On the Non-Gaussianity of Sea Surface Elevations

Abstract

The sea surface elevations are generally stated as Gaussian processes in the literature. To show the inaccuracy of this statement, an empirical study of the buoys in the US coast at a random day is performed, which results in rejecting the null hypothesis of Gaussianity in over 80$\%$ of the cases. The analysis pursued relates to a recent one by the author in which the heights of sea waves are proved to be non-Gaussian. It is similar in that the Gaussianity of the process is studied as a whole and not just of its one-dimensional marginal, as it is common in the literature. It differs, however, in that the analysis of the sea surface elevations is harder from a statistical point of view, as the one-dimensional marginals are commonly Gaussian, which is observed throughout the study.