How extreme is extreme? An assessment of daily rainfall distribution tails

S.M. Papalexiou, D. Koutsoyiannis, and C. Makropoulos, How extreme is extreme? An assessment of daily rainfall distribution tails, Hydrology and Earth System Sciences, 17, 851–862, doi:10.5194/hess-17-851-2013, 2013.



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 in two families: heavy-tailed and light-tailed distributions, with the latter generating more “mild” and infrequent extremes compared to the former. This emphasizes how important for hydrological design is to assess correctly the tail behaviour. Traditionally, the wet-day daily rainfall has been described by light-tailed distributions like the Gamma, although heavier-tailed distributions have also been proposed and used, e.g. the Lognormal, the Pareto, the Kappa, and others. Here, we investigate the issue of tails for daily rainfall by comparing the up- per 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 to 163 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, with clear implications on extreme event modelling and engineering design.

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The initial version of the article and the discussion in Hydrology and Earth System Sciences Discussions (9, 5757–5778, 2012) can be seen at

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Our works that reference this work:

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Works that cite this document: View on Google Scholar or ResearchGate

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Tagged under: Extremes