Regional Terrestrial Water Storage Recovery Using Spherical Cap Harmonics from GNSS-Derived Vertical Displacements

Terrestrial Water Storage (TWS) is a vital component of the Earth's hydrological and climate systems, influencing water resource management and ecosystem dynamics. However, current TWS estimation techniques, such as those derived from global spherical harmonics, suffer from low spatial and temporal resolutions, limiting their application for regional studies. To address this issue, this study proposes a framework for regional TWS estimation based on Spherical Cap Harmonic Analysis (SCHA) applied to GNSS-derived vertical crustal displacements. The proposed methodology employs the remove-restore strategy to isolate the hydrological load within the cap. First, mass redistribution signals from outside the cap are removed using GRACE (Gravity Recovery and Climate Experiment) data. The GNSS-derived residual vertical displacements are then expanded into SCHA coefficients, incorporating modified load Love numbers that account for the spherical cap geometry. The modified load Love numbers ensure a physically consistent representation of the Earth's elastic response within the cap boundary. The estimated coefficients (residual) are used to recover residual TWS variations, after which the removed external contributions are restored. The proposed approach provides enhanced spatial resolution and accuracy compared to traditional global spherical harmonics by tailoring the analysis to the geometry of a spherical cap.

Both simulated and observed GNSS data from a network of stations across Brazil, covering diverse hydrological regimes—from the Amazon Basin to the semi-arid Northeast—are analyzed to validate this approach. The results reveal spatial and temporal patterns of TWS changes, demonstrating agreement with independent GRACE estimates and hydrological models. These findings emphasize the ability of SCHA-based regional analysis to capture local-scale hydrological processes with higher precision than global methods. Furthermore, this study highlights the potential of SCHA to complement GRACE datasets in regions with dense GNSS observational coverage and advances geodetic techniques for hydrological monitoring.