A Gaussian Sliding Windows Regression Model for Hydrological Inference

TL;DR

This paper introduces a Gaussian Sliding Windows Regression Model that improves hydrological inference by providing interpretable parameters for understanding flow paths and delays in streamflow response to rainfall.

Contribution

It presents a novel regression model combining multiple Gaussian-shaped sliding windows with linear regression to better capture complex hydrological processes.

Findings

Accurately estimates parameters in simulated scenarios

Achieves competitive predictive performance on real data

Enhances interpretability of hydrological flow paths

Abstract

Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes in streamflow is of high practical importance. Since water can take a variety of flow paths to generate streamflow, a series of distinct runoff pulses 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, thus preventing novel insights about the dynamics of distinct flow paths from being formed. 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, straightforward process inference can be achieved since each window can represent one flow path. 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.