Critical transition of peak discharge in small mountainous basins

In mountainous small watersheds, intense rainfall and other hydrological disturbances commonly induce a reduction in runoff response lag and a sharp, nonlinear increase in peak flow. Focusing on a representative small watershed in the Wenchuan earthquake-affected region, this study integrates high-temporal-resolution field measurements of rainfall and runoff with the Soil Conservation Service (SCS) hydrological model. Multiple scenario simulations integrating rainfall patterns (e.g., duration, intensity, etc.) and key model parameters were conducted. Therefore, we quantitatively identify the critical conditions governing peak flow mutation and elucidate the nonlinear behavior of runoff generation. Results show that the critical rainfall depth triggering peak flow mutation (P_t) decreases as a power function of the CN value (P_t =50712·CN ^-1.65); conversely, the critical CN value decreases with total rainfall (P) according to CN_t = 228.88·P ^-0.36. Once either threshold is exceeded, peak flow transitions into a linear response regime, exhibiting statistically significant positive correlations with both P and CN. Under constant total rainfall, the rainfall pattern exerts a pronounced control on both runoff yield and abrupt thresholds: earlier rainfall peaks correspond to higher CN values and the lowest post-mutation peak flow growth rates. In contrast, when total rainfall, rainfall pattern, and CN are held constant, variations in watershed area produce negligible shifts in the peak flow abrupt point, confirming that area is not a dominant control on runoff mutation. This work establishes a physically interpretable, multi-variable framework for nonlinear runoff response and provides a theoretical basis for disaster prevention and mitigation work such as flash flood early warning.