三维正压潮汐潮流伴随同化模型数值建模及应用研究
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摘要
潮汐潮流运动是海洋中的基本运动之一,它是动力海洋学研究的重要组成部分,对它的研究直接影响着波浪、风暴潮、环流、水团等其他海洋现象的研究,在大陆架浅海海洋中,对潮汐潮流的研究更具重要性.伴随同化方法是建立在严格的数学基础之上的一种有效的四维变分同化技术,它将变分原理与最优控制理论相结合,以海洋动力模型作为约束条件,通过同化可观测到的海洋要素优化控制变量,达到反演无法观测到的海洋要素的目的.潮汐潮流数值模拟中最大的难点莫过于开边界条件和底摩擦系数的确定,在数学物理反问题的框架下,伴随同化方法可以把开边界条件和底摩擦系数的确定变成依赖于区域内部观测资料的数值迭代过程,实现了调试控制参数的自动化和最优化.本文对伴随同化方法在潮汐潮流数值模拟中的应用进行了深入研究.
本文建立了一个球坐标系下的二维非线性潮波伴随同化模型,并基于渤、黄、东海M2分潮的数值模拟,对空间分布底摩擦系数处理方法进行了伴随法反演研究.孪生实验结果表明,空间分布底摩擦系数与伴随同化方法相结合,可以成功反演出给定的空间结构非常复杂的底摩擦系数分布,这是传统的处理方法所不能做到的.底摩擦效应由海底地形决定,本文尝试了根据海底地形的空间分布特征选取独立底摩擦系数的做法;数值实验结果表明,与均匀选取相比,根据底地形的空间分布特征选取独立参数,能在减少独立变量个数的情况下提高模拟精度.通过同化T/P高度计资料,本文数值模拟了渤、黄、东海的M2潮波;实验结果表明,与传统的底摩擦系数处理方法相比,空间分布的底摩擦系数能有效提高模拟精度,实验结果准确体现了渤、黄、东海M2潮波的分布特征.
使用上述二维非线性潮波伴随同化模型,考虑分潮间的非线性相互作用,本文通过同化T/P高度计资料,优化模式开边界条件及空间分布的底摩擦系数,数值模拟了渤、黄、东海的M2、S2、K1、O1四个主要分潮,模拟结果与验潮站资料(独立资料)之间的绝均差分别为(5 .7cm ,5.2)、(3 .2cm ,6.9)、( 2.6cm ,6.3)和( 2.1cm ,8.5).实验所得同潮图准确体现了渤、黄、东海四个主要分潮的潮位分布特征,半日分潮共有三个无潮点和一个退化型无潮点,全日分潮有三个无潮点,分别位于渤海海峡、南黄海和对马海峡.
基于内外模态分离技术,本文建立了一个三维正压非线性潮汐潮流模型,外模态采用ADI方法离散,时间步长不受CFL条件的限制;内模态的时间步长则可以远大于外模态时间步长,从而显著提高计算效率.将上述模型作为正向模型,本文建立了其伴随模型.此三维伴随模式建立之后,运算过程中开边界条件、底摩擦系数和垂向涡动粘性系数等控制参数的选取、数值模式和观测结果的有机结合等问题就可迎刃而解.与前人的有关三维潮汐潮流伴随同化模型的工作不同,本模式将底应力项设置为底层流速的函数,从而在物理上更加合理.
在数学物理反问题的框架下,本文设计孪生实验研究了三维正压潮汐潮流模型中开边界条件、空间分布底摩擦系数和垂向混合涡动粘性系数的伴随法反演问题,以验证伴随模型的有效性和正确性.同时,本文分别讨论了参数的不同类型分布、参数初值、观测误差以及观测数量对参数估计反问题的影响,对反问题适定性进行了初步研究.
The research on the tide and tidal current, which has close relation to those of the wind wave, ocean circulation, storm surge and other ocean phenomenon, is very important for the understanding of the dynamics of the ocean, especially in the continental marginal seas. Among all the data assimilation methods, four-dimensional variational (4DVAR) data assimilation is one of the most effective and powerful approaches. It is an advanced data assimilation method which involves the adjoint method and has the advantage of directly assimilating various observations distributed in time and space into numerical models while maintaining dynamical and physical consistency with the model. The major difficulties faced by numerical models of tidal flow concern the treatment of open boundary conditions (OBC) and bottom friction coefficients (BFC). By assimilating the data in the interior region, the adjoint method can optimize the OBC and BFC automatically and reach a global optimization of the model parameters. This paper researches the application of adjoint assimilation method in the numerical simulation of tides and tidal currents in-depth.
This paper develops a two-dimensional (2-D) adjoint tidal model and studies the spatially varying BFC based on the numerical simulation of M2 tide in the Bohai, Yellow and East China Seas (BYECS). In the twin experiments the prescribed BFC distributions that the spatial structure is very complex are inverted successfully with the combination of spatially varying BFC and the adjoint method. Obviously the inversion would not succeed if the traditional ways about BFC were used. The bottom friction effect is decided by the ocean bottom topography. This study establishes a method of selecting the independent BFC according to the spatial characteristics of ocean topography. The numerical results show that the method can increase the simulation precision even if a small number of independent parameters are employed. The M2 tide in BYECS is simulated by assimilating the TOPEX/Poseidon (T/P) altimeter data. The results also prove that the spatially varying BFC is more powerful than the traditional ways in obtaining reasonable simulation results. The co-tidal charts obtained coincide with the observed M2 tide in BYECS fairly well.
By assimilating the T/P data, the 2-D tidal model above is employed to optimize the OBC and BFC for the simulation of M2, S2, K1 and O1 constituents in BYECS, and the average absolute differences of amplitudes and phase-lags between simulation results and observations of 152 tidal gauge stations (independent data) are (5 .7cm ,5.2), (3 .2cm ,6.9), ( 2.6cm ,6.3) and ( 2.1cm ,8.5), respectively. The co-tidal charts obtained show that both the M2 and S2 constituents have three amphidromic points: one in the Bohai Sea and two in the Yellow Sea. Near the Yellow River mouth the amphidromes appear as degenerated systems. There are three amphidromic points for both the K1 and O1 constituents located in the Bohai Strait, in the Southern Yellow Sea and in the Tsushima Strait, respectively.
In this study a numerical tidal model based on the discretization of three-dimensional (3-D) primitive equations is established to simulate the barotropic tides and tidal currents in the Bohai Sea and the North Yellow Sea (BNYS). The numerical schemes for solving the equations of motion and continuity use the internal-external mode splitting technique. The ADI method is employed for the external mode computations which give the surface elevations and depth-averaged currents. The time step of external mode is thus not restricted by the CFL condition. A semi-implicit scheme is used for the internal mode computations which give the vertical structure of the currents. The time step of internal mode can be significantly longer than that of the external mode. As a consequence, the overall computational speed can be several times faster than that of the general explicit models. For the bottom friction effect, turbulent boundary layer models of the near-bottom flow indicate that it is physically realistic to use a quadratic dependence of bottom friction on the bottom velocity. In our model the bottom friction is expressed in terms of bottom velocity, which is different from the previous works on 3-D adjoint tidal models.
Based on the simulation of M2 tide and tidal current in BNYS, this study carries out twin experiments to invert the prescribed distributions of model parameters. The parameters inverted are the Fourier coefficients of OBC, the BFC and the vertical eddy viscosity profiles. In these twin experiments, the real topography of BNYS is installed. The inversion has obtained satisfying results and the prescribed distributions have been successfully inverted, which demonstrates the strong ability of the adjoint model. In order to research the ill-posedness of parameter estimation inverse problems, the experiments also discuss the influences of parameter distributions, initial guesses, model errors and data number on the inversion. The results indicate the inversion of BFC is more sensitive to data error than that of OBC and vertical eddy viscosity profiles.
本文建立了一个球坐标系下的二维非线性潮波伴随同化模型,并基于渤、黄、东海M2分潮的数值模拟,对空间分布底摩擦系数处理方法进行了伴随法反演研究.孪生实验结果表明,空间分布底摩擦系数与伴随同化方法相结合,可以成功反演出给定的空间结构非常复杂的底摩擦系数分布,这是传统的处理方法所不能做到的.底摩擦效应由海底地形决定,本文尝试了根据海底地形的空间分布特征选取独立底摩擦系数的做法;数值实验结果表明,与均匀选取相比,根据底地形的空间分布特征选取独立参数,能在减少独立变量个数的情况下提高模拟精度.通过同化T/P高度计资料,本文数值模拟了渤、黄、东海的M2潮波;实验结果表明,与传统的底摩擦系数处理方法相比,空间分布的底摩擦系数能有效提高模拟精度,实验结果准确体现了渤、黄、东海M2潮波的分布特征.
使用上述二维非线性潮波伴随同化模型,考虑分潮间的非线性相互作用,本文通过同化T/P高度计资料,优化模式开边界条件及空间分布的底摩擦系数,数值模拟了渤、黄、东海的M2、S2、K1、O1四个主要分潮,模拟结果与验潮站资料(独立资料)之间的绝均差分别为(5 .7cm ,5.2)、(3 .2cm ,6.9)、( 2.6cm ,6.3)和( 2.1cm ,8.5).实验所得同潮图准确体现了渤、黄、东海四个主要分潮的潮位分布特征,半日分潮共有三个无潮点和一个退化型无潮点,全日分潮有三个无潮点,分别位于渤海海峡、南黄海和对马海峡.
