The probability density of the total curvature of a uniform random Gaussian sea surface in the specular points

Abstract

Assuming that sea surface is a random uniform Gaussian function, an analytical expression is developed for the probability distribution density of the total curvature of the surface in specular reflection points. The density can be expressed in terms of an integral, and its asymptotics acquire a simple form for large values of the total curvature. A numerical experiment to verify the probability distribution density is also given.