Weighted multichannel singular spectrum analysis for post-processing GRACE monthly gravity field models by considering the formal errors

SUMMARY Gravity Recovery and Climate Experiment (GRACE) Spherical Harmonics (SH) solutions are usually provided together with the corresponding formal errors, however, all multichannel singular spectrum analysis (MSSA) approaches neglect the formal errors of SH coefficients in processing the GRACE time-series. In this contribution, we propose a weighted MSSA to directly process the incomplete time-series of GRACE monthly gravity models by taking the formal errors into account. A 14-yr time-series of Release 06 (RL06) monthly gravity field models from the Center for Space Research (CSR) truncated to degree and order 60 for the period April 2002 to August 2016 is analysed by weighted MSSA, the results are compared with those from the improved MSSA that directly processes the incomplete time-series without considering the formal errors. The first 10 principal components derived by using the weighted MSSA can capture the variance in total up to 82.05 per cent, higher than 80.19 per cent by the improved MSSA. All the fitting errors of GRACE SH coefficients by the weighted MSSA are smaller than those by the improved MSSA, which indicates that weighted MSSA can extract more geophysical signals than the improved MSSA approach. To evaluate the efficiency of the weighted MSSA to eliminate noise, the ratios of the latitude weighted RMS of signals over lands and oceans are computed. Based on all the available months of GRACE solutions, the mean RMS ratio of signals over lands relative to oceans derived by the weighted MSSA is 5.04, higher than 4.96 by the improved MSSA. Therefore, we can conclude that the proposed weighted MSSA can suppress noise more efficiently and extract more geophysical signals from the GRACE time-series, which highlights the necessity of considering formal errors and the effectiveness of the weighted MSSA in post-processing the GRACE monthly gravity field models.