Modelling Significant Wave Height Data of North Sea: Rayleigh vs Weibull Distribution

Abstract

Significant wave height is generally defined as the mean height of the highest one third of the waves in the sample and is widely regarded as an approximate equivalent to the visually observed height. Some studies assumed that wave heights can be described in terms of Log-normal, Generalized Gamma and Beta distribution, while others proposed Rayleigh distributions. In this paper, we wish to compare Rayleigh distribution with those obtained using two-parameter Weibull distributions. Both Rayleigh and Weibull distributions are used to fit the empirical data obtained from the world's oceans Global Wave Statistics. The Rayleigh distribution parameter is estimated using Maximum Likelihood Estimation (MLE) while, for the two-parameter Weibull distribution, parameter values are obtained using Maximum Likelihood Estimation and Quantile Estimation (QE). A Chi-square goodness of fit test is then used to see how the fitted distributions compare with the empirical distribution. It is found that Weibull distributions are better fits than the Rayleigh distribution, and that the MLE estimation is the best in this respect.