Evaluation of Inference Adequacy in Cumulative Logistic Regression Models： An Empirical Validation of ISW-Ridge Relationships

Internal solitary wave propagation over a submarine ridge results in energy dissipation, in which the hydrodynamic interaction between a wave and ridge affects marine environment. This study analyzes the effects of ridge height and potential energy during wave-ridge interaction with a binary and cumulative logistic regression model. In testing the Global Null Hypothesis, all values are p<0.001, with three statistical methods, such as Likelihood Ratio, Score, and Wald. While comparing with two kinds of models, tests values obtained by cumulative logistic regression models are better than those by binary logistic regression models. Although this study employed cumulative logistic regression model, three probability functions p^1, p^2 and p^3, are utilized for investigating the weighted influence of factors on wave reflection. Deviance and Pearson tests are applied to check the goodness-of-fit of the proposed model. The analytical results demonstrated that both ridge height (X1) and potential energy (X2) significantly impact (p<0.0001) the amplitude-based reflected rate; the P-values for the deviance and Pearson are all >0.05 (0.2839, 0.3438, respectively). That is, the goodness-of-fit between ridge height (X1) and potential energy (X2) can further predict parameters under the scenario of the best parsimonious model.Investigation of 6 predictive powers (R2, Max-rescaled R2, Somers'D, Gamma, Tau-a, and c, respectively) indicate that these predictive estimates of the proposed model have better predictive ability than ridge height alone, and are very similar to the interaction of ridge height and potential energy. It can be concluded that the goodness-of-fit and prediction ability of the cumulative logistic regression model are better than that of the binary logistic regression model.     

Evaluation of Inference Adequacy in Cumulative Logistic Regression Models: An Empirical Validation of ISW Ridge Relationships

Internal solitary wave propagation over a submarine ridge results in energy dissipation, in which the hydrodynamic interaction between a wave and ridge affects marine environment. This study analyzes the effects of ridge height and potential energy during wave-ridge interaction with a binary and cumulative logistic regression model. In testing the Global Null Hypothesis, all values are p＜0.001, with three statistical methods, such as Likelihood Ratio, Score, and Wald. While comparing with two kinds of models, tests values obtained by cumulative logistic regression models are better than those by binary logistic regression models. Although this study employed cumulative logistic regression model, three probability functions 1, 2 and 3, are utilized for investigating the weighted influence of factors on wave reflection. Deviance and Pearson tests are applied to check the goodness-of-fit of the proposed model. The analytical results demonstrated that both ridge height (X1) and potential energy (X2) significantly impact (p＜0.0001) the amplitude-based reflected rate; the P-values for the deviance and Pearson are all ＞0.05 (0.2839, 0.3438, respectively). That is, the goodness-of-fit between ridge height (X1) and potential energy (X2) can further predict parameters under the scenario of the best parsimonious model.Investigation of 6 predictive powers (R2, Max-rescaled R2, Somers''D, Gamma, Tau-a, and c, respectively) indicate that these predictive estimates of the proposed model have better predictive ability than ridge height alone, and are very similar to the interaction of ridge height and potential energy. It can be concluded that the goodness-of-fit and prediction ability of the cumulative logistic regression model are better than that of the binary logistic regression model.     

Accuracy Evaluation of A Diagnostic Test by Detecting Outliers and Influential Observations

Logit regression analysis is widely applied in scientific studies and laboratory experiments, where skewed observations on a data set are often encountered. A number of problems with this method, for example, oudiers and influential observations, can cause overdispersion when a model is fitted. In this study a systematic statistical approach, including the plotting of several indices is used to diagnose the lack-of-fit of a logistic regression model. The outliers and influential observations on data from laboratory experiments are then detected. Specifically we take account of the interaction of an internal sohtary wave （ISW） with an obstacle, i.e., an underwater ridge, and also analyze the effects of the ridge height, the lower layer water depth, and the potential energy on the amplitude-based transmission rate of the ISW. As concluded, the goodness-of-fit of the revised logit regression model is better than that of the model without this approach.     

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     

Evolution and breaking of a propagating internal wave in stratified ocean

The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.     

