Journal of the Meteorological Society of Japan, Vol. 82, No. 1B, pp. 587--596, 2004 587

Characterization of Atmospheric Parameters using

a Ground Based GPS Network in North Europe

Borys STOEW and Gunnar ELGERED

Onsala Space Observatory, Chalmers University of Technology, Onsala, Sweden

(Manuscript received 18 April 2003, in revised form 15 November 2003)

Abstract

We characterize the temporal and spatial variation of the Zenith Wet Delay (ZWD) and the ZenithTotal Delay (ZTD), estimated using a network of Global Positioning System (GPS) receivers. This char-acterization is important for the improvement and validation of atmospheric water vapor models, appli-cable in GPS meteorology, as well as in the navigation.

We treat the estimates of Zenith Hydrostatic Delay (ZHD) and ZWD as realizations of random walkstochastic processes and we derive the corresponding parameters for different locations and measure-ment techniques for data acquired at intervals of 1 to 3 hours. The monthly standard deviation (StD) ofthe ZTD is less than 50 mm and does not exhibit a strong seasonal signature over the period 1997–1998for any of the studied GPS sites. However, the StDs of the pairwise-differenced ZTD time series show aseasonal dependence, mainly due to the spatial variations of the ZWD, which should be considered whenGPS data are assimilated in weather prediction models.

We show the differences in typical spatial characteristics of ZHD and ZWD for the winter and sum-mer seasons in North Europe. Finally, we describe the use of temporal structure functions for detectionof rapid changes in ZTD.

1. Introduction

The radio signals transmitted from GPS sat-ellites experience a delay as they propagatethrough the neutral atmosphere. By conven-tion, the delays along the line of sight to eachsatellite are mapped to one single parameter—the zenith total delay (ZTD). The ZTD can besplit into two parts: the zenith hydrostatic de-lay (ZHD), and the zenith wet delay (ZWD), i.e.

l ¼ lh þ lw: ð1Þ

The ZHD is due to the refractivity associatedwith the ‘dry’ gases and the induced dipole mo-ment of the water molecule, while the ZWD isrelated to its permanent dipole moment. TheZHD can be estimated from atmospheric pres-

sure data, acquired on the ground, as opposedto the ZWD; furthermore, in most weather con-ditions the ZWD experiences much faster var-iations compared to ZHD. Hence the ZWD is animportant source of error in GPS positioningand geodesy (Emardson and Jarlemark 1999).

Other independent techniques are oftenused for comparison and calibration purposes(Keihm et al. 2002). Among these are the pro-files of relative humidity acquired with radio-sondes (RS), and wet delay estimates fromwater vapor radiometers (WVR). These techni-ques, however, lack the spatial and/or temporalresolution of the GPS approach, which makesGPS a very attractive data source for numericalweather prediction (NWP). The data from RSalso suffer from problems related to sensor cal-ibration and aging issues (e.g., Lesht 1999).

GPS data can be used in the develop-ment and evaluation of global models foratmospheric-path correction. Such models may

Corresponding author: Borys Stoew, Onsala SpaceObservatory, Chalmers University of Technology,439 92 Onsala, Sweden.E-mail: boris@oso.chalmers.se( 2004, Meteorological Society of Japan

be utilized in hand-held GPS receivers as analternative to other systems, e.g., incorporat-ing radio-broadcasted corrections—especiallyin remote geographical regions. The validationand use of such models requires good under-standing of both the spatial and temporal char-acteristics of the atmospheric water vapor.

For the description of the temporal and spa-tial variation of water-vapor related parame-ters, we have used data from a network of GPSreceivers (see Fig. 1), which has continuouslyoperated during the years 1997–2002. A com-prehensive study of the long term trends inintegrated water vapor (IWV) time series, us-ing the same data set, has been carried outby Gradinarsky (2002). A characterization ofthe diurnal cycle of IWV was done by Bouma(2002). An overview of the relation betweenspatial and temporal scales of the atmosphericvariations can be found in Daley (1991).

