A Gaussian sliding windows regression model for hydrological inference
提出高斯滑动窗口回归模型，通过多个高斯形状窗口沿时间轴滑动并结合多元线性回归，来推断降雨与径流之间的时间滞后关系，每个窗口代表一条流动路径，在模拟和真实数据上参数估计准确且预测性能好。
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 modelling.