ALBERT

Description: The accuracy and validation of global gravity models based on satellite data are discussed, responding to the statistical analysis of Lambeck and Coleman (1983) (LC). Included are an evaluation of the LC error spectra, a summary of independent-observation calibrations of the error estimates of the Goddard Earth Models (GEM) 9 and L2 (Lerch et al., 1977, 1979, 1982, 1983, and 1985), a comparison of GEM-L2 with GRIM-3B (Reigber et al., 1983), a comparison of recent models with LAGEOS laser ranging, and a summary of resonant-orbit model tests. It is concluded that the accuracy of GEMs 9, 10, and L2 is much higher than claimed by LC, that the GEMs are in good agreement with independent observations and with GRIM-3B, and that the GEM calibrations were adequate. In a reply by LC, a number of specific questions regarding the error estimates are addressed, and it is pointed out that the intermodel discrepancies of the greatest geophysical interest are those in the higher-order coefficients, not discussed in the present comment. It is argued that the differences among the geoid heights of even the most recent models are large enough to call for considerable improvements.

Description: Several tests were designed to determine the correct error variances for the GEM-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient by coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment.

Description: Major new computations of terrestrial gravitational field models were performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). This development has incorporated the present state of the art results in satellite geodesy and have relied upon a more consistent set of reference constants than was heretofore utilized in GSFC's GEM models. The solutions are complete in spherical harmonic coefficients out to degree 50 for the gravity field parameters. These models include adjustment for a subset of 66 ocean tidal coefficients for the long wavelength components of 12 major ocean tides. This tidal adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor ocean tides and the Wahr frequency dependent solid earth tidal model. In addition 5-day averaged values for Earth rotation and polar motion were derived for the time period of 1980 onward. Two types of models were computed. These are satellite only models relying exclusively on tracking data and combination models which have incorporated satellite altimetry and surface gravity data. The satellite observational data base consists of over 1100 orbital arcs of data on 31 satellites. A large percentage of these observations were provided by third generation laser stations (less than 5 cm). A calibration of the model accuracy of the GEM-T2 satellite only solution indicated that it was a significant improvement over previous models based solely upon tracking data. The rms geoid error for this field is 110 cm to degree and order 36. This is a major advancement over GEM-T1 whose errors were estimated to be 160 cm. An error propagation using the covariances of the GEM-T2 model for the TOPEX radial orbit component indicates that the rms radial errors are expected to be 12 cm. The combination solution, PGS-3337, is a preliminary effort leading to the development of GEM-T3. PGS-3337 has incorporated global sets of surface gravity data and the Seasat altimetry to produce a model complete to (50,50). A solution for the dynamic ocean topography to degree and order 10 was included as part of this adjustment.

Description: The Goddard Space Flight Center (GSFC) has occupied a central position within NASA with respect to the development of earth gravity models. The gravity models at Goddard, which are referred to as the Goddard earth models (GEM's) have been under development for more than 15 years. The fields have increased in size and (apparent) accuracy with the inclusion of new tracking data, better nongravitational force modeling, and more orbits over a wide range of inclinations and mean motions. The usefulness of the considered models depends largely on accuracy estimates. The present paper is concerned with a reevaluation of earlier accuracy assessments, taking into account the accuracies of the GEM 9 and the GEM-L2 models. It is found that GEM 9 is about 30 percent more accurate than originally estimated in 1979 from older gravimetry data.

Description: The Laser Geodynamics Satellite (Lageos) was the first NASA satellite which was placed into orbit exclusively for laser ranging applications. Lageos was designed to permit extremely accurate measurements of the earth's rotation and the movement of the tectonic plates. The Goddard earth model, GEM-L2, was derived mainly on the basis of the precise laser ranging data taken on many satellites. Douglas et al. (1984) have demonstrated the utility of GEM-L2 in detecting the broadest ocean circulations. As Lageos data constitute the most extensive set of satellite laser observations ever collected, the incorporation of 2-1/2 years of these data into the Goddard earth models (GEM) has substantially advanced the geodynamical objectives. The present paper discusses the products of the GEM-L2 solution.

Description: A computation of a terrestrial gravitational field model called the Goddard Earth Model GEM-T1 is discussed and compared to previous models, including the GEM-L2. The software tools were redesigned for the model, allowing for the optimization of the technique of relative data weighting and model estimation used in GEM solutions. The GEM-T1 model provides a simultaneous solution for a gravity model in spherical harmonics complete to degree and order 36, a subset of 66 ocean tidal coefficients for the long-wavelength components of 12 major tides, and 5-day averaged earth rotation and polar motion parameters for the 1980 period on. GEM-T1 was derived from satellite tracking data acquired on 17 different satellites whose inclinations ranged from 15 degrees to polar. A simulation of the TOPEX/POSEIDON orbit using the covariances of the GEM-T1 model was made. Estimated radial error for the simulation was reduced to less than 30 cm rms.

Description: Goddard Earth Model T1 (GEM-T1), which was developed from an analysis of direct satellite tracking observations, is the first in a new series of such models. GEM-T1 is complete to degree and order 36. It was developed using consistent reference parameters and extensive earth and ocean tidal models. It was simultaneously solved for gravitational and tidal terms, earth orientation parameters, and the orbital parameters of 580 individual satellite arcs. The solution used only satellite tracking data acquired on 17 different satellites and is predominantly based upon the precise laser data taken by third generation systems. In all, 800,000 observations were used. A major improvement in field accuracy was obtained. For marine geodetic applications, long wavelength geoidal modeling is twice as good as in earlier satellite-only GEM models. Orbit determination accuracy has also been substantially advanced over a wide range of satellites that have been tested.

Description: Several tests were designed to determine the correct error variances for the Goddard Earth Model (GEM)-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment. These calibrations (utilizing each of the major data subsets within the solution) yield very stable calibration factors which vary by approximately 10 percent over the range of tests employed. Measurements of gravity anomalies obtained from altimetry were also used directly as observations to show that GEM-T1 is calibrated. The mathematical representation of the covariance error in the presence of unmodeled systematic error effects in the data is analyzed and an optimum weighting technique is developed for these conditions. This technique yields an internal self-calibration of the error model, a process which GEM-T1 is shown to approximate.

Description: The Gravity Probe-B Mission will carry the Stanford Gyroscope relativity experiment into orbit in the mid 1990's, as well as a Global Positioning System (GPS) receiver whose tracking data will be used to study the earth gravity field. Estimates of the likely quality of a gravity field model to be derived from the GPS data are presented, and the significance of this experiment to geodesy and geophysics are discussed.

Description: A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 (Goddard Earth Model, 36x36 spherical harmonic field) were employed toward application of this technique for gravity field parameters. Also, GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized here. The method employs subset solutions of the data associated with the complete solution and uses an algorithm to adjust the data weights by requiring the differences of parameters between solutions to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting as compared to the nominal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.