The Development of the Joint NASA GSFC and the
National Imagery and Mapping Agency (NIMA)
Geopotential Model EGM96

NASA/TP-1998-206861

Table of Contents

Abstract

Errata

     
     
       
Section Title Author(s) Page
       
1. Introduction RHR 1-1
1.1 References   1-3
       
2. The Development of the Global Topographic Data Base JGP95E   2-1
2.1 Introduction JKF 2-1
2.2 Data Requirements and Data Availability NKP 2-2
2.3 The 5´x5´ Global Digital Topographic Model Development NKP 2-4
2.3.1 Data Base Development Activities at NIMA JKF 2-4
2.3.2 Data Base Development Activities at RSTX NKP 2-6
2.3.3 The Merging of the NIMA and RSTX Data Bases NKP/JKF 2-14
2.3.4 The Evolution of the JGP95 Data Bases NKP/JKF 2-19
2.4 Local Elevation Grids for Terrain Corrections and Residual Terrain JKF 2-24
  Model Effects    
2.5 Development of Spherical Harmonic Coefficient Sets Related to the NKP 2-26
  Topography    
2.6 Summary NKP 2-28
2.7 References   2-29
       
3. The Surface Gravity Data   3-1
3.1 Introduction NKP 3-1
3.2 Detailed Surface Gravity Files SCK 3-2
3.2.1 North America SCK 3-3
3.2.2 South America SCK 3-4
3.2.3 Europe SCK 3-5
3.2.4 Africa SCK 3-6
3.2.5 Asia SCK 3-7
3.2.6 Australia SCK 3-9
3.2.7 Greenland SCK 3-9
3.3 Computational Methodology SCK 3-12
3.3.1 Preprocessing of Detailed Gravity Anomaly Data SCK 3-13
3.3.2 Methodology for 30´ Mean Free-Air Anomaly Computation SCK 3-15
  From Point Bouguer Gravity Anomalies    
3.3.3 Methodology for 30´ Mean Free-Air Anomaly Computation SCK 3-19
From Point Free-air Gravity Anomalies    
3.3.4 Downward Continuation of Airborne Gravity Data Over the Arctic SCK 3-19
and Antarctica    
3.4 Final 30´ Mean Gravity Anomalies Over Land Areas NKP/SCK 3-22
3.5 Final 1° Mean Gravity Anomalies NKP/SCK 3-26
3.5.1 1° Mean Surface Gravity Anomalies Over Land Areas SCK 3-29
3.5.2 1° Mean Surface Gravity Anomalies Over Ocean Areas SCK 3-29
3.6 Summary SCK 3-30
3.7 References   3-30
       
4. The Altimeter-Derived Gravity Anomalies RGT 4-1
4.1 GEOSAT RGT 4-2
4.1.1 NIMA GEOSAT Processing, 1985-1994 RGT 4-2
4.1.2 NIMA GEOSAT Processing, 1994-1996 RGT 4-9
4.2 ERS-1 RGT 4-22
4.3 The Final Altimetry 30´ Mean Gravity Anomaly File RGT 4-24
4.4 Summary RGT 4-26
4.5 References RGT 4-27
       
