Data-driven estimation of the hydrologic response using generalized additive models

Abstract. Estimating the hydrologic response of watersheds to precipitation events is key to understanding streamflow generation processes. Impulse Response Functions, commonly referred to as the Instantaneous Unit Hydrograph (IUH) in hydrology, have been used for over 50 years to predict stormflow and compare catchment behaviors. These response functions are often strongly affected by modelers' choices of parameters and data preprocessing procedures, limiting their diagnostic utility and generalizability across different sites and time periods. With the increasing availability of compiled rainfall-runoff series, there is now a growing opportunity to develop new approaches that fully exploit such datasets. This paper introduces GAMCR, a novel data-driven approach that employs Generalized Additive Models (GAM) to estimate time-dependent Catchment Responses (CR). GAMCR is designed to capture the complex, nonlinear relationships between precipitation and runoff, offering a flexible and interpretable framework for the systematic analysis of hydrological responses. The model is successfully validated on synthetic data, where the true response functions are known. Additionally, we demonstrate the model's potential using observed data from six Swiss basins with distinct hydrological behaviors. Results are fully consistent with those obtained from ERRA, another recent data-driven approach with a very different architecture, as well as with the climate and physical properties of the sites. Overall, GAMCR is a modern and effective tool for leveraging rainfall-runoff datasets to investigate the controls on hydrologic responses in small to midsize basins under conditions similar to those studied here, and it provides a framework that can be further explored in other climatic and physiographic settings in future research.