  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.
