For many applications, the Earth’s gravitational potential, V, is represented by a spherical harmonic expansion, where the potential coefficients in this expansion have been determined by various techniques. Significant improvement in the estimation of the potential coefficients has taken place over the past 35 years [Nerem, Jekeli, and Kaula, 1995], in two general ways. First, the highest degree in the expansion has been extended to increasingly higher degree through the use of additional satellite data and terrestrial gravity data, thereby improving the resolution of the models. Second, the accuracy of the coefficients has been continually improved through the inclusion of additional data that improve in geographic coverage and accuracy over time.

For satellite orbit determination, a spherical harmonic expansion to degree 70 using the heretofore available data has been sufficient for all current applications. However, new geopotential-sensing missions such as GRACE [Bettadpur and Tapley, 1996] will require consideration of a better resolved field. Likewise, detailed geoid models require a resolution better than that available from the present satellite-based models. In the 1970’s, spherical harmonic representations to degree 180 were estimated. In the 1980’s, expansions to degree 360 became available. In 1991, Rapp, Wang, and Pavlis [1991] reported a degree 360 model that was based on the satellite-derived model GEM—T2 [Marsh et al., 1990], sea-surface heights from GEOSAT altimeter data, gravity anomalies derived from satellite altimeter data, surface gravity data, and topographic information. Although a simultaneous solution to degree 360 was described in this report, the final model released, OSU91A, was a blend of a low-degree (50) combination model (including satellite tracking and altimetry data and surface gravity data) and the expansion from degree 51 to 360 from the simultaneous solution. The rationale for such a procedure was described in the cited report. The major limitation in OSU91A stemmed from the lack of precise surface gravity data over large continental regions–for instance, most of Asia.

Since 1991, improvements have continued in the development of "low degree" (to 70) combination models using primarily satellite tracking data and surface gravity data. Examples of this type of solution are the JGM—1 and —2 geopotential models developed to aid the orbit determination of the TOPEX/POSEIDON (T/P) satellite [Nerem et al., 1994]. The JGM—2 model, complete to degree 70, was a postlaunch model incorporating T/P laser ranging data and DORIS tracking data. The low-degree combination model development continued, with the determination of an improvement to the JGM—1 model called JGM—3 [Tapley et al., 1996], using additional laser tracking data, DORIS data, and, for the first time, GPS tracking of the TOPEX/POSEIDON satellite. Degree 360 models were reported by Gruber and Anzenhofer [1993] and Gruber, Anzenhofer, and Rentsch [1995]. The basis for these models was the GRIM4—C4 geopotential model [Schwintzer et al., 1997].

In 1993, the need for improved geoid undulation determinations was becoming increasingly apparent. The primary need was related to the conversion of ellipsoidal height information from GPS determinations to orthometric heights. A related goal for an improved geoid was the establishment of a globally defined geoid that could form the reference surface for a global vertical datum. At this time, the OSU91A model [Rapp, Wang, and Pavlis, 1991] was being widely used for many applications with a known weakness related to using an older generation satellite model as a base, and poor or no surface gravity data in many regions of the world.

A preliminary meeting was held at the 1993 Spring AGU meeting involving Dr. David Smith (National Aeronautics and Space Administration, Goddard Space Flight Center [NASA GSFC]), Muneendra Kumar (Defense Mapping Agency [DMA], which later became the National Imagery and Mapping Agency [NIMA]), and Richard Rapp (The Ohio State University [OSU]) to discuss a possible cooperation between the groups to leverage their long history of research in satellite geopotential recovery and the processing of terrestrial gravity data. Following this positive meeting, followup meetings were held in July and September 1993 at GSFC. With a tentative understanding of mutual interest, a more formal meeting was held at GSFC on October 14, 1993, with presentations by GSFC and NIMA personnel. A discussion took place to draft a Memorandum of Understanding (MOU) between NASA and DMA. The MOU was between the DMA and NASA, on the "Joint Gravity Field and Geoid Improvement Project." As stated in the MOU, "the primary goal is to improve the Earth Gravity Model (EGM), and its associated global geoid, to support terrestrial and extraterrestrial scientific endeavors, as well as to meet the mapping, charting and navigation requirements of both the civil and military sectors." The MOU was signed by NASA on March 11, 1994, and by DMA on April 1, 1994.

The October meeting developed the organization of the joint project through a science working group. To facilitate the activities of the project, four working groups were established: Working Group I, Combination Methods and High Degree Expansions (Chair: Nikolaos Pavlis), Working Group II, Surface Gravity Data Preparations (Chair: Richard Salman), Working Group III, Evaluation of Altimeter Implied Gravity Anomalies (Chair: Ronald Trimmer), and Working Group IV, Satellite Gravity Model Development (Chair: R. Steven Nerem). The chairperson of each working group initially developed the plans and data needed for each area of interest. As the project progressed, personnel and responsibility changes took place. Steve Kenyon from NIMA became involved in the detailed computations with the terrestrial gravity anomaly data, and Frank Lemoine at GSFC continued the direction of the satellite model development after R.S. Nerem accepted a position at the University of Texas at Austin in January 1996.

