Joint probability distribution of winds and waves from wave simulation of 20 years ( ) in Bohai Bay

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1 Water Science and Engineering, 2013, 6(3): doi: /j.in Joint probability ditribution of wind and wave from wave imulation of 20 year ( ) in Bohai Bay Xiao-chen YANG, Qing-he ZANG* State Key Laboratory of ydraulic Engineering Simulation and Safety, Tianjin Univerity, Tianjin , P. R. China Abtract: The joint probability ditribution of wind peed and ignificant wave height in the Bohai Bay wa invetigated by comparing the Gumbel logitic model, the Gumbel-ougaard (G) copula function, and the Clayton copula function. Twenty year of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecat (ECMWF) databae and the blended wind data of the Quick Scatterometer (QSCAT) atellite data et and re-analyi data from the United State National Center for Environmental Prediction (NCEP). Several typhoon were taken into account and merged with the background wind field from the ECMWF or QSCAT/NCEP databae. The 20-year data of ignificant wave height were calculated with the untructured-grid verion of the third-generation wind wave model Simulating WAve Nearhore (SWAN) under extreme wind proce condition. The Gumbel ditribution wa ued for univariate and marginal ditribution. The ditribution parameter were etimated with the method of L-moment. Baed on the marginal ditribution, the joint probability ditribution, the aociated return period, and the conditional probability ditribution were obtained. The G copula function wa found to be optimal according to the ordinary leat quare (OLS) tet. The reult how that wind wave are the prevailing type of wave in the Bohai Bay. Key word: wind peed; wave imulation; joint probability ditribution; copula function; conditional probability ditribution 1 Introduction In recent year, offhore platform have been widely ued for oil and ga production in the Bohai Bay. Traditionally, univariate ditribution are ued to obtain deign wind parameter and wave parameter with different return period for the tructure. owever, a wind and wave are actually non-independent, bivariate joint probability ditribution and conditional ditribution may be more realitic. In ocean and coatal engineering, bivariate joint probability ditribution of wave and wind have been invetigated through the Poion-mixed Gumbel ditribution (Liu et al. 2002; Dong et al. 2003), Gumbel logitic model (Zhou and Duan 2003), Poion bivariate logitic Thi work wa upported by the Science Fund for Creative Reearch Group of the National Natural Science Foundation of China (Grant No ) and the National igh Technology Reearch and Development Program of China (863 Program, Grant No. 2012AA and 2012AA051702). *Correponding author ( coatlab@163.com) Received Jul. 14, 2012; accepted Oct. 12, 2012

2 ditribution (Dong et al. 2005), and bivariate Pearon type III ditribution (Dong et al. 2006). owever, the marginal ditribution are uually retricted to a certain type. Reearcher have therefore introduced the copula function (Joe 1997; Nelen 2006), which i capable of linking arbitrary marginal ditribution to the joint probability ditribution. A an efficient tool, the copula function ha been applied widely in the financial ector, and recently in hydrology (De Michele and Salvadori 2003; Favre et al. 2004; Salvadori and De Michele 2004a, 2004b, 2006; De Michele et al. 2005; Grimaldi and Serinaldi 2006; Niu et al. 2009), wherea only a few tudie on the copula-baed joint probability ditribution have been carried out for coatal and ocean engineering (Nerzic and Prevoto 2000; Wit et al. 2004; De Michele et al. 2007; Qin et al. 2007; Dong et al. 2011; Chen 2011). For the copula-baed joint probability ditribution analyi of extreme wave height and wind peed, Gumbel-ougaard (G) and Clayton copula of the Archimedean copula family have been mot commonly ued. Qin et al. (2007) analyzed the wind-wave joint probability ditribution in the South China Sea uing the Clayton copula function. Dong et al. (2011) introduced the bivariate Gumbel Clayton copula ditribution baed on the Clayton copula function. Chen (2011) ued bivariate copula function to analyze the joint probability ditribution of extreme wave height and wind peed in the Shanwei ea area. Several copula function were compared and the G copula function wa found to be the optimal election through goodne-of-fit tet. In general, the optimal ditribution wa related to the ample. Therefore, the objective of thi tudy wa to ue the common ditribution, uch a the Gumbel logitic model, the G copula function, and the Clayton copula function, to invetigate the bivariate joint probability ditribution and extreme value with certain return period for wind and wave in the Bohai Bay. In order to invetigate the joint probability ditribution of wind and wave in the Bohai Bay, continuou wind and wave data for at leat 20 year are required to calculate the probability ditribution of extreme wind and wave. owever, the meaurement of ea urface wind over the Bohai Sea are too pare to provide a wind field for thi tudy. A a reult, the wind data were obtained from the QSCAT/NCEP blended ocean wind data et ( and the ECMWF 40-year re-analyi data et ( portal.ecmwf.int/data/d/era40_daily/). Due to the increaing performance of computational reource, the numerical method may provide an alternative to the oberved wave data. The well-etablihed third-generation wind wave model Simulating WAve Nearhore (SWAN) (Booij et al. 1999) ha played an important role in wind wave numerical modeling, and in recent year the model ha been widely applied in the Yellow-Bohai Sea (Wang et al. 2004; Li and Bo 2005; Deng et al. 2007; Zheng et al. 2010). Recently, Zijlema (2010) propoed an untructured meh for SWAN, which can decribe the complex coatal boundarie and offer a good alternative to the traditional tructured-grid neted model. In thi tudy, numerical imulation of wave procee during extreme wind procee in each year wa carried out uing the untructured-grid verion of the SWAN model for a 20-year duration from 1989 to Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