基于内外模态分离技术,本文建立了一个三维正压非线性潮汐潮流模型,外模态采用ADI方法离散,时间步长不受CFL条件的限制;内模态的时间步长则可以远大于外模态时间步长,从而显著提高计算效率.将上述模型作为正向模型,本文建立了其伴随模型.此三维伴随模式建立之后,运算过程中开边界条件、底摩擦系数和垂向涡动粘性系数等控制参数的选取、数值模式和观测结果的有机结合等问题就可迎刃而解.与前人的有关三维潮汐潮流伴随同化模型的工作不同,本模式将底应力项设置为底层流速的函数,从而在物理上更加合理.
在数学物理反问题的框架下,本文设计孪生实验研究了三维正压潮汐潮流模型中开边界条件、空间分布底摩擦系数和垂向混合涡动粘性系数的伴随法反演问题,以验证伴随模型的有效性和正确性.同时,本文分别讨论了参数的不同类型分布、参数初值、观测误差以及观测数量对参数估计反问题的影响,对反问题适定性进行了初步研究.
The research on the tide and tidal current, which has close relation to those of the wind wave, ocean circulation, storm surge and other ocean phenomenon, is very important for the understanding of the dynamics of the ocean, especially in the continental marginal seas. Among all the data assimilation methods, four-dimensional variational (4DVAR) data assimilation is one of the most effective and powerful approaches. It is an advanced data assimilation method which involves the adjoint method and has the advantage of directly assimilating various observations distributed in time and space into numerical models while maintaining dynamical and physical consistency with the model. The major difficulties faced by numerical models of tidal flow concern the treatment of open boundary conditions (OBC) and bottom friction coefficients (BFC). By assimilating the data in the interior region, the adjoint method can optimize the OBC and BFC automatically and reach a global optimization of the model parameters. This paper researches the application of adjoint assimilation method in the numerical simulation of tides and tidal currents in-depth.
This paper develops a two-dimensional (2-D) adjoint tidal model and studies the spatially varying BFC based on the numerical simulation of M2 tide in the Bohai, Yellow and East China Seas (BYECS). In the twin experiments the prescribed BFC distributions that the spatial structure is very complex are inverted successfully with the combination of spatially varying BFC and the adjoint method. Obviously the inversion would not succeed if the traditional ways about BFC were used. The bottom friction effect is decided by the ocean bottom topography. This study establishes a method of selecting the independent BFC according to the spatial characteristics of ocean topography. The numerical results show that the method can increase the simulation precision even if a small number of independent parameters are employed. The M2 tide in BYECS is simulated by assimilating the TOPEX/Poseidon (T/P) altimeter data. The results also prove that the spatially varying BFC is more powerful than the traditional ways in obtaining reasonable simulation results. The co-tidal charts obtained coincide with the observed M2 tide in BYECS fairly well.
By assimilating the T/P data, the 2-D tidal model above is employed to optimize the OBC and BFC for the simulation of M2, S2, K1 and O1 constituents in BYECS, and the average absolute differences of amplitudes and phase-lags between simulation results and observations of 152 tidal gauge stations (independent data) are (5 .7cm ,5.2), (3 .2cm ,6.9), ( 2.6cm ,6.3) and ( 2.1cm ,8.5), respectively. The co-tidal charts obtained show that both the M2 and S2 constituents have three amphidromic points: one in the Bohai Sea and two in the Yellow Sea. Near the Yellow River mouth the amphidromes appear as degenerated systems. There are three amphidromic points for both the K1 and O1 constituents located in the Bohai Strait, in the Southern Yellow Sea and in the Tsushima Strait, respectively.
In this study a numerical tidal model based on the discretization of three-dimensional (3-D) primitive equations is established to simulate the barotropic tides and tidal currents in the Bohai Sea and the North Yellow Sea (BNYS). The numerical schemes for solving the equations of motion and continuity use the internal-external mode splitting technique. The ADI method is employed for the external mode computations which give the surface elevations and depth-averaged currents. The time step of external mode is thus not restricted by the CFL condition. A semi-implicit scheme is used for the internal mode computations which give the vertical structure of the currents. The time step of internal mode can be significantly longer than that of the external mode. As a consequence, the overall computational speed can be several times faster than that of the general explicit models. For the bottom friction effect, turbulent boundary layer models of the near-bottom flow indicate that it is physically realistic to use a quadratic dependence of bottom friction on the bottom velocity. In our model the bottom friction is expressed in terms of bottom velocity, which is different from the previous works on 3-D adjoint tidal models.
Based on the simulation of M2 tide and tidal current in BNYS, this study carries out twin experiments to invert the prescribed distributions of model parameters. The parameters inverted are the Fourier coefficients of OBC, the BFC and the vertical eddy viscosity profiles. In these twin experiments, the real topography of BNYS is installed. The inversion has obtained satisfying results and the prescribed distributions have been successfully inverted, which demonstrates the strong ability of the adjoint model. In order to research the ill-posedness of parameter estimation inverse problems, the experiments also discuss the influences of parameter distributions, initial guesses, model errors and data number on the inversion. The results indicate the inversion of BFC is more sensitive to data error than that of OBC and vertical eddy viscosity profiles.
引文
[1] Newton I. Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), London, 1687
[2] Laplace P S. Recherches sur plusieurs points du système du monde. Mém. Acad. Roy. d. Sci., 1775, 88: 75~182
[3] Laplace P S. Recherches sur plusieurs points du système du monde. Mém. Acad. Roy. d. Sci., 1776, 89: 177~264
[4] Airy G B. Tides and waves. In: Encyclopedia Metropolitana. London, 1845, 5: 241~396
[5] Hough S S. On the Application of Harmonic Analysis to the Dynamical Theory of the Tides. Part I. On Laplace's 'Oscillations of the First Species,' and on the Dynamics of Ocean Currents. Proceedings of the Royal Society, London, 1897, 61: 236~238
[6] Hough S S. On the Application of Harmonic Analysis to the Dynamical Theory of the Tides. Part II: On the General Integration of Laplace's Dynamical Equations. Philosophical Transactions of the Royal Society, London, 1898, 191: 139~185
[7] Goldsbrough G R. The dynamical theory of the tides in a polar basin. Proc. Lond. Math. Soc., 1913, 14: 31~66
[8] Goldsbrough G R. The dynamical theory of the tides in a zonal ocean. Proc. Lond. Math. Soc., 1914, 14: 207~229