We proceed with a discussion on GPS dataquality in Section 2. In Section 3 we character-ize the short term variability (periods up to 3hours) of ZHD and ZWD. These results describe

the change in the uncertainty of a model esti-mate with time. Section 4 presents the monthlyand seasonal behavior of the ZTD/ZWD vari-ability, which should be taken into account inatmospheric models for both weather predic-tion and positioning in North Europe. The spa-tial characteristics of ZTD/ZWD are describedin Section 5, and show the uncertainty of amodel estimate as a function of distance andseason. Rapid changes in the ZTD, related toforecasting of severe weather, are discussed inSection 6. The conclusions follow in Section 7.

2. Estimating ZTD using GPS data

The estimated ZTD is an average of the in-tegrated refractive index along all the propaga-tion paths from the observed GPS satellitesto the receiver on the ground referred to thezenith direction. When relating the estimatedZTD to the meteorological parameters, we in-troduce an uncertainty from the equation usedfor the refractivity. This is normally written

N ¼ k1pd

Tþ k2

e

Tþ k3

e

T2; ð2Þ

where pd is the partial pressure of all the drygases; e is the partial pressure of water vapour;T is the absolute temperature, and the coeffi-cients k1; k2, and k3 are empirically determinedfrom laboratory experiments.

A commonly used value for k1 is 77.691 K/hPa which is based on a CO2 content of 300ppm. The expected average value in 2004 is375 ppm which will imply a value of k1 equal to77.695 K/hPa (Rueger 1999). The change inthe ZHD, caused by this updated value of theCO2 content, is only 0.1 mm. The largest un-certainty is in k3, and is approximately 1%(Boudouris 1963).

The accuracy of the ZTD estimates dependson many other parameters. Most important arethe uncertainties in the orbit parameters of thesatellites, the model used for the receiver coor-dinates, and the minimum elevation angle usedfor the observations.

The orbit uncertainties are reduced by usinga large tracking network. The InternationalGPS Service for Geodynamics (IGS) providesdifferent products of various quality, wherethe most accurate orbit parameters are avail-able many days after the time of the data ac-quisition (Beutler et al. 1996). The ZTD errors

Fig. 1. Map presenting the network ofGPS receivers on the territory of NorthEurope.

Journal of the Meteorological Society of Japan588 Vol. 82, No. 1B

caused by orbit uncertainties are correlatedboth temporally and spatially, meaning thatobserved rapid changes and differences be-tween nearby GPS sites have a high commonmode rejection of orbit induced errors. Uncer-tainties in the orbit parameters are the maindifficulty encountered in the application of theZTD in weather forecasting, where the require-ment of data availability in near real time oftenmeans within 1–2 hours from data acquisition.The ZTD obtained from post-processing, usingthe most accurate orbit parameters, have avalue as an independent source of informationfor validation purposes.

In continuously operating GPS networks thesite coordinates are often well known, and byfixing the position to these values the formaluncertainties of the ZTD are improved. Physi-cal phenomena causing variations in the ZTDestimates, such as tides, ocean and atmosphericloading effects, need to be modeled.

Changing the elevation cut-off angle is not anerror source in itself but it introduces system-atic biases due to multipath effects, a changingphase pattern of the antenna, and a differentsatellite constellation. The mapping from theobserved elevation angles to the zenith value ofthe total delay can be performed using variousmapping functions (Spilker 1996; Niell 1996).The Niell mapping functions, which are utilizedhere, introduce an rms error in total delay ofless than 6 mm at satellite elevation angleslarger than 10� (Bisnath et al. 1997).

The processing of GPS data has been carriedout using the GIPSY data analysis software,developed at the Jet Propulsion Laboratory(Webb and Zumberge 1993). This setup uti-lizes the Final orbits released by IGS in a post-processing mode (Beutler et al. 1996). The ele-vation cut-off angle was set to 10�.

Let us conclude this background discussionby noting that the absolute accuracy of ZTDsestimated from ground-based GPS networksis affected by the used elevation-dependentmodels for antenna phase center, multipath,etc., which introduce a model-dependent bias.However, a major part of this unknown biastype of error should be possible to keep con-stant over time scales of years, as long as theused models, and the elevation cut-off angle arenot changed. The strength of the method is thepossibility to observe continuously with a good

temporal resolution; the horizontal resolutionis simply determined by the distance betweenthe GPS sites.

