Processing GRACE Level 2 data based on efficient calculation and statistical optional Slepian method

The GRACE (Gravity Recovery and Climate Experiment) mission provides critical data for understanding Earth's mass transport, yet its Level 2 products are affected by high-frequency and north-south stripe errors.Traditional Slepian methods, while valuable for regional analysis, face significant computational and storage limitations for high band-limits due to their L 2 ×L 2 matrix operations.This study introduces a Fast Statistically Optimal Slepian (FSO-Slepian) method to address these challenges.FSO-Slepian integrates an efficient Slepian function computation (Fast-Slepian), which extends polar cap Slepian techniques to arbitrary regions, with a robust regularization scheme.This regularization employs a generalized Kaula criterion-based prior covariance matrix, Tikhonov regularization, and Generalized Cross-Validation (GCV) for optimal parameter determination, effectively suppressing errors.Experimental results demonstrate that Fast-Slepian significantly accelerates computation (e.g., 3-4 times faster for L=60) while maintaining numerical accuracy comparable to traditional Slepian methods.After regularization, FSO-Slepian effectively removes stripe errors and high-frequency noise, achieving filtering performance comparable to or superior to existing Statistically Optimal Slepian (SO-Slepian) and DDK (Decorrelation and Denoising Kernel) methods in terms of RMSE and uncertainty (e.g., lowest uncertainty of 10.85 cm in the Amazon basin).Time series analysis further confirms its stability and reliability for long-term monitoring, which also highlights the rationality of the application of regularization in the Slepian modeling stage.In conclusion, FSO-Slepian offers an efficient, accurate, and robust solution for GRACE Level 2 data processing, enhancing the practical application of Slepian functions in regional mass change studies and contributing to a more precise understanding of Earth system dynamics.