[9] Proudman J. The tides of the Atlantic Ocean. Month. Not. Roy. Astron. Soc., 1944, 104: 244~256
[10] Thomson W (Lord Kelvin). On gravitational oscillations of rotating water. Proceedings of the Royal Society, Edinburgh, 1879, 10: 92~100
[11] Taylor G I. Tidal oscillations in gulfs and rectangular basins. Proc. Lond. Math. Soc., 1920, 20: 148~181
[12]陈宗镛.长方形浅水海湾的一种潮波模式.海洋与湖沼,1965,7(2):85~93
[13]方国洪,王仁树.海湾的潮汐与潮流.海洋与湖沼,1966,8(1):60~77
[14] Hansen W. Gezeiten und Gezeitenstr?me der halbt?gigen Hauptmondtide M2 in der Nordsee. Deutsche Hydrografische Zeitschrift, Erg?nzungsheft, 1952, 1~46
[15] Thomson W (Lord Kelvin). Committee for the purpose of promoting the extension, improvement, and harmonic analysis of tidal observations’. British Association for the Advancement of Science, report, 1868
[16] Darwin G H, Turner H H. On the Correction to the Equilibrium Theory of Tides for the Continents. Proceedings of the Royal Society, London, 1886, 40: 303~315
[17] Doodson A T. The harmonic development of the tide generating potential. Proceedings of the Royal Society, London, 1921, A100: 306~328
[18] Doodson A T. The analysis of tidal observa- tions. Philosophical Transactions of the Royal Society, London, 1928, A227: 223~279
[19]方国洪.潮汐分析和预报的准调合分潮方法,I,准调合分潮.海洋科学集刊,1974,9:1~15
[20]方国洪.潮汐分析和预报的准调合分潮方法,II,短期观测的方法.海洋科学集刊,1976,11:33~56
[21]方国洪.潮汐分析和预报的准调合分潮方法,III,潮流和潮汐分析的一个实际计算过程.海洋科学集刊,1981,18:19~39
[22] Horn W. Some recent approaches to tidal problems. Int. Hydrogr. Rev., 1960, 37: 65~84
[23] Munk W H, Cartwright D E. Tidal spectroscopy and prediction. Philosophical Transactions of the Royal Society, London, 1966, A259(ll05): 533~581
[24] Groves G W, Reynolds R W. An orthogonalized convolution method of tide prediction, Journal of Geophysical Research, 1975, 80: 4131~4138
[25]郑文振.实用潮汐学.天津:海军测量部,1959
[26]陈宗镛.潮汐学.北京:科学出版社,1980
[27]方国洪,郑文振,陈宗镛,王骥.潮汐和潮流的分析与预报.北京:海洋出版社,1986
[28]秦曾灏,冯士筰.浅海风暴潮动力机制的初步研究.中国科学(A),1975,1:64
[29]王化桐,方欣华,匡国瑞,杨殿荣,陈时俊.胶州湾环流和污染扩散的数值模拟——Ⅰ胶州湾潮流数值计算.山东海洋学院学报,1980,10(1):26～63
[30]沈育疆.东中国海潮汐数值计算.山东海洋学院学报,1980,10(3):28～35
[31]丁文兰.东海潮汐和潮流特征的研究.海洋科学集刊,1984,21:135～148
[32]沈育疆,叶安乐.东中国海三维半日潮流的数值计算.海洋与湖沼通报,1984,1:1～11
[33] Fang G H. Tide and tidal current charts for the marginal seas adjacent to China. Chinese Journal of Oceanography and Limnology, 1986, 4(1): 1~16
[34]赵保仁,方国洪,曹德明.渤、黄、东海潮汐潮流的数值模拟.海洋学报,1994,1(5):1～10
[35]叶安乐,梅丽明.渤黄东海潮波数值模拟.海洋与湖沼,1995,26(1):63～69
[36] Guo X Y, Yanagi T. Three-dimensional structure of tidal current in the East China Sea and the Yellow Sea. Journal of Oceanography, 1998, 54: 651~668
[37]万振文,乔方利,袁业立.渤、黄、东海三维潮波运动数值模拟.海洋与湖沼,1998,29(6):611～616
[38] Kang S K, Lee S R, Lie H J. Fine grid tidal modeling of the Yellow and East China Seas. Continental Shelf Research, 1998, 18: 739~772
[39] Lee J C, Jung K T. Application of eddy viscosity closure models for the M2 tide and tidal currents in the Yellow Sea and the East China Sea. Continental Shelf Research, 1999, 19: 445~475
[40]王凯,方国洪,冯士筰.渤海、黄海、东海M2潮汐潮波的三维数值模拟.海洋学报,1999,21(4):1～13
[41] Lefevre F, Le Provost C, Lyard F H. How can we improve a global ocean tide model at a regional scale? A test on the Yellow Sea and the East China Sea. Journal of Geophysical Research, 2000, 105: 8707~8725
[42] Bao X W, Gao G P, Yan J.Three dimensional simulation of tide current characteristics in the East China Sea. Oceanologica Acta, 2001, 24(2): 1~15
[43] Lee H J, Jung K T, So J K, Chung J Y. A Three-dimensional mixed finite-difference Galerkin function model for the oceanic circulation in the Yellow Sea and the East China Sea in the presence of M2 tide. Continental Shelf Research, 2002, 22: 67~91
[44] He Y J, Lu X Q, Qiu Z F, Zhao J P. Shallow water tidal constituents in the Bohai Sea and the Yellow Sea from a numerical adjoint model with T/P altimeter data. Continental Shelf Research, 2004, 24: 1521~1529
[45]王永刚,方国洪,曹德明,魏泽勋,乔方利.渤、黄、东海潮汐的一种验潮站资料同化数值模式.海洋科学进展,2004,22(3):253～274
[46]李培良,左军成,吴德星,李磊,赵玮.渤、黄、东海同化T/P高度计资料的半日分潮数值模拟.海洋与湖沼,2005,36(1):24～30
[47] Qiu Z F, He Y J, Lu X Q. Tidal constituents in the Bohai and Yellow Seas from an adjoint numerical model with T/P data. Journal of Hydrodynamics(B), 2005, 17(3): 275~282
[48]丘仲锋,何宜军,吕咸青.黄海、渤海TOPEX/ Poseidon高度计资料潮汐伴随同化.海洋学报,2005,27(4):10～18
[49]丘仲锋,何宜军.T/P高度计资料用于中国近海M2分潮的同化反演.海洋与湖沼,2005,36(4):376～384
[50]张衡,朱建荣,吴辉.东海黄海渤海8个主要分潮的数值模拟.华东师范大学学报(自然科学版),2005,3:71～77
[51] Cheng Y C, Lu X Q, Liu Y G, Xu Q. Application of adjoint assimilation technique in simulating tides and tidal currents of the Bohai Sea, the Yellow Sea and the East China Sea. High Technology Letters, 2007, 13(1): 58~64
[52] Zhang J C, Lu X Q. On the simulation of M2 tide in the Bohai, Yellow and East China Seaswith T/P altimeter data. Terrestrial, Atmosphere and Oceanic Sciences, 2008. (Accepted)
[53]李磊.渤黄东海潮波系统的有限元模拟:[博士学位论文].青岛:中国海洋大学海洋环境学院,2003
[54]李培良.渤黄东海潮波同化数值模拟和潮能耗散的研究:[博士学位论文].青岛:中国海洋大学海洋环境学院,2002
[55] Ye A L, Robinson I S. Tidal dynamics in the South China Sea. Geophys. J. R. Astron. Soc., 1983, 72: 691~707
[56]俞慕耕.南海潮汐特征的初步探讨.海洋学报,1984,6(3):293~300
[57]沈育疆.南海潮汐数值计算.海洋湖沼通报,1985,1:1~11
[58]丁文兰.南海潮汐和潮流的分布特征.海洋与湖沼,1986,17(6):468~480
[59]方国洪,曹德明,黄企洲.南海潮汐潮流的数值模拟.海洋学报,1994,16(4):1~12
[60] Yanagi T, Takao T. Clockwise Phase Propagation of Semi-Diurnal Tides in the Gulf of Thailand. Journal of Oceanography, 1998, 54: 143~150
[61] Fang G H, Kwok Y K, Yu K J, Zhu Y. Numerical simulation of principal tidal constituents in the South China Sea, Gulf of Tonkin and Gulf of Thailand. Continental Shelf Research, 1999, 19: 845~ 869
[62]李培良,左军成,李磊等.南海TOPEX/POSEIDON高度计资料的正交响应法潮汐分析.海洋与湖沼,2002,33(3):287~295
[63]吴自库,田纪伟,吕咸青,等.南海潮汐的伴随同化数值模拟.海洋与湖沼,2003,34(1):101~108
[64]吴自库,田纪伟,赵骞.南海潮波三维同化数值模拟.水动力学研究与进展A辑,2004,4:98~103
[65]吴自库.南海内潮三维数值同化模拟:[博士学位论文].青岛:中国海洋大学海洋环境学院,2005
[66] Cai S Q, Long X M, Liu H L, Wang S G. Tide model evaluation under different conditions. Continental Shelf Research, 2006, 26(1): 104~112
[67] Panofsky H A. Objective weather map analysis. Journal of Meteorology, 1949, 6: 386~392
[68] Gilchrist B, Cressman G. An experiment in Objective Analysis. Tellus, 1954, 6: 309~318
[69] Bergthorsson P, D??s B R. Numerical weather map analysis. Tellus, 1955, 7: 329~340
[70] Cressman G P. An operational objective analysis system. Monthly Weather Review, 1959, 87: 367~374
[71] Eliassen A. Provisional report on calculation of spatial covariance and autocorrelation of the pressure field. Oslo: Inst. Weather and Climate Research, Academy of Sciences, 1954, Report No. 5
[72] Gandin L. Objective Analysis of Meteorological Fields (translated from Russian). Jerusalem: Israel Program for Scientific Translation, 1965.
