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.     

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.     

Numerical Study of Storm Surge Inundation in the Southwestern Hangzhou Bay Region During Typhoon Chan-Hom in 2015

Storm surge inundation is a major concern in marine hazard risk assessment during extreme weather conditions.In this study,a high-resolution coupled model(the ADVanced CIRCulation model+the Simulating WAves Nearshore model)was used to investigate the storm surge inundation in the southwestern Hangzhou Bay region during Typhoon Chan-hom in 2015.The simulated hydrodynamic processes(sea surface wave and storm tide)were validated with measured data from wave buoys and tide gauges,indicating that the overall performance of the model was satisfactory.The storm surge inundation in the coastal area was simulated for several idealized control experiments,including different wave effects(wave-enhanced wind stress,wave-enhanced bottom stress,and wave radiation stress).Dike overflowing cases with different dike heights and dike breaking cases with different dike breach lengths were considered in the simulation.The results highlight the necessity of incorporating wave effects in the accurate simulation of storm surge inundation.Dike height significantly influences the magnitude and phase of the maximum inundation area in the dike overflowing cases,and dike breach length is an important factor impacting the magnitude of the maximum inundation area in the dike breaking cases.This study may serve as a useful reference for accurate coastal inundation simulation and risk assessment.     

Wind wave characteristics and engineering environment of the South China Sea

Wave simulation was conducted for the period 1976 to 2005 in the South China Sea (SCS) using the wave model, WAVEWATCH-III. Wave characteristics and engineering environment were studied in the region. The wind input data are from the objective reanalysis wind datasets, which assimilate meteorological data from several sources. Comparisons of significant wave heights between simulation and TOPEX/Poseidon altimeter and buoy data show a good agreement in general. By statistical analysis, the wave characteristics, such as significant wave heights, dominant wave directions, and their seasonal variations, were discussed. The largest significant wave heights are found in winter and the smallest in spring. The annual mean dominant wave direction is northeast (NE) along the southwest (SW)-NE axis, east northeast in the northwest (NW) part of SCS, and north northeast in the southeast (SE) part of SCS. The joint distributions of wave heights and wave periods (directions) were studied. The results show a single peak pattern for joint significant wave heights and periods, and a double peak pattern for joint significant wave heights and mean directions. Furthermore, the main wave extreme parameters and directional extreme values, particularly for the 100-year return period, were also investigated. The main extreme values of significant wave heights are larger in the northern part of SCS than in the southern part, with the maximum value occurring to the southeast of Hainan Island. The direction of large directional extreme H _s values is focus in E in the northern and middle sea areas of SCS, while the direction of those is focus in N in the southeast sea areas of SCS.     

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.     

Numerical simulation of wave field in the South China Sea using WAVEWATCH III

Wave fi elds of the South China Sea(SCS) from 1976 to 2005 were simulated using WAVEWATCH III by inputting high-resolution reanalysis wind fi eld datasets assimilated from several meteorological data sources. Comparisons of wave heights between WAVEWATCH III and TOPEX/Poseidon altimeter and buoy data show a good agreement. Our results show seasonal variation of wave direction as follows: 1. During the summer monsoon(April–September), waves from south occur from April through September in the southern SCS region, which prevail taking about 40% of the time; 2. During the winter monsoon(December–March), waves from northeast prevail throughout the SCS for 56% of the period; 3. The dominant wave direction in SCS is NE. The seasonal variation of wave height H s in SCS shows that in spring, H s ≥1 m in the central SCS region and is less than 1 m in other areas. In summer, H s is higher than in spring. During September–November, infl uenced by tropical cyclones, H s is mostly higher than 1 m. East of Hainan Island, H s 2 m. In winter, H s reaches its maximum value infl uenced by the north-east monsoon, and heights over 2 m are found over a large part of SCS. Finally, we calculated the extreme wave parameters in SCS and found that the extreme wind speed and wave height for the 100-year return period for SCS peaked at 45 m/s and 19 m, respectively, SE of Hainan Island and decreased from north to south.     

