This paper aims to address the limitations of the distribution number and uniformity of Continuously Operating Reference Stations (CORS) and their impact on the reliability of inverting regional groundwater storage (GWS) based on Green’s function method and using global navigation satellite system (GNSS) data. A fusion method on the inversion of regional GWS changes from GNSS and the Gravity Recovery and Climate Experiment (GRACE) was proposed in this paper. Taking the Shaanxi–Gansu–Ningxia (SGN) region as an example, the in situ groundwater level data from ten CORS stations and eight wells were used for test analyses. In this paper, an atmospheric pressure model from the European Centre for Medium-Range Weather Forecasts (ECMWF), a global land data assimilation system (GLDAS), a WaterGAP global hydrology model (WGHM), and mean sea level anomaly (MSLA) data were used to quantitatively monitor the influence of vertical deformation caused by non-tidal environmental load. After deducing these loading deformations from the filtered time series of non-linear monthly geodetic height from the GNSS, the GWS changes in the SGN region from 2011 to 2014 were inverted. Meanwhile, the change in surface water storage from the GLDAS and WGHM models were removed from the terrestrial water storage (TWS) changes derived from GRACE. On this basis, the remove–restore theory in the Earth’s gravity field was introduced to both fuse the inversion results and obtain the regional GWS changes based on the fusion method. The results showed the following: (1) The local characteristics from the fusion results were more prominent than those of GRACE on the spatial scale, such as in the southwest and northeast in the study area. In addition, the fusion results were more uniform than those from GNSS, especially for the sparse and missing areas in which CORS stations were located, and the local effect was weakened. (2) On the time scale, compared with GRACE, the trends in GWS changes obtained from the fusion method and from GNSS inversion were roughly the same as the in situ groundwater level changes. (3) For the in situ groundwater wells “6105010031” and “6101260010”, the correlation coefficients of the fusion result were 0.53 and 0.56, respectively. The accuracy of the fusion method was slightly higher than that from GNSS, which indicates that the fusion method may be more effective for areas where CORS stations are missing or sparsely distributed. The methods in this paper can provide significant reference material for hydrodynamic research, sustainable management of water resources, and the dynamic maintenance of height data.

Altimeter data processing is very important to improve the quality of sea surface height (SSH) measurements. Sea state bias (SSB) correction is a relatively uncertain error correction due to the lack of a clear theoretical model. At present, the commonly used methods for SSB correction are polynomial models (parametric models) and non-parametric models. The non-parametric model usually was constructed by collinear data. However, the amount of collinear data was enormous, and it contained redundant information. In this study, the non-parametric regression estimation model was optimized by using the parameter replacement method of ascending and descending tracks based on the crossover data. In this method, significant wave heights from the Jason-2 altimeter data during cycles 200–301 and wind speed from the ERA5 reanalysis data were used. The non-parametric regression estimation model of Jason-2 was constructed by combining it with local linear regression, Epanechnikov kernel function and local window width. At the same time, based on the significant wave height and wind speed at the crossover points, the SSB polynomial model containing six parameters was constructed by using the Taylor series expansion, and the model was optimized. By comparing polynomial model construction with different parameters, the optimized model was obtained. The SSH of the crossover points and the tide gauge records were used to validate these results derived from two models and GDR. Compared with the crossover discrepancies of SSH corrected by the polynomial model, the RMS of the crossover discrepancies of SSH corrected by the non-parametric regression estimation model was reduced by 7.9%. Compared with the crossover discrepancies of SSH corrected by the conventional non-parametric model from GDR, the RMS of the crossover discrepancies of SSH corrected by the non-parametric regression estimation model was reduced by 4.1%. This shows that the precision of the SSHs derived by after the SSB correction, as calculated by the non-parametric regression estimation model, was better than that of the polynomial model and the SSB correction from GDR. Using the Jason-2 altimeter data, the along-track geoid gradient and the sea level change rate of the global ocean were determined by using two models to correct the SSB. By comparing the results of the two models, the accuracy of the geoid gradient along the orbit that was obtained by the non-parametric regression estimation model was better than that of the polynomial model and GDR. The global average sea level change rate after the non-parametric regression estimation model correction was 3.47 ± 0.09 mm/y, which was the closest to the average sea level change rate that has been published in the international literature within this field.

The quality of the SWOT-derived marine gravity field and its subsequent refinement are investigated in the Western Pacific (120–140°E, 0–30°N). Inverting 41 cycles of the SWOT L3_LR_SSH v2.0.1 product yields a gravity field with RMSEs of 2.476 and 4.321 mGal against independent JAMSTEC and NCEI shipborne gravity, respectively, and the accuracy gain converges as the number of SWOT altimetry repeat cycles increases, showing diminishing marginal returns. To further refine this field, three tree-based ensemble learning methods—Random Forest (RF), histogram-based gradient boosting (HGB) and LightGBM (LGBM)—are trained on 67 multi-source features with the SWOT-minus-shipborne residual as the target, and validated under two spatially isolated strategies: a 2° × 2° spatial block hold-out with a 10 km buffer and a cruise-wise hold-out over seven complete cruises, in which training samples within 10 km of any test point are removed. All three methods reduce the error. On the block hold-out, LGBM performs best (RMSE 2.398 mGal, a 3.6% improvement over the 2.488 mGal baseline), followed by HGB (2.402 mGal, 3.5%) and RF (2.422 mGal, 2.7%); on the cruise hold-out the gains are markedly larger, with HGB best (RMSE 1.703 mGal, a 8.6% improvement over the 1.863 mGal baseline), then LGBM (1.714 mGal, 8.0%) and RF (1.794 mGal, 3.7%). A consistent reversal is found between the two assessment levels: RF leads on the in-training out-of-fold RMSE but is weakest on unseen cruises, indicating that RF is competitive within the training distribution yet weaker than boosting methods when extrapolating to unsurveyed areas. Power spectral density analysis shows that the improvements concentrate at wavelengths of 8–45 km, whereas wavenumber below 0.0221 km⁻¹ are slightly degraded.