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：统计模型是模拟、预测和理解流域水文过程的重要工具。特别是，与降雨发生至随后流量变化之间的时间滞后相关的建模具有很高的实际重要性。由于水可通过多种流路产生径流，来自不同流路的一系列离散径流脉冲可能共同形成观测到的流量时间序列。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，而这种参数化可以揭示不同流路的动态特性，从而支持水文推断。本文提出的高斯滑动窗回归模型通过将沿时间轴滑动的多窗口概念与多元线性回归相结合来解决这一问题。窗口核（表示应用于不同时间滞后的权重）采用高斯形状核实现。因此，每个窗口可代表一条流路，从而为直接的过程推断提供了可能性。在模拟和真实场景上的实验表明，所提出的模型能够获得准确的参数估计和具有竞争力的预测性能，同时促进了可解释和可理解的水文建模。