*2.2. Statistical and Numerical Strategy*

The purpose was to determine triplets (Hs; SWL; U) of a 100-year joint exceedance return period and their covariates (Tp, Dp, Du) to populate coastal hydrodynamic models. In order to perform the statistical analysis, we used MATLAB® software. The statistical method was implemented using the WAFO toolbox [34] and developments by Guanche Garcia [35]. The different steps are illustrated in Figure 2a and exposed here:

	- (a) Between the extreme variables Hs, SWL, U, and based on the semiparametric approach described by [12]. The readers may also consult [37] for detailed information and application of this approach;
	- (b) Between Hs et Tp using the empirical conditional distribution of wave steepness (St) knowing Hs described by [38];

**Figure 2.** (**a**) Recap of our multivariate extreme value analysis. (**b**) Nested boxes used all around Corsica Island for the numerical simulations; 50 m resolution grids are in red and 10 m resolution boxes are in orange.

We applied the statistical analysis for points located in each of the red boxes shown in Figure 2b. The triplets obtained and their covariates finally forced the SWAN and SWASH-2DH models. For more information on the SWAN and SWASH-2DH open source models, the reader is invited to refer to [39–45].

Moreover, as mentioned at step 6, some safety margins are taken into account in the numerical simulations. Following the French regulation [46], the water level must account the Sea Level Rise (SLR) potentially due to climate change. To do so, 0.20 m is added to the water level of the 100-year event defined offshore. In order to consider a "2100" future scenario, 0.60 m has to be added to the 100-year return level defined offshore by following the French regulation guideline. The values recommended in the guideline are based on the Fifth Assessment Report (AR5), chapter 13 [47] published by the Intergovernmental Panel on Climate Change (IPCC). Note that the value of 0.60 m is in agreemen<sup>t</sup> with the mean SLR value estimated for the Mediterranean basin in [48,49], when considering the pessimistic scenario of Representative Concentration Pathway (RCP) 8.5. Moreover, [46] recommends taking into account uncertainties adding a margin of 0.25 m to the 100-year return level if all the uncertainties cannot be estimated. There are many sources of uncertainties, and even if many of them showed small-to-moderate degree of uncertainty (confidence interval given with marginals, correction on Hs), and that parametric tests regarding the statistical approach showed moderate impact as well (diagnosis on thresholds in H&T04), residual uncertainties remain. These residual uncertainties correspond to altimetric variations of Earth's crust, local vertical ground motions (e.g., due to groundwater pumping), impacts of remote contributions in a semi-enclosed basin such as the Mediterranean Sea or complex oceanic processes in the Strait of Gibraltar. To account for them, a margin of 0.25 m is applied following the French regulators' recommendations of [46]. We have considered two cases:

