Hydrologically constrained genetic programming for interpretable rainfall–runoff model discovery

Abstract

Advances in machine learning have improved rainfall–runoff prediction, but integrating these capabilities with interpretable, process-based model structures remains an open challenge. This study seeks a middle ground between conceptual hydrological modelling and modern data-driven prediction by automating model structure discovery while retaining interpretability and hydrological consistency. We introduce HydroXGP (Hydrological Model eXplorer using Genetic Programming) to reduce reliance on legacy model choices and subjective a priori structural assumptions by learning model structure directly from data during optimization. The framework evolves models from a modular, process-based component library adapted from the open-source MARRMoT toolbox, making the search process-informed through reusable flux and routing components and hydrologically constrained by enforcing mass balance during simulation. GP jointly optimizes model structure and parameters, while each discovered model remains explicit and interpretable. Evaluation on the CAMELS-US dataset showed that a proof-of-concept test in a snow-dominated basin achieved strong performance over the out-of-sample test period (NSE=0.849), and, when transferred to a hydrologically similar basin, the learned structure retained useful predictive skill (NSE=0.724). Across 18 basins (one representative basin per U.S. hydrologic region), median NSE reached 0.702, generally outperforming the mean performance of an ensemble of conceptual benchmark models while remaining competitive with some regional LSTM baselines. The findings support a modelling perspective in which structural hypotheses can be revisited and adapted as new data, diagnostics, or environmental signals become available, enabling basin-specific configurations that evolve in response to changing information rather than relying on a single fixed template.