Joint Inversion of GNSS and GRACE for Terrestrial Water Storage Change in California

Global Navigation Satellite System (GNSS) vertical displacements measuring the elastic response of Earth's crust to changes in hydrologic mass have been used to produce terrestrial water storage change ( increment TWS) estimates for studying both annual increment TWS as well as multi-year trends. However, these estimates require a high observation station density and minimal contamination by nonhydrologic deformation sources. The Gravity Recovery and Climate Experiment (GRACE) is another satellite-based measurement system that can be used to measure regional TWS fluctuations. The satellites provide highly accurate increment TWS estimates with global coverage but have a low spatial resolution of similar to 400 km. Here, we put forward the mathematical framework for a joint inversion of GNSS vertical displacement time series with GRACE increment TWS to produce more accurate spatiotemporal maps of increment TWS, accounting for the observation errors, data gaps, and nonhydrologic signals. We aim to utilize the regional sensitivity to increment TWS provided by GRACE mascon solutions with higher spatial resolution provided by GNSS observations. Our approach utilizes a continuous wavelet transform to decompose signals into their building blocks and separately invert for long-term and short-term mass variations. This allows us to preserve trends, annual, interannual, and multi-year changes in TWS that were previously challenging to capture by satellite-based measurement systems or hydrological models, alone. We focus our study in California, USA, which has a dense GNSS network and where recurrent, intense droughts put pressure on freshwater supplies. We highlight the advantages of our joint inversion results for a tectonically active study region by comparing them against inversion results that use only GNSS vertical deformation as well as with maps of increment TWS from hydrological models and other GRACE solutions. We find that our joint inversion framework results in a solution that is regionally consistent with the GRACE increment TWS solutions at different temporal scales but has an increased spatial resolution that allows us to differentiate between regions of high and low mass change better than using GRACE alone.