Recovery of Greenland Ice Sheet mass variation from GRACE using improved Slepian function

We propose an enhanced Slepian method to estimate mass variations of the Greenland Ice Sheet (GrIS) using GRACE monthly spherical harmonic coefficient (SHC) solutions. This approach incorporates the full error covariance matrices of the monthly SHC solutions and employs a novel regularization matrix constructed based on the satellite altimeter data. The monthly Slepian coefficients are estimated through a least-squares inversion process and subsequently converted into monthly GrIS mass variations. The mass balance (MB), derived from surface mass balance (SMB) and ice discharge data, was utilized to determine the statistically optimal parameter range for the improved Slepian method. Using these optimized parameters, we estimated mass anomalies over six individual drainage systems and the entire GrIS. The method demonstrated its highest performance at the monthly scale, achieving reductions in discrepancies between the improved Slepian solutions and MB by 36% to 71%, depending on the drainage system, compared to the original Slepian approach. Additionally, we evaluated discrepancies between mass anomalies derived from three Mascon RL06 solutions (JPL, CSR, GSFC) and MB. The results indicate that the improved Slepian method exhibits comparable performance to Mascon products, further validating its efficacy in GrIS mass variation estimation.