5. Model Evaluation Techniques and Data FGL 5-1
5.1 Orbit Test Description FGL 5-2
5.1.1 SLR Satellite Test Set-1 FGL 5-2
5.1.2 SLR Satellite Test Set-2 FGL 5-2
5.1.3 ERS-1 Orbit tests CMC 5-4
5.1.4 TDRSS Orbit Tests CMC 5-4
5.1.5 TOPEX/POSEIDON First Generation Orbit Residual Tests CMC 5-7
5.1.6 TOPEX/POSEIDON Orbit Comparisons With JPL Reduced- FGL 5-8
  Dynamic Solutions    
5.2 GPS/Leveling Tests RHR 5-9
5.2.1 Geoid Undulation Determination From a Potential Coefficient RHR 5-9
  Model    
5.2.2 The NGS GPS/Leveling Data RHR 5-14
5.3 GPS/Leveling Tests at GSFC NKP 5-16
5.4 Geoid Undulation Tests Through Doppler-Positioned Stations RHR 5-18
5.5 Geoid Undulation Evaluation Using Dynamic Ocean Topography RHR 5-20
Comparisons With Orthonormal Functions    
5.5.1 Basic Equations and Procedures for the DOT Estimations and RHR 5-20
Comparisons    
5.5.2 Geoid Undulation Accuracy in the ON System RHR 5-22
5.5.3 Geostrophic Flow Determination and Comparison RHR 5-24
5.6 Discrete Comparisons With Undulations Implied by Altimeter NKP 5-24
Data and a Circulation Model    
5.7 Undulation Comparisons Along an ERS-1 Track in the Antarctic RHR 5-28
  Region    
5.8 Comparisons With Altimetry-Derived Anomalies NKP 5-29
5.9 References   5-32
       
6. Estimation of the Geopotential Model Implied by the Satellite Tracking Data   6-1
6.1 Introduction FGL 6-1
6.1.1 History and Previous Models SMK 6-1
6.1.2 Background on Geopotential Recovery From Satellite Tracking SMK 6-3
  Data    
6.1.3 EGM96 Force, Measurement, and Reference Frame Models SMK 6-8
6.1.4 Software Used and Method of Solution SMK 6-11
6.2 Satellite Data Processing Description SMK 6-12
6.2.1 Data Employed in JGM-2 and Earlier GSFC Solutions SMK 6-14
6.2.2 TOPEX/POSEIDON (T/P)   6-18
6.2.2.1 Analysis of the T/P GPS Tracking Data ECP 6-18
6.2.2.2 T/P SLR and DORIS Data Processing MHT 6-30
6.2.3 Explorer Platform/Extreme Ultraviolet Explorer (EP/EUVE) TRO/ECP/CMC 6-34
6.2.3.1 EP/EUVE Attitude Considerations TRO/ECP/CMC 6-35
6.2.3.2 Orbit Harmonic Analysis TRO/ECP 6-38
6.2.3.3 GPS-Based EP/EUVE Orbit Determination TRO/ECP 6-43
6.2.3.4 Processing of Tracking and Data Relay Satellite System (TDRSS) Data for EP/EUVE CMC 6-60
6.2.4 GPS/MET FGL 6-69
6.2.4.1 Spacecraft Description FGL 6-69
6.2.4.2 Data Description FGL 6-70
6.2.4.3 Data Processing Methodology and Modeling FGL 6-70
6.2.4.4 GPS/MET Orbit Determination Results FGL 6-71
6.2.5 Additional TRANET Doppler Data RGW 6-75
6.2.5.1 The Early Doppler Data RGW 6-76
6.2.5.2 The Modern Doppler Data RGW 6-79
6.2.6 Additional SLR Data Used in EGM96 MHT 6-83
6.2.6.1 Summary of New Satellites MHT 6-83
6.2.6.2 Tracking Coverage, Modeling, and Parameterization MHT 6-84
6.2.7 Summary of Tracking Data in EGM96 CMC 6-96
6.3 Satellite-Only Model Development FGL 6-98
6.3.1 The IUGG Satellite-Only Solution, PGS5737 FGL 6-98
6.3.2 The Role of the A Priori Power Law Constraint FGL 6-102
6.3.3 The April 1996 Satellite-Only Model, PGS6394 FGL 6-105
6.3.4 Issues Leading to the Final Satellite-Only Model, EGM96S FGL 6-107
6.4 Final Satellite-Only Model Definition FGL 6-109
6.4.1 Weight Selection and Solution Calibration Procedure FGL 6-109
6.4.2 Preliminary Calibration of Continuous Tracking Data Types FGL 6-112
6.4.2.1 GPS/MET FGL 6-112
6.4.2.2 EP/EUVE FGL 6-116
6.4.3 Primary Calibration FGL 6-118
6.4.4 Recalibration Activities FGL 6-126
6.4.4.1 GPS/MET: Further Calibrations FGL 6-127
6.4.4.2 SPOT-2 FGL 6-129
6.4.4.3 Starlette FGL 6-130
6.4.4.4 EP/EUVE FGL 6-131
6.4.4.5 GEOS-3 Tests FGL 6-132
6.4.5 Independent Solution Calibrations FGL 6-134
6.4.6 Final EGM96S Satellite Date Weights CMC 6-136
6.4.7 GM Issues FGL 6-137
6.4.8 Treatment of Tides in EGM96(S) SMK 6-137
6.4.8.1 Solid Earth Tide Modeling SMK 6-138
6.4.8.2 Background Ocean Tide Model: Elimination of Significant SMK 6-139
  Omitted Terms    
6.4.8.3 Design of the EGM96(S) Ocean Tidal Solution SMK 6-142
6.4.8.4 EGM96S Adjusted Ocean Tides SMK 6-144
6.4.8.5 EGM96S Ocean Tides CMC 6-144
6.5 Verification and Validation CMC 6-146
6.5.1 SLR and TDRSS Orbit Tests CMC 6-146
6.5.2 TOPEX/POSEIDON (T/P) Reduced-Dynamic Orbit Comparisons CMC 6-150
6.5.3 Altimeter-Derived Gravity Anomaly Tests CMC 6-151
6.5.4 GPS/Leveling Tests CMC 6-152
6.5.5 Comparisons of EGM96S With JGM-2S CMC 6-153
6.5.6 Covariance Predictions   6-156
6.5.6.1 Geoid Undulation and Gravity Anomaly Error Prediction CMC 6-156
6.5.6.2 Projected Radial Orbit Errors vs. Inclination CMC 6-161
6.6 References   6-164
       