3. Short term variation

If atmospheric corrections, calculated usingan NWP model, are applied by a GPS user, oneneeds to consider how the uncertainty of thesecorrections changes with time. In this sectionwe consider the time series of ZWD and ZHDto be realizations of a random walk process(Brown and Hwang 1997). Such a process isdescribed statistically by the StD of its drivingwhite noise sequence, known as the randomwalk parameter (rwp). The ground pressuremeasurements are needed for the estimationof ZHD, and hence for the calcualtion of ZWDand IWV from GPS data. ZWD data can beindependently acquired using a WVR. We de-scribe the corresponding rwp’s in order to char-acterize the temporal behavior of the ZWD andthe ZHD.

Spatially interpolated pressure data sam-pled every 3 hours are delivered by the Swed-ish Meteorological and Hydrological Institute(SMHI) for each of the GPS sites. Davis et al.(1985) proposed an approximate formula forestimating the ZHD at a given site with lati-tude y in degrees, and height H in km abovethe ellipsoid (Fowler 1990), from ground pres-sure measurements:

lh ¼ ð2:2768G 0:0024Þ P

f ðy;HÞ ; ð3Þ

f ðy;HÞ ¼ 1 � 0:00266 cosð2yÞ � 0:00028H;ð4Þ

where lh is in mm and the pressure P is in hPa.This formula aided the calculation of the rwpfor a year long time series of pressure and thecorresponding ZHD data. The results are pre-sented in Table 1.

The technique for deriving zenith wet delaywith the aid of a WVR has been used exten-sively (Elgered et al. 1991 and Jarlemark1997). We performed an estimation of the rwpfor the ZWD data acquired by a WVR, operat-ing at the Onsala Space Observatory, for theyears 2000 and 2001. The algorithm for deriv-ing ZWD from WVR data experiences problemswhen data are acquired during rainfall. There-fore, the time series have been edited, and

B. STOEW and G. ELGERED 589March 2004

the noisy data, implying liquid water contentgreater than 0.7 mm, have been removed priorto the analysis (Elgered and Jarlemark 1998).We carried out the corresponding calculationsfor the rwp of the ZWD derived from GPS. Inorder to compare the two techniques, we ana-lyzed the data at the rates of 1 sample perhour, and 1 sample each 3 hours. Emardson(1998) has shown that for the short time scales,less than one hour, the radiometer time seriesare affected by white noise (increasing the esti-mated rwp values). The results for the ZWDderived from WVR and GPS are presented inTable 2. The apparent variability of the ZWD ishigher than that of the ZHD (cf. Table 1). Thisshows that the ZWD dominates the variabilityof ZTD in the atmosphere for time periods upto 3 hours, which is a typical update-intervalof short-range weather forecasts. We also notethat, averaged over a whole year, the shortterm variability of ZWD (the estimated rwp) isalmost the same for the years 2000 and 2001.

4. Monthly and yearly characteristics

The comparison of biases and rms differencesbetween estimates of integrated water vaporfrom WVR, GPS and radiosondes has been asubject of previous short term studies (Emard-son et al. 1998). In this section, we attempt tocharacterize the behavior of ZTD and ZWD onthe monthly and seasonal scales.

Using the network of GPS receivers de-scribed earlier (see Fig. 1), we calculated themonthly means and standard deviations of theZTD data for the years 1997 and 1998. Fig. 2shows the monthly means of the ZTD estimatesfor the four GPS sites Hassleholm (HASS),Kiruna (KIRU), Jonkoping (JONK), and On-sala (ONSA). There exists a dependence ofthese values on the physical position of the cor-responding GPS site. The biases between thesites are explained by the fact that KIRU has aheight above sea level of 469 m and is in thenorth (latitude 68 degrees), whereas the otherthree sites are at lower altitudes (JONK ¼228 m, HASS ¼ 78 m, and ONSA ¼ 10 m) andin the south (latitude 56–58 degrees). Eventhough the seasonal variations differ signifi-cantly between the two years, it can be seenthat there is a rather strong spatial correla-tion (the distance between KIRU and HASSis 1362 km, while HASS and ONSA are only181 km apart).

Table 1. Random walk parametersestimated from pressure data forboth atmospheric pressure and ZHD.Pressure data are sampled every 3hours.

