Influence of storm magnitude and watershed size on runoff nonlinearity

Abstract

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 rainfall-runoff 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.