GEOPHYSICAL RESEARCH LETTERS, VOL. 25, NO. 19, PAGES 3583-3586, OCTOBER 1, 1998
GPS meteorology: Reducing systematic errors in geodetic estimates for zenith delay PengFang, 1 MichaelBevis, 2 YehudaBock,1SethGutman 3 andDanWolfe3 Abstract.
This paper addresses the problem of reducingsystematic errors in GPS-derived PW estimates, specifically the
Differences betweenlong term precipitable water
(PW) time series derived from radiosondes, microwave water
vapor radiometers,and GPS stations reveal offsets that are oftenasmuchas 1-2 mm PW. All three techniquesare thought to sufferfrom systematicerrorsof order 1 mm PW. Standard GPS processingalgorithms are known to be sensitive to the choice of elevation cutoff angle at this level. We present a processingprotocol that is shown to reduceelevation angle dependence in geodeticestimatesof zenith delay and, hence, reducethe systematicerrorsin derivedprecipitable water. This protocol includes use of the Niell zenith delay mapping functionsand InternationalGPS Servicephasecentermodels.
systematic errorsassociated withthe geodetic inversion •for troposphere zenith delay parameters. Recall that GPS measurements are usedto infer the zenithneutraldelay ('•/qD") historyat a site,that surfacepressuremeasurements are usedto decomposethis delay into its water vapor ("wet") and hydrostatic("dry")components, and that surfacetemperature measurements are usedto transformthe wet delay historyinto a PW time series[Beviset al., 1994]. Biasesin the zenith delays will propagatethrough the subsequent post-geodeticanalysis into the estimated PW time series; the PW bias is about 15% of
the zenith tropospheredelay bias. In order to assessthe biases associatedwith the geodetic solutions for zenith delay, we employ the well known diagnostic technique known as ContinuousGlobal Positioning System (CGPS)networks elevationcutoff angle variation.We will not considerhere the suchas the ContinuouslyOperatingReferenceStation (CORS) typically minor long-term biases associated with the network operatedby the National Oceanicand Atmospheric assumption that the atmospheric delay affecting each GPS Administration(NOAA)/NationalGeodeticSurvey(NGS) can stationis azimuthallyisotropic[Ware et al., 1997]. Introduction
be usedto estimatethe total (integrated)atmosphericwater vapor(or precipitablewater- PW) overlying eachGPS station Elevation cutoff angle variation with an accuracyof 1-2 mm anda temporalresolutionof about The analysis of very long baseline interferometry data has shown that there are high correlations between estimates of al., 1996]in whicha networkof six stationsmostlylocatedat zenith atmosphericdelaysand heights of geodeticsites dueto NOAAProfiler Sites in the centralU.S. were operatedfor a errors in the atmospheric mapping functions [Davis et al., period of 30 days. In 1994 the NOAA Forecast System 1985; Herring, 1996]. Likewise, elevationdependenterrors in Laboratory(FSL)beganto establisha larger and permanent GPS phase measurementswill introducecorrelations among versionof this network.At the time of writing (August,1998) the estimatedparameters.Site-specific noise sourcessuch as the FSL network includes34 stations, including 11 at U.S. multipath[Georgiadouand Kleusberg,1988], signal scattering Coast Guard Differential GPS sites and 3 in Alaska. [Eltsegui et al., 1995], and antenna phase center errors Duan et al. [1996] found very little bias between the PW [Schupleret al., 1994] are also sensitive to the elevation of 30 minutes. The first major test of PW measurementwas the 1993 experimentGPS/STORM [Rocken et al., 1995; Duan et
time seriesderivedfrom GPSandwell calibratedwatervapor the satellite above the horizon as viewed from the GPS station. errorscan usually be detectedby varying radiometers (WVRs) duringGPS/STORM.But they did observe Elevation-dependent a large bias (~2 ram) at one station relative to PW estimates
the cutoff angle in the GPS data analysis. The rate at which
