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

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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.
Original languageEnglish
Title of host publicationProceedings of the The 33rd European Safety and Reliability Conference (ESREL 2023)
EditorsMário P. Brito, Terje Aven, Piero Baraldi, Marko Čepin, Enrico Zio
Number of pages8
ISBN (Electronic)978-981-18-8071-1
Publication statusPublished - 2023
EventThe 33rd European Safety and Reliability Conference (ESREL 2023): The Future od Safety in a Reconnected World - University of Southampton, Southampton, United Kingdom
Duration: 3 Sept 20237 Sept 2023


ConferenceThe 33rd European Safety and Reliability Conference (ESREL 2023)
Abbreviated titleESREL 2023
Country/TerritoryUnited Kingdom
Internet address

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • waves
  • wind
  • stochastic process
  • k-means
  • Bayesian networks
  • copulas


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