Wave analysis by Slepian models

Ocean waves exhibit more or less a Gaussian distribution for the instantaneous water surface height, and there is a need to develop simple models for generation of the characteristic non-Gaussian statistics, namely the asymmetric distributions of water surface height and wave slope. We argue that a simple class of non-linear oscillators can reproduce some of the characteristic features of random water wave processes and linear or non-linear response to ocean waves. We describe the Slepian model for the Gaussian case, and explain the use of the regression approximation for level crossing distances and associated variables, such as wave period and amplitude. Finally we speculate about a generalization of the regression technique to the non-linear Markov process case.