A Gaussian Sliding Windows Regression Model for Hydrological Inference

Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the modeling of time lags associated with the time between rainfall occurrence and subsequent changes in streamflow, is of high practical importance. Since water can take a variety of flowpaths to generate streamflow, a series of distinct runoff pulses from different flowpath may combine to create the observed streamflow time series. Current state-of-the-art models are not able to sufficiently confront the problem complexity with interpretable parametrization, which would allow insights into the dynamics of the distinct flow paths for hydrological inference. The proposed Gaussian Sliding Windows Regression Model targets this problem by combining the concept of multiple windows sliding along the time axis with multiple linear regression. The window kernels, which indicate the weights applied to different time lags, are implemented via Gaussian-shaped kernels. As a result, each window can represent one flowpath and, thus, offers the potential for straightforward process inference. Experiments on simulated and real-world scenarios underline that the proposed model achieves accurate parameter estimates and competitive predictive performance, while fostering explainable and interpretable hydrological modeling.