一个两时间层原始方程三维海洋环流模式平台的构建和检验
|
摘要
本文介绍了一个采用两时间层有限差分格式的、Boussinesq近似的、自由表面、模态分离的、采用地形坐标系的原始方程三维海洋环流数值模式(MASNUM)平台的建立。
本文从完整的地球流体力学控制方程组出发,在Boussinesq假定和静力学假定下,详细推导了地形坐标下雷诺平均的海水运动控制方程组,以此建立了模式的数学模型。数值算法上,内外模态的时间差分均采用了两时间层的欧拉前后差分格式(FB),空间采用Arakawa-C交错网格;为了抑制由于非线性作用产生的短波扰动的增长,构造了在任意海陆分布下保持计算区域内水体体积守恒的空间平滑算法。
斜压梯度力项的计算采用三次样条插值的密度雅克比式算法,并对原算法中的调和平均进行了修正,进一步减小了误差；对现有垂向速度的诊断算法中存在的问题进行了详细的检讨,证明在当前模式框架下难以找到一种完美的垂向速度计算方案。本文还对主要热力学变量如海水状态方程和静力稳定度的算法进行了讨论和更新；在前人工作基础上对常用的三大类共18种应用于环流模式的运动学开边界条件进行了归纳、对其构造算法进行了详细的推导,并将其作为子程序编入模式,供不同数值实验调用。
模式性能检验方面,首先对中国近海潮汐进行了模拟,MASNUM环流模式对迟角的模拟表现出一定的改善；其次,MASNUM环流模式能够模拟出典型斜压现象黄海冷水团的主要特征和季节演化规律,与观测有较好的一致性；第三,使用该模式对西北太平洋海域进行了进行了1/6度分辨率的计算,任意选取了30个计算点与相同条件下的POM模式的结果进行了3年时间序列的比较,参与比较的4个预报量无论在振幅还是相位上均表现出很好的一致性。这些实验和比较证实了本模式的可靠性。
A finite-difference, primitive equation, three-dimensional ocean circulation model (MASNUM circulation model) was established. This model is characterized by its Boussinesq approximation, free-surface, mode-splitting, terrain-following features, and temporally discretized with a two-level scheme.
The mathematical model of the oceanic motions is based on the terrain-following, Reynolds-averaged ocean governing equations, which are derived from the complete geophysical fluid dynamical equations under the hydrostatic and Boussinesq approximations. As the numerical techniques, a simplest two-level, single-step algorithm, Eulerian forward and backward difference method (FB), is adopted for the temporal difference. The staggered Arakawa-C stencil is used for spatial arrangements of the model variables. A volume-conserved spatial smoothing method is devised to surppress the growing of the short perturbations due to nonlinear terms.
The spline interpolated density Jacobian algorithm is cited in calculating the internal pressure gradient force. However, certain correction has to be made to the harmonic mean in the original algorithm to reduce the error. The error analysis and correction has been made to the diagnostic computation of the vertical velocity. The problem that the kinetic boundary conditions at the surface and the bottom cannot be strictly satisfied simultaneously in the original algorithm has been fixed.
The algorithms of some main thermodynamic variables, such as in-situ density and static stability have been reviewed and updated with up-to-date and stable computation methods. The detailed numerical forms are derived for three categories,18kinds of open boundary condtions for the kinetic variables prevelant in current ocean models. Most of these conditions have been included in the MASNUM circulation model, to be invoked in all kinds of numerical experiments.
To verify the performance of the MASNUM circulation model, the coastal tide of the China Seas is first simulated, and MASNUM circulation model appears improvements in the phase lag. Secondly, MASNUM circulation model could simulate the main features and seasonal evolutions of the Yellow-Sea Cold Water Mass, a typical baroclinic phenomenon. Thirdly, the MASNUM circulation model has been setup to compute the Northwest Pacific with horizontal resolution of1/6degrees and vertically16layers. The3-year time series of four prognostic variables has been compared with those of the POM model. The comparisons show farily good consistent in both amplitude and phase between the two models. These experiments and comparisons verified the reliablity and applicability of the newly-built circulation model to a large extent.
本文从完整的地球流体力学控制方程组出发,在Boussinesq假定和静力学假定下,详细推导了地形坐标下雷诺平均的海水运动控制方程组,以此建立了模式的数学模型。数值算法上,内外模态的时间差分均采用了两时间层的欧拉前后差分格式(FB),空间采用Arakawa-C交错网格;为了抑制由于非线性作用产生的短波扰动的增长,构造了在任意海陆分布下保持计算区域内水体体积守恒的空间平滑算法。
斜压梯度力项的计算采用三次样条插值的密度雅克比式算法,并对原算法中的调和平均进行了修正,进一步减小了误差；对现有垂向速度的诊断算法中存在的问题进行了详细的检讨,证明在当前模式框架下难以找到一种完美的垂向速度计算方案。本文还对主要热力学变量如海水状态方程和静力稳定度的算法进行了讨论和更新；在前人工作基础上对常用的三大类共18种应用于环流模式的运动学开边界条件进行了归纳、对其构造算法进行了详细的推导,并将其作为子程序编入模式,供不同数值实验调用。
模式性能检验方面,首先对中国近海潮汐进行了模拟,MASNUM环流模式对迟角的模拟表现出一定的改善；其次,MASNUM环流模式能够模拟出典型斜压现象黄海冷水团的主要特征和季节演化规律,与观测有较好的一致性；第三,使用该模式对西北太平洋海域进行了进行了1/6度分辨率的计算,任意选取了30个计算点与相同条件下的POM模式的结果进行了3年时间序列的比较,参与比较的4个预报量无论在振幅还是相位上均表现出很好的一致性。这些实验和比较证实了本模式的可靠性。
A finite-difference, primitive equation, three-dimensional ocean circulation model (MASNUM circulation model) was established. This model is characterized by its Boussinesq approximation, free-surface, mode-splitting, terrain-following features, and temporally discretized with a two-level scheme.
The mathematical model of the oceanic motions is based on the terrain-following, Reynolds-averaged ocean governing equations, which are derived from the complete geophysical fluid dynamical equations under the hydrostatic and Boussinesq approximations. As the numerical techniques, a simplest two-level, single-step algorithm, Eulerian forward and backward difference method (FB), is adopted for the temporal difference. The staggered Arakawa-C stencil is used for spatial arrangements of the model variables. A volume-conserved spatial smoothing method is devised to surppress the growing of the short perturbations due to nonlinear terms.
The spline interpolated density Jacobian algorithm is cited in calculating the internal pressure gradient force. However, certain correction has to be made to the harmonic mean in the original algorithm to reduce the error. The error analysis and correction has been made to the diagnostic computation of the vertical velocity. The problem that the kinetic boundary conditions at the surface and the bottom cannot be strictly satisfied simultaneously in the original algorithm has been fixed.
The algorithms of some main thermodynamic variables, such as in-situ density and static stability have been reviewed and updated with up-to-date and stable computation methods. The detailed numerical forms are derived for three categories,18kinds of open boundary condtions for the kinetic variables prevelant in current ocean models. Most of these conditions have been included in the MASNUM circulation model, to be invoked in all kinds of numerical experiments.
To verify the performance of the MASNUM circulation model, the coastal tide of the China Seas is first simulated, and MASNUM circulation model appears improvements in the phase lag. Secondly, MASNUM circulation model could simulate the main features and seasonal evolutions of the Yellow-Sea Cold Water Mass, a typical baroclinic phenomenon. Thirdly, the MASNUM circulation model has been setup to compute the Northwest Pacific with horizontal resolution of1/6degrees and vertically16layers. The3-year time series of four prognostic variables has been compared with those of the POM model. The comparisons show farily good consistent in both amplitude and phase between the two models. These experiments and comparisons verified the reliablity and applicability of the newly-built circulation model to a large extent.
引文
[1]Anderson J D. Computational Fluid Dynamics[M]. McGraw-Hill College,1995.
[2]Arakawa A. Computational design for long-term numerical integraton of the equations of fluid motion:Two-dimensional incompressible flow. Part I[J]. J Comput Phys.1966,1:119-143.