3 2 Joint probability ditribution model 2.1 Gumbel logitic model The Gumbel logitic model ha been ued in the field of ocean engineering (Zhou and Duan 2003) and hydrology (Yue 2001), with the Gumbel ditribution a the marginal ditribution. It i expreed a follow: 1 m m m F( x, y) = exp ( ln F( x) ) + ( ln F( y) ) m 1, ) (1) where F( x ) and F( y ) are the marginal ditribution of two random variable X and Y, repectively; and m repreent the aociation between the two random variable, etimated a 1 m = 0 ρ 1 (2) 1 ρ ( ) where ρ i the correlation coefficient and i expreed a E ( x μx )( y μy ) ρ = (3) σ σ where μ X and μ Y are the mean of X and Y, repectively, and σ X and σ Y are the tandard deviation of X and Y, repectively. 2.2 Copula function X Copula function are not retricted to a certain type of ditribution like the marginal ditribution. The Gumbel-ougaard (G) copula and the Clayton copula have been mot commonly ued in coatal and ocean engineering and performed well (Qin et al. 2007; Dong et al. 2011; Chen 2011). The G copula function i expreed a follow: θ θ 1 θ C( x, y) = exp ( ln x) + ( ln y) θ 1, (4) Y { } ) 1 τ = 1 (5) θ where τ i the Kendall correlation coefficient, and θ i a parameter decribing the dependency relationhip between the two variable. The Clayton copula function i expreed a θ θ 1 θ (, ) ( 1 ) θ ( 0, ) C x y = x + y (6) θ τ = (7) θ + 2 Baed on the copula function, the bivariate joint probability ditribution i expreed a (, ) ( ( ), ( )) F x y = C F x F y (8) 2.3 Return period and conditional probability ditribution The return period for the variable X and Y exceeding certain value are expreed, 298 Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

4 repectively, a follow: T x T y = 1 1 F x (9) 1 F( y) The joint return period T( x, y ) of either X or Y or both exceeding the correponding value x and y (X The joint return period T ( ) 0, ( ) = 1 (10) > x, Y > y, or X > x and Y > y) can be expreed a 1 T( x, y) = 1 F x, y (11) ( ) x y of both X and Y exceeding the correponding value x and y (X > x and Y > y) i expreed a 1 T0 ( x, y) = (12) 1 F x F y + F x, y ( ) ( ) ( ) The conditional probability of X x given that Y y i expreed a P( X x, Y y) 1 F x F y + F x, y P( X xy y) = = P X x 1 F x ( ) ( ) ( ) ( ) ( ) The conditional probability of other condition can alo be calculated. 3 Application 3.1 Wind data The extreme wind procee and annual extreme wind peed from 1989 to 1999 were taken from the ECMWF data (from September 1957 to Augut 2002) and the wind data from 2000 to 2008 were taken from the QSCAT/NCEP data (from July 1999 to July 2009). The patial reolution of the QSCAT/NCEP and ECMWF data were and , repectively. The temporal reolution of both data et wa 6 h. According to the wind data time erie from the Bohai Bay, extreme wind procee with greater wind peed and wind fetch length, a well a longer acting time, were elected for wave imulation. When comparing the extreme wind peed data from QSCAT/NCEP with thoe from ECMWF at the ame place during the ame extreme wind procee, value of mot extreme wind peed from QSCAT/NCEP were larger than thoe from ECMWF. Since the QSCAT/NCEP urface wind data were blended with the atellite-oberved data, in order to unify thee two et of data, the ECMWF wind peed hould be modified. A linear relation, with a correlation coefficient of 0.70, wa found between the extreme wind peed from QSCAT/NCEP and ECMWF during the ame period. It wa demontrated that the value of the wind peed from QSCAT/NCEP were 1.79 time thoe from ECMWF. Furthermore, during the entire 20 year, typhoon Ellie in 1994, Winnie in 1997, and Mata in 2005 were taken into account becaue their path were near the Bohai Bay and could probably caue extreme wave. The path, preure, wind peed, and other information about (13) Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

