Statistics of extremes and estimation of extreme rainfall: II. Empirical investigation of long rainfall records / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: II. Recherche empirique sur de longues séries de précipitations

Abstract

In the first part of this study, theoretical analyses showed that the Gumbel distribution is quite unlikely to apply to hydrological extremes and that the extreme value distribution of type II (EV2) is a more consistent choice. Based on these theoretical analyses, an extensive empirical investigation is performed using a collection of 169 of the longest available rainfall records worldwide, each having 100-154 years of data. This verifies the theoretical results. In addition, it shows that the shape parameter of the EV2 distribution is constant for all examined geographical zones (Europe and North America), with value κ = 0.15. This simplifies the fitting and the general mathematical handling of the distribution, which become as simple as those of the Gumbel distribution.Key words design rainfall; extreme rainfall; generalized extreme value distribution; Gumbel distribution; hydrological design; hydrological extremes; probable maximum precipitation; risk Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: II. Recherche empirique sur de longues séries de précipitationsRésumé Dans la première partie de cette étude, des analyses théoriques ont prouvé que la distribution de Gumbel est peu susceptible de s'appliquer aux valeurs extrêmes de variables hydrologiques et que la distribution de valeurs extrêmes du type II (EV2) est un choix plus cohérent. Une recherche empirique étendue est effectuée, en se basant sur ces analyses théoriques, avec une collection de 169 séries de précipitations, parmi les plus longues de celles qui sont disponibles dans le monde entier, comportant chacune 100-154 ans de données. Ceci vérifie les résultats théoriques. En outre, on montre que le paramètre de forme de la distribution EV2 est constant pour toutes les zones géographiques examinées (l'Europe et l'Amérique du Nord), avec la valeur 0.15. Ceci simplifie l'ajustement et la manipulation mathématique générale de la distribution, qui deviennent aussi simples que pour la distribution de Gumbel.Mots clefs pluie de projet; précipitation extrême; distribution généralisée de valeurs extrêmes; distribution de Gumbel; dimensionnement hydrologique; valeurs extrêmes en hydrologie; précipitation maximum probable; risque

Censored rainfall modelling for estimation of fine-scale extremes

“…This curvature is more pronounced for the BL1M model, which would be consistent with a higher positive shape parameter. While extreme value theory encompasses a range of distributions characterized by the sign of the shape parameter, Koutsoyiannis (2004a) argues that rainfall extremes naturally follow the Fréchet distribution for annual maxima (equivalent to the GEV with ξ > 0), supported by empirical evidence in Koutsoyiannis (2004b). The positive growth in extremes observed in our results is consistent with this hypothesis, and suggests that important information about the distribution of extremes is captured in the full storm profile hyetograph over the low censor.…”

Generalized extreme value shape parameter and its nature for extreme precipitation using long time series and the Bayesian approach

“…Koutsoyiannis (2004aKoutsoyiannis ( , 2004b has analysed the statistics of daily rainfall extremes and argued for the use of the EV2 distribution (with positive shape parameter) instead of the Gumbel distribution (EV1) when analysing rainfall data to avoid an underestimation of risk associated with extreme rainfall. L-moment estimation of the distribution's shape parameter, ξ, led Koutsoyiannis (2004aKoutsoyiannis ( , 2004b to conclude that ffi 0:15 and that it is "constant for all examined geographical zones (Europe and North America)". Recent work on the generalized Pareto (GP) distribution's shape parameter, GEV ffi GP (Serinaldi and Kilsby 2014), supports > 0 Gershunov 2015, Cavanaugh et al 2015).…”

“…Recent work on the generalized Pareto (GP) distribution's shape parameter, GEV ffi GP (Serinaldi and Kilsby 2014), supports > 0 Gershunov 2015, Cavanaugh et al 2015). The conclusion made by Koutsoyiannis (2004aKoutsoyiannis ( , 2004b was drawn from a comparison of the spread of ξ estimates in the data with that of simulations where ξ is constant. However, a strict statistical test with the assumption of a constant ξ was not carried out.…”

Estimating probability of extreme rainfall over Japan using Extended Regional Frequency Analysis

“…In some regions, the number of combined data may not be large enough to reliably estimate the probability of extreme daily rainfall with a long return period. Koutsoyiannis (2004) reported that a reliable probability of extreme daily rainfall can be estimated by applying frequency analysis to combined data in a very large region. He performed frequency analysis for the combined 100-154 year daily rainfall data from 169 stations in the United States and Europe (the total number of the combined data was 18,065 station-year).…”

“…In the proposed method, Extended Regional Frequency Analysis (ERFA), we perform frequency analysis for combined data in a much wider region than the conventional RFA to ensure a sufficiently large number of data for the frequency analysis. Koutsoyiannis (2004) applied frequency analysis to the data normalized based on the sample mean of the annual maximum data at each station as in conventional RFA. Similarly, in ERFA we perform frequency analysis for the data normalized based on the sample mean of the annual maximum data at each site in the region.…”