[73] Bratseth A M. Statistical interpolation by means of successive corrections. Tellus, 1986, 38A: 439~447
[74] Miller R N. Toward the application of the Kalman filter to regional open ocean modeling. Journal of Physical Oceanography, 1986, 16: 72~86
[75] Bennett A F, Budgell W P. Ocean data assimilation and the Kalman filter, spatial regularity. Journal of Physical Oceanography, 1987, 17: 1583~1601
[76] LeDimet F X, Talagrand O. Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus, 1986, 38A: 97~110
[77] Thacker W C, Long R B. Fitting dynamics to data. Journal of Geophysical Research, 1988, 93: 1227~1240
[78] Evensen G. Sequential data assimilation with a nonlinear quasi-geostrophic model using Montre Carlo methods to forecast error statistics. Journal of Geophysical Research, 1994, 99(10): 143~162
[79] Gelb A. Applied Optimal Estimation. Cambridge: MIT Press, 1974
[80] Ghil M, Malanotte-Rizzoli P. Data assimilation in meteorology and oceanography. In: Saltzman B eds. In Advances in Geophysics. San Diego: Academic Press, 1991, 33. 141~266
[81] Anderson D L T, Sheinbaum J, Haines K. Data assimilation in ocean models. Reports on Progress in Physics, 1996, 59: 1209~1266
[82] Malanotte-Rizzoli P, Tziperman E. The Oceanographic Data Assimilation Problem: Overview, Motivation and Purposes. In: Malanotte-Rizzoli P Eds. Modern approaches to data assimilation in ocean modeling. Amsterdam: Elsevier, 1996. 3~17
[83]王东晓,朱江.伴随方法在海洋数值模式中的应用.地球物理学进展,1997,12(1):98～107
[84] Navon I M. Practical and Theoretical Aspects of Adjoint Parameter Estimation and Identifiability in Meteorology and Oceanography. Dynamics of Atmospheres and Oceans (Special Issue in honor of Richard Pfeffer), 1998, 27: 55~79
[85]乔方利,Zhang S Q.现代海洋/大气资料同化方法的统一性及其应用进展.海洋科学进展,2002,20(4):79～93
[86]马寨璞,井爱芹.海洋科学中的数据同化方法——意义、结构与发展现状.海岸工程,2005,4:83～99
[87] Talagrand O, Courtier P. Variational assimilation of meteorological observations with the adjoint vorticity equation Part I: Theory. Quarterly Journal of the Royal MeteorologicalSociety, 1987, 113: 1311~1328
[88] Smedstad O M, O’Brien J J. Variational data assimilation and parameter estimation in an equatorial Pacific Ocean model. Progress in Oceanography, 1991, 26: 179~241
[89] Bouttier F, Courtier P. Data assimilation concepts and methods. 1999, Available on: http://www.ecmwf.int/newsevents/training/rcourse_notes/DATA_ASSIMILATION/ASSIM_CONCEPTS/Assim_concepts2.html
[90] Robinson A R, Lermusiaux P F J. Overview of Data Assimilation. Cambridge: Harvard Reports in Physical/Interdisciplinary Ocean Science, 2000, Number 62
[91] Daley R. Atmospheric Data Analysis. New York: Cambridge Atmospheric and Space Science Series, Cambridge University Press, 1991. 363~402
[92] Sasaki Y. Some basic formalisms in numerical variational analysis. Monthly Weather Review, 1970, 98: 875~883
[93]吕咸青.海洋数值建模中伴随方法的研究:[博士后研究工作报告].青岛:中国科学院海洋研究所,2000
[94] Bertsekas D P. Constrained optimization and Lagrange multiplier methods. London: Academic Press, 1982
[95] Derber J C. A variational continuous assimilation technique. Monthly Weather Review, 1989, 117: 2437~2446
[96] Long R B, Thacker W C. Data Assimilation into A Numerical Equatorial Ocean Model. I. The Model and The Assimilation Algorithm. Dynamics of Atmospheres and Oceans, 1989, 13: 379~412
[97] Long R B, Thacker W C. Data Assimilation into A Numerical Equatorial Ocean Model. II. Assimilation Experiments. Dynamics of Atmospheres and Oceans, 1989, 13: 413~439
[98] Panchang V G, O'Brien J J. On the determination of hydraulic model parameters using the adjoint state formulation. In: Davis A M eds. Modelling Marine System. Boca Rayon: CRC Press, 1989. 6~18
[99] Yu L S, O’Brien J J. Variational estimation of the wind stress drag coefficient and the oceanic eddy viscosity profile. Journal of Physical Oceanography, 1991, 21: 709~719
[100]Das S K, Lardner R W. On the estimation of parameters of hydraulic models by assimilation of periodic tidal data. Journal of Geophysical Research, 1991, 96(C8): 15187~15196
[101]Das S K, Lardner R W. Variational parameter estimation for a two dimensional numerical tidal model. International Journal for Numerical Methods in Fluids, 1992, 15: 313~327
[102]Lardner R W, Al-Rabeh A H, Gunay N. Optimal Estimation of Parameters for a Two-Dimensional Hydro-dynamical Model of the Arabian Gulf. Journal of GeophysicalResearch, 1993, 98(C10): 18229~18242
[103]Lardner R W, Das S K. Optimal estimation of eddy viscosity for a quasi-three dimensional numerical tidal and storm surge model. International Journal for Numerical Methods in Fluids, 1994, 18: 295~312
[104]Lardner R W, Song Y. Optimal estimation of eddy viscosity and friction coefficients for a quasi-three-dimensional numerical tidal model. Atmosphere-Ocean, 1995, 33(3): 581~611
[105]Lu J, Hsieh W W. Adjoint data assimilation in coupled atmosphere–ocean models: determining initial model parameters in a simple equatorial model. Quarterly Journal of the Royal Meteorological Society, 1997, 123: 2115~2139
[106]Lu J, Hsieh W W. Adjoint data assimilation in coupled atmosphere–ocean models: determining initial conditions in a simple equatorial model. Journal of the Meteorological Society of Japan, 1998a, 76: 737~748
[107]Lu J, Hsieh W W. On determining initial conditions and parameters in a simple couple atmosphere–ocean model by adjoint data assimilation. Tellus, 1998b, 50A: 534~544
[108]Ullman D S, Wilson R E. Model parameter estimation from data assimilation modelling: temporal and spatial variability of the bottom drag coefficient. Journal of Geophysical Research, 1998, 103: 5531~5549
[109]吕咸青.数据同化反演风应力拖曳系数以及垂向涡动黏性系数的分布.海洋学报,2001,23(1):13～20
[110]吕咸青,田纪伟,吴自库.渤、黄海的底摩擦系数.力学学报,2003b,35(4):465～468
[111]吕咸青,吴自库,谷艺,田纪伟.数据同化中的伴随方法的有关问题的研究.应用数学和力学,2004,25(6):581～590
[112]Heemink A W, Mouthaan E E A, Roest M R T, Vollebregt E A H, Robaczewska K B, Verlaam M. Inverse 3D shallow water flow modeling of the continental shelf. Continental Shelf Research, 2002, 22: 465~484
[113]Zhang A J, Parker B B, Wei E. Assimilation of water level data into a coastal hydrodynamic model by an adjoint optimal technique. Continental Shelf Research, 2002, 22: 1909~1934
[114]Lu X Q, Wu Z K, Gu Y, Tian J W. Study on the adjoint method in data assimilation and the related problems. Applied Mathematics and Mechanics, 2004, 25(6): 636~646
[115]张继才,吕咸青.空间分布底摩擦系数的伴随法反演研究.自然科学进展,2005,15(9):1086～1093
[116]Zhang J C, Zhu J G, Lu X Q. Numerical Study on the Bottom Friction Coefficient of the Bohai Sea, the Yellow Sea and the East China Sea. Chinese Journal of Computational Physics,2006, 23(6): 731~737
[117]Lu X Q, Zhang J C. Numerical Study on Spatially Varying Bottom Friction Coefficient of a 2D Tidal Model with Adjoint Method. Continental Shelf Research, 2006, 26: 1905~1923
[118]Zhang J C, Lu X Q. Parameter Estimation for a Three-Dimensional Numerical Barotropic Tidal Model with Adjoint Method. International Journal for Numerical Methods in Fluids, 2007. (Available online)
[119]Moore A M. Data assimilation in a quasi-geostrophic open ocean model of the Gulf Stream region using the adjoint method. Journal of Physical Oceanography, 1991, 21: 398~427
[120]Yu L S, O'Brien J J. On the initial condition parameter estimation. Journal of Physical Oceanography, 1992, 22: 1361~1364
[121]Gunson J R, Malanotte-Rizzoli P. Assimilation studies of open-ocean flows, Part I: Estimation of initial and boundary conditions, Journal of Geophysical Research, 1996a, 101: 28457~28472
