Confidence Intervals for Flood Return Level Estimates using a Bootstrap Approach

Standard flood return level estimation is based on extreme value analysis assuming independent extremes, i.e. fitting a model to excesses over a threshold or to annual maximum discharge. The assumption of independence might not be justifiable in many practical applications. The dependence of the daily run-off observations might in some cases be carried forward to the annual maximum discharge. Unfortunately, using the autocorrelation function, this effect is hard to detect in a short maxima series. One consequence of dependent annual maxima is an increasing uncertainty of the return level estimates, and is illustrated using a simulation study. The confidence intervals obtained from the asymptotic distribution of the Maximum-Likelihood estimator (MLE) for the generalized extreme value distribution (GEV) turned out to be too small to capture the resulting variability. In order to obtain more reliable confidence intervals, we compare four bootstrap strategies, out of which one yields promising results. The performance of this semi-parametric bootstrap strategy is studied in more detail. We exemplify this approach with a case study: a confidence limit for a 100-year return level estimate from a run-off series in southern Germany was calculated and compared to the result obtained using the asymptotic distribution of the MLE.