Adv. Space Res. Vol. 6. No. 9, pp. 89—98. 1986 0273—1177/86 S0.OO + .50Printed in Great Britain. Al! rights reserved. Copynght© COSPAR

GRAVITY MODEL DEVELOPMENT FORPRECISE ORBIT COMPUTATIONSFOR SATELLITE ALTIMETRYJamesG. Marsh,* Francis J. Lerch,* David E. Smith,*

Steven M. Klosko,** Erricos Pav1is~~*and Ronald G. Williamson**

*NASA Goddard Space Flight Center, GeodynamicsBranch!

Code 621, Greenbelt, MD 20771, U.S.A.**EG&G Washington Analytical ServicesCenter, Incorporated,Lanham, MD 20706, U.S.A.

ABSTRACT

Satellite altimeters have been developed which have the capability of’ measuring the surfacetopography of the ocean over entire basins for time periods of several years with aprecision of a few cm. The combination of these data with accurate satellite positionInformation, subsurface measurements and models of the density field can be used todetermine the general circulation of the ocean and its variability. The Topex altimeteroceanographic experiment proposed for the early 1990’s requires a radial orbit accuracyapproaching 10 cm. Considerable progress has been made at the Goddard Space Flight Centerin developing precision orbit determination to support satellite altimetry analysis. Thisprogress is attributed to the development of more accurate models of the earth gravityfield, earth and ocean tidal effects, a reference coordinate system as well as Improveddrag and solar radiation pressure computations. This computational system has been usedfor the Seasat data acquired during the 1978 time period and has produced an rms radialaccuracy of about 50 cm. A first step towards the development of a new Interim gravitymodel is presented. Global orbit determination accuracies have been improved using thesenew PGS-T1 and T2 fields.

INTRODUCTION -

Gravity field development has been art on—going activity at Goddard Space Flight Center(GSFC) for at least fifteen years. The models which have been produced, have beendesignated with the acronyms “GEM” standing for Goddard Earth Models and “PGS” forPreliminary Gravity Solutions. When published, global models are given the GEM designation,whereas models of interest (e.g. tailored fields, preliminary solutions) are named PGS.Over the last decade these models have generally kept pace with the rapid improvementswhich have occurred in the precision by which near—earth satellites are tracked and theorbital accuracy requirements of the missions themselves. In order to do so when globalmodels were inadequate, some models of a satellite—specific, tailored character weredeveloped. However, new NASA missions foreseen for the 1990’s require further globalgravity model improvement to achieve their mission objectives. In particular, theTopex/Poseidon oceanographic satellite (planned for the early 1990’s) which will carry aradar altimeter, as its primary instrument, requires a radial orbit accuracy of ±13cm.

The achievement of ±13cm radial accuracy for the 1300km altitude TOPEX/Poseidon satelliteis quite difficult. Many force and measurement models must be evaluated and undoubtedlyimproved to achieve this stringent requirement. Table 1 lists some of the requirementswhich need to be addressed. Although the adequacy of each of these models needsreassessment, the principal limitation in reaching the TOPEX! Poseidon objective is theadequacy of the gravity field modeling available today. Current orbit determination capa-bilities using any contemporary gravity model would produce a ±50 cm or so radial uncer-tainty on TOPEX/Poseidon. Even after an extensive development effort for the improvementof the geopotential model, gravity error is expected to remain as the largest contributingerror source for altimetry utilization. Table 2 /1/ presents the error budget projectedfor TOPEX altimeter experiments.

The recovery of a new Interim Gravity Model is both costly and time consuming. Itrequires the arduous analysis of large amounts of data spanning diverse observationalsystems and the building of large numerical systems of equations permitting a simultaneoussolution of several thousand unknowns. Consequently, the preparation of an improved modelfor missions which are still in the planning stages requires extensive pre—launchresearch. Also, the errors in the the field must be thoroughly understood to obtainreasonable estimates of future trajectory determination accuracy on TOPEX.

