Steven M. Klosko

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.

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. >

13 Years of TOPEX/POSEIDON Precision Orbit Determination and the 10-fold Improvement in Expected Orbit Accuracy

Launched in the summer of 1992, TOPEX/POSEIDON (T/P) was a joint mission between NASA and the Centre National d Etudes Spatiales (CNES), the French Space Agency, to make precise radar altimeter measurements of the ocean surface. After the remarkably successful 13-years of mapping the ocean surface T/P lost its ability to maneuver and was de-commissioned January 2006. T/P revolutionized the study of the Earth s oceans by vastly exceeding pre-launch estimates of surface height accuracy recoverable from radar altimeter measurements. The precision orbit lies at the heart of the altimeter measurement providing the reference frame from which the radar altimeter measurements are made. The expected quality of orbit knowledge had limited the measurement accuracy expectations of past altimeter missions, and still remains a major component in the error budget of all altimeter missions. This paper describes critical improvements made to the T/P orbit time series over the 13-years of precise orbit determination (POD) provided by the GSFC Space Geodesy Laboratory. The POD improvements from the pre-launch T/P expectation of radial orbit accuracy and Mission requirement of 13-cm to an expected accuracy of about 1.5-cm with today s latest orbits will be discussed. The latest orbits with 1.5 cm RMS radial accuracy represent a significant improvement to the 2.0-cm accuracy orbits currently available on the T/P Geophysical Data Record (GDR) altimeter product.

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.

Plate Motions and Deformation from Lageos

LAGEOS laser ranging observations collected by the global tracking network between May 1976 and December 1988 have been analysed to yield a comprehensive geodetic parameter solution. Some of the stations in the participating network have a continuous tracking record over the full LAGEOS mission lifetime and can be used to monitor positions in a limited network for over 12 years. However, the introduction of several new stations of improved precision has allowed determination of relative positions to centimeter accuracy for each quarter of as year solution since the beginning of 1980. A nine year history of these three-dimensional positions yields horizontal inter-station baseline rates to an accuracy of a few mm/yr as well as vertical displacement rates to similar accuracy. Comparisons of the measurements of plate motion between sites centrally located within the plates with those predicted by current geological models agree to better than 9 mm/yr RMS. The phenomena of post-glacial rebound is considered as an explanation for the vertical motion.