A structurally constrained expo-linear rainfall–runoff model: enforcing physical admissibility in event-based hydrology

The Soil Conservation Service curve number (SCS-CN) method remains useful for event runoff estimation, although it aggregates several processes into one parameter. The expo-linear rainfall-runoff model was proposed and separates the maximum incremental response, the activation level and its rate, but predicts positive direct runoff when event precipitation is zero. This article proposes a zero-origin correction that preserves the original logistic derivative while enforcing Q(0) = 0. The formulation was evaluated using small experimental catchments in south-central Chile (0.22–1.12 km2), CAMELS-CL basins, and then compared with SCS-CN and the original model. A sensitivity analysis considered nine parameter combinations of the Eckhardt baseflow filter. The corrected model produced nearly identical predictive performance to the original formulation across catchments and filter settings, while removing the non-zero runoff artefact. The correction is not intended to guarantee lower RMSE but provides a physically admissible expo-linear formulation for repeated event-based or spatial applications.