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Battle of extreme value distributions : a global survey on extreme daily rainfall
Publikationstyp
Review Article
Date Issued
2013-04-29
Sprache
English
Journal
Volume
49
Issue
1
Start Page
187
End Page
201
Citation
Water resources research 49 (1): 187-201 (2013)
Publisher DOI
Scopus ID
Publisher
American Geophysical Union
Theoretically, if the distribution of daily rainfall is known or justifiably assumed, then one could argue, based on extreme value theory, that the distribution of the annual maxima of daily rainfall would resemble one of the three limiting types : (a) type I, known as Gumbel; (b) type II, known as Frechet; and (c) type III, known as reversed Weibull. Yet, the parent distribution usually is not known and often only records of annual maxima are available. Thus, the question that naturally arises is which one of the three types better describes the annual maxima of daily rainfall. The question is of great importance as the naive adoption of a particular type may lead to serious underestimation or overestimation of the return period assigned to specific rainfall amounts. To answer this question, we analyze the annual maximum daily rainfall of 15,137 records from all over the world, with lengths varying from 40 to 163 years. We fit the generalized extreme value (GEV) distribution, which comprises the three limiting types as special cases for specific values of its shape parameter, and analyze the fitting results focusing on the behavior of the shape parameter. The analysis reveals that (a) the record length strongly affects the estimate of the GEV shape parameter and long records are needed for reliable estimates ; (b) when the effect of the record length is corrected, the shape parameter varies in a narrow range ; (c) the geographical location of the globe may affect the value of the shape parameter; and (d) the winner of this battle is the Frechet law.
DDC Class
600: Technology