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

By Simon Michael Papalexiou, Demetris Koutsoyiannis, Christos K. Makropoulos. 2012

229 citations recorded by the source corpus.

The upper part of a probability distribution, usu- ally known as the tail, governs both the magnitude and the frequency of extreme events. The tail behaviour of all prob- ability 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, al- though 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 the- oretical tails: those of the Pareto, Lognormal, Weibull and Gamma distributions. Specifically, we use 15 029 daily rain- fall records from around the world with record lengths from 50 to 172 yr. The analysis shows that heavier-tailed distribu- tions are in better agreement with the observed rainfall ex- tremes than the more often used lighter tailed distributions. This result has clear implications on extreme event modelling and engineering design.

Subfields: Finance, Global and Planetary Change, Soil Science

View Paper: https://www.semanticscholar.org/paper/bc82a3746484783bbbe04b9df7b7a01043541ae6

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Citations in the corpus

Stochastic generation of multi-site daily precipitation focusing on extreme events (2018, background): “However, as shown by many recent studies on a very large number of daily precipitation series (Papalexiou et al., 2013; Serinaldi and Kilsby, 2014a; Cavanaugh et al., 2015), exponentially decaying tails often result in a severe underestimation of extreme event probabilities.”
Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity (2020, background): “…as the Gamma and the Exponential have thin tails and cannot model adequately extremes of heavy‐tailed variables; for example, global analyses show that nonzero daily precipitation has, in general, heavier tails than the exponential (see, e.g., Papalexiou et al., 2013; Serinaldi & Kilsby, 2014).”
Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrology (2013, methodology): “…laws, what those laws are, and whether they have some degree of universality (Nykanen and Harris, 2003; Veneziano et al., 2006; Molnar and Burlando, 2008; Molini et al., 2009; Serinaldi, 2010; Verrier et al., 2010, 2011; Gires et al., 2012; Veneziano and Lepore, 2012; Papalexiou et al., 2013).”
Battle of extreme value distributions: A global survey on extreme daily rainfall (2013, result): “Noteworthy, a recent study [Papalexiou et al., 2012], where more than 15,000 daily records were analyzed focusing on the tail behavior of the parent distribution, revealed that the daily rainfall tail is better described by heavy tails.”
A global survey on the seasonal variation of the marginal distribution of daily precipitation (2016, background): “Actually, two recent studies [20,21], where 74 daily precipitation extremes were analyzed in more than 15,000 stations worldwide, revealed that 75”
Irreversibility and complex network behavior of stream flow fluctuations (2016, methodology): “5)) is also considered a heavy-tailed distribution (it belongs to the subexponential family) and can approximate power 26 law distributions for a large portion of the body of the distribution [46,42].”
Scaled distribution mapping: a bias correction method that preserves raw climate model projected changes (2016, background): “However, the gamma distribution will likely not be suitable for all studies involving precipitation, especially with respect to extremes (Papalexiou et al., 2013).”