J. C. Ries

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.

Accuracy assessment of the large‐scale dynamic ocean topography from TOPEX/POSEIDON altimetry

The quality of TOPEX/POSEIDON determinations of the global scale dynamic ocean topography have been assessed by determining mean topography solutions for successive 10-day repeat cycles and by examining the temporal changes in the sea surface topography to identify known features. The assessment is based on the analysis of TOPEX altimeter data for cycles 1 through 36. Important errors in the tide model used to correct the altimeter data have been identified. The errors were reduced significantly by use of a new tide model derived with the TOPEX/POSEIDON measurements. Maps of the global 1-year mean topography, produced using four of the most accurate models of the marine geoid, show that the largest error in the dynamic ocean topography is now the uncertainty in the geoid. Temporal variations in the spatially smoothed maps of the annual sea surface topography show expected features, such as the known annual hemispherical sea surface rise and fall and the seasonal variability due to monsoon influence in the Indian Ocean. Changes in the sequence of 10-day topography maps show the development and propagation of an equatorial Kelvin wave in the Pacific beginning in December 1992 with a propagation velocity of approximately 3 m/s. The observations are consistent with observed changes in the equatorial trade winds, and with tide gauge and other in situ observations of the strengthening of the 1992 El Nino. Comparison of TOPEX-determined sea surface height at points near oceanic tide gauges shows agreement at the 4 cm RMS level over the tropical Pacific. The results show that the TOPEX altimeter data set can be used to map the ocean surface with a temporal resolution of 10 days and an accuracy which is consistent with traditional in situ methods for the determination of sea level variations.

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 .

Geocenter Variations from Analysis of SLR Data

The Earth’s center of mass (CM) is defined in the satellite orbit dynamics as the center of mass of the entire Earth system, including the solid earth, oceans, cryosphere and atmosphere. Satellite Laser Ranging (SLR) provides accurate and unambiguous range measurements to geodetic satellites to determine variations in the vector from the origin of the ITRF to the CM. Estimates of the Global mass redistribution induced geocenter variations at seasonal scales from SLR are in good agreement with the results from the global inversion from the displacements of the dense network of GPS sites and from ocean bottom pressure model and GRACE-derived geoid changes.

Calibration and Verification of Jason-1 Using Global Along-Track Residuals with TOPEX

It is demonstrated that the Jason-1 measurements of sea surface height (SSH), wet path delay, and ionosphere path delay are within required accuracies, via a global cross-calibration with similar measurements made by TOPEX/Poseidon (T/P) over a 6-month period. Since the two satellites were on the same groundtrack separated in time by only 70 s, measurements were recorded at approximately the same location and time. The variations in the wet path delay measured by Jason-1 compared to T/P are only 5 mm RMS, well within the required performance of 1.2 cm RMS. The RMS of the ionosphere differences is also well within the expected values, with a mean RMS of 1.2 cm. The largest difference is that the Jason-1 SSH is biased high relative to T/P SSH by 144 mm after the T/P and Jason-1 data are both corrected with improved sea state bias (SSB) models. However, the bias will change if a different SSB model is used, so the user should be cautious that the bias used matches the SSB models. The bias is generally constant within ± 10 mm in the open ocean, but appears to be higher or lower in some regions. Additionally, the SSH has been verified by comparison with 36 island tide gauges over the same period. After removing the global relative bias, the Jason-1 SSH data agree with tide gauges within 3.7 cm RMS and with T/P data within about 3.5 cm RMS on average for 1-s measurements, meeting the required accuracy of 4.2 cm RMS.

RELATIVISTIC EFFECTS FOR NEAR-EARTH SATELLITE ORBIT DETERMINATION

The relativistic formulations for the equations which describe the motion of a near-Earth satellite are compared for two commonly used coordinate reference systems (RS). The discussion describes the transformation between the solar system barycentric RS and both the non-inertial and inertial geocentric RSs. A relativistic correction for the Earths geopotential expressed in the solar system barycentric RS and the effect of geodesic precession on the satellite orbit in the geocentric RS are derived in detail. The effect of the definition of coordinate time on scale is also examined. A long-arc solution using 3 years of laser range measurements of the motion of the Lageos satellite is used to demonstrate that the effects of relativity formulated in the geocentric RS and in the solar system barycentric RS are equivalent to a high degree of accuracy.

Current status of the doris pilot experiment and the future international doris service

Abstract The aim of the DORIS Pilot Experiment is to assess the need and feasibility of an International DORIS Service. A Call for Proposals was broadcasted in September 1999 to prompt qualified organizations to submit proposals for components of the future IDS. DORIS Days were held in Toulouse (May 2–3, 2000). This second version of these Doris days was in particular devoted to a review of the start-up of the Doris Pilot Experiment. This paper recalls the objectives of the future IDS, points out its components and structure, and gives information on the current and future activities.

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).