Bridging Terrestrial Water Storage Anomaly During GRACE/GRACE-FO Gap Using SSA Method: A Case Study in China

Reconstruction of GRACE Mass Change Time Series Using a Bayesian Framework

Gravity Recovery and Climate Experiment and its Follow On (GRACE (-FO)) missions have resulted in a paradigm shift in understanding the temporal changes in the Earth's gravity field and its drivers. To provide continuous observations to the user community, missing monthly solutions within and between GRACE (-FO) missions (33 solutions) need to be imputed. Here, we modeled GRACE (-FO) data (196 solutions) between 04/2002-04/2021 to infer missing solutions and derive uncertainties in the existing and missing observations using Bayesian inference. First, we parametrized the GRACE (-FO) time series using an additive generative model comprising long-term variability (secular trend + interannual to decadal variations), annual, and semi-annual cycles. Informative priors for each component were used and Markov Chain Monte Carlo (MCMC) was applied to generate 2,000 samples for each component to quantify the posterior distributions. Second, we reconstructed the new data (229 solutions) by joining medians of posterior distributions of all components and adding back the residuals to secure the variability of the original data. Results show that the reconstructed solutions explain 99% of the variability of the original data at the basin scale and 78% at the one-degree grid scale. The results outperform other reconstructed data in terms of accuracy relative to land surface modeling. Our data-driven approach relies only on GRACE (-FO) observations and provides a total uncertainty over GRACE (-FO) data from the data-generation process perspective. Moreover, the predictive posterior distribution can be potentially used for "nowcasting" in GRACE (-FO) near-real-time applications (e.g., data assimilations), which minimize the current mission data latency (40-60 days).

Filling Temporal Gaps within and between GRACE and GRACE-FO Terrestrial Water Storage Records: An Innovative Approach

Temporal gaps within the Gravity Recovery and Climate Experiment (GRACE) (gap: 20 months), between GRACE and GRACE Follow-On (GRACE-FO) missions (gap: 11 months), and within GRACE-FO record (gap: 2 months) make it difficult to analyze and interpret spatiotemporal variability in GRACE- and GRACE-FO-derived terrestrial water storage (TWSGRACE) time series. In this study, an overview of data and approaches used to fill these gaps and reconstruct the TWSGRACE record at the global scale is provided. In addition, the study provides an innovative approach that integrates three machine learning techniques (deep-learning neural networks [DNN], generalized linear model [GLM], and gradient boosting machine [GBM]) and eight climatic and hydrological input variables to fill these gaps and reconstruct the TWSGRACE data record at both global grid and basin scales. For each basin and grid cell, the model performance was assessed using Nash–Sutcliffe efficiency coefficient (NSE), correlation coefficient (CC), and normalized root-mean-square error (NRMSE), a leader model was selected based on the model performance, and variables that significantly control leader model outputs were defined. Results indicate that (1) the leader model reconstructed the TWSGRACE with high accuracy over both grid and local scales, particularly in wet and low anthropogenically active regions (grid scale: NSE = 0.65 ± 0.20, CC = 0.81 ± 0.13, and NSE = 0.56 ± 0.16; basin scale: NSE = 0.78 ± 0.14, CC = 0.89 ± 0.07, and NRMSE = 0.43 ± 0.14); (2) no single model was flawless in reconstructing the TWSGRACE over all grids or basins, so a combination of models is necessary; (3) basin-scale models outperform grid-scale models; (4) the DNN model outperforms both GLM and GBM at the basin scale, whereas the GBM outperforms at the grid scale; (5) among other inputs, the Global Land Data Assimilation System (GLDAS)-derived TWS controls the model performance on both basin and grid scales; and (6) the reconstructed TWSGRACE data captured extreme climatic events over the investigated basins and grid cells. The developed approach is robust, effective, and could be used to accurately reconstruct TWSGRACE for any hydrologic system across the globe.

Improving the Inversion Accuracy of Terrestrial Water Storage Anomaly by Combining GNSS and LSTM Algorithm and Its Application in Mainland China

Densely distributed Global Navigation Satellite System (GNSS) stations can invert the terrestrial water storage anomaly (TWSA) with high precision. However, the uneven distribution of GNSS stations greatly limits the application of TWSA inversion. The purpose of this study was to compensate for the spatial coverage of GNSS stations by simulating the vertical deformation in unobserved grids. First, a new deep learning weight loading inversion model (DWLIM) was constructed by combining the long short-term memory (LSTM) algorithm, inverse distance weight, and the crustal load model. DWLIM is beneficial for improving the inversion accuracy of TWSA based on the GNSS vertical displacement. Second, the DWLIM-based and traditional GNSS-derived TWSA methods were utilized to derive TWSA over mainland China. Furthermore, the TWSA results were compared with the TWSA solutions of the Gravity Recovery and Climate Experiment (GRACE) and Global Land Data Assimilation System (GLDAS) model. The results indicate that the maximum Pearson’s correlation coefficient (PCC), Nash–Sutcliffe efficiency (NSE) coefficient, and root mean square error (RMSE) equal 0.81, 0.61, and 2.18 cm, respectively. The accuracy of DWLIM was higher than that of the traditional GNSS inversion method according to PCC, NSE, and RMSE, which were increased by 67.11, 128.15, and 22.75%. The inversion strategy of DWLIM can effectively improve the accuracy of TWSA inversion in regions with unevenly distributed GNSS stations. Third, this study investigated the variation characteristics of TWSA based on DWLIM in 10 river basins over mainland China. The analysis shows that the TWSA amplitudes of Songhua and Liaohe River basins are significantly higher than those of the other basins. Moreover, TWSA sequences in each river basin contain annual seasonal signals, and the wave peaks of TWSA estimates emerge between June and July. Overall, DWLIM provides a useful measure to derive TWSA in regions where GNSS stations are uneven or sparse.

Regional Crustal Vertical Deformation Driven by Terrestrial Water Load Depending on CORS Network and Environmental Loading Data: A Case Study of Southeast Zhejiang

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.