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Non-stationary Extreme Models and a Climatic Application : Volume 14, Issue 3 (25/06/2007)

By Nogaj, M.

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Book Id: WPLBN0004019829
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File Size: Pages 12
Reproduction Date: 2015

Title: Non-stationary Extreme Models and a Climatic Application : Volume 14, Issue 3 (25/06/2007)  
Author: Nogaj, M.
Volume: Vol. 14, Issue 3
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2007
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Dacunha-Castelle, D., Parey, S., & Nogaj, M. (2007). Non-stationary Extreme Models and a Climatic Application : Volume 14, Issue 3 (25/06/2007). Retrieved from http://hawaiilibrary.net/


Description
Description: EDF R&D, 6 Quai Watier, 78401 Chatou, France. In this paper, we study extreme values of non-stationary climatic phenomena. In the usually considered stationary case, the modelling of extremes is only based on the behaviour of the tails of the distribution of the remainder of the data set. In the non-stationary case though, it seems reasonable to assume that the temporal dynamics of the entire data set and that of extremes are closely related and thus all the available information about this link should be used in statistical studies of these events. We try to study how centered and normalized data which are closer to stationary data than the observation allows easier statistical analysis and to understand if we are very far from a hypothesis stating that the extreme events of centered and normed data follow a stationary distribution. The location and scale parameters used for this transformation (the central field), as well as extreme parameters obtained for the transformed data enable us to retrieve the trends in extreme events of the initial data set. Through non-parametric statistical methods, we thus compare a model directly built on the extreme events and a model reconstructed from estimations of the trends of the location and scale parameters of the entire data set and stationary extremes obtained from the centered and normed data set. In case of a correct reconstruction, we can clearly state that variations of the characteristics of extremes are well explained by the central field. Through these analyses we bring arguments to choose constant shape parameters of extreme distributions. We show that for the frequency of the moments of high threshold excesses (or for the mean of annual extremes), the general dynamics explains a large part of the trends on frequency of extreme events. The conclusion is less obvious for the amplitudes of threshold exceedances (or the variance of annual extremes) – especially for cold temperatures, partly justified by the statistical tools used, which require further analyses on the variability definition.

Summary
Non-stationary extreme models and a climatic application

Excerpt
Beniston, M. and Stephenson, D.: \newblock Extreme climatic events and their evolution under changing climatic conditions, Global Planet. Change, 44, 1–9, 2004.; Chavez-Demoulin, V.: Ajustement de vraisemblance selon Mccullagh et Tibshirani, Internal Report 97.1, Department of Mathematics, EPFL, 1997.; Coles, S.: An Introduction to Statistical Modeling of Extreme Values, Springer, New York, 2001.; Davison, A. and Ramesh, N.: Local likelihood smoothing of sample extremes, J. Roy. Statist. Soc., 62, 191–208, 2000.; Embrechts, P., Kluppelberg, C., and Mikosch, T.: Modelling Extremal Events for Insurance and Finance, Springer, Berlin, 1997.; Ferro, C. A.,~Hannachi, A., and Stephenson, D.: Simple non-parametric techniques for exploring changing probability distributions of weather, J. Climate, 18(21), 4344–4354, 2005.; Green, P. and Silverman, B.: Nonparametric Regression and Generalized Linear Models, Chapman and Hall, 1994.; Katz, R. and Brown, B.: Extreme events in a changing climate: variability is more important than averages, Clim. Change, 21, 289–302, 1992.; Klein~Tank, A., Wijngaard, J., Können, G., Böhm, R., Demarée, G., Gocheva, A., Mileta, M., Pashiardis, S., Kern-Hansen, L. H C., Heino, R., Bessemoulin, P., Tzanakou, G. M.-W M., Szalai, S., Pálsdóttir, T., Fitzgerald, D., Rubin, S., Capaldo, M., Maugeri, M., Leitass, A., Aberfeld, A B. R., van Engelen, A., Forland, E., Mietus, M., Coelho, F., Mares, C., Razuvaev, V., Nieplova, E., Cegnar, T., López, J., Dahlström, B., Moberg, A., Kirchhofer, W., Pachaliuk, A. C O., Alexander, L., and Petrovic, P.: Daily dataset of 20th-century surface air temperature and precipitation series for the european climate assessment, Int. J. Climatol., 22, 1441–1453, Data and metadata available at http://eca.knmi.nl, 2002.; Nogaj, M., Yiou, P., Parey, S., Malek, F., and Naveau, P.: Amplitude and frequency of temperature extremes over the North Atlantic region, Geophys. Res. Lett., 33, L10801, doi:10.1029/2005GL024251, 2006. %; ; Palmer, T N. and Räisänen, J.: Quantifying the risk of extreme seasonal precipitation events in a changing climate, Nature, 415, 512–514, 2002.; Parey, S., F. M., Laurent, C., and Dacunha-Castelle, D.: Trends and climate evolution: statistical approach for very high temperatures in france, J. Climate, 81(3–4), 331, 2006.; Silverman, B.: Density Estimation for Statistics and Data Analysis, Chapman and Hall, 1986.; Smith, C., Toumi, R., and Haigh, J.: Seasonal trends in stratospheric water vapor, Geophys. Res. Lett., 27, 1687–1690, 2000.; Stott, P A., Stone, D A., and Allen, M R.: Human contribution to the European heatwave of 2003, Nature, 432, 610–614, 2003.; Tawn, J., Dixon, M., and Woodworth, P.: Statistics for the Environment 2: Water related issues, chapter Trends in sea-level, pages 147–181, Chichester, Wiley, 1994.; Wahba, G.: Spline Models for Observational Data, SIAM, Philadelphia, 1990.

 

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