An event-based, Bayesian approach for estimating floods in urban and natural catchments

Numerous methods have been previously developed for design flood estimation. Where sufficient runoff data are available, statistical methods for flood frequency analysis are often the preferred approach. In cases where such data are scarce, methods involving hydrological simulation are an attractive alternative. Simulation methods range in complexity from the very simple, formula-based, Rational Method to the simulation of runoff using complex hydrological models also with stochastic input. In the simple models, the return period of runoff often inherits the return period from the input, i.e. the precipitation intensity for a given return period. In this case, arbitrary assumptions are often made regarding initial conditions, e.g. soil moisture states. Here, we investigate the relationship between extreme precipitation, precipitation sequences, initial soil moisture states and peak discharge to estimate extreme floods using hydrological simulations. We use the parameters and simulation results of the DDD (Distance Distribution Dynamics) hydrological model to parameterise an event-based model (DDDEvent) which is run for a range of precipitation intensities, precipitation sequences, and initial soil moisture states. When running the event model, a value of a specific precipitation intensity is used and initial soil moisture state and precipitation sequence are stochastically drawn from a gamma distribution and a beta distribution, respectively. This procedure is repeated for a range of precipitation intensities. The (simulated) initial soil moisture states are, in many catchments, found to be correlated with precipitation so we use a (gamma) distribution of antecedent soil moisture states conditioned on precipitation. Results show, expectedly, that varying the soil moisture state and precipitation sequence can give a range of runoff responses to a given precipitation input. When we simulate runoff for a single precipitation intensity and vary the soil moisture states and precipitation sequence, we obtain a conditional distribution of runoff, given the precipitation intensity. Similarly, for a simulated runoff value we find a range of possible precipitation intensities, and we obtain a conditional distribution of precipitation given the runoff value. From such (empirical) conditional distributions we can use Bayes’ theorem to assess the exceedance probability for a fixed value of runoff given the exceedance probability of the precipitation event. Simulation results using synthetic data show that the proposed approach is justified when runoff and precipitation are highly correlated, which is typically the case for extreme precipitation events. The approach is validated against extreme value estimates of floods using flood frequency analysis on long time series from the Norwegian Water Resources and Energy Directorate. Preliminary results for estimating instantaneous floods are promising for catchments where floods are primarily generated by extreme rainfall and snowmelt plays a minor role. The proposed method also has potential for estimating floods in ungauged catchments if reliable extreme value estimates of precipitation exist using a regionalised version of the DDD model.