• Journal of the Korean Society for Marine Environment & Energy
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• v.13 no.2
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• pp.112-120
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• 2010

In this paper time series wave data measured continuously for 24 hours during a storm in Yura Sea Area are used to investigate statistical characteristics of nonlinear waves. The exceedance probability of wave height is compared using the Rayleigh distribution and the Edgeworth-Rayleigh (ER) distribution. Wave data which show stationary state for 10 hours contain 4600 waves approximately. The Gram-Chalier distribution fits the probability of wave elevation better than the Gaussian distribution. The Rayleigh ($H_{rms}$) distribution follows the exceedance probability of wave height in general and predicts the probability of freak waves well. The ER distribution overpredicts the exceedance probability of wave heights and the occurrence of freak waves. If wave data measured for 30 minute period which contains 250 waves are used, the ER distribution can predict the occurrence probability of freak waves well. But it overpredicts the probability of overall wave height If no freak wave occurs, the Rayleigh ($H_{rms}$) distribution agrees well with wave height distribution for the most of wave height ranges. The wave height distribution of freak waves of which height are less than 10 m shows similar tendency compared with freak waves greater than 10 m. The value of $H_{max}/H_{1/3}$ is related to the kurtosis of wave elevation. It seems that there exists threshold value of the kurtosis for the occurrence of freak waves.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.367-372
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• 2006

If the sea is narrowband, the Rayleigh distribution introduced by Longuet-Higgins can be used for the individual wave height distribution. However the Rayleigh distribution over-predicts the probability of high waves. Longuet-Higgins introduced alternative form of the Rayleigh distribution with an empirical constant. The wave height distribution can be fitted well by one parameter Rayleigh distribution with a proper choice of the empirical constant. The empirical constant is the ratio of the significant wave height based the time domain analysis and the spectral analysis. Here we examine wave data which contain extreme waves. Once again we confirmed that extreme wave height distribution can be modelled well by a modified Rayleigh distribution.

• Water for future
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• v.7 no.2
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• pp.99-106
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• 1974

The records of wave heights which were observed at Muk ho and Po hang of the East Coast of Korea were analized by several probility functions. The exponential 2 parameter distribution was found as the best fit probability function to the historical distribution of wave heights by the test of goodness of fit. But log-normal 2 parameter and log-extremal type A distributions were also fit to the historical distribution, especially in the Smirnov-Kolmogorov test. Therefore, it can't be always regarded that those two distributions are not fit to the wave heiht's distribution. In the test of goodness of fit, the Chi-Square test gave very sensitive results and Smirnov-Kolmogorov test, which is a distribution free and non-parametric test, gave more inclusive results. At the next stage, the inter-relationship between the mean and the one-third wave heights, the mean and the one-=tenth wave heights, the one-third and the one-tenth wave heights, the one-third and the highest wave heights were obtained and discussed.

• International Journal of Ocean System Engineering
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• v.2 no.4
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• pp.250-258
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• 2012

The distribution of wave heights is assumed to be a Rayleigh distribution, based on the assumption of a narrow band and Gaussian distribution of wave elevation. The present study was started with doubts about the narrow band assumption. We selected the wave spectra widely used to simulate irregular random waves. The wave spectra used in this study included the Pierson-Moskowitz spectrum, Bretschneider-Mitsuyasu spectrum, and JONSWAP spectrum. The directionality of the waves was considered. The cosine 2-l type directional spreading function and mixed form of the half-cosine 2-s type with Mitsuyasu type directional spreading are considered here to investigate the effects of a directional spreading function on random waves. The simulated wave height distribution is compared with a Rayleigh distribution.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.31 no.5
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• pp.278-293
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• 2019

The joint distribution of wave height and period has been maltreated despite of its great engineering value due to the absence of any analytical model for wave period, and as a result, no consensus has been reached about the effect of nonlinearity on these joint distribution. On the other hand, there was a great deal of efforts to study the effects of non-linearity on the wave height distribution over the last decades, and big strides has been made. However, these achievements has not been extended to the joint distribution of wave height and period. In this rationale, we first express the joint distribution of wave height and period as the product of the marginal distribution of wave heights with the conditional distribution of associated periods, and proceed to derive the joint distribution of wave heights and periods utilizing the models of Longuet-Higgins (1975, 1983), and Cavanie et al. (1976) for conditional distribution of wave periods, and height distribution derived in this study. The verification was carried out using numerically simulated data based on the Wallops spectrum, and the nonlinear wave data obtained via the numerical simulation of random waves approaching toward the uniform beach of 1:15 slope. It turns out that the joint distribution based on the height distribution for finite banded nonlinear waves, and Cavanie et al.'s model (1976) is most promising.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.479-483
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• 2004

