WIT Press

Construction Of Confidence Intervals For Extreme Rainfall Quantiles


Free (open access)





Page Range

293 - 304




455 kb

Paper DOI



WIT Press


A. T. Silva, M. M. Portela, J. Baez & M. Naghettini


In hydrological practice, the design values of extreme rainfalls are generally estimated by means of frequency analysis applied to a finite sample of extreme rainfall values. The most usual approach taken in such analysis is to fit a statistical distribution to an annual maximum series (AMS) built upon one value per year. As an alternative approach, the peaks-over-threshold (POT) technique considers all the peak values above a given threshold and thusly allows for a more rational selection of events to include in the frequency analysis. The research presented in this paper reviews the relative merits of the two aforementioned approaches by analyzing the confidence intervals of extreme rainfall quantiles that result from their application. Despite the usually larger extreme value sample sizes made possible by the POT technique, the estimation of design values by such approach requires the analysis of both the magnitude and the times of arrival of extreme rainfall events. Hence the uncertainty associated with the estimated quantiles results from the combination of the two models applied to ascertain the magnitude and the frequency. Using daily rainfall data samples from Portugal and from Paraguay, four statistical models are applied (two AMS models and two POT models) and a comparison of the estimated quantiles is made. Furthermore, quantile confidence intervals were constructed using both asymptotic theory and the Monte Carlo simulation technique. Such intervals assume an important role in hydrological risk analyses, as they enable the assessment of the uncertainties associated with estimating distribution parameters and quantiles from finite samples of extreme rainfalls. The research was carried out in the scope of the European joint project CapWEM – Capacity development in Water Engineering and Environmental Management


quantile confidence intervals, peaks-over-threshold, Monte Carlo simulation