cGRHyMoLAP: A compact continuous state-space formulation of GRHyMoLAP for rainfall–runoff modelling

Abstract. Despite the rapid advances and strong rainfall–runoff predictive performance of AI models, process-based models remain essential because of their interpretability and their role as structural backbones of hybrid hydrological–AI frameworks. Recently, GRHyMoLAP was developed as an ODE framework that explicitly links GR4J-based runoff generation and power law recession dynamics. However, within this framework, it remains unclear whether the full model dynamics can be consistently represented within a continuous dynamical system while preserving interpretability, parsimony, and predictive skill. To address this, we introduce cGRHyMoLAP, a fully continuous state-space formulation defined as a compact two-state system governing storage (S) and runoff (Q) using only two coupled ODEs. This compact formulation enables direct implementation of the model without intermediate computational steps. Evaluation over 623 CAMELS-GB catchments shows that cGRHyMoLAP maintains consistency of internal states, demonstrating that the original hydrological behaviour is preserved within the continuous framework. cGRHyMoLAP improves the representation of the timing of the runoff-generation process. Furthermore, it remains robust under short calibration periods and achieves the lowest computational cost among the evaluated models despite relying on sub-time stepping. Convergence analysis indicates that numerical convergence and predictive performance are not necessarily aligned in the present formulation. Although finer time steps result in solutions that are less sensitive to further refinement, they generally yield lower predictive performance. Sensitivity results show that simulation accuracy depends strongly on the temporal representation of model inputs. Explainable ML analysis combining the Random Forest model and SHAP further shows that higher cGRHyMoLAP performance is associated with less pronounced precipitation seasonality, limited snow influence, steeper flow-duration curves, and larger catchment areas, whereas frequent high-flow events are associated with lower performance.