Wave cycle distributions are notoriously difficult to calculate. Available analytic approximations, like those suggested by Longuet-Higgins (1983) and Cavanie, Arhan and Ezraty (1976) make use only of a few spectral moments, and are unreliable for moderate waves. To find distributions under general spectrum shape and parameters one has to use efficient numerical algorithms based on high dimensional integrals. The paper presents a number of examples of wave cycle distributions computed by the software package WAFO developed at Lund Institute of Technology; http://www.maths.lth.se/matstat/wafo/. All results are compared to simulated or real data. The wave cycles studied are the max-min cycle, the crest-trough wave cycles, the rainflow cycle distribution, and the mean-separated max-min cycle.
Cycle Definitions Gaussian wave models are the basic model for deep water ocean waves in naval engineering, and for the implied loads on marine structures. In marine safety analysis, the distribution of cycle amplitudes and periods is important. Depending on application, several types of cycles have to be considered; see Figure 1. max-min cycles: Cycles formed by a pair of a local maximum of height M+ and the following local minimum of height M−. The height difference HMm = M+ - M- between the maximum and the minimum is called a max-min amplitude. crest-trough cycles: Cycles formed by the maximum value Ac between an upcrossing of the mean level and the following downcrossings, and the minimal value - At between the downcrossing and the next upcrossing. The height difference HCT = Ac + At is called a crest-trough amplitude or upcrossing amplitude, and the distance between the mean level upcrossings is the upcrossing wave period/wavelength. This type of cycle definition is the common one for wave statistics.