Ko, D.-H.; Lee, U.-J.; Cho, H., and Lee, B.W., 2021. Estimation of relations between representative wave heights using measured wave data for the west sea of Korea. 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. 51–55. Coconut Creek (Florida), ISSN 0749-0208.
The Rayleigh distribution was first defined as the distribution of individual wave heights for irregular waves. The relationships between representative wave heights have since been determined by manipulating the probability density function of the Rayleigh distribution. However, since the Rayleigh distribution is based on the linear wave theory assumption for narrow-band spectra, it is necessary to examine its applicability to shallow water. Thus, in this study, individual wave heights were calculated using water surface elevation data (2013.08.01 - 31) obtained from the HeMOSU-1 offshore measurement tower. The zero-up crossing method was used to define individual waves, and representative wave heights of highest, significant, highest one-tenth, mean, and root mean square waves were calculated using individual waves for 20 minutes. The Kolmogorov-Smirnov (K-S) test was used to determine the goodness of fit of the Rayleigh distribution for individual wave heights. Relationships between representative wave heights were also estimated and compared to the theoretical relationships. Approximately 91% of the total data did not follow the Rayleigh distribution. Meanwhile, the estimated coefficients of relationships (y = α × x) were compared to theoretical coefficients. The estimates obtained are greater than the theoretical estimates derived from the Rayleigh distribution with an error range of 1.68% to 13.25%.