• 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 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 Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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• pp.376-381
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• 2003

The reliability analysis of overtopping probability is proposed. In order to estimate the expected overtopping probability of the rubble mound breakwater, the experimental results of individual wave runup height is applied for the analysis of irregular wave system. The joint distribution of wave heights and periods is used for the input data of runup calculation because the runup height depends on the wave height and period. The runup heights during the one event that the design wave attacks the rubble mound breakwater extend to the one life cycle of 60 years. Utilizing the Monte-Carlo method, the one life cycle is tried more about 60 times for obtaining the expected value of overtopping probability. It is found that the inclusion of the variability of wave tidal and wave steepness has great influence on the computation of the expected overtopping probability of rubble mound breakwater. The previous design disregarding the tidal fluctuation largely overestimates or underestimates the expected overtopping probability depending on tidal range and wave steepness.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.4
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• pp.204-210
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• 1998

This paper presents the development of the probability density function applicable for wave heights (peak-to-trough excursions) in finite water depth including shallow water depth. The probability distribution applicable to wave heights of a non-Gaussian random process is derived based on the concept of the maximum entropy method. When wave heights are limited by breaking wave heights (or water depth) and only first and second moments of wave heights are given, the probability density function developed is closed form and expressed in terms of wave parameters such as $H_m$(mean wave height), $H_{rms}$(root-mean-square wave height), $H_b$(breaking wave height). When higher than third moment of wave heights are given, it is necessary to solve the system of nonlinear integral equations numerically using Newton-Raphson method to obtain the parameters of probability density function which is maximizing the entropy function. The probability density function thusly derived agrees very well with the histogram of wave heights in finite water depth obtained during storm. The probability density function of wave heights developed using maximum entropy method appears to be useful in estimating extreme values and statistical properties of wave heights for the design of coastal structures.

• 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.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.1
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• pp.88-93
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• 1994

This study is concerned with an analytic derivation of the probability density function applicable for wave heights in finite water depth using two different methods. As the first method of the study, a probability density function is developed by applying a series of polynomials which is orthogonal with respect to Rayleigh probability density function. The newly derived probability density function is compared with the histogram constructed from wave data obtained in finite water depth which indicate strong non-Gaussian characteristics. Although the probability density represents the histogram very well. it has negative density at large values. Although the magnitude of the negative density is small. it negates the use of the distribution function fer estimating extreme values. As the second method of the study, a probability density function of wave height is developed by applying the maximum entropy method. The probability density function thusly derived agrees very well with the wave height distribution in shallow water, and appears to be useful in estimating extreme values and statistical properties of wave heights in finite water depth. However, a functional relationship between the probability distribution and the non-Gaussian characteristics of the data cannot be obtained by applying the maximum entropy method.

• 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.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.22 no.2
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• pp.120-125
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• 2010

A Monte-Carlo simulation method is proposed which can take uncertainties of scale and location parameters of Gumbel distribution into account straightforwardly in evaluating significant design wave heights with respect to return periods. The uncertainties of design wave heights may directly depend on the amounts of uncertainties of scale parameter and those distributions may be followed by Gumbel distribution. In case of that the expected values of maximum significant wave height during lifetime of structures are considered to be the design wave heights, more uncertainties are happened than in those evaluated according to return periods with encounter probability concepts. In addition, reliability analyses on the armor units are carried out to investigate into the effects of the uncertainties of design wave heights on the probability of failure. The failure probabilities of armor units to 5% damage level for 50 return periods are evaluated and compared according to the methods of taking uncertainties of design wave heights into account. It is found that the probabilities of failure may be distributed into wide ranges of bounds when the uncertainties of design wave heights are assumed to be same as those of annual maximum significant wave heights.

• Journal of the Society of Naval Architects of Korea
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• v.33 no.1
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• pp.145-152
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• 1996

In this study, the technique to evaluate the extreme design wave height of certain return period is developed from the given measured or hindcasted sea state data of concerned area for limited period. By using the order statistics and Monte Carlo Simulation method, the best fit probability distribution function with proper parameters describing the given wave height data is chosen, from which extreme design wave height can be predicted by extrapolation to the desired return period. The fitness and the confidence limit of the chosen probability function are also discussed. Application calculation is carried out for the wave height data given by applying the Wilson wave model theory to major 50 typhoon wind data affecting Korean South coast during the year from 1938 to 1987.

• 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.