Estimation of Relations between Represenatative Wave Heights using Measured Wave Data in the West Sea of Korea

Abstract

As the distribution of individual wave heights for irregular waves, the Rayleigh distribution was first introduced by Longuet-Higgins. The relations between representative wave heights were proposed 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 the applicability in the shallow water with the nonlinearity. Thus in this study, individual wave heights were calculated using the water level data (2013.08.01~31) obtained from the HeMOSU-1 offshore met-mast. The zero-up crossing method was used to define individual waves, and the Kolmogorov-Smirnov (K-S) test was used for Goodness-of-Fit of the Rayleigh distribution for the individual wave heights. Besides representative wave heights such as the highest wave, the significant wave, the highest one-tenth wave, the mean wave, and the root mean square wave were calculated using the individual waves for 20 minutes. Relations between representative wave heights were estimated and compared with the theoretical relations. As a result, about 68.6% of the 2016 data sets were found to follow the Rayleigh distribution. Notably, it was shown that the measured data during typhoon Kong-rey (Typhoon no. 201315) did not follow the Rayleigh distribution because the typhoon invasion from August 30 to 31 caused the wavelength to become longer and the relative water depth to become shallow. Meanwhile, as a result of comparing the theoretical relations with the estimated relations (y = a*x), the error range was from 1.68% to 13.25%. In the future, it was judged that it is necessary to estimate the optimal distribution for the shallow water waves and to properly estimate the relations between representative wave heights using the measured data on the Korean coast.