Covariance Matrix Reconstruction of GRACE Monthly Solutions Using Common Factors and Individual Formal Errors

Accurate error covariance is crucial for postprocessing gravity recovery and climate experiment (GRACE) gravity field solutions in terms of spherical harmonic coefficients (SHCs). Unfortunately, most GRACE SHC products only provide formal errors of SHCs due to the large storage requirements of covariance matrices. A covariance matrix can be decomposed into a diagonal matrix and an orthogonal matrix. The orthogonal matrix of a monthly GRACE covariance matrix relates to the monthly repeated ground coverage of the GRACE orbit and remains similar across all monthly covariance matrices. Therefore, we propose a semiparametric approach for reconstructing monthly covariance matrices using a common orthogonal matrix and monthly individual formal errors. Covariance matrices of Tongji-Grace2018 and GFZ RL06 SHC products from April 2002 to December 2016 serve as training data to derive common orthogonal matrices and the model for mapping monthly individual formal errors to diagonal matrices, which are utilized to reconstruct covariance matrices of ITSG-Grace2018, CSR RL06, and JPL RL06 SHC products in this study. The results filtered with the reconstructed covariance matrices closely match with those filtered with actual covariance matrices of ITSG-Grace2018 SHC product and those of CSR and JPL mascon products in global spectral filtering and regional point-mass modeling estimates, significantly better than those estimated using corresponding formal errors. Besides, data storage space for reconstructing covariance matrices is reduced by 98.6% compared to the original matrices. Simulation experiments with ITSG-Grace2018 SHC products demonstrate that the root-mean-square-errors of filtered SHCs and global terrestrial water storage anomalies using reconstructed covariance matrices have minimal differences of 3.8% and 2.7% relative to those using actual covariance matrices, and the errors are significantly reduced by 18.2% and 10.8% compared to those only using formal errors.