[3]Arakawa A, Lamb V R. Computational design of the basic dynamical processes in the UCLA general circulation model[M]. Methods in Computational Physics. Vol.17:General circulation models of the atmosphere, Chang J, Academic Press,1977.
[4]Asselin R. Frequency filters for time integrations[J]. Mon Weather Rev.1972,100:487-490.
[5]Baumert H Z, Simpson J, Sundermann J. Marine turbulence:Theories, observations, and models[M]. Cambridge University Press,2011:654.
[6]Beardsley R C, Haidvogel D B. Model studies of the wind driven transient circulation in the Middle Atlantic Bight,1, Adiabatic boundary conditions[J]. J Phys Oceanogr.1981,11: 355-375.
[7]Beckmann A, Boning C W, Koberle C, Willebrand J. Effects of increased horizontal resolution in a simulation of the North Atlantic Ocean[J]. J Phys Oceanogr.1994,24:326-344.
[8]Bennett A F, Kloeden P E. Boundary conditions for limited-area forecasts[J]. J Atmos Sci. 1978,35:355-375.
[9]Blazek J. Computational Fluid Dynamics:Principles and Applications,2nd Edition[M]. Elsevier,2005.
[10]Bleck R, Benjamin S. Regional weather prediction with a model combining terrain-following and isentropic coordinates. Part I:Model description[J]. Mon Weather Rev.1993,121: 1770-1785.
[11]Bleck R, Boudra D. Initial testing of a numerical ncean circulation model using a hybrid (quasi-isopycnic) vertical coordinate[J]. J Phys Oceanogr.1981,11:755-770.
[12]Blumberg A F, Kantha L H. Open boundary conditions for circulation models[J]. J Hydraul Eng.1985,11:237-255.
[13]Boussinesq J V. Theorie Analytique de la Chaleur. Vol. Ⅱ[M]. Paris:Gauthier-Villars,1903.
[14]Bricaud A, Babin M, Morel A, Claustre H. Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton:Analysis and parameterization[J]. J Geophys Res.1995, 100:13,313-321,332.
[15]Bryan F O. A numerical model for the study of the circulation of the world oceans[J]. J Comput Phys.1969,4:347-359.
[16]Bryden H L. New polynomials for thermal expansion, adiabatic temperature gradient and potential temperature gradient of sea water[J]. Deep-Sea Res.1973,20:401-408.
[17]Buiteveld H, Hakvoort J H M, Donze M. The optical properties of pure water[M]. Ocean Optics Ⅻ, SPIE,1994:2258,174-183.
[18]Chapman D C. Numerical treatment of cross-shelof pen boundaries in a barotropic coastal ocean modelfJ]. J Phys Oceanogr.1985,15:1060-1075.
[19]Chelton D B, Schlax M G. Global observations of oceanic Rossby waves[J]. Science.1996, 272:234-238.
[20]Chelton D B, Deszoeke R A, Schlax M G, Naggar K E, Siwertz N. Geographical variability of the first baroclinic Rossby radius of deformation[J]. J Phys Oceanogr.1998,28:433-460.
[21]Chen C T, Millero F J. Precise thermodynamic properties for natural waters covering only the limnological range[J]. Limnol Oceanogr.1986,31:657-662.
[22]Chu P C, Fan C. Hydrostatic correction for sigma coordinate ocean models[J]. J Geophys Res. 2003(108(C6)):3206.
[23]Csanady G T. Air-Sea Interaction:Laws and Mechanisms[M]. Cambridge University Press, 2001:239.
[24]Curry J A, Webster P J. Thermodynamics of atmospheres and oceans[M]. San Diego: Academic Press,1999:471.
[25]Dai D, Qiao F, Sulisz W, Han L, Babanin A. An experiment on the non-breaking surface-wave-induced vertical mixing[J]. J Phys Oceanogr.2010,40:2180-2188.
[26]Dietrich D E, Marietta M G, Roach J P. An ocean modeling system with turbulent boundary layers and topography[J]. Int J Numer Meth Fl.1987,7:833-855.
[27]Dinniman M S, Klinck J M. The influence of open versus periodic alongshore boundaries on circulation near submarine canyons[J]. J Atmos Ocean Tech.2002,19:1722-1737.
[28]Dong-Feng X, Yao-Chu Y, Yuan L. The baroclinic circulation structure of Yellow Sea Cold Water Mass[J]. Sci China Ser D.2003,46(2):117-126.
[29]Dukowicz J K, Smith R D, Malone R C.A reformulation and implementation of the Bryan-Cox-Semtner ocean model on the Connection Machine[J]. J Atmos Ocean Tech.1993, 10:195.
[30]Dukowicz J K. Mesh Effects for Rossby Waves[J]. J Comput Phys.1995,119:188-194.
[31]Durran D R. Numerical methods for wave equations in geophysical fluid dynamics [M]. Springer,1999:470.
[32]Eckart C. Properties of water:Ⅱ. The equation of state of water and sea water at low temperatures and pressures[J]. Amer J Sci.1958,256:225-240.
[33]Fang G, Jinfei Y. Modeling and prediction of tidal currents in the Korea Strait[J]. Prog Oceanogr.1988,21:307-318.
[34]Fang G, Wang Y, Wei Z, Choi B H, Wang X, Wang J. Empirical cotidal charts of the Bohai, Yellow, and East China Seas from 10 years of TOPEX/Poseidon altimetry[J]. J Geophys Res. 2004,109:C11006.
[35]Fang G, Yang J, Thao Y. A two-dimensional numerical model for tidal motion in the Taiwan Strait[J]. Mar Geophys Res.1984,7(1):267-276.
[36]Feistel R. A new extended Gibbs thermodynamic potential of seawater[J]. Prog Oceanogr. 2003,58:43-114.
[37]Feistel R, Hagen E. On the GIBBS thermodynamic potential of seawater[J]. Prog Oceanogr. 1995,36:249-327.
[38]Flather R A. A tidal model of the northwest European continental shelf[J]. Mem Soc R Sci Liege.1976,6(10):141-164.
[39]Freeman J C, Baer L. Pseudo-characteristics[J]. Trans Amer Geophys Union.1957,38: 65-67.
[40]Freeman J C, Baer L. The method of wave derivatives[J]. Trans Amer Geophys Union.1957, 38:483-494.
[41]Gan J P, Allen J S. On open boundary conditions for a limited-area coastal model off Oregon. Part 1. Response to idealized wind forcing[J]. Ocean Modell.2005,8:155-173.
[42]Gent P R, Mcwilliams J C. Isopycnal mixing in ocean circulation models[J]. J Phys Oceanogr. 1990,20:150-155.
[43]Gill A. Atmosphere-ocean dynamics[M]. Academic Press,1982:662.
[44]Griffies S M, Gnanadesikan A, Pacanowski R C, Larichev V D, Dukowicz J K, Smith R D. Isoneutral diffusion in a z-coordinate ocean model[J]. J Phys Oceanogr.1998,28:805-830.
[45]Guo B H. The Ocean Environment of the Marginal Seas Adjacent to China[M]. Beijing: China Ocean Press,2004:446.
[46]Guo Y F, Yu Y Q, Liu X Y, Zhang X H. Simulation of climate change induced by CO2 increasing for East Asia with IAP/LASG GOALS model[J]. Adv Atmos Sci.2001,18:53-66.
[47]Haidvogel D B, Arango H, Budgell W P, Cornuelle B D, Curchitser E, Di Lorenzo E, Fennel K, Geyer W R, Hermann A J, Lanerolle L, Levin J, Mcwilliams J C, Miller A J, Moore A M, Powell T M, Shchepetkin A F, Sherwood C R, Signell R P, Warner J C, Wilkin J. Ocean forecasting in terrain-following coordinates:Formulation and skill assessment of the Regional Ocean Modeling System[J]. J Comput Phys.2008,227:3595-3624.
[48]Haidvogel D B, Beckmann A. Numerical Ocean Circulation Modeling[M]. Imperial College Press,1999:319.
[49]Hartree D R. Some practical methods of using characteristics in the calculation of non-steady compressible flow[C].Rep. AECU-2713 Washington, D.C.:U.S. At. Energy Comm.,1953.
