Craig Allen Wagner

Accuracy of the GEM‐T2 geopotential from Geosat and ERS 1 crossover altimetry

Extensive analyses of altimetrically determined sea height differences at crossovers have been used to assess the accuracy of the GEM-T2 geopotential. The orbits used were determined with GEM-T2 for Geosat in its 17-day Exact Repeat Mission (ERM) in 1986–1989 and ERS 1 in both its 3-day ERM in 1991–1992 and its 35-day ERM in 1992. The data examined are completely independent of the data used in GEM-T2s development though GEM-T2 had considerable use of Doppler tracking information on Geosat. The test of the radial accuracy of the ERS 1 orbit (98.5° inclination) is especially significant because it is not “close” to any other orbit well represented in GEM-T2. The assessment consists of a comparison of observed mean height differences at thousands of distinct geographic locations with error projections from the GEM-T2 covariance matrix which was estimated from other data sources. This first comprehensive, independent test of the purely radial accuracy of an orbit-geopotential model clearly shows that the covariant predictions for GEM-T2 are broadly reliable for this purpose. Thus, the agreement of crossover predictions and observations suggests that the total radial errors for these ERMs, due only to GEM-T2 (but excluding the effects of initial state error) are about 23 cm for Geosat and 115 cm (rms) for ERS 1. However, there is little detailed agreement of measurements and predictions for ERS 1 and only partial agreement in detail for Geosat. Our 30,000 mean crossover discrepancies for Geosat (derived from ERM cycles 1–44) are also shown to reduce substantially the crossover height differences in cycles 45–61, almost exactly as predicted if these are the true GEM-T2 errors for this orbit.

The Use of Resonant Orbits in Satellite Geodesy: A Review

Dynamic resonance, arising from commensurate (orbital or rotational) periods of satellites or planets with each other, has been a strong force in the development of the solar system. The repetition of conditions over the commensurate periods can result in amplified long-term changes in the positions of the bodies involved. Such resonant phenomena driven by the commensurability between the mean motion of certain artificial Earth satellites and the Earth’s rotation originally contributed to the evaluation and assessment of the Stokes parameters (harmonic geopotential coefficients) that specify the Earth’s gravitational field. The technique constrains linear combinations of the harmonic coefficients that are of relevant resonant order (lumped coefficients). The attraction of the method eventually dwindled, but the very accurate orbits of CHAMP and GRACE have recently led to more general insights for commensurate orbits applied to satellite geodesy involving the best resolution for all coefficients, not just resonant ones. From the GRACE mission, we learnt how to explain and predict temporary decreases in the resolution and accuracy of derived geopotential parameters, due to passages through low-order commensurabilities, which lead to low-density ground-track patterns. For GOCE we suggest how to change a repeat orbit height slightly, to achieve the best feasible recovery of the field parameters derived from on-board gradiometric measurements by direct inversion from the measurements to the harmonic geopotential coefficients, not by the way of lumped coefficients. For orbiters of Mars, we have suggestions which orbits should be avoided. The slow rotation of Venus results in dense ground-tracks and excellent gravitational recovery for almost all orbiters.

Geosat and ERS-1 Datum Offsets Relative to Topex/Poseidon Estimated Simultaneously with Geopotential Corrections from Multi-Satellite Crossover Altimetry

Crossover residuals, averaged over a sufficient long time period carry the signature of geopotentially based orbit errors. In addition they may exhibit geographical pattern which are inconsistent with orbit dynamics. Tracking system offsets and different orientations, for example, map to the so called “forbidden” harmonics: the degree 1 and the degree 2, order 1 coefficients. Long-term averaged dual satellite crossover residuals among Geosat, ERS-1 and Topex/Poseidon, all with JGM3 based orbits, have been used to solve simultaneously for i) corrections to the gravity field harmonics and ii) parameters which account for a coordinate frame offset relative to Topex/Poseidon. The parameters are estimated by a least squares adjustment. The paper investigates in particular the obstacle of large correlation between the shift parameters and the low degree order one harmonic coefficients. Results of the inversion indicate significant shifts between the coordinate frames of the altimeter missions involved. They must be taken into account, if secular sea level changes are to be investigated.

Accuracy Assessment of Gravity Field Models by Independent Satellite Crossover Altimetry

Continual progress in Earth gravity field modelling requires ever more precise data sets for their accuracy assessment as well as refinements in the assessment procedures. The method used here is based on Latitude Lumped Coefficients and makes use of single-satellite crossover altimetry data (independent of the tested model). The method effectively rationa-lizes the residuals in LLC measurements with the model’s covariance matrix. It has been developed in years 1992 – 2000 and applied various gravity field models, from GEM T2 to the GRIM5’s. We now apply it to EIGEN-1S & 2 which include highly precise continuous tracking data from the CHAMP mission. For the first time these CHAMP models recommend degreedependent calibration fa-ctors for its covariance matrix. We find these factors are needed to explain the independent LLC measurements on the ERS and GEOSAT orbits.