Inferring changes in terrestrial water storage from seasonal and transient deformation: an application of Kalman filtering on vertical GPS signal in the United States

Global Positioning System (GPS) has recently emerged as a new method for providing direct geodetic observations of terrestrial water storage (TWS) on Earth's surface. Changes in surface hydrologic load cause elastic deformation predominantly in the vertical direction, and can be precisely measured by continuous GPS stations at fine temporal resolution. Here, we analyze vertical GPS time series in the United States from 2010 to 2020 to understand the spatio-temporal evolution of surface deformation due to changes in TWS. To account for variations in both seasonal amplitudes and multi-year transients, time-varying trend and seasonal components are extracted from each GPS time series by solving a linear state space model using Kalman filter. Our results show distinct seasonal and transient deformation features that correlate with hydrologic and physiographic provinces, and indicate redistribution of terrestrial water mass within watersheds. We particularly focus on California's coastal mountains and the southern Appalachians, where TWS inverted from the GPS analysis is used in conjunction with precipitation data to infer evapotranspiration and runoff mechanisms. Ground deformation in these two regions exhibit contrasting spatial scales and temporal behaviors, and the ability to constrain TWS estimates with geodetic observations can help inform water resource policies for nearby populations. We further compare and validate GPS-derived results with land hydrology models (e.g. NLDAS, ERA-5) and NASA's Gravity Recovery and Climate Experiment (GRACE), paving way for future joint analysis for improving TWS estimates.