On the derived flood frequency distribution: analytical formulation and the influence of antecedent soil moisture condition

Abstract In this paper we present an analytical formulation of the derived distribution of peak flood and maximum annual peak flood, starting from a simplified description of rainfall and surface runoff processes, and we show how such a distribution is useful in practical applications. The assumptions on rainfall dynamics include the hypotheses that the maximum storm depth has a Generalized Pareto distribution, and that the temporal variability of rainfall depth in a storm can be described via power–law relationships. The SCS-CN model is used to describe the soil response, and a lumped model is adopted to transform the rainfall excess into peak flood; in particular, we analyse the influence of antecedent soil moisture condition on the flood frequency distribution. We then calculate the analytical expressions of the derived distributions of peak flood and maximum annual peak flood. Finally, practical case studies are presented and discussed.

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