Joint distribution of individual wave heights and periods in mixed sea states using finite mixture models

Abstract

The bivariate distribution of zero-up-crossing wave heights and associated periods is important in the stochastic modelling of ocean waves and is of theoretical and practical interest among scientists and engineers. Recently, joint descriptions in mixed sea states have garnered attention. The present study proposes a mixture bivariate lognormal model to characterise the joint distribution in sea states with two-peaked spectra. A parametric distribution based on conditional modelling is compared with the presented model. To verify the fitted models, secondary waves, which can be formed when waves propagate over marine obstacles, were generated in laboratory conditions and simulated data were obtained by the Ochi–Hubble model. The joint distributions of wave heights and periods, as well as the marginal distributions of these two wave parameters in three types of combined sea states are studied and discussed. Results show that the conditional model is not suitable for fitting the bivariate distribution, which may be primarily owing to its inaccurate description of the wave period distribution. Joint probability density functions of wave heights and periods created using a finite mixture model provide improved performance and can describe the bimodal nature of the distribution relatively well.