Stochastic Model for Estimating Extreme Water Level in Port and Coastal Engineering Design

Extreme water level is an important consideration when designing coastal protection structures. However, frequency analysis recommended by standard codes only considers the annual maximum water level, whereas water levels should actually be regarded as a combination of astronomical tide and storm surge. The two impacting factors are both random variables, and this paper discusses their dependency structures and proposes a new joint probability method to determine extreme design water levels. The lognormal, Gumbel, Weibull, Pearson type 3, traditional maximum entropy, and modified maximum entropy distributions are applied to fit univariate data of astronomical tides and storm surges separately, and the bivariate normal, Gumbel-Hougaard, Frank and Clayton copulas are then utilized to construct their joint probability distributions. To ensure that the new design method is suitable for use with typhoon data, the annual occurrence frequency of typhoon processes is considered and corresponding bivariate compound probability distributions are proposed. Based on maximum water level data obtained from Hengmen hydrological station in the Pearl River Basin, China, these probability models are applied to obtain designs for extreme water levels using the largest sum of the astronomical tide and storm surge obtained under fixed joint return periods. These design values provide an improved approach for determining the necessary height of coastal and offshore structures.     

Estimating Design Loads with Environmental Contour Approach Using Copulas for an Offshore Jacket Platform

Jacket-type offshore platforms are widely used for oil, gas field, and energy development in shallow water. The design of a jacket structure is highly dependent on target environmental variables. This study focuses on a strategy to estimate design loads for offshore jacket structures based on an environmental contour approach. In addition to the popular conditional distribution model, various classes of bivariate copulas are adopted to construct joint distributions of environmental variables. Analytical formulations of environmental contours based on various models are presented and discussed in this study. The design loads are examined by dynamic response analysis of jacket platform. Results suggest that the conditional model is not recommended for use in estimating design loads in sampling locations due to poor fitting results. Independent copula produces conservative design loads and the extreme response obtained using the conditional model are smaller than those determined by copulas. The suitability of a model for contour construction varies with the origin of wave data. This study provides a reference for the design load estimation of jacket structures and offers an alternative procedure to determine the design criteria for offshore structures.     

Joint occurrence period of wind speed and wave height based on both service term and risk probability

Return periods calculated for different environmental conditions are key parameters for ocean platform design.Many codes for offshore structure design give no consideration about the correlativity among multi-loads and over-estimate design values.This frequently leads to not only higher investment but also distortion of structural reliability analysis.The definition of design return period in existing codes and industry criteria in China are summarized.Then joint return periods of different ocean environmental parameters are determined from the view of service term and danger risk.Based on a bivariate equivalent maximum entropy distribution,joint design parameters are estimated for the concomitant wave height and wind speed at a site in the Bohai Sea.The calculated results show that even if the return period of each environmental factor,such as wave height or wind speed,is small,their combinations can lead to larger joint return periods.Proper design criteria for joint return period associated with concomitant environmental conditions will reduce structural size and lead to lower investment of ocean platforms for the exploitation of marginal oil field.     

Study of vertical breakwater reliability based on copulas

The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions. The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions, respectively. The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions, including the bivariate logistic Gumbel distribution, the bivariate lognormal distribution, and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously. We use the fully nested copulas to construct multivariate distributions taking into account related variables. Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater. We show that a bivariate model constructed by Frank copula gives the best reliability analysis, using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater, respectively. The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods. As copulas are suitable for constructing a bivariate or multivariate joint distribution, they have great potential in reliability analysis for other coastal structures.     

A preliminary study on the intensity of cold wave storm surges of Laizhou Bay

Dike failure and marine losses are quite prominent in Laizhou Bay during the period of cold wave storm surges because of its open coastline to the north and flat topography. In order to evaluate the intensity of cold wave storm surge, the hindcast of marine elements induced by cold waves in Laizhou Bay from 1985 to 2004 is conducted using a cold wave storm surge–wave coupled model and the joint return period of extreme water level, concomitant wave height, and concomitant wind speed are calculated. A new criterion of cold wave storm surge intensity based on such studies is developed. Considering the frequency of cold wave, this paper introduces a Poisson trivariate compound reconstruction model to calculate the joint return period, which is closer to the reality. By using the newly defined cold wave storm surge intensity, the ‘cold wave grade' in meteorology can better describe the severity of cold wave storm surges and the warning level is well corresponding to different intensities of cold wave storm surges. Therefore, it provides a proper guidance to marine hydrological analysis, disaster prevention and marine structure design in Laizhou Bay.     

