Can the Rayleigh distribution be used to determine extreme wave heights in non-breaking swell conditions?

A reliable set of tools for prediction of low-exceedance design waves is of high importance when designing coastal protection structures. The significant wave parameters are typically obtained from buoys or numerical wave propagation models and design values are found by extreme analysis. Statistical wave height distributions are used to transform the significant wave height to lower exceedance wave heights. These extreme single waves will cause the highest loads and wave overtopping volumes on structures and thereby represent the design conditions. An under-prediction of the design maximum wave height causes unsafe designs, while an over-prediction causes too conservative and thus expensive designs. The wave height distribution by Longuet-Higgins (1952) (Rayleigh-distribution) for deep-water non-breaking waves is in the present paper evaluated against data from numerical tests with long period and long-crested swell waves. The numerical model is validated against data from physical model tests. Generally, it is concluded that the Rayleigh-distribution is under-predicting the low-exceedance wave heights in irregular swell waves. This is expected to be caused by wave non-linearity and thus a new modified wave height distribution is suggested, where the shape parameter in the distribution is dependent on the wave non-linearity, represented by the Ursell-number. The new proposed wave height distribution for non-linear and non-breaking waves is highly applicable for practical engineering design of both near-shore and offshore structures under influence of swell-waves.