约束条件对滑坡涌浪特征影响的室内试验研究

水库滑坡约束条件影响其运动过程的几何形态, 是滑坡涌浪预测的重要参数之一。为了探究约束条件对滑坡涌浪特征(波高、波幅与周期)的影响, 采用正交试验设计法开展了54组滑坡涌浪室内模型试验, 并基于统计学理论对约束散体和半约束散体的涌浪特征进行了分析。结果表明: 涌浪波周期基本不受滑体约束条件的影响; 而半约束散体模型的波高和波幅小于约束散体的波高和波幅, 半约束散体的初始涌浪波高约为约束散体的0.95倍, 半约束散体模型的最大波峰波幅约为约束散体模型的0.9倍。因此, 在开展滑坡涌浪快速预测时, 虽然滑体入水形态与破坏前形态差异巨大, 但基于滑坡初始几何形态参数对其初始涌浪波高和最大涌浪波幅的预测结果是偏安全的。研究结论可以为更准确地预测水库滑坡涌浪提供理论依据。      

我国不同历时年最大降雨量的随机性及空间差异性

极端降水极易引发山洪和城市内涝等水灾害,给生态环境安全、社会经济发展、人民生命财产安全等带来极大损失,认识其（尤其是短历时）空间分布差异对洪涝灾害防治等具有重要意义。本文利用60 min、6 h和24 h共3种历时的年最大降雨量的统计特征参数,生成服从皮尔逊-Ⅲ型分布的长序列样本,并选用信息熵指标研究其随机性及空间分布差异。结果显示：各历时年最大降雨量的随机性均呈现由东南向西北逐渐减小的空间格局,但不同历时降水随机性的空间分布存在差异,主要体现在青藏高原东部、海河流域和淮河流域3个区域。此外,所求年最大降雨量信息熵值主要考虑了其取值的相对离散情况,故该信息熵值与整个序列绝对离散程度（即标准差）的关系不明显,而主要由序列均值处峰值高低的峰度系数决定,二者呈现明显的负相关关系;且由于峰度系数和变差系数的良好相关性也导致了变差系数与信息熵值之间呈现出良好关系。季风、台风、局地天气系统和人类活动等因素综合影响,决定了不同历时极端降水的空间分布格局及其差异。信息熵指标可以很好地反映中国各历时年最大降雨量随机性的空间分布格局,因而结果可为洪涝灾害防治、农业规划布局、生态环境规划保护等提供科学依据。     

Numerical Simulation and Analysis of Storm Surges Under Different Extreme Weather Event and Typhoon Experiments in the South Yellow Sea

In this study,a coupled tide-surge-wave model was developed and applied to the South Yellow Sea.The coupled model simulated the evolution of storm surges and waves caused by extreme weather events,such as tropical cyclones,cold waves,extratropical cyclones coupled with a cold wave,and tropical cyclones coupled with a cold wave.The modeled surge level and significant wave height matched the measured data well.Simulation results of the typhoon with different intensities revealed that the radius to the maximum wind speed of a typhoon with 1.5 times wind speed decreased,and its influence range was farther away from the Jiangsu coastal region;moreover,the impact on surge levels was weakened.Thereafter,eight hypothetical typhoons based on Typhoon Chan-hom were designed to investigate the effects of varying typhoon tracks on the extreme value and spatial distribution of storm surges in the offshore area of Jiangsu Province.The typhoon along path 2 mainly affected the Rudong coast,and the topography of the Rudong coast was conducive to the increase in surge level.Therefore,the typhoon along path 2 induced the largest surge level,which reached up to 2.91 m in the radial sand ridge area.The maximum surge levels in the Haizhou Bay area and the middle straight coastline area reached up to 2.37 and 2.08 m,respectively.In terms of typhoons active in offshore areas,the radial sand ridge area was most likely to be threatened by typhoon-induced storm surges.     