Approximately two years ago, a major gravity field improvement effort was undertaken byGSFC and the Center for Space Research at the University of Texas. This reportdiscusses two preliminary gravity models which have been recently developed as a first stepin reaching the TOPEX/Poseidon modeling goals. They have been obtained by GSFC from an

89JASR 6~9—G

90 J. G. Marshetal.

analysis of exclusively satellite tracking observations. These spherical harmonic modelsare complete to degree and order 36 and are called Preliminary Gravity Solutions - Ti andT2. Other models which will include satellite—to—satellite tracking, spaceborne radaraltimeter observations and surface gravity measurementsare in the planning stages. Theselater fields will all be based upon the long wavelength information contained within the Tiand 12 fields.

Although the demands of future orbital missions made the re—recovery of’ a gravity modeldesirable, the availability of the CYBER 205 “super—computer” at GSFC played a large rolein making this task both feasible within the time constraints imposed upon us and practicalfrom a resource assessment. The vectorization of our orbit determination GEODYNsystem andthe SOLVE least squares solution system was a major step in laying the foundation for acomplete and total re—iteration of our previous gravity modeling activities. The last suchre—iteration of all least—squares normal matrices occured more than ten years ago inpreparation for the GEM—7gravity model /3/.

THE DEVELOPMENTOF PGS-Ti and 12

The total reiteration of the data analysis and matrix generation activities for PGS—T1 andT2 permitted a consistency heretofore unobtainable in earlier GEM models in terms ofadopted constants, data treatment, non-conservative force modeling and in the definition ofa reference frame. In the past, as the state of the science evolved, only the most recentdata sets benefitted from improved modeling. The inconsistencies associated with anevolving science and the lag time required for their implementation in our data analysishave been avoided by design in the creation of PGS-T1 and —T2. Models with “clearparentage” have now been produced which are based largely on the constants defined by theMERIT Standards /14/ with some significant improvements. Additionally, other NASA activ-ities like the Crustal Dynamics Program have provided a priori station coordinates andearth rotation series going into the development of our new fields. These models, valuesand treatments are described within this report. The speedof the Cyber 205 system allowedthe new computation of 500 normal matrices in less than three months time.

A brief overview of the activities which have been completed at Goddard to develop PGS—T1and T2 is shown in Table 3. The woCk which is described therein was quite extensive, butwas found to be necessary. The unique internal consistency of the fields could only beobtained through this elaborate preparation of reference parameters, station coordinates,and constants and the implementation of’ significant advancementsin our software systems.A general description of’ the constants and force models employed in solution is found inTable l4~ The details of the computation of a new set of apriori tracking stationcoordinates Is found in Table 5. Never before have we spent so much effort in thepreparation of the apriori reference coordinate system and correspondingstation geodeticsfor a new gravity field.

An overview of the P05—Ti and 72 solutions is presented in Figure 1. The fields areidentical in size and data content. However in PGS—T2, 66 ocean tidal parameters wereadjusted simultaneously with the gravity field. The PGS—T1 and T2 are very close sinceboth fields were calculated using large models for earth and ocean tides. The earth tidalmodel was that developed by Wahr /5/. The ocean tidal models were developedas part of oursolution preparation and were predicted from point admittances wi~hin the long period,semi— diurnal and diurnal bands. As a result, over 600 ocean tidal coefficients wereutilized to give long wavelength modeling for thirty—two major and minor tidal constituents/6/.

TRACKING DATA

There are perhaps Sixty satellites which received Sufficient tracking to warrant theirconsideration for inclusion in our gravity modeling activities. The TOPEX orbitdetermination requirements are such that at least a four—fold Improvement over existingfield accuracies is necessary. Such an improvement can only be accomplishedwith improveddata handling and validation directed at existing historical data sets. Some manageableframework for selecting, qualifying and processing those data which were deemed mostimportant was developedas a preliminary step in the creation of PGS—Ti and T2.