5 the typhoon were collected from the Zhejiang Real-Time Typhoon Data Sytem ( and the Uniy Weather Sytem ( hurricane). The QSCAT/NCEP or ECMWF wind data, a the background wind field, were merged with the typhoon data to obtain the wind field during typhoon. Both the QSCAT/NCEP and ECMWF wind data et have been employed in atmopheric analyi (Tu and Yao 2010; Zhang et al. 2011). In thi tudy, real-time wind data from the QK18 platform in the Bohai Sea (Fig. 1) and an obervation tation A with a water depth of 50 m in the Yellow Sea (Fig. 1) were collected for verification. Comparion between the obervation and the QSCAT/NCEP and ECMWF wind data are hown in Fig. 2. Both the QSCAT/NCEP and ECMWF wind data how reaonable agreement with the meaured wind data. In addition, the oberved wind data from the obervation tation B (with a longitude of E and a latitude of 27.3 N) in the Eat Sea during typhoon Mata in 2005 were collected to verify the wind data under the condition of typhoon. Fig. 3 how the comparion between the obervation and the wind data merged by the QSCAT/NCEP data and typhoon data at tation B. It demontrate that the accuracy of the wind data during typhoon weather i acceptable. Fig. 1 Sketch map of Yellow-Bohai Sea and location of obervation tation and ampling point Fig. 2 Comparion of wind peed between obervation and data from different wind databae at different obervation tation 300 Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

6 Fig. 3 Comparion of wind peed between obervation and wind data merged by QSCAT/NCEP data and typhoon data at tation B 3.2 Wave imulation The wind wave model SWAN, which i baed on the action balance equation (Booij et al. 1999), wa employed in thi tudy. Several ource and ink term were included in the equation to take account of the procee that generate, diipate, or reditribute wave energy. Recently, the untructured-grid verion of the SWAN model wa preented by Zijlema (2010) with a vertex-baed, fully implicit, finite difference method. The untructured grid allowed for a locally refined grid and wa more uitable for decribing the irregular horeline. Therefore, the untructured-grid verion of the SWAN model wa ued in thi tudy. Zijlema (2010) elected two academic tet cae and one realitic wind-ea cae to how the correctne and numerical accuracy of the untructured-grid verion of the SWAN model. In thi tudy, ignificant wave height collected at the BZ28 platform in the Bohai Sea (Fig. 1) and tation A in the Yellow Sea (Fig. 1) were compared with the imulated reult and are hown in Fig. 4. The computation domain included the Yellow-Bohai Sea area with an open boundary at a latitude of 37 N to give the wave a fully developed proce. The model grid wa locally refined at the Bohai Bay area, with a minimum ize of about 350 m. The bathymetry wa interpolated onto the grid and i hown in Fig. 1. Wave were driven by wind, Fig. 4 Comparion of meaured and imulated ignificant wave height Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

