Long-Term Extreme Wave Characteristics in the Water Adjacent to China Based on ERA5 Reanalysis Data

Extreme waves have a profound impact on coastal infrastructure;thus,understanding the variation law of risky analysis and disaster prevention in coastal zones is necessary.This paper analyzed the spatiotemporal characteristics of extreme wave heights adjacent to China from 1979 to 2018 based on the ERA5 datasets.Nonstationary extreme value analysis is undertaken in eight repre-sentative points to investigate the trends in the values of 50-and 100-year wave heights.Results show that the mean value of extreme waves is the largest in the eastern part of Taiwan Island and the smallest in the Bohai Sea from 1979 to 2018.Only the extreme wave height in the northeastern part of Taiwan Island shows a significant increase trend in the study area.Nonstationary analysis shows remarkable variations in the values of 50-and 100-year significant wave heights in eight points.Considering the annual mean change,E1,E2,S1,and S2 present an increasing trend,while S3 shows a decreasing trend.Most points for the seasonal mean change demon-strate an increasing trend in spring and winter,while other points show a decreasing trend in summer and autumn.Notably,the E1 point growth rate is large in autumn,which is related to the change in typhoon intensity and the northward movement of the typhoon path.

A Statistical Linkage between Extreme Cold Wave Events in Southern China and Sea Ice Extent in the Barents-Kara Seas from 1289 to 2017

Arctic sea ice loss and the associated enhanced warming has been related to midlatitude weather and climate changes through modulate meridional temperature gradients linked to circulation. However, contrasting lines of evidence result in low confidence in the influence of Arctic warming on midlatitude climate. This study examines the additional perspectives that palaeoclimate evidence provides on the decadal relationship between autumn sea ice extent (SIE) in the Barents-Kara (B-K) Seas and extreme cold wave events (ECWEs) in southern China. Reconstruction of the winter Cold Index and SIE in the B-K Seas from 1289 to 2017 shows that a significant anti-phase relationship occurred during most periods of decreasing SIE, indicating that cold winters are more likely in low SIE years due to the “bridge” role of the North Atlantic Oscillation and Siberian High. It is confirmed that the recent increase in ECWEs in southern China is closely related to the sea ice decline in the B-K Seas. However, our results show that the linkage is unstable, especially in high SIE periods, and it is probably modulated by atmospheric internal variability.

A simplified model for extreme-wave kinematics in deep sea

Based on the fifth-order Stokes regular wave theory, a simplified model for extreme-wave kinematics in deep sea was developed. In this model, from the wave records the average of two neighboring wave periods for the extreme crest or trough was defined as the period of the Stokes wave by the up and down zero-crossing methods. Then the input wave amplitude was deduced by substituting the wave period and extreme crest or trough into the expression for the fifth-order Stokes wave elevation. Thus the corresponding formula for the wave velocity can be used to describe kinematics beneath the extreme wave. By comparison with the published numerical models and experimental data, the proposed model is validated to be able to calculate the extreme wave velocity rather easily and accurately.

Modeling nonstationary extreme wave heights in present and future climates of Greek Seas

In this study the generalized extreme value （GEV） distribution function was used to assess nonstationarity in annual maximum wave heights for selected locations in the Greek Seas, both in the present and future climates. The available significant wave height data were divided into groups corresponding to the present period （1951-2000）, a first future period （2001-2050）, and a second future period （2051-2100）. For each time period, the parameters of the GEV distribution were specified as functions of time-varying covariates and estimated using the conditional density network （CDN）. For each location and selected time period, a total number of 29 linear and nonlinear models were fitted to the wave data, for a given combination of covariates. The covariates used in the GEV-CDN models consisted of wind fields resulting from the Regional Climate Model version 3 （RegCM3） developed by the International Center for Theoretical Physics （ICTP） with a spatial resolution of 10 km ×10 km, after being processed using principal component analysis （PCA）. The results obtained from the best fitted models in the present and future periods for each location were compared, revealing different patterns of relationships between wind components and extreme wave height quantiles in different parts of the Greek Seas and different periods. The analysis demonstrates an increase of extreme wave heights in the first future period as compared with the present period, causing a significant threat to Greek coastal areas in the North Aegean Sea and the Ionian Sea.

