**1. Introduction**

Coastal flooding often occurs because of several dynamic components that are dependent on each other (wind, waves, water levels—tide, atmospheric surge, currents); hence, the analysis of the return period of a single component is not representative of the return period of the total water level at the coast [1]. As such, it is important to estimate the joint return period, taking into account the dependency between all of the components. Marcos et al. [2] even show that return periods of extreme sea levels are underestimated (by a factor of 2 or higher) in 30% of the coasts (at global scale), if the dependency is neglected.

The dependency can also be based on a spatial linkage assumption. Galiatsatou and Prinos [3] took into account the degree of spatial dependence between the sites, in order to estimates extreme storm surges along the Dutch coast on the North Sea.

Some authors considered extreme quantiles of metocean data (significant wave height, wave period, and wind speed) estimated jointly, using a subset exceeding appropriately

**Citation:** Louisor, J.; Rohmer, J.; Bulteau, T.; Boulahya, F.; Pedreros, R.; Maspataud, A.; Mugica, J. Deriving the 100-Year Total Water Level around the Coast of Corsica by Combining Trivariate Extreme Value Analysis and Coastal Hydrodynamic Models. *J. Mar. Sci. Eng.* **2021**, *9*, 1347. https://doi.org/10.3390/jmse9121347

Academic Editors: Wei-Bo Chen, Shih-Chun Hsiao and Wen-Son Chiang

Received: 30 September 2021 Accepted: 24 November 2021 Published: 30 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

defined thresholds [4]. Moreover, several joint probability approaches applied to sea conditions have been used by [5–9], for example. The reader might also be interested in the review proposed by [10]. One of the limitations encountered within the classical joint probability approaches are related to the restrictive assumptions regarding the dependence structure when extrapolating to extremes. Idier et al. [11] mentioned that one of the difficulties with such approaches could be the number of offshore parameters, which can complicates the detection of the critical conditions. Heffernan and Town [12] developed a semiparametric approach (hereinafter called H&T04 methods), which overcomes the limitations imposed by dimensionality. This approach was first applied to air pollution data. Since then, several authors applied the H&T04 methods to metocean offshore conditions: [13–16].

In the present study, we are interested in coastal flooding all around Corsica Island in the Mediterranean Sea. To our best knowledge, a multivariate extreme value analysis has never been implemented along these coasts, though some studies undertook statistical analysis over the Mediterranean Sea or around Corsica, e.g., [17]. In particular, in 2004, the Western European Union funded a Wind and Wave Atlas of the Mediterranean Sea, providing both bivariate and univariate statistics, and spatial distribution of statistical quantities for wind and wave parameters [18]. This atlas was built 20 years ago with a 10-year dataset consisting of less than 1000 data points (spatial resolution of the outputs ~50 km), distributed throughout the whole Mediterranean Sea using dynamical models which have been updated since the beginning of the 21st century. Other initiatives in this basin should be noted. For example, the WaveForUs (Wave climate and coastal circulation Forecasts for public Use) platform provides 3-day meteorological and sea state forecasts in the Mediterranean Sea since 2013 with a 0.15◦ spatial resolution [19]. To date, these archives are too short to be used as such in local coastal flooding assessments.

To be more accurate at local scale, a solution could be to apply dynamical downscaling using a complex nested model chain. However, this is particularly delicate in the Mediterranean Sea because of specific issues mentioned in [20]: especially the orography (for winds and pressure), and the complex bathymetry, and limited fetch extension (for waves). Several authors proposed an alternative in order to reduce the complexity and the computational cost of such a numerical chain [21,22]. Indeed, based on the forcing event selection, which consist in: (1) determining the joint probabilities that significant wave heights Hs, wind intensity at 10 m above the ground U, and still water level SWL exceed jointly imposed thresholds; (2) defining the extreme combinations; (3) populating the coastal hydrodynamic models at a local scale with the extreme combinations as input. For instance, the authors in reference [23] used dozens of scenarios of offshore forcing conditions (significant wave height and total water level) associated with the same joint probability of exceedance (here with a 100-year return period) as inputs of their modeling chain. The appealing feature of this approach is its computational simplicity and efficiency, because it is only based on a limited number of scenarios, i.e., on a limited number of long-running numerical simulations.

From an operational point of view, our primary motivation is based on the fact that, since 2013, a unique value of 2 m relative to the French national topographic reference (NGF) was taken into account to map entire zones potentially exposed to coastal flooding in Corsica (e.g., http://carto.geo-ide.application.developpement-durable.gouv.fr/429/ risques\_naturels\_02a.map (accessed on 2 September 2020)). The reader may note that all data and results presented in this study are relative to the NGF. For the local stakeholders and coastal managers, it is important to assess if this 2 m value is relevant in their region [24]. The main purpose of the present study is to show how multivariate extreme value analysis can help to better define low-lying zones potentially exposed to coastal flooding.

In this paper, we have first described the site (location, and context), and data used in Section 2. We then exposed the methods applied to constitute extreme scenarios based on triplets (Hs; SWL; U) for significant wave height, still water level, and wind speed. The strategy used to propagate offshore conditions to the coastline has also been presented in this section. In Section 3, we have applied the proposed strategy all around Corsica, considering extreme scenarios under both, current and climate change conditions. The results are presented in Section 4. Finally, a discussion of our results, and the limitations of the method are presented in Section 5.
