Adaptive DDK Filter for GRACE Time-Variable Gravity Field with a Novel Anisotropic Filtering Strength Metric

Abstract

Filtering for GRACE temporal gravity fields is a necessary step before calculating surface mass anomalies. In this study, we propose a new denoising and decorrelation kernel (DDK) filtering scheme called adaptive DDK filter. The involved error covariance matrix (ECM) adopts nothing but the monthly time-variable released by several data centers. The signal covariance matrix (SCM) involved is monthly time-variable also. Specifically, it is parameterized into two parameters, namely the regularization coefficient and the power index of signal covariances, which are adaptively determined from the data themselves according to the generalized cross validation (GCV) criterion. The regularization coefficient controls the global constraint on the signal variances of all degrees, while the power index adjusts the attenuation of the signal variances from low to high degrees, namely local constraint. By tuning these two parameters for the monthly SCM, the adaptability to the data and the optimality of filtering strength can be expected. In addition, we also devise a half-weight polygon area (HWPA) of the filter kernel to measure the filtering strength of the anisotropic filter more reasonably. The proposed adaptive DDK filter and filtering strength metric are tested based on CSR GRACE temporal gravity solutions with their ECMs from January 2004 to December 2010. Results show that the selected optimal power indices range from 3.5 to 6.9, with the corresponding regularization parameters range from 1 × 1014 to 5 × 1019. The adaptive DDK filter can retain comparable/more signal amplitude and suppress more high-degree noise than the conventional DDK filters. Compared with the equivalent smoothing radius (ESR) of filtering strength, the HWPA has stronger a distinguishing ability, especially when the filtering strength is similar.