Short-term forecasting from GRACE data via dynamic mode decomposition with sequential update

Dynamical systems theory is often used for short-term forecasting of hydrologic processes, because it preserves physical interpretability while remaining computationally efficient. One of its tools, dynamic mode decomposition (DMD), provides a modal representation of high-dimensional systems capable of capturing dominant spatiotemporal dynamics in observed data. We investigate the ability of xDMD, a DMD variant that allows for inhomogeneous dynamics, to predict short-term anomalies in basin-averaged total water storage across 15 major river basins worldwide. We compare global and basin-scale training strategies and evaluate the impact of sequential retraining frequency. Our results demonstrate that globally trained models with sequential updating on average outperform basin-scale approaches, indicating that spatial coherence provides a more stable and representative modal basis for temporal extrapolation. Periodic retraining is essential to accommodate gradual evolution of the temporal coefficients and to maintain the robust forecast capacity for update intervals of up to six months. Extension of the retraining interval to annual updates degrades the performance, suggesting the emergence of non-autonomous behavior in some systems and linking the prediction horizon of the xDMD-based forecast to the drift time scale of the temporal coefficients of each basin. A benchmark against recurrent LSTM-GRU networks confirms markedly smaller systematic biases at a fraction of the computational cost. A sliding-window spectral diagnostic confirms that the non-autonomous behavior is almost entirely confined to the temporal coefficients of a nearly time-invariant spatial basis, and provides a transferable, a-priori criterion for selecting the model-updating strategy for generic spatiotemporal signals.