k varies less than 1% even under severe weatherconditions.

As the hydrostatic component ZHD accounts for approxi-mately 90% of ZTD, ZTD is strongly correlated with surfacepressure p0 at the site. It can be seen that if subdiurnal surfacepressure varies by 1 hPa, the scale factor predicts a subdiurnalZTD variation with an amplitude of 2.28 mm.

The GPS-derived S1 and S2 signals in ZTD are compa-red with three-hour surface synoptic pressure observations

Fig. 13 Diurnal ZTDamplitudes (mm) from GPSanalysis for four seasons.MAM: March–April–May,JJA: June–July–August,SON: September–October–November andDJF: December–January–February

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Diurnal ZTD cycles from GPS observations 543

Fig. 14 Semidiurnal ZTDamplitudes (mm) from GPSanalysis for all four seasons.MAM, JJA, SON and DJF aresame as Fig. 13

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from 1997 to 2007 that are archived at the National Centerfor Atmospheric Research (NCAR) (DS464.0; (http://dss.ucar.edu/datasets/ds464.0). Notably, these results are adjus-ted by a scale factor 2.28 mm/hPa, which are accounted for inthe comparison. These pressure data origin from more than8,000 land and ocean weather stations including the globaltelecomuncation system (GTS) and marine reports from theComprehensive Ocean-Atmosphere Data Set (COADS) (Daiand Wang 1999). The plots of diurnal ZTD cycles (Figs. 5and 7) and semidiurnal ZTD cycles (Figs. 8 and 10) showgeneral similarities, indicating that the diurnal and semidiur-nal atmospheric tides are probably the main driver of thediurnal and semidiurnal ZTD variations derived from GPS.However, there are also some discrepancies with the globalsurface pressure estimates, particularly in the S1. The largerdiscrepancies occur in the Pacific Ocean area and tropicalregions, e.g. tropical south-east Asia, but also in North Ame-rica and Western Europe. These discrepancies probably canbe related to observation errors, different locations of theweather and GPS observation sites, the underlying geophy-sical signals and other processes.

On the one hand, reasons for differences in S1 and S2

between the GPS-derived results and those calculated fromsurface pressure data are suspected to lie in the appliedmapping functions and the loading of the earth’s crust, asthese have unique diurnal and semidiurnal characteristics thatare different from the S1 and S2 pressure tides. However, arecent simulation study by Humphreys et al. (2005) showedthat the impact of the mapping functions of Niell (1996) isless than 11% on the amplitude of the subdiurnal oscilla-tions in ZTD, assuming an average distribution of elevationangles and an elevation cutoff of 7◦. The effect of atmospheric

pressure loading was found to be less than 11% on theamplitude of the subdiurnal oscillations in ZTD (Humphreyset al. 2005). Also the estimated errors due to the solid Earthtide (Watson et al. 2006) and the ocean loadings (Dach andDietrich 2000; Vey et al. 2002) on the amplitude of the sub-diurnal oscillations in ZTD are found to be as high as 17%.However, these effects are mitigated by applying correc-tions based on the solid Earth tide model IERS03 and oceantide model FES2004, respectively. In addition, the watervapor diurnal variations will affect surface and atmosphericlongwave radiation and atmospheric absorption of solarradiation (Dai et al. 2002; Pramualsakdikul et al. 2007) andpossible atmospheric tides. However, this is difficult to verifyas IGS stations have few co-located meteorological observa-tions which would allow us to determine the amount of watervapor at the IGS stations independently. Further work is nee-ded to investigate the importance of diurnal and semidiurnalvariations in water vapor on ZTD. On the other hand, thedifferences in subdiurnal variations (particularly S1) may bedue to other processes, such as the diurnal cycle of convec-tion and atmospheric large-scale vertical motion. Actuallythe classic tidal theory predicts that the diurnal tide S1 is verycomplex and irregularly distributed (Chapman and Lindzen1970). It needs to further investigate the complex subdiurnalvariations and mechanism with more data in the future.

4 Conclusions

Traditional techniques (e.g., radiosondes) for estimating thediurnal and semidiurnal oscillations in ZTD on a global scaleare insufficient due to a lack of observation data with high

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temporal resolution. The time series of 2-hour GPS-ZTD(1997–2007) from the global IGS network provide animportant data set to investigate its diurnal and semidiurnaloscillations. The results of this study have shown significantdiurnal and semidiurnal variations of ZTD at all IGS sta-tions. The diurnal cycles (S1, 24 h) have amplitudes between0.2 and 10.9 mm and the semidiurnal cycles (S2, 12 h period)have amplitudes between 0.1 and 4.3 mm. The formal uncer-tainties are on the order of 0.5 and 0.2 mm for the diurnaland semidiurnal amplitudes, respectively. In both cases, thesignal amplitudes show a strong and consistent dependenceon the latitude with the largest amplitudes of the diurnal andsemidiurnal ZTD cycles found in the low-latitude equatorialareas. The peak times of the diurnal cycles spread over thewhole day, while the peak value of the semidiurnal cyclesoccurs typically about local noon. In addition, the diurnalZTD cycle has significant seasonal dependences with largeramplitudes in summer and smaller ones in winter. However,the seasonal variations of the semidiurnal ZTD cycles arenot obvious. The GPS-derived diurnal and semidiurnal ZTDsignals are reasonably consistent, but also reveal discrepan-cies with the surface pressure tides S1 and S2. This impliesthat the atmospheric tides are probably the main driver ofthe diurnal and semidiurnal ZTD variations. They are mostlikely not due to the solid earth effects, ocean and atmos-pheric loadings and mapping function errors that give lessthan 17% contributions, respectively. The larger discrepan-cies occur in regions of the Pacific Ocean area and some tropi-cal regions, which most probably can be related to the diurnalcycle of convection, atmospheric large-scale vertical motion,tropospheric water vapor and other observation errors whichis difficult to verify without co-located weather and GPSstations.

Acknowledgments The authors acknowledge the use of GPS data thatwere retrieved from the IGS data archive and surface synoptic pressuredata archived at the National Center for Atmospheric Research (NCAR).We also thank the referees for valuable suggestions to significantlyimprove the article. This work was supported by a grant (07KLSGC02)from Cutting-edge Urban Development—Korean Land SpatializationResearch Project funded by Ministry of Land, Transport and MaritimeAffairs.

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