7. The Comprehensive Low-Degree Combination Geopotential Model SMK 7-1
7.1 Altimeter Data as a Satellite Tracking Observation SMK 7-2
7.1.1 Mathematical Model SMK 7-3
7.1.2 Orbit Reduction and Data Weighting Strategies SMK 7-7
  Employed for Direct Use of Altimeter Data    
7.1.3 Data Reduction of Altimeter Satellites   7-7
7.1.3.1 Data Editing Criteria SMK 7-7
7.1.3.2 Variable Data Weighting SMK 7-9
7.1.3.3 Summary of Altimeter Data Used in EGM96 SMK 7-10
7.1.4 Orbit Reduction Results: Altimeter Normal Equations   7-10
7.1.4.1 GEOSAT SMK 7-10
7.1.4.3 TOPEX/POSEIDON CMC 7-12
7.1.4.3 ERS-1 CMC 7-15
7.2 Use of Surface Gravity Data   7-18
7.2.1 Introduction NKP 7-18
7.2.2 Data Preprocessing NKP 7-18
7.2.3 Normal Equations and Geopotential Coefficients NKP 7-23
From Surface Gravity Data    
7.3 Combination Model Development   7-27
7.3.1 The Preliminary Project Combination Models: A Summary FGL 7-27
7.3.1.1 The IUGG Combination Model: PGS5741 FGL 7-27
7.3.1.2 The April 1996 Combination Model: PGS6399 FGL 7-27
7.3.1.3 An Evaluation of the Preliminary Combination Models FGL 7-28
  PGS5741 and PGS6399    
7.3.2 The Path to the Final Project Combination Model FGL 7-29
       