[122]Gunson J R, Malanotte-Rizzoli P. Assimilation studies of open-ocean flows, Part II: Error measures with strongly nonlinear dynamics. Journal of Geophysical Research, 1996b, 101: 28473~28488
[123]Greiner E, Perigaud C. Assimilation of Geo-sat altimetric data in a nonlinear reduced-gravity model of the Indian Ocean, Part I: adjoint approach and model-data consistency. Journal of Physical Oceanography, 1994, 24(8): 1783~1804
[124]Greiner E, Perigaud C. Assimilation of Geo-sat altimetric data in a nonlinear reduced-gravity model of the Indian Ocean, Part II: Some Validation and Interpretation of the assimilated results. Journal of Physical Oceanography, 1996, 26: 1735~1746
[125]Greiner E, Arnault S, Morliaère A. Twelve-monthly experiments of 4D-variational assimilation in the tropical Atlantic during 1987, Part 1: Method and statistical results. Progress in Oceanography, 1998a, 41: 141~202
[126]Greiner E, Arnault S, Morliaère A. Twelve-monthly experiments of 4D-variational assimilation in the tropical Atlantic during 1987, Part 2: Oceanographic interpretation. Progress in Oceanography, 1998b, 41: 203~247
[127]马继瑞,韩桂军,李冬.变分伴随数据同化在海表面温度预报中的应用研究.海洋学报,2002,24(5):1～7
[128]Seiler U. Estimation of open boundary conditions with the adjoint method. Journal of Geophysical Research, 1993, 98: 22855~22870
[129]Lardner R W. Optimal control of an open boundary conditions for a numerical tidal model. Computer Methods in Applied Mechanics and Engineering, 1993, 102: 367~387
[130]Mewis P, Holz KP. Inverse boundary value estimation for a shallow water model. Computational Methods in Water Resources XI, Cancun, Volume 2, Computational Methods in Surface Flow and transport Problems, 1996: 223~230
[131]朱江,曾庆存,郭冬建,刘卓.利用伴随算法从岸边潮位站资料估计近岸模式的开边界条件.中国科学(D辑),1997,27(5):462～468
[132]Marotzke J, Giering R, Zhang Q K, Stammer D, Hill C N, Lee T. Construction of the adjoint MIT ocean general circulation model and application to Atlantic heat transport sensitivity. Journal of Geophysical Research, 1999, 104: 29529~29548
[133]吕咸青,张杰.如何利用水位资料反演开边界条件(1).水动力学研究与进展,1999,14:92～102
[134]韩桂军,何柏荣,马继瑞,刘克修,李冬.利用伴随法优化非线性潮汐模型的开边界条件I:伴随方程的建立及“孪生”数值试验.海洋学报,2000,22(6):134～140
[135]韩桂军,何柏荣,马继瑞,刘克修,李冬.利用伴随法优化非线性潮汐模型的开边界条件II:黄海、东海潮汐资料的同化试验.海洋学报,2001,23(2):25～31
[136]Zhang A J, Wei E, Parker B B. Optimal estimation of tidal open boundary conditions using predicted tides and adjoint data assimilation technique. Continental Shelf Research, 2003, 23: 1055~1070
[137]吕咸青,吴自库,殷忠斌,田纪伟.渤、黄、东海潮汐开边界的1种反演方法.青岛海洋大学学报,2003a,33(2):155～172
[138]尹训强,杨永增,乔方利.浅水潮波模式变分同化共轭码技术研究.海洋科学进展,2003,21(4):413～423
[139]Peng S Q, Xie L. Effect of determining initial conditions by four-dimensional variational data assimilation on storm surge forecasting. Ocean Modelling, 2006, 14: 1~18
[140]Tziperman E, Thacker W C. An Optimal Control/Adjoint equations approach to studying the oceanic general circulation. Journal of Physical Oceanography, 1989, 19: 1471~1485
[141]Tziperman E, Thacker W C, Bryan K. Computing the steady state oceanic circulation using an optimization approach. Dynamics of Atmospheres and Oceans, 1992, 16(5): 379~404
[142]Bergamasco A, Malanotte-Rizzoli P, Thacker W C, Long R B. The seasonal steady circulation of the Eastern Mediterranean determined with the adjoint method. In Topical Studies in Oceanography: Physical Oceanography of the Eastern Mediterranean Sea, special issue of Deep Sea Research II, 1993, 40(6): 1269~1298
[143]Marotzke J, Wunsch C. Finding the steady state of a general circulation model through data assimilation: application to the North Atlantic Ocean. Journal of Geophysical Research, 1993, 98: 20149~20167
[144]Schlitzer R. Determining the mean, large-scale circulation of the Atlantic with adjoint method. Journal of Physical Oceanography, 1993, 23: 1935~1952
[145]Griffin D A, Thompson K R. The adjoint method of data assimilation used operationally for shelf circulation. Journal of Geophysical Research, 1996, 101(C2): 3457~3478
[146]Yu L S, Malanotte-Rizzoli P. Analysis of the North Atlantic climatologies using the combined OGCM/adjoint approach. Journal of Marine Research, 1996, 54: 867~913
[147]Yu L S, Malanotte-Rizzoli P. Inverse modeling of the seasonal variations in the North Atlantic Ocean. Journal of Physical Oceanography, 1998, 28: 902~922
[148]王东晓,兰健,吴国雄,朱江.一个海洋环流模式伴随系统的初步实验.自然科学进展,1999,9(9):824～833
[149]王东晓,吴国雄,朱江,兰健.大洋风生环流观测优化的伴随分析.中国科学(D),2000,30(1):97～106
[150]Roquet H, Planton S. Determination of Ocean Heat Fluxes by a Variational Method. Journal of Geophysical Research, 1993, 98: 10211~10221
[151]Schiller A. The mean circulation of the Atlantic Ocean north of 30S determined with the adjoint method applied to an ocean general circulation model. Journal of Marine Research, 1995, 53(3): 453~497
[152]Yu L S, O'Brien J J. Variational data assimilation for determining the seasonal net surface heat flux using a tropical Pacific Ocean model. Journal of Physical Oceanography, 1995, 25: 2319~2343
[153]Yuan D L, Rienecker M M. Inverse estimation of sea surface heat flux over the equatorial Pacific Ocean: Seasonal cycle. Journal of Geophysical Research, 2003, 108(C8): 3247
[154]Lawson L M, Spitz Y H, Hofmann E E, Long R B. A data assimilation technique applied to a predator-prey model. Bulletin of Mathematical Biology, 1995, 57: 593~617
[155]Lawson L M, Hofmann E E, Spitz Y H. Time series sampling and data assimilation in a simple marine ecosystem model. Deep-Sea Research II, 1996, 43: 625~651
[156]Spitz Y H, Moisan J R, Abbort M R, Richman J G. Data assimilation and a pelagic ecosystem model: parameterization using time series observations. Journal of Marine Systems, 1998, 16: 51~68
[157]Spitz Y H, Moisan J R, Abbort M R. Configuration an ecosystem model using data from the Bermuda, Atlantic Time Series (BATS). Deep-Sea Research II, 2001, 48: 1733~1768
[158]Friedrichs M A M. A data assimilative marine ecosystem model of the central equatorial Pacific: numerical twin experiments. Journal of Marine Research, 2001, 59: 859~894
[159]Friedrichs M A M. Assimilation of JGOFS EqPac and SeaWiFS data into a marine ecosystemmodel of the central equatorial Pacific Ocean. Deep-Sea Research II, 2002, 49: 289~319
[160]Kuroda H, Kishi M J. A data assimilation technique applied to estimate parameters for the NEMURO marine ecosystem model. Ecological Modelling, 2004, 172: 69~85
[161]Xu Q, Liu Y G, Lu X Q. Adjoint assimilation in marine ecosystem models and an example of application. Journal of Ocean University of China, 2005, 4(1): 14~20
[162]Zhao L, Wei H, Xu Y, Feng S Z. An adjoint data assimilation approach for estimating parameters in a three-dimensional ecosystem model. Ecological Modelling, 2005, 186: 234~249
[163]徐青,刘玉光,程永存,吕咸青.伴随同化技术在渤、黄海生态模式中的应用:控制变量的选取与孪生实验.高科技通讯,2006,16(1):78～83
[164]Yeh W W G. Review of parameter identification procedures in groundwater hydrology: The inverse problem. Water Resources Research, 1986, 22: 95~108
[165]Carrera J, Neuman S P. Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incorporating prior information. Water Resource Research, 1986a, 22(2): 199~210
[166]Carrera J, Neuman S P. Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability and solution algorithms. Water Resource Research, 1986b, 22(2): 211~227
[167]Carrera J, Neuman S P. Estimation of aquifer parameters under transient and steady state conditions: 3. Application to synthetic and field data. Water Resource Research, 1986c, 22(2): 228~242