Analysis of Wave Loads on A Semi-Submersible Platform

For the global and structural fatigue strength analysis of a semi-submersible platform, wave loads under design conditions are calculated by use of the three-dimensional boundary element method. Methods for calculating the forward-speed free-surface Green function are discussed and a computer program with this Green function is developed. According to the special rules, the wave loads under several typical design conditions of the platform are calculated. The maximum vertical bending moment, torsion moment and horizontal split force are determined from a series of contour maps of wave loads for the wave period of 5 to 18 seconds at a certain interval and the wave phase of 0degrees to 360degrees at a certain interval. The wave height is determined by the function of wave period with a given exceedance probability. The maximum wave loads under the combination of wave parameters are used as the input of hydrodynamic pressure in the three-dimensional finite element analysis process. The transfer functions of wave loads on the platform are used for the fatigue strength analysis of the K-tubular joint and the sub-model of the structure.

Estimation of Extreme Coastal Wave Heightsfrom Time Series of Wave Data

A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Australia, is analyzed to generate a set of storm peak wave heights by use of the Peaks-Over-Threshold method. The probability distribution is calculated by grouping the observod storm peak wave heights into a number of wave height classes and assigning a probability to each wave height class. The observed probability distribution is then fitted to eight different probability distribution functions and found to be fitted best by the Weibull distribution （a = 1.17）, nearly best by the FT-Ⅰ, quite well by the exponential, and poorly by the lognormal function based on the criterion of the sum of squares of the errors, SSE （H）. The effect of the threshold wave height on the estimated extreme wave height is also studied and is found insignificant in this study. The 95 % prediction intervals of the best-fit FT-Ⅰ , exponential and Weibull functions are also derived.

A New Method for Determining Threshold in Using PGCEVD to Calculate Return Values of Typhoon Wave Height

In using the PGCEVD （Poisson-Gumbel Compound Extreme Value Distribution） model to calculate return values of typhoon wave height, the quantitative selection of the threshold has blocked its application. By analyzing the principle of the threshold selection of PGCEVD model and in combination of the change point statistical methods, this paper proposes a new method for quantitative calculation of the threshold in PGCEVD model. Eleven samples from five engineering points in several coastal waters of Guangdong and Hainan, China, are calculated and analyzed by using PGCEVD model and the traditional Pearson type III distribution （P-III） model, respectively. By comparing the results of the two models, it is shown that the new method of selecting the optimal threshold is feasible. PGCEVD model has more stable results than that of P-III model and can be used for the return wave height in every direction.

Wind-wave hindcast in the Yellow Sea and the Bohai Sea from the year 1988 to 2002

We performed long-term wind-wave hindcast in the Yellow Sea and the Bohai Sea from the year 1988 to 2002, and then analyzed the regional wave climate. Comparisons between model results and satellite data are generally consistent on monthly mean significant wave height. Then we discuss the temporal and spatial characteristics of the climatological monthly mean significant wave heights and mean wave periods. The climatologically spatial patterns are observed as increasing from northwest to southeast and from offshore to deep-water area for both significant wave height and mean wave period, and the patterns are highly related to the wind forcing and local topography. Seasonal variations of wave parameters are also significant. Furthermore, we compute the extreme values of wind and significant wave height using statistical methods. Results reveal the spatial patterns of N-year return significant wave height in the Yellow Sea and the Bohai Sea, and we discuss the relationship between extreme values of significant wave height and wind forcing.

A Refined Method for Estimating the Annual Extreme Wave Heights at A Project Site

This paper presents a refined method for estimating the annual extreme wave heights at a coastal or offshore project site on the basis of the data acquired at some nearby routine hydrographic stations. This method is based on the orthogonality principle in linear mean square estimation of stochastic processes. The error of the method is analyzed and compared with that of the conventional method. It is found that the method is able to effectively reduce the error so long as some feasible measures are adopted. A simulated test of the method has been conducted in a large scale wind wave flume. The test results are in good agreement with those given by theoretical error analysis. A scheme to implement the method is proposed on the basis of error analysis. The scheme is so designed as to reduce the estimation error as far as possible. This method is also suitable to utilizing satellite wave data for the estimation.

