High-order cumulants of sea surface elevations

The variability of cumulants of the fifth and sixth orders of the sea surface elevations is studied. The investigations are carried out on the basis of the data of direct wave measurements carried out in the field conditions. It is demonstrated that the cumulants of the fifth order are weakly correlated with the variations of the mean sea surface slope generated by the dominant waves. The variations of the cumulant of the sixth order are not correlated with the mean slope variations. The errors of the sea surface elevation probability density approximated by the models based on the use of Gram-Charlier series are analyzed. The analysis is carried out for the models including various numbers of terms of the Gram-Charlier series.