A new calculation method of expected overtopping probability of rubble mound breakwater considering real tide occurrence has been proposed. A calculation method of expected overtopping probability of rubble mound breakwater was proposed by Kweon and Suh (2003). In their calculation, the fluctuation of tidal elevation was expressed by the sinusoidal change that yields the uniform distribution of occurrence frequency. However, the realistic distribution of tidal elevation should influence on the overtopping chance. In this study, the occurrence frequency of tidal elevation obtained from the real sea is included. The tidal elevation used in this study is collected from the east coastal part of Korean peninsular. Analyzing the annual data of the tidal fluctuation measured hourly during 355 days, the distribution of occurrence frequency is formulated utilizing by the normal distribution with one peak. Among the calculation procedures of annual maximum wave height, wave height-period joint distribution, wave run-up height and occurrence frequency of tide, only the annual maximum wave height is again chosen randomly from normal distribution to consider the uncertainty. The others are treated by utilizing the distribution function or relationship itself, It is found that the inclusion of the variability of tidal elevation has great influence on the computation of the expected overtopping probability of rubble mound breakwater. The bigger standard deviation of occurrence frequency is, the lower the overtopping probability of rubble mound breakwater is.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.17 no.3
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• pp.178-187
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• 2005

A reliability analysis model f3r studying the influence of joint distribution of wave heights and periods on wave un-up is presented in this paper. From the definition of failure mode related to wave run-up, a reliability function may be formulated which can be considered uncertainties of water level. In particular, the reliability analysis model can be directly taken into account statistical properties and distributions of wave periods by considering wave period in the reliability function to be a random variable. Also, variations of wave height distribution conditioned to mean wave periods can be taken into account correctly. By comparison of results of additional reliability analysis using extreme distributions with those resulted from joint distribution of wave height and periods, it is found that probabilities of failure evaluated by the latter is larger than those by the former. Although the freeboard of sloped-breakwater structures can be determined by extreme distribution based on the long-term measurements, it may be necessary to investigate additionally into wave run-up by using the present reliability analysis model formulated to consider joint distribution of a single storm event. In addition, it may be found that the effect of spectral bandwidth parameter on reliability index may be little, but the effect of wave height distribution conditioned to mean wave periods is straightforward. Therefore, it may be confirmed that effects of wave periods on the probability of failure of wave run-up may be taken into account through the conditional distribution of wave heights. Finally, the probabilities of failure with respect to freeboard of sloped-breakwater structures can be estimated by which the rational determination of crest level of sloped-breakwater structures may be possible.

• Water for future
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• v.10 no.1
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• pp.101-117
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• 1977

The statatistical characteristics and spectra of sea waves at Mookho were analysed by several statistical methods. As the results, the following conclusions are obtained: 1. Values of surface elevation of sea wave are better fitted to Gram Charlier distribution than Gaussian distribution. This proves that sea waves have not only characters of irregularity but also non-linearity. 2. Distribution of maxima of surface elevation practically follows the distribution of Cartwright and Longuet-Higgins, also spectral width parameter is found to be increased with the increase of root mean square of surface elevation. 3. Sea wave may have spectrum of broad frequency band, however distributions of wave heights and periods follow the Rayleigh distribution which is derived from the assumption of narrow frequency band. 4. Ratios among mean wave heights from observed data show good agreements with theoretical values from Rayleigh distribution. 5. Spectral density and spectral width parameter increase with increase of wind velocity. And wave period at optimum band gas higher value than significant wave period by about 10 percent.

• Journal of Ocean Engineering and Technology
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• v.15 no.3
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• pp.20-27
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• 2001

After using the filtering method, wave parameters are calculated by the spectral analysis and wave by wave analysis. Extreme environments and higher wave characteristics int he Chujeon Sea are analyzed using the observed wave data. Higher wave has been intensely emphasized as an important environmental force parameter in several recent research works. The aims of this study are to summarize the distribution of extreme environment for wind waves, and to find occurrence probability of higher wave in Chujeon Sea. Ocean wave statistics varying with sea state are found to respond linearly to the spectral peakedness parameter Qp, mean run-length and Ursell number. Although the spreading of the field results is large, it may be concluded that the tendency of wave group formation depends on the spectral peakedness parameter Qp. Extreme wave is estimated to apply various model distribution functions by using the monthly maximum significant wave parameters which can be used to the design and analysis of coastal structures.

• Journal of Ocean Engineering and Technology
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• v.18 no.6 s.61
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• pp.8-15
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• 2004

Wave power distribution is investigated to determine the optimal sites for wave power generation at Jeju sea which has the highest wave energy density in the Korean coastal waters. The spatial and seasonal variation of wave power per unit length is calculated in the Jeju sea area based on the monthly mean wave data from 1979 to 2002 which is produced by the SWAN wave model simulation in prior research. The selected favorable locations for wave power generation are compared in terms of magnitude of wave energy density and distribution characteristics of wave parameters. The results suggest that Chagui-Do is the most optimal site for wave power generation in the Jeju sea. The seasonal distribution of wave energy density reveals that the highest wave energy density occurs in the northwest sea in the winter and it is dominated by wind waves, while the second highest one happens at south sea in the summer and it is dominated by a swell sea. The annual average of wave energy density shows that it gradually increases from east to west of the Jeju sea. At Chagui-Do, the energy density of the sea swell sea is relatively uniform while the energy density of the wind waves is variable and strong in the winter.