Joint statistical models for significant wave height and wave period in a changing climate

• Several statistical modelling approaches for the joint distribution of ocean wave parameters are investigated.
• Several copula-based models are compared to a conditional model and a bivariate lognormal.
• The potential effect of climate change on the joint distribution of significant wave height and wave period are analysed.
• Results indicate that wave height and wave period might be more correlated in a future climate.

In many marine and coastal engineering applications, the simultaneous distribution of several met-ocean variables is required for risk assessment and load and response calculations. For example, a joint probabilistic description is needed to construct environmental contours for probabilistic structural reliability analyses. Typically, the joint distribution of significant wave height and wave period is needed as a minimum, but other environmental parameters such as wind, current, surges and tides might also be relevant.This paper presents a study on various joint models for the simultaneous distribution of significant wave height and zero-crossing wave period. The alternative models that have been investigated are a conditional model, a bivariate parametric model and several models based on parametric families of copulas. Each of the models is fitted to data generated from a numerical wave model for the current climate and for two future climates consistent with alternative climate scenarios. Additionally, the potential effect of climate change on the simultaneous distribution will be investigated.Initial investigation reveals that straightforward application of some of the most commonly used copulas will not give reasonable joint models. The reason for this is that they are symmetric whereas the empirical copulas display asymmetric behaviour. However, asymmetric copulas can be constructed based on these families of copula, and this significantly improves the fit. Analyses of the extremal dependence in the data indicate that the variables are asymptotically independent. Furthermore, the results suggest that extreme significant wave height and zero-crossing wave period tend to be more correlated in a future climate compared to the current climate.