Proceedings of the

The 33rd European Safety and Reliability Conference (ESREL 2023)
3 – 8 September 2023, Southampton, UK

A Copula-Based Bayesian Network to Model Wave Climate Multivariate Uncertainty in the Alboran Sea

Patricia Mares-Nasarre1,a, Julio García-Maribona2, Miguel A. Mendoza-Lugo1,b and Oswaldo Morales-Nápoles1,c

1Hydraulic Structures and Flood Risk, Delft University of Technology, Delft, the Netherlands.

2DHI A/S, Copenhagen, Denmark.


An accurate estimation of wind and wave variables is key for coastal and offshore applications. Recently, copulas have gained popularity for modelling wind and waves multivariate dependence, since accounting for the hydrodynamic relationships between them is needed to ensure reliable estimations of the required design values. In this study, copula-based Bayesian networks (BNs) are explored as a tool to model extreme values of significant wave height (Hs), wave period, wave direction, wind speed and wind direction. The model is applied to a case study located in the Alboran sea, close to the Spanish coast, using ERA5 database. Extreme values of Hs are sampled using Yearly Maxima and concomitant values of the missing variables are used. K-means clustering algorithm is applied to separate the different wave components and a BN is built for each of them. The assumption of modelling the dependence between the variables using Gaussian copulas and the structure of BNs are supported with the d-calibratioson score. Fitted marginal distributions are introduced in the nodes of the BNs and their performance is assessed using in-sample data and the coefficient of determination. The BN models proposed present high performance with a low computational cost proving to be powerful tools for modelling the variables under investigation. Future research will include different locations and databases.

Keywords: Waves, Wind, Stochastic process, Copulas, k-means, Bayesian networks.

Download PDF