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Although rainfall is assumed spatially uniform in conventional hydrological modelling for rainfall-runoff simulations, moving storms have been shown to have substantial influence on flow hydrographs. In this study, criteria for attainment of the equilibrium discharge from watersheds subjected to moving storms were examined. Non-linear numerical kinematic-wave models were developed to simulate runoff from an overland plane and from a V-shaped catchment. Dimensional analysis was applied to obtain the independent variables to be used as control factors in performing a series of numerical tests. The results indicate that, for storms moving downstream, runoff can attain equilibrium discharge even though the storm length is shorter than the watershed length and the rainfall duration is less than the time to equilibrium of the watershed for stationary uniform storms. The phenomenon of attainment of equilibrium discharge from watersheds subjected to moving storms is contradictory to conventional hydrologic design, which assumes the storm duration must equal the time to equilibrium to attain the maximum discharge.

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The inherent nonlinear characteristics of the watershed runoff process related to storm magnitude and watershed size are discussed in detail in this study. The first type of nonlinearity is referred to rainfallrunoff dynamic process and the second type is with respect to a Power-law relation between peak discharge and upstream drainage area. The dynamic nonlinearity induced by storm magnitude was first demonstrated by inspecting rainfall-runoff records at three watersheds in Taiwan. Then the derivation of the watershed unit hydrograph (UH) using two linear hydrological models shows that the peak discharge and time to peak discharge that characterize the shape of UH vary event-to-event. Hence, the intention of deriving a unique and universal UH for all rainfall-runoff simulation cases is questionable. In contrast, the UHs by the other two adopted nonlinear hydrological models were responsive to rainfall intensity without relying on linear proportion principle, and are excellent in presenting dynamic nonlinearity. Based on the two-segment regression, the scaling nonlinearity between peak discharge and drainage area was investigated by analyzing the variation of Power-law exponent. The results demonstrate that the scaling nonlinearity is particularly significant for a watershed having larger area and subjecting to a small-size of storm. For three study watersheds, a large tributary that contributes relatively great drainage area or inflow is found to cause a transition break in scaling relationship and convert the scaling relationship from linearity to nonlinearity.Keywords. Rainfall-runoff process; scaling effect; runoff nonlinearity; kinematic-wave-based geomorphologic instantaneous unit hydrograph; storm magnitude; watershed size.

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