7 and the wind data from QSCAT/NCEP or ECMWF were ued, a decribed in ection 3.1. The time tep wa et at 10 min. The dicrete frequency wa et from 0.04 to 1.0 z, and the bottom friction wa et at 0.01 m 2 / 3. The imulated ignificant wave height fit well with the meaured data, which further demontrated the capability of the untructured-grid verion of the SWAN model. Uing elected wind procee, the entire 20-year wave field were imulated. We elected a ampling point (Fig. 1) on a 20 m-depth contour for further analyi. From the wind data and the imulated wave data, the annual extreme wind peed and the correponding ignificant wave height, and the annual extreme ignificant wave height and the correponding wind peed can be obtained and ued in the analyi of univariate and bivariate joint probability ditribution. 3.3 Univariate analyi The annual extreme wind peed ( V m ) and annual extreme ignificant wave height ( m ) were collected for univariate analyi. We ued the Gumbel ditribution for both V m and m : x u x F( x) = exp exp (14) α x where u x and α x are, repectively, the location and cale parameter of the Gumbel ditribution and can be etimated with the method of L-moment. The univariate ditribution of V m and m are hown in Fig. 5, where P i the cumulative frequency, and the univariate deign factor for different return period are hown in Table 1. Fig. 5 Univariate ditribution of annual extreme wind peed and annual extreme ignificant wave height 3.4 Bivariate analyi Two pair of data, the annual extreme wind peed and the correponding ignificant wave 302 Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

8 Data pair ( Vm, ) (, V ) m Table 1 Deign value of wind peed and ignificant wave height for different return period Return period of marginal ditribution T (year) Joint return period T( x, y ) (year) Joint return period T ( x, y ) 0 (year) Univariate deign factor V (m/) (m) Marginal deign factor V (m/) (m) Joint deign factor for T( x, y) = T V (m/) height ( V m, ), and the annual extreme ignificant wave height and the correponding wind peed (, m V ) were collected for bivariate analyi. The marginal ditribution of wind peed and ignificant wave height were alo etimated by the Gumbel ditribution and are preented in Fig. 6. (m) Fig. 6 Marginal ditribution of wind peed and ignificant wave height The ordinary leat quare (OLS) method wa introduced to ae the joint probability ditribution model. The OLS value ( OLS ) wa etimated a follow: n i = 1 i i 1 n ( ) 2 e (15) OLS = P P where P i and P ei are, repectively, the theoretical frequency and empirical frequency, and n i the ample ize. The OLS value for the Gumbel logitic model, the G copula function, and the Clayton Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

9 copula function were 0.073, 0.065, and 0.066, repectively. The G copula function wa elected becaue it had the mallet OLS value. The three-dimenional diagram of the joint cumulative ditribution function (CDF) and the contour of the joint return period T( x, y ) for ( V m, ) are hown in Fig. 7 and Fig. 8, repectively. For each pair, auming a ame frequency of X and Y, with a given return period T, the joint deign wave height and wind peed can be obtained. Reult of marginal and joint deign wave and wind a well a the joint return period for both data pair are hown in Table 1. Fig. 7 Three-dimenional diagram of joint cumulative Fig. 8 Joint return period T( x, y ) contour ditribution function for ( Vm, ) for ( Vm, ) (Unit: year) According to Table 1, the marginal return period i larger than the joint return period T( x, y ), but maller than T0 ( x, y ). The joint deign wave height and wind peed have larger value than the marginal deign factor. Compared with the univariate ditribution, for ( V m, ), the joint deign wind peed are 1.6% to 3.2% larger than the univariate deign wind peed and the joint deign wave height are 12.9% to 21.8% maller. owever, thi i revered for (, m V ), where the joint deign wind peed are 1.4% to 11.4% maller and the joint deign wave height are 4.1% to 7.5% larger. The conditional probability ditribution i neceary becaue it provide information on the encounter probability of two condition. From Table 2 and Table 3, for ( V m, ), the encounter probability of the condition with the ame frequency i larger than 62%, and for Table 2 Conditional probability of Vm x given y for ( Vm, ) Conditional probability (%) V m P (m/) (%) = 6.64 m = 6.00 m = 5.36 m = 4.51 m = 3.85 m = 3.16 m P = 0.5% P = 1% P = 2% P = 5% P = 10% P = 20% Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

