gr • Q NASA Technical Memorandum 4019 An Improved Model of the Earth's Gravitational Field: *GEM-TI* J. G. Marsh, F. J. Lerch, B. H. Putney, D. C. Christodoulidis, T. L. Felsentreger, B. V. Sanchez, D. E. Smith, S. M. Klosko, T. V. Martin, E. C. Pavlis, J. W. Robbins, R. G. Williamson, O. L. Colombo, N. L. Chandler, K. E. Rachlin, G. B. Patel, S. Bhati, and D. S. Chinn N87-29967 {NASA-TM-_019| AN IMPROVED MODEL OF THE EAETH'S GRAVITATIONAL FIELD: GE_-TI 'NASA) 351 p Avail: NTIS HC A|6/MF A01 CSCL 08G Unclas Hi/_6 00998_3 JULY 1987 NASA I I NASA Technical Memorandum 4019 An Improved Model of the Earth's Gravitational Field: *GEM-TI* J. G. Marsh, F. J. Lerch, B. H. Putney, D. C. Christodoulidis, T. L. Felsentreger, B. V. Sanchez, and D. E. Smith Geodynamics Branch S. M. Klosko, T. V. Martin, E. C. Pavlis, J. W. Robbins, R. G. Williamson, O. L. Colombo, N. L. Chandler, and K. E. Rachlin EG&G Washington Analytical Services Center, Inc. G. B. Patel, S. Bhati, and D. S. Chinn Science Applications and Research Corporation JULY 1987 National Aeronautics and Space Administration Goddard Space Flight Center 1987 TABLE OF CONTENTS INTRODUCTION ............................... 1 THE GEODYN AND SOLVE SYSTEMS • ° ° ° ° ..... ° ° ° • ° ° • • o ° 9 2.1 SOFTWARE DESCRIPTION ..................... 9 Vectorization of SOLVE .............. 11 Evolution of GEODYN ................ 12 GEODYN II Design Philosophy . 13 GEODYN II Benefits ......... 20 2.1.3 GEODYN II, SOLVE and the TOPEX Gravity Models ........................ 21 2.2 OPERATIONS .... ° ................... ° • ° 25 3.0 REFERENCE FRAME • • . ........ ° • . • . ..... • • • .... 29 3.1 INTRODUCTION .......................... 29 3.2 DESCRIPTION OF THE CONTRIBUTING DATA .......... 29 3.3 DISCREPANCIES BETWEEN DATA SETS ............. 30 3.4 MATHEMATICAL FORMULATION ................. ° 33 3.5 DYNAMIC POLAR MOTION ..................... 38 3.6 SUMMARY • • • ° ° • .... ° .......... • ° • • ° ° ° ° 41 4.0 A PRIORI CONSTANTS ADOPTED IN THE GENERATION OF THE TOPEX GRAVITY MODEL ...... ° .... • ° ° ° ° ° ° ° ° ° • .... 43 4.1 COMMON PARAMETERS ....................... 43 4.1 .I Earth Tides ....... ° • . ° ° • • .... ° ° 43 4.1.2 Ocean Tides ........ • ..... • • . ° ° . 43 4.1.3 Tidal Deformations 44 4.1.4 Earth Parameters ................. 44 4.1.5 Polar Motion and AI-UTI ............. 44 4.1.6 Station Coordinates ............... 45 4.1.7 Third Body Effects ................ 45 4.1.8 Z-Axis Definition ................ 45 4.1.9 Coordinate System ................ 45 4.1.10 Relativity ..................... 46 4.1.11 A Priori Gravity Modeling ........... 46 PR'_F-_DING PAG_ BLANK b/._T _'R_t_ iii _i___'[[_ItOf_ALLY _LANK TABLEOFCONTENTS(cont.) 4.1 .11.I Selection of an A Priori Gravity Model: General Vs. Several Tailored Fields ..................... 47 4.1.11.2 Simulations for Geopotential Solution Using Tailor-Made Vs. General A Priori Models .................... 49 5.0 TRACKINGDATA ................................. 59 5.1 DATASELECTION............................ 60 5.2 INDIVIDUALSATELLITEANALYSES.................. 68 5.2.1 Analysis of SEASATDoppler and Laser Data .... 68 5.2.2 Analysis of OSCARDoppler Data ........... 69 5.2.3 Analysis of GEOS-ILaser Ranging Data ....... 78 5.2.4 GEOS-3Analysis of Laser Ranging Data ...... 84 5.2.5 Analysis of STARLETTELaser Ranging Data ..... 89 5.2.6 Analysis of LAGEOSLaser Ranging Data ....... 98 5.2.7 Analysis of GEOS-2Laser Ranging Data ....... 107 5.2.8 Analysis of Optical and Low Inclination Satellite Observations ................. 108 5.2.9 Analysis of BE-CLaser Ranging Data ........ 128 6.0 DEFINITIONOFA PRIORI GEOCENTRICTRACKINGSTATION COORDINATES.................................. 133 6.1 COORDINATESYSTEMDEFINITION................... 133 6.2 INITIAL STATUSOFSTATIONCOORDINATES............. 134 6.3 THETRANSFORMATIONMODELS..................... 134 Seven Parameter Transformation ........... 136 The Linear Translation ................ 137 6.4 NUMERICALRESULTS.......................... 137 6.4.1 NAD27 to SL-6 Transformation ........... 139 6.4.2 GEM-9to SL-6 Transformation ............ 139 6.4.3 GSFC-73to GEM-9Transformation .......... 139 6.4.4 Other Transformations ................. 140 6.5 DISCUSSION.............................. 140 6.5.1 Transformation Parameters and Accuracies ..... 140 6.5.2 Precision of the Transformations .......... 142 6.5.3 Error Sources ...................... 144 6.5.4 Distortion in the NAD27 Datum ........... 145 6.6 SUMMARYOFSTATIONDEFINITION.................. 147 TABLE OF CONTENTS (cont.) 7.0 FORCE MODELING ............................... 149 7.1 POTENTIAL EFFECTS ........................ 149 7.1.1 Mathematical Formulation of the Potentials 149 7.1.2 The A Priori Static Geopotential Models . 152 7.1.3 The A Priori Body Tide Model ........... 