Abstract: The sea surface elevations are generally stated as non-Gaussian processes in the current literature, being considered Gaussian for short periods of relatively low wave heights. The objective here is to study the evolution of the distribution of the sea surface elevation from Gaussian to non-Gaussian as the period of time in which the associated time series is recorded increases. To do this, an empirical study based on the measurements of the buoys in the US coast downloaded at a casual day is performed. This study results in rejecting the null hypothesis of Gaussianity in below 25% of the cases for short periods of time and in over 95% of the cases for long periods of time. 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 can be Gaussian, which is observed throughout the study and in that a longitudinal study is performed here.

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