[50]Hedley M, Yau M K. Radiation boundary conditions in numerical modeling[J]. Mon Weather Rev.1988,116:1721-1736.
[51]Hedstrom G W. Nonreflecting boundary conditions for nonlinear hyperbolic systems [J]. J Comput Phys.1979,30:222-237.
[52]Hersbach H. Sea surface roughness and drag coefficient as functions of neutral wind speed[J]. J Phys Oceanogr.2011,41:247-251.
[53]Higdon R L, Bennett A F. Modeling, Stability Analysis Of Operator for large-scale ocean modeling[J]. J Comput Phys.1996,123:311.
[54]Higdon R L, de Szoeke R A. Barotropic-baroclinic time splitting for ocean circulation modeling[J]. J Comput Phys.1997,135(30).
[55]Holland W R. Quasi-geostrophic modeling of eddy-resolved ocean circulation[M]. Advanced Physical Oceanographic Numerical Modeling, O'Brien J J, Dordrecht:Reidel,1985,203-231.
[56]Hu D X. Some striking features of circulation in Huanghai Sea and East China Sea[M]. Oceanology of China Seas, Zhou D,1994:1,27-38.
[57]Huang C J, Qiao F. Wave-turbulence interaction and its induced mixing in the upper ocean[J]. J Geophys Res.2010,115:C4026.
[58]Hulburt H E, Thompson J D. A numerical study of the Loop Current intrusions and eddy shedding[J]. J Phys Oceanogr.1982,10:1611-1631.
[59]Isaacson E, Keller H B. Analysis of Numerical Methods[M]. New York:Jone Wiley and Sons,1966.
[60]Israeli M, Orszag S A. Approximation of radiation boundary conditions [J]. J Comput Phys. 1981,21:115-135.
[61]Jackett D R, Mcdougall T J, Feistel R, Wright D G, Griffies S M. Algorithms for density, potential temperature, conservative temperature, and the freezing temperature of seawater[J]. J Atmos Ocean Tech.2006,23:1709-1728.
[62]Jensen T G. Open boundary conditions in stratified ocean models[J]. J Marine Syst.1998,16: 297-322.
[63]Jensen T G. Equatorial variability and resonance in a wind-driven Indian Ocean Model[J]. J Geophys Res.1993,98:22533-22552.
[64]Jerlov N G. Marine Optics[M]. Amsterdam:Elsvier Science,1976:231.
[65]Kamenkovich V M. Fundamentals of ocean dynamics[M]. Amsterdam:Elsevier,1977.
[66]Kanarska Y, Shchepetkin A F, Mcwilliams J C. Algorithm for non-hydrostatic dynamics in the Regional Oceanic Modeling System[J]. Ocean Modell.2007,18:143-174.
[67]Kantha L H, Clayson C A. Numerical Models of Oceans and Oceanic Processes[M]. Academic Press,2000:750.
[68]Kar S K, Janjic Z. A Three-Time-Level Explicit Economical (3TL-EEC) Time-Difference Scheme[Z]. New Orleans, LA:2012.
[69]Large W G, Mcwilliams J C, Doney S C. Oceanic vertical mixing:A review and a model with a nonlocal boundary layer parameterization[J]. Rev Geophys.1994,32:363-403.
[70]Lee Z, Du K, Arnone R, Liew S, Penta B. Penetration of solar radiation in the upper ocean:A numerical model for oceanic and coastal waters [J]. J Geophys Res.2005,110:C9019.
[71]Lin X, Xie S P, Chen X, Xu L. A well-mixed warm water column in the central Bohai Sea in summer:Effects of tidal and surface wave mixing[J]. J Geophys Res.2006,111:C11017.
[72]Lorenz E N. The nature and theory of the general circulation of the atmosphere[R]. Geneva: World Meteorological Organization,1967.
[73]Louis J E. A parametric model of vertical eddy fluxes in the atmosphere [J]. Bound-Lay Meteorol.1979,17:187-202.
[74]Lynn R J, Reid J L. Characteristics and circulation of deep and abyssal waters[J]. Deep-Sea Res.1968,15:577-598.
[75]Madala R V, Piacsek S A. Numerical simulation of asymmetric hurricanes on a B-plane with vertical shear[J]. Tellus.1975,27:453-468.
[76]Mamaev O I. Temperature-salinity analysis of world ocean waters[M]. Amsterdam:Elsevier, 1975:374.
[77]Marchesiello P, Mcwilliams J C, Shchepetkin A F. Open boundary conditions for long-term integration of regional oceanic models[J]. Ocean Modell.2001,3:1-20.
[78]Marshall J, Adcroft A, Hill C, Perelman L, Heisey C. A finite-volume, incompressible Navier-Stokes model for studies of the ocean on parallel computers[J]. J Geophys Res.1997, 102:5753-5766.
[79]Martinsen E A, Engedah H. Implementation and testing of a lateral boundary scheme as an open boundary condition in a barotropic ocean model[J]. Coast Eng.1987,11:603-627.
[80]Martinsen E A, Gjevik B, Roed L P. A numerical model for long barotropic waves and storm surges along the western coast of Norway[J]. J Phys Oceanogr.1979,9:1126-1138.
[81]Mcdougall T J. Thermobaricity, Cabbeling, and Water-Mass Conversion[J]. J Geophys Res. 1987,92(C5):5448-5464.
[82]Mcdougall T J, Jackett D R, Wright D G, Feistel R. Accurate and computationally efficient algorithms for potential temperature and density of seawater[J]. J Atmos Ocean Tech.2003, 20:730-741.
[83]Mellor G L, Blumberg A F. Modeling vertical and horizontal diffusivities with the sigma coordinate system[J]. Mon Weather Rev.1985,113:1380-1383.
[84]Mellor G L, Yamada T. Development of a turbulence closure model for geophysical fluid problems[J]. Rev Geophys Space Phys.1982,20:851-875.
[85]Mellor G L. An Equation of State for numerical modeling of oceans and estuaries[J]. J Atmos Ocean Tech.1991,8:609-611.
[86]Mellor G L. User's guide for a three-dimensional, primitive equation, numerical ocean model. Report of the Atmospheric and Ocean Sciences Program[M]. Princeton, NJ:Princeton University,1998:41.
[87]Mesinger F, Arakawa A. Numerical methods used in atmospheric models. Volume I[M]. GARP Publication Series,17,1976:64.
[88]Mihaljan J M. A Rigorous exposition of the Boussinesq approximations applicable to a thin layer of fluid[J]. Astrophys J.1962,136:1126-1133.
[89]Mihaljan J M. A rigorous exposition of the Boussinesq approximations applicable to a thin layer of fluid [J]. Astrophys J.1962,136:1126-1133.
[90]Miller M J, Thorpe A J. Radiation conditions for the lateral boundaries of limited-area numerical models[J]. Q J Roy Meteor Soc.1981,107:615-628.
[91]Mirinova Z F. Albedo of the Earth's surface and clouds[M]. Radiation characteristics of the Atmosphere and the Earth's Surface, Kondratev I A, VA:NASA, Springfield,1973,580.
[92]Mobley C D. Light and Water[M]. Academic Press,1994:592.
[93]Morel A. Optical modeling of the upper ocean in relation to its biogenous matter content (case I waters)[J]. J Geophys Res.1988,93:10,710-749,768.
[94]Morel A, Antoine D. Heating rate within the upper ocean in relation to its bio-optical state[J]. J Phys Oceanogr.1994,24:1652-1665.
[95]Morel A, Gentili B, Claustre H, Babin M, Bricaud A, Ras J, Fanny T. Optical properties of the ''clearest'' natural waters [J]. Limnol Oceanogr.2007,52(1):217-229.
[96]Munk W. Abyssal recipes[J]. Deep-Sea Res Pt Ⅰ.1966,13:707-730.
[97]Nitta T. On the reflective computational wave caused by the outflow boundary condition[J]. J Meteorol Soc Jpn.1964,42:274-276.
[98]O'Brien J J, Reid R O. The non-linear response of a two-layer, baroclinic ocean due to a stationary, axially symmetric hurricane,1:Upwelling induced by momentum transfer[J]. J Atmos Sci.1967,24:197-207.
