National Imagery and Mapping Agency (NIMA)

Geopotential Model EGM96

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.