One of the first tasks was the selection of the most important data sets upon which a“satellite—only” field could be computed. The sixty objects which had geodetic qualitydata sets and orbits which were reasonably free of large perturbations due to air drag wereevaluated according to certain criteria: (a) the quality, quantity and global distributionof’ their tracking data sets, (b) the uniqueness of orbital characteristics, Cc) an estimateof the size of the non-conservative perturbations on the satellite, Cd) the similarity ofthe orbit to that anticipated for TOPEX, Ce) the distribution of the data set over thesatelite’s apsidal period and (f) the sensitivity of the satellite’s orbit to presentweaknesses in existing gravity models.

Gravity Model Development 91

Laser systems are currently the most accurate and advanced means of precision satellitetracking. These ranging systems have also substantially evolved and have undergone nearlya ten—fold improvement in system precision every five years of the last decade. The evolu-tion of laser systems typify the progress which has been made in monitoring the motion ofnear-earth satellites and has resulted in much more stringent demands for geopotentialmodels capable of utilizing data which now are accurate to a few centimeters. Obviously,our data selection criteria found that the laser data was very important and it was heavilyused in the development of PGS—T1 and T2. There are ten satellites which were tracked byNASA’s laser systems. The seven satellites which had third generation laser tracking wereused In our new models.

Eleven satellites which were ranked in the top fifteen overall, were selected. A summaryof’ the data which were used to form the new models is presented in Table 6. The number ofobservations, the number of individual normal matrices and the data types are described.While approximately 80% of the data found in PGS—Ti and 72 have not been used previously inGEM solutions, the overall amount of data which is now utilized is comparable to that whichwas analyzed to produce “satellite—only” fields such as GEM—9 /7/. Preparation of sevenadditional low inclination satellite data sets for inclusion in the TI and T2 models isalready underway. A field containing these additional data sets (a 19 satellite solution)will be published as GEM—Ti. Preliminary tests with a subset of these new low inclinationdata incorporated within the solution indicate that the zonal harmonics are betterresolved, but little else changes in the performance of the field on our test data sets.

EVALUATION OF THE PGS—T1 AND T2 GRAVITY MODELS

One of the best ways, and in our case, most relevant means for assessing the accuracy of agravity model comes through tests using orbital tracking data. A stzeable number of suchtests have been performed on our new fields. Table 7 compares the RMS of fit to satellitetracking data sets obtained from several contemporary geopotential models (both ours andthose from Europe) with what is now obtained in PGS—T2. The results indicate a verysignificant amount of improvement in orbital modeling with the use of PGS-T2. Thisimprovement is noteworthy because PGS—T2now out—performs even “tailored” models in orbitcomputational accuracy.

Starlette is an excellent vehicle for field assessment. It is orbiting at a much loweraltitude than Lageos (950Km vs 5900km) yet has small non—conservative perturbations (likeLageos) given its great density and small surface area. Starlette has been tracked by aglobal network of’ lasers and has a geographically well—distributed data complement. Byorbiting at 950km, Starlette sees a richer and more complicated gravity field than TOPEXand therefore is important for assessing TOPEX modeling capabilities. In the past atailored gravity model /2/ called PGS-1331 was developed for Starlette and adopted for useon this orbit for the MERIT Campaign. Remarkably, as shown in Figure 2, the new PGS—T2nowfits the Starlette data at the 20cm RMS level compared to 75cm found with PGS—i331. Thisis a very dramatic reduction in rms fit and indicates to us that all of our work towardsthe recovery of’ an improved gravity model has been successful. We believe that 10cm radialaccuracies are now being achieved for Starlette based upon these results. Test againstindependent Lageos observations comparing GEM—L2and PGS—T2 also indicate field improve-ment. These results are shown in Table 8. GEM-L2 was adopted for MERIT Lageos analyses.