[99]Oey L Y, Chen P. A model simulation of circulation in the northeast Atlantic shelves and seas[J]. J Geophys Res.1992,97:20087-20115.
[100]Ohlmann J C, Siegel D A. Ocean radiant heating.Part Ⅱ:Parameterizing solar radiation Transmission through the upper ocean[J]. J Phys Oceanogr.2000,30:1849-1865.
[101]Ohlmann J C, Siegel D A, Mobley C D. Ocean radiant heating. Part Ⅰ:Optical influences [J]. J Phys Oceanogr.2000,30:1833-1848.
[102]Oliger J, Sundstrom A. Theoretical and practical aspects of some initial boundary value problems in fluid dynamics[J]. Siam J Appl Math.1978,35:419-446.
[103]Orlanski I. A simple boundary condition for unbounded hyperbolic flows[J]. J Comput Phys. 1976,21:251-269.
[104]Pacanowski R C, Philander G. Parameterization of vertical mixing in numerical models of the tropical ocean[J]. J Phys Oceanogr.1981,11:1442-1451.
[105]Palma E D, Matano R P. On the implementation of open boundary conditions for a general circulation model:The three-dimensional case[J]. J Geophys Res.2000,105(C4):8605-8627.
[106]Palma E D, Matano R P. On the implementation of open boundary conditions to a general circulation model:The barotropic mode[J]. J Geophys Res.1998,103:1319-1341.
[107]Pedlosky J. Geophysical Fluid Dynamics[M]. New York:Springer Verlag,1987:710.
[108]Peeters F, Piepke G, Kipfer R, Hohmann R, Imboden D M. Description of stability and neutrally buoyant transport in freshwater lakes[J]. Limnol Oceanogr.1996,41(8):1711-1724.
[109]Peifeng M, Madsen O S. An open boundary condition for application in numerical coastal models[J]. Coast Eng.2010,32.
[110]Perkins A L, Smedstad L F, Blake D W, Heburn G W, Wallcraft A J. A new nested boundary condition for a Primitive-Equation ocean model[J]. J Geophys Res.1997,102: 3485-3500.
[111]Phillips N A. A coordinate system having some special advantages for numerical forecasting[J]. J Meteorol.1957,14:184-185.
[112]Qiao F, Yuan Y, Yang Y, Zheng Q, Xia C, Ma J. Wave-induced mixing in the upper ocean: Distribution and application in a global ocean circulation model[J]. Geophys Res Lett. 2004(31):L11303.
[113]Raymond X H, Kuo H L. A radiation boundary condition for multi-dimensional flows[J]. Q J Roy Meteor Soc.1984,535-551(110).
[114]Reed R K. On estimating insolation over the ocean[J]. J Phys Org Chem.1977,7:482-485.
[115]Roed L P, Cooper C. A study of various open boundary conditions for wind-forced barotropic numerical ocean models[M]. Three-dimensional Models of Marine and Estuarine Dynamics, Nihoul J C J, Jamart B N, New York:Elsevier,1987,305-335.
[116]Roed L P, Smedstad O M. Open boundary conditions for forced waves in a rotating fluid[J]. SIAM J Sci Comput.1984,5:414-426.
[117]Sarmiento J L. On the North and Tropical Atlantic heat balance[J]. J Geophys Res.1986,91: 11677-11689.
[118]Semtner A J, Chervin R M. Ocean general circulation from a global eddy-resolving model[J]. J Geophys Res.1992,97:5493-5550.
[119]Shchepetkin A F, Mcwilliams J C. Accurate Boussinesq oceanic modeling with a practical, "stiffened" Equation of State [J]. Ocean Modell.2011,38(1-2):41-71.
[120]Shchepetkin A F, Mcwilliams J C. A method for computing horizontal pressure-gradient force in an oceanic model with a nonaligned vertical coordinate[J]. J Geophys Res.2003, 108(C3):3090.
[121]Smagorinsky J. General circulation experiments with the primitive equations[J]. Mon Weather Rev.1963,91:99-164.
[122]Smith W D. A non-reflecting plane boundary condition for wave propagation problems[J]. J Comput Phys.1974,15:492-503.
[123]Soloviev A, Lukas R. The Near-Surface Layer of the Ocean[M]. Springer,2006:572.
[124]Sommerfeld A. Partial Differential Equation[M]. San Diego:Academic Press,1949.
[125]Song Y T, Wright D G. A general pressure gradient formulation for ocean models,2, Energy, momentum and bottom torque consistency[J]. Mon Weather Rev.1998,126: 3213-3230.
[126]Song Y T. A General Pressure Gradient Formulation for Ocean Models. Part I:Scheme Design and Diagnostic Analysis [J]. Mon Weather Rev.1998,126:3213-3230.
[127]Stevens D P. On open boundary conditions for three dimensional primitive equation ocean circulation models[J]. Geophys Astrophys Fluid Dyn.1990,51:103-133.
[128]Stevens I G, Johnson J A. Sensitivity to open boundary forcing in a fine-resolution model of the Iberian shelfslope region[J]. Ann Geophys.1997.
[129]Sun W. Instability in Leapfrog and Forward-Backward Schemes[J]. Mon Weather Rev. 2010,138:1497-1501.
[130]Sun W. Instability in leapfrog and forward-backward schemes Part II:Numerical simulations of dam break[J]. Comput Fluids.2011,45:70-76.
[131]Swinbank W C. Long-wave radiation from clear skies[J]. Q J Roy Meteor Soc.1963,89: 339-348.
[132]Tang Y, Grimshaw R. Radiation boundary conditions in barotropic coastal ocean numerical models[J].J Mar Res.1996,123:96-110.
[133]Unesco. Tenth report of the joint panel on oceanographic tables and standards[Z]. Paris: UNESCO Tech. Pap.in Marine Science,1981:36,25.
[134]Vastano A C, Reid R O. Tsunami responsefo r islands:Verification of a numerical procedure[J]. J Mar Res.1967,25:129-139.
[135]Wang Y, Fang G, Wei Z, Qiao F, Chen H. Interannual variation of the South China Sea circulation and its relation to El Nino, as seen from a variable grid global ocean model[J]. J Geophys Res.2006,111:C11S-C14S.
[136]White A A, Bromley R A. Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force[J]. Q J Roy Meteor Soc.1995, 121:399-418.
[137]Williams P D. A proposed modification to the Robert-Asselin time filter [J]. Mon Weather Rev.2009,137(8):2538-2546.
[138]Wright D G. An Equation of State for use in ocean models:Eckart's formula revisited[J]. J Atmos Ocean Tech.1997,14:735-741.
[139]Wright D G, Stocker T F. A zonally averaged ocean model for the thermohaline circulation. Part Ⅰ:Model development and flow dynamics[J]. J Phys Oceanogr.1991,21:1713-1724.
[140]Wurtele M G, Paegle J, Sieiecki A. The use of open boundary condition with the storm-surge equations[J]. Mon Weather Rev.1971,99(6):537-544.
[141]Xia C, Qiao F, Yang Y, Ma J, Yuan Y. Three-dimensional structure of the summertime circulation in the Yellow Sea from a wave-tide-circulation coupled model[J]. J Geophys Res. 2006,111:C11S-C13S.
[142]Yu Y Q, Yu R C, Zhang X H, Liu H L. A flexible global coupled climate model[J]. Adv Atmos Sci.2002,19:169-190.
[143]Yuan Y, Pan Z, Sun L. LAGDF-WAM numerical wave model[J]. Acta Oceanologica Sinica. 1991,10:483-488.
[144]Yuan Y, Han L, Qiao F, Yang Y, Lu M. A unified linear theory of wavelike perturbations under general ocean conditions[J]. Dynam Atmos Oceans.2011,51:55-74.
[145]Zeng Q C. Some numerical ocean-atmosphere coupling modes[C].Proceedings of the first international symposium on the integrated global ocean monitorning Tallinn, USSR:1983.
[146]Zhang S W, Wang Q Y, Lue Y, Cui H, Yuan Y L. Observation of the seasonal evolution of the Yellow Sea Cold Water Mass in 1996-1998[J]. Cont Shelf Res.2008,28(3):442-457.
