“…This section briefly describes statistical distributions in theories for wave fields which have been verified against data obtained from bottom--mounted sensors, buoys and altimeters (Bretschneider, 1959;Dobson et al, 1987;Sterl et al, 1998;Tucker and Pitt, 2001;Stansell, 2004;Vandever et al, 2008;Casas--Prat and Holthuijsen, 2010 Individual wave heights with a narrow--band spectrum are found to follow a Rayleigh distribution in the deep sea (Longuet--Higgins, 1952). Within this narrow--band spectrum of wave heights, the average height of the highest one--third of the waves over an observational period, H1/3, is practically equal to the significant wave height, Hs, that can be derived from the spectrum (Phillips, 1977).…”