Deep Learning as a Nexus Optimizer: Extracting Hydrological Response functions for Rainfall-Runoff Simulation

Understanding how rainfall is transformed into streamflow is a cornerstone of hydrological science. Despite decades of progress, it remains uncertain whether physical or semi-empirical process equations formulated at the field scale can be transferred to the catchment scale without loss of realism. We assumed that this scale-mismatch is a key reason why conventional conceptual/process-based models often fail to achieve simulation accuracy comparable to purely data-driven deep learning models. Motivated by ensemble rainfall–runoff analysis (ERRA), which suggests that streamflow can be expressed as a convolution between precipitation and a nonlinear catchment response function, we develop an LSTM-based framework to learn catchment-scale response functions for each hydrological process directly from data while retaining physically consistent structure.

The proposed framework couples a generic bucket model architecture with an LSTM that acts as a nexus optimizer. Physical consistency is enforced through residual-style loss regulation, embedding mass-conservation constraints within the training objective. Within this setting, key processes, including canopy interception, infiltration, evapotranspiration, river routing, and groundwater recharge, emerge as extractable functions of meteorological forcing sequences rather than being prescribed a priori. We founded that the learned catchment-scale response functions exhibit pronounced nonlinearity and memory effects. Our results further indicate that catchment-scale process representations effectively mix field-scale empirical relationships with precipitation spatiotemporal heterogeneity, and that the deformation from field to catchment scale response function is strongly driven by the spatial heterogeneity of precipitation intensity. By restructuring the learning pathway to reduce recurrent dependencies, the framework supports efficient parallel training while maintaining physical consistency. The approach aims to simultaneously simulate streamflow and induce catchment scale response functions, offering a pathway to diagnose why conventional models fail and to advance process discovery via data-driven induction.