[168]Courtier P, Talagrand O. Variational assimilation of meteorological observations with the adjoint vorticity equation Part II: Numerical result. Quarterly Journal of the Royal Meteorological Society, 1987, 113: 1329~1348
[169]Courtier P, Talagrand O. Variational assimilation of meteorological observations with the direct and adjoint shallow-water equation. Tellus, 1990, 42A: 531~549
[170]LeDimet F X, Navon I M. Variational and optimization methods in meteorology: a review. Technology Report FSU-SCRI-88-144, Florida State University, Tallahassee, Florida, 83pp, 1988
[171]Zou X, Navon I M, LeDimet F X. An optimal nudging data assimilation scheme using parameter estimation. Quarterly Journal of the Royal Meteorological Society, 1992, 118: 1163~1186
[172]Schroter J, Seiler U, Wenzel M. Variational Assimilation of Geo-sat Data into an Eddy-resolving Model of the Gulf Stream Extension Area. Journal of PhysicalOceanography, 1993, 23: 925~953
[173]Sirkes Z, Tziperman E. Finite Difference of Adjoint or Adjoint of Finite Difference? Monthly Weather Review, 1997, 125: 3373~3378
[174]韩桂军.伴随法在潮汐和海温数值计算中的应用研究:[博士学位论文].青岛:中国科学院海洋研究所,2001
[175]Segal M, Pielke R A. Numerical model simulation of human biometeorological heat load conditions - summer day case study for the Chesapeake Bay area. Journal of Applied Meteorology, 1981, 20: 735~749
[176]Barnes S L. A technique for maximizing details in numerical map analysis. Journal of Applied Meteorology, 1964, 3: 395~409
[178]Egbert G D, Ray R D, Bills B G. Numerical modeling of the global semidiurnal tide in the present day and in the last glacial maximum. Journal of Geophysical Research, 2004, 109: C03003
[179]Zhao B R, Fang G H, Cao D M. Numerical modeling on the tides and tidal currents in the eastern China Seas. Yellow Sea Research, 1993, 5: 41~61
[180]Sannino G, Bargagli A, Artale V. Numerical modeling of the semidiurnal tidal exchange through the strait of Gibraltar. Journal of Geophysical Research, 2004, 109: C05011
[181]吕咸青,方国洪.渤海M2分潮的伴随模式数值实验.海洋学报,2002a,24(1):17～24
[182]吕咸青,方国洪.渤海开边界潮汐的伴随法反演.海洋与湖沼,2002b,33(2):113～120
[183]张继才,吕咸青.渤、黄、东海二维潮汐模式底摩擦系数的反演研究.计算力学学报,2007,22(3):214～219
[184]Fang G H, Wang Y G, Wei Z X, Choi B H, Wang X Y, Wang J. Empirical cotidal charts of the Bohai, Yellow, and East China Seas from 10 years of T/P altimetry. Journal of Geophysical Research, 2004, 109: C11006
[185]Choi B H. A fine-grid three-dimensional M2 tidal model of the East China Sea. In: Davies A M eds. Modelling Marine Systems. Boca Raton, Florida: CRC Press, 1989. 167~185
[186]Yanagi T, Inoue K. Tide and tidal current in the Yellow/East China Seas. Lamer, 1994, 32: 153~165
[187]Mofjeld H O. Depth Dependence of Bottom Stress and Quadratic Drag Coefficient for Barotropic Pressure-Driven Currents. Journal of Physical Oceanography, 1988, 18: 1658~1669
[188]Le Provost C, Genco M L, Lyard F, Vincent P, Canceil P. Spectroscopy of the world oceantides from a finite element hydrodynamic model. Journal of Geophysical Research, 1994, 99(C12): 24777~24798
[189]Aldridge J N, Davies A M. A high resolution three-dimensional hydrodynamic tidal model of the Eastern Irish Sea. Journal of Physical Oceanography, 1993, 23: 207~224
[190]孙丽艳.渤黄东海潮汐底摩擦系数的优化研究:[硕士学位论文].青岛:中国海洋大学海洋环境学院,2005
[191]Mazzega P, Berge M. Ocean tides in the Asian semienclosed seas from TOPEX/POSEIDON. Journal of Geophysical Research, 1994, 99(C12): 24867~24882
[192]Egbert G D, Bennett A F, Foreman M G. TOPEX/POSEIDON tides estimated using a global inverse model. Journal of Geophysical Research, 1994, 99(C12): 24821~24852
[193]Kantha L H. Barotropic tides in the global oceans from a nonlinear tidal model assimilating altimetric tides, 1, Model description and results. Journal of Geophysical Research, 1995, 100(C12): 25283~25308
[194]Kantha L H, Tierney C, Lopez J W, Desai S D, Parke M E, Drexler L. Barotropic tides in the global oceans from a nonlinear tidal model assimilating altimetric tides, 2, Altimetric and geophysical implications. Journal of Geophysical Research, 1995, 100(C12): 25309~25317
[195]Andersen O B, Woodworth P L, Flather R A. Intercomparison of recent ocean tide models. Journal of Geophysical Research, 1995, 100(C12): 25261~25282
[196]Yanagi T, Morimoto A, Ichikawa K. Co-tidal and co-range charts for the East China Sea and the Yellow Sea derived from satellite altimetric data. Journal of Oceanography, 1997, 53: 303~309
[197]张占海,吴辉碇.渤海潮汐和潮流数值计算.海洋预报,1994,11(1):48～54
[198]Leendertse J J, Alexander R C, Liu S K. A Three Dimensional Model for Estuaries and Coastal Seas, Vol. I: Principles of computations. Report R-1417-OWRR, Rand Corporation, Santa Monica, 1973.
[199]Backhaus J. A three-dimensional model for the simulation of shelf sea dynamics. Deutsche Hydrographische Zeitschrift, 1985, 38: 165~187
[200]Casulli V, Cheng R T. Semi-implicit finite difference methods for the three dimensional shallow water flow. International Journal for Numerical Methods in Fluids, 1992, 15: 629~648
[201]Casulli V. A semi-implicit finite difference method for the non-hydrostatic free-surface flow. International Journal for Numerical Methods in Fluids, 1999, 30: 425~440
[202]Yuan H L, Wu C H. An implicit three-dimensional fully non-hydrostatic model for free-surface flows. International Journal for Numerical Methods in Fluids, 2004, 46: 709~733
[203]Roache P J. Fundamentals of Computational Fluid Dynamics. New Mexico: Hermosa Publishers, Albuquerque, 1982
[204]方国洪,于克俊.斜压海洋动力学的一种三维数值模式Ⅰ.动力学方程数值格式.海洋与湖沼,1998,29(3):232~240
[205]于克俊,方国洪.斜压海洋动力学的一种三维数值模式Ⅱ.温度、盐度和垂直涡动粘性系数的计算.海洋与湖沼,1998,29(4):381~388
[206]Simons T J. Verification of numerical models of Lake Ontario, Part 1: circulation in spring and early summer. Journal of Physical Oceanography, 1974, 4: 507~523
[207]Bennett A F, McIntosh P C. Open ocean modeling as an inverse problem: tidal theory. Journal of Physical Oceanography, 1982, 12: 1004~1018
[208]Prevost C, Salmon R. A variational method for inverting hydrographic data. Journal of Marine Science, 1986, 44: 1~34
[209]孙文心,江文胜,李磊.近海环境流体动力学数值模型.北京:科学出版社,2004
[210]Winninghoff F J. On the adjustment toward a geostrophic balance in a simple primitive equation model with application to the problems of initialization and objective analysis: [Ph.D. Thesis]. Los Angeles: University of California, 1968. pp.161
[211]Chapman D C. Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model. Journal of Physical Oceanography, 1985, 15: 1060~1075
[212]肖庭延,于慎根,王彦飞.反问题的数值解法.北京:科学出版社,2003
[213]Lanseth A T. Sources and applications of integral equations. SIAM Review, 1977, 19: 241~278
[214]Baumeister J. Stable solution of inverse problems. Brauschweig: Vieweg, 1987
[215]Engl H W. Regularization methods for the stable solution of inverse problems. Surv. Math. Ind., 1993, 3: 71~143
[216]苏超伟.偏微分方程逆问题的数值解法及其应用.西安:西北工业大学出版社,1995
[217]Hadamard J. Lectures on the Cauthy problems in linear partial differential equations. New Haven: Yale university Press, 1923
[218]Tarantola A. Inverse problem theory: Methods for data fitting and model parameter estimation. Amsterdam: Elsevier, 613 pp., 1987
[219]Ayoub N. Estimation of boundary values in a North Atlantic circulation model using an adjoint method. Ocean Modelling, 2006, 12: 319~347
[220]Gejadze I Y, Copeland G J M, Navon I M. Open boundary control problem for Navier-Stokes equations including a free surface: data assimilation. Computers and Mathematics with Applications, 2006, 52: 1269~1288.
