tatistically optimal Slepian method for processing GRACE Level 2 data

The global surface mass variations obtained by the Gravity Recovery and Climate Experiment (GRACE) satellite Level-2 products show significant north-south strip noise, which seriously affects the estimation of regional surface mass variations. Most existing filtering methods are based on the processing of spherical harmonic basis functions to remove stripes. However, because spherical harmonic basis functions are only orthogonal globally, they may not be orthogonal in regions, which hinders the effective constraint of quality changes in specific regions. Therefore, this paper converts the spherical harmonic base of GRACE Level-2 to the Slepian base of the interested region and truncates it based on the Shannon number of the region. Even though the signals are concentrated in the region, there are still many stripes present. In order to remove the stripes, it is necessary to introduce the regularization and consider the statistical information of the spherical harmonic coefficient. The Tikhonov regularization matrix of the Slepian coefficient is obtained, combined with a power-law model to construct the prior covariance matrix of the signal and the optimal regularization coefficient is selected by using the generalized cross-validation (GCV) method, which is represented as the statistically optimal Slepian method (SO-Slepian) in this study. The results show that the ability of SO-Slepian and decorrelation and denoising kernel (DDK) filtering with the same regularization parameters as SO-Slepian to remove stripes and retain signals in the selected region is comparable. The line chart comparing the differences between SO-Slepian and DDK not only demonstrates the close similarity in results between SO-Slepian and traditional DDK filtering in the regional domain but also emphasizes the logical application of regularization during the Slepian modeling stage. It further supports the rationality of developing a regularization scheme for GRACE data processing based on Slepian.