Physics-informed hybrid GR4J–XGBoost model for streamflow prediction: integrating conceptual states, SHAP interpretability, and uncertainty analysis

Accurate streamflow prediction remains challenging due to the nonlinear and dynamic nature of rainfall-runoff processes. Conceptual hydrological models provide physically interpretable representations, yet their predictive performance is often limited, while data-driven models may suffer from overfitting and a lack of interpretability. To address these limitations, this study proposes a physics-informed hybrid modeling framework that integrates the GR4J conceptual model with the XGBoost machine learning algorithm. Unlike conventional hybrid approaches, the proposed method incorporates GR4J-derived state and flux variables (including simulated discharge, storage state, effective rainfall, evapotranspiration, percolation, and exchange fluxes) as input features, enabling a process-based representation of catchment dynamics within the machine learning framework. The proposed framework was evaluated using a catchment selected from the CAMELS-DE (Catchment Attributes and Meteorology for Large-sample Studies-Germany) dataset. Model performance was assessed using multiple lag configurations (7, 14, and 30 days) across training, validation, and independent test datasets. The results demonstrate that the hybrid GR4J-XGBoost model generally outperforms the standalone GR4J and XGBoost models, particularly in terms of generalization capability and predictive stability. While the standalone XGBoost model benefits from longer lag structures, the hybrid model achieves comparable or superior predictive performance with shorter lag inputs, indicating reduced dependence on extended temporal memory while providing physically meaningful conceptual information for model interpretation. SHAP analysis reveals that physically meaningful variables, especially GR4J-derived state and flux components, play a dominant role in governing model predictions. Furthermore, residual-based uncertainty assessment shows that the hybrid model produces lower prediction bias, reduced residual dispersion, and narrower residual uncertainty bounds than the standalone approaches, indicating improved prediction reliability. Overall, the proposed framework provides a physics-informed, process-based, and interpretable approach for rainfall-runoff modeling while offering an additional assessment of prediction reliability through residual-based uncertainty evaluation.