依据作者提出的海浪能量外观分布，即外频谱的概念，重新推导了Bretschne Lder风浪谱，极大地简化了Bret schneider原来的推演过程，并对谱的系数予以订正，将订正后的Bretschneider谱与Pie rSOll和Mos cowitz谱进行了比较，结果表明，两种风浪频谱在数学表述上是完全等价的。

依据波动的射线理论及随机波的线性模型，提出了一种三维海浪要素统计分布的完整理论。依此理论，只要获得方向谱的10个参数就能确定各种波浪要素的统计分布。结果表明，波高仍然服从Rayleigh分布；波高与周期的联合分布仅取决于一维谱而与给定的弥散关系无关；与波长有关的分布不仅依赖于谱的高频行为并取决于谱的方向特征；波陡分布由方向谱的6个参数确定；周期与波长的联合分布是存在的。当然，详尽的观测或实验检验是完全必要的。

Based upon the nonlinear model of Languet-Higgins the joint distribution of wave surface slopes is theoretically investigated. It is shown that in the fourth order approximation, the distribution is given by truncated Gram-Charlier series. The types of wave-wave coupling interactions are related to the order of approximation to nonlinearity of sea surface, which eventually defines the truncated term of the Gram-Charlier series. For each order approximation, the coefficients in the series are modified comparatively to the corresponding ones for the previous order approximation. If the nonlinear effect of the kurtosis is considered, the wave surface must be as accurate at least as to the third order approximation, and with regard to skewness, the wave surface must be as accurate at least as to the fourth order approximation.

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。