GEM‐T2 is the latest in a series of Goddard Earth models of the terrestrial gravitational field. It is the second in a planned sequence of gravity models designed to improve both the modeling capabilities for determining the TOPEX/Poseidon satellite's radial position to an accuracy of 10‐cm RMS and for defining the long‐wavelength geoid to support many oceanographic and geophysical applications. GEM‐T2 includes more than 6OU coefficients above degree 36, the limit for GEM‐T1, and provides a dynamically determined model of the major tidal components which contains 90 terms. Like GEM‐T1, it was produced entirely from satellite tracking data. GEM‐T2 however, now uses nearly twice as many satellites (31 versus 17), contains 3 times the number of observations (2.4 million), and has twice the number of data arcs (1130). GEM‐T2 utilizes laser tracking from 11 satellites, Doppler data from four satellites, two‐ and three‐way range rate data from Landsat‐1, satellite‐to‐satellite tracking data between the geosynchronous ATS 6 and GEOS 3, and optical observations on 20 different orbits. This observation set effectively exhausts the inclination distribution available for gravitational field development from our historical data base. The recovery of the higher degree and order coefficients in GEM‐T2 was made possible through the application of a constrained least squares technique using the known spectrum of the Earth's gravity field as a priori information. The error calibration of the model was performed concurrently with its generation by comparing the complete model against test solutions which omit each individually identifiable data set in turn. The differences between the solutions isolate the contribution of a given data set, and the magnitudes of these differences are compared for consistency against their expected values from the respective solution covariances. The process yields near optimal data weights and assures that the model will be both self‐consistent and well calibrated. GEM‐T2 has benefitted by its application as demonstrated through comparisons using independently derived gravity anomalies from altimelry. Results for the GEM‐T2 error calibration indicate significant improvement over previous satellite‐only GEM models. The accuracy assessment of the lower degree and order coefficients of GEM‐T2 shows that their uncertainties have been reduced by 20% compared to GEM‐T1. The commission error of the geoid has been reduced from 160 cm for GEM‐T1 to 130 cm for GEM‐T2 for the 36 × 36 portion of the field. The orbital accuracies achieved using GEM‐T2 are likewise improved. This is especially true for the Starlette and GEOS 3 orbits where higher‐order resonance terms not present in GEM‐T1 (e.g., terms with m = 42,43) are now well represented in GEM‐T2. The improvement in orbital accuracy of GEM‐T2 over GEM‐T1 extends across all orbit inclinations. This confirms our conclusion that GEM‐T2 offers a significant advance in knowledge of the Earth's gravity field.

A major new computation of a terrestrial gravitational field model has been performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). In the development of this new model, designated Goddard Earth Model GEM‐T1, the design decisions of the past have been reassessed in light of the present state of the art in satellite geodesy. With GEM‐T1 a level of internal consistency has been achieved which is superior to any earlier Goddard Earth Model. For the first time a simultaneous solution has been made for spherical harmonic parameters of both invariant and tidal parts of the gravitational field. The solution of this satellite model to degree 36 is a major factor accounting for its improved accuracy. The addition of more precise and previously unused laser data and the introduction of consistent models were also accomplished with GEM‐T1. Another major factor allowing the creation of this model was the redesign and vectorization of our main software tools (GEODYN II and SOLVE) for the GSFC Cyber 205 computer. In particular, the high‐speed advantage (50:1), gained with the new SOLVE program, made possible an optimization of the weighting and parameter estimation scheme used in previous GEM models resulting in significant improvement in GEM‐T1. The solution for the GEM‐T1 model made use of the latest International Association of Geodesy reference constants, including the J2000 Reference System. It provided a simultaneous solution for (1) a gravity model in spherical harmonics complete to degree and order 36; (2) a subset of 66 ocean tidal coefficients for the long‐wavelength components of 12 major tides. This adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor tides and the Wahr frequency dependent solid earth tidal model; and (3) 5‐day averaged Earth rotation and polar motion parameters for the 1980 period onward. GEM‐T1 was derived exclusively from satellite tracking data acquired on 17 different satellites whose inclinations ranged from 15° to polar. In all, almost 800,000 observations were used, half of which were from third generation (<5 cm) laser systems. A calibration of the model accuracies has been performed showing GEM‐T1 to be a significant improvement over earlier GSFC “satellite‐only” models based purely on tracking data for both orbital and geoidal modeling applications. For the longest wavelength portion of the geoid (to 8×8), GEM‐T1 is a major advancement over all GEM models, even those containing altimetry and surface gravimetry. The radial accuracy for the anticipated TOPEX/POSEIDON orbit was estimated using the covariances of the GEM‐T1 model. The radial errors were found to be at the 25‐cm rms level as compared to 65 cm found using GEM‐L2. This simulation evaluated only errors arising from geopotential sources. GEM‐L2 was the best available model for TOPEX prior to the work described herein. A major step toward reaching the accuracy of gravity modeling necessary for the TOPEX/POSEIDON mission has been achieved.

The TOPEX/POSEIDON mission objective requires that the radial position of the spacecraft be determined with an accuracy better than 13 cm RMS (root mean square). This stringent requirement is an order of magnitude below the accuracy achieved for any altimeter mission prior to the definition of the TOPEX/POSEIDON mission. To satisfy this objective, the TOPEX Precision Orbit Determination (POD) Team was established as a joint effort between the NASA Goddard Space Flight Center and the University of Texas at Austin, with collaboration from the University of Colorado and the Jet Propulsion Laboratory. During the prelaunch development and the postlaunch verification phases, the POD team improved, calibrated, and validated the precision orbit determination computer software systems. The accomplishments include (1) increased accuracy of the gravity and surface force models and (2) improved performance of both the laser ranging and Doppler tracking systems. The result of these efforts led to orbit accuracies for TOPEX/POSEIDON which are significantly better than the original mission requirement. Tests based on data fits, covariance analysis, and orbit comparisons indicate that the radial component of the TOPEX/POSEIDON spacecraft is determined, relative to the Earth's mass center, with an RMS error in the range of 3 to 4 cm RMS. This orbit accuracy, together with the near continuous dual‐frequency altimetry from this mission, provides the means to determine the ocean's dynamic topography with an unprecedented accuracy.

The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model‐1 (JGM‐I) and the postlaunch JGM‐2 Earth gravitational models have been developed to support precision orbit determination for T/P. Each of these models is complete to degree 70 in spherical harmonics and was computed from a combination of satellite tracking data, satellite altimetry, and surface gravimetry. While improved orbit determination accuracies for T/P have driven the improvements in the models, the models are general in application and also provide an improved geoid for oceanographic computations. The postlaunch model, JGM‐2, which includes T/P satellite laser ranging (SLR) and Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking data, introduces radial orbit errors for T/P that are only 2 cm RMS with the commission errors of the marine geoid for terms to degree 70 being ±25 cm. Errors in modeling the nonconservative forces acting on T/P increase the total radial errors to only 3–4 cm RMS, a result much better than premission goals. While the orbit accuracy goal for T/P has been far surpassed, geoid errors still prevent the absolute determination of the ocean dynamic topography for wavelengths shorter than about 2500 km. Only a dedicated gravitational field satellite mission will likely provide the necessary improvement in the geoid.

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