Seasat altimetry has also been used to test the radial performance of the new fields. Byusing an altimeter crossing arc technique, the non—geographically correlated radial errorsin the orbit can be directly measured. In the past, as indicated in Figure 3, altimetrydata was needed in the gravity solution to achieve sub—meter radial modeling on thisorbit. To achieve the best results, Seasat altimetry was used. Our PGS-T2 model isindependent of all altimetry yet still performs at a considerably improved level from thatobtainable in PGS—S14 /8/ which was a Seasat tailored field. The improvement presented inFigure 3 Is global in nature, as shown in Figure 14 where PGS—T2 outperforms PGS-S

14 in allgeographic locations.

The results which have been shown indicate that a single new model out—performs eventailored models on all satellite orbits tested. Clearly, at least to us, an improvedglobal estimate of the field has been achieved with an improved description of the geoid.This later conclusion Is confirmed with tests against Seasat derived oceanic mean gravityanomalies. A base model has been developed which, when augmented with additional satellitetracking, satellite tracking satellite, altimetry, and surface gravity data sets, willyield a highly accurate new interim gravity model for TOPEX operations.

SUMMARY

The salient points describing GSFC’s latest gravity field development activities are shownin Table 9. While preliminary, we feel that the accomplishments to date are of great

92 J. G. Marsh et al.

significance and Indicate major modeling advancements. Much remains to be accomplished asour TOPEX objective Is approached. The plans for our future are shown in Table 10.Nevertheless, results to date Indicate that substantial progress has been made in ourcontemporary models of the earth’s geopotential.

REFERENCES

1. R. Stewart, L.L. Fu, and M. Lefebvre, “Science opportunities from the Topex/Poseidonmission,” Jet Propulsion Laboratory Publication 86—18, (1986)

2. J.G. Marsh, F.J. Lerch, and R.G. Williamson, “Precision geodesy and geodynamics usingStarlette laser ranging,” J. Geophys. Res., 90, 811, 93335-93145, (1985)

3. C.A. Wagner, F.J. Lerch, 3. Brownd, and J. Richardson, “Improvement In thegeopotentialderived from satellite and surface data (GEM 7 and 8),” J. Geophys. Res.,

82, 5, (1977)

LI. N. Melbourne, et al., “Project Merit Standards,” U.S.N.0. Circular No. 167, December(1983)

5. J. Wahr, “The tidal motions of a rotating, elliptical, elastic, and oceanlessearth,”Ph.D. Dissertation, Univ. of Colorado, (1980)

6. D.C. Christodoulidis, R.G. Williamson, 0. Chinn and R. Estes, “On the prediction ofocean tides for minor constituents,” 10th InternatIonal Symposium on Earth Tides,Madrid, Spain, 1986.

7. F.J. Lerch, S.M. Klosko, R.E. Laubscher, and C.A. Wagner, “Gravity model Improvementusing GEOS—3 (GEM 9 and 10),” J. Geophys. Rem., 84, 138, 3897-3915 (1979)

8. F.J. Lerch, J.G. Marsh, S.M. Klosko, and R.G. Williamson, “Gravity model improvementfor Seasat,” J. Geophys. Rem., 87, C5, 3281—3296 (1982.1)

Gravity Model Development 93

TAStE 1 Precision Orbit Computations in Support of Satellite Altimetry: Requirements

• SOFTWARE DEVELOPMENT FOR PRECISIONORBIT DETERMINATION AND GEODETICPARAMETER ESTIMATION

• IMPROVED EARTH GRAVITY AND TIDAL MODELS

• IMPROVED NON-CONSERVATIVE FORCE MODELS

S ACCURATE EARTH ORIENTATION ANDTRACKING STATION COORDINATES

S CONSISTENT CONSTANTS

S GOOD UNDERSTANDING OF HISTORICAL DATA

S ACCURATE TRACKING SYSTEMS

TABLE 2 Topex/Poseidon Measurement Uncertainty (1 Sigma)

