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| Titel |
A Unified Theory of Rainfall Extremes, Rainfall Excesses, and IDF Curves |
| VerfasserIn |
D. Veneziano, S. Yoon |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250060508
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| Zusammenfassung |
| Extreme rainfall events are a key component of hydrologic risk management and design. Yet,
a consistent mathematical theory of such extremes remains elusive. This study aims at laying
new statistical foundations for such a theory.
The quantities of interest are the distribution of the annual maximum, the distribution of
the excess above a high threshold z, and the intensity-duration-frequency (IDF) curves.
Traditionally, the modeling of annual maxima and excesses is based on extreme value (EV)
and extreme excess (EE) theories. These theories establish that the maximum of n iid
variables is attracted as n -- to a generalized extreme value (GEV) distribution with a
certain index k and the distribution of the excess is attracted as z -- to a generalized
Pareto distribution with the same index. The empirical value of k tends to decrease as the
averaging duration d increases.
To a first approximation, the IDF intensities scale with d and the return period T .
Explanations for this approximate scaling behavior and theoretical predictions of the scaling
exponents have emerged over the past few years. This theoretical work has been
largely independent of that on the annual maxima and the excesses. Deviations
from exact scaling include a tendency of the IDF curves to converge as d and T
increase.
To bring conceptual clarity and explain the above observations, we analyze the
extremes of stationary multifractal measures, which provide good representations of
rainfall within storms. These extremes follow from large deviation theory rather
than EV/EE theory. A unified framework emerges that (a) encompasses annual
maxima, excesses and IDF values without relying on EV or EE asymptotics, (b)
predicts the index k and the IDF scaling exponents, (c) explains the dependence of
k on d and the deviations from exact scaling of the IDF curves, and (d) explains
why the empirical estimates of k tend to be positive (in the Frechet range) while,
based on frequently assumed marginal distributions, EV/EE theory gives k = 0. |
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