Dozens of missing epochs in the monthly gravity product of the satellite mission Gravity Recovery and Climate Experiment (GRACE) and its follow‐on (GRACE‐FO) mission greatly inhibit the complete analysis and full utilization of the data. Despite previous attempts to handle this problem, a general all‐purpose gap‐filling solution is still lacking. Here we propose a non‐parametric, data‐adaptive and easy‐to‐implement approach—composed of the Singular Spectrum Analysis gap‐filling technique, cross‐validation, and spectral testing for significant components—to produce reasonable gap‐filling results in the form of spherical harmonic coefficients (SHCs). We demonstrate that this approach is adept at inferring missing data from long‐term and oscillatory changes extracted from available observations. A comparison in the spectral domain reveals that the gap‐filling result in the same signal intensity as the product of GRACE missions for spherical harmonic degrees below 30. As the degree increases above 30, the degree variance of the gap‐filling result decreases more rapidly than that of GRACE/GRACE‐FO SHCs, demonstrating effective suppression of noise. As a result, our approach can reduce noise in the oceans without sacrificing resolutions on land. The quality of the gap‐filling product is evaluated through comparison with a surface mass balance based estimate in Greenland, Swarm gravity solutions and a climate‐driven water storage model, all of which confirm the good performance of our results. This study makes a ready‐to‐use gap‐filling product in the form of SHCs together with proper error estimates available. Nonetheless, our method is also applicable to smoothed gridded observations.

The Gravity Recovery And Climate Experiment (GRACE) satellite mission recorded temporal variations in the Earth’s gravity field, which are then converted to Total Water Storage Change (TWSC) fields representing an anomaly in the water mass stored in all three physical states, on and below the surface of the Earth. GRACE provided a first global observational record of water mass redistribution at spatial scales greater than 63000 km². This limits their usability in regional hydrological applications. In this study, we implement a statistical downscaling approach that assimilates 0.5° × 0.5° water storage fields from the WaterGAP hydrology model (WGHM), precipitation fields from 3 models, evapotranspiration and runoff from 2 models, with GRACE data to obtain TWSC at a 0.5° × 0.5° grid. The downscaled product exploits dominant common statistical modes between all the hydrological datasets to improve the spatial resolution of GRACE. We also provide open access to scripts that researchers can use to produce downscaled TWSC fields with input observations and models of their own choice.

Summary. Methods of global spherical harmonic analysis of discrete data on a sphere are placed in a historical context. The paper concentrates on the loss of o