Wave setup estimation at regional scale: Empirical and modeling-based multi-approach analysis in the Mediterranean Sea

Wave setup is a physical process that induces a temporal increase of the mean water level due to wave dissipation by bottom friction and breaking in the surf zone, extending over tens to hundreds of meters in the cross-shore direction. Wave setup contribution to coastal sea level solely induced by wind and atmospheric effects can increase by more than 100% under extreme events and conditions favoring its formation. It is therefore crucial to consider this phenomenon when assessing sea-level-related coastal hazards. Previous studies estimated the wave setup effect by means of numerical modeling and empirical formulations at regional and global scale. Such analyses require either high computational capacity to implement high-resolution numerical models over large domains, and/or accurate information on coastal morphological features from global or regional databases. Although the Mediterranean Sea is a fetch-limited environment, waves generated from extra-tropical cyclones are powerful enough for wave setup to develop, and subsequently for a potential significant wave setup contribution to extreme coastal sea level. Through the use of both numerical and empirical methods, we investigate the uncertainty associated to wave setup representation on the frequency and magnitude of coastal extreme sea levels occurring on sandy beaches in the Mediterranean Sea. Wave setup values are compared at beach scale between process-based modeling and empirical approaches, showing highly variable results. We also quantify the impact of wave setup on return levels of coastal sea level extremes using reconstructed sea levels. We employ various methods to calculate the wave setup component. Results show high spatial dispersion, with clear differences between the numerical and empirical approaches, especially in regions prone to the development of energetic waves. The total inter-method dispersion of 100-year return levels is often higher than 30 cm for average values of 62.4 cm. We emphasize the important limitations related to wave setup modeling (i.e., its underestimation) at large scale, and call for caution when applying empirical formulations (generally developed from local studies) at regional to global scale, which can lead to unrealistic wave setup values.