Based upon the nonlinear model of random sea waves, a commonly applicable statistical distribution of wave surface elevation exact to the third order is derived through the" direct calculations of each order moment. The distribution arrived reduces, in the sense of being exact to He, to the Gram-Charlier series due to Longuet-Higgins for deep water, provided that only the two simplest kinds of wave-wave interactions are Taken into account. The reason why the agreement of Oram-Charlier series with experimental data becomes worse and worse as the terms of series are increased is explicited for the first time.

A concept of apparent energy distribution of sea waves is suggested and named "the outer Dequency spectrum" to distinguish it from the frequency spectrum in common sense In line with the concept, a kind or outer spectrum with three parameters in Cauchy's form is derived theoretically from the joint distribution of wave periods and heights reached previously by the present authors and the Bretschnelder spectrum is rededuced simply in a distinct manner. The foundation of medlanics of the snnilarity between the frequency, spectrum m common sense and the outer one is briefly discussed, in view of the fact that Bretschneider spectrum has a wide application in engineering, the advantages and probabihty of asmg the outer spectrum as a common one are also considered.

本文是随机海浪二阶非线性特征量研究的第一部分。在精确导出任意均匀水域上三维随机波动一阶解、二阶解的基础上，更严密、更合理地重新推导了波面高度分布的偏度与二阶功率谱的理论表达式，并首次给出了有限水深波面二阶谱的理论形式。

Based upon the nonlinear model of random sea waves, the statistical distribution of wave surface elevation exact to the fourth order is derived as the truncated Gram-Charlier series, by calculating directly each order moment. The phenomenon found by Huang et al. that the agreement between observed data and investigated series deteriorates much more when the series is kept to λs is explained, The effect of the appmximation order on the truncation of series and the determination of coefficients is investigated. For the mth order approximation, the derived series is truncated at H3m-3 with the absence of H3m-4, and the coefficients of H3m-3 and H3m-6 are connected by a simple algebraic relation.