Bivariate copula modelling of significant wave height temporal dependence: a comparison study between buoy and reanalysis data

A comprehensive understanding of the wave climate at a site of interest is essential for offshore and coastal engineering applications such as flood risk analysis, structural reliability assessment, or the design of coastal interventions. Specifically, the significant wave height, H_s, plays a central role in these designs and assessments, as it characterizes the severity of each sea state and, therefore, governs the loads on coastal and offshore structures, controls key coastal morphodynamic phenomena, among other processes. To conduct these designs and assessments, practitioners need reliable wave data for statistical characterization. Several sources are available, such as buoys and reanalysis data. Buoy records are the ideal option but they are often spatially and temporally scarce. Therefore, reanalysis data has become more popular in recent decades, providing more continuous and longer time series. However, it is necessary to understand to what extent is reanalysis data representing reality. This study, conducted in the Canary Islands, Spain, focuses on comparing the temporal evolution of wave conditions derived from reanalysis data and from a spatially overlapping buoy in probabilistic terms. Each database is clustered through the K-means++ algorithm to identify wave conditions by using the main metocean variables. In order to estimate the optimal number of clusters, the Elbow method is used. It yields a value of k=5 for both datasets. Afterwards, an autocorrelation analysis is performed for each database and clusters; in general, higher correlations are observed for the reanalysis time series. Bivariate copulas are used to model the temporal dependence of the significant wave height in each cluster, i.e., the joint distribution of H_s(t) and H_s(t+1). Both, the fitted copulas and empirical marginals are compared for each cluster and database observing significant differences. Overall, relevant differences are observed between reanalysis and buoy data from a probabilistic perspective that might have consequences in design.

Keywords: Bivariate copulas, temporal dependence, significant wave height, dataset validation, stochastic modelling, wave climate, probabilistic models.