Non-isotropic filtering of GRACE temporal gravity for geophysical signal enhancement

Monthly mass variations within the Earth system produce temporal gravity changes, which are observable by the NASA/GFZ Gravity Recovery and Climate Experiment (GRACE) twin-satellite system. Mass load changes with spatial scales larger than 1000 km have been observed using conventional filters based on a Gaussian smoother, which applies a weight to GRACE spherical harmonic (SH) coefficients depending only on SH degree. This practice is consistent with a degree-dependent error model for GRACE monthly geopotential solutions. The Gaussian filters effectively dampen all power of ill-determined higher-degree components in the estimates. However, the spatial sampling provided by GRACE yields errors that vary with both SH degree and order. The consequence is that maps of spatial loads shall not be smoothed with an isotropic (degree-only) filter, but shall be constructed using anisotropic smoothing thus also yielding better spatial resolution in latitude. We have developed a non-isotropic filter to optimize the smoothing of GRACE temporal gravity observations by considering the degree- and order-dependent quality of GRACE estimates, the latter analysed from the correlation with the predicted signals of hydrologic and ocean models. In order to retain GRACE coefficients in the filtering process that show reasonable correlation with the geophysical (hydrology and ocean) models, we applied Gaussian-type smoothing but with averaging radius depending on the order of the geopotential coefficient estimates. Applied to 2 yr of GRACE data, we showed that the resulting non-isotropic filter yields enhanced GRACE signals with significantly higher resolution in latitude and the same resolution in longitude without reducing the accuracy as compared to the conventional Gaussian smoother.