Confidence intervals for return levels for the peaks-over-threshold approach

Abstract

The peaks-over-threshold (POT) approach is an important alternative to the annual block maxima (ABM) method in flood frequency analysis. POT requires the mathematical description of both, the number of exceedances over the threshold as well as the values of those exceedances. Regardless the method, estimates of extreme flood events are typically associated with a large range of uncertainty, which is usually showcased by appropriate confidence intervals (CIs). However, existing methods to estimate CIs for return levels for the POT approach have mostly neglected its dual-domain character and focused on the distribution of the magnitudes only. We present here a customization of two methods, the Profile Likelihood (PL) and test inversion bootstrap (TIB), which account for the dual-domain structure of POT. Both, PL and TIB, are in the framework of ABM already successfully employed for estimating CIs of extreme flood events. A comparison of the performance of the estimated CIs (in terms of coverage error) of the PL, TIB, and percentile bootstrap is done. As result, it is seen that both the lower and upper boundary of the CIs are strongly underestimated for the percentile bootstrap approach. A similar effect (although in a much less pronounced way) can be observed for PL. The performance of the TIB is usually superior to the percentile bootstrap and PL and yielded reasonable estimates for the CIs for large return periods.