154 7.1.4 A Priori Ocean Tides Models ........... 154 7.2 ATMOSPHERIC DRAG AND SOLAR RADIATION PRESSURE ..... 170 Mathematical Formulation of the Models .... !70 Atmospheric Drag Model Testing ......... 17] Orbit Comparison Results ...... 173 Evaluation of Apparent Timing... 177 Errors .................. 177 7.2.2.3 Conclusions .............. 179 8.0 SOLUTION DESIGN .............................. 183 8.1 COLLOCATION ............................ 183 8.2 STRATEGY FOR DATA WEIGHTING AND FIELD CALIBRATION... 187 8.3 PROBLEMS AND ASSOCIATED BENEFITS WITH A "SATELLITE-ONLY" 36 x 36 SOLUTIONS ........................ 198 9.0 THE GEM-TI SOLUTION RESULTS ...................... 209 9.1 THE GRAVITY MODEL ........................ 209 9.2 OCEAN TIDE SOLUTION ...................... 209 9.3 STATION COORDINATE SOLUTIONS AND COMPARISONS ...... 229 9.3.1 Introduction ..................... 229 9.3.2 GEM-TI Stations ................... 229 9.3.3 Laser Station Solutions .............. 230 9.3.4 Doppler Station Solutions ............. 232 9.3.5 Summary ........................ 235 9.4 EVALUATION OF THE SOLVED POLAR MOTION .......... 235 9.4.1 Introduction ..................... 235 9.4.2 The 1980-84 Solution ................ 236 9.4.3 The Annual and Chandler Cycles ......... 240 9.4.4 Summary ........................ 248 TABLEOFCONTENTS(cont.) 10.0 A CALIBRATIONOFGEM-TIMODELACCURACY............... 249 10.1 THEGEM-TICALIBRATIONOF A SATELLITEMODEL'SERRORS USINGGRAVITYANOMALYDATA................... 254 10.2 CALIBRATIONBASEDUPONFIELDSUBSETSOLUTIONTESTING 263 10.3 COMPARISONSBETWEENGEM-TIANDGEM-L2........... 277 10.4 THENEEDFORLOWINCLINATIONDATA--REVISITED...... 280 10.5 SUMMARY.............................. 287 11.0 GRAVITYFIELDTESTINGONGEM-TI ................... 289 11.1 ORBITTESTING.......................... 289 11.1.1 Orbital Tests on Laser Satellites ....... 290 11.1.2 Orbit Tests On Doppler Satellites ....... 302 11.1.3 Tests Using Low Inclination Data ........ 304 11.1.4 Radial Accuracy on SEASAT............ 307 11.1.5 Tests Using the Longitudinal Acceleration on Ten 24 Hour Satellites ............ 310 11.2 GEOIDMODELING.... ° ............... • • . • 312 11.3 ESTIMATED TOPEX/POSEIDON ORBITAL ACCURACY ........ 313 11.4 ORTHOMETRIC HEIGHTS COMPARISONS .............. 318 12.0 SUMMARY .................................. 325 ACKNOWLEDGEMENTS ................................. 327 REFERENCES ..................................... 329 APPENDIX I: TOPEX GEODETIC FILE: TRANET DOPPLER, LASER, S-BAND TRACKING SITES .......................... 337 APPENDIX II: TOPEX GEODETIC FILE: OPTICAL AND EARLY DOPPLER TRACKING SITES ............................... 343 APPENDIX IIl: A PRIORI OCEAN TIDAL MODEL .................. 347 vi SECTION 1.0 INTRODUCTION Ground-based tracking of artificial satellites has provided an observational data set which has been used to develop spherical harmonic models of the global long wavelength gravity field of the earth. Analyses of these data by the authors and many others have provided a major advance in the field of Geodesy. Since the creation of the National Geodetic Satellite Program in the middle 1960's, a continuous effort has been underway at NASA/Goddard Space Flight Center (GSFC) and other research centers (notably the Smithsonian Astrophysical Observatory, the U.S. Department of Defense, and a cooperative effort between Germany's Deutsches Geodaetisches Forschungsinstitut and France's Groupe de Recherehes de Geodesie Spatiale -- to name a few) to use satellite observations to improve our understanding of the gravity field and enhance our capabilities for modeling near-earth satellite orbital motion. Better knowledge of the geopotential has created dramatic advances in point positioning, in the study of the earth's kinematics and tectonics, in understanding the earth's theology and interior, and in the study of global oceanic processes with spaceborne instrumentation. The geopotential models developed by GSFC are known by their acronym, GEM, standing for Goddard Earth Models. The GEM have generally kept pace with the rapid advances made in the precision by which near-earth satellites are tracked and the orbital accuracy requirements of the missions themselves. However, new NASA missions foreseen for the 1990's require further gravity model improvement to achieve their mission objectives. Of most immediate concern is geodetic support (e.g., for orbit computations and the marine geoid) for the TOPEX oceanographic satellite which is under development for launch in 1991. The 10 to 15 cm radial orbit accuracy requirement of TOPEX, driven by the radar altimeter system, is at least a factor of three beyond the capability of gravity models existing in 1985. There is an additional need for an Interim model