From the time-wise to space-wise GOCE observables

The observables of the GOCE three-axis gradiometer are taken in time, along the orbit and, in the timewise proposal, filtered to stay in the measurement bandwidth, i.e. in the frequency interval between 0.005 and 0.1 Hz. As a consequence, the resulting “observable” is a convolution of the original data stream with a time-wise weighting kernel. In other words, we cannot assume that the observations are point-wise evaluations of any function and so, in a spacewise approach, any averaging or interpolating operation to obtain gridded spatial data has little sense. The problem is therefore to model correctly the observational functionals, including the correlation along the orbit. This can be done by exploiting the Wiener filter theory, using the prior knowledge of a geopotential model and the power spectral density (PSD) of the measurement error. A numerical simulation from the EGM96 model (degrees between 50 and 300) is performed, showing that the along track Wiener filter produces Trr spatialized observables with an error standard deviation of the order of 5 mE. A covariance function of the estimation error is also provided by the Wiener filter theory. The use of these filtered observables in a space-wise approach allows for the reconstruction of the gravity field in terms of spherical harmonics up to degree 200.