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It is a typical ill-conditioned problem to invert GPS-measured loading deformations for terrestrial water storage (TWS) changes. While previous studies commonly applied the 2nd-order Tikhonov regularization, we demonstrate the truncated singular value decomposition (TSVD) regularization can also be applied to solve the inversion problem. Given the fact that a regularized estimate is always biased, it is valuable to obtain estimates with different methods for better assessing the uncertainty in the solution. We also show the general cross validation (GCV) can be applied to select the truncation term for the TSVD regularization, producing a solution that minimizes predictive mean-square errors. Analyzing decade-long GPS position time series over Taiwan, we apply the TSVD regularization to estimate mean annual TWS variations for Taiwan. Our results show that the TSVD estimates can sufficiently fit the GPS-measured annual displacements, resulting in randomly distributed displacement residuals with a zero mean and small standard deviation (around 0.1 cm). On the island-wide scale, the GPS-inferred annual TWS variation is consistent with the general seasonal cycle of precipitations. However, on smaller spatial scales, we observe significant differences between the TWS changes estimated by GPS and simulated by GLDAS land surface models in terms of spatiotemporal pattern and magnitude. Based on the results, we discuss some challenges in the characterization of TWS variations using GPS observations over Taiwan.

Truncated Singular Value Decomposition Regularization for Estimating Terrestrial Water Storage Changes Using GPS: A Case Study over Taiwan