derivedfrom a nearbyradiosondestation. The much longer height error is tradedoff with zenith delay error is modulated time seriesproducedby the FSL networkhavemadeit clearthat by the distribution of the GPS datawith respectto elevation there are small but significant biases or offsets between PW angle, and this correlation is particularly sensitive to the time seriesderivedby GPS andby radiosondeobservations.It amountof data collectedat low elevationangles, and therefore is now widelyagreedthat all threetechniqueshave PW biases to the cutoff angle [Santerre, 1991]. We illustrate a cutoff of theorderof 1 mm [e.g.,Ernardson et al., 1998;Tregoninget angle test in Figure 1. This shows the ZND time series al., 1998]. It is not possible,however,to establishthe exact estimated for two stations over the course of one week. Two valueof the bias associatedwith any one techniquebecause solutionsare shownfor each station- one with a cutoff angle of 7ø andthe otherwith a cutoff angleof 15ø. Note that there i s thereis no certainway of identifyingthe "right answer." very little offset between the two ZND series for the IGS 1CecilH. andIda M. GreenInstitute of Geophysics andPlanetary station at Algonquin, whereasthe ZND solutions for Lamont Physics,ScrippsInstitutionof Oceanography, La Jolla,California. 2HawaiiInstituteof Geophysics and Planetology, Universityof show a pronouncedsensitivity to cutoff angle (one of the largestwe encountered in this study). One of the problems we Hawaii, Honolulu. , 3NationalOceanicand Atmospheric Administration, Boulder. seek to addressis why some GPS stations are more sensitive Colorado. than othersto variation in cutoff angle. The key task however is to eliminate the systematicerrors causingcutoff sensitivity. Copyright1998by theAmericanGeophysical Union.
If we consider the two ZND
times
series at Lamont
we see that
they are offset by about 11.2 mm, equivalent to an unacceptablylarge offset of 1.7 mm in PW.
Papernumber9gGL02755. 0094-8534/98/9gGL-02755505.00
3583
3 5 84
FANG ET AL.: REDUCING
ERRORS IN GPS ZENITH DELAY
2.55
The phasecenterof an antennais a point in spaceto which ALGO
a measurement of phaseis referenced. Manufacturers of GPS
--7ø
antennasspecify a nominal phase center for the measurement of the phaseof the L1 carrierwave (1575.42 MHz) and another nominal phase center for L2 (1227.60 MI-Iz) relative to a physical referencepoint on the antenna.In reality the phase
2.5
2.45
center
2.4
2.35
2.3
= o
Median ZNDbias= 0.77mm;PWequ, iv= 0.12mm i
i
i
i
2.5
2:
an instantaneous
We collected observations
t,q 2.45
measurement
of
a carrier
wave
for 21 GPS stations within North
Americafor a seven-dayperiodin 1996 (Table 1) and processed these datausing four protocols. The cutoff tests illustrated in Figure 1 were based on CfA2.2 (with its parametersleft to default values) and no phase center modeling employed ("CfA"). We also examined three other protocols: the CfA mappingfunctionand IGS phasecentermodels("CfA+PCM"), the Niell mapping function and no phase center model ("NMF"), and the Niell mappingfunctionand IGS phase center models ("NMF+PCM"). For each protocol we processedthe datatwice,using7ø and 15ø cutoffangles.Atmospheric delay •i for an elevationanglee was computedby
2.4
2.35
2.3
252
of
emitted by a given satellite varies accordingto the elevation angle (and, in some cases,the azimuth angle) of the satellite. The movementof the phasecenteraroundits nominal position as a satellite moves acrossthe sky is called antenna phase center variation. Early attempts to correct for phase center variationby providing modelsfor each class of antennawere complicatedby the fact that the models producedby distinct groupswereoften significantly different. This situation has changedsincethe adoptionby the IGS of phase center models for severalgeodeticantennas[Schupleret al., 1994; Rothacher et al., 1995; Mader and MacKay, 1997; Meertenset al., 1997].
253
254
255
256
257
258
259
Day of Year 1996
Figure 1. Total zenith delays estimatedevery 30 minutesat two stations(ALGO andLMNO- Table 1) over the courseof a week, for 7ø and 15ø elevation cutoff angles. Estimates were obtained with GAMIT softwareusing CfA mapping function and no elevation-dependent antennaphasecentermodels.