Simulation of the extreme waves generated by typhoon Bolaven (1215) in the East China Sea and Yellow Sea

Record-breaking high waves occurred during the passage of the typhoon Bolaven（1215）（TYB） in the East China Sea（ECS） and Yellow Sea（YS） although its intensity did not reach the level of a super typhoon.Winds and directional wave measurements were made using a range of in-situ instruments mounted on an ocean tower and buoys.In order to understand how such high waves with long duration occurred,analyses have been made through measurement and numerical simulations.TYB winds were generated using the TC96 typhoon wind model with the best track data calibrated with the measurements.And then the wind fields were blended with the reanalyzed synoptic-scale wind fields for a wave model.Wave fields were simulated using WAM4.5 with adjustment of C_d for gust of winds and bottom friction for the study area.Thus the accuracy of simulations is considerably enhanced,and the computed results are also in better agreement with measured data than before.It is found that the extremely high waves evolved as a result of the superposition of distant large swells and high wind seas generated by strong winds from the front/right quadrant of the typhoon track.As the typhoon moved at a speed a little slower than the dominant wave group velocity in a consistent direction for two days,the wave growth was significantly enhanced by strong wind input in an extended fetch and non-linear interaction.

Nonlinear numerical simulation on extreme-wave kine-matics

A fully nonlinear numerical model based on a time-domain higher-order boundary element method （HOBEM） is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.

Estimation of Design Wave Heights for Coastal Sea Areas

Based on historical wind fields in the Bohai Sea, a sequence of annual extremal wave heights is produced with numerical wave models for deep-water and shallow water. The design wave heights with different return periods for the nearest deep-water point and for the shallow water point are estimated on the basis of P-III type, Weibull distribution, and Gumbel distribution; and the corresponding values for the shallow water point are also estimated based on the HISWA model with the input of design wave heights for the nearest deep-water point. Comparisons between design wave heights for the shallow water point estimated on the basis of both distribution functions are HISWA model show that the results from different distribution functions scatter considerably, and influenced strongly by return periods; however, the results from the HISWA model are convergent, that is, the influence of the design wave heights estimated with different distribution functions for deep water is weakened, and the estimated values decrease for long return periods and increase for short return periods. Therefore, the numerical wave model gives a more stable result in shallow water design wave estimation because of the consideration of the effect of physical processes which occur in shallow water.

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 south- ern part, with the maximum value occurring to the southeast of Hainan Island. The direction of large directional extreme Hs values is focus in E in the northem and middle sea areas of SCS, while the direction of those is focus in N in the southeast sea areas of SCS.

Numerical modelling of nonlinear extreme waves in presence of wind

A numerical wave flume with fully nonlinear free surface boundary conditions is adopted to investigate the temporal characteristics of extreme waves in the presence of wind at various speeds. Incident wave trains are numerically generated by a piston-type wave maker, and the wind-excited pressure is introduced into dynamic boundary conditions using a pressure distribution over steep crests, as defined by Jeffreys＇ sheltering mechanism.A boundary value problem is solved by a higher-order boundary element method（HOBEM） and a mixed Eulerian-Lagrangian time marching scheme. The proposed model is validated through comparison with published experimental data from a focused wave group. The influence of wind on extreme wave properties,including maximum extreme wave crest, focal position shift, and spectrum evolution, is also studied. To consider the effects of the wind-driven currents on a wave evolution, the simulations assume a uniform current over varying water depth. The results show that wind causes weak increases in the extreme wave crest, and makes the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide a comparison to demonstrate the shifts at focal points, considering the combined effects of the winds and the wind-driven currents.