Evaluating the Accuracy of ERA5 Wave Reanalysis in the Water Around China

Wave parameters, such as wave height and wave period, are important for human activities, such as navigation, ocean engineering and sediment transport, etc. In this study, wave data from six buoys around Chinese waters, are used to assess the quality of wave height and wave period in the ERA5 reanalysis of the European Centre for Medium-Range Weather Forecasts. Annual hourly data with temporal resolution are used. The difference between the significant wave height(SWH) of ERA 5 and that of the buoy varies from-0.35 m to 0.30 m for the three shallow locations;for the three deep locations, the variation ranges from-0.09 m to 0.09 m. The ERA5 SWH data show positive biases, indicating an overall overestimation for all locations, except for E2 and S1 where underestimation is observed. During the tropical cyclone period, a large(about 32%) underestimation of the maximum SWH in the ERA5 data is observed. Hence, the ERA5 SWH data cannot be used for design applications without site-specific validation. The difference between the annual wave period from ERA5 and the mean wave period from the buoys varies from-1.31 s to 0.4 s. Inter-comparisons suggest that the ERA5 dataset is consistent with the annual mean SWH. However, for the average period, the performance is not good, and half of the correlation coefficients in the four points are less 50%. Overall, the deep water area simulation effect is better than that in the shallow water.     

Climatology of Wind-Seas and Swells in the China Seas from Wave Hindcast

The wind-sea and swell climates in the China Seas are investigated by using the 27-yr Integrated Ocean Waves for Geophysical and other Applications(IOWAGA)hindcast data.A comparison is made between the significant wave height from the IOWAGA hindcasts and that from a jointly calibrated altimetry dataset,showing the good performance of the IOWAGA hindcasts in the China Seas.A simple but practical method of diagnosing whether the sea state is wind-sea-dominant or swell-dominant is proposed based on spectral partitioning.Different from the characteristics of wind-seas and swells in the open ocean,the wave fields in the enclosed seas such as the China Seas are predominated by wind-sea events in respect of both frequencies of occurrences and energy weights,due to the island sheltering and limited fetches.The energy weights of wind-seas in a given location is usually more significant than the occurrence probability of wind-sea-dominated events,as the wave energy is higher in the wind-sea events than in the swell events on average and extreme wave heights are mostly related to wind-seas.The most energetic swells in the China Seas(and other enclosed seas)are‘local swells’,having just propagated out of their generation areas.However,the swells coming from the West Pacific also play an important role in the wave climate of the China Seas,which can only be revealed by partitioning different swell systems in the wave spectra as the energy of them is significantly less than the‘local swells’.     

A COMBINED REFRACTION-DIFFRACTION-DISSIPATION MODEL OF WAVE PROPAGATION

A numerical model based on the mild-slope equation of water wave propagation over complicated bathymetry,taking into account the combined effects of refraction,diffraction and dissipation due to wavebreaking is presented.Wave breaking is simulated by modifying the wave height probability density func-tion and the wave energy dissipation mechanism is parameterized according to that of the hydraulic jumpformulation.Solutions of the wave height,phase function,and the wave direction at every grid point areobtained by finite difference approximation of the governing equations,using Gauss-Seidel Iterative Method(GSIM)row by row.Its computational convenience allows it to be applied to large coast regions tostudy the wave transformation problem.Several case studies have been made and the results compare verywell with the experiment data and other model solutions.The capability and utility of the model forreal coast areas are illustrated by application to a shallow bay of northeast Australia.     

Wave height statistical characteristic analysis

When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year observation data to derive 100-year return period design wave height. Therefore,the study of inherent self-similarity in ocean hydrological elements becomes increasingly important to the study of multi-year return period design wave height derivation. In this paper, we introduced multifractal to analyze the statistical characteristics of wave height series data observed from oceanic hydrological station.An improvement is made to address the existing problems of the multifractal detrended fluctuation analysis(MF-DFA) method, where trend function showed a discontinuity between intervals. The improved MFDFA method is based on signal mode decomposition, replacing piecewise polynomial fitting used in the original method. We applied the proposed method to the wave height data collected at Chaolian Island,Shandong, China, from 1963 to 1989 and was able to conclude the wave height sequence presented weak multi-fractality. This result provided strong support to the past research on the derivation of multi-year return period design wave height with observed data. Moreover, the new method proposed in this paper also provides a new perspective to explore the intrinsic characteristic of data.     

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.     

