Pietro Bernardara, Franck Mazas, Jérôme Weiss, Marc Andreewsky, Xavier Kergadallan, Michel Benoît, Luc Hamm


In the general framework of over-threshold modelling (OTM) for estimating extreme values of met-ocean variables, such as waves, surges or water levels, the threshold selection logically requires two steps: the physical declustering of time series of the variable in order to obtain samples of independent and identically distributed data then the application of the extreme value theory, which predicts the convergence of the upper part of the sample toward the Generalized Pareto Distribution. These two steps were often merged and confused in the past. A clear framework for distinguishing them is presented here. A review of the methods available in literature to carry out these two steps is given here together with the illustration of two simple and practical examples.


POT; threshold; extremes; physical declustering; statistical optimization

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Bernardara, P., M. Andreewsky, et al. 2011. Application of the Regional Frequency Analysis to the estimation of extreme storm surges. J. Geophys. Res., 116(C02008).

Coles, S. 2001. An Introduction to Statistical Modeling of Extreme Values, Springer-Verlag, London.

Cunnane, C. 1988. Methods and merits of regional flood frequency analysis. Journal of Hydrology, 100, 269-290.http://dx.doi.org/10.1016/0022-1694(88)90188-6

Hosking, J. R. M. and J. R. Wallis. 1997. Regional Frequency Analysis. An approach based on L-moments. Cambridge, Cambridge University Press.http://dx.doi.org/10.1017/CBO9780511529443

Lang, M., T. B. M. J. Ouarda, et al. 1999. Towards operational guidelines for over-threshold modeling. Journal of Hydrology, 225, 103-117.http://dx.doi.org/10.1016/S0022-1694(99)00167-5

Mazas, F., and L. Hamm. 2011. A multi-distribution approach for determining extreme wave heights. Coastal Engineering, 58, 385-394.http://dx.doi.org/10.1016/j.coastaleng.2010.12.003

Pickands, J. 1975. Statistical Inference Using Extreme Order Statistics. The Annals of Statistics, 3(1), 119-131.http://dx.doi.org/10.1214/aos/1176343003

Smith, R. L. 1984. Threshold methods for sampling extremes. Statistical extremes and applications, T. d. O. J. Dordrecht, 621-638.

DOI: https://doi.org/10.9753/icce.v33.management.42