Modelling and Clustering Sea Conditions: Bivariate FiniteMixtures of Generalized Additive Models for Location, Shape, and Scale Applied to the Analysis of Meteorological Tides and Wave Heights

Modelling sea conditions is a complex task that requires a comprehensive analysis, considering various influencing factors. Observed and unobserved factors jointly play a role in the definition of sea conditions. Here, we consider finite mixtures of generalized linear additive models for location scale, and shape (GAMLSSs) to capture the effects of both environmental variables and omitted variables, whose effects are summarized using latent variables. The GAMLSS approach is flexible enough to allow for different data features such as non-normality, skewness, heavy tails, etc., and for the definition of a regression model not only for the expected values of the observed process but also for all the other distribution parameters, e.g., the variance. We collected data on multiple sea-related and environmental variables in Ancona (Italy) from two Italian networks: the Sea Level Measurement Network (Rete Mareografica Nazionale, RMN) and the Sea Waves Measurement Network (Rete Ondametrica Nazionale, RON). Our main outcomes were the meteorological tides (often also referred to as “residuals”) and the significant wave height. Atmospheric pressure and wind speed were considered as main drivers of the sea conditions, as well as the fetch associated with wind direction, linking these variables to the outcomes through the definition of multiple linear predictors in a regression framework. Our results confirm the importance of accounting for environmental variables and reveal that their effect is heterogeneous, where heterogeneity is modelled by three distinct mixture components, each capturing different sea conditions. These findings contribute to a deeper understanding of sea state dynamics and provide evidence of a clustering structure characterizing different sea conditions.