Pressure rwp,hPa �

ffiffiffiffiffiffiffi

s�1p ZHD rwp,

mm �ffiffiffiffiffiffiffi

s�1p

Site 2000 2001 2000 2001

ONSA 1.3 � 10�2 1.2 � 10�2 3.0 � 10�2 2.8 � 10�2

HASS 1.3 � 10�2 1.2 � 10�2 2.9 � 10�2 2.7 � 10�2

JONK 1.3 � 10�2 1.2 � 10�2 2.8 � 10�2 2.7 � 10�2

KIRU 1.2 � 10�2 1.2 � 10�2 2.7 � 10�2 2.8 � 10�2

Table 2. ZWD random walk parame-ters estimated from WVR(*) and GPSdata for the years 2000 and 2001. TheZWD data were selected at intervalsof 1 and 3 hours, respectively.

1-hourly ZWD rwp,mm �

ffiffiffiffiffiffiffi

s�1p 3-hourly ZWD rwp,

mm �ffiffiffiffiffiffiffi

s�1pWVR/

GPSsite 2000 2001 2000 2001

Onsala* 1.2 � 10�1 1.5 � 10�1 1.2 � 10�1 1.4 � 10�1

ONSA 1.1 � 10�1 1.1 � 10�1 1.3 � 10�1 1.3 � 10�1

HASS 1.1 � 10�1 1.2 � 10�1 1.4 � 10�1 1.2 � 10�1

JONK 1.1 � 10�1 1.1 � 10�1 1.3 � 10�1 1.2 � 10�1

KIRU 1.0 � 10�1 1.0 � 10�1 1.0 � 10�1 9.4 � 10�2

Fig. 2. Monthly means of the ZTD esti-mates from 1997 and 1998 for the fourGPS sites at Hassleholm, Jonkoping,Onsala and Kiruna.

Journal of the Meteorological Society of Japan590 Vol. 82, No. 1B

The standard deviations about each monthlymean of the ZTD throughout the same periodcan be seen in Fig. 3. There is no strong signa-ture in the monthly StDs for any of the sites.However, we note that KIRU, in the north, onthe average shows slightly less variation, andthat the summer months are slightly morevariable compared to the winter months. Themonthly StDs of the ZTD time series do not ex-ceed 0.05 m.

The monthly means of the ZWD are shownin Fig. 4. The dependence of the ZWD monthlymeans on the site location (height and altitude)is not as pronounced as for the ZTD (see Fig. 2).This can be explained with the small relativecontribution of the ZWD estimates, comparedto that of the ZHD. For the studied geographi-cal area, the ZWD has typical values of about0.1 m, while the ZHD, which is related to at-mospheric pressure, takes values around 2.2 m,depending on the location and weather condi-tions (Webb and Zumberge 1993).

5. Spatial characteristics

In the following we assume that the ZWD/ZHD/ZTD fields are stationary within thestudied periods. This assumption ensures thatthe variances of the individual time series re-main constant, while the means are removed inthe site-pairwise differencing described below.We do not assume, however, that these fieldsare homogeneous, because the variabilities ofthe ZWD and ZHD depend on the altitude ofthe observing station. This approach is relatedto the spatial structure functions (Tatarskii1971), which describe the spatial variabilityof atmospheric parameters in turbulence afterthe data means are removed. For a study of therandom fields related to water vapor under theassumption of homogeneity we refer to Stoewet al. (2001).

To describe the spatial characteristics ofthe ZWD estimates, we calculated the standarddeviations of the differences between timeseries for each pair of GPS sites. The resultsare shown in Fig. 5. The ZWD estimates weretaken for one winter month (January), onesummer month (July), and the whole year of1998.

The ZWD (and hence the water vapor con-tent) is more spatially variable in the summerthan in the winter; this is also seen in a com-parison with the results for the whole year. It isa consequence of the higher convective activityin the troposphere in the summer; the watervapor content is also related to the air temper-ature, which may introduce variations withinthe diurnal cycle. Moist convection occurs overa large spectrum of spatial scales, ranging frommicroscale turbulence to systems that spanhundreds of kilometers (Emanuel 1994). Con-versely, the winter-time atmosphere is colderand more advective, rendering the smallerrange in the variability of ZWD.

In all three cases shown in Fig. 5, we notice alimit in the site separation, beyond which theStD of the differences does not increase. We re-late this to the spatial scales at which the at-mospheric water vapor processes are no longercorrelated, and the StDs of the pairwise differ-ences become dominated by the local variationsof the ZWD.