       
7.3.2.1 Validation of the "New" T/P Normal Equations and FGL 7-30
  Selection of the Degree of Truncation for the Dynamic    
  Ocean Topography Solution    
7.3.2.2 Calibration of the TOPEX/POSEIDON Altimeter Data FGL 7-32
7.3.2.3 Selection of the ERS-1 Altimeter Data Weights FGL 7-34
7.3.2.4 Validation of the GEOSAT Altimeter Data FGL 7-36
7.3.2.5 Initial Calibration of the Altimeter Data FGL 7-41
7.3.2.6 GPS/Leveling Tests With Combination Solutions FGL 7-41
7.3.3 The Final Project Combination Solution FGL 7-44
7.3.3.1 Geopotential Comparisons and Error Characteristics FGL 7-44
7.3.3.2 Evaluation of the DOT Solutions for the Final FGL 7-49
  Combination Model PGS7337B    
7.3.3.3 The Altimeter Biases From the PGS7337B (EGM96) Solution FGL 7-58
7.3.3.4 Final Testing of PGS7337B Variants FGL 7-60
7.3.4 Tides CMC 7-63
7.3.4.1 Orbit Tests DSC 7-65
7.3.4.2 Expanded Background Ocean Tide Model: A Recommendation SMK 7-69
7.3.5 Reference Frame Realization MHT 7-70
7.3.5.1 The EGM96 Earth Orientation Parameters MHT 7-73
7.3.5.2 The Relationship of the EGM96 Solution to ITRF94 MHT 7-75
7.3.5.3 The Relationship of the EGM96 Solution to WGS84 ECP 7-78
7.4 Summary CMC 7-81
7.5 References   7-82
       
8. The Estimation of the High Degree Geopotential Models   8-1
8.1 Introduction NKP 8-1
8.2 Alternative Estimation Techniques NKP 8-1
8.2.1 The Numerical Quadrature Approach NKP 8-2
8.2.2 The Block-Diagonal Least-Squares Approach NKP 8-4
8.2.3 Analytical Comparison of the Numerical NKP 8-6
Quadrature and the Least-Squares Approach    
8.2.4 The Block-Diagonal Least-Squares Algorithm: NKP 8-8
Development and Preliminary Investigation    
8.3 The Merged 30´x30´ Mean Anomaly File NKP 8-16
8.4 The Analytical Downward Continuation of Surface YMW 8-21
  Gravity Anomalies to the Reference Ellipsoid    
8.4.1 Numerical Aspects of the Computation of the g1 term YMW 8-24
8.4.2 g1 Term Comparisons in a Local Region YMW 8-26
8.4.3 Global g1 Term Computations and Comparisons YMW 8-27
8.5 Preliminary High-Degree Expansion Developments NKP 8-30
8.5.1 Gravity Anomaly Weighting Procedure NKP 8-33
8.5.2 Analytical Continuation Techniques NKP 8-36
8.5.3 Preliminary Block-Diagonal Solutions NKP 8-38
8.5.4 Treatment of Aliasing Effects in Block-Diagonal Solutions NKP 8-43
8.5.5 Numerical Quadrature Solutions Extending Beyond the NKP 8-49
  Nyquist Degree    
8.5.6 The Use of A Priori Constraints in Block-Diagonal Solutions NKP 8-59
       
8.6 The Final Numerical Quadrature and Block-Diagonal NKP 8-66
  High-Degree Models    
8.6.1 Intercomparison of the V068 and HDM190 Models NKP 8-67
8.7 Summary NKP 8-76
8.8 References   8-78
       
9. The Preliminary Geopotential Models and Their Evaluationo by the SWG   9-1
9.1 Background RHR 9-1
9.2 Results RHR 9-2
9.3 References   9-3
       