[1471 Zillman J W. A study of some aspects of the radiation and heat budgets of the Southern Hemisphere oceans [M]. Meteorological Studies,26, Bureau of Meteorology, Department of the Interior, Canberra, Australia:1972,562.
[148]毕业文,赵保仁.黄海西南部陆架锋区锋断面环流数值模拟[J].海洋科学.1993,6：61-63.
[149]方国洪.黄海东部M2潮流的数值计算及其与观测结果的比较[C].第一届潮汐与海平面学术讨论会论文集1986.
[150]方国洪.潮波方程的有限差分一最小二乘方法及其对模拟黄海M2潮的应用[J].中国科学.1985,28(4)：356-364.
[151]方国洪,魏泽勋,王永刚.我国潮汐潮流区域预报的发展[J].地球科学进展.2008,23(4)：331-336.
[152]方国洪,杨景飞.渤海潮运动的一个二维数值模型[J].海洋与湖沼.1985,6(5)：337-346.
[153]方国洪,杨景飞.东海东部和南部潮流的数值计算[J].海洋学报.1987,9(4)：403-412.
[154]管秉贤.黄海冷水团的水温变化以及环流特低的初步分析[J].海洋与湖沼.1963,5(4)：255-284.
[155]赫崇本,汪园祥,雷宗友,徐斯.黄海冷水团的形成及其性质的初步探讨[J].海洋与湖沼.1959,2(1)：11-15.
[156]李惠卿,袁业立.黄海冷水团热结构及其环流解析研究[J].海洋与湖沼.1992,23(1)：7-13.
[157]刘海龙,俞永强,李薇,张学洪LASG/IAP气候系统海洋模式(LICOM 1.0)参考手册[M].北京：科学出版社,2003：108.
[158]缪经榜,刘兴泉,薛亚.北黄海冷水团形成机制的初步探讨1[J].中国科学B.1990,20(12)：131-132.
[159]任慧君,詹杰民.黄海冷水团的季节变化特征及其形成机制研究[J].水动力学研究与进展增刊.2005,20：887-896.
[160]宋振亚,乔方利,雷晓燕,杨永增.大气-海浪-海洋环流耦合数值模式的建立及北太平洋SST模拟[J].水动力学研究与进展A辑.2007,22(5)：545-548.
[161]宋振亚,乔方利,杨永增,袁业立.波致混合对热带太平洋海气耦合模式中冷舌模拟的改进[J].自然科学进展.2006,16(9)：1138-1145.
[162]苏纪兰,黄大吉.黄海冷水团的环流结构[J].海洋与湖沼增刊.1995,26(5)：1-7.
[163]田永祥,沈桐立,葛孝贞,陆维松.数值天气预报教程[M].气象出版社,1995.
[164]王福军.计算流体动力学分析：CFD软件原理与应用[M].清华大学出版社,2004.
[165]吴望一.流体力学[M].北京大学出版社,2004.
[166]阎超.计算流体力学方法及应用[M].北京航空航天大学出版社,2006：266.
[167]于非,张志欣,刁新源,郭景松,汤毓祥.黄海冷水团演变过程及其与邻近水团关系的分析[J].海洋学报.2006,28(5)：26-34.
[168]袁业立,李惠卿.黄海冷水团环流结构及生成机制研究——Ⅰ.0阶解及冷水团的环流结构[J].中国科学.1993,23(1)：93-103.
[169]赵保仁.黄海冷水闭锋面与潮混合[J].海洋与湖沼.1985,27(4)：431-436.
[170]赵保仁.北黄海冷水团环流结构探讨——潮混合锋对环流结构的影响[J].海洋与湖沼.1996,27(4)：429-435.
[171]赵滨,钟青.蛙跳格式的替代方案及其在大气环流模式中的应用[J].气候与环境研究.2009,14(1)：21-30.
[172]周光炯,严宗毅,许世雄,章克本.流体力学(第二版)[M].高等教育出版社,2000.
[173]朱建荣,肖成猷,沈焕庭,朱首贤.黄海冷水团对长江冲淡水的影响[J].海洋与湖沼.1998,29(4)：389-394.
[2]Arakawa A. Computational design for long-term numerical integraton of the equations of fluid motion:Two-dimensional incompressible flow. Part I[J]. J Comput Phys.1966,1:119-143.
[3]Arakawa A, Lamb V R. Computational design of the basic dynamical processes in the UCLA general circulation model[M]. Methods in Computational Physics. Vol.17:General circulation models of the atmosphere, Chang J, Academic Press,1977.
[4]Asselin R. Frequency filters for time integrations[J]. Mon Weather Rev.1972,100:487-490.
[5]Baumert H Z, Simpson J, Sundermann J. Marine turbulence:Theories, observations, and models[M]. Cambridge University Press,2011:654.
[6]Beardsley R C, Haidvogel D B. Model studies of the wind driven transient circulation in the Middle Atlantic Bight,1, Adiabatic boundary conditions[J]. J Phys Oceanogr.1981,11: 355-375.
[7]Beckmann A, Boning C W, Koberle C, Willebrand J. Effects of increased horizontal resolution in a simulation of the North Atlantic Ocean[J]. J Phys Oceanogr.1994,24:326-344.
[8]Bennett A F, Kloeden P E. Boundary conditions for limited-area forecasts[J]. J Atmos Sci. 1978,35:355-375.
[9]Blazek J. Computational Fluid Dynamics:Principles and Applications,2nd Edition[M]. Elsevier,2005.
[10]Bleck R, Benjamin S. Regional weather prediction with a model combining terrain-following and isentropic coordinates. Part I:Model description[J]. Mon Weather Rev.1993,121: 1770-1785.
[11]Bleck R, Boudra D. Initial testing of a numerical ncean circulation model using a hybrid (quasi-isopycnic) vertical coordinate[J]. J Phys Oceanogr.1981,11:755-770.
[12]Blumberg A F, Kantha L H. Open boundary conditions for circulation models[J]. J Hydraul Eng.1985,11:237-255.
[13]Boussinesq J V. Theorie Analytique de la Chaleur. Vol. Ⅱ[M]. Paris:Gauthier-Villars,1903.
[14]Bricaud A, Babin M, Morel A, Claustre H. Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton:Analysis and parameterization[J]. J Geophys Res.1995, 100:13,313-321,332.
[15]Bryan F O. A numerical model for the study of the circulation of the world oceans[J]. J Comput Phys.1969,4:347-359.
[16]Bryden H L. New polynomials for thermal expansion, adiabatic temperature gradient and potential temperature gradient of sea water[J]. Deep-Sea Res.1973,20:401-408.
[17]Buiteveld H, Hakvoort J H M, Donze M. The optical properties of pure water[M]. Ocean Optics Ⅻ, SPIE,1994:2258,174-183.
[18]Chapman D C. Numerical treatment of cross-shelof pen boundaries in a barotropic coastal ocean modelfJ]. J Phys Oceanogr.1985,15:1060-1075.
[19]Chelton D B, Schlax M G. Global observations of oceanic Rossby waves[J]. Science.1996, 272:234-238.
[20]Chelton D B, Deszoeke R A, Schlax M G, Naggar K E, Siwertz N. Geographical variability of the first baroclinic Rossby radius of deformation[J]. J Phys Oceanogr.1998,28:433-460.
[21]Chen C T, Millero F J. Precise thermodynamic properties for natural waters covering only the limnological range[J]. Limnol Oceanogr.1986,31:657-662.
[22]Chu P C, Fan C. Hydrostatic correction for sigma coordinate ocean models[J]. J Geophys Res. 2003(108(C6)):3206.
[23]Csanady G T. Air-Sea Interaction:Laws and Mechanisms[M]. Cambridge University Press, 2001:239.
[24]Curry J A, Webster P J. Thermodynamics of atmospheres and oceans[M]. San Diego: Academic Press,1999:471.
[25]Dai D, Qiao F, Sulisz W, Han L, Babanin A. An experiment on the non-breaking surface-wave-induced vertical mixing[J]. J Phys Oceanogr.2010,40:2180-2188.
[26]Dietrich D E, Marietta M G, Roach J P. An ocean modeling system with turbulent boundary layers and topography[J]. Int J Numer Meth Fl.1987,7:833-855.