In Fig. 6, we show a plot constructed ina similar way from ZTD data. Together with

Fig. 3. Monthly standard deaviations ofthe ZTD estimates from 1997 and 1998for the four GPS sites at Hassleholm,Jonkoping, Onsala and Kiruna.

Fig. 4. Monthly means of the ZWD esti-mates from 1997 and 1998 for the fourGPS sites at Hassleholm, Jonkoping,Onsala and Kiruna. Note the sharpersummer-time signature for Kirunawhich is located much further northand experiences longer winters.

B. STOEW and G. ELGERED 591March 2004

Fig. 7, this demonstrates the effects of thehigher variability of the ZWD (compared tothat of the ZHD) on the ZTD estimates.

The StDs of the pairwise differenced ZHDtime series are plotted against site separationin Fig. 7. The ZHD data are derived from at-mospheric pressure using the method describedin Section 3. The apparent spatial variability ofthe ZHD estimates is much lower than that ofthe ZWD. Note that the pressure fields used in(3) and (4) were resampled from the original 3-hour- to a 5-minute sampling interval, usingpiecewise cubic spline interpolation (e.g., Presset al. 1992). The interpolation partly lowers thescatter of the ZHD StDs in Fig. 7, compared tothe results shown in Figs. 5 and 6. In the pro-cess, a small portion of the short-term varia-tions in the true ZHD is removed and is effec-

tively attributed to the GPS-estimated ZWD;a signature from the spatial interpolation ofthe pressure field is also introduced to theZWD estimates through (3) and (1). We com-pared time-interpolated pressure data to actualmeasurements at Onsala, and found that theStD of the differences between the two is lessthan 1 mm equivalent zenith delay. To reducethis effect, one of two approaches is in order: (a)use pressure data sampled at the same rate asthe GPS data, or (b) use directly the ZTD esti-mates for assimilation into NWP models.

Note that data from ‘windy’ months are go-ing to introduce higher variability in the ZHDfields, compared to the ‘quiet’ months during agiven season, due to the advective nature of theprocesses. It is well established that the meanpressure fields above Scandinavia are morevariable during the winter than the summer.

Fig. 5. Standard deviations of the pair-wise differences in the ZWD time seriesderived from GPS data from 1998. Theresults were calculated for (a) one win-ter month (January), (b) one summermonth (July), and (c) for the whole year.

Fig. 6. Standard deviations of the pair-wise differences in the ZTD time seriesderived from GPS data from 1998 for (a)January, (b) July, and (c) the entireyear.

Journal of the Meteorological Society of Japan592 Vol. 82, No. 1B

Typical average winter conditions are shownin Fig. 8. Stormy weather dominated in Janu-ary 1995, while in January 1996 there was ahigh pressure formation east of the Scandi-navian peninsula, characteristic for low vari-ability of the mean pressure. In Fig. 9 we showthe calculated StDs of the differenced time se-ries of ZHD for the corresponding months.

The mean pressure fields for the months ofJuly 1997 and July 1998 are presented inFig. 10. July 1997 was dominated by a highpressure system over Scandinavia, which keptthe conditions rather stable; July 1998 had alow pressure system centered over the region,hence the higher variability in ZHD for this pe-riod. In Fig. 11 we compare the StDs in ZHDfrom these two months. To conclude, the pair-wise StDs in the ZHD field during winter/summer months of high atmospheric activity

can be 50% higher than those during the corre-sponding low-activity months.

6. Searching for extreme events

In Section 3 we treated the time series ofthe atmospheric path delay above a given siteas a random walk. This, however, is a first

Fig. 7. Standard deviations of the pair-wise differences in the ZHD time seriesderived from pressure data from 1998for (a) January, (b) July, and (c) thewhole year.

Fig. 8. Mean pressure fields over Scandi-navia for a characteristic pair of wintermonths. January 1995 (left) was gov-erned by westerly flows, low pressurestructure in the North, and storms;January 1996 (right) was governed by ahigh pressure formation in the East andthe weather was more stable. CourtesyC. Jones (personal communication,2002).

Fig. 9. Standard deviations of the pair-wise differences in the ZHD time seriesderived from pressure data from (a)January 1995, and (b) January 1996.January of 1995 had dominating west-erly flows and storm activity, and showsmuch higher spatial variability in theZHD time series.

