Distribution of Crest-to-Trough Wave Heights

The theoretical distribution of wave heights as given by the Rayleigh law is based on the wave envelope. However, empirical distributions derived from field data utilize a crest-to-trough representation. The latter definition corresponds to an averaging operation on the envelope which results in an excess of waves with heights near the midrange and in deficiencies at the two extremes in a manner increasing with the spectrum band width. The ultimate effect of a deficiency towards the high wave tail is an underestimate in the exceeding probability of larger wave heights. Hence, this kind of discrepancy (systematically observed between the Rayleigh law and various field data) can be explained on this basis.