The terrestrial water storage anomaly (TWSA) gap between the Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission (GRACE-FO) is now a significant issue for scientific research in high-resolution time-variable gravity fields. This paper proposes the use of singular spectrum analysis (SSA) to predict the TWSA derived from GRACE. We designed a case study in six regions in China (North China Plain (NCP), Southwest China (SWC), Three-River Headwaters Region (TRHR), Tianshan Mountains Region (TSMR), Heihe River Basin (HRB), and Lishui and Wenzhou area (LSWZ)) using GRACE RL06 data from January 2003 to August 2016 for inversion, which were compared with Center for Space Research (CSR), Helmholtz-Centre Potsdam-German Research Centre for Geosciences (GFZ), Jet Propulsion Laboratory (JPL)’s Mascon (Mass Concentration) RL05, and JPL’s Mascon RL06. We evaluated the accuracy of SSA prediction on different temporal scales based on the correlation coefficient (R), Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE), which were compared with that of an auto-regressive and moving average (ARMA) model. The TWSA from September 2016 to May 2019 were predicted using SSA, which was verified using Mascon RL06, the Global Land Data Assimilation System model, and GRACE-FO results. The results show that: (1) TWSA derived from GRACE agreed well with Mascon in most regions, with the highest consistency with Mascon RL06 and (2) prediction accuracy of GRACE in TRHR and SWC was higher. SSA reconstruction improved R, NSE, and RMSE compared with those of ARMA. The R values for predicting TWS in the six regions using the SSA method were 0.34–0.98, which was better than those for ARMA (0.26–0.97), and the RMSE values were 0.03–5.55 cm, which were better than the 2.29–5.11 cm RMSE for ARMA as a whole. (3) The SSA method produced better predictions for obvious periodic and trending characteristics in the TWSA in most regions, whereas the detailed signal could not be effectively predicted. (4) The predicted TWSA from September 2016 to May 2019 were basically consistent with Global Land Data Assimilation System (GLDAS) results, and the predicted TWSA during June 2018 to May 2019 agreed well with GRACE-FO results. The research method in this paper provides a reference for bridging the gap in the TWSA between GRACE and GRACE-FO.

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.

The terrestrial water resources in Shaanxi–Gansu–Ningxia (SGN) region are relatively scarce, and its climate change is unstable. Research on the deformation driven by terrestrial water load is of great significance to the dynamic maintenance of reference station networks. In this paper, data derived from Gravity Recovery and Climate Experiment (GRACE) and Global Navigation Satellite System (GNSS) from 2010 to 2014 were combined to monitor the spatiotemporal characteristics of surface vertical deformation caused by terrestrial water load change. The single scale factor was calculated by comparing CPC, WGHM, and GLDAS hydrological model to restore filtering leakage signal. The singular spectrum analysis (SSA) method was used to extract the principal component of temporal vertical deformation, and its spatial distribution was analyzed. At the same time, in order to study the relationship between the terrestrial water load deformation from GRACE and that from GNSS, the first-order term correction, the Atmosphere and Ocean De-aliasing Level-1B product (GAC) correction, and the first-order load LOVE number correction for GRACE were adopted in this paper. In addition, a quantitative comparative analysis of both the monitoring results was carried out. The results show that the time-variable characteristics of surface vertical deformation characterized by the filtered three hydrological models were consistent with those of GRACE. The correlation coefficient and Nash–Sutcliffe efficiency coefficient (NSE) values were the highest in the GLDAS model and the GRACE model, respectively; the former index is 0.93, while the latter is 0.85. The crustal vertical deformation from terrestrial water load showed a declining rate from 2010 to 2014. Its spatial change rate showed an obvious ladder distribution, with the surface subsidence rate gradually decreasing from south to north. In addition, weighted root mean square (WRMS) contribution rate of the crustal vertical deformation resulting from GRACE with GAC correction between the different GNSS stations ranged from 18.52% to 54.82%. The correlation coefficient between them was close to 0.70. After deducting the mass load impact of GRACE only, the WRMS contribution rate of the corresponding stations decreased from −8.42% to 21.18%. The correlation coefficient between them reduced noticeably. Adding GAC back can increase the comparability with GRACE and GNSS in terms of monitoring the crustal vertical deformation. The annual amplitude and phase of surface vertical deformation resulting from GRACE with GAC correction were close to those of GNSS. The research results can help to explore the motion mechanism between water migration and surface deformation, which is of benefit in the protection of the water ecological environment in the region.

The non-tectonic deformation caused by hydrological loads is an important influencing factor in GNSS vertical displacement. Limited by the temporal and spatial resolution of global models and model errors, the hydrological load results calculated by traditional methods are difficult to meet the high temporal and spatial resolution requirements of small to medium-scale regions. This paper introduces the idea of the remove–restore method, assimilates regional high-resolution hydrological data, and obtains higher temporal and spatial-resolution hydrological load results. Subsequently, utilizing data from 12 CORS observed in the western Yunnan region between January 2018 and December 2020, the quantitative relationship and variation characteristics between GNSS vertical displacement and hydrological load displacement were analyzed in detail. Furthermore, the annual signals of both were extracted using the SSA method for comparative analysis. After removing the effects of atmospheric load and non-tidal ocean load, the average correlation coefficient between GNSS vertical displacement and hydrological load displacement is 0.84, with an average reduction of WRMS (%) reaching 37.17%. The average correlation coefficient of the annual signals between GNSS vertical displacement and hydrological load deformation is 0.94, with an average reduction of WRMS (%) reaching 46.5%, indicating that the contribution of hydrological load to the GNSS non-tectonic vertical displacement annual signal is close to 50%. The research results provide scientific support and important references for studying surface tectonic deformation by removing non-tectonic deformations such as hydrological loads from GNSS vertical displacement. Additionally, it helps to explore the mechanisms of interaction between water storage migration and surface deformation.

Monitoring regional terrestrial water load deformation is of great significance to the dynamic maintenance and hydrodynamic study of the regional benchmark framework. In view of the lack of a spatial interpolation method based on the GNSS (Global Navigation Satellite System) elevation time series for obtaining terrestrial water load deformation information, this paper proposes to employ a CORS (Continuously Operating Reference Stations) network combined with environmental loading data, such as ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric data, the GLDAS (Global Land Data Assimilation System) hydrological model, and MSLA (Mean Sea Level Anomaly) data. Based on the load deformation theory and spherical harmonic analysis method, we took 38 CORS stations in southeast Zhejiang province as an example and comprehensively determined the vertical deformation of the crust as caused by regional terrestrial water load changes from January 2015 to December 2017, and then compared these data with the GRACE (Gravity Recovery and Climate Experiment) satellite. The results show that the vertical deformation value of the terrestrial water load in southeast Zhejiang, as monitored by the CORS network, can reach a centimeter, and the amplitude changes from −1.8 cm to 2.4 cm. The seasonal change is obvious, and the spatial distribution takes a ladder form from inland to coastal regions. The surface vertical deformation caused by groundwater load changes in the east–west–south–north–central sub-regions show obvious fluctuations from 2015 to 2017, and the trends of the five sub-regions are consistent. The amplitude of surface vertical deformation caused by groundwater load change in the west is higher than that in the east. We tested the use of GRACE for the verification of CORS network monitoring results and found a relatively consistent temporal distribution between both data sets after phase delay correction on GRACE, except for in three months—November in 2015, and January and February in 2016. The results show that the comprehensive solution based on the CORS network can effectively improve the monitoring of crustal vertical deformation during regional terrestrial water load change.