| Following a review of internal and external studies on the statistical distributions of sea wave variables, a maximum entropy probability density function (PDF) for the wave height H of nonlinear sea wavesf4(H) = αHre-βH4 (1)is derived through solving a conditional variation problem based on the maximum entropy principle, and its parameters α, β, γ are expressed explicitly in terms of thedistribution moments of H, (Hm|ˉ) , m=1, 2, 3, 4. This PDF has the followingadvantages: 1) Its parameters involve the 3rd and 4th moments, (H3|ˉ) and (H4|ˉ), which play the roles analogous to the skewness λ3 and kurtosis λ4 in the PDFs forsurface elevation of nonlinear sea waves, such as the Gram-Charlier series PDF and beta PDF, so this PDF is suitable to describing the distributions of nonlinear sea wave heights in various sea sates; 2) This PDF maximizes the information entropy of H and accords with the maximum entropy principle, so it is competent for nonlinear sea waves whose uncertainty is large; and 3) this PDF is simple and its parameters are easy to be determined from known data, so it is convenient to theoretical and practical applications.To test the validity, the PDF (1) is compared with thirty-six observed distributions of wave heights measured at different wind speeds and different fetches in a wind-wave tunnel, along with the Rayleigh PDF which has been widely employed to describe the distribution of sea wave heights. The results shown that while the Reyleigh PDF deviates significantly form the observed distributions, the PDF (1) quite well agree with them.Also reported in this thesis are the applications of the PDF (1) to estimating the T-year return-period annual extreme wave height and Typhoon wind-speed from available data. Comparing with the commonly used methods, such as the Gumbel andPearson-III methods, shown that the present methods has also certain advantages.
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