Data-driven and physically informed modelling of the Terrestrial Water Storage dynamics

The Gravity Recovery and Climate Experiment (GRACE) mission, and its successor GRACE Follow-On, have enabled to map on a monthly basis the Terrestrial Water Storage Anomaly (TWSA) since 2002. This unprecedented capability has provided hydrologists with new observations of the spatiotemporal evolution of TWSA, which have been used, among others, to better constrain numerical runoff models, to characterize empirically the relations between runoff and TWSA, or to simply monitor and quantify groundwater depletions. In this study, we explore the possibility to infer from GRACE observations a physically informed and linear dynamical system that models the intrinsic dynamics of TWSA at sub-basin scales.

First, we apply a hexagonal binning over the study area and aggregate the total water volume anomaly derived from GRACE data for each bin. Assuming that each bin exchanges water with the others in proportion to its water content, we then reformulate the mass balance equation of the whole basin as a first order matrix differential equation. All the proportionality coefficients encoding the bin exchanges are gathered in an unknown transition matrix to be determined.  Such a transition matrix must satisfy different algebraic properties to be physically consistent and interpretable. In particular, we show that this matrix is necessarily a left stochastic matrix. Finally, we used the time series of total water volume anomaly to estimate this transition matrix by solving an optimization problem on the manifold defined by the aforementioned matrix constraint. This method is applied to the Amazon basin and to mainland Australia respectively, and the predictive performances of the derived dynamical systems are quantified and discussed.