A Statistical Filtering Approach for Gravity Recovery and Climate Experiment (GRACE) Gravity Data
We describe and analyze a statistical filtering approach for GRACE data that uses a parametrized model for the temporal evolution of the GRACE coefficients. After least-squares adjustment, a statistical test is performed to assess the significance of the estimated parameters. If the test is passed, the parameters are used by the filter in the reconstruction of the field; otherwise they are rejected. The test is performed, and the filter is formed, separately for annual components of the model and the trend. This new approach is distinct from Gaussian smoothing since it uses the data themselves to test for specific components of the time-varying gravity field. The statistical filter appears inherently to remove most of the "stripes" present in the GRACE fields, although destriping the fields prior to filtering seems to help the trend recovery. We demonstrate that the statistical filter produces reasonable maps for the annual components and trend. We furthermore assess the statistical filter for the annual components using ground-based GPS data in South America by assuming that the annual component of the gravity signal is associated only with groundwater storage. The un-destriped, statistically filtered field has a X2 value relative to the GPS data consistent with the best result from smoothing. In the space domain, the statistical filters are qualitatively similar to Gaussian smoothing. Unlike Gaussian smoothing, however, the statistical filter has significant sidelobes, including large negative sidelobes on the north-south axis, potentially revealing information on the errors, and the correlations among the errors, for the GRACE coefficients.