Statistical Distributions of Sea Surface Elevations

Abstract

The adequacy of the existing models of the sea surface elevation probability density function to the real wave field is analyzed. The limitations and possibilities in using the density function of the sea surface elevation probabilities built on the basis of truncated Gram-Charlier series are considered. The limitations are due to the fact that in real calculations it is possible to use a relatively small number of members of the series, whose coefficients are determined by estimates of statistical moments. The use of truncated Gram-Charlier series leads to negative values in the models of the probability density function. This chapter suggests a new approach that preserves the advantages of Gram-Charlier distribution and reduces its disadvantages. It is shown that statistical distributions built on the basis of a model (for example, the Stokes model), in which the only parameter is the significant slope, incorrectly describe the field of sea waves. In these distributions, the third and fourth order accumulators are functionally connected, while according to direct wave measurements, such a connection is absent.