Point-mass inversion is widely employed in GRACE level-2 data processing. Conventionally, the spherical harmonic (SH) coefficients are used indirectly: a set of pseudo measurements is generated first using the SH coefficients through SH synthesis; then the point-mass inversion is done with these pseudo measurements. To be statistically optimal, the covariance matrix of pseudo measurements should be calculated and used to appropriately weigh the parameter estimation. In this work, we propose a statistically optimal point-mass inversion scheme by directly using the SH coefficients as measurements. We prove the equivalence between this direct approach and the conventional indirect approaches. We also demonstrated their comparable performance through both simulation and real GRACE data processing. Choosing and calculating pseudo measurements, propagating covariance matrix, and potentially dealing with the singularity of the covariance matrix involved in the conventional indirect approaches are avoided in the proposed direct approach. This statistically optimal direct approach can readily be employed in mascon inversion of GRACE data and other radial basis functions-based approaches in regional gravity modeling.@en

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 conven-tional 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.

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High-frequency and correlated noise filtering is one of the important preprocessing steps for GRACE level-2 products before calculating mass anomaly. Decorrelation and denoising kernel (DDK) filters are usually considered as such optimal filters to solve this problem. In this work, a sparse DDK filter is proposed. This is achieved by replacing Tikhonov regularization in traditional DDK filters with weighted L1 norm regularization. The proposed sparse DDK filter adopts a time-varying error covariance matrix, while the equivalent signal covariance matrix is adaptively determined by the Gravity Recovery and Climate Experiment (GRACE) monthly solution. The covariance matrix of the sparse DDK filtered solution is also developed from the Bayesian and error-propagation perspectives, respectively. Furthermore, we also compare and discuss the properties of different filters. The proposed sparse DDK has all the advantages of traditional filters, such as time-varying, location inhomogeneity, and anisotropy, etc. In addition, the filtered solution is sparse; that is, some high-degree and high-order terms are strictly zeros. This sparsity is beneficial in the following sense: high-degree and high-order sparsity mean that the dominating noise in high-degree and high-order terms is completely suppressed, at a slight cost that the tiny signals of these terms are also discarded. The Center for Space Research (CSR) GRACE monthly solutions and their error covariance matrices, from January 2004 to December 2010, are used to test the performance of the proposed sparse DDK filter. The results show that the sparse DDK can effectively decorrelate and denoise these data.

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