Wave statistics in non-linear random sea

The sea elevation at a fixed point is modeled as a sum of Gaussian process plus a quadratic random correction term. It is shown that the process can also be written as a quadratic form of a vector valued Gaussian process with arbitrary mean. The saddlepoint method is used to approximate the intensity μ(u), say, the sea level crosses the level u. The accuracy of the proposed method is studied. In examples the computed intensity is used to bound the wave crest distribution. The bounds are compared with empirical distributions derived from simulations.