Long-term variation of storm surge-associated waves in the Bohai Sea

When investigating the long-term variation of wave characteristics as associated with storm surges in the Bohai Sea, the Simulating Waves Nearshore(SWAN) model and ADvanced CIRCulation(ADCIRC) model were coupled to simulate 32 storm surges between 1985 and 2014. This simulation was validated by reproducing three actual wave processes, showing that the simulated significant wave height(SWH) and mean wave period agreed well with the actual measurements. In addition, the long-term variations in SWH, patterns in SWH extremes along the Bohai Sea coast, the 100-year return period SWH extreme distribution, and waves conditional probability distribution were calculated and analyzed. We find that the trend of SWH extremes in most of the coastal stations was negative, among which the largest trend was-0.03 m/a in the western part of Liaodong Bay. From the 100-year return period of the SWH distribution calculated in the Gumbel method, we find that the SWH extremes associated with storm surges decreased gradually from the center of the Bohai Sea to the coast. In addition, the joint probability of wave and surge for the entire Bohai Sea in 100-year return period was determined by the Gumbel logistic method. We therefore, assuming a minimum surge of one meter across the entire Bohai Sea, obtained the spatial SWH distribution. The conclusions of this study are significant for offshore and coastal engineering design.     

Impacts of wave and current on drag coefficient and wind stress over the tropical and northern Pacific

By taking into consideration the effects of ocean surface wave-induced Stokes drift velocity U,w and current velocityU,c on the drag coefficient,the spatial distributions of drag coefficient and wind stress in 2004 are computed over the tropical andnorthern Pacific using an empirical drag coefficient parameterization formula based on wave steepness and wind speed.The globalocean current field is generated from the Hybrid Coordinate Ocean Model (HYCOM) and the wave data are generated from Wave-watch Ⅲ (WW3).The spatial variability of the drag coefficient and wind stress is analyzed.Preliminary results indicate that theocean surface Stokes drift velocity and current velocity exert an important influence on the wind stress.The results also show thatconsideration of the effects of the ocean surface Stokes drift velocity and current velocity on the wind stress can significantly im-prove the modeling of ocean circulation and air-sea interaction processes.     

Analysis of Dynamic Characteristics of the 21st Century Maritime Silk Road

The 21st century Maritime Silk Road(MSR) proposed by China strongly promotes the maritime industry. In this paper, we use wind and ocean wave datasets from 1979 to 2014 to analyze the spatial and temporal distributions of the wind speed, significant wave height(SWH), mean wave direction(MWD), and mean wave period(MWP) in the MSR. The analysis results indicate that the Luzon Strait and Gulf of Aden have the most obvious seasonal variations and that the central Indian Ocean is relatively stable. We analyzed the distributions of the maximum wind speed and SWH in the MSR over this 36-year period. The results show that the distribution of the monthly average frequency for SWH exceeds 4 m(huge waves) and that of the corresponding wind speed exceeds 13.9 ms~(-1)(high wind speed). The occurrence frequencies of huge waves and high winds in regions east of the Gulf of Aden are as high as 56% and 80%, respectively. We also assessed the wave and wind energies in different seasons. Based on our analyses, we propose a risk factor(RF) for determining navigation safety levels, based on the wind speed and SWH. We determine the spatial and temporal RF distributions for different seasons and analyze the corresponding impact on four major sea routes. Finally, we determine the spatial distribution of tropical cyclones from 2000 to 2015 and analyze the corresponding impact on the four sea routes. The analysis of the dynamic characteristics of the MSR provides references for ship navigation as well as ocean engineering.     

The effect of current and wave on whitecap coverage via relative speed： the Atlantic Ocean case

Whitecapping plays an important role in many air-sea exchange and upper ocean processes. Traditionally, whitecap coverage is parameterized as a function of wind speed only. At present, the relative speed of ocean current to wind is considered to be important in the air-sea exchange parameterization which is the function of wind speed only. In this paper, the effects of ocean surface velocity (current velocity and wave induced velocity) and the wave parameters on whitecap coverage through relative speeds are investigated, by applying a 2-parameter whitecap coverage model to the Atlantic Ocean. It is found that the impacts of both current and wave on whitecap coverage are considerable in the most part of the Atlantic Ocean. It is interesting that the effect of wave is more significant than that of current.     

