Stochastic filtering for determining spatiotemporal gravity variations from GRACE and GRACE Follow-On observations

We present a new stochastic filter technique for statistically rigorous separation of gravity signals and correlated "stripe" noises in a series of monthly gravitational spherical harmonic coefficients (SHCs) produced by the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On missions. Unlike the standard destriping process that removes the stripe contamination empirically, the stochastic approach simultaneously estimates gravity signals and correlated noises relying on covariance information that reflects both the spatial spectral features and temporal correlations among them. A major benefit of the technique is that by estimating the stripe noise in a Bayesian framework, we are able to propagate statistically rigorous covariances for the destriped GRACE SHCs, i.e. incorporating the impact of the destriping on the SHC uncertainties. The Bayesian approach yields a natural resolution for the gravity signal that reflects the correlated stripe noise, and thus achieve a kind of spatial smoothing in and of itself. No spatial Gaussian smoothing is formally required although it might be useful for some circumstances. Using the stochastic filter, we process a decade-length series of GRACE monthly gravity solutions, and compare the results with GRACE Tellus data products that are processed using the "standard" destriping procedure. The results show that the stochastic filter is able to remove the correlated stripe noise to a remarkable degree even without an explicit smoothing step. The estimates from the stochastic filter for each destriped GRACE field are suitable for Bayesian integration of GRACE with other geodetic measurements and models, and the statistically rigorous estimation of the time-varying rates and seasonal cycles in GRACE time series.