The performance of the space-wise approach to GOCE data analysis, when statistical homogenization is applied

The space-wise approach to GOCE data reduction exploits the spatial correlation of the observations by “projecting” them on a spherical grid at mean satellite altitude; to this aim a local collocation prediction based on a global covariance function of the potential T can be used. Since the implicit hypothesis of rotational invariance is not fulfilled by the gravitational potential, the global covariance function cannot describe the local characteristics of the field in the different interpolation areas. As a consequence the estimation error of the gridded values is not homogeneously distributed all over the reference sphere, but it is much higher over the Himalaya, the Alps, the Andes, etc., i.e. over areas where the random field presents an “unexpectedly” high variability. These errors may degrade the performance of the subsequent spherical harmonic analysis for the recovery of the potential coefficients, especially at very high degrees. In the light of this reasoning, the whole procedure of the space-wise approach is expected to benefit by a priori making the analysed random field smoother and thereby more homogeneous. This can be done by first determining a global model which describes the main features of the potential distribution on the spherical grid and then by subtracting it from the observed data once and for all. The signal covariance function has to be corrected accordingly. In principle, the resulting field is more “stationary”, also when it is regarded as a time-wise process. This procedure has been applied on simulated GOCE data, showing that the errors of the estimated spherical harmonic coefficients slightly but systematically decrease. Moreover the improvement is much more significant in critical areas.