10. The Selection of the EGM96 Geopotential Model FGL 10-1
10.1 Evaluation of Selected Models FGL 10-1
10.1.1 Orbit Evaluations   10-2
10.1.1.1 Orbit Evaluations Using SLR Data FGL 10-2
10.1.1.2 Orbit Tests With TOPEX/POSEIDON FGL/CMC 10-6
10.1.1.3 Results of TDRSS Orbit Tests CMC 10-8
10.1.1.4 Evaluation of EGM96 Using Reduced-Dynamic Orbits From the SBL 10-9
  STS-72 Shuttle Laser Altimeter (SLA) Mission    
10.1.2 Evaluation of Candidates Models via GPS/Leveling Data at RHR 10-10
Ohio State    
10.1.3 GSFC GPS/Leveling Tests of Candidate Final Models FGL 10-14
10.1.4 Evaluation of Candidate Models via Doppler Positioned Stations RHR 10-15
10.1.5 Evaluation of Geopotential Models via Ocean   10-15
Circulation Model Comparisons    
10.1.5.1 Dynamic Ocean Topography RHR 10-15
10.1.5.2 Current Velocity Comparisons RHR 10-19
10.1.5.3 A Few Comments on the GCM Comparisons RHR 10-20
10.1.5.4 Geoid Undulation Accuracy and the Highest Degree for Which the RHR 10-21
Determination of Dynamic Ocean Topography Appears Reasonable    
10.1.6 Comparisons With an ERS-1 Profile in the Antarctic Region RHR 10-24
10.1.7 Discrete Comparisons With Geoid Undulations Implied by NKP 10-25
  Altimeter Data and an Ocean Circulation Model    
10.2 The Definition of the EGM96 High-Degree Geopotential Model NKP 10-29
10.3 Spectral Estimates of Gravimetric Signals and Their Associated NKP 10-31
  Errors    
10.3.1 Gravity Anomaly Signal and Error Spectra NKP 10-31
10.3.2 Geoid Undulation Error Estimates NKP 10-35
10.3.3 Error Estimates of Geoid Undulation Differences NKP 10-37
10.4 Radial Orbit Error Predictions From the Geopotential Solution FGL 10-39
  Error Covariances    
10.5 References   10-48
       
11. The EGM96 Geoid Undulation With Respect to the WGS84 Ellipsoid RHR 11-1
11.1 Permanent Tide Considerations RHR 11-1
11.2 The Determination of the Zero Degree Term ((Z) RHR 11-3
11.3 The Coordinate Origin Issue for Undulation Calculation RHR 11-4
11.4 The Calculation of the Geoid Undulation Values RHR 11-4
11.5 References   11-6
       
12. Summary   12-1
12.1 EGM96 Solution Achievements SMK/FGL 12-1
12.2 Future Challenges SMK/FGL 12-5
12.3 References   12-7
       
Acknowledgments      
Appendixes      
A EGM96 A Priori Station Coordinates MHT A-1
B EGM96 A Posteriori Station Coordinates MHT B-1
C EGM96 Gravitational Coefficients and Their Standard Deviations CMC C-1
D EGM96 Dynamic Ocean Topography Coefficients NKP/YMW D-1
E EGM96 and ITRF94 Site Position Differences MHT E-1
       
       
       
Key to Authors      
       
Initials Author Affiliation  
       
CMC Christopher M. Cox Raytheon STX  
DSC Douglas S. Chinn Raytheon STX  
ECP Erricos C. Pavlis University of Maryland  
FGL Frank G. Lemoine NASA Goddard Space Flight Center  
JKF John K. Factor National Imagery and Mapping Agency  
MHT Mark H. Torrence Raytheon STX  
NKP Nikolaos K. Pavlis Raytheon STX  
RGT Ronald G. Trimmer National Imagery and Mapping Agency  
RGW Ronald G. Williamson Raytheon STX  
RHR Richard H. Rapp The Ohio State University  
SBL Scott B. Luthcke Raytheon STX  
SCK Steve C. Kenyon National Imagery and Mapping Agency  
SMK Steven M. Klosko Raytheon STX  
TRO T. Rob Olson University of Colorado, Boulder  
YMW Yan Ming Wang Raytheon STX  
       

Last Updated on March 6, 2001 17:00 UTC.