Nonparametric Bayesian flood frequency estimation

Abstract

A novel nonparametric Bayesian Monte-Carlo method is presented to estimate flood frequency. This method accommodates complex flood behaviors such as event clustering (repeated instances of similar magnitude floods) and can use varied data, such as gage and historical peak discharges, and paleohydrologic upper and lower bounds on peak discharge, while rigorously accounting for a wide variety of measurement uncertainties. In contrast to nonparametric kernel estimation approaches, the stochastic assumption is used to generate flood frequency models that span the data and provide about twice the number of degrees of freedom of the data. Each generated flood frequency model is scored using likelihoods that account for data measurement uncertainties. A parametric estimation approach ensures high precision because posterior sampling is known. However, parametric approaches can produce substantial biases because the classes of allowed flood frequency models are restricted. These biases are completely undetectable within a parametric paradigm. The nonparametric approach used here surrenders some precision in the pursuit of reduced bias and greater overall accuracy and assurance; it reveals the annual probabilities where discharge becomes unconstrained by the data, thereby eliminating unsubstantiated extrapolation. Parametric flood frequency estimation introduces strong extrapolation priors that make it difficult, if not impossible, to determine when flood frequency is not longer constrained by the data. Nonparametric and parametric flood frequency estimation using a demonstration data set shows that while parametric functions may sometimes provide reasonable fits to subsets of paleohydrologic data, parametric flood frequency estimates are likely to produce substantial biases over entire log cycles of annual exceedance probability, when using paleohydrologic data spanning thousands of years.