Abstract
Abstract. The upper part of a probability distribution, usually known as the tail, governs both the magnitude and the frequency of extreme events. The tail behaviour of all probability distributions may be, loosely speaking, categorized into two families: heavy-tailed and light-tailed distributions, with the latter generating "milder" and less frequent extremes compared to the former. This emphasizes how important for hydrological design it is to assess the tail behaviour correctly. Traditionally, the wet-day daily rainfall has been described by light-tailed distributions like the Gamma distribution, although heavier-tailed distributions have also been proposed and used, e.g., the Lognormal, the Pareto, the Kappa, and other distributions. Here we investigate the distribution tails for daily rainfall by comparing the upper part of empirical distributions of thousands of records with four common theoretical tails: those of the Pareto, Lognormal, Weibull and Gamma distributions. Specifically, we use 15 029 daily rainfall records from around the world with record lengths from 50 to 172 yr. The analysis shows that heavier-tailed distributions are in better agreement with the observed rainfall extremes than the more often used lighter tailed distributions. This result has clear implications on extreme event modelling and engineering design.
Highlights
Heavy rainfall may induce serious infrastructure failures and may even result in loss of human lives
What can be considered “extreme” rainfall? Behind any discussion on the subjective nature of such pronouncements, there lies the fundamental issue of infrastructure design, and the crucial question of the threshold beyond which events need not be taken into account as they are considered too rare for practical purposes
Rainfall records from 15 029 stations are used to investigate the performance of four common tails that correspond to the Pareto, the Weibull, the Lognormal and the Gamma distributions
Summary
Heavy rainfall may induce serious infrastructure failures and may even result in loss of human lives. Behind any discussion on the subjective nature of such pronouncements, there lies the fundamental issue of infrastructure design, and the crucial question of the threshold beyond which events need not be taken into account as they are considered too rare for practical purposes. This question is all the more pertinent in view of the EU Flooding Directive’s requirement to consider “extreme (flood) event scenarios” (European Commission, 2007). We treat rainfall in a probabilistic manner, i.e., we consider rainfall as a random variable (RV) governed by a distribution law. Which distribution law we should choose is still a matter of debate
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