Bayesian Approach for Estimating the Distribution of Annual Maximum Floods with a Mixture Model

Abstract

Annual flood peaks frequently stem from distinct flood-producing mechanisms. However, most inference procedures rely on a single distributional model, which can lead to ill-posed inferences of its upper-tail behavior. For addressing this problem, this paper explores a Bayesian mixture model, which combines the Gamma and generalized Pareto distributions under the concept of penalized complexity prior distribution (PCPD) for the tail index, for modeling annual flood peaks. The proposed approach was applied in two catchments in the western US, in which empirical evidence of mixed population exists and historical and paleoflood information is available for validation purposes. The results suggested that despite the increased complexity of the mixture model, describing flood events with distinct distributions was beneficial for the goodness of fit and for extrapolating to large return periods. In addition, the PCPD proved effective in constraining the tail index inference because narrower credible intervals compared with well-established models were obtained for most flood quantiles. Overall, the proposed approach seems feasible for reconciling distinct flood-generating mechanisms and reliability in statistical estimation in flood frequency analysis.