**5. Discussion and Conclusions**

The key motivation of this study was to show how a multivariate extreme value analysis improve the estimate of low-lying zones potentially exposed to coastal flooding in Corsica. Indeed, in this zone, coastal sectors with altitudes below 2 m (and 2.4 m under "2100" future conditions), are considered potentially exposed to flooding. In order to asses if this value was relevant or not, we have first determined the joint probabilities that significant wave heights (Hs), wind intensity at 10 m above the ground (U), and water level (WL) exceed jointly imposed thresholds by applying a semiparametric multivariate extreme value analysis. Covariate peak direction (Dp), the peak period (Tp), and the wind direction (Du) were also accounted for. Once the (Hs, Tp, SWL, U) combinations were identified, we ran the coastal hydrodynamic models, SWAN and SWASH-2DH forced by these extreme scenarios. For current conditions, the results show that the TWL all along the shoreline in the study area are between 0.80 and 1.8 m, compared to 2 m currently applied on every low-lying zone. For "2100" future conditions, the values are between 1.2 and 2.2 m, compared to 2.4 m currently applied on every low-lying zone. In conclusion, the value 2 m (2.4 m when considering future conditions) seems to be overestimated regarding, the methods applied and the results of our study. This highlights the benefit of performing a full integration of extreme offshore conditions together with their dependence in hydrodynamic simulations for screening out the coastal areas potentially exposed to flooding around Corsica. More generally, the method can be adapted to areas where only topobathymetric studies have been carried out to map potential flooding areas.

There are however several aspects that might nuance this finding. First, uncertainty in the multivariate extreme value analysis was only partly integrated. Indeed, although we have taken into account some of the uncertainties (CI given with marginals, correction on Hs, and diagnosis on thresholds in H&T04), a full propagation of all the sources of uncertainty has not been performed. Thus, a simple-but-efficient approach consisting in affecting a 0.25 m margin on the TWL results showed that even in this situation, the 2 m threshold was hardly reached in several places around the island. Second, we did not apply the method in some areas like some cliffs or areas where topobathymetric data where insufficient at the time of the study. This constitutes a line for future research. Furthermore, the uncertainties also lie in the variables studied and the choice of dominant variable. Indeed, other variables could be studied, such as precipitation, river discharges, or even storm duration the same way as Hs [54]. A sensitivity analysis on these variables could be conducted on this area as in [55]. We can also note that we defined an independent wave event as a 3-day window (see Section 3.1), but [56] note that 25% of extreme wave events are consecutive events that hit the same location in less than a day. This could be relevant, to be taken into consideration, especially for "2100" future conditions (the 25% rate could be higher).

There are other points that we still need to work on. Indeed, we used the hydrodynamic models in a static way; it means that the propagation from offshore to nearshore does not take into account the dynamics of the phenomenon (dynamics of the event, flow velocity, etc.). With our static approach, the dynamic of an event is not taken into account and therefore the volume of water is only limited by the capacity of the low lying zone to fill up to an altitude corresponding to the total water level at the shoreline. Even if we attached importance to the dependency between several variables leading to flooding, the main component to determine low-lying zones potentially exposed to coastal flooding remains the topography. It could be relevant to consider a dynamic approach, which is more computationally demanding, but more precise in terms of overflow, breach flooding, volume of water assessment, or flood phenomena coming from rivers. Regarding methodological developments, future work could also concentrate on the comparison with alternatives approaches, such as a response approach [21], potentially aided by metamodeling techniques [57].

Furthermore, we looked at "2100" future conditions and, following the regulator's recommendations [46], we applied a 0.6 m value by 2100 to account the SLR in the hy-

drodynamic models. Even if this value was derived from the RCP 8.5 scenario "likely range", it is interesting to note that, regarding national SLR planning, France has a low amount of SLR used in planning compared to neighboring countries. Indeed, the amount of SLR used in planning in France is less than 1 m by 2100, whereas in Greece, it is about 1 m by 2100, and in Belgium, it is almost 2 m when considering 2100 high-end SLR [58]. Thiéblemont et al. showed that under the RCP 8.5, the 0.6 m value could be possibly doubled or tripled along the France coastline when considering high-end estimates of different components of sea-level projections [59]. Besides, the recent Special Report on the Ocean and Cryosphere in a Changing Climate (SROCC), then the Sixth Assessment Report AR6 emphasized that there is a substantial likelihood that SLR will be outside the likely range [60,61]. We note that these reports also identify deep uncertainties related to rare or indirectly deduced phenomenon, as the marine ice cliff instabilities taken into account in some global climate models.

Finally, the purpose here was the assessment of the total water level at the shoreline in order to inform on the low-lying zones in Corsica potentially exposed to flooding. The next steps of the method were to determine areas that were geomorphologically homogenous based on orthophotos and fieldwork analyses, in order to complete the mapping [62]. Specific information on the swash were also computed using the SWASH model in its 1D configuration on some beaches identified as potentially impacted by swash and mechanical shocks due to waves, in current and/or future conditions.

**Author Contributions:** Conceptualization, J.L., J.R., T.B. and R.P.; methodology, J.L., J.R., T.B., R.P., A.M. and J.M.; software, J.L., J.R., T.B., F.B.; validation, J.L.; formal analysis, J.L., J.R., T.B.; investigation, J.L., J.R., T.B., R.P., F.B., A.M. and J.M.; resources, J.L., J.R., T.B., F.B., R.P., A.M. and J.M.; data curation, J.L. and A.M.; writing—original draft preparation, J.L. and J.R.; writing—review and editing, J.L., J.R., T.B., R.P., F.B., A.M. and J.M.; project administration, J.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was co-funded by the DDTM Corse-du-Sud (AP16CSC008, AP17BAS013) and by the DREAL Haute-Corse and the BRGM (AP18BAS019).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used is available on request from the providers mentioned.

**Acknowledgments:** The following data providers are acknowledged: Cerema (Candhis), CNES/AVISO, the NOAA, IGN, ISPRA, Météo-France, the Shom. The authors are very grateful to the anonymous reviewers for their comments and expert advice. We also thank F. Paris for his support on the preliminary phase of this study.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

### **Appendix A. Validation of the Numerical Models**

To validate the hydrodynamic model, we compared still water level observations at the Ajaccio tide gauge to the simulations.

**Figure A1.** Q–Q plot and scatter plot of hourly still water levels measured at Ajaccio tide gauge (OBSERVATIONS) and values obtained by numerical simulation (MARS\_MED\_BRGM).

A linear correction is applied to the NWW3 MED data. This correction is derived from the linear regression between the observations and the original model data and is expressed as follows:

$$\text{NNW3 MET corrected} = 1.21 \times \text{NNW3 MET} + 0.14 \tag{A1}$$

**Figure A2.** Observed and simulated Hs at the Cap Corse buoy, period 1999–2008.

### **Appendix B. Elements Used for Adjusting Marginal Probability Distributions for Hs, SWL, and U around Corsica**

**Figure A3.** Selected thresholds u, methods used (MOM, PWM, MLE) to estimate GPD parameters, and the resulting 100-year return level for Hs (m), SWL (m), and U (m/s).

### **Appendix C. Wave Directions Affecting the Coastline for Extreme Conditions**

**Figure A4.** Wave roses; and Dp(◦) plotted against Hs(m) for three offshore points. The red dots and red circles indicate the wave directions, which could most affect the coastline for extreme conditions regarding the coast morphology.


**Appendix D. Dependence Coefficients**


**Figure A5.** Dependence coefficients a and b, residuals Z for selected threshold ν for two coastal regions of Corsica.
