A Joint Probability Distribution for Multivariate Wind-Wave Conditions and Discussions on Uncertainties

Erik Vanem*, Elias Fekhari, Nikolay Dimitrov, Mark Kelly, Alexis Cousin, Martin Guiton

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


This article presents a joint statistical model, which is needed in probabilistic design and structural risk assessment, that has been fitted to data of wind and wave conditions for an offshore location off South Brittany. The data are from a numerical model and contain hourly values for several wind and wave variables over a period of 32 years. The joint distribution presented in this article considers the variables wind direction, mean wind speed, significant wave height, wave direction, and peak period. A conditional model for turbulence given wind speed is introduced to yield an additional variable for the joint model. The joint model is constructed as a product of marginal and conditional models for the various variables. Additionally, the fitted models will be used to construct environmental contours for some of the variables. For significant wave height, various models are used to obtain different extreme value estimates, illustrating the uncertainties involved in extrapolating statistical models beyond the support of the data, and a discussion on the use of nonparametric copulas for the joint distribution is presented. Moreover, bootstrap has been performed to estimate the uncertainty in estimated model parameters from sampling variability. The effect of changing which variable to model as the marginal in a conditional model is illustrated by switching from wind speed to significant wave height. Such joint distribution models are important inputs for design of offshore structures, and in particular for offshore wind turbines, and the influence of the joint model in design is illustrated by a simple case study. This article is an extension of the conference paper by Vanem et al. (2023, “A Joint Probability Distribution Model for Multivariate Wind and Wave Conditions,” 42nd International Conference on Ocean, Offshore and Arctic Engineering).
Original languageEnglish
Article number061701
JournalJournal of Offshore Mechanics and Arctic Engineering
Issue number6
Number of pages15
Publication statusPublished - 2024


  • Joint probability distributions
  • Wind-wave environment
  • Offshore wind
  • Renewable energy environmental loads
  • Ocean waves and associated statistics
  • Offshore safety and reliability
  • Probability and spectral wave modeling
  • Structural safety and risk analysis


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