Obviouscandidatesourcesfor the systematicerrors giving rise to cutoff angle sensitivity are multipath noise, antenna phase center variation, and the mapping functions used to relate zenith delays to delays at arbitrary elevation angles [Davis et al., 1985; Herring, 1986; Niell, 1996]. There is relativelylittle we can currentlydo duringGPS data processing to suppress the effectsof multipathnoise at the GPS stations. On the otherhandwe can modify our processingproceduresin an attempt to suppressthe systematicerrors associatedwith the mappingfunctionsand antennaphasecentervariation. In our casewe usethe GAM1T software[King and Bock, 1996]. Traditionally GAM1T usershave adopteda mapping function CfA2.2 (CfA)describedby Davis et al. [1985]. This mapping function is rather sophisticated,but in order to optimize its value the user should.tune certain meteorological parameters accordingto station location and season.In practice GAM1T usersallow thesemappingfunctionparametersto assumetheir default values. A new mapping function developedby Niell [1996] was designedto eliminate the needto tune any of the atmosphericparametersincorporatedin the mapping function software. The atmospheric parameters are automatically assignedvaluesreflectingboth the locationof the GPS station and the time of year that the data were collected. This site and season tuning was obtained by estimating these parameters from a set of globally distributedradiosondedata.
• (e) = ZH' mH(e)+ ZW'mw(e)
(1)
whereZHis thedry zenithdelay,zw is thewet zenithdelay,mH is the dry delay mapping function and mw is the wet delay mappingfunction. The defaultmodelsfor the dry and wet zenith delay for all protocols is that described by Saastamoinen[1972]. For the NMF protocol the mapping functionsfor the dry and wet delaysare those of Niell [1996], andfor the CfA protocolthe singlemappingfunctionof Davis et al. [1985] wasusedfor both dry andwet delays.The partial derivativeof GPS phasewith respectto the ZND parameterwas takenin all casesto be the wet mapping function. The ZND i s estimatedat each station every 30 minutes, using piecewise linear splines [Duan et al. 1996]. All other aspectsof our
processing strategy were identical for each protocol. Coordinates of four of the IGS sites (AI.CJO,DRAO, GOL2,
RCM5) weretightly constrainedto ITRF94 [Boucheret al., 1996]. Orbital parameterswere estimatedbut were tightly constrained to values estimated at the Scripps Orbit and PermanentArray Center(http://lox.ucsd.edu) for the IGS. The resultsusingthe four protocolsare depictedin Figure2 accordingto what type of GPS equipmentwas operating at a station (Table 1). The motivation for this grouping is describedin the next section.The results are averagedover all stationswithin eachof thesetwo groups(Table 2). In all cases
usingthe CfA mappingfunctionwith no elevation-dependent antennaphasecentermodelsled to the largest offset between the 7ø and 15ø PW solutions.Switchingfrom the CfA mapping function to the Niell mapping function led to a significant reduction in cutoff angle sensitivity, as did performing corrections for phasecentervariation by using the IGS phase centermodels.By using both the Niell mapping function and the IGS models the sensitivity to cutoff angle achieved its :minimum value. This last protocol almost completely
FANG ET AL.: REDUCING ERRORS IN GPS ZENITH DELAY
3 585
Table 1. North AmericanGPS stationsduringsevenday period(day numbers252 - 258, 1996) usedin this study SiteName
Code
Network
Receiver*
Firmware
Antenna*
Algonquin,Canada
ALGO
IGS
AOA SNR 8000
3.2
AOA Dome MargolinT
Penticton,Canada Goldstone,CA Hillsboro,KS Haskell, OK Haviland, KS Lamont, OK McDonald Obs., TX NASA SSC,MS Neodesha,KS
