Dynamic Mode Decomposition enables decoding dominant spatiotemporal structures in global scale hydrological datasets

As climate change and human activities impact water availability worldwide, a better understanding of large-scale hydrologic phenomena is crucial to identify and design appropriate strategies for adaptation and mitigation. While decoding the interactions and evolution of the climate, human activities, and the water cycle can ease the assessment and forecasting of water resource availability, the complexity, and the computational demand limit the feasibility of these analyses on a global scale. Data-driven techniques are often used to gain physical insights in global hydrological phenomena and build efficient and computationally efficient models for future state prediction. One such technique, dynamic mode decomposition (DMD), enables one to capture the hidden information embedded in large hydrological datasets. This data-driven and equation-free technique is suitable for identifying spatiotemporal features of both observational and simulated data. DMD performs a low-dimensional spectral decomposition of the data to obtain a reduced-order model of the system behavior directly from temporal snapshots. DMD provides low-cost reconstructions and predictions of the observed variable, and its structure contains information about the temporal and spatial patterns of the system evolution. It provides a set of spatial modes whose contribution evolves in time according to a specific time dynamic which defines the frequency, the growth rate, and a related amplitude. Trend and seasonal variations are identified, and a physically meaningful interpretation are sought for the most important modes. We test the ability of a suite of different DMD algorithms to model and interpret the 20-year-long series of monthly total water storage anomalies provided by the Gravity Recovery and Climate Experiment (GRACE) satellite missions. The scope is twofold: learn directly from satellite observations and build efficient DMD-based models to ease forecasts and reconstructions, and at the same time, unveil the systems leading order behavior and derive insights on Earths water cycle evolution.