Estimation and Assessment on the Optimal Probability Distribution of the Monitoring Wave Height Data in the Korean Coast

The estimation of probability distribution models for wave data enables an understanding of the probabilistic characteristics of wave conditions and the quantitative evaluation of engineering design variables. In this study, the optimal probability distributions were fitted using by significant wave height data observed at 20 points around the Korean coast, and the probabilistic characteristics and tail behaviors of the data were analyzed. A total of nine distribution models were considered, including the Normal, Log-normal, Weibull-3, Gamma-3, Generalized Gamma, Generalized Beta-2, Johnson SB, Generalized Hyperbolic, and Extended Generalized Inverse Gaussian distributions. The parameters for each distribution were estimated using the Maximum Likelihood Estimation (MLE) method. To evaluate the performance of each model, goodness-of-fit tests such as the Kolmogorov–Smirnov test and the Kullback–Leibler divergence metric were used, and Q-Q plots were employed to assess the fit in the tail regions of the distributions. As a result, the Generalized Hyperbolic, Johnson SB, and Generalized Gamma distributions showed high goodness-of-fit at many stations. Distributions with multiple shape parameters were found to effectively capture the asymmetry and tail characteristics of the significant wave height data. However, some distribution models tended to underestimate or overestimate the extreme quantile regions. Therefore, it is considered appropriate to select and apply the probability distribution model that best fits the wave data at each target site in order to more accurately describe the characteristics of significant wave heights.