Nikolaos K. Pavlis

The Development of the NASA GSFC and NIMA Joint Geopotential Model

The NASA Goddard Space Flight Center, the National Imagery and Mapping Agency (NIMA; formerly the Defense Mapping Agency or DMA) and The Ohio State University have collaborated to produce EGM96, an improved degree 360 spherical harmonic model representing the Earth’s gravitational potential. This model was developed using: (1) satellite tracking data from more than 20 satellites, including new data from GPS and TDRSS, as well as altimeter data from TOPEX, GEOSAT and ERS-1. (2) 30’ x 30’ terrestrial gravity data from NIMA’s comprehensive archives, including new measurements from areas such as the former Soviet Union, South America, Africa, Greenland, and elsewhere. (3) 30’ x 30’ gravity anomalies derived from the GEOSAT Geodetic Mission altimeter data, as well as altimeter derived anomalies derived from ERS-1 by KMS (Kort and Matrikelstyrelsen, Denmark) in regions outside the GEOSAT coverage. The high degree solutions were developed using two different model estimation techniques: quadrature, and block diagonal. The final model is a composite solution consisting a combination solution to degree 70, a block diagonal solution to degree 359, and the quadrature model at degree 360. This new model will be used to define an undulation model that will be the basis for an update of the WGS-84 geoid. In addition, the model will contribute to oceanographic studies by improving the modeling of the ocean geoid and to geodetic positioning using the Global Positioning System (GPS).

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.

Temporal variations of the earth's gravitational field from satellite laser ranging to LAGEOS

We have estimated monthly values of the J2 and J3 Earth gravitational coefficients using LAGEOS satellite laser ranging (SLR) data collected between 1980 and 1989. For the same time period, we have also computed corresponding estimates of the variations in these coefficients caused by atmospheric mass redistribution using surface atmospheric pressure estimates from the European Center for Medium Range Weather Forecasts (ECMWF). These data were processed both with and without a correction for the “inverted barometer effect,” the oceans isostatic response to atmospheric loading. While the estimated zonal harmonics in the orbit analysis accommodate gravitational changes at a reduced level arising from all other higher degree zonal effects, the LAGEOS and atmospheric time series for J2 compare quite well and it appears that the non-secular variation in J2 can be largely attributed to the redistribution of the atmospheric mass. While the observed changes in the “effective” J3 parameters are not well predicted by the third degree zonal harmonic changes in the atmosphere, both odd zonal time series display strong seasonality. The LAGEOS J3 estimates are very sensitive to as yet unmodeled forces acting on the satellite and these effects must be better understood before determining the dominant geophysical signals contributing to the estimate of this time series.

Towards The Next Earth Gravitational Model

The development of a new Earth Gravitational Model (EGM) to degree 2160 is progressing with the availability of improved versions of worldwide 5′×5′ gravity databases and GRACE-derived satellite solutions. Critical to the success of this endeavour is the compilation of a complete and accurate 5′×5′ global gravity anomaly database that takes advantage of all the latest data and modeling for both land and marine areas worldwide. This paper will provide an overview of the data being used in the model, describe the status of the development of the new EGM, show comparisons of preliminary models with independent truth data, and discuss the plans for finalizing the model.

Observed Inconsistencies between Satellite-Only and Surface Gravity-Only Geopotential Models

The long wavelength inconsistencies observed between satellite-only and terrestrial-only gravitational solutions were re-examined, in view of the recent release by NIMA of an updated 1° mean gravity anomaly file (which was used in the development of the EGM96 geopotential model). The differences between the satellite-only model EGM96S and corresponding solutions obtained from 1°×1° terrestrial mean Ag were examined both spectrally and geographically. Up to N max = 20, the global RMS geoid undulation difference (δN) between these models was ±3.7 m, for the NIMA 1° Ag data. This is an improvement over the ±4.4 m, obtained when the older OSU 1° Ag data were used. In some geographic regions however, the NIMA Δg data produce larger δN values with EGM96S, than the corresponding OSU anomalies. When the marine Δg data were replaced by altimetric values, the RMS δN dropped to ±1.6 m, indicating that more than 50% of the observed differences at long wavelengths is due to the poor quality of the available marine Ag. The spectrum of δN (EGM96S minus a terrestrial-only solution) exceeds by more than an order of magnitude the undulation spectra predicted by some postulated models of vertical datum inconsistencies. The spectrum of undulation effects implied by the approximation H* ≈ H, is quite similar to that predicted by one of the vertical datum inconsistency models postulated by Laskowski [1983].

Gravity Field Improvement Activities at NASA GSFC

Since the completion of the EGM96 geopotential model, additional satellite tracking data has been added to the satellite-only geopotential model solution. The new data include, TRANET Doppler tracking data from the GEOSAT Geodetic Mission, TDRSS tracking of the Gamma Ray Observatory (GRO), the X-Ray Timing Explorer (XTE), the Earth Radiation Budget Satellite (ERBS), as well as additional data from the Extreme Ultraviolet Explorer (EUVE). The new data from the TDRSS tracked satellites make an important contribution to the satellite-only geopotential solution. Comparisons with independent 30′ × 30′ altimeter derived anomalies from the GEOSAT Geodetic Mission provided by NIMA show that the ERBS data contribute by reducing the residual at degree 70 by 0.47 mGal2. The data from XTE are valuable because of their unique inclination of 23°. Data from low inclination satellites is sparse in most satellite-only derived geopotential models, although substantial amounts of tracking data from EUVE (at an inclination of 28.5°) were included in EGM96. The performance of permutations and subsets of the EGM96 model are also shown to highlight different aspects of the model’s performance.

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.

The Calculation of the Dynamic Sea Surface Topography and the Associated Flow Field from Altimetry Data: A Characteristic Function Method

Abstract The quasi-stationary sea surface topography (QSST) and associated oceanic circulation is determined by means of a characteristic function technique. The method was originally implemented in an ideal simplified case. The present application involves a 4° × 4° grid in spherical coordinates approximating the boundaries of the main ocean basins. The data field is provided by the first year of altimetric data from the TOPEX/POSEIDON mission. The method requires the numerical determination of the eigenfunctions spanning the streamfunction field and the associated characteristic functions from the balance equation. The former yields the flow field and the latter the surface height distribution, or QSST. These functions are determined by the geometry and topography of the ocean basins and satisfy the linear steady-state dynamical equations. They are defined within the basins only and avoid the problems encountered when using functions defined over the entire sphere. The velocity field can be computed ove...

Global Gravitational Models

This chapter discusses the development and use of Global Gravitational Models (GGMs), specifically those GGMs that are represented in the form of spherical (and/or ellipsoidal) harmonic coefficients. With the mathematical details having been presented in Chap. 3 of Part I of this book, the focus here is on the main concepts and considerations involved in the design and in the choice of alternative techniques and strategies that can be used to develop GGMs.