Examination of wind-wave interaction source term in WAVEWATCH III with tropical cyclone wind forcing

Results of drag coefficient(CD) from field observations and laboratory wave tank experiments indicate that the operational wave model can overestimate wind energy input under high wind conditions. The wind-wave interaction source term in WAVEWATCH Ⅲ has been modified to examine its behavior with tropical cyclone wind forcing. Using high resolution wind input,numerical experiments under idealized wind field and tropical cyclone Bonnie(1998) were designed to evaluate performance of the modified models. Both experiments indicate that the modified models with reduced CD significantly decrease wind energy input into the wave model and then simulate lower significant wave height(SWH) than the original model. However,the effects on spatial distribution of SWH,mean wavelength,mean wave direction,and directional wave spectra are insignificant. Due to the reduced wind energy input,the idealized experiment shows that the modified models simulate lower SWH than the original model in all four quadrants. The decrease in the front quadrants is significantly larger than that in the rear quadrants;it is larger under higher winds than lower winds. The realistic experiment on tropical cyclone Bonnie shows that the modified model with the various downward trends of CD in high winds creates a simulation that agrees best with scanning radar altimeter observations.     

An evaluation of input/dissipation terms in WAVEWATCH Ⅲ using in situ and satellite significant wave height data in the South China Sea

A WAVEWATCH III version 3.14(WW3) wave model is used to evaluate input/dissipation source term packages WAM3, WAM4 and TC96 considering the effect of atmospheric instability. The comparisons of a significant wave height acquired from the model with different packages have been performed based on wave observation radar and HY-2 altimetry significant wave height data through five experiments in the South China Sea domain spanning latitudes of 0°–35°N and longitudes of 100°–135°E. The sensitivity of the wind speed correction parameter in the TC96 package also has been analyzed. From the results, the model is unable to dissipate the wave energy efficiently during a swell propagation with either source packages. It is found that TC96 formulation with the "effective wind speed" strategy performs better than WAM3 and WAM4 formulations. The wind speed correction parameter in the TC96 source package is very sensitive and needs to be calibrated and selected before the WW3 model can be applied to a specific region.     

Numerical study on the characteristics of flow field and wave propagation near submerged breakwater on slope

In this study,characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical twodimensional model are Reynolds Averaged Navier Stokes equations. The Reynolds stress terms are closed by a nonlinear k ε turbulence transportation model. The free surface is traced through the PILC-VOF method. The proposed numerical model is verified with experimental results. The numerical result shows that the wave profile may become more asymmetrical when wave propa-gates over breakwater. When wave crest propagates over breakwater,the anticlockwise vortex may generate. On the contrary,when wave hollow propagates over breakwater,the clockwise vortex may generate. Meanwhile,the influenced zone of vortex created by wave crest is larger than that created by wave hollow. All the maximum values of the turbulent kinetic energy,turbulent dissi-pation and eddy viscosity occur on the top of breakwater. Both the turbulent dissipation and eddy viscosity increase as the turbulent kinetic energy increases. Wave energy may rapidly decrease near the breakwater because turbulent dissipation increases and energy in lower harmonics is transferred into higher harmonics.     

Generalized Extreme Value-Pareto Distribution Function and Its Applications in Ocean Engineering

In this paper, we establish a generalized extreme Value-Pareto distribution model and derive an analytical expression of Weibull–Pareto distribution model. Based on a data sample of 26-year wave height, we adopt the new model to estimate the design wave height for 500, 700 and 1000-year return periods. Results show that the design wave height from Weibull–Pareto distribution is between that of the Weibull distribution and that of the Pearson-Ⅲ distribution.For the 500-year return period design wave height, the results from the new model is 1.601% lower than those from the Weibull distribution and 1.319% higher than those from the Pearson-Ⅲ distribution. The Weibull–Pareto distribution innovatively considers the fractal features, extreme-value statistics and the truncated data in the derivation process. Therefore, it is a more holistic and practical model for estimating the design parameters in marine and coastal environments.     

基于SVM回归模型的SAR图像有效波高估测

A new method for estimating significant wave height(SWH) from advanced synthetic aperture radar(ASAR) wave mode data based on a support vector machine(SVM) regression model is presented. The model is established based on a nonlinear relationship between σ0, the variance of the normalized SAR image, SAR image spectrum spectral decomposition parameters and ocean wave SWH. The feature parameters of the SAR images are the input parameters of the SVM regression model, and the SWH provided by the European Centre for Medium-range Weather Forecasts(ECMWF) is the output parameter. On the basis of ASAR matching data set, a particle swarm optimization(PSO) algorithm is used to optimize the input kernel parameters of the SVM regression model and to establish the SVM model. The SWH estimation results yielded by this model are compared with the ECMWF reanalysis data and the buoy data. The RMSE values of the SWH are 0.34 and 0.48 m, and the correlation coefficient is 0.94 and 0.81, respectively. The results show that the SVM regression model is an effective method for estimating the SWH from the SAR data. The advantage of this model is that SAR data may serve as an independent data source for retrieving the SWH, which can avoid the complicated solution process associated with wave spectra.     

