Height distribution of stochastic Lagrange ocean waves

The Gaussian wave model has been successfully used in ocean engineering for more than half a century. It is well understood, and there exists both exact theory and efficient numerical algorithms for calculation of the distribution of safety related wave characteristics, such as crest height and steepness. Its drawback is its lack of realism: it produces waves which are stochastically symmetric, both in the vertical and in the horizontal direction. From that point of view, the Lagrangian wave model is more realistic, but its stochastic properties have not been studied until quite recently. We present an explicit expression for the occupation density (approximately the univariate probability density) of the Lagrangian wave model. We also draw some conclusions about the definition of freak or rogue waves.