The overall responsibility for the joint project development was given to the Project Steering Committee. The representatives to the committee were Dr. David Smith from NASA GSFC and Dr. Randall Smith from NIMA. Professor Rapp also served on the Steering Committee.

The next meetings of the science working group took place on January 19, 1994, where the emphasis was on data availability and data needs, and April 5, 1994, where progress reports were given and a milestone plan for overall project deliverables was drafted. This plan called for the delivery of the final potential coefficient model in March 1996. Additional meetings were held throughout 1995 and 1996 to discuss progress and challenges to meeting the agreed-upon goals.

Early in the project planning, it was recognized that international participation in project activities was desirable. A key component in the project was the evaluation of candidate geopotential models. The evaluation of preliminary models through various global and regional tests such as satellite tracking data fits and GPS/leveling undulation comparisons was desired. In November 1994, Professor Rapp, on behalf of the joint project, wrote to Professor Fernando Sansò, Director of the International Geoid Service, asking if this organization would be willing to establish a Special Working Group (SWG) to evaluate the preliminary geopotential models produced by the joint project. These evaluations would be used to aid in the evaluation and selection of the final geopotential model. Professor Sansò kindly agreed to the request and asked Professor Michael Sideris, of the University of Calgary, to chair the SWG subcommittee that took on this role. Professor Sideris agreed and issued the first circular letter to the members of the SWG on January 17, 1995, requesting their support for the effort. With significant SWG-sponsored international participation, a valuable insight into the models was provided, leading to significant help in the selection of the final model.


1.1 References

Bettadpur, S.V., and B.D. Tapley, Assessments of Future Geopotential Mapping Missions, Abstract U22A-2, Eos Trans. AGU Suppl., 77, 17, AGU Spring Meeting, Baltimore, 1996.

Gruber, T., and M. Anzenhofer, The GFZ 360 gravity field model, in Proc. of Session G3–European Geophysical Society XVIII General Assembly, R. Forsberg, H. Denker (eds), 13—18, Geodetic Division, Kort—og Matrikelstyrelsen, Copenhagen, 1993.

Gruber, T., M. Anzenhofer, and M. Rentsch, The 1995 GFZ high resolution gravity model, in: Global Gravity Field, and Its Temporal Variations, Rapp, Cazenave, Nerem (eds), 61—70, IAG Symposium 116, Springer—Verlag, Berlin, 1995.

Marsh, J.G., F.J. Lerch, B.H. Putney, T.L. Felsentreger, B.V. Sanchez, S.M. Klosko, G.B. Patel, J.R. Robbins, R.G. Williamson, T.E. Engelis, W.F. Eddy, N.L. Chandler, D.S. Chinn, S. Kapoor, K.E. Rachlin, L.E. Braatz, and E.C. Pavlis, The GEM—T2 gravitational model, J. Geophys. Res., 95, B13, 22043—22070, 1990.

Nerem, R.S., C. Jekeli, and W.M. Kaula, Gravity field determination and characteristics retrospective and prospective, J. Geophys. Res., 100, B8, 15053—15074, 1995.

Nerem, R.S., F.J. Lerch, J.A. Marshall, E.C. Pavlis, B.H. Putney, B.D. Tapley, R.J. Eanes, J.C. Ries, B.E. Schutz, C.K. Shum, M.M. Watkins, S.M. Klosko, J.C. Chan, S.B. Luthcke, G.B. Patel, N.K. Pavlis, R.G. Williamson, R.H. Rapp, R. Biancle, and F. Noule, Gravity Model Development for TOPEX/POSEIDON: Joint Gravity Models 1 and 2, J. Geophys. Res., 24421—24447, 1994.

Rapp, R.H., Y.M. Wang, and N.K. Pavlis, The Ohio State 1991 Geopotential and Sea Surface Topography Harmonic Coefficient Models, Rept. 410, Dept. of Geod. Sci. and Surv, Ohio State University, Columbus, August 1991.

Schwintzer, P., C. Reigber, A. Bode, Z. Kang, S.Y. Zhu, F.H. Massmann, J.C. Raimondo, R. Biancale, G. Balmino, J.M. Lemoine, B. Moynot, J.C. Marty, F. Barlier, and Y. Boudon, Long-wavelength global gravity field models: GRIM4—S4, GRIM4—C4, J. of Geod., 71, 189—208, 1997.

Tapley, B.D., M.M Watkins, J.C. Ries, G.W. Davis, R.J. Eanes, S.R. Poole, H.J. Rim, B.E. Schutz, C.K. Shum, R.S. Nerem, F.J. Lerch, J.A. Marshall, S.M. Klosko, N.K. Pavlis, and R.G. Williamson, The Joint Gravity Model 3, J. Geophys. Res., 101 (B12), 28029—28049, 1996.