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.

翻译：统计模型是建模、预测和理解流域水文过程的重要工具。特别是，与降雨发生和后续径流变化之间的时间滞后建模具有很高的实际重要性。由于水可通过多种流动路径产生径流，来自不同流动路径的一系列不同脉冲可能组合形成观测到的径流时间序列。当前最先进的模型无法通过可解释的参数化充分应对问题复杂性，从而难以洞察不同流动路径的动态以进行水文推断。本文提出的高斯滑动窗口回归模型通过将沿时间轴滑动的多个窗口概念与多元线性回归相结合来解决该问题。窗口核函数（指示应用于不同时间滞后的权重）通过高斯形状核函数实现。因此，每个窗口可表示一条流动路径，从而为直接的过程推断提供可能。在模拟和真实场景中的实验表明，该模型能够实现准确的参数估计和具有竞争力的预测性能，同时促进可解释和可理解的水文建模。