Advancements in satellite technology yield environmental data with ever-improving spatial coverage and temporal resolution. This requires techniques to extract actionable insights from the vast amounts of data generated. In our study, we investigate the potential of dynamic mode decomposition (DMD) to uncover the dynamics of spatially correlated structures in global-scale data, using observations of total water storage anomalies from the GRACE satellite missions. DMD, which originates from applied mathematics and fluid dynamics, offers a robust method for data-driven analysis of dynamical systems. It decomposes high-dimensional, time-dependent datasets to reveal coherent structures and intrinsic dynamic behaviours. DMD is non-intrusive and adept at managing large datasets, making it a valuable tool for understanding complex systems and aiding in anomaly detection and forecasting. Our results show that DMD effectively compresses data and extrapolates dominant spatiotemporal structures from GRACE data. It maintains accuracy in predicting global system dynamics while reconstructing local time series. Moreover, by interpreting the dominant modes and their temporal dynamics, we can identify regions with similar trends and seasonal patterns, thereby elucidating the complex interactions between climate conditions and resource exploitation. These findings highlight the potential of DMD in analysing remote-sensing data for hydrologic applications.