• 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.

• Journal of the Korean Society for Marine Environment & Energy
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• v.12 no.2
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• pp.61-67
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• 2009

In this paper time series wave data which contain a freak wave is investigated. Various wave characteristics are compared between wave data with a freak wave and without. Among 24 hour wave data measured in the Yura Sea, two adjacent 30 min wave data with and without a freak wave are examined intensively. It is seen that the highest waves do not have the longest wave period. The wave period of the longest period waves is a little longer than the average wave period and much shorter than the significant wave period. Although the sea state is quite high, the Rayleigh distribution fits well to the probability of wave height. The characteristics of the wave spectra do not change much, but the nonlinearity increases for the wave data with a freak wave. The significant wave height without a freak wave is larger than that with a freak wave. Hence, the higher significant wave height does not always increase the probability of the occurrence of the freak waves.

• 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 Power System Engineering
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• v.13 no.2
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• pp.63-70
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• 2009

This paper discusses the influence on long-tenn predictions of the ship response in ocean by using the Global Wave Statistics data, GWS, and wave information from the remote sensing satellites. GWS's standard scatter diagrams of significant wave height and zero-crossing wave period are suggested to be corrected to a round number of 0.01/1000 fitted with a statistical analytic model of the conditional lognormal distribution for zero-crossing wave period. The GEOSAT satellite data are utilized which presented by I. R. Young and G. J. Holland (1996, named as GEOSAT data). At first, qualities of this data are investigated, and statistical characteristic trends are studied by means of applying known probability distribution functions. The wave height data of GEOSAT are compared to the data observed onboard merchant ships, the data observed by measure instrument installed on the ocean-going container ship and so on. To execute a long-tenn prediction of ship response, joint probability functions between wave height and wave period are introduced, therefore long-term statistical predictions are executed by using the functions.

• 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 Ocean Engineering and Technology
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• v.27 no.1
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• pp.102-108
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• 2013

In this paper time series wave data, which were measured at the Draupner platform in the North Sea on 1995, are used to investigate statistical characteristics of nonlinear wave. Various statistical properties based on time and frequency domain are examined. The Gram-Chalier distribution fits the probability of wave elevation better than the Gaussian distribution. The skewness of wave profile is 0.393 and the kurtosis is 4.037 when the freak wave is occurred. The nonlinearity of D1520 data is higher than two adjacent wave data. AI index of the New Year Wave is 2.11 and the wave height is 25.6m. The zero crossing wave period of the New Year Wave is 12.5s which is compared to the average zero up-crossing period 11.3s. The significant steepness of wave data is 0.077 when the freak wave was occurred. H1/3/${\eta}_s$ does not increases as the kurtosis increases and the values is close to 4. The New Year Wave belongs to highly nonlinear wave data packet but the AI index is within linear focusing range.

• Journal of Ocean Engineering and Technology
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• v.34 no.1
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• pp.26-36
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• 2020

An extreme value analysis of metocean data which include wave, wind, and current data is a prerequisite for the operation and survival of offshore structures. The purpose of this study was to provide information about the return wave, wind, and current values for the Barents Sea using extreme value analysis. Hindcast datasets of the Global Reanalysis of Ocean Waves 2012 (GROW2012) for a waves, winds and currents were obtained from the Oceanweather Inc. The Gumbel distribution, 2 and 3 parameters Weibull distributions and log-normal distribution were used for the extreme value analysis. The least square method was used to estimate the parameters for the extreme value distribution. The return values, including the significant wave height, spectral peak wave period, wind speed and current speed at surface, were calculated and it will be utilized to design offshore structures to be operated in the Barents Sea.

• Journal of the Korean Society for Marine Environment & Energy
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• v.7 no.3
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• pp.137-145
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• 2004

Long-term wave distribution at Jeju sea is investigated by a numerical simulation based on the thirdgeneration wave model SWAN (Simulating WAves Nearshore). The Jeju sea which retains relatively high wave energy density among Korean coastal regions is considered to be a suitable site for wave power generation and the efficiency of wave power generation is closely related to local wave characteristics. The monthly mean of a large-scale long-term wave data from 1979 to 2002, which is provided by Korea Ocean Research & Development Institute. is used as the boundary condition of SWAN model simulation with 1km grid. An analysis of wave distribution concentrates on the seasonal variation and spatial distribution of significant wave heights, mean wave directions and mean wave periods. Significant wave heights are higher in winter and summer and the west sea of Jeju appears relatively higher than east's. The highest significant wave height occurs at the northeast sea in winter and the second highest significant wave height appears at the southeast sea in summer, while the significant wave heights in spring and autumn are relatively low but homogeneous. The distribution of wave directions reveals that except the rear region influenced by wave refraction, the northwest wave direction is dominant in summer and the southeast in winter. Wave periods are longer in summer and winter and the west sea of Jeju appears relatively longer than east's. The longest wave period occurs at the west sea in winter, and in summer it appears relatively homogeneous with a little longer period at the south sea.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.2
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• pp.75-82
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• 1990

A Wave transformation including wave breaking in shallow water region is a non-linear and discontinuous Phenomenon. Therefore, a so-called individual wave analysis (or a wave by wave analysis) rather than spectral approach seems to be adequate to investigate the wave transformation in such regions. In this study, a theoretical joint distribution of wave height, period and wave direction of zero-down crossing waves, which is required in the individual wave analysis in the shallow water region, is derived based on the hypothesis that sea surface is a Gaussian stochastic process and that a band-width of energy spectra is sufficiently narrow. The derived i oint distribution is found to be an effective measure to investigate characteristics of three-dimensional random wave field in shallow water through field measurements.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.31 no.3
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• pp.115-128
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• 2019

In this study, a probabilistic model for the estimation of yearly workable wave condition period for offshore operations is developed. In doing so, we first hindcast the significant wave heights and peak periods off the Ulsan every hour from 2003.1.1 to 2017.12.31 based on the meteorological data by JMA (Japan Meterological Agency) and NOAA (National Oceanic and Atmospheric Administration), and SWAN. Then, we proceed to derive the long term significant wave height distribution from the simulated time series using a least square method. It was shown that the agreements are more remarkable in the distribution in line with the Modified Glukhovskiy Distribution than in the three parameters Weibull distribution which has been preferred in the literature. In an effort to develop a more comprehensive probabilistic model for the estimation of yearly workable wave condition period for offshore operations, wave height distribution over the 15 years with individual waves occurring within the unit simulation period (1 hour) being fully taken into account is also derived based on the Borgman Convolution Integral. It is shown that the coefficients of the Modified Glukhovskiy distribution are $A_p=15.92$, $H_p=4.374m$, ${\kappa}_p=1.824$, and the yearly workable wave condition period for offshore work is estimated to be 319 days when a threshold wave height for offshore work is $H_S=1.5m$. In search of a way to validate the probabilistic model derived in this study, we also carry out the wave by wave analysis of the entire time series of numerically simulated significant wave heights over the 15 years to collect every duration periods of waves the height of which are surpassing the threshold height which has been reported to be $H_S=1.5m$ in the field practice in South Korea. It turns out that the average duration period is 45.5 days from 2003 to 2017, which is very close to 46 days from the probabilistic model derived in this study.