Analytical derivation of urban flood frequency models accounting saturation-excess runoff generation

Derived flood frequency models developed specifically for urban stormwater management purposes are referred to as analytical probabilistic stormwater models. These models use closed-form analytical equations to estimate flood frequencies under various land use conditions which facilitate quick analysis of different design alternatives. In this paper, in order to further improve the capability of the analytical probabilistic models, additional analytical expressions relating a catchment’s peak discharge rate to its physical characteristics and the local rainfall statistics are derived considering saturation-excess in addition to infiltration-excess runoff generation and various possible hydrograph shapes. These analytical expressions along with the frequency distributions of the input rainfall event volume and duration are used to develop a new derived flood frequency model suitable for catchments where saturation-excess runoff generation is possible. An example application of the new model to a test catchment in Hamilton, Ontario, Canada is illustrated to verify the accuracy of the new model. Assuming hypothetically that the same catchment is instead located at several other places in the United States, the reliability of the analytical probabilistic models under different climatic conditions is verified as well.