Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period.

For better displaying the statistical properties of measured data, it is particularly important to select a suitable multivariate joint distribution model in ocean engineering. According to the characteristics and properties of Copula functions and the correlation analysis of measured data, the nonlinear relationship between random variables can be captured. Additionally, the models based on the Copula theory have more general applicability. A series of correlation measure index, derived from Copula functions, can expand the correlation measure range among variables. In this paper, by means of the correlation analysis between the annual extreme wave height and the corresponding wind speed, their joint distribution models were studied. The newly established two-dimensional joint distribution functions of the extreme wave height and the corresponding wind speed were compared with the existing two-dimensional joint distributions.

The extreme sea conditions caused by typhoons pose a threat to the design safety of marine and coastal engineering structures. In the past, design wave height calculation models that only considered the frequency of typhoons ignored the influence of other hazard factors of typhoons, resulting in lower design standards. In this paper, typhoon frequency, intensity, and distance are selected, and dimensional influences of different factors are eliminated through standardization processing. Based on the correlation between different hazard factors, we have obtained a multi-dimensional discrete joint probability distribution of typhoon hazard factors and constructed a new design wave height that considers the comprehensive effects of typhoon frequency, intensity, and distance. Our results show that the design wave height values of the 50-year, 100-year, and 200-year events are 12.59%, 8.10%, and 3.14% higher than the Gumbel distribution, which is more in line with the distribution of the wave height of waves under severe typhoon conditions. The new model can fully reflect the impact of typhoons on wave height, which can provide a reference for the design safety of marine engineering in the South China Sea.