Investigating extreme sea level components and their interactions in the Adriatic and Tyrrhenian Seas

Coastal hazards represent an existential threat to Italian coastal regions since they host important economic centers related to manufacturing and tourism. Knowledge of potential extreme sea levels (ESL), their component, and their interactions are essential to better evaluate potentially hazardous future extreme events in a changing climate and possible effects on the design of coastal structures. Hence, in this study, we investigate the interaction between tide and surge for extreme conditions of sea level in 9 locations along the Italian coastline facing both the Adriatic and the Tyrrhenian Seas and all in a semi-diurnal tidal regime. First, we introduce a novel dependence metric, i.e., the β factor, in support of the classical Kendall's τ, to preliminary assess the effect of the dependence between tide and surge when conditioned on ESL on the variance of ESL, and then we quantify such effect using a copula-based framework. Here, the surge component is determined via the concept of skew surge, i.e., the difference within a tidal cycle between the maximum observed sea level and the predicted high tide (irrespective of the time of occurrence), to remove any random effect in the interaction due to the timing of the tidal peak. Our results show that ESL components, i.e., tide and skew surge, are negatively dependent, i.e., high/low values of the surge are associated with low/high values of the tide, in all the stations investigated, and that higher values of dependence, measured with Kendall's τ, can be observed in the Adriatic Sea, around -0.6, while lower values in the Tyrrhenian Sea, around -0.45, with the exception of Palermo. In general, an increase in ESL for higher quantiles is observed when the negative dependence between tide and surge is explicitly modeled. Moreover, our results show that the β factor can help quantify the relative contribution of tide and surge on the variability of ESLs. More specifically, small β refers to cases when tide and surge are similar in their magnitude, e.g., Palermo, while values of β close to 1 refer to the case when one component dominates the other. In the former case, ESLs obtained from a model that does not account for the dependence between tide and surge will result in ESL estimates with larger variability. On the other hand, when one component dominates the other, the variability of ESLs is slightly influenced by the model used for tide and surge, i.e., dependent or independent. We can then conclude that by explicitly modeling the dependence between tide and skew surge we can improve estimates and inference of ESLs.