Predicting Nonlinear Wave Trough Distributions Utilizing A Transformed Linear Simulation Method

This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial and calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave trough distributions of a nonlinear sea state with the surface elevation data measured at the coast of Yura in the Japan Sea, and its accuracy and efficiency are convincingly validated by comparisons with the results from two theoretical distribution models, from a linear simulation model and a second-order nonlinear simulation model. Finally, it is further demonstrated in this paper that the new approach can be applied to all the situations characterized by similar nondimensional spectrum.     

Modified Rayleigh Distribution of Wave Heights in Transitional Water Depths

This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The proposed new method has been applied for calculating the wave height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform. It is demonstrated in this case that the proposed new method can offer better predictions than those by using the conventional Rayleigh wave height distribution model. The proposed new method has been further applied for calculating the total horizontal loads on a generic jacket, and its accuracy has once again been substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh model can be utilized as a promising alternative to the well-established nonlinear wave height distribution models.     

Modified Rayleigh distribution of wave heights in transitional water depths

This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The proposed new method has been applied for calculating the wave height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform. It is demonstrated in this case that the proposed new method can offer better predictions than those by using the conventional Rayleigh wave height distribution model. The proposed new method has been further applied for calculating the total horizontal loads on a generic jacket, and its accuracy has once again been substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh model can be utilized as a promising alternative to the well-established nonlinear wave height distribution models.     

On the long-term joint distribution of characteristic wave height and period and its application

By analysing the scatter diagrams of characteristic the wave height H and the period T on the basis of instrumental data from various ocean wave stations, we found that the conditional expectation and standard deviation of wave period for a given wave height can be better predicted by using the equations of normal linear regression rather than by those based on the log- normal law. The latter was implied in Ochi' s bivariate log-normal model(Ochi. 1978) for the long-term joint distribution of H and T. With the expectation and standard deviation predicted by the normal linear regression equations and applying proper types of distribution, we have obtained the conditional distribution of T for given H. Then combining this conditional P(T / H) with long-term marginal distribution of the wave height P(H) we establish a new parameterized model for the long-term joint distribution P(H,T). As an example of the application of the new model we give a method for estimating wave period associated with an extreme w     

The physical simulation of wave groups and their variations in a wave flume

The physical simulation method of wave groups in a wave flume is proposed and verified by the exper- iments. The experimental results demonstrate that random waves with desired wave groupiness, which simultaneously includes the wave group height and length, can be generated satisfactorily at the specified position in a wave flume using the proposed method. Furthermore, the transformation properties of the wave groupiness along the fiat-bottomed wave flume are investigated based on the physically simulated waves. Associated proposals with the physical simulation of wave groups are given.     

Correlation of extreme waves and water levels using a third-generation wave model and a 3D flow model

A procedure to correlate extreme wave heights and extreme water levels in coastal waters using numerical models together with joint probability analysis has been proposed. A third-generation wave model for wave simulation and a three-dimensional flow model for water level simulation are coupled through the surface atmospheric boundary layer. The model has been calibrated and validated against wind, wave and water level data collected in the coastal waters of Hong Kong. The annual maximum wave height and the concomitant water level have been obtained by simulating the annual extreme typhoon event for 50 consecutive years. The results from bivariate extreme value analysis of the simulated data show that the commonly used empirical method may lead to underestimation of the design water level.     

一种改进的随机起伏海面的仿真方法

根据线性滤波器模型的基本原理,提出了一种改进的基于高阶滤波器的随机起伏海面仿真方法.利用Pierson的半经验海浪谱模型,得到了各种不同风速条件下海面随机起伏的仿真结果,并且对仿真结果进行了比较和讨论,结果表明,利用高阶滤波器方法能更加准确地仿真不同风速下的实际海面、更好地再现随机起伏海面的海浪谱特征.这一方法的提出为海浪的物理模拟实验提供了更为准确的数值计算方法,也为研究目标与海面共存条件下高频地波雷达信号的回波特性提供了更好的数值仿真平台.     

Verification of significant wave representation method

The significant wave representation method is the simplest method for computing the transformation of significant wave height across-shore. However, many engineers are reluctant to use this method because many researchers have pointed out that the method possibly contains a large estimation error. Nevertheless, Rattanapitikon et al. [Rattanapitikon, W., Karunchintadit, R., Shibayama, T., 2003. Irregular wave height transformation using representative wave approach. Coastal Engineering Journal, JSCE 45(3), 489–510.] showed that the wave representation method could be used to compute the transformation of root mean square wave heights. It may also be possible to use it for computing the significant wave height transformation. Therefore, this study was carried out to examine the possibility of simulating significant wave height transformation across-shore by using the significant wave representation method. Laboratory data from small- and large-scale wave flumes were used to calibrate and examine the models. Six regular wave models were applied directly to irregular waves by using the significant wave height and spectral peak period. The examination showed that three regular wave models (with new coefficients) could be used to compute the significant wave height transformation with very good accuracy. On the strength of both accuracy and simplicity of the three models, a suitable model is recommended for computing the significant wave height transformation. The suitable model was also modified for better predictions. The modified model (with different coefficients) can be used to compute either regular wave height or significant wave height transformation across-shore.     

