The Methodology of Bayesian Inference and Decision Making Applied to Extreme Hydrologic Events

Abstract

This study presents the methodology of Bayesian inference and decision making applied to extreme hydrologic events. Inference procedures must consider both the natural or 'modelled' uncertainty of the hydrologic process and the statistical uncertainty due to a lack of information. Two types of statistical uncertainty were considered in this study. The first type is the uncertainty in modelling the hydrologic process, and the second type is the uncertainty in the values of the model parameters. The uncertainty is reduced by considering prior sources of information (regional regression, theoretical flood frequency analysis or subjective assessment) and historical flood data. A 'Bayesian distribution' of flood discharges is developed that fully accounts for parameter uncertainty. In an analogous manner, model uncertainty is analyzed, which leads to a 'composite Bayesian distribution'. The uncertainty in flood frequency curves from rainfall-runoff models is also analyzed, due to the uncertainty in the parameters of the models. The Bayesian inference model is then applied to a Bayesian decision model, where the decision rule is the maximization of expected net monetary benefits. A case study of determining the optimal size of local flood protection for Woonsocket, Rhode Island, was considered, using realistic flood damage and cost functions. The results indicate that Bayesian inference procedures can be used to fully account for statistical uncertainty and that Bayesian decision procedures provide a rational approach for making decisions under uncertainty.