F. J. Lerch

The Joint Gravity Model 3

An improved Earth geopotential model, complete to spherical harmonic degree and order 70, has been determined by combining the Joint Gravity Model 1 (JGM 1) geopotential coefficients, and their associated error covariance, with new information from SLR, DORIS, and GPS tracking of TOPEX/Poseidon, laser tracking of LAGEOS 1, LAGEOS 2, and Stella, and additional DORIS tracking of SPOT 2. The resulting field, JGM 3, which has been adopted for the TOPEX/Poseidon altimeter data rerelease, yields improved orbit accuracies as demonstrated by better fits to withheld tracking data and substantially reduced geographically correlated orbit error. Methods for analyzing the performance of the gravity field using high-precision tracking station positioning were applied. Geodetic results, including station coordinates and Earth orientation parameters, are significantly improved with the JGM 3 model. Sea surface topography solutions from TOPEX/Poseidon altimetry indicate that the ocean geoid has been improved. Subset solutions performed by withholding either the GPS data or the SLR/DORIS data were computed to demonstrate the effect of these particular data sets on the gravity model used for TOPEX/Poseidon orbit determination.

Gravity model development for TOPEX/POSEIDON: Joint gravity models 1 and 2

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.

Goddard earth models for oceanographic applications (GEM 10B and IOC)

Abstract Some important oceanographic results have been obtained with Goddard Earth Models using satellite altimetry. GEM 9 and GEM 10 have been extended through the addition of worldwide GEOS‐3 altimetry to give new solutions, GEM 10B and IOC, fields that are complete in harmonics to degree 36 and 180, respectively. GEM 9 is a field derived solely from satellite tracking observations, whereas GEM 10 is a combination solution containing surface gravimetry. The accuracy of the oceanic geoid for these models has been estimated by using independent altimeter tracks of GEOS‐3. After empirically removing long wavelength orbital errors, residuals of 1.8 m (rms) were obtained for GEM 10, 0.94 m for GEM 10B, while GEM IOC gave 0.75 m. Large discrepancies, as much as 60 mgals, were found when ocean gravimetry anomalies (5° blocks) were compared to altimetry‐derived values. Altimeter values were verified through comparison with anomalies from GEM‐9, yielding an rms difference of only 5 mgals. An estimate of the lon...

An improved gravity model for Mars: Goddard Mars model 1

Doppler tracking data of three orbiting spacecraft have been reanalyzed to develop a new gravitational field model for the planet Mars, Goddard Mars Model 1 (GMM-1). This model employs nearly all available data, consisting of approximately 1100 days of S band tracking data collected by NASAs Deep Space Network from the Mariner 9 and Viking 1 and Viking 2 spacecraft, in seven different orbits, between 1971 and 1979. GMM-1 is complete to spherical harmonic degree and order 50, which corresponds to a half-wavelength spatial resolution of 200–300 km where the data permit. GMM-1 represents satellite orbits with considerably better accuracy than previous Mars gravity models and shows greater resolution of identifiable geological structures. The notable improvement in GMM-1 over previous models is a consequence of several factors: improved computational capabilities, the use of optimum weighting and least squares collocation solution techniques which stabilized the behavior of the solution at high degree and order, and the use of longer satellite arcs than employed in previous solutions that were made possible by improved force and measurement models. The inclusion of X band tracking data from the 379-km altitude, near-polar orbiting Mars Observer spacecraft should provide a significant improvement over GMM-1, particularly at high latitudes where current data poorly resolve the gravitational signature of the planet.

Optimum data weighting and error calibration for estimation of gravitational parameters

SummaryA new approach has been developed for determining consistent satellite-tracking data weights in solutions for the satellite-only gravitational models. The method employs subset least-squares solutions of the satellite data contained within the complete solution and requires that the differences of the parameters of subset solutions and the complete solution to be in agreement with their error estimates by adjusting the data weights. GEM-T2 model was recently computed and adjusted through a direct application of this method. The estimated data weights are markedly smaller than the weights implied by the formal uncertainties of the measurements. Orbital arc tests as well as surface gravity comparisons show significant improvements for solutions when more realistic data weighting is achieved.

