Validation of GOCE Gravitational Gradients by Satellite Altimetry

Abstract:

This contribution presents new integral-based estimators for evaluation of gravitational gradients at satellite altitudes from ground values of the disturbing gravitational potential derived from satellite sea surface altimetry. The estimators are based on surface integral equations of Green’s type. The respective tensor-valued Green’s function is derived in both spectral and spatial forms and its spatio-spectral properties are studied and discussed. Computer implementation of the new apparatus is based on truncated spherical integration due to spatially limited altimetry data with truncation errors evaluated by a spherical harmonic series from available global gravitational models. The algorithm was validated using synthetic data in closed-loop tests which were also used for propagation of data errors through spatially restricted surface integration. Moreover, the effect of omission and commission errors associated with global gravitational models used for evaluation of truncation errors were also estimated. These studies prove that spatially restricted altimetry data with the 10 cm white noise and truncation errors derived from GRACE-based global gravitational models result in estimation of satellite gravitational gradients with the 1 mE level accuracy. The new estimators were applied for validation of actual satellite gravitational gradients measured by the GOCE gradiometer. As input sea surface altimetry data DTU10MSS (corrected by mean dynamic ocean topography) and the GRACE-based global gravitational model GGM05S were used. Gravitational gradients estimated by the new apparatus were compared with GOCE observations and respective differences were spectrally analyzed. Results of the analyses show a large potential of the new algorithms in connection with available altimetry data for validation and calibration of satellite gravitational gradients.