On the Non-Gaussianity of the Height of Sea Waves

The objective of this paper is to prove that the sea wave height is not a Gaussian process. This is contrary to the common belief, as the height of a sea wave is generally considered a Gaussian process. With this aim in mind, an empirical study of the buoys along the US coast at a random day is pursued. The analysis differs from those in the literature in that we study the Gaussianity of the process as a whole and not just of its one-dimensional marginal. This is done by making use of random projections and a variety of tests that are powerful against different types of alternatives. The study has resulted in a rejection of the Gaussianity in over 96% of the studied cases.