The Effect of Pseudo-Stochastic Orbit Parameters on GRACE Monthly Gravity Fields: Insights from Lumped Coefficients

Abstract

The official GFZ RL05 monthly GRACE gravity models were processed in a two-step approach. In the first step the orbits were determined. In the second step corrections to the gravity field parameters were estimated, while the orbits were kept fixed. This led to a significant de-noising of the resulting monthly models, but accidentally also to a regularization, i.e., the estimated gravity field coefficients were biased towards the a priori model. We compare the GFZ RL05 models to a revised version RL05a that was determined in a common estimation of orbit and force model parameters. A large number of gravity field coefficients is significantly affected. We relate this effect to the one-hourly stochastic accelerations estimated for orbit determination, and to ignoring the correlations.

In the main part of this paper we study the interaction between pseudo-stochastic orbit parameters and gravity field coefficients. To explain this interaction we make use of a time-wise approach to gravity field determination. We apply the linear perturbation theory developed by Hill for circular orbits to compute lumped coefficients of the inter-satellite range-rate observations. We illustrate that the pseudo-stochastic orbit parameters act as a high-pass filter on the lumped coefficients spectra of the range-rates. Because the lumped coefficients are related to the spherical harmonics coefficients via a summation over all degrees, the whole range of gravity field coefficients is affected.

This result is of relevance for all approaches to gravity field estimation from orbit observations, where dynamic orbits are introduced a priori and the arc-specific parameters are kept fixed.