[27]Dinniman M S, Klinck J M. The influence of open versus periodic alongshore boundaries on circulation near submarine canyons[J]. J Atmos Ocean Tech.2002,19:1722-1737.
[28]Dong-Feng X, Yao-Chu Y, Yuan L. The baroclinic circulation structure of Yellow Sea Cold Water Mass[J]. Sci China Ser D.2003,46(2):117-126.
[29]Dukowicz J K, Smith R D, Malone R C.A reformulation and implementation of the Bryan-Cox-Semtner ocean model on the Connection Machine[J]. J Atmos Ocean Tech.1993, 10:195.
[30]Dukowicz J K. Mesh Effects for Rossby Waves[J]. J Comput Phys.1995,119:188-194.
[31]Durran D R. Numerical methods for wave equations in geophysical fluid dynamics [M]. Springer,1999:470.
[32]Eckart C. Properties of water:Ⅱ. The equation of state of water and sea water at low temperatures and pressures[J]. Amer J Sci.1958,256:225-240.
[33]Fang G, Jinfei Y. Modeling and prediction of tidal currents in the Korea Strait[J]. Prog Oceanogr.1988,21:307-318.
[34]Fang G, Wang Y, Wei Z, Choi B H, Wang X, Wang J. Empirical cotidal charts of the Bohai, Yellow, and East China Seas from 10 years of TOPEX/Poseidon altimetry[J]. J Geophys Res. 2004,109:C11006.
[35]Fang G, Yang J, Thao Y. A two-dimensional numerical model for tidal motion in the Taiwan Strait[J]. Mar Geophys Res.1984,7(1):267-276.
[36]Feistel R. A new extended Gibbs thermodynamic potential of seawater[J]. Prog Oceanogr. 2003,58:43-114.
[37]Feistel R, Hagen E. On the GIBBS thermodynamic potential of seawater[J]. Prog Oceanogr. 1995,36:249-327.
[38]Flather R A. A tidal model of the northwest European continental shelf[J]. Mem Soc R Sci Liege.1976,6(10):141-164.
[39]Freeman J C, Baer L. Pseudo-characteristics[J]. Trans Amer Geophys Union.1957,38: 65-67.
[40]Freeman J C, Baer L. The method of wave derivatives[J]. Trans Amer Geophys Union.1957, 38:483-494.
[41]Gan J P, Allen J S. On open boundary conditions for a limited-area coastal model off Oregon. Part 1. Response to idealized wind forcing[J]. Ocean Modell.2005,8:155-173.
[42]Gent P R, Mcwilliams J C. Isopycnal mixing in ocean circulation models[J]. J Phys Oceanogr. 1990,20:150-155.
[43]Gill A. Atmosphere-ocean dynamics[M]. Academic Press,1982:662.
[44]Griffies S M, Gnanadesikan A, Pacanowski R C, Larichev V D, Dukowicz J K, Smith R D. Isoneutral diffusion in a z-coordinate ocean model[J]. J Phys Oceanogr.1998,28:805-830.
[45]Guo B H. The Ocean Environment of the Marginal Seas Adjacent to China[M]. Beijing: China Ocean Press,2004:446.
[46]Guo Y F, Yu Y Q, Liu X Y, Zhang X H. Simulation of climate change induced by CO2 increasing for East Asia with IAP/LASG GOALS model[J]. Adv Atmos Sci.2001,18:53-66.
[47]Haidvogel D B, Arango H, Budgell W P, Cornuelle B D, Curchitser E, Di Lorenzo E, Fennel K, Geyer W R, Hermann A J, Lanerolle L, Levin J, Mcwilliams J C, Miller A J, Moore A M, Powell T M, Shchepetkin A F, Sherwood C R, Signell R P, Warner J C, Wilkin J. Ocean forecasting in terrain-following coordinates:Formulation and skill assessment of the Regional Ocean Modeling System[J]. J Comput Phys.2008,227:3595-3624.
[48]Haidvogel D B, Beckmann A. Numerical Ocean Circulation Modeling[M]. Imperial College Press,1999:319.
[49]Hartree D R. Some practical methods of using characteristics in the calculation of non-steady compressible flow[C].Rep. AECU-2713 Washington, D.C.:U.S. At. Energy Comm.,1953.
[50]Hedley M, Yau M K. Radiation boundary conditions in numerical modeling[J]. Mon Weather Rev.1988,116:1721-1736.
[51]Hedstrom G W. Nonreflecting boundary conditions for nonlinear hyperbolic systems [J]. J Comput Phys.1979,30:222-237.
[52]Hersbach H. Sea surface roughness and drag coefficient as functions of neutral wind speed[J]. J Phys Oceanogr.2011,41:247-251.
[53]Higdon R L, Bennett A F. Modeling, Stability Analysis Of Operator for large-scale ocean modeling[J]. J Comput Phys.1996,123:311.
[54]Higdon R L, de Szoeke R A. Barotropic-baroclinic time splitting for ocean circulation modeling[J]. J Comput Phys.1997,135(30).
[55]Holland W R. Quasi-geostrophic modeling of eddy-resolved ocean circulation[M]. Advanced Physical Oceanographic Numerical Modeling, O'Brien J J, Dordrecht:Reidel,1985,203-231.
[56]Hu D X. Some striking features of circulation in Huanghai Sea and East China Sea[M]. Oceanology of China Seas, Zhou D,1994:1,27-38.
[57]Huang C J, Qiao F. Wave-turbulence interaction and its induced mixing in the upper ocean[J]. J Geophys Res.2010,115:C4026.
[58]Hulburt H E, Thompson J D. A numerical study of the Loop Current intrusions and eddy shedding[J]. J Phys Oceanogr.1982,10:1611-1631.
[59]Isaacson E, Keller H B. Analysis of Numerical Methods[M]. New York:Jone Wiley and Sons,1966.
[60]Israeli M, Orszag S A. Approximation of radiation boundary conditions [J]. J Comput Phys. 1981,21:115-135.
[61]Jackett D R, Mcdougall T J, Feistel R, Wright D G, Griffies S M. Algorithms for density, potential temperature, conservative temperature, and the freezing temperature of seawater[J]. J Atmos Ocean Tech.2006,23:1709-1728.
[62]Jensen T G. Open boundary conditions in stratified ocean models[J]. J Marine Syst.1998,16: 297-322.
[63]Jensen T G. Equatorial variability and resonance in a wind-driven Indian Ocean Model[J]. J Geophys Res.1993,98:22533-22552.
[64]Jerlov N G. Marine Optics[M]. Amsterdam:Elsvier Science,1976:231.
[65]Kamenkovich V M. Fundamentals of ocean dynamics[M]. Amsterdam:Elsevier,1977.
[66]Kanarska Y, Shchepetkin A F, Mcwilliams J C. Algorithm for non-hydrostatic dynamics in the Regional Oceanic Modeling System[J]. Ocean Modell.2007,18:143-174.
[67]Kantha L H, Clayson C A. Numerical Models of Oceans and Oceanic Processes[M]. Academic Press,2000:750.
[68]Kar S K, Janjic Z. A Three-Time-Level Explicit Economical (3TL-EEC) Time-Difference Scheme[Z]. New Orleans, LA:2012.
[69]Large W G, Mcwilliams J C, Doney S C. Oceanic vertical mixing:A review and a model with a nonlocal boundary layer parameterization[J]. Rev Geophys.1994,32:363-403.
[70]Lee Z, Du K, Arnone R, Liew S, Penta B. Penetration of solar radiation in the upper ocean:A numerical model for oceanic and coastal waters [J]. J Geophys Res.2005,110:C9019.
[71]Lin X, Xie S P, Chen X, Xu L. A well-mixed warm water column in the central Bohai Sea in summer:Effects of tidal and surface wave mixing[J]. J Geophys Res.2006,111:C11017.
[72]Lorenz E N. The nature and theory of the general circulation of the atmosphere[R]. Geneva: World Meteorological Organization,1967.
[73]Louis J E. A parametric model of vertical eddy fluxes in the atmosphere [J]. Bound-Lay Meteorol.1979,17:187-202.
[74]Lynn R J, Reid J L. Characteristics and circulation of deep and abyssal waters[J]. Deep-Sea Res.1968,15:577-598.