DRAO GOL2 HBRK HKLO HVLK LMNO MDO 1 NDBC NDSK
IGS IGS NOAA NOAA NOAA NOAA IGS NOAA NOAA
AOA SNR 8000 AOA SNR 8000 Trimble 4000 SSE Trimble 4000 SSE Trimble 4000 SSI Trimble4000 SSE AOA SNR 8000 Trimble 4000 SSI Trimble 4000 SSI
3.2 3.2 7.12 7.12 7.12 7.12 3.0 7.12 7.12
AOA Dome Margolin T AOA Dome Margolin T Trimble 22020-00 Trilnble 23903-00 Trimble 22020-00 Trimble 14532-00 AOA Dome Margolin T Trimble 22020-00 Trimble 22020-00
NorthLiberty,IA
NLIB
IGS
AOA SNR 8000
3.0
AOA DomeMargolinT
Pietown,NM Platteville,CO Purcell, OK
PIE1 PLTC PRCO
IGS NOAA NOAA
AOA SNR 8000 Trimble4000 SSE Trimble4000 SSE
3.2 7.12 7.12
AOA Dome Margolin T Trimble 14532-00 Trimble 14532-00
Quincy,CA
QUIN
IGS
AOA SNR 8000
3.2
AOA DomeMargolinT
Richmond,FL
RCM5
IGS
AOA SNR 8000
3.2
AOA Dome Margolin T
Sterling,VA
STRL
NOAA
AOA SNR 8000
3.2
AOA DomeMargolinT
Table Mtn, CO Vici, OK
TMGO VCIO
NOAA NOAA
AOA SNR 8000 Trimble 4000 SSE
3.0 7.12
AOA Dome Margolin T Trimble 23903-00
WallopsIs., VA
WLPS
NOAA
AOA SNR 8000
3.2
AOA DomeMargolinT
White Sands,NM
WSMN
NOAA
Trimble 4000 SSI
7.12
Trimble 23903-00
*SNR8000m "TurboRogues"; AOA-- AllenOsborne Associates; TrimbleNavigation model23903-00Geodetic"Compact" L1/L2 antennahas removable groundplanebutnearlyidenticaldimensions asmodel22020-00Geodetic"Permanent" L1/L2 antennawith a fixed groundplane. Model 14532-00 "Trimble 4000 ST L1/L2" antennahas very similarphasecenter pattern but has +3.9 mm vertical L1 offset and a +5.2 mm L2 offset
compared to model22020.We cannotdistinguish anysignificant differences betweenthe threeTrimbleantennasfor 7ø cutoffangle,comparedto 15ø.IGS hasnot adopteda phasecentermodelfor 23903-00 antenna,and we used,in lieu, the 22020-00phasecentermodel.The phasecenter modelsfor the Trimbleantennas areonlyspecifieddownto 10ø elevation.GAMIT linearlyinterpolates to a valueof 0.0 at 5ø elevationwhich is not optimal,buthasminorimpacton ouranalysis.
suppresses the systematicerrorsresponsiblefor cutoff angle sensitivity.In this experimentit producesa shift of only 0.12 mm in ZND, which is equivalentto an insignificant PW shift of just 0.02 mm, if we averageover all 21 stations.
Trimble
TurboRogueStations i
i
i
•
ß
.
.
.
ß
.
.
ß
.
.
Stations
• ,
....
,
.
....
.
o
ß
.
• NMF+PCM ....
.
NMF
.
.
'
ß
'
I CFA+PCM ' '
ALGO
CFA
ß
ß
ß
ß
.
RCM5
.... I
' ß
....
PIE1
e,e,•x•a,•,-•,-•::ß .: .'. ß
ß ß
ß
i
'
..... :•.,,•,'• •. :..,•.:.:. ................
MDO1
....
ß
.
QUIN .
ß
.
NLIB ß
GOL2
'.•
TMGO
....
......
•
ß
DRAO
cutoff from 7 ø to 15 ø eliminates far more data from the stations
Table 2. Summaryof elevationcutoff angle experiments
ß
ß
i
We needto explain why adopting a non-optimumprotocol causeslarger cutoff sensitivity at stations with Trimble GPS equipmentthan it does at stations with TurboRogue GPS equipment. This is because the TurboRogue receivers, in general,are recordingmuchlessusabledatabelow 15ø than are the Trimble receivers, as shown in Figure 3. Most Trimble receiversare collecting some data below 10ø and a significant amount below 15ø. On the other hand, the TurboRogue receivers collect far less usable low elevation angle data, and their low angle performance is far more variable. This is probablydue to a limitation in TurboRoguereceiver firmware version 3.2 (M. Watkins, personalcommunication)and not to any limitation in the antennas.Becauseof this, increasingthe with Trimble receivers. The TurboRogue stations are less sensitive to cutoff angle changes because they record relatively little usable data between 7ø and 15ø. Also, the Dome Margolin antennawith choke rings ("Dome Margolin T") that is part of the TurboRogueequipmentpackage(and now is the standardfor all manufacturersof geodetic GPS receivers)
.
