The wave height distribution with Edgeworth's form of a cumulative expansion of probability density function(PDF) of surface elevation are investigated. The non-Gaussian model of wave height distribution shows a good agreement with experimental data. It is discussed that the fourth order moment(kurtosis) of water surface elevation corresponds to the first order nonlinear correction of wave heights.
Wave height statistics(e.g, wave height distribution, run length and so on) of random waves play important roles in designing coastal and ocean structures. The Rayleigh distribution is regarded as the distribution of wave heights in stochastic processes with a linear and narrow banded spectrum. Over a few decades, a considerable number of studies have been made on the validity of the Rayleigh distribution. It is commonly known that large wave heights in field do not necessarily obey the Rayleigh distribution. For example, Haring(1976) shows that large wave heights observed in storms are on the order of 10 percent less than those predicted by the Rayleigh distribution. After that, Forristall(1984), and Myrhaug and Kjeldsen(1987) also reported that occurrence probabilities of large wave heights in field are smaller than the predicted value of the Rayleigh distribution, respectively. Yasuda et a/.(1992,1994) numerically investigated that the third order nonlinear interactions have significant effects on the statistical properties of random wave train in deep water. That is, the third order nonlinear effects increase the occurrence probabilities of large wave heights more than the linear and second order ones do. Stansburg(1993) also obtained the same results in his experimental work. However, there is no theoretical distribution which agrees with the data, although many studies have attempted to establish the wave height distribution using either a linear wave assumption or narrow banded spectrum one.
