Comparison of Gev and Weibull Distributions in the Extreme Analysis of Wave Height

Abstract

Deep sea design wave heights for coastal or harbor design works can be determined by seeking the wave heights corresponding to arbitrarily pre-designated return periods through an extreme value analysis for field observed or wave hindcast data. Traditionally, the Weibull distribution with three parameters has been used in the extreme analysis of wave data but is recently being replaced by generalized extreme value (GEV) distribution. In the present study, the applicability of the GEV and Weibull distributions to wave data was analyzed and compared. The  tests with two distributions were conducted on wave data sets of various sizes. The test results showed no significant differences between them. In addition, the upper bound of the reversed Weibull distribution contained in the GEV exceeded the general data range of the wave hindcasts. The GEV can thus be applied to the extreme analysis of waves with the same accuracy as the Weibull distribution. Furthermore, the GEV can take the elapsed time in the data set as a covariate and hence can be easily extended to a non-stationary extreme analysis by employing a maximum likelihood method for parameter estimations.