ß
Discussion
.
....... ß
Mean ZND Offset and StandardError (mm)
ß .....
ß
ß
.
STRL •
GAMIT Protocol
ß ß
ß
WLPS
.
-2.5 0
.
ß
CfA
NMF
+PCM
.....
....
ß
CfA
.
NMF +PCM
.
..
.
2.5 5 7.51012.5
-2.50
2.55
7.51012.5
All stations
6.8_+0.8
Trimbleonly TurboRogue only
10.0-!-0.4 3.3_+0.5 6.8_+0.3 0.2_+0.4 4.0-!-0.9 2.4_+0.3 1.5_+0.8 0.0-!0.3
2.8-1-0.3
4.0-•.7
0.1_+0.3
EquivalentPW Offset(mm)(ZND - 65 PW)
Figure 2. Median shiftsin zenithdelayestimatesbetween7ø and 15ø elevation angle cutoffs for each site, two receiver types, and 4 GAM1T processingprotocols (see text). Mean shifts for all sites are listed in Table 2.
All stations
1.0
0.4
0.6
0.0
Trimbleonly TurboRogue only
1.5 0.6
0.5 0.4
1.1 0.2
0.0 0.0
3 5 86
FANG ET AL.: REDUCING ERRORS IN GPS ZENITH DELAY
angles. In general the geodetic errors affecting CGPS PW
(a) 11 TurboRogueStations,77 Station-Days 600
measurements fall into two classes: those that are sensitive
........
500
-..._::._._..• --=_: ......• !
:'-::=:'-:'
400
300
100010 ø
---" 80 ø i
20 ø
o
30
o
40
o
o
50 ø
60
o
to
elevation cutoff angles and those that are not. We have been able to significantly reduce the first classof biases.
70 ø
70ø
Acknowledgments. We thank Bob King, Tom Herring, and Simon McClusky at MIT for GAMIT support,Arthur Niell and an anonymous reviewer for useful suggestions. This study was supportedby NOAA grantsto ScrippsInstitutionof Oceanography and Universityof Hawaii.
ElevationAngle
50
References
40
•
30
=
20
•
10
Bevis, M., S. Businger,S. Chiswell, T. A. Herring, R. Anthes,C. Rocken, R. H. Ware, GPS Meteorology: Mapping Zenith Wet Delays onto PrecipitableWater. J. Appl. Met. 33, 379-386, 1994. Boucher,C., Z. Altamimi, M. Feissel,and P. Sillard, Resultsand Analysis of the ITRF94, IERS Technical Note 20, Observatoire de Paris, 1996.
0
0
1
2
3
4
5
6
7
8
9
10
Percentage of Observations Below 15ø
1607, 1985.
(b) 10 Trimble Stations,66 Station-Days 6OO 5OO =
400
ß•
300
' '.........
L 200 I
..• 100
¸
0 o
ilml
10 ø
20 ø
30 o
40o
50 o
60 ø
70 ø
-1
80 ø
Davis, J. L., T. A. Herring, I. I. Shapiro, A. E. E. Rogers, and G. Elgered, Geodesy by radio interferometry: Effects of atmospheric modelingerrorson estimatesof baselinelength,Radio Sci., 20, 1593-
90 ø
ElevationAngle
Duan, J., M, et al., Remotesensingof atmospheric water vaporusing the Global PositioningSystem,J. Appl. Met., 35, 830-838, 1996. E16segui,P., J. L. Davis, R. T. K. Jaldehag,J. M. Johansson,A. E. Niell, and I. I. Shapiro,Geodesy usingthe Global PositioningSystem:The effectsof signalscatteringon estimatesof site position,J. Geophys. Res., 100, 9921-9934, 1995.
Emardson,T. R., G. Elgered and J. M. Johansson,Three months of continuousmonitoringof atmosphericwater vapor with a network of Global PositioningSystemreceivers,Geophys.Res. Lett., 103, 18071820, 1998.
