C. K. Shum

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.

Accuracy assessment of recent ocean tide models

Over 20 global ocean tide models have been developed since 1994, primarily as a consequence of analysis of the precise altimetric measurements from TOPEX/POSEIDON and as a result of parallel developments in numerical tidal modeling and data assimilation. This paper provides an accuracy assessment of 10 such tide models and discusses their benefits in many fields including geodesy, oceanography, and geophysics. A variety of tests indicate that all these tide models agree within 2-3 cm in the deep ocean, and they represent a significant improvement over the classical Schwiderski 1980 model by approximately 5 cm rms. As a result, two tide models were selected for the reprocessing of TOPEX/POSEIDON Geophysical Data Records in late 1995. Current ocean tide models allow an improved observation of deep ocean surface dynamic topography using satellite altimetry. Other significant contributions include theft applications in an improved orbit computation for TOPEX/POSEIDON and other geodetic satellites, to yield accurate predictions of Earth rotation excitations and improved estimates of ocean loading corrections for geodetic observatories, and to allow better separation of astronomical tides from phenomena with meteorological and geophysical origins. The largest differences between these tide models occur in shallow waters, indicating that the current models are still problematic in these areas. Future improvement of global tide models is anticipated with additional high-quality altimeter data and with advances in numerical techniques to assimilate data into high-resolution hydrodynamic models.

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.

Determination of long-term changes in the Earth's gravity field from satellite laser ranging observations

Temporal changes in the Earths gravity field have been determined by analyzing satellite laser ranging (SLR) observations of eight geodetic satellites using data spanning an interval of over 20 years. The satellites used in the analysis include Starlette, LAGEOS 1 and 2, Ajisai, Etalon 1 and 2, Stella, and BE-C. Geophysical parameters, related to both secular and long-period variations in the Earths gravity field, including the geopotential zonal rates ( , , , , and ) and the 18.6-year tide parameter, were estimated. The estimated values for these parameters are ; ; ; ; ; (centimeters) and S18.6+20 = −0.1±0.2 (centimeters). The amplitude and phase for the 18.6-year tide are in general agreement with the effects predicted by the Earths mantle anelasticity. The solution accuracy was evaluated by considering the effects of errors in various non-estimated dynamical model parameters and by varying the data span and data sets used in the solution. Estimates for from individual LAGEOS 1 and Starlette SLR data sets are in good agreement. The lumped sum values for and are very different for LAGEOS 1 and Starlette. The zonal rate determination is limited to degree 6 with the current SLR data sets. Analysis of the sensitivity of the solution for the zonal rates to the satellite tracking data span suggests that the temporal extension of the current SLR data sets will enhance the solution of zonal rates beyond degree 6.

Progress in the determination of the gravitational coefficient of the Earth

In most of the recent determinations of the geocentric gravitational coefficient (GM) of the Earth, the laser ranging data to the Lageos satellite have had the greatest influence on the solution. These data, however, have generally been processed with a small but significant error in one of the range corrections. In a new determination of GM using the corrected center-of-mass offset, a value of 398600.4415 km3/sec2 (including the mass of the atmosphere) has been obtained, with an estimated uncertainty (1 σ) of 0.0008 km3/sec2.

On the use of tide gauges to determine altimeter drift

TOPEX measurements of sea level variability have been compared to tide gauge measurements from 40 sites and to dynamic topography measurements computed from temperatures recorded at 23 Tropical Ocean-Global Atmosphere (TOGA)-Tropical Atmosphere-Ocean (TAO) buoys in the eastern Pacific and mean temperature-salinity profiles. Buoy data in the western Pacific were not used because of large long-term slopes in the data that appear to be due to interannual salinity variations. The relative drift between TOPEX and the two different in situ sets of data agree within 1 mm yr -1 , with a weighted average of -2.6 mm yr -1 and an estimated uncertainty of 1.5 mm yr -1 , if values from an internal calibration of the TOPEX altimeter are applied. The consistency of the two relative drifts suggests that the slope is due at least in part to a drift in the TOPEX measurement. A substantial portion of this drift may be due to a drift in the TOPEX microwave radiometer (TMR), since comparisons with three independent external measurements indicate a drift in sea level due to the TMR measurement of about -2 mm yr -1 .

Tidal corrections in the TOPEX/POSEIDON geophysical data records

The aim of this paper is to give an assessment to TOPEX/POSEIDON data users of the two available oceanic tidal corrections, which are based on the Schwiderski model (SCH) and the Cartwright and Ray model (CR), respectively. Large instantaneous differences are observed between the two corrections, and use of either model may sometimes lead to inadequate understanding of the remaining oceanic signals. In this paper we give an objective comparison of SCH and CR models and point out the major features of both models. Our methodology is applicable to the validating and testing of future tide models that will soon be appearing.

An improved model for the Earth's gravity field

Precision orbit determination methods, along with a new technique to compute relative data weights, have been applied to the determination of the Earth’s gravity field and other geophysical parameters from the combination of satellite ground based tracking data, satellite altimetry data, and the surface gravimetry data. The University of Texas Earth’s gravity field models, PTGF-4 and PTGF-4A, were determined from data sets collected for fifteen satellites, spanning the inclination ranges from 15° to 115°, and surface gravity data. The satellite measurements include laser ranging data, doppler range-rate data, and satellite-to-ocean radar altimeter data, which include the direct height measurement and the differenced measurements at ground track crossings (crossover measurements). The surface gravity data were used in terms of geopotential normal equations (complete to degree and order 50) derived from the Ohio State University 1°×1° gravity anomaly data. PTGF-4 was computed using satellite tracking data and altimeter crossover data, whereas PTGF-4A was determined using these data sets as well as direct altimeter data and surface gravity data. The estimated parameters for PTGF-4A included geopotential coefficients for a model complete to degree and order 50, tidal coefficients, tracking station coordinates and models for the quasi-stationary sea surface topography. Error analysis and calibration of the formal covariance indicate that GEOSAT orbits can be computed radially at the 15–21 cm level.

The TEG-3 Geopotential Model

A new solution for the static geopotential, TEG-3, complete to 70×70 in spherical harmonics, has been obtained. The solution represents one of the latest efforts to improve the Earth’s gravity model. The solution was obtained by combining inhomogeneous satellite and in situ data sets, and by simultaneously estimating the relative weights for individual satellite data sets. Data from over 20 satellites and terrestrial surface gravity data were used in the latest solution. The satellite data include groundbased satellite laser and radiometric (Doris and Tranet) tracking data, spaceborne GPS, and radar altimeter measurements. Analysis indicates that TEG-3 provides an incremental improvement in overall satellite orbit determination when compared with recent models, including JGM-3, GRIM4C4, and EGM96. In particular, notable improvement has been achieved for TEG-3 in reducing geographically-correlated gravity errors for orbit determination of altimetric satellites (Geosat and ERS-1). Error analysis indicates that there is no notable improvement in marine geoid accuracy in TEG-3 as compared to JGM-3, while the EGM-96 model represents an improvement in the marine geoid accuracy as indicated by comparing with ground-truth measurements (Levitus 94 hydrography) and mean topography from numerical ocean circulation model simulations (POCM_4B).