Wave energy assessment based on trivariate distribution of significant wave height,mean period and direction

Based on the Vine copula theory, a trivariate statistical model of significant wave height, characterized wave period and mean wave direction was constructed. To maintain the properties of the different types of variables, a special copula function was derived from the model developed by Johnson and Wehrly based on the maximum entropy principle. It was then combined with the Archimedean copulas to construct the proposed model. An effective algorithm for generating corresponding joint pseudo-random numbers was also developed. Statistical analysis of hindcast data for the significant wave height, mean wave period, and direction, which were collected from an observation point in the North Atlantic every three hours from 1997 to 2001, was performed. The marginal distributions of the significant wave height and mean wave period were fitted by a modified maximum entropy distribution, and the mean wave direction was fitted by a mixture of von Mises distributions. It was shown that the proposed model is a good fit for the data. The seasonal wave energy resources in the target area were assessed using the model estimates. Histograms of the directional wave energy, wave energy roses, and scatter and energy diagrams were presented.     

Statistical simulation of wave climate and extreme beach erosion

Recent developments in extreme values modelling have been used to develop a framework for determining the coastal erosion hazard on sandy coastlines. This framework quantitatively reproduced the extreme beach erosion volumes obtained from field measurements at Narrabeen Beach, Australia. This encouraging finding was achieved using Kriebel and Dean's [Kriebel, D.L. and Dean, R.G., 1993. Convolution method for time-dependent beach profile response. Journal of Waterway, Port, Coastal and Ocean Engineering, 119(2): 204–226.] simple beach erosion and accretion model. The method includes allowances for joint probability between all basic erosion variates including; wave height, period and direction, event duration, tidal anomalies and event spacing. A new formulation for the dependency between wave height and period has been developed. It includes the physical wave steepness limitation. Event grouping, where significantly more erosion can occur from two closely spaced storms is handled by temporally simulating the synthetic wave climate and the resulting beach erosion and accretion.     

满足给定数字特征和谱的随机信号的产生

本文给出了满足给定数字特征和谱的随机序列的产生方法，即用无记忆非线性变换实现非正态随机信号的模拟．该法与Ｇｕｊａｒ法相比较，放宽了变量概率分布的限制，只要求变量矩的存在。同时考虑无记忆非线性变换对谱的影响，用异于Ｌｉｕ的方法在频域上求解输入正态分布随机序列的谱．     

The distribution of zero-crossing wave heights and periods in a stationary sea state

Existing theoretical distributions of wave height and period do not reflect measured joint distributions from field data. A simulation methodology is introduced to retain the essential features of the theoretical background in Gaussian random noise but to avoid further compromising assumptions in the interpretation of height and period in the amplitude domain. A joint distribution can be associated directly with an empirical or measured variance spectrum. Spectral shape appears to dominate the detail of predicted joint distributions. There is generally a much sharper decay in probability levels at higher periods than is predicted by theoretical models. For Jonswap spectra, there is a dominant central ridge and a distinct bimodal structure in the joint distribution, features that are not evident in symmetric Gaussian spectral forms. The wave height distributions for Jonswap spectra differ little from the Rayleigh distribution, except at extreme wave heights where Rayleigh overpredicts. The period distributions are strongly sensitive to spectral shape. In the conditional distribution of periods, given the height, the asymptotic median period at extreme wave heights is significantly longer than the mean period for Jonswap spectra, but not for symmetric Gaussian forms.     

Physical simulation of multidirectional irregular wave groups

Real waves are multidirectional waves.In the present study,the calculation method for the wave maker driving signals for generating multidirectional wave groups in physical wave basin is proposed.Its validity is first confirmed by a numerical model for which the incident boundary condition is determined by use of the proposed method.Then,the physical simulation of multidirectional wave groups is performed in laboratory wave basin.The experimental results show that multidirectional waves with expected wave groupiness,which includes not only its group height but also its group length,can be satisfactorily generated at the specified position in the physical wave basin.     

渤海和黄海北部波高与周期联合分析

分析波高与周期的联合分布特征对于海洋平台设计、海洋工程建筑等有着重要的意义。基于SWAN模型模拟的波浪后报数据对渤海和黄海北部1999~2018年的波浪特征进行了统计分析。分别对20年的波高和周期数据进行了统计分析,得到了研究区域20年有效波高和波周期的季平均值和最大值的区域分布特征。然后以散布图的形式刻画了整个区域20年波高和周期的联合分布特征。为了更深入地研究波高和周期的联合分布规律,选择了两个研究点A1和A2,A1在渤海内部相对近岸,A2在黄海北部深海区。统计结果表明,在A1和A2,波高与周期的联合分布特征较为相似,均呈现斜三角形的分布特征,然而大波高大周期的波浪却呈现不同的分布特征。最后,利用20年的波浪后报数据,在A1和A2点构建了有效波高和谱峰周期的联合概率模型,并采用IFORM法得到了50年、100年和200年重现周期的环境等值线,为研究海域海上结构物的可靠性设计提供了参考。     

