Estimate GPS-inferred Terrestrial Water Storage Variations in Taiwan with Two Inversion Strategies: Tikhonov Regularization and Truncated Singular Value Decomposition

The elastic loading deformation of ground surface in response to terrestrial water storage (TWS) changes can be precisely measured by GPS, and provides independent constraints on the spatiotemporal change of the TWS. Analyzing the vertical components of the continuous GPS position time series over Taiwan spanning from 2000 to 2015, we study the seasonal TWS change of that region. The elastic-loading Green's function used in this study represents the impulse response of ground surface to a unit rectangular load by assuming an elastic half-space. In order to invert the GPS-measured loading deformation for the TWS change, which is an ill-conditioned inversion problem, we compare two inversion methods: (1) Tikhonov regularization (TR) with second-order Laplace smoothing constraint, and (2) truncated singular value decomposition (TSVD). While the TR produces an estimate that reflects a compromise between data misfits and the spatial smoothness of the estimate, the TSVD retains the maximum local sensitivity of the data. By inverting the measurements from 306 continuous GPS stations over Taiwan, we found that the TWS over Taiwan shows significant spatiotemporal variabilities. The pattern of the TWS change highly correlates with the precipitation distribution. Thus, the dense continuous GPS network over Taiwan provides a geodetic constraint on the estimation of the TWS, which would be of interest to the decision making in water resources policy and management.