Expected orbit determination performance for the TOPEX/Poseidon mission

The research that has been conducted in the Space Geodesy Branch at NASA/Goddard Space Flight Center in preparation for meeting the 13-cm radial orbit accuracy requirement for the TOPEX/Poseidon (T/P) mission is described. New developments in modeling the Earths gravitational field and modeling the complex nonconservative forces acting on T/P are highlighted. The T/P error budget is reviewed, and a prelaunch assessment of the predicted orbit determination accuracies is summarized. >

An improved error assessment for the GEM‐T1 Gravitational Model

Several tests have been designed to estimate the correct error variances for the GEM-T1 gravitational solution that was derived exclusively from satellite tracking data. The basic method uses both independent and dependent subset data solutions and produces a coefficient by coefficient estimate of the model uncertainties. The GEM-T1 errors have been further analyzed using a method based on eigenvalue-eigenvector analysis, which calibrates the entire covariance matrix. Dependent satellite data sets and independent altimetric, resonant satellite, and surface gravity data sets all confirm essentially the same error assessment The calibration test results yield very stable calibration factors, which vary only by approximately 10% over the range of tests performed. Based on these calibrated error estimates, GEM-T1 is a significantly improved solution, which to degree and order 8 is twice as accurate as earlier satellite derived models like GEM-L2. Also, by being complete to degree and order 36, GEM-T1 is more complete and has significantly reduced aliasing effects that were present in previous models.

NEW ERROR CALIBRATION TESTS FOR GRAVITY MODELS USING SUBSET SOLUTIONS AND INDEPENDENT DATA : APPLIED TO GEM-T3

Orbit error projections based on the error covariance estimates of Goddard Earth Model (GEM)-T3 have been shown to be reliable through their projection on observation residuals within independent data sets. Special geopotential solutions were developed based upon the same data set and weighting used in the GEM-T3 gravity model, but with a significant satellite data set eliminated from the solution. These subset gravity models are then used to compute the observation residuals within orbital solutions for the omitted satellite and the results are compared to their predicted values based on the error covariance of these models. To ensure meaningful results, the tests were designed so that the observation residuals are dominated by geopotential modeling errors. This yields a reliable test of the error estimates of the subset solutions and hence tests the data weighting used in the construction of these models (GEM-T3 and subset solutions alike). The error estimates for GEM-T3 are based upon an optimal data weighting method and have been obtained in a separate calibration process. The test results shown here indicate that the GEM-T3 error estimates for the gravity parameters are calibrated and that the predicted orbit errors correspond well with actual orbit accuracies. Test results of the complete GEM-T3 model with totally independent high precision DORIS Doppler tracking data acquired on the French SPOT-2 satellite confirms these conclusions.

Alternative Estimation Techniques for Global High-Degree Gravity Modeling

High-degree (Nmax=360) gravitational models require surface gravity data to resolve the fine structure of the field. Given a global gravity anomaly data set, one can extract this information using either quadrature formulae (orthogonality relations) or by solving a system of observation equations. Under certain conditions such a system yields a normal matrix of block-diagonal structure. To determine accurately the lower part of the spectrum requires the least-squares combination of the surface gravity information with a satellite-only gravity model. Depending on the technique employed to develop the surface gravity solution, the estimation of a combined model can be performed in different ways.

Preliminary Results from the Joint GSFC/DMA Gravity Model Project

The NASA Goddard Space Flight Center (GSFC) and the U.S. Defense Mapping Agency (DMA) with the aid of other organizations such as The Ohio State University are cooperating in a joint effort to determine a significantly improved degree 360 spherical harmonic model representing the Earth’s gravitational potential. This new model will be of immediate use in defining an undulation model that will be the basis for an enhanced WGS-84 geoid, but the model will be general in use and will provide enhancements for a wide range of applications. The development of the new model is driven, in part, by the need to determine an accurate geoid undulation model that will be the vertical reference surface for WGS-84. In addition, the new geoid model will help satisfy increasingly important studies in ocean circulation (sea surface topography) and geodetic positioning through GPS.