Romain Chailan, Gwladys Toulemonde, Frederic Bouchette, Anne Laurent, Florence Sevault, Heloïse Michaud


In the analysis of coastal hazards, the features of extreme waves are determining information to question the impact of storms to the coast. The spatial behaviour of extreme waves is even more valuable especially since it is sparsely provided. Regarding recent applications in other contexts, a kind of statistical models called max-stable processes is relevant for modelling spatial extreme events. Max-stable processes are extensions of the well-known Generalised Extreme Value (GEV) distribution. Unlike univariate approaches, max-stable processes consider spatial dependence of a phenomenon. Such a modelling also overtakes a standard multivariate approach by providing information continuously over the area studied, even where no observation is available. Relying on such a stochastic modelling, the aim of this study is to discuss the extreme waves hazards in the Gulf of Lions, focusing on their spatial behaviour.


extreme waves hazards; extreme value analysis; max-stable processes; spatial extreme modelling; spatial dependence; wave hindcast; Gulf of Lions

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J.-N. Bacro and C. Gaetan. A review on spatial extreme modelling. In Advances and Challenges in Space- time Modelling of Natural Events, pages 103–124. Springer, 2012.

J. Beuvier, F. Sevault, M. Herrmann, H. Kontoyiannis, W. Ludwig, M. Rixen, E. Stanev, K. Béranger, and S. Somot. Modeling the mediterranean sea interannual variability during 1961–2000: focus on the eastern mediterranean transient. Journal of Geophysical Research: Oceans (1978–2012), 115(C8), 2010.

J. Blanchet and A. C. Davison. Spatial modeling of extreme snow depth. The Annals of Applied Statistics, 5(3):1699–1725, 2011.

D. Cooley, P. Naveau, and P. Poncet. Variograms for spatial max-stable random fields. In Dependence in probability and statistics, pages 373–390. Springer, 2006.

A. C. Davison and M. M. Gholamrezaee. Geostatistics of extremes Subject collections. The Royal Society, (October), 2011.

L. de Haan and T. T. Pereira. Spatial extremes: Models for the stationary case. The annals of statistics, pages 146–168, 2006.14

L. de Haan et al. A spectral representation for max-stable processes. The Annals of Probability, 12(04): 1194–1204, 1984.

R. A. Fisher and L. H. C. Tippett. Limiting forms of the frequency distribution of the largest or smallest member of a sample. In Mathematical Proceedings of the Cambridge Philosophical Society, volume 24, pages 180–190. Cambridge Univ Press, 1928.

B. Gnedenko. Sur la distribution limite du terme maximum d’une serie aleatoire. Annals of Mathematics, pages 423–453, 1943.

M. J. Herrmann and S. Somot. Relevance of era40 dynamical downscaling for modeling deep convection in the mediterranean sea. Geophysical Research Letters, 35(4), 2008.

P. Jonathan, D. Randell, Y. Wu, and K. Ewans. Return level estimation from non-stationary spatial data exhibiting multidimensional covariate effects. Submitted to Ocean Engineering October, 2013.

Z. Kabluchko, M. Schlather, and L. De Haan. Stationary max-stable fields associated to negative definite functions. The Annals of Probability, pages 2042–2065, 2009.

S. A. Padoan, M. Ribatet, and S. A. Sisson. Likelihood-based inference for max-stable processes. Journal of the American Statistical Association, 105(489):263–277, 2010.

N. Raillard, P. Ailliot, and J. Yao. Modeling extreme values of processes observed at irregular time steps: Application to significant wave height. Annals of Applied Statistics, pages 1–26, 2014.

M. Ribatet, R. Singleton, and R. Team. Spatialextremes: modelling spatial extremes. R package version, pages 1–8, 2011.

M. Schlather. Models for stationary max-stable random fields. Extremes, 5(1):33–44, 2002.

M. Schlather and J. A. Tawn. A dependence measure for multivariate and spatial extreme values: Properties

and inference. Biometrika, 90(1):139–156, 2003.

R. L. Smith. Max-stable processes and spatial extremes. Unpublished manuscript, Univer, 1990.

H. L. Tolman. User manual and system documentation of wavewatch iii R version 4.18. Technical Report 316, 2014.

C. Varin and P. Vidoni. A note on composite likelihood inference and model selection. Biometrika, 92(3): 519–528, 2005.