The Probability Density Estimation of Wave Direction Data in Korea

Abstract

Although wave direction is important information along with wave height and period, distribution estimation studies have been limited to traditional schematic analysis, including rose diagrams. In addition, studies on the estimation of the distribution function of wave direction are relatively insufficient compared to wave height and period distribution. In this study, estimations of basic statistical information and the distribution function were performed using hourly wave direction data at 16 points in the last 4 years (2016-2019) measured by the KMA (Korea Meteorological Administration) buoy. The von Mises Mixture (VMM) distribution function was used to estimate the directional data distribution, and the optimal parameters for each order were estimated using the EM algorithm. The optimal order was selected based on Bayesian Information Criterion (BIC), and generally, 4-5 VMM distribution functions were identified as the optimal distribution functions (70%). The optimal VMM distribution function was compared with the histogram and the non-parametric method for Kernel Density estimation. In addition, quantitative analysis was performed on the temporal change pattern of the mean and standard deviation of the direction data corresponding to a representative statistical measure. As a result of the analysis, it was found that a multimodal distribution was appropriate for estimating wave direction according to the overall stations and times. Therefore, one representative wave direction and standard deviation information was found to be insufficient for estimating the distribution type, and the parameters (weighting coefficient, mean, and variance) of the VMM model were found to be more effective for estimating the distribution type. The results of this study can be used in various fields of coastal engineering that require the input of wave information (coastal transport and predominance of design waves).