[221]Gejadze I Y, Copeland G J M. Open boundary control problem for Navier-Stokes equations including a free surface: adjoint sensitivity analysis. Computers and Mathematics with Applications, 2006, 52: 1243~1268
[222]Richardson J E, Panchang V G. A modified adjoint method for inverse eddy viscosity estimation in coastal circulation models. In: Spaulding M L, Bedford K, Blumberg A, Cheng R, Swanson C eds. Estuarine and Coastal Modeling. New York: Academic Press, 1992. 733~745
[223]Tikhonov A N. Solution of incorrectly formulated problems and the regularization method. Sov. Math. Dokl., 1963a, 4: 1035~1038
[224]Tikhonov A N. Regularization of incorrectly posed problems. Sov. Math. Dokl., 1963a, 4: 1624~1627
[225]Wang Z, Navon I M, LeDimet F X, Zou X L. The Second Order Adjoint Analysis: Theory and Application. Meteorology and Atmospheric Physics, 1992, 50: 3~20
[226]韩桂军,何柏荣,马继瑞,李冬.关于二阶伴随模型的理论研究.海洋学报,2000,22(3):16～20
[227]李守巨.基于计算智能的岩土力学模型参数反演方法及其工程应用:[博士学位论文].大连:大连理工大学工程,2004
[2] Laplace P S. Recherches sur plusieurs points du système du monde. Mém. Acad. Roy. d. Sci., 1775, 88: 75~182
[3] Laplace P S. Recherches sur plusieurs points du système du monde. Mém. Acad. Roy. d. Sci., 1776, 89: 177~264
[4] Airy G B. Tides and waves. In: Encyclopedia Metropolitana. London, 1845, 5: 241~396
[5] Hough S S. On the Application of Harmonic Analysis to the Dynamical Theory of the Tides. Part I. On Laplace's 'Oscillations of the First Species,' and on the Dynamics of Ocean Currents. Proceedings of the Royal Society, London, 1897, 61: 236~238
[6] Hough S S. On the Application of Harmonic Analysis to the Dynamical Theory of the Tides. Part II: On the General Integration of Laplace's Dynamical Equations. Philosophical Transactions of the Royal Society, London, 1898, 191: 139~185
[7] Goldsbrough G R. The dynamical theory of the tides in a polar basin. Proc. Lond. Math. Soc., 1913, 14: 31~66
[8] Goldsbrough G R. The dynamical theory of the tides in a zonal ocean. Proc. Lond. Math. Soc., 1914, 14: 207~229
[9] Proudman J. The tides of the Atlantic Ocean. Month. Not. Roy. Astron. Soc., 1944, 104: 244~256
[10] Thomson W (Lord Kelvin). On gravitational oscillations of rotating water. Proceedings of the Royal Society, Edinburgh, 1879, 10: 92~100
[11] Taylor G I. Tidal oscillations in gulfs and rectangular basins. Proc. Lond. Math. Soc., 1920, 20: 148~181
[12]陈宗镛.长方形浅水海湾的一种潮波模式.海洋与湖沼,1965,7(2):85~93
[13]方国洪,王仁树.海湾的潮汐与潮流.海洋与湖沼,1966,8(1):60~77
[14] Hansen W. Gezeiten und Gezeitenstr?me der halbt?gigen Hauptmondtide M2 in der Nordsee. Deutsche Hydrografische Zeitschrift, Erg?nzungsheft, 1952, 1~46
[15] Thomson W (Lord Kelvin). Committee for the purpose of promoting the extension, improvement, and harmonic analysis of tidal observations’. British Association for the Advancement of Science, report, 1868
[16] Darwin G H, Turner H H. On the Correction to the Equilibrium Theory of Tides for the Continents. Proceedings of the Royal Society, London, 1886, 40: 303~315
[17] Doodson A T. The harmonic development of the tide generating potential. Proceedings of the Royal Society, London, 1921, A100: 306~328
[18] Doodson A T. The analysis of tidal observa- tions. Philosophical Transactions of the Royal Society, London, 1928, A227: 223~279
[19]方国洪.潮汐分析和预报的准调合分潮方法,I,准调合分潮.海洋科学集刊,1974,9:1~15
[20]方国洪.潮汐分析和预报的准调合分潮方法,II,短期观测的方法.海洋科学集刊,1976,11:33~56
[21]方国洪.潮汐分析和预报的准调合分潮方法,III,潮流和潮汐分析的一个实际计算过程.海洋科学集刊,1981,18:19~39
[22] Horn W. Some recent approaches to tidal problems. Int. Hydrogr. Rev., 1960, 37: 65~84
[23] Munk W H, Cartwright D E. Tidal spectroscopy and prediction. Philosophical Transactions of the Royal Society, London, 1966, A259(ll05): 533~581
[24] Groves G W, Reynolds R W. An orthogonalized convolution method of tide prediction, Journal of Geophysical Research, 1975, 80: 4131~4138
[25]郑文振.实用潮汐学.天津:海军测量部,1959
[26]陈宗镛.潮汐学.北京:科学出版社,1980
[27]方国洪,郑文振,陈宗镛,王骥.潮汐和潮流的分析与预报.北京:海洋出版社,1986
[28]秦曾灏,冯士筰.浅海风暴潮动力机制的初步研究.中国科学(A),1975,1:64
[29]王化桐,方欣华,匡国瑞,杨殿荣,陈时俊.胶州湾环流和污染扩散的数值模拟——Ⅰ胶州湾潮流数值计算.山东海洋学院学报,1980,10(1):26～63
[30]沈育疆.东中国海潮汐数值计算.山东海洋学院学报,1980,10(3):28～35
[31]丁文兰.东海潮汐和潮流特征的研究.海洋科学集刊,1984,21:135～148
[32]沈育疆,叶安乐.东中国海三维半日潮流的数值计算.海洋与湖沼通报,1984,1:1～11
[33] Fang G H. Tide and tidal current charts for the marginal seas adjacent to China. Chinese Journal of Oceanography and Limnology, 1986, 4(1): 1~16
[34]赵保仁,方国洪,曹德明.渤、黄、东海潮汐潮流的数值模拟.海洋学报,1994,1(5):1～10
[35]叶安乐,梅丽明.渤黄东海潮波数值模拟.海洋与湖沼,1995,26(1):63～69
[36] Guo X Y, Yanagi T. Three-dimensional structure of tidal current in the East China Sea and the Yellow Sea. Journal of Oceanography, 1998, 54: 651~668
[37]万振文,乔方利,袁业立.渤、黄、东海三维潮波运动数值模拟.海洋与湖沼,1998,29(6):611～616
[38] Kang S K, Lee S R, Lie H J. Fine grid tidal modeling of the Yellow and East China Seas. Continental Shelf Research, 1998, 18: 739~772
[39] Lee J C, Jung K T. Application of eddy viscosity closure models for the M2 tide and tidal currents in the Yellow Sea and the East China Sea. Continental Shelf Research, 1999, 19: 445~475
[40]王凯,方国洪,冯士筰.渤海、黄海、东海M2潮汐潮波的三维数值模拟.海洋学报,1999,21(4):1～13
[41] Lefevre F, Le Provost C, Lyard F H. How can we improve a global ocean tide model at a regional scale? A test on the Yellow Sea and the East China Sea. Journal of Geophysical Research, 2000, 105: 8707~8725
[42] Bao X W, Gao G P, Yan J.Three dimensional simulation of tide current characteristics in the East China Sea. Oceanologica Acta, 2001, 24(2): 1~15
[43] Lee H J, Jung K T, So J K, Chung J Y. A Three-dimensional mixed finite-difference Galerkin function model for the oceanic circulation in the Yellow Sea and the East China Sea in the presence of M2 tide. Continental Shelf Research, 2002, 22: 67~91
[44] He Y J, Lu X Q, Qiu Z F, Zhao J P. Shallow water tidal constituents in the Bohai Sea and the Yellow Sea from a numerical adjoint model with T/P altimeter data. Continental Shelf Research, 2004, 24: 1521~1529
[45]王永刚,方国洪,曹德明,魏泽勋,乔方利.渤、黄、东海潮汐的一种验潮站资料同化数值模式.海洋科学进展,2004,22(3):253～274
[46]李培良,左军成,吴德星,李磊,赵玮.渤、黄、东海同化T/P高度计资料的半日分潮数值模拟.海洋与湖沼,2005,36(1):24～30
[47] Qiu Z F, He Y J, Lu X Q. Tidal constituents in the Bohai and Yellow Seas from an adjoint numerical model with T/P data. Journal of Hydrodynamics(B), 2005, 17(3): 275~282
[48]丘仲锋,何宜军,吕咸青.黄海、渤海TOPEX/ Poseidon高度计资料潮汐伴随同化.海洋学报,2005,27(4):10～18
[49]丘仲锋,何宜军.T/P高度计资料用于中国近海M2分潮的同化反演.海洋与湖沼,2005,36(4):376～384
[50]张衡,朱建荣,吴辉.东海黄海渤海8个主要分潮的数值模拟.华东师范大学学报(自然科学版),2005,3:71～77
[51] Cheng Y C, Lu X Q, Liu Y G, Xu Q. Application of adjoint assimilation technique in simulating tides and tidal currents of the Bohai Sea, the Yellow Sea and the East China Sea. High Technology Letters, 2007, 13(1): 58~64
[52] Zhang J C, Lu X Q. On the simulation of M2 tide in the Bohai, Yellow and East China Seaswith T/P altimeter data. Terrestrial, Atmosphere and Oceanic Sciences, 2008. (Accepted)
[53]李磊.渤黄东海潮波系统的有限元模拟:[博士学位论文].青岛:中国海洋大学海洋环境学院,2003
[54]李培良.渤黄东海潮波同化数值模拟和潮能耗散的研究:[博士学位论文].青岛:中国海洋大学海洋环境学院,2002
[55] Ye A L, Robinson I S. Tidal dynamics in the South China Sea. Geophys. J. R. Astron. Soc., 1983, 72: 691~707
[56]俞慕耕.南海潮汐特征的初步探讨.海洋学报,1984,6(3):293~300
[57]沈育疆.南海潮汐数值计算.海洋湖沼通报,1985,1:1~11
[58]丁文兰.南海潮汐和潮流的分布特征.海洋与湖沼,1986,17(6):468~480
[59]方国洪,曹德明,黄企洲.南海潮汐潮流的数值模拟.海洋学报,1994,16(4):1~12
[60] Yanagi T, Takao T. Clockwise Phase Propagation of Semi-Diurnal Tides in the Gulf of Thailand. Journal of Oceanography, 1998, 54: 143~150
[61] Fang G H, Kwok Y K, Yu K J, Zhu Y. Numerical simulation of principal tidal constituents in the South China Sea, Gulf of Tonkin and Gulf of Thailand. Continental Shelf Research, 1999, 19: 845~ 869
[62]李培良,左军成,李磊等.南海TOPEX/POSEIDON高度计资料的正交响应法潮汐分析.海洋与湖沼,2002,33(3):287~295
[63]吴自库,田纪伟,吕咸青,等.南海潮汐的伴随同化数值模拟.海洋与湖沼,2003,34(1):101~108
[64]吴自库,田纪伟,赵骞.南海潮波三维同化数值模拟.水动力学研究与进展A辑,2004,4:98~103
[65]吴自库.南海内潮三维数值同化模拟:[博士学位论文].青岛:中国海洋大学海洋环境学院,2005
[66] Cai S Q, Long X M, Liu H L, Wang S G. Tide model evaluation under different conditions. Continental Shelf Research, 2006, 26(1): 104~112
[67] Panofsky H A. Objective weather map analysis. Journal of Meteorology, 1949, 6: 386~392
[68] Gilchrist B, Cressman G. An experiment in Objective Analysis. Tellus, 1954, 6: 309~318
[69] Bergthorsson P, D??s B R. Numerical weather map analysis. Tellus, 1955, 7: 329~340
[70] Cressman G P. An operational objective analysis system. Monthly Weather Review, 1959, 87: 367~374
[71] Eliassen A. Provisional report on calculation of spatial covariance and autocorrelation of the pressure field. Oslo: Inst. Weather and Climate Research, Academy of Sciences, 1954, Report No. 5
[72] Gandin L. Objective Analysis of Meteorological Fields (translated from Russian). Jerusalem: Israel Program for Scientific Translation, 1965.