[ERRORSOURCE [UNCERTAINTY[

ALTIMETER• instrument noise 2.0 cm• bias/drIft 2.0

MEDIA• EM bias 2.0• skewness 1.0• tropospheric refraction-dry term 0.7• tropospheric refraction-wet term 1.2• ionospheric refraction 1.3

0R~IT• gravity 10.0• station geodetics 5.0• higher order ionosphere (doppler) 5.0•GM 2.0• atmospheric drag 1.0• solar radiation pressure 1.0• earth albedo radiation 1.0• earth and ocean tides 1.0• station and spacecraft clock 1.0• tropospheric effects 1.0

RSSAbsolute Error [~i3.3cmi

MAJOR ASSUMPTIONS

I. duel frequencq altimeter ‘1. -‘1300 km altitude2. duel frequencij radiometer 8. no anomalous dots3. upgraded TRAN(T tracking sqstem (eq no rain)

(40 ,tstion,) 9. improved qr.vit~j model4. altimeter data averaged over 3s tO. ~3 mbar surface pressure5. H 1/3 =2m, wave skewness 0.1 from weather charts6. tabular corrections b.~edon limited Il. 100 ~.ts spececraft clock

waveform tracker comparisons

94 J. G. Marshec al.

TABLE 3 Summary of GSFC Activities Culminating in a Preliminary Topex Gravity Model

• SATELLITE RANKING

• DATA CATALOGINGAND ARC SELECTION

• DATA VALIDATION

• NON-CONSERVATIVE FORCE MODEL TESTING

• GENERATION OF NEW POLAR ?IOTION SERIES

• CREATION OF STATION GEODETIC FILE IN NEWREFERENCE SYSTEM

S DEVELOPMENT OF EXTENSIVE LONG WAVELENGTHOCEAN TIDAL MODEL

• ADOPTION OF UNIFORM SET OF CONSTANTS

• VECTORIZATION OF SOFTWARE ON CYBER 205 COMPUTER

• CREATION OF DATA ANALYSIS AND MATRIX GENERATIONPROCEDURES COMPATIBLE WITH CYBER RESOURCES

TABLE 4 Constants for Normal Equation Generation at GSFC Adopted for PGS—T1 and PGS—T2

APRIORI GRAVITY MODEL

GE1I-L2 FOR LAGEOSPGS-I33I FOR STARLETTEP05-54 FOR SEASATGEM-lOB’ FOR OTHER SATELLITES

PRIME () INDICATES FIELDS RESOLVEDHOLDING C,S ~ a 0

EARTH TIDES

WAHR WITH k3NOMINAL - .3, OPHASE

OCEAN TIDES

CHRIST000ULIDIS fT AL MODEL WITH§00 INDIVIDUAL TERMS, PREDICTED FROMOCEANOGRAPHIC MODELS USINGAO?IITTANCES

TIDAL DEFORMATIONS

h, AND 3 AT MERIT VALUES

~ .JIL.

GM = 398600 436~. 6378I37kmI/f = 298257

POLAR MOTION AND Al-UTI

ZERO MEAN SET OF POLAR MOTIONSBASED ON 6 YEARS OF SLR DETERMINATIONS

STATION COORDINATES

250 STATIONS TRANSFORMED TO LAGEOSSI-b AND ROTATED INTO NEW POLARMOTION SYSTEM

THIRD BODY EFFECTS

PLANETS MERCURY THROUGH NEPTUNE

ZA~INSTANTANEOUS SPIN-AXIS

COORDINATE SYSTEM

J2000

RELATIVITY

NONE

Gravity Model Development 95

TABLE 5 Station Coordinate Determination

OBJECTIVE:

TO DETERMINE THE APRIORI COORDINATES FOROVER 250 TRACKING STATIONS BASED UPONTHE PRECISELY DETERMINED GLOBAL LASER

STATIONS DEVELOPED WITHIN NASASCRUSTAL DYNAMICS PROGRAM.

