Wave characteristic distributions for Gaussian waves—Wave-length, amplitude and steepness

In as tationary stochastic process the wave-length and amplitude are defined as the difference in time and height between a crest and the following trough. The distributions of these quantities are of great practical importance, but no closed form expressions are known at present. In previous papers we have presented an approximation which gives correct upper and lower bounds, regardless of the covariance structure under Gaussian assumptions. In this paper the suggested approximations are compared to two simpler approximations, one due to Cavanié et al. (1976) based on a cosine process and a new one, derived by replacing the model process by its regression curve.