[75]Madala R V, Piacsek S A. Numerical simulation of asymmetric hurricanes on a B-plane with vertical shear[J]. Tellus.1975,27:453-468.
[76]Mamaev O I. Temperature-salinity analysis of world ocean waters[M]. Amsterdam:Elsevier, 1975:374.
[77]Marchesiello P, Mcwilliams J C, Shchepetkin A F. Open boundary conditions for long-term integration of regional oceanic models[J]. Ocean Modell.2001,3:1-20.
[78]Marshall J, Adcroft A, Hill C, Perelman L, Heisey C. A finite-volume, incompressible Navier-Stokes model for studies of the ocean on parallel computers[J]. J Geophys Res.1997, 102:5753-5766.
[79]Martinsen E A, Engedah H. Implementation and testing of a lateral boundary scheme as an open boundary condition in a barotropic ocean model[J]. Coast Eng.1987,11:603-627.
[80]Martinsen E A, Gjevik B, Roed L P. A numerical model for long barotropic waves and storm surges along the western coast of Norway[J]. J Phys Oceanogr.1979,9:1126-1138.
[81]Mcdougall T J. Thermobaricity, Cabbeling, and Water-Mass Conversion[J]. J Geophys Res. 1987,92(C5):5448-5464.
[82]Mcdougall T J, Jackett D R, Wright D G, Feistel R. Accurate and computationally efficient algorithms for potential temperature and density of seawater[J]. J Atmos Ocean Tech.2003, 20:730-741.
[83]Mellor G L, Blumberg A F. Modeling vertical and horizontal diffusivities with the sigma coordinate system[J]. Mon Weather Rev.1985,113:1380-1383.
[84]Mellor G L, Yamada T. Development of a turbulence closure model for geophysical fluid problems[J]. Rev Geophys Space Phys.1982,20:851-875.
[85]Mellor G L. An Equation of State for numerical modeling of oceans and estuaries[J]. J Atmos Ocean Tech.1991,8:609-611.
[86]Mellor G L. User's guide for a three-dimensional, primitive equation, numerical ocean model. Report of the Atmospheric and Ocean Sciences Program[M]. Princeton, NJ:Princeton University,1998:41.
[87]Mesinger F, Arakawa A. Numerical methods used in atmospheric models. Volume I[M]. GARP Publication Series,17,1976:64.
[88]Mihaljan J M. A Rigorous exposition of the Boussinesq approximations applicable to a thin layer of fluid[J]. Astrophys J.1962,136:1126-1133.
[89]Mihaljan J M. A rigorous exposition of the Boussinesq approximations applicable to a thin layer of fluid [J]. Astrophys J.1962,136:1126-1133.
[90]Miller M J, Thorpe A J. Radiation conditions for the lateral boundaries of limited-area numerical models[J]. Q J Roy Meteor Soc.1981,107:615-628.
[91]Mirinova Z F. Albedo of the Earth's surface and clouds[M]. Radiation characteristics of the Atmosphere and the Earth's Surface, Kondratev I A, VA:NASA, Springfield,1973,580.
[92]Mobley C D. Light and Water[M]. Academic Press,1994:592.
[93]Morel A. Optical modeling of the upper ocean in relation to its biogenous matter content (case I waters)[J]. J Geophys Res.1988,93:10,710-749,768.
[94]Morel A, Antoine D. Heating rate within the upper ocean in relation to its bio-optical state[J]. J Phys Oceanogr.1994,24:1652-1665.
[95]Morel A, Gentili B, Claustre H, Babin M, Bricaud A, Ras J, Fanny T. Optical properties of the ''clearest'' natural waters [J]. Limnol Oceanogr.2007,52(1):217-229.
[96]Munk W. Abyssal recipes[J]. Deep-Sea Res Pt Ⅰ.1966,13:707-730.
[97]Nitta T. On the reflective computational wave caused by the outflow boundary condition[J]. J Meteorol Soc Jpn.1964,42:274-276.
[98]O'Brien J J, Reid R O. The non-linear response of a two-layer, baroclinic ocean due to a stationary, axially symmetric hurricane,1:Upwelling induced by momentum transfer[J]. J Atmos Sci.1967,24:197-207.
[99]Oey L Y, Chen P. A model simulation of circulation in the northeast Atlantic shelves and seas[J]. J Geophys Res.1992,97:20087-20115.
[100]Ohlmann J C, Siegel D A. Ocean radiant heating.Part Ⅱ:Parameterizing solar radiation Transmission through the upper ocean[J]. J Phys Oceanogr.2000,30:1849-1865.
[101]Ohlmann J C, Siegel D A, Mobley C D. Ocean radiant heating. Part Ⅰ:Optical influences [J]. J Phys Oceanogr.2000,30:1833-1848.
[102]Oliger J, Sundstrom A. Theoretical and practical aspects of some initial boundary value problems in fluid dynamics[J]. Siam J Appl Math.1978,35:419-446.
[103]Orlanski I. A simple boundary condition for unbounded hyperbolic flows[J]. J Comput Phys. 1976,21:251-269.
[104]Pacanowski R C, Philander G. Parameterization of vertical mixing in numerical models of the tropical ocean[J]. J Phys Oceanogr.1981,11:1442-1451.
[105]Palma E D, Matano R P. On the implementation of open boundary conditions for a general circulation model:The three-dimensional case[J]. J Geophys Res.2000,105(C4):8605-8627.
[106]Palma E D, Matano R P. On the implementation of open boundary conditions to a general circulation model:The barotropic mode[J]. J Geophys Res.1998,103:1319-1341.
[107]Pedlosky J. Geophysical Fluid Dynamics[M]. New York:Springer Verlag,1987:710.
[108]Peeters F, Piepke G, Kipfer R, Hohmann R, Imboden D M. Description of stability and neutrally buoyant transport in freshwater lakes[J]. Limnol Oceanogr.1996,41(8):1711-1724.
[109]Peifeng M, Madsen O S. An open boundary condition for application in numerical coastal models[J]. Coast Eng.2010,32.
[110]Perkins A L, Smedstad L F, Blake D W, Heburn G W, Wallcraft A J. A new nested boundary condition for a Primitive-Equation ocean model[J]. J Geophys Res.1997,102: 3485-3500.
[111]Phillips N A. A coordinate system having some special advantages for numerical forecasting[J]. J Meteorol.1957,14:184-185.
[112]Qiao F, Yuan Y, Yang Y, Zheng Q, Xia C, Ma J. Wave-induced mixing in the upper ocean: Distribution and application in a global ocean circulation model[J]. Geophys Res Lett. 2004(31):L11303.
[113]Raymond X H, Kuo H L. A radiation boundary condition for multi-dimensional flows[J]. Q J Roy Meteor Soc.1984,535-551(110).
[114]Reed R K. On estimating insolation over the ocean[J]. J Phys Org Chem.1977,7:482-485.
[115]Roed L P, Cooper C. A study of various open boundary conditions for wind-forced barotropic numerical ocean models[M]. Three-dimensional Models of Marine and Estuarine Dynamics, Nihoul J C J, Jamart B N, New York:Elsevier,1987,305-335.
[116]Roed L P, Smedstad O M. Open boundary conditions for forced waves in a rotating fluid[J]. SIAM J Sci Comput.1984,5:414-426.
[117]Sarmiento J L. On the North and Tropical Atlantic heat balance[J]. J Geophys Res.1986,91: 11677-11689.
[118]Semtner A J, Chervin R M. Ocean general circulation from a global eddy-resolving model[J]. J Geophys Res.1992,97:5493-5550.
[119]Shchepetkin A F, Mcwilliams J C. Accurate Boussinesq oceanic modeling with a practical, "stiffened" Equation of State [J]. Ocean Modell.2011,38(1-2):41-71.
[120]Shchepetkin A F, Mcwilliams J C. A method for computing horizontal pressure-gradient force in an oceanic model with a nonaligned vertical coordinate[J]. J Geophys Res.2003, 108(C3):3090.
[121]Smagorinsky J. General circulation experiments with the primitive equations[J]. Mon Weather Rev.1963,91:99-164.
[122]Smith W D. A non-reflecting plane boundary condition for wave propagation problems[J]. J Comput Phys.1974,15:492-503.