tIETHOD:

STATION COORDINATES ARE OBTAINEDAS FOLLOWS IN ORDER OF PREFERENCE:

• LASER STATIONS FROM SL-6ARE USED DIRECTLY

• SURVEY TIES FOR NEAR-DY SITESARE USED TO TIE NON-LASER TOSI-B LASER POSITIONS

• TRANSFORMATION RELATING LOCALDATUMS TO THE SL-6 GEOCENTRICSYSTEM ARE USED TO TIE ALLCOORDINATES FOUND ON SURVEYEDDATUM

• TRANSFORMATIONS BETWEEN GEPI-9AND SI-B COORDINATE SYSTEMSHAVE BEEN UTILIZED IF NO OTHERTIES ARE AVAILABLE.

DOPPLER STATIONS WERE DIRECTLY DETERMINEDWITHIN THE SL-6 SYSTEMS THROUGH THE USEOF SEASAT LASER AND DOPPLER DATA SETS.

Fig. 1. Pgs—T1 and PGS—T2 description of preliminary Topex gravity solution

MODELED ADJUSTED

PGS-Tl PGS-T2 ~ PGS-Tl PGS-T2

GRAVITYFIELD 36X36 36X36 ~ (36X361 136X36]

EARTH TIDES WAHR WAHR none none

OCEAN TIDES 600 TERMS BOO TERMS none 66 TERMSI

STATIONS SL - 6 SL - B none none

TIDAL DEFORM. MERIT MERIT none none

GM 398600.436 398600.436 none none

~! ~JbON newOrneon new ~ ~ Il979~~1 [1979-831

96 J. G. Marshet at.

TABLE 6 Data Utilized in Preliminary Topex Gravity Model : 1986

NUMBER OF NUMBER OF

SATELLITE DATA TYPE NORMAL MATRICES OBSERVATIONS

LAGEOS LASER 58 144527STARLETTE 46 57356GEOS-1 46 71267GEOS-2 28 26613GEOS-3 35 42407BE-C 39 64240SEASAT 14 14923[St/B TOTAL -LASER 269 42t353~

SEASAT DOPPLER 15 136042OSCAR-14 .L 13 63096[SI/B TOTAL - DOPPLER 26 201140 I

GEOS—l CAMERA 43 60750GEOS-2 46 61403ANNA 30 4463TELSTAR 30 3962BE-C 50 7501BE-6 20 1739St/B TOTAL - CAMERA 219 139,616

TOTAL 516 762,311

There ore 140 odditionel motrices reedyto be used in the solution.

TABLE 7 Gravity Model Comparisons Using Tracking Data (rms of fit)

SATELLITE ~ODEL

GEm-L2 GEm-loB GRIm- 3B IPGST2I

[LASER (m)[

LRGEOS 0.014 0.162 0.251 0.060

0.102 0.170 0.206 0.073STHHLETTE 1.26 1.12 3.65 0.19

BE-C 0.91 ~•75 5.4g 0.47

GEOS-1 0.95 0.61 1.62 0.66

f~EOS-2 1.06 1.34 3.32 0.71

GEDS-3 1.57 1.37 3.11 0.73

[~PPLER (Cm/SEC)j

SERSAT 1.49 1.21 2.55 0.63

OSCRR-14 1.46 iiq 2.34 1.11

Gravity Model Development 97

Fig. 2. Precision orbit computations for the Starlette satellite using the May 1986 Topex earth gravity model

STAPLETTE I

PERIGESIcr. 51010.1 I1.5 APOG~~. 11O5~ IO~RADIUS 12CM I

~~ ~,INCI_ 49.0 osolMASS 41295KG

w~ 1.0 ‘ APRIORIIAOOEL

~ 0.73 METERSU-U- _____________________________________0Cl,~ 05

TOPEX MODEL

~7~IIIIII 0.23 METERSIII I

JAN FEB MAR APR

DATE (1984)

TABLE 8 Comparison of Gravity Models With Lageos Laser Data: Annual 1985 Solution

[~~EL RMS (CM) FOR ANNUAL ISOLUTION

GEtI-L2 7.4

PGS—T2 6.0

0 1985 DATA HAS NOT BEEN UTILIZED IN EITHERGEM-L2 OR PGS-T2. ANNUAL SOLUTION ADJUSTSSTATION COORDINATES AND POLAR MOTION.

