Research Communication: Use of the Spatial Extremogram to Form a Homogeneous Region Centered on a Target Site for the Regional Frequency Analysis of Extreme Storm Surges

Research Communication: Use of the Spatial Extremogram to Form a Homogeneous Region Centered on a Target Site for the Regional Frequency Analysis of Extreme Storm Surges

Y. Hamdi C-M. Duluc L. Bardet V. Rebour 

Institut de Radioprotection et de Sûreté Nucléaire, France

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Nuclear power plants in France are designed for low probabilities of failure. Nevertheless, some exceptional surges, considered as outliers, are not properly addressed by statistical models. Regional information may be used to mitigate the paucity of data and the influence of outliers. A regional frequency analysis (RFA) model assumes a homogenous behavior of the variable of interest at a regional scale. The first stage in an RFA is the delineation of homogeneous regions. We propose herein a new approach to form a homogenous region centered on a target site and using the spatial extremal dependence between observations (the spatial extremogram) to measure the neighborhood between sites. Skew surge data set collated at a total of 19 sites located on the French coast (Atlantic and English Channel) were used as the case study for this contribution (with La Rochelle as a target site). Once a physically plausible region of interest is defined, a related issue regards the statistical homogeneity of the region of interest. The L-moment-based homogeneity tests of Hosking and Wallis, widely used in hydrology, are used in this paper. The principle of the extremogram allows us to form a physically and statistically homogenous group of sites centered on a target site. It also allows to overcome the problem of the so-called “border effect” and these are two key original points of the developed concept.


extreme surges, homogenous region, regional frequency analysis, spatial extremogram,  target site


[1] Dalrymple, T., Flood-Frequency Analyses. Manual of Hydrology: Flood-Flow Techniques, Geological Survey Water-Supply: Washington, 1960.

[2] Rao, A.R. & Hamed, K.H. (eds), Flood Frequency Analysis, CRC Press, Boca Raton, Florida, USA, 2000.

[3] Coles, S. (ed), An Introduction to Statistical Modeling of Extreme Values, Springer, Berlin, 2001.

[4] Hosking, J.R.M. & Wallis, J.R., Some statistics useful in regional frequency analysis. 

Water Resources Research, 29, pp. 271–282, 1993. https:/

[5] Hosking, J.R.M. & Wallis, J.R., Regional Frequency Analysis: An Approach Based on L-Moments, Cambridge University Press: Cambridge, U.K, 1997.


[6] Ouarda, T.B.M.J., Girard, C., Cavadias, G.S. & Bobée, B., Regional flood frequency estimation with canonical correlation analysis. Journal of Hydrology, 254, pp. 157– 173, 2001. https:/

[7] Groupe de Recherche en Hydrologie Statistique, Presentation and review of some methods for regional flood frequency analysis. Journal of Hydrology, 186, pp. 63–84, 1996a. https:/

[8] Groupe de Recherche en Hydrologie Statistique, Inter-comparison of regional flood frequency procedures for Canadian rivers. Journal Hydrology, 186, pp. 85–103, 1996b. https:/

[9] Bardet, L. & Duluc, C.-M., Apport et limites d’une analyse statistique régionale pour l’estimation de surcotes extrêmes en France. Proceeding of the SHF Conference, Paris, France, 2012.

[10] Bernardara, P., Andreewsky, M. & Benoit, M., Application of regional frequency analysis to the estimation of extreme storm surges. Journal of Geophysical Research, 116, C02008, 2011. https:/

[11] Renard, B., A Bayesian hierarchical approach to regional frequency analysis. Water Resources Research, 47(11), W11513, 2011. https:/

[12] Weiss, J., Analyse régionale des aléas maritimes extrêmes. Thèse de doctorat. Sciences de l’ingénieur, Université Paris-Est, France, p. 256, 2014. 

[13] Davis, R.A. & Mikosch, T., The extremogram: a correlogram for extreme events. Bernoulli, 15(4), pp. 977–1009, 2009.


[14] Chavez, D.V. & Davison, A.C., Modelling time series extremes. Statistical Journal, 10(1), pp. 109–133, 2012.

[15] Ledford, A.W. & Tawn, J.A., Diagnostics for dependence within time series extremes. 

Journal of the Royal Statistical Society Series B, 65, pp. 521–543, 2003. https:/

[16] Cho, Y.B., Davis, R.A., & Ghosh, S., Asymptotic Properties of the Empirical Spatial Extremogram. Scand J Statist, 43, pp. 757–773, 2016. https:/