[123]Soloviev A, Lukas R. The Near-Surface Layer of the Ocean[M]. Springer,2006:572.
[124]Sommerfeld A. Partial Differential Equation[M]. San Diego:Academic Press,1949.
[125]Song Y T, Wright D G. A general pressure gradient formulation for ocean models,2, Energy, momentum and bottom torque consistency[J]. Mon Weather Rev.1998,126: 3213-3230.
[126]Song Y T. A General Pressure Gradient Formulation for Ocean Models. Part I:Scheme Design and Diagnostic Analysis [J]. Mon Weather Rev.1998,126:3213-3230.
[127]Stevens D P. On open boundary conditions for three dimensional primitive equation ocean circulation models[J]. Geophys Astrophys Fluid Dyn.1990,51:103-133.
[128]Stevens I G, Johnson J A. Sensitivity to open boundary forcing in a fine-resolution model of the Iberian shelfslope region[J]. Ann Geophys.1997.
[129]Sun W. Instability in Leapfrog and Forward-Backward Schemes[J]. Mon Weather Rev. 2010,138:1497-1501.
[130]Sun W. Instability in leapfrog and forward-backward schemes Part II:Numerical simulations of dam break[J]. Comput Fluids.2011,45:70-76.
[131]Swinbank W C. Long-wave radiation from clear skies[J]. Q J Roy Meteor Soc.1963,89: 339-348.
[132]Tang Y, Grimshaw R. Radiation boundary conditions in barotropic coastal ocean numerical models[J].J Mar Res.1996,123:96-110.
[133]Unesco. Tenth report of the joint panel on oceanographic tables and standards[Z]. Paris: UNESCO Tech. Pap.in Marine Science,1981:36,25.
[134]Vastano A C, Reid R O. Tsunami responsefo r islands:Verification of a numerical procedure[J]. J Mar Res.1967,25:129-139.
[135]Wang Y, Fang G, Wei Z, Qiao F, Chen H. Interannual variation of the South China Sea circulation and its relation to El Nino, as seen from a variable grid global ocean model[J]. J Geophys Res.2006,111:C11S-C14S.
[136]White A A, Bromley R A. Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force[J]. Q J Roy Meteor Soc.1995, 121:399-418.
[137]Williams P D. A proposed modification to the Robert-Asselin time filter [J]. Mon Weather Rev.2009,137(8):2538-2546.
[138]Wright D G. An Equation of State for use in ocean models:Eckart's formula revisited[J]. J Atmos Ocean Tech.1997,14:735-741.
[139]Wright D G, Stocker T F. A zonally averaged ocean model for the thermohaline circulation. Part Ⅰ:Model development and flow dynamics[J]. J Phys Oceanogr.1991,21:1713-1724.
[140]Wurtele M G, Paegle J, Sieiecki A. The use of open boundary condition with the storm-surge equations[J]. Mon Weather Rev.1971,99(6):537-544.
[141]Xia C, Qiao F, Yang Y, Ma J, Yuan Y. Three-dimensional structure of the summertime circulation in the Yellow Sea from a wave-tide-circulation coupled model[J]. J Geophys Res. 2006,111:C11S-C13S.
[142]Yu Y Q, Yu R C, Zhang X H, Liu H L. A flexible global coupled climate model[J]. Adv Atmos Sci.2002,19:169-190.
[143]Yuan Y, Pan Z, Sun L. LAGDF-WAM numerical wave model[J]. Acta Oceanologica Sinica. 1991,10:483-488.
[144]Yuan Y, Han L, Qiao F, Yang Y, Lu M. A unified linear theory of wavelike perturbations under general ocean conditions[J]. Dynam Atmos Oceans.2011,51:55-74.
[145]Zeng Q C. Some numerical ocean-atmosphere coupling modes[C].Proceedings of the first international symposium on the integrated global ocean monitorning Tallinn, USSR:1983.
[146]Zhang S W, Wang Q Y, Lue Y, Cui H, Yuan Y L. Observation of the seasonal evolution of the Yellow Sea Cold Water Mass in 1996-1998[J]. Cont Shelf Res.2008,28(3):442-457.
[1471 Zillman J W. A study of some aspects of the radiation and heat budgets of the Southern Hemisphere oceans [M]. Meteorological Studies,26, Bureau of Meteorology, Department of the Interior, Canberra, Australia:1972,562.
[148]毕业文,赵保仁.黄海西南部陆架锋区锋断面环流数值模拟[J].海洋科学.1993,6：61-63.
[149]方国洪.黄海东部M2潮流的数值计算及其与观测结果的比较[C].第一届潮汐与海平面学术讨论会论文集1986.
[150]方国洪.潮波方程的有限差分一最小二乘方法及其对模拟黄海M2潮的应用[J].中国科学.1985,28(4)：356-364.
[151]方国洪,魏泽勋,王永刚.我国潮汐潮流区域预报的发展[J].地球科学进展.2008,23(4)：331-336.
[152]方国洪,杨景飞.渤海潮运动的一个二维数值模型[J].海洋与湖沼.1985,6(5)：337-346.
[153]方国洪,杨景飞.东海东部和南部潮流的数值计算[J].海洋学报.1987,9(4)：403-412.
[154]管秉贤.黄海冷水团的水温变化以及环流特低的初步分析[J].海洋与湖沼.1963,5(4)：255-284.
[155]赫崇本,汪园祥,雷宗友,徐斯.黄海冷水团的形成及其性质的初步探讨[J].海洋与湖沼.1959,2(1)：11-15.
[156]李惠卿,袁业立.黄海冷水团热结构及其环流解析研究[J].海洋与湖沼.1992,23(1)：7-13.
[157]刘海龙,俞永强,李薇,张学洪LASG/IAP气候系统海洋模式(LICOM 1.0)参考手册[M].北京：科学出版社,2003：108.
[158]缪经榜,刘兴泉,薛亚.北黄海冷水团形成机制的初步探讨1[J].中国科学B.1990,20(12)：131-132.
[159]任慧君,詹杰民.黄海冷水团的季节变化特征及其形成机制研究[J].水动力学研究与进展增刊.2005,20：887-896.
[160]宋振亚,乔方利,雷晓燕,杨永增.大气-海浪-海洋环流耦合数值模式的建立及北太平洋SST模拟[J].水动力学研究与进展A辑.2007,22(5)：545-548.
[161]宋振亚,乔方利,杨永增,袁业立.波致混合对热带太平洋海气耦合模式中冷舌模拟的改进[J].自然科学进展.2006,16(9)：1138-1145.
[162]苏纪兰,黄大吉.黄海冷水团的环流结构[J].海洋与湖沼增刊.1995,26(5)：1-7.
[163]田永祥,沈桐立,葛孝贞,陆维松.数值天气预报教程[M].气象出版社,1995.
[164]王福军.计算流体动力学分析：CFD软件原理与应用[M].清华大学出版社,2004.
[165]吴望一.流体力学[M].北京大学出版社,2004.
[166]阎超.计算流体力学方法及应用[M].北京航空航天大学出版社,2006：266.
[167]于非,张志欣,刁新源,郭景松,汤毓祥.黄海冷水团演变过程及其与邻近水团关系的分析[J].海洋学报.2006,28(5)：26-34.
[168]袁业立,李惠卿.黄海冷水团环流结构及生成机制研究——Ⅰ.0阶解及冷水团的环流结构[J].中国科学.1993,23(1)：93-103.
[169]赵保仁.黄海冷水闭锋面与潮混合[J].海洋与湖沼.1985,27(4)：431-436.
[170]赵保仁.北黄海冷水团环流结构探讨——潮混合锋对环流结构的影响[J].海洋与湖沼.1996,27(4)：429-435.
[171]赵滨,钟青.蛙跳格式的替代方案及其在大气环流模式中的应用[J].气候与环境研究.2009,14(1)：21-30.
[172]周光炯,严宗毅,许世雄,章克本.流体力学(第二版)[M].高等教育出版社,2000.
[173]朱建荣,肖成猷,沈焕庭,朱首贤.黄海冷水团对长江冲淡水的影响[J].海洋与湖沼.1998,29(4)：389-394.