B. STOEW and G. ELGERED 593March 2004

order approximation, needed for comparisonsbetween different measurement techniques.One could extend the treatment of the randomprocess by using a random walk with absorbingbarriers model (e.g., Grimmett and Stirzaker1992). We consider meteorological phenomenarelated to local variations in the ZWD/ZTD.These variations can be used for detection/monitoring of passing atmospheric fronts. Onerelatively new use of GPS data is in the emerg-ing GPS tomography (Elosegui et al. 1999;Flores et al. 2001). GPS data may aid the pre-diction of extreme weather conditions, such as

thunder storms, night-time fog, or intense pre-cipitation/flooding. Therefore, we need to de-scribe statistically the ZTD variations on tem-poral scales of up to 1 hour.

Depending on the meteorological conditions,the ZTD can have properties differing fromthose of the random walk. For the statisticaldescription of the process in the general caseJarlemark et al. (1998) used a structure func-tion:

DZTDðtÞ ¼defEf½lðt þ tÞ � lðtÞ�2g; ð5Þ

which describes the changes over time of thezenith total delay l depending on the time lagt. Note that the special case of a random walkyields linear dependence between DZTDðtÞ andt. Similar functions can be defined also forZHD/ZWD. Analytical approximations of thestructure functions are presented by Treuhaftand Lanyi (1987).

We derived daily estimates of DZTDðtÞ for theyear of 1998, for each of the GPS stations pre-sented in Fig. 1. The values of the structurefunction were calculated for three different val-ues of the time lag t: 5, 15, and 60 minutes. Thecalculated DZTDðtÞ for all GPS sites were thenused to produce a histogram. Rare, extremechanges in the ZTD contribute to the right tailof the histogram, while low variability amountsto the left tail, as shown in Fig. 12. A thresholdcan be suitably chosen, using such a histogram,in order to monitor rapid changes of ZWD inthe vicinity of any given GPS site in near-realtime.

7. Conclusions and future work

The importance of the knowledge of thebiases and rms errors in the GPS estimatesof ZTD cannot be overstated, especially whenthese data are to be used in operational fore-casting. The overestimation of the water vaporcontent in the atmosphere leads to unrealisticprecipitation levels in the weather forecastafter the GPS data are assimilated into theNWP model (Cucurull 2001).

The seasonal changes in the short term var-iations of ZTD/ZWD, discussed in Sections 3and 4, indicate the type and magnitude of fluc-tuations which should be taken into accountwhen GPS data are assimilated. When mobileGPS users perform atmospheric correctionto their position estimates, these seasonal

Fig. 10. Mean pressure fields over Scan-dinavia for a characteristic pair of sum-mer months—July 1997 (left) and July1998 (right). Courtesy C. Jones (per-sonal communication, 2002).

Fig. 11. Standard deviations of the pair-wise differences in the ZHD time seriesderived from pressure data from (a)July 1997, and (b) July 1998. July of1997 was more stable in terms of airpressure than July 1998 (see text).

Journal of the Meteorological Society of Japan594 Vol. 82, No. 1B

changes should be considered also as variationsin the uncertainty of the correction models. Thespatial characteristics of the type discussed inSection 5 also describe the uncertainties ofatmospheric corrections (in the case when thecorrections are being broadcasted to GPS usersin a given geographical area).

Thus the analysis of long time series of GPSdata over a certain area can be used to derivethe design parameters for some applications ofGPS-derived ZTD, namely weather forecastingand an improved GPS positioning.

The prediction of extreme weather, such asthunderstorms and floods, is a complex problemthat requires accurate and timely information

about many physical parameters and the spa-tial scales of their variations. Because of therelation between the scale of an atmosphericsystem and the time needed for it to move overa geographic area (Daley 1991), a large re-gional network of GPS receivers can be used toimprove the monitoring of the atmosphere.

Acknowledgements

We are grateful to Colin Jones (SMHI) forthe valuable comments on choosing represen-tative periods of synoptic activity, and to LarsMeuller (SMHI) for interpolating the pressurefields to the GPS site locations. Our gratitudegoes also to the two anonymous reviewers forhelping improve the quality of our presenta-tion.

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