Fig. 3. Altimeter crossover results for Seasat

RADIAL IMODEL_[ DATA CONTENT ORBIT ERROR

_____ __________ (M)

PGS-S1 GEM-9+ SEASAT LASER 2.1

PGS-S2 GEM-9~SEASAT LASER 1 .8AND S-BAND RADAR

PGS-S3 GEM-l08 (GEOS-3 ALT) 1.2+ SEASAT LASER/S-BAND

PGS-S4 P6S-S3 + SEASAT ALTIMETRY 0.7

IPG~T2j NEW SATELLITE ONLY MODEL 0.5WITH SEASAT DOPPLER

DAT A

98 1. G. Marsheta!.

Fig. 4. Geographic comparison of crossover errors between PGS—S4 and PGS—T2

~?t~ ~6/76~ ~lI~0/g6 ____ ____

~1.05/75 1.23/,93 1.301.91. l.IOF.74 104/.70‘

I *6/79 1.16/73 =(*39/65 1,071.57 l’.95f.50________ _________ _________ ~ l• 1 I

.97/.72 1.0:1.63 *09/.71 ~ l.061.7e

.911.90 .901.03 1,041.59 1.06/.7* .90/.93 .651.70

tElls IN SIOCE: lItTERS)

TOTAL RMSFOR 4444 CROSSOVERS4

P65=12 • .81 PGS—S4~ 1.05 ELY: 54/12

FIOPI S SIX OAT AUCS

TABLE 9 Summary : PGS—T1 and PGS—T2 Gravity Models

• THE MODEL

(1) A SATELLITE-ONLY MODELCOMPLETETO DEGREEANDORDER36 GENERATED FROM II TOP PRIORITY DATA SETS

(2) PGS-T2 INCLUDES MOST COMPLETE TO DATE SATELLITE

DERIVED OCEAN TIDAL MODEL (66 TERMS).(3) MODELS ARE BASED ON THE BEST AVAILABLE SET OF

CONSTANTS AND FORCE MODELS.

.ACCURACY(I) RIIS OF FITS TO TRACKING DATA HAVE BEEN GREATLY

REDUCED EVEN WHEN COMPARED TO EARLIER TAILORED”MODELS.

(2) OVERALLIMPROVEMENTSEEN IN ALTIMETER CROSSOVERSON SEASAT ALTHOUGH UNLIKE EARLIER SOLUTIONS,NEW MODEL DOES NOT YET CONTAIN ALTIMETRY.

(3) GEOID COMPARES QUITE FAVORABLY. EVEN AT HIGH DEGREE,WITH MODELS UTILIZING ALTIMETRY AND ALTIMETRICALLYDERIVEO MEAN SEA SURFACES.

TABLE 10 Future Plans

• GRAVITY ~0DEL DEVEL0P~EflT

ADDITIOTIAL DATA: SST. ALTImETRY,

SURFACE GRAVITY, moRE SATELLITES

CALiBRATIOn OF FIELD ACCURACY

ITERATIOfl OF FIELD

• GEODETICS

ImPROVED DOPPLER COORDInATES

ImPLEmEnT PLATE ITIOTIOfl mODEL

OCEAn LOADInG

• I~PLE~EflTSOFTWARE SYSTE~S

On flEW CO~PUTERS• DEVELOP I~PROVED TESTIflG

TECHflIOUES FOR EVALUATIOfl OFOF ORBIT DETERITIIflATIOfl ERRORS

• flEW TRACKInG CAmPAIGns