Multifractal properties of the peak flow distribution on stochastic drainage networks

Abstract

In this paper, we examined the peak flow distribution on a realization of networks obtained with stochastic network models. Three network models including the uniform model, the Scheidegger model, and the Gibbsian model were utilized to generate networks. The network efficiency in terms of drainage time is highest on the Scheidegger model, whereas it is lowest on the uniform model. The Gibbsian model covers both depending on the parameter value of β. The magnitude of the peak flow at the outlet itself is higher on the Scheidegger model compared to the uniform model. However, the results indicate that the maximum peak flows can be observed not just at the outlet but also other parts of the mainstream. The results show that the peak flow distribution on each stochastic model has a common multifractal spectrum. The minimum value of α, which is obtained in the limit of a sufficiently large q, is equal to the fractal dimension of a single river. The multifractal properties clearly show the difference among three stochastic network models and how they are related. Moreover, the results imply that the multifractal properties can be utilized to estimate the value of β for a given drainage network.