Flood estimation in natural and urban catchments using hydrological simulation and Bayes theorem

Abstract. There are many methods developed for the estimation of design flood values. If sufficient runoff data are available, statistical methods for flood frequency analysis (FFA) can be applied. In cases where runoff data are scarce, methods involving hydrological simulation are often used. These methods range in complexity from the very simple, formula-based Rational Method to the simulation of runoff using very detailed, complex hydrological models. Often, when using these models, the return period of runoff inherits the return period from the input, i.e. the precipitation, and significant assumptions are necessarily made regarding initial soil moisture states (S). This study investigates the relationship between extreme precipitation, the precipitation sequence, the initial S and extreme flows and provides a method for estimating floods by combining a continuous rainfall-runoff model (DDD) and a stochastic event model (DDDEvent). The models share the same model parameters, and the continuous model provides the required distributions of the initial S for the event model. When running the event model for a specific precipitation intensity, the initial S and precipitation sequence are stochastically sampled, generating a range of runoff responses to a given rainfall intensity. When we simulate runoff for a single precipitation intensity and vary the initialS and precipitation sequences, we obtain a conditional distribution of runoff, given the precipitation intensity. Similarly, when we simulate runoff for all possible (realistic) precipitation intensities, we obtain a conditional distribution of precipitation given a runoff value. From such (empirical) conditional distributions we can use Bayes theorem to assess the exceedance probability for a specific value of runoff given the exceedance probability of the precipitation event. Results for estimating peak flows are promising for catchments with areas ranging from 0.06 to 1092 km² where high flows are generated primarily by rainfall. The estimates are comparable to those obtained using the well-established SCHADEX method for design floods. In contrast to purely statistical FFA based on observed discharge, we can, with the proposed method, perform an analysis of flood quantiles as a function of initial S, precipitation intensities and sequences. We can also investigate the composition of the total runoff with respect to water originating from the precipitation event and water originating from the initial S for extreme flood quantiles in a given catchment. The proposed method can also be applied for estimating floods in ungauged catchments using a regionalised version of the DDD model.