Runoff Simulation and Analysis in the Upper Yellow River Basin Using a Budyko–XGBoost Coupled Model

The Upper Yellow River (UYR) basin is the predominant runoff-yielding area of the entire watershed. Accurately simulating annual runoff is crucial for water resources management. While the Budyko framework effectively captures long-term hydro-thermal equilibrium, it struggles to represent nonlinear dynamics, flow channel routing, and spatial interconnections. Here, we propose a hybrid physics- and data-driven approach by coupling the Budyko framework (Fu’s equation) with an eXtreme Gradient Boosting (XGBoost) model, integrating upstream channel routing and antecedent storage-lag features using long-term hydrologic observations for nonlinear runoff simulation and driver attribution. To resolve the feature multicollinearity on machine learning attributions, input variables were consolidated into three groups: precipitation driven, evaporation limitation, and flow storage lag. The results demonstrate that the Budyko–XGBoost coupled model enhances annual runoff prediction accuracy compared to the standalone Fu equation and pure XGBoost, raising the coefficient of determination (R2) to 0.63–0.86 (mean R2 = 0.75) and capturing both nonlinear dynamics and turning points, alongside reductions of 6.2% in the mean RMSE (18.77 mm) and 11.0% in the MAE (13.66 mm) compared to the pure XGBoost model (mean R2 = 0.70, RMSE = 20.01 mm, and MAE = 15.35 mm). Group-level SHAP attributions reveal that flow storage-lag drivers (Rlag and Rlag′) exert a primary control on runoff evolution across all the stations. Spatially, secondary drivers exhibit heterogeneity: in relatively humid, energy-limited regions (Maqu), high precipitation promotes positive runoff deviations, whereas in arid/semi-arid, water-limited reaches (e.g., Guide, Xunhua, Xiaochuan, and Lanzhou stations), high precipitation is absorbed by severe soil moisture deficits and reservoir interception, exerting a negative effect on runoff deviation.