A Differentiable Spatially Varying Ensemble Modelling Framework for Runoff Model Heterogeneity

Conceptual rainfall–runoff models usually apply a single runoff generation structure to an entire catchment, although contrasts in soil, terrain, climate, and vegetation can produce different runoff responses within it. We developed a differentiable spatially varying ensemble (Spatial ENS) that combines GR4J, a vertically mixed runoff model (VMM), and HBV, and applied it to the Jiagenba catchment in the Yalong River Basin, southwestern China. A neural gating network maps gridded climate and land surface attributes to model weights for each cell, and the weighted runoff is routed through a shared Muskingum river network. Under leave-one-year-out cross-validation for 2017–2022, Spatial ENS achieved a flood season (June–October) Nash–Sutcliffe efficiency (NSE) of 0.78, compared with 0.77, 0.70, and 0.74 for GR4J, VMM, and HBV, respectively, and the highest Kling–Gupta efficiency (0.80). Its mean annual NSE gains were 0.02, 0.09, and 0.05. The learned weights varied systematically in space, and permutation diagnostics identified clay fraction, terrain slope, and potential evapotranspiration as the dominant inputs to the gating network. These results indicate that outlet discharge can constrain spatially structured model weights and that the resulting ensemble improves flood season simulation in this catchment.