Harmonic Energy Transfer for Extreme Waves in Current

Ning et al. （2015） developed a 2D fully nonlinear potential model to investigate the interaction between focused waves and uniform currents. The effects of uniform current on focusing wave crest, focal time and focal position were given. As its extension, harmonic energy transfer for focused waves in uniform current is studied using the proposed model by Ning et al. （2015） and Fast Fourier Transformation （FFT） technique in this study. It shows that the strong opposing currents, inducing partial wave blocking and reducing the extreme wave crest, make the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide an explanation to address the shifts of focal points in consideration of the combination effects of wave nonlinearity and current.

Experimental Investigation on the Extreme Waves Induced by Single Wave Packets in Finite Water Depth

Single Gaussian wave groups with different initial wave steepness εand width N are produced in laboratory in finite depth to study the nonlinear evolution, the extreme events and breaking. The results show that wave groups with larger εwill evolve to be several envelope solitons(short wave groups). By analyzing geometric parameters, a break in the evolution of the wave elevation and asymmetric parameters after extreme wave may be an indicator for the inception of refocus and the maximal wave moving to the middle, namely, wave down-shift occurs. The analysis of the surface elevations with HHT(Hilbert-Huang Transform), which presents the concrete local variation of energy in time and frequency can be exhibited clearly, reveals that the higher frequency components play a major role in forming the extreme event and the contribution to the nonlinearity. Instantaneous energy and frequency in the vicinity of the extreme wave are also examined locally. For spilling breakers, the energy residing in the whole wave front dissipates much more due to breaking, while the energy in the rear of wave crest loses little, and the intra-wave frequency modulation increases as focus. It illustrates that the maximal first order instantaneous frequency fand the largest crest tend to emerge at the same time after extreme wave when significant energy dissipation happens, and vice versa. In addition, it shows that there is no obvious relation of the CDN(combined degree of nonlinearity) to the wave breaking for the single Gaussian wave group in finite water depth.

Long-Period Distribution of Wave Heights and Its Application

This paper reveals that the long-period statistic distribution of the characteristic heights of deep-water waves assumes the lognormal distribution. Thereafter, the largest wave-height which may occur in the service life of coastal structures is derived in this paper.

Extreme Wave Simulation with Iterative Adaptive Approach in Numerical Wave Flume

Extreme wave is highly nonlinear and may occur due to diverse reasons unexpectedly.The simulated results of extreme wave based on wave focusing,which were generated using high order spectrum method,are presented.The influences of the steepness,frequency bandwidth as well as frequency spectrum on focusing position shift were examined,showing that they can affect the wave focusing significantly.Hence,controlled accurate generation of extreme wave at a predefined position in wave flume is a difficult but important task.In this paper,an iterative adaptive approach is applied using linear dispersion theory to optimize the control signal of the wavemaker.The performance of the proposed approach is numerically investigated for a wide variety of scenarios.The results demonstrate that this approach can reproduce accurate wave focusing effectively.

A METHOD FOR DETERMINING EXTREME WAVE HEIGHT

A method to determine the design value of the extreme wave height is introduced in this paper. The method is, based on the theoretical distribution of wave heights or the experiential probability distribution of wave heights, to calculate the mode of the extreme wave height and the design value with good assuredness. In fitting the experiential distribution of the observed wave heights, the paper adopts the simulating function of F(x) = 1 - exp[ ?axb exp( -cxd )] and the non-linear parameter in the function is determined by the Non-Linear Least Square Method. The practical application of the method has proved that it is not only simple and convenient, but also very effective in engineering design practice.

Response Spectrum Method for Extreme Wave Loading With Higher Order Components of Drag Force

Response spectra of fixed offshore structures impacted by extreme waves are investigated based on the higher order components of the nonlinear drag force. In this way, steel jacket platforms are simplified as a mass attached to a light cantilever cylinder and their corresponding deformation response spectra are estimated by utilizing a generalized single degree of freedom system. Based on the wave data recorded in the Persian Gulf region, extreme wave loading conditions corresponding to different return periods are exerted on the offshore structures. Accordingly, the effect of the higher order components of the drag force is considered and compared to the linearized state for different sea surface levels. When the fundamental period of the offshore structure is about one third of the main period of wave loading, the results indicate the linearized drag term is not capable of achieving a reliable deformation response spectrum.