Elimination of the impact of vessels on ocean wave height inversion with X-band wave monitoring radar

Directional wave spectra and integrated wave parameters can be derived from X-band radar sea surface images.A vessel on the sea surface has a significant influence on wave parameter inversions that can be seen as intensive backscatter speckles in X-band wave monitoring radar sea surface images.A novel algorithm to eliminate the interference of vessels in ocean wave height inversions from X-band wave monitoring radar is proposed.This algorithm is based on the characteristics of the interference.The principal components(PCs) of a sea surface image sequence are extracted using empirical orthogonal function(EOF)analysis.The standard deviation of the PCs is then used to identify vessel interference within the image sequence.To mitigate the interference,a suppression method based on a frequency domain geometric model is applied.The algorithm framework has been applied to OSMAR-X,a wave monitoring system developed by Wuhan University,based on nautical X-band radar.Several sea surface images captured on vessels by OSMAR-X are processed using the method proposed in this paper.Inversion schemes are validated by comparisons with data from in situ wave buoys.The root-mean-square error between the significant wave heights(SWH) retrieved from original interference radar images and those measured by the buoy is reduced by 0.25 m.The determinations of surface gravity wave parameters,in particular SWH,confirm the applicability of the proposed method.     

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.     

Hydrodynamic conditions in front of a vertical wall with an overhanging horizontal cantilever slab

Transforming wave heights from offshore to the shoreline is the first step of any coastal engineering work. Wave breaking is analyzed to understand hydrodynamic conditions. For vertical breakwaters and sea walls, wave reflection is an important process that affects the determination of the wave height. Many of the design formulas presented in the literature depend on empirical studies based on the structures tested. In this study, the hydrodynamic conditions in front of a vertical wall with an overhanging horizontal cantilever slab with a foreshore slope of 1/20 are determined experimentally under regular wave conditions to assess the applicability of the formulas of Goda (2000) for predicting the nearshore wave height and breaker index equation (Goda, 2010). The selection of wave measurements used to determine the design wave height, the reflection coefficients, and wave breaking is also analyzed, and the reflection equations are derived from the dataset covering different breaker types. Small-scale tests show that the incident wave height is a good representative of the design wave height and that the values predicted by Goda are in good agreement with actual measurements. However, the predicted H_max values are overestimated. In addition, the inception of the wave breaking point is postponed because of the reflection and/or turbulence left over from preceding waves, which is an effect of the vertical wall. At higher water levels, the effect of the vertical wall on the inception point becomes more significant.     

Investigation of wave characteristics in a semi-enclosed bay based on SWAN model validated with buoys and ADP-observed currents

In this study, the simulating waves nearshore(SWAN) model with a locally refined curvilinear grid system was constructed to simulate waves in Jervis Bay and the neighbouring ocean of Australia, with the aim of examining the wave characteristics in an area with special topography and practical importance.This model was verified by field observations from buoys and acoustic Doppler profilers(ADPs). The model precisions were validated for both wind-generated waves and open-ocean swells. We present an approach with which to convert ADP-observed current data from near the bottom into the significant wave height. Our approach is deduced from the Fourier transform technique and the linear wave theory. The results illustrate that the location of the bay entrance is important because it allows the swells in the dominant direction to propagate into the bay despite the narrowness of the bay entrance. The wave period T p is also strongly related to the wave direction in the semi-enclosed bay. The T p is great enough along the entire propagating direction from the bay entrance to the top of the bay, and the largest T p appears along the north-west coast,which is the end tip of the swells' propagation.     

Impacts of tropical cyclone inflow angle on ocean surface waves

The inflow angle of tropical cyclones(TC) is generally neglected in numerical studies of ocean surface waves induced by TC.In this study,the impacts of TC inflow angle on ocean surface waves were investigated using a high-resolution wave model.Six numerical experiments were conducted to examine,in detail,the effects of inflow angle on mean wave parameters and the spectrum of wave directions.A comparison of the waves simulated in these experiments shows that inflow angle significantly modifies TC-induced ocean surface waves.As the inflow angle increases,the asymmetric axis of the significant wave height(SWH) field shifts 30u clockwise,and the maximum SWH moves from the front-right to the rear-right quadrant.Inflow angle also affects other mean wave parameters,especially in the rear-left quadrant,such as the mean wave direction,the mean wavelength,and the peak direction.Inflow angle is a key factor in wave models for the reproduction of double-peak or multi-peak patterns in the spectrum of wave directions.Sensitivity experiments also show that the simulation with a 40u inflow angle is the closest to that of the NOAA statistical SLOSH inflow angle.This suggests that 40u can be used as the inflow angle in future TC-induced ocean surface wave simulations when SLOSH or observed inflow angles are not available.