Selection of environmental conditions for nearshore structure design

1　Introduction　InChina ,coastalcitiesaremostlyregionaleconomicdevelopmentcenters.Becauseoftheirspecialgeogra phiclocations ,typhoonsandassociatedstormsurgescauseheavylossesoflivesandproperties.In 1 992 Qing daowasfloodedduetothecoincidenceoftheastrono m…     

Study of the Wind Conditions in the South China Sea and Its Adjacent Sea Area

An increasing number of marine structures have been built for coastal protection and marine development in recent years,and wind,which is crucial to marine structures,should be analyzed.Therefore,typhoon frequency,wind climate,wind energy assess-ment,and extreme wind speed in the South China Sea(SCS)are investigated in detail in this study.The data are obtained from the China Meteorological Administration,the European Centre for Medium-range Weather Forecasts,and the National Centers for Envi-ronmental Prediction.The offshore wind energy potential is analyzed at five sites near the coast.The spatial and monthly frequencies of tropical cyclones for different intensity categories are analyzed.The extreme wind speed is fitted by five distribution models,and the generalized extreme value(GEV)distribution is selected as the most suitable function according to the goodness of fit.The spa-tial distributions of extreme wind speeds in the SCS are plotted on the basis of the GEV distribution and ERA5 data sets.The influ-ences of the distribution models and data sets on the calculated results are discussed.Moreover,the monthly extreme wind speed and comparison with the results of previous studies are analyzed.This study provides a reference for the design of wind turbines.     

Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37°27.6′ N, 122°15.1′ E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (ν=0.3−0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.     

Experimental Investigation of Wave Load and Run-up on the Composite Bucket Foundation Influenced by Regular Waves

In the design of wind turbine foundations for offshore wind farms, the wave load and run-up slamming on the supporting structure are the quantities that need to be considered. Because of a special arc transition, the interaction between the wave field and the composite bucket foundation(CBF) becomes complicated. In this study, the hydrodynamic characteristics, including wave pressure, load, upwelling, and run-up, around the arc transition of a CBF influenced by regular waves are investigated through physical tests at Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China. The distributions of the wave pressures and upwelling ratios around the CBF are described, and the relationship between the wave load and the wave parameters is discussed. New formulae based on the velocity stagnation head theory with linear wave theory and the second-order Stokes wave theory for wave kinematics are proposed to estimate the wave run-up. Moreover, the multiple regression method with nonlinear technology is employed to deduce an empirical formula for predicting run-up heights. Results show that the non-dimensional wave load increases with the increase in the values of the wave scattering parameter and relative wave height. The wave upwelling height is high in front of the CBF and has the lowest value at an angle of 135? with the incoming wave direction. The performance of the new formulae proposed in this study is compared using statistical indices to demonstrate that a good fit is obtained by the multiple regression method and the analytical model based on the velocity stagnation head theory is underdeveloped.     

两种海浪模式对一次台风浪过程的模拟分析

以CCMP（Cross—Calibrated,Multi—Platfoml）风场为驱动场,分别驱动目前国际先进的第3代海浪模式ww3（WAVEWATCH—III）、SWAN（Simulating WAves Nearshore）,对2010年9月发生在东中国海的台风“圆规”所致的台风浪进行数值模拟,就台风浪的特征进行分析,并对比分析两个海浪模式的模拟效果。结果表明：1）以CCMP风场分别驱动WW3、SWAN海浪模式,可以较好地模拟发生在东中国海的台风浪,风向与波向保持了大体一致,波高与风速的分布特征保持了很好的一致性;2）综合相关系数、偏差、均方根误差、平均绝对误差来看,两个模式模拟的有效波高（SWH—Significant Wdve Height）都具有较高精度,SWAN模拟的SWH略低于观测值,WW3模拟的SWH与观测值更为接近;3）台风浪可给琉球群岛海域带来5m左右的大浪,台风浪进入东海后,波高、风速都有一定程度的增加,当台风沿西北路径穿越朝鲜半岛时,受到半岛地形的巨大影响,风速和波高都明显降低。     

Slope wavenumber spectrum models of capillary and capillary-gravity waves

Capillary and capillary-gravity waves possess a random character, and the slope wavenumber spectra of them can be used to represent mean distributions of wave energy with respect to spatial scale of variability. But simple and practical models of the slope wavenumber spectra have not been put forward so far. In this article, we address the accurate definition of the slope wavenumber spectra of water surface capillary and capillary-gravity waves. By combining the existing slope wavenumber models and using the dispersion relation of water surface waves, we derive the slope wavenumber spectrum models of capillary and capillary-gravity waves. Simultaneously, by using the slope wavenumber models, the dependence of the slope wavenumber spectrum on wind speed is analyzed using data obtained in an experiment which was performed in a laboratory wind wave tank. Generally speaking, the slope wavenumber spectra are influenced profoundly by the wind speed above water surface. The slope wavenumber spectrum increases with wind speed obviously and do not cross each other for different wind speeds. But, for the same wind speed, the slope wavenumber spectra are essentially identical, even though the capillary and capillary-gravity waves are excited at different times and locations. Furthermore, the slope wavenumber spectra obtained from the models agree quite well with experimental results as regards both the values and the shape of the curve.     