[73] Bratseth A M. Statistical interpolation by means of successive corrections. Tellus, 1986, 38A: 439~447
[74] Miller R N. Toward the application of the Kalman filter to regional open ocean modeling. Journal of Physical Oceanography, 1986, 16: 72~86
[75] Bennett A F, Budgell W P. Ocean data assimilation and the Kalman filter, spatial regularity. Journal of Physical Oceanography, 1987, 17: 1583~1601
[76] LeDimet F X, Talagrand O. Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus, 1986, 38A: 97~110
[77] Thacker W C, Long R B. Fitting dynamics to data. Journal of Geophysical Research, 1988, 93: 1227~1240
[78] Evensen G. Sequential data assimilation with a nonlinear quasi-geostrophic model using Montre Carlo methods to forecast error statistics. Journal of Geophysical Research, 1994, 99(10): 143~162
[79] Gelb A. Applied Optimal Estimation. Cambridge: MIT Press, 1974
[80] Ghil M, Malanotte-Rizzoli P. Data assimilation in meteorology and oceanography. In: Saltzman B eds. In Advances in Geophysics. San Diego: Academic Press, 1991, 33. 141~266
[81] Anderson D L T, Sheinbaum J, Haines K. Data assimilation in ocean models. Reports on Progress in Physics, 1996, 59: 1209~1266
[82] Malanotte-Rizzoli P, Tziperman E. The Oceanographic Data Assimilation Problem: Overview, Motivation and Purposes. In: Malanotte-Rizzoli P Eds. Modern approaches to data assimilation in ocean modeling. Amsterdam: Elsevier, 1996. 3~17
[83]王东晓,朱江.伴随方法在海洋数值模式中的应用.地球物理学进展,1997,12(1):98～107
[84] Navon I M. Practical and Theoretical Aspects of Adjoint Parameter Estimation and Identifiability in Meteorology and Oceanography. Dynamics of Atmospheres and Oceans (Special Issue in honor of Richard Pfeffer), 1998, 27: 55~79
[85]乔方利,Zhang S Q.现代海洋/大气资料同化方法的统一性及其应用进展.海洋科学进展,2002,20(4):79～93
[86]马寨璞,井爱芹.海洋科学中的数据同化方法——意义、结构与发展现状.海岸工程,2005,4:83～99
[87] Talagrand O, Courtier P. Variational assimilation of meteorological observations with the adjoint vorticity equation Part I: Theory. Quarterly Journal of the Royal MeteorologicalSociety, 1987, 113: 1311~1328
[88] Smedstad O M, O’Brien J J. Variational data assimilation and parameter estimation in an equatorial Pacific Ocean model. Progress in Oceanography, 1991, 26: 179~241
[89] Bouttier F, Courtier P. Data assimilation concepts and methods. 1999, Available on: http://www.ecmwf.int/newsevents/training/rcourse_notes/DATA_ASSIMILATION/ASSIM_CONCEPTS/Assim_concepts2.html
[90] Robinson A R, Lermusiaux P F J. Overview of Data Assimilation. Cambridge: Harvard Reports in Physical/Interdisciplinary Ocean Science, 2000, Number 62
[91] Daley R. Atmospheric Data Analysis. New York: Cambridge Atmospheric and Space Science Series, Cambridge University Press, 1991. 363~402
[92] Sasaki Y. Some basic formalisms in numerical variational analysis. Monthly Weather Review, 1970, 98: 875~883
[93]吕咸青.海洋数值建模中伴随方法的研究:[博士后研究工作报告].青岛:中国科学院海洋研究所,2000
[94] Bertsekas D P. Constrained optimization and Lagrange multiplier methods. London: Academic Press, 1982
[95] Derber J C. A variational continuous assimilation technique. Monthly Weather Review, 1989, 117: 2437~2446
[96] Long R B, Thacker W C. Data Assimilation into A Numerical Equatorial Ocean Model. I. The Model and The Assimilation Algorithm. Dynamics of Atmospheres and Oceans, 1989, 13: 379~412
[97] Long R B, Thacker W C. Data Assimilation into A Numerical Equatorial Ocean Model. II. Assimilation Experiments. Dynamics of Atmospheres and Oceans, 1989, 13: 413~439
[98] Panchang V G, O'Brien J J. On the determination of hydraulic model parameters using the adjoint state formulation. In: Davis A M eds. Modelling Marine System. Boca Rayon: CRC Press, 1989. 6~18
[99] Yu L S, O’Brien J J. Variational estimation of the wind stress drag coefficient and the oceanic eddy viscosity profile. Journal of Physical Oceanography, 1991, 21: 709~719
[100]Das S K, Lardner R W. On the estimation of parameters of hydraulic models by assimilation of periodic tidal data. Journal of Geophysical Research, 1991, 96(C8): 15187~15196
[101]Das S K, Lardner R W. Variational parameter estimation for a two dimensional numerical tidal model. International Journal for Numerical Methods in Fluids, 1992, 15: 313~327
[102]Lardner R W, Al-Rabeh A H, Gunay N. Optimal Estimation of Parameters for a Two-Dimensional Hydro-dynamical Model of the Arabian Gulf. Journal of GeophysicalResearch, 1993, 98(C10): 18229~18242
[103]Lardner R W, Das S K. Optimal estimation of eddy viscosity for a quasi-three dimensional numerical tidal and storm surge model. International Journal for Numerical Methods in Fluids, 1994, 18: 295~312
[104]Lardner R W, Song Y. Optimal estimation of eddy viscosity and friction coefficients for a quasi-three-dimensional numerical tidal model. Atmosphere-Ocean, 1995, 33(3): 581~611
[105]Lu J, Hsieh W W. Adjoint data assimilation in coupled atmosphere–ocean models: determining initial model parameters in a simple equatorial model. Quarterly Journal of the Royal Meteorological Society, 1997, 123: 2115~2139
[106]Lu J, Hsieh W W. Adjoint data assimilation in coupled atmosphere–ocean models: determining initial conditions in a simple equatorial model. Journal of the Meteorological Society of Japan, 1998a, 76: 737~748
[107]Lu J, Hsieh W W. On determining initial conditions and parameters in a simple couple atmosphere–ocean model by adjoint data assimilation. Tellus, 1998b, 50A: 534~544
[108]Ullman D S, Wilson R E. Model parameter estimation from data assimilation modelling: temporal and spatial variability of the bottom drag coefficient. Journal of Geophysical Research, 1998, 103: 5531~5549
[109]吕咸青.数据同化反演风应力拖曳系数以及垂向涡动黏性系数的分布.海洋学报,2001,23(1):13～20
[110]吕咸青,田纪伟,吴自库.渤、黄海的底摩擦系数.力学学报,2003b,35(4):465～468
[111]吕咸青,吴自库,谷艺,田纪伟.数据同化中的伴随方法的有关问题的研究.应用数学和力学,2004,25(6):581～590
[112]Heemink A W, Mouthaan E E A, Roest M R T, Vollebregt E A H, Robaczewska K B, Verlaam M. Inverse 3D shallow water flow modeling of the continental shelf. Continental Shelf Research, 2002, 22: 465~484
[113]Zhang A J, Parker B B, Wei E. Assimilation of water level data into a coastal hydrodynamic model by an adjoint optimal technique. Continental Shelf Research, 2002, 22: 1909~1934
[114]Lu X Q, Wu Z K, Gu Y, Tian J W. Study on the adjoint method in data assimilation and the related problems. Applied Mathematics and Mechanics, 2004, 25(6): 636~646
[115]张继才,吕咸青.空间分布底摩擦系数的伴随法反演研究.自然科学进展,2005,15(9):1086～1093
[116]Zhang J C, Zhu J G, Lu X Q. Numerical Study on the Bottom Friction Coefficient of the Bohai Sea, the Yellow Sea and the East China Sea. Chinese Journal of Computational Physics,2006, 23(6): 731~737
[117]Lu X Q, Zhang J C. Numerical Study on Spatially Varying Bottom Friction Coefficient of a 2D Tidal Model with Adjoint Method. Continental Shelf Research, 2006, 26: 1905~1923
[118]Zhang J C, Lu X Q. Parameter Estimation for a Three-Dimensional Numerical Barotropic Tidal Model with Adjoint Method. International Journal for Numerical Methods in Fluids, 2007. (Available online)
[119]Moore A M. Data assimilation in