Georgiadou,Y., and A. Kleusberg,On carriersignalmultipatheffectsin relativeGPS positioning,Manuscr. Geod., 13, 172-179, 1988. 15 Herring,T. A., Precisionof vertical estimatesfrom very long baseline interferometry,J. Geophys.Res.,91, 9177-9182, 1986. 10 King, R. W., and Y. Bock, Documentationof the GAMIT GPS Analysis Softwareversion9.3, Mass. Inst. of Technol.,Cambridge,1996. 5 Mader, G. L. and J. R. MacKay, Calibration of GPS antennas, Proc. 1996 AnalysisCenter Workshop,International GPS Service Central 0 4 6 8 10 12 14 16 Bureau,R. E. Neilan, P. A. Van Scoy, and J. F. Zumberge, eds., Jet PropulsionLaboratory,Pasadena,pp. 81-105, 1997. Percentage of Observations Below 15ø Meertens,C., C. Rocken,J. Braun,B. Stephens,C. Alber, and R. Ware, Figure 3. Stackedhistograms showing distribution of Antennatype,mount,height,mixing and snow effects in high accuracy GPS observations,The Global Positioning System for the elevationangles(above7ø cutoff) in 5ø bins (uppergraph) and Geosciences,pp. 211-218, National Academy Press,Washington, histogram of percentage of usable double-difference D.C., 1997. observations below 15ø to which a site contributed (lower Niell, A. E., Global mapping functionsfor the atmosphericdelay, J. graph)for (a) TurboRoguestations,and(b) Trimble stations. Geophys.Res.,101, 3227-3246, 1996. 20
Rocken, C., T. Van Hove, J. Johnson,F. Solheim, R. Ware, M. Bevis, S.
is the reference antenna for the IGS antenna phase center Chiswell, S. Businger,GPS/STORM - GPS sensingof atmospheric water vapor for meteorology.J. Atmos.Oceanic Tech., 12, 468-478, models[e.g., Mader and MacKay, 1997]. That is, all elevation1995. related phase center corrections provided by the IGS and Rothacher, M. S., Scha. er, S., L. Mervart,and G. Beutler,Determination incorporatedinto GAMIT are relative to this referenceantenna. of antennaphasecentervariationsusingGPS data, IGS Workshopon This and the fact that the Dome Margolin T has smaller SpecialTopicsandNewDirections,Potsdam,Germany, pp. 205-220, elevation-dependentphase center variations [e.g., Meertens et May 15-17, 1995. al., 1997] are the reasons why we see such a marked Santerre,R., Impact of GPS sky distribution,Man. Geod., 16, 28-53, 1991. improvement in zenith delay estimates at stations with Schupler,B. R., R. L. Allhouse,andT. A. Clark, Signalcharacteristics of Trimble antennaswhen the IGS phasecentermodelis included. GPS userantennas,Navigation,41,277-295, 1994. We have demonstratedthat incorporatingthe Niell mapping Tregoning,P., R. Boers,D. M. O'Brien,and M. Hendy, Accuracy of absoluteprecipitablewater estimatesfrom GPS observations,J. function and the IGS elevation-dependentphase center model Geophys.Res.,in press,1998. for Trimble antennashas greatly reducedthe dependenceof Ware, R., C. Aber, C. Rocken,andF. Solheim,Sensingintegratedwater sub-hourlyestimatesof total zenith delay on satellite cutoff
angle. PW variationscan be of order1-2 mm in precipitable water if these measuresare not taken. Biases among WVR, radiosonde,and GPS estimatesof precipitable water are of the sameorder.Analysis of longer spansof FSL data has shown that these measuresare effective in improving the long-term
precisionof GPSPW estimates. We cannotclaim, however,to haveimprovedaccuracysincethereis no independentstandard available for comparison. New biases may appear when absolutephase center models become available for Dome Margolin chokering antennas,particularlyat low elevation
vaporalongGPS ray paths,Geophys.Res.Lett., 24, 417-420, 1997.
Y. Bock, P. Fang,Cecil H. andIda M. Green Instituteof Geophysics and Planetary Physics,Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, CA 92093-0225. (email:
[email protected];
[email protected]). M. Bevis,Hawaii Instituteof Geophysicsand Planetology,University
of Hawaii,Honolulu,HI 96822(email:
[email protected]). S. Gutman, D. Wolfe, NOAA, 325 Broadway, Boulder, CO 80303 (email:
[email protected];
[email protected]).
(ReceivedApril 1, 1998;revisedJuly20, 1998; acceptedAugust13, 1998)
