R. G. Williamson

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.

Precision orbit determination for TOPEX/POSEIDON

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 Earths 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 oceans dynamic topography with an unprecedented accuracy.

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.

The temporal and spatial characteristics of TOPEX/POSEIDON radial orbit error

Satellite orbit error has long been the bane of oceanographers who analyze altimetry data. However, radial orbit error on TOPEX/POSEIDON (T/P) has been reduced to the 3 to 4-cm root-mean-square (rms) level over a 10-day repeat cycle, which represents an order of magnitude improvement over earlier altimetry missions such as Geosat. Consequently, oceanographers are now able to directly evaluate the absolute ocean topography to unprecedented accuracy levels. While significantly reduced, the T/P orbit error still requires quantification. This study examines the spatial and temporal characteristics of the T/P radial orbit error, as assessed through the analysis of laser tracking residuals and orbit comparisons with independently generated trajectories. Spectral analyses of the orbit differences between the orbits determined from satellite laser ranging and Doppler Orbitography and Radiopositioning Integrated by Satellite data and the independently determined reduced dynamic Global Positioning System (GPS) ephemerides indicate that the predominant power is at the once-per-orbital revolution frequency with 2- to 3-cm peaks. When the orbit differences are colinearly aligned to a fixed geographic grid and spectral analysis is performed at each geographic grid point, a nearly 60-day period is found with maximum amplitudes in the 2- to 4-cm range. The contribution of both conservative and nonconservative force and measurement mismodeling to this error signal are assessed. We demonstrate that the ∼60-day error period seen at fixed geographic locations arises from weaknesses in the dynamic ocean tidal models used in the orbit calculations. New tidal models have been developed which significantly reduce this error. Second-generation orbits incorporating many model improvements have been computed and demonstrate a significant reduction in the radial orbit error signals. Some orbit error still exists, and methods for further model improvements and the possibility of achieving 1-cm radial rms orbit accuracy in T/P are discussed.

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. >

Application of the GEM-T2 gravity field to altimetric satellite orbit computation

As part of a continuing effort to provide improved orbits for use with existing altimeter data, we have recomputed ephemerides for both the Seasat and Geosat Exact Repeat altimeter missions. The orbits were computed in a consistent fashion, using the Goddard Earth Model T2 gravity field along with available ground-based tracking data. Such an approach allows direct comparisons of sea level between the two altimeter systems. Evaluation of the resulting ephemerides indicates that root-mean-square accuracies of 30–50 cm have been achieved for the radial component of the orbits for both satellites. An exception occurs for the last year of the Geosat Exact Repeat Mission, when the rms radial orbit accuracy degrades to the 1-m level at times owing to the inability to adequately model the drag force arising from the increased solar activity.

Precision orbit computations for Starlette

The Starlette satellite, launched in February 1975 by the French Centre National d’Etudes Spatiales, was designed to minimize the effects of non-gravitational forces and to obtain the highest possible accuracy for laser range measurements. Analyses of the first four months of laser tracking data from nine stations. have confirmed the stability of the orbit and the precision to which the satellite’s position can be established.Initial orbit computations using the GSFC GEM-7 gravity model produced rms fits of about 8 to 10 meters for arc lengths of 5 days. After tailoring a gravity model specifically to Starlette, the rms fits for the 5 day arcs were reduced significantly to the 1 to 2 meter level. An rms fit of 4.3 meters was obtained for a 90 day arc. Five day arcs overlapped by 2.5 days showed rms satellite position differences generally less than 2 meters. Prediction errors at the end of two months were less than 30 milliseconds.

Precision orbit determination for TOPEX/Poseidon using TDRSS doppler tracking data

Abstract Precision orbit determination on the TOPEX/Poseidon (T/P) altimeter satellite is now being routinely achieved with sub-5cm radial and sub-15 cm total positioning accuracy using state-of-the-art modeling with precision tracking provided by a combination of: (a) global Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), or (b) the Global Positioning System (GPS) Constellation which provides pseudo-range and carrier phase observations. The geostationary Tracking and Data Relay Satellite System (TDRSS) satellites are providing the operational tracking and communication support for this mission. The TDRSS Doppler data are of high precision (0.3 mm/s nominal noise levels). Unlike other satellite missions supported operationally by TDRSS, T/P has high quality independent tracking which enables absolute orbit accuracy assessments. In addition, the T/P satellite provides extensive geometry for positioning a satellite at geostationary altitude, and thus the TDRSS-T/P data provides an excellent means for determining the TDRS orbits. Arc lengths of 7 and 10 days with varying degrees of T/P spacecraft attitude complexity are studied. Sub-meter T/P total positioning error is achieved when using the TDRSS range-rate data, with radial orbit errors of 10.6 cm and 15.5 cm RMS for the two arcs studied. Current limitations in the TDRSS precision orbit determination capability include mismodeling of numerous TDRSS satellite-specific dynamic and electronic effects, and in the inadequate treatment of the propagation delay and bending arising from the wet troposphere and ionosphere.

The role of laser determined orbits in geodesy and geophysics

Abstract Since the US National Aeronautics and Space Administration (NASA) launch of the LAGEOS (LAser GEOdynamics Satellite) in May of 1976, a wealth of information enhancing the knowledge of geodesy and geophysics has become available to the scientific community. Both the quality and quantity of data have improved. The precision of satellite laser ranging (SLR) is now at the sub-centimeter level, and cooperation with other nations in the purchase and deployment of SLR systems and laser satellites has led to an extensive SLR data base. Scientists are now able to make precise estimates of the product of the gravitational constant and the Earths mass (GM), polar motion, Earth rotation, laser station coordinates, distances between stations, and tectonic plate motions. SLR also contributes strongly to improved estimates of the Earths gravitational field. Recent NASA solutions using the laser ranging data indicate the value of GM is 398600.4408 ± 0.0006 km3/s2. The one sigma precision of the other geodetic parameters obtained are on average 1.9 marc sec polar motion, 0.09 ms length of day, 35 mm center of mass geodetic positioning, 20 mm baselines, and 5 mm/yr tectonic plate rates. The precision of a number of these quantities has been confirmed by comparison of an independent data set obtained by very long baseline interferometry antennas located near several of the SLR sites.