State-space models for maxima precipitation

Philippe Naveau; Paul Poncet

Journal de la société française de statistique (2007)

  • Volume: 148, Issue: 1, page 107-120
  • ISSN: 1962-5197

Abstract

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A very active research field in atmospheric sciences is centered around the modeling of weather extremes. This is mainly due to the large economic and human impacts of such extreme events. In this paper, we focus on the statistical temporal modeling of precipitation maxima because daily and monthly maxima have been recorded for many decades and at various sites. Our goal is to propose two new state-space models whose distributional foundations lie in Extreme Value Theory (EVT). Our first model takes advantage of max-stable processes, previously studied by Davis and Resnick (1989), among others. It can be viewed as a “translation“ of the gaussian linear Kalman filter into a Fréchet-type world in which the classical addition a + b has been replaced by the max operator a ∨ b = max ( a , b ) and the noise component is from a heavy-tailed distribution instead of being gaussian. Our second state-space model is built from the mixture extremes framework proposed by Fougères et al., (2006). Its strong points are its flexibility and richness with respect to applications. In addition to addressing the theoretical questions brought by our models, the main benefit of introducing them is to propose simple and powerful connections between EVT and data assimilation communities. The latter term “data assimilation” regroups statistical/dynamical techniques extensively used in climate studies. These procedures involve the combination of observational data with the underlying dynamical principles governing the physical system under observation. Hence, improving our knowledge about the representation of extremes in a state-space model framework is of strong interest from a data assimilation point of view.

How to cite

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Naveau, Philippe, and Poncet, Paul. "State-space models for maxima precipitation." Journal de la société française de statistique 148.1 (2007): 107-120. <http://eudml.org/doc/93452>.

@article{Naveau2007,
abstract = {A very active research field in atmospheric sciences is centered around the modeling of weather extremes. This is mainly due to the large economic and human impacts of such extreme events. In this paper, we focus on the statistical temporal modeling of precipitation maxima because daily and monthly maxima have been recorded for many decades and at various sites. Our goal is to propose two new state-space models whose distributional foundations lie in Extreme Value Theory (EVT). Our first model takes advantage of max-stable processes, previously studied by Davis and Resnick (1989), among others. It can be viewed as a “translation“ of the gaussian linear Kalman filter into a Fréchet-type world in which the classical addition $a+b$ has been replaced by the max operator $a \vee b = \max (a,b)$ and the noise component is from a heavy-tailed distribution instead of being gaussian. Our second state-space model is built from the mixture extremes framework proposed by Fougères et al., (2006). Its strong points are its flexibility and richness with respect to applications. In addition to addressing the theoretical questions brought by our models, the main benefit of introducing them is to propose simple and powerful connections between EVT and data assimilation communities. The latter term “data assimilation” regroups statistical/dynamical techniques extensively used in climate studies. These procedures involve the combination of observational data with the underlying dynamical principles governing the physical system under observation. Hence, improving our knowledge about the representation of extremes in a state-space model framework is of strong interest from a data assimilation point of view.},
author = {Naveau, Philippe, Poncet, Paul},
journal = {Journal de la société française de statistique},
keywords = {data assimilation; Kalman filter; extreme value theory; generalized extreme value distribution; max-stable state-space model; GEV state-space model},
language = {eng},
number = {1},
pages = {107-120},
publisher = {Société française de statistique},
title = {State-space models for maxima precipitation},
url = {http://eudml.org/doc/93452},
volume = {148},
year = {2007},
}

TY - JOUR
AU - Naveau, Philippe
AU - Poncet, Paul
TI - State-space models for maxima precipitation
JO - Journal de la société française de statistique
PY - 2007
PB - Société française de statistique
VL - 148
IS - 1
SP - 107
EP - 120
AB - A very active research field in atmospheric sciences is centered around the modeling of weather extremes. This is mainly due to the large economic and human impacts of such extreme events. In this paper, we focus on the statistical temporal modeling of precipitation maxima because daily and monthly maxima have been recorded for many decades and at various sites. Our goal is to propose two new state-space models whose distributional foundations lie in Extreme Value Theory (EVT). Our first model takes advantage of max-stable processes, previously studied by Davis and Resnick (1989), among others. It can be viewed as a “translation“ of the gaussian linear Kalman filter into a Fréchet-type world in which the classical addition $a+b$ has been replaced by the max operator $a \vee b = \max (a,b)$ and the noise component is from a heavy-tailed distribution instead of being gaussian. Our second state-space model is built from the mixture extremes framework proposed by Fougères et al., (2006). Its strong points are its flexibility and richness with respect to applications. In addition to addressing the theoretical questions brought by our models, the main benefit of introducing them is to propose simple and powerful connections between EVT and data assimilation communities. The latter term “data assimilation” regroups statistical/dynamical techniques extensively used in climate studies. These procedures involve the combination of observational data with the underlying dynamical principles governing the physical system under observation. Hence, improving our knowledge about the representation of extremes in a state-space model framework is of strong interest from a data assimilation point of view.
LA - eng
KW - data assimilation; Kalman filter; extreme value theory; generalized extreme value distribution; max-stable state-space model; GEV state-space model
UR - http://eudml.org/doc/93452
ER -

References

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