Due to nonlinear effect, the surface elevation distribution is non- Gaussian. Longuet-Higgins (1963) derived theoretically the non- Gaussian distribution in Gram-Charlier series, Huang and Long (1980) checked the series by laboratory experiments and stated that the series is in good agreement with the observed data when the series is truncated at the term of λ4 and becomes worse as the truncated term increases to λ6, and even still worse when the truncated term further increases to λ8. In order to check Huang and Long's conclusion experiments are conducted in our laboratory. In the experiments the phenomena observed by Huang and Long does not appear and the Gram-Charlier series agrees better and better with the observed data as the truncated term increases.
The statistical distribution of surface elevation is, as well known, the basis to further investigate the other sea waves characteristic's probability distribution, and it is widely used both in ocean engineering and in ship construction. On the framework of linear theory we can easily derive that the surface elevation distribution is Gaussian from the central limitation theorem. But a great deal of data from either field observation or laboratory experiments have shown that the surface elevation distribution is non-Gaussian. On the other hand, Gaussian distribution couldn't reflect the essential mechanism governing the sea wave processes at least from a purely theoretical point of view. Kinsman (1960, 1965) was the first to fit the observed surface elevation distribution with Gram-Charlier series, and Longuet-Higgins gave it a reasonable explanation. Tayfun (1980) considered the sea wave with narrow spectrum as a kind of Stokes waves with mean frequency, random initial phase and modulated amplitude and showed that the surface elevation distribution is approximate to the Gram-Charlier series. Huang and Long checked the series by laboratory experiments and stated that the series is in good agreement with the observed data when the series is truncated at the term of λ4 and becomes worse as the truncated term increases to λ6, and even still worse when the truncated term further increases to λ8. Sun Fu (1994) tried to explain the phenomenon observed by Huang and Long from the point of physical
