Lim, C.; Lee, J.L., and Lee, S., 2021. Analyzing wave height and direction using the Rayleigh distribution function. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 534–538. Coconut Creek (Florida), ISSN 0749-0208.
As erosion changes the shape of the shoreline of South Korea, many studies have been conducted to analyze the accurate shape of the shoreline. While many factors contribute to the change of the shoreline, one of the top contributing factors is the change in wave direction. However, accurate measurements of the wave direction were not possible until recently, and studies on the wave direction are insufficient compared to the studies on the wave height and period. Although long-term wave observation data is required to analyze waves, only short-term observation data is available in Korea because observation systems have been established in Korea since 2001. Therefore, the distribution characteristics of wave direction and wave height were analyzed using long-term wave hind-cast data provided by NOAA data. It is not straightforward to find regular characteristics that determine the annual average wave direction distribution from the NOAA data. However, if the wave direction is analyzed by season, an asymmetric distribution characteristic with respect to the main direction can be found. The wave directions of four seasons in the East Sea were very similar (summer: 50°/winter: 35°), while those in the West Sea were very different (summer: 205°/winter: 300°). In this study, it was assumed that the wave height and wave direction are independent of each other. Furthermore, it was also assumed that the wave height in each wave direction has the Rayleigh distribution to propose a wave height distribution function. The Rayleigh distribution function was modified by introducing the wave direction spreading coefficient, which controls the peak, and the distribution area coefficient, which reflects the energy of each wave direction component. Finally, this function was compared with NOAA data of the East Sea and West Sea of South Korea to verify the applicability.