Long-term statistics of extreme tsunami height at Crescent City

Historically, Crescent City is one of the most vulnerable communities impacted by tsunamis along the west coast of the United States, largely attributed to its offshore geography. Trans-ocean tsunamis usually produce large wave runup at Crescent Harbor resulting in catastrophic damages, property loss and human death. How to determine the return values of tsunami height using relatively short-term observation data is of great significance to assess the tsunami hazards and improve engineering design along the coast of Crescent City. In the present study, the extreme tsunami heights observed along the coast of Crescent City from 1938 to 2015 are fitted using six different probabilistic distributions, namely, the Gumbel distribution, the Weibull distribution, the maximum entropy distribution, the lognormal distribution, the generalized extreme value distribution and the generalized Pareto distribution. The maximum likelihood method is applied to estimate the parameters of all above distributions. Both Kolmogorov-Smirnov test and root mean square error method are utilized for goodness-of-fit test and the better fitting distribution is selected. Assuming that the occurrence frequency of tsunami in each year follows the Poisson distribution, the Poisson compound extreme value distribution can be used to fit the annual maximum tsunami amplitude, and then the point and interval estimations of return tsunami heights are calculated for structural design. The results show that the Poisson compound extreme value distribution fits tsunami heights very well and is suitable to determine the return tsunami heights for coastal disaster prevention.     

Crest-height distribution of nonlinear random waves

The wave crest is an important factor for the design of both fixed and floating marine structures. Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damage. Many empirical and theoretical distribution functions for wave crest heights have been proposed, but there is a lack of agreement between them. It is of significance to develop a better new nonlinear wave crest height distribution model. The progress in the research of wave crest heights is reviewed in this paper. Based on Stokes’ wave theory, an approximate nonlinear wave crest-height distribution formula with simple parameters is derived. Two sets of measured data are presented and compared with various theoretical distributions of wave crests obtained from nonlinear wave models and analysis of the comparison is given in detail. The new crest-height distribution model agrees well with observations. Also, the new theoretical distribution is more accurate than the other methods cited in this paper and has a greater range of applications.     

NEW METHOD TO OBTAIN THE POWER SPECTRA OF HIDDEN VARIABLES AND ITS APPLICATION TO OCEAN DATA

A novel method is proposed to obtain the power spectra of hidden variables in a chaotic time series. By embedding the data in phase space , and recording the conditional probability densityof points that the trajectory encounters as it evolves in the reconstructed phase space, it is possible torecover the power spectra of hidden variables in chaotic time series through a spectral analysis over theconditional probability density time series. The method is robust in the application to Lorenz system, 4-di-mension Rossler system and rigid body motion by linear feedback system (LFRBM). Applying the method the time series of sea surface temperature (SST) of the South China Sea, we obtained the power spectraof the wind speed (WS) from SST data. Furthermore, the results showged that there exists an importantnonlinear interaction between the SST and the WS.     

Typhoon wind hazard model and estimation on return period of typhoon wind speed

Typhoons are one of the most serious natural disasters that occur annually on China's southeast coast.A technique for analyzing the typhoon wind hazard was developed based on the empirical track model,and used to generate 1 000-year virtual typhoons for Northwest Pacific basin.The influences of typhoon decay model,track model,and the extreme value distribution on the predicted extreme wind speed were investigated.We found that different typhoon decay models have least influence on the predicted extreme wind speed.Over most of the southeast coast of China,the predicted wind speed by the nonsimplified empirical track model is larger than that from the simplified tracking model.The extreme wind speed predicted by different extreme value distribution is quite different.Four super typhoons Meranti(2016),Hato(2017),Mangkhut(2018),and Lekima(2019) were selected and the return periods of typhoon wind speeds along the China southeast coast were estimated in order to assess the typhoon wind hazard.     

Determination of water level design for an estuarine city

Based on the extreme value theory,self-affinity,and scale invariance,we studied the temporal and spatial relationship and the variation of water level and established a model of Gumbel-Pareto distribution for designed flood calculation.The model includes the previous extreme value models,the over-threshold data,and the fractal features shared by previous extreme value models.The model was simplified into a logarithmic normal distribution and a Pareto distribution for specific parameter values,and was used to calculate the designed flood values for the Shanghai Wusong Station in 100-and 1 000-year return periods.The calculated results show that the value of the designed flood height calculated in the Gumbel-Pareto distribution is between those in the Gumbel and Pearson-III distributions.The designed flood values in the100-and 1 000-year return periods of the model were 0.0 3%and 0.11%lower,respectively,than the Gumbel distribution and 0.06%and 1.54%higher,respectively,than the Pearson-III distribution.Compared to the traditional model based solely on extreme probability,the Gumbel-Pareto distribution model could better describe the probabilistic characteristics of extreme marine elements and better use the data.