Short-term analysis of wind waves is often based on the assumption that the sea surface elevation is a stationary and Gaussian process. In this work, measured sea surface elevation data obtained from a deep water wave buoy were analyzed. The work focuses in obtaining the best fit for normalized wave height data using Weibull, Rayleigh and Kumaraswamy distributions. For each sea-state, down-crossing wave heights were identified and the aforementioned theoretical distributions were fitted and assessed. The fit of the Kumaraswamy distribution to the wave height data was found to be much better than that of Weibull and Rayleigh distributions.
According to Pierson (1952) and Longuet-Higgins (1952), free sea-surface elevation at a fixed position of the free sea surface, can be modeled as a zero-mean, stationary, ergodic and Gaussian linear process. For the short-term statistical analysis of wind waves the Pierson (1952) and Longuet-Higgins (1952) model is often assumed. In the relevant literature, a number of theoretical distributions for modeling of wave height has been discussed; specifically, Rayleigh distribution and its' modifications are the most used, even though they all overestimate the probability of the higher waves in a sea state (Sobey, 1992). As noted in (Tayfun and Fedele, 2007), nonlinear effects are small for wave heights though they may be large for wave crests. In relation to these, the average time interval between crest and trough of a wave is also considered, but in Naess (1989) it is suggested that it is not of great importance. For narrow banded spectra or unity correlations, Rayleigh-like distributions reduce into the conventional Rayleigh. (Casas-Prat, et al., 2010) suggest that the conventional Rayleigh distribution under predicts by 3% the normalized crest heights and predicts well the trough depths measured by the buoys.