**3. Multivariate Extreme Value Analysis**

In this section, we provide further implementation details on the steps 1–5 of the procedure described in Section 2.2, which aims at estimating the extreme offshore conditions to be used as forcing inputs of the SWAN-SWASH 2DH modeling chain (see Figure 2a). These steps are illustrated with the box around the Gulf of Porto (Figure 2b)

### *3.1. Selection of Events and Dataset Set Up (Step 1)*

The first step of the procedure consists in selecting independent combinations (Hs; SWL; U). To do so, we first performed a block maxima selection to define each wave event (statistically independent) [50]. Indeed, based on a 40-year historical research in archives, press and in-situ data; and in consultation with the deconcentrated services of the state, we assumed that Hs is the primary driver of coastal flooding around the coast of Corsica. Following [23,51], we defined a block as a 3-day period with 1.5 days between each Hs peak in order to ensure the independence between each peak. Then, for each Hs peak, the SWL and U maxima were sought in a 12-h window centered on the Hs peak. This 12 h window allows the data of SWL to be scanned over approximately one tidal cycle. Each Hs peak is associated to the corresponding covariates, peak period Tp and peak direction Dp. Likewise, each value of U is associated with its direction Du. Thus, several combinations (Hs; Tp; Dp; SWL; U; Du) corresponding to 30 years of common data with ~100 events per year were selected in 7 different zones around Corsica.