日照帆船港港域波高的数值计算

考虑波浪的浅水变化、折射、绕射、反射和破碎等现象的影响,以文氏谱作为输入谱,建立了浅水区域随机波浪传播变形的改进数值模型。对日照帆船港港域波高的数值计算结果表明:在没有越浪的情况下,计算值与物理模型试验观测值吻合。改进的数值模型成为求解港口水域波高的1种有效方法。     

Estimation of Design Wave Height for the Waters around the Korean Peninsula

Long term wave climate of both extreme wave and operational wave height is essential for planning and designing coastal structures. Since the field wave data for the waters around Korean peninsula is not enough to provide reliable wave statistics, the wave climate information has been generated by means of long-term wave hindcasting using available meteorological data. Basic data base of hindcasted wave parameters such as significant wave height, peak period and direction has been established continuously for the period of 25 years starting from 1979 and for major 106 typhoons for the past 53 years since 1951 for each grid point of the North East Asia Regional Seas with grid size of 18 km. Wind field reanalyzed by European Center for Midrange Weather Forecasts (ECMWF) was used for the simulation of waves for the extratropical storms, while wind field calculated by typhoon wind model with typhoon parameters carefully analyzed using most of the available data was used for the simulation of typhoon waves. Design wave heights for the return period of 10, 20, 30, 50 and 100 years for 16 directions at each grid point have been estimated by means of extreme wave analysis using the wave simulation data. As in conventional methodsi of design criteria estimation, it is assumed that the climate is stationary and the statistics and extreme analysis using the long-term hindcasting data are used in the statistical prediction for the future. The method of extreme statistical analysis in handling the extreme events like typhoon Maemi in 2003 was evaluated for more stable results of design wave height estimation for the return periods of 30–50 years for the cost effective construction of coastal structures.     

Transformation model of wave height distribution on planar beaches

A new probability density function (pdf) for the transformation of depth-limited wave height distributions is presented. Assuming the bore approach for modeling the energy dissipation in the inner surf zone to be valid, an analytical expression for the transformation of wave height distribution including shoaling and breaking on a planar beach is obtained. The resulting expression for the pdf is formulated with a single function and only one shape parameter, which is calibrated as a function of the local root-mean-square (rms) wave height-to-water depth ratio and the local Iribarren number. The transformed pdf is able to reproduce the shape of field and laboratory measured wave height histograms and the sharp change in the shape of the wave height distribution in depth-limited breaking conditions for low exceedance probability. Results show that the theory is appropriate to represent wave height distribution transformation over shallow foreshores or in the surf zone. Alternatively, a combination of the new model with existing state-of-the-art wave energy propagation models allows the complete definition of the wave height distribution transformation on a planar beach.     

复杂地形下海浪数值模式的特征线计算格式

LAGFD-WAM海浪数值模式是一种第三代海浪数值模式，通过求解波数谱平衡方程，并考虑风输入、波浪破碎耗散、底摩擦耗散、波波非线性相互作用和波流相互作用等源函数，模拟波数空间下的海浪方向谱，并依此获得海浪的波高、周期和平均波向。该模式的一个显著特点是采用特征线嵌入格式求解海浪的传播。在进行浅水区域的海浪模拟时，特征线嵌入格式的数值计算方案是否合理对海浪数值模拟结果产生直接的影响。为此LAGFD-WAM海浪数值模式提出了一种新的特征线混合数值计算格式，并应用于浅水海浪数值模拟。结果表明，采用该计算方法，能够使数值模拟结果与实测结果很好符合。     

Response cumulant analysis of a linear oscillator driven by Morison force

A frequency-domain cumulant spectral analysis method is developed in this study to estimate the higher-order statistics of the linear oscillator responses driven by Morison wave force. The fourth-order cumulant function of the nonlinear drag force is formulated in terms of the autocorrelation functions of water particle velocity. Price's theorem is applied to evaluate the associated higher-order joint moments. Three-dimensional Fourier Transforms are employed to obtain the trispectra of Morison force and oscillator responses. The estimated force and response kurtosis are in good agreement with those obtained from time-domain simulations; while the proposed method is found to be much more efficient. The numerical results also show that the drag force cubicization based on the least square approximation results in an overestimation of the kurtosis values; in addition, it is necessary to include the joint moments of order higher than eighth.     

Wave hindcasting by coupling numerical model and artificial neural networks

By coupling numerical wave model (NWM) and artificial neural networks (ANNs), a new procedure for wave prediction is proposed. In many situations, numerical wave modeling is not justified due to economical consideration. Although incorporation of an ANN model is inexpensive, such a model needs a long time period of wave data for training, which is generally inconvenient to achieve. A proper combination of these two methods could carry the potentials of both. Based on the proposed approach, wave data are generated by a NWM by means of a short period of assumed winds at a concerned point. Then, an ANN is designed and trained using the above-mentioned generated wind-wave data. This ANN model is capable of mapping wind-velocity time series to wave height and period time series with low cost and acceptable accuracy. The method was applied for wave hindcasting to two different sites; Lake Superior and the Pacific Ocean. Simulation results show the superiority of the proposed approach.