A multiple-parameter regularization approach for filtering monthly GRACE/GRACE-FO gravity models

The Gravity Recovery and Climate Experiment (GRACE) and its subsequent GRACE Follow-On (GRACE-FO) missions have been instrumental in monitoring Earth’s mass changes through time-variable gravity field models. However, these models suffer from high-frequency noise and significant north-south striping (NSS) noise. The most widely used spectral filter for addressing these issues is the decorrelation and denoising kernel (DDK) filter, utilized by official processing agencies. The key operation of DDK filtering is to regularize the normal equation built by the Level-1b data. However, the regularization parameter used in original DDK filters is empirically determined by the signal-to-noise ratios and remains unchanged across all months. This is improper due to the heterogeneity of the monthly covariance matrix. Additionally, a single regularization parameter may not effectively address the ill-posedness of the inversion equation. For this reason, we propose a multiple-parameter regularization approach for filtering GRACE gravity field models, with regularization parameters determined by minimizing the mean squared error (MSE) for each month. The proposed method is used to process the ITSG-Grace2018 and ITSG-Grace_operational Level-2 spherical harmonic coefficients with degree/order 96 from April 2002 to December 2022. The results show that our method produces the filtered mass anomalies, global trend, and annual signal amplitudes that align better with three mascon solutions (CSR, JPL, and GSFC) compared to DDK filters and ordinary Tikhonov regularization with a single regularization parameter. In some typical areas with significant signals, our approach retains more detailed characteristics in filtered signals compared to DDK filters and ordinary Tikhonov regularization. Repeated simulations demonstrate that the filtered signals by our approach are closer to the simulated true signals than those by other methods.