Numerical Simulation of Wave Height and Wave Set-Up in Nearshore Regions

Based on the time dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation, and then a practical method for the simulation of wave height and wave set-up in nearshore regions is presented. The variation of the complex wave amplitude is numerically simulated by use of the parabolic mild slope equation including the effect of wave energy dissipation due to wave breaking. The components of wave radiation stress are calculated subsequently by new expressions for them according to the obtained complex wave amplitude, and then the depth-averaged equation is applied to the calculation of wave set-up due to wave breaking. Numerical results are in good agreement with experimental data, showing that the expression for the energy dissipation factor is reasonable and that the new method is effective for the simulation of wave set-up due to wave breaking in nearshore regions.     

Application of Maximum Entropy Principle to Studying the Distribution of Wave Heights in A Random Wave Field

Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh fonu, involves two parameters: the average wave height H^- and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.     

A hybrid model for numerical wave forecasting and its implementation——Ⅰ. The wind wave model

The authors make an endeavor to explain why a new hybrid wave model is here proposed when several such models have already been in operation and the so- called third generation wave modej is proving attractive. This part of the paper is devoted to the wind wave model. Both deep and shallow water models have been developed, the former being actually a special case of the latter when water depth is great. The deep water model is exceptionally simple in form. Significant wave height is the only prognostic variable. In comparison with the usual methods to compute the energy input and dissipations empirically or by "tuning", the proposed model has the merit that the effects of all source terms are combined into one term which is computed through empirical growth relations for significant waves, these relations being, relatively speaking, easier and more reliable to obtain than those for the source terms in the spectral energy balance equation. The discrete part of the model and the implementation of the mode     

Exploitable wave energy assessment based on ERA-Interim reanalysis data—A case study in the East China Sea and the South China Sea

Wave energy resources assessment is a very important process before the exploitation and utilization of the wave energy. At present, the existing wave energy assessment is focused on theoretical wave energy conditions for interesting areas. While the evaluation for exploitable wave energy conditions is scarcely ever performed.Generally speaking, the wave energy are non-exploitable under a high sea state and a lower sea state which must be ignored when assessing wave energy. Aiming at this situation, a case study of the East China Sea and the South China Sea is performed. First, a division basis between the theoretical wave energy and the exploitable wave energy is studied. Next, based on recent 20 a ERA-Interim wave field data, some indexes including the spatial and temporal distribution of wave power density, a wave energy exploitable ratio, a wave energy level, a wave energy stability, a total wave energy density, the seasonal variation of the total wave energy and a high sea condition frequency are calculated. And then the theoretical wave energy and the exploitable wave energy are compared each other; the distributions of the exploitable wave energy are assessed and a regional division for exploitable wave energy resources is carried out; the influence of the high sea state is evaluated. The results show that considering collapsing force of the high sea state and the utilization efficiency for wave energy, it is determined that the energy by wave with a significant wave height being not less 1 m or not greater than 4 m is the exploitable wave energy. Compared with the theoretical wave energy, the average wave power density, energy level, total wave energy density and total wave energy of the exploitable wave energy decrease obviously and the stability enhances somewhat. Pronounced differences between the theoretical wave energy and the exploitable wave energy are present. In the East China Sea and the South China Sea, the areas of an abundant and stable exploitable wave energy are primarily located in the north-central part of the South China Sea, the Luzon Strait,east of Taiwan, China and north of Ryukyu Islands; annual average exploitable wave power density values in these areas are approximately 10–15 k W/m; the exploitable coefficient of variation(COV) and seasonal variation(SV)values in these areas are less than 1.2 and 1, respectively. Some coastal areas of the Beibu Gulf, the Changjiang Estuary, the Hangzhou Bay and the Zhujiang Estuary are the poor areas of the wave energy. The areas of the high wave energy exploitable ratio is primarily in nearshore waters. The influence of the high sea state for the wave energy in nearshore waters is less than that in offshore waters. In the areas of the abundant wave energy, the influence of the high sea state for the wave energy is prominent and the utilization of wave energy is relatively difficult. The developed evaluation method may give some references for an exploitable wave energy assessment and is valuable for practical applications.     