10 Table 3 Conditional probability of m x given V y for (, V ) m m (m) P (%) V = m/ P = 0.5% V = m/ P = 1% Conditional probability (%) V = m/ P = 2% V = m/ P = 5% V = m/ P = 10% V = m/ P = 20% (, V ), it i larger than 56%. For ( m Vm, ), the encounter probability between large deign wind peed and mall deign wave height i very mall. Alo, the probability of large deign wave height encountering mall deign wind peed i mall for (, m V ). It i demontrated that wind wave are prevailing in the Bohai Bay, with trong wave alway encountering trong wind. Thi i conitent with the reearch of Wang et al. (2004) and Deng et al. (2007). 4 Concluion Baed on the ECMWF and QSCAT/NCEP wind data and the wave data imulated by the untructured-grid verion of the SWAN model for 20 year, a univariate ditribution and a bivariate joint probability ditribution were applied to the calculation of the deign wind peed and wave height with different return period in the Bohai Bay. The method i robut becaue the wind data and the imulated wave reult were well matched with the meaured data. The joint return period, joint deign factor, and conditional probability ditribution were obtained. Thi tudy provide more information for the choice of the deign factor in the Bohai Bay. The main concluion are a follow: (1) According to the comparion of the Gumbel logitic model, the G copula function, and the Clayton copula function, the OLS value of the G copula function wa the mallet, which demontrated that the G copula function wa optimal for the preent ample. (2) According to the comparion of the bivariate joint probability ditribution and the marginal ditribution, it can be een that the joint return period of either wind peed or wave height or both exceeding certain value i maller than the marginal return period, and the joint return period of both wind peed and wave height exceeding certain value i larger than the marginal return period. The joint deign wave height and wind peed are both larger than the marginal deign value. (3) According to the comparion of the bivariate joint probability ditribution and the univariate ditribution, it can be een that for data pair of the annual extreme wind peed and the correponding ignificant wave height, the joint deign wind peed are larger than the univariate deign wind peed and the joint deign wave height are maller. Thi i revered, however, for data pair of the annual extreme ignificant wave height and the correponding Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

11 wind peed. (4) The conditional probability for both data pair how that the encounter probability of the condition with the ame frequency i larger than 56%. The probability of mall deign wind peed encountering large deign wave height i very mall, and the encounter probability between mall deign wave height and large deign wind peed i alo mall. According to the conditional ditribution, wind wave are regarded to be prevailing in the Bohai Bay. (5) Though the accuracy of wind data ued in the preent tudy wa acceptable, an improvement in reolution would yield better reult. Wind data calculated by an atmopheric model with better wind data et, newly available, will be carried out in future tudie. Reference Booij, N., Ri, R. C., and olthuijen, L A third-generation wave model for coatal region: 1. Model decription and validation. Journal of Geophyical Reearch, 104(C4), [doi: / 98JC02622] Chen, Z. S Study on joint probability ditribution of wave height and wind velocity. Marine Science Bulletin, 30(2), (in Chinee) De Michele, C., and Salvadori, G A generalized Pareto intenity-duration model of torm rainfall exploiting 2-Copula. Journal of Geophyical Reearch: Atmophere, 108(D2), [doi: / 2002JD002534] De Michele, C., Salvadori, G., Canoi, M., Petaccia, A., and Roo, R Bivariate tatitical approach to check adequacy of dam pillway. Journal of ydrologic Engineering, 10(1), [doi: /(asce) (2005)10:1(50)] De Michele, C., Salvadori, G., Paoni, G., and Vezzoli, R A multivariate model of ea torm uing copula. Coatal Engineering, 54(10), [doi: /j.coataleng ] Deng, Z. Q., Zhou, L. M., Wu, L. Y., and Guo, P. F Numerical computation of wave height of multiyear return period in the Bohai Sea. Tranaction of Oceanology and Limnology, (1), (in Chinee) [doi: /j.in z1.002] Dong, S., ao, X. L., Jiao, G. Y., and Liu, D. F Joint probability calculation of extreme wind peed and wave height in the exploitation of marginal field. Ship Building of China, 44(1), (in Chinee) [doi: /j.in z1.041] Dong, S., ao, X. L., and Fan, D. Q Joint probability ditribution of wind velocity and wave height in ocean engineering deign. Acta Oceanologica Sinica, 27(3), (in Chinee) [doi: /j.in ] Dong, S., Cong, J. S., and Yu,. J Deign parameter etimation of joint extreme ignificant wave height and wind peed at Weizhoudao obervation tation. Periodical of Ocean Univerity of China, 36(3), (in Chinee) Dong, S., Zhou, C., Tao, S. S., and Xue, D. S Bivariate Gumbel ditribution baed on Clayton Copula and it application in offhore platform deign. Periodical of Ocean Univerity of China, 41(10), (in Chinee) [doi: /j.in ] Favre, A. C., El Adlouni, S., Perreault, L., Thiémonge, N., and Bobée, B Multivariate hydrological frequency analyi uing copula. Water Reource Reearch, 40(1), [doi: /2003wr002456] Grimaldi, S., and Serinaldi, F Aymmetric copula in multivariate flood frequency analyi. Advance in Water Reource, 29(8), [doi: /j.advwatre ] Joe, Multivariate Model and Multivariate Dependence Concept. London: Chapman and all/crc. Li, Y., and Bo, Z The imulation tet of SWAN model in the wave height in the Yellow-Bo Sea area. Marine Forecat, 22(3), (in Chinee) [doi: /j.in ] 306 Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,

