New error calibration tests for gravity models using subset solutions and independent data: Applied to GEM‐T3

Abstract

Orbit error projections based on the error covariance estimates of Goddard Earth Model (GEM)‐T3 have been shown to be reliable through their projection on observation residuals within independent data sets. Special geopotential solutions were developed based upon the same data set and weighting used in the GEM‐T3 gravity model, but with a significant satellite data set eliminated from the solution. These subset gravity models are then used to compute the observation residuals within orbital solutions for the omitted satellite and the results are compared to their predicted values based on the error covariance of these models. To ensure meaningful results, the tests were designed so that the observation residuals are dominated by geopotential modeling errors. This yields a reliable test of the error estimates of the subset solutions and hence tests the data weighting used in the construction of these models (GEM‐T3 and subset solutions alike). The error estimates for GEM‐T3 are based upon an optimal data weighting method and have been obtained in a separate calibration process. The test results shown here indicate that the GEM‐T3 error estimates for the gravity parameters are calibrated and that the predicted orbit errors correspond well with actual orbit accuracies. Test results of the complete GEM‐T3 model with totally independent high precision DORIS Doppler tracking data acquired on the French SPOT‐2 satellite confirms these conclusions.

Gravity model development for TOPEX/POSEIDON: Joint Gravity Models 1 and 2

“…Rigorous statistical techniques have been developed to opfimally combine these data and produce realistic accuracy estimates. The T/P-era modeling efforts have been in the forefront of developing calibration and optimal data weighting techniques to enable systematic errors in specific data sets to be better understood [Lerch et al, 1985;Lerch, 1991;Lerch et at., 1991;Lerch et at., 1993a;Yuan, 1991].…”

“…The series of gravitational models developed in anticipation of the T/P mission and the computational techniques employed are well documented in the open literature. Details of these procedures are given by Marsh et al [1988Marsh et al [ , 1990aMarsh et al [ , 1990b; Lerch et al [1991Lerch et al [ , 1993aLerch et al [ , 1993bLerch et al [ , 1994; Nerem et al [1990Nerem et al [ , 1994a; Tapley et al [1988]; Shum et al [1990]; and Yuan [ 1991 ]. However, the development of the JGM models necessitated significant changes in some approaches and these are briefly reviewed below.…”

“…On the basis of an orbital sensitivity analysis [cf. Casotto, 1989], these omission errors were kept below the 1-cm level in their root-sum-square (rss) radial contribution to the T/P orbit [Nerem et al, 1993a].…”

“…Because of the large number of tidal terms required, an algorithm for efficiently computing all tides within a tidal family is utilized to reduce the computational burden. Using a formulation developed by O. L. Colombo (unpublished notes and private communications, 1989), these expanded tidal models have been used in the JGM models and are described by Nerem et al [1993a]. Briefly, under the assumption that the admittances of the Earth are sensibly identical at the nearby frequencies within each tidal family, the algorithm takes advantage of the slow modulation of the mainline tides by their sidebands and computes the contribution to the tidal potential of the sidebands through a linear scaling using tidal admittances.…”

A geopotential model from satellite tracking, altimeter, and surface gravity data: GEM‐T3

“…These accurate observations thcmselves were then used to test the solution and its covariance. This testing was accomplished by projecting the gravitational, tide, station coordinate, and polar motion uncertainties on the observation residuals and comparing the results with the actual fit obtained with d•ese data (see Lerch et al [1993] for the mathematical development). Because only the uncertainties for gravitational parameters were calibrated, cases which were dominated by the errors in the gravitational field were the most meaningful.…”