A combination of Time-Variable Gravity Field Solutions from Multi-Satellite Datasets (1993–2024) via Least-Squares Collocation

Abstract. Time-variable gravity field solutions from GRACE and GRACE-FO have been successfully applied in hydrological and geophysical studies; however, inter- and intra-mission gaps and limited record length constrain their broader utility. Current approaches involve hydrometeorological-forced machine-learning reconstructions and satellite-tracking-observation combinations; however, the former is constrained by the accuracy and completeness of data inputs, while the latter requires additional filtering due to limited spectral sensitivity, resulting in filtering-dependent solutions. Both approaches neglect covariance information of observation noise and signal, precluding optimal solutions. To address these limitations, this study develops gapless monthly solutions up to degree/order 60 spanning January 1993 to December 2024 using constrained Least-Squares Collocation (LSC), which integrates combination and denoising processes of gravity field solutions without explicit filtering. LSC-based Combined Solutions (LSC-CS) integrates trends, annual and semi-annual variations, and non-seasonal signals from multi-satellite observations (GRACE/-FO, Low Earth Orbit satellites, and Satellite Laser Ranging) without external hydrometeorological inputs, while incorporating covariance matrices of observation errors and combined signals to optimally balance error reduction and signal preservation. Evaluation results indicate that LSC-CS significantly eliminates striping noise and high-degree coefficient noise while effectively preserving low-degree gravity signals (e.g., C20 and C30) and achieving high signal-to-noise ratios. Comparison with three reconstructed products (IGG-SLR-DORIS, RESDCAE, BNML) shows that LSC-CS achieves the lowest sea level budget misclosures, with reductions of 40 %, 2.9 %, and 49 %, respectively. Across 52 major basins, LSC-CS has the smallest water balance errors, with reductions of 4.6 %, 2.6 %, and 1.5 %, respectively. For Antarctic and Greenland ice sheet mass changes, LSC-CS closely match IMBIE estimates, with trend consistency improvements of 46.8 % and 32.7 % over IGG-SLR-DORIS and 48.6 % and 67.4 % over RESDCAE, respectively. The combined monthly gravity field solutions are available at https://zenodo.org/records/18543287 (Zhang et al., 2026).