Joint Probability Distribution of Significant Wave Height and Peak Wave Period using Gaussian Copula Method

Abstract

In this study, the joint probability distribution was calculated using the significant wave height and peak wave period observed at the HeMOSU oceanographic and meteorological observation tower located on the west coast of Korea. Representative wave parameters such as significant wave height and peak wave period show a high correlation between the two variables, and it is required in various fields to express the contour-line (CL) for the target exceedance probability under the condition of considering these correlation characteristics. In the case of waves, the design frequency level, the return period of 5, 10, 20, 30, 50, and 100 years, the frequency is calculated according to the data used to calculate the CL. To calculate this CL, it is necessary to 1) calculate the optimal probability density distribution for each wave variable, and 2) calculate the joint probability distribution using methods such as copula and I-FORM. In this study, a Gaussian copula among the copula method was used. To estimate the fitted probability density function of each wave variable, the most widely used Maximum Likelihood Estimation was used. The optimal probability density function of each wave variable was estimated by applying the ‘Normal’, ‘Lognormal’, ‘Gamma’, ‘Weibull-3P’ distribution for the significant wave height and the ‘Normal’, ‘Lognormal’, ‘Gamma’ distribution for the peak period. Meanwhile, the KS test (KolmogorovSmirnov Test) and KL Divergence (Kullback-Leibler Divergence) were used to perform the distribution fit test. The correlation coefficient between the significant wave height and peak period observed in HeMOSU was 0.77, the significant wave height was Log-Normal distribution and the peak period was Normal distribution. It was found that this method can be applied (excluding the introduction of physical boundary conditions) even when information on correlation is absent along with data sets such as wind speed and wave height where high correlation is expected.