Flood frequency analysis: Confidence interval estimation by test inversion bootstrapping

Abstract

A common approach to estimate extreme flood events is the annual block maxima approach, where for each year the peak streamflow is determined and a distribution (usually the generalized extreme value distribution (GEV)) is fitted to this series of maxima. Eventually this distribution is used to estimate the return level for a defined return period. However, due to the finite sample size, the estimated return levels are associated with a range of uncertainity, usually expressed via confidence intervals. Previous publications have shown that existing bootstrapping methods for estimating the confidence intervals of the GEV yield too narrow estimates of these uncertainty ranges. Therefore, we present in this article a novel approach based on the less known test inversion bootstrapping, which we adapted especially for complex quantities like the return level. The reliability of this approach is studied and its performance is compared to other bootstrapping methods as well as the Profile Likelihood technique. It is shown that the new approach improves significantly the coverage of confidence intervals compared to other bootstrapping methods and for small sample sizes should even be favoured over the Profile Likelihood.