12 Liu, D. F., Wen, S. Q., and Wang, L. P Compound bivariate extreme ditribution of typhoon induced ea environment and it application. Proceeding of the 12th International Offhore and Polar Engineering Conference, Kitakyuhu: ISOPE. Nelen, R. B An Introduction to Copula. 2nd ed. New York: Springer-Verlag. Nerzic, R., and Prevoto, M Modelling of wind and wave joint occurrence probability and peritence duration from atellite obervation data. Proceeding of the 10th International Offhore and Polar Engineering Conference, Seattle: ISOPE. Niu, J. Y., Feng, P., and Ding, Z Study of the wetne-dryne compenation characteritic of Luan river diverion reervoir inflow baed on multivariate Copula function. Journal of Jilin Univerity (Earth Science Edition), 39(6), (in Chinee) [doi: /j.in ] Qin, Z. J., Sun, G.., Yan, T. X., Song,., and Zhang, J Application of multivariate probability analyi uing copula to ocean engineering. Marine Forecat, 24(2), (in Chinee) [doi: /j.in ] Salvadori, G., and De Michele, C. 2004a. Analytical calculation of torm volume tatitic involving Pareto-like intenity-duration marginal. Geophyical Reearch Letter, 31, L [doi: / 2003GL018767] Salvadori, G., and De Michele, C. 2004b. Frequency analyi via copula: Theoretical apect and application to hydrological event. Water Reource Reearch, 40(12). [doi: /2004wr003133] Salvadori, G., and De Michele, C Statitical characterization of temporal tructure of torm. Advance in Water Reource, 29(6), [doi: /j.advwatre ] Tu, X. P., and Yao, R. S Analyi on ECMWF NWP product in TC tracking forecating. Journal of Tropical Meteorology, 26(6), (in Chinee) [doi: /j.in ] Wang, D. Z., Zhang, Q.., and Shi, Z Modeling of wind wave in the Bohai Bay, China. Marine Science Bulletin, 23(5), (in Chinee) [doi: /j.in ] Wit,. T., Myrhaug, D., and Rue, Statitical propertie of ucceive wave height and ucceive wave period. Applied Ocean Reearch, 26(3-4), [doi: /j.apor ] Yue, S The Gumbel logitic model for repreenting a multivariate torm event. Advance in Water Reource, 24(2), [doi: /s (00) ] Zhang, D. T., Zheng, C. W., Shi, L. L., Liu, Z.., and Chen, X. B Sea urface wind field analyze from 1999 to 2009 in the China Sea by QuickSCAT/NCEP data. Marine Forecat, 28(4), (in Chinee) [doi: /j.in ] Zheng, G. D., Zhao,. J., Xu, F. M., and Zhang, S Numerical imulation of wind wave in Bohai Sea induced by cold wave. Port and Waterway Engineering, (2), (in Chinee) [doi: /j.in ] Zhou, D. C., and Duan, Z. D The Gumbel-logitic model for joint probability ditribution of extreme-value wind peed and effective wave height. The Ocean Engineering, 21(2), (in Chinee) [doi: /j.in ] Zijlema, M Computation of wind-wave pectra in coatal water with SWAN on untructured grid. Coatal Engineering, 57(3), [doi: /j.coataleng ] (Edited by Yun-li YU) Xiao-chen YANG et al. Water Science and Engineering, Jul. 2013, Vol. 6, No. 3,