Least Squares Collocation for Estimating Terrestrial Water Storage Variations from GNSS Vertical Displacement on the Island of Haiti

Abstract

Water masses are continuously redistributing across the Earth, so accurately estimating their availability is essential. Global Navigation Satellite Systems (GNSSs) have demonstrated potential for observing vertical deformations, which is partly driven by terrestrial water storage (TWS) variations. This capability has been used in hydrogeodesy to estimate TWS variations. However, GNSS data inversions are often ill-posed, requiring regularization for stable solutions. This study considers the Least Squares Collocation (LSC) statistical method as an alternative. LSC uses covariance functions to characterize observations, parameters, and their interdependence. By incorporating additional physical information into inverse models, LSC allows ill-posed problems stabilization. To assess LSC effectiveness, we apply it to observed and simulated GNSS vertical displacement on Haiti island. Hydrological signals are modeled using Global Land Data Assimilation (GLDAS) data. In sparse GNSS data regions, findings indicate poor agreement between TWS and hydrological input, with a Root-Mean-Square-Error (RMSE) of 115 kg/m², a correlation of 0.3, and a reduction of 73%. However, in dense simulated GNSS areas, TWS and hydrological input show strong agreement, with an RMSE of 41 kg/m², a correlation of 0.83, and a reduction of 92%. The results confirm LSC potentiality for assessing TWS changes and improving water quantification in dense GNSS station region.