Abstract. The evaluation of the probability of occurrence of extreme natural events is important for the protection of urban areas, industrial facilities and others. Traditionally, the extreme value theory (EVT) offers a valid theoretical framework on this topic. In an over-threshold modelling (OTM) approach, Pickands' theorem, (Pickands, 1975) states that, for a sample composed by independent and identically distributed (i.i.d.) values, the distribution of the data exceeding a given threshold converges through a generalized Pareto distribution (GPD). Following this theoretical result, the analysis of realizations of environmental variables exceeding a threshold spread widely in the literature. However, applying this theorem to an auto-correlated time series logically involves two successive and complementary steps: the first one is required to build a sample of i.i.d. values from the available information, as required by the EVT; the second to set the threshold for the optimal convergence toward the GPD. In the past, the same threshold was often employed both for sampling observations and for meeting the hypothesis of extreme value convergence. This confusion can lead to an erroneous understanding of methodologies and tools available in the literature. This paper aims at clarifying the conceptual framework involved in threshold selection, reviewing the available methods for the application of both steps and illustrating it with a double threshold approach.

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The knowledge of the statistical distribution of extreme sea levels at the coast is of utmost importance for the characterization of flood risks in coastal areas. In this study we consider that the sea level results from two components: the (astronomical) tide and the (meteorological) surge, without considering the effects of waves. We focus our attention on the dependence of the surge height on the tidal level. At sites with a strong tidal range, the classical analysis methods rely on working only with high tide data (namely high tidal levels and skew surges). A statistical method of adjustment of extreme values is applied to the surge component, leading to the Revisited Joint Probability Method. In that case, we consider that surge and tide components are independent. However, comparisons with measured data show that in several cases this procedure leads to an overestimation of the water levels for a given return period. We therefore propose here to study the dependence of skew surges on high tidal levels, with two different approaches: one based on a so-called seasonal dependence, and the other one based on the interaction between surge and tide. Three methods are adapted or developed to test the influence of these two forms of dependence. They are applied to a series of 19 French harbours along the Atlantic and English Channel coasts of France for which more than 10 years of data are available. The results show that the seasonal dependence does not affect the result significantly, while the interaction between the skew surge and the high tidal level appear to be significant for over half the harbours studied. A revisited model proposed here, as an extension of the model by Dixon and Twan (1994), seems to be more satisfactory at least for most harbours studied.

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.