Experimental Study of Perforated Caisson Breakwater

This paper describes the design of a perforated caisson breakwater and presents the results of model test. Tests with regular and irregular waves have demonstrated that the perforated caisson breakwater has the advantages of low reflection coefficient, good wave-absorbing performance, relatively small wave height in front of the breakwater, and small amount of overtopping. Analyses have been made of the coefficient of reflection, wave height in front of the breakwater, and wave overtopping. Relevant figures and tables are presented for reference.     

Efficient Generation of Freak Waves in Laboratory

In the present study,Kriebel's method is improved to generate freak waves in laboratory.The improved method superposes a random wave train with two transient wave trains to simulate freak wave events in a wave tank.The freak waves are more nonlinear than what generated with Kriebel's method of the same energy.It can also generate freak waves to satisfy all the qualifications of the adopted definition with less energy than Kriebel's and can hardly influence the significant wave height.     

基于多星融合高度计数据的中国海波浪能资源评估

Wave energy resources are abundant in both offshore and nearshore areas of the China's seas. A reliable assessment of the wave energy resources must be performed before they can be exploited. First, for a water depth in offshore waters of China, a parameterized wave power density model that considers the effects of the water depth is introduced to improve the calculating accuracy of the wave power density. Second, wave heights and wind speeds on the surface of the China's seas are retrieved from an AVISO multi-satellite altimeter data set for the period from 2009 to 2013. Three mean wave period inversion models are developed and used to calculate the wave energy period. Third, a practical application value for developing the wave energy is analyzed based on buoy data. Finally, the wave power density is then calculated using the wave field data. Using the distribution of wave power density, the energy level frequency, the time variability indexes, the total wave energy and the distribution of total wave energy density according to a wave state, the offshore wave energy in the China's seas is assessed. The results show that the areas of abundant and stable wave energy are primarily located in the north-central part of the South China Sea, the Luzon Strait, southeast of Taiwan in the China's seas; the wave power density values in these areas are approximately 14.0–18.5 k W/m. The wave energy in the China's seas presents obvious seasonal variations and optimal seasons for a wave energy utilization are in winter and autumn. Except for very coastal waters, in other sea areas in the China's seas, the energy is primarily from the wave state with 0.5 m≤H s≤4 m, 4 s≤T e≤10 s where H s is a significant wave height and T e is an energy period; within this wave state, the wave energy accounts for 80% above of the total wave energy. This characteristic is advantageous to designing wave energy convertors(WECs). The practical application value of the wave energy is higher which can be as an effective supplement for an energy consumption in some areas. The above results are consistent with the wave model which indicates fully that this new microwave remote sensing method altimeter is effective and feasible for the wave energy assessment.     

Experimental Study of A Pile-Restrained Floating Breakwater Constructed of Pontoon and Plates

A pile-restrained pontoon-plate floating breakwater is proposed in this paper.The laboratory physical-model tests are conducted to investigate the wave-dissipation property and heave-motion response of a model.The influence of the model′s geometric parameters including relative pontoon width,plate width,number of plates and pontoon draft on wave-dissipation performance and heave-motion response are discussed,as well as the correlation between these two factors.The result indicates that wave-dissipation performance of the proposed structure is better than the pontoon structure:its transmission coefficient and heave-motion height are reduced by 0.2 and 0.3,respectively,in comparison with those of the pile-restrained pontoon model at a relative pontoon width of 0.2.     

On Radiation Boundary Conditions and Wave Transformation Across the Surf Zone

The purpose of this paper is to extend the validity of Li's parabolic model (1994) by incorporating a combined energy factor in the mild-slope equation and by improving the traditional radiation boundary conditions. With wave breaking and energy dissipation expressed in a direct form in the equation, the proposed model could provide an efficient numerical scheme and accurate predictions of wave transformation across the surf zone. The radiation boundary conditions are iterated in the model without use of approximations. The numerical predictions for wave height distributions across the surf zone are compared with experimental data over typical beach profiles. In addition, tests of waves scattering around a circular pile show that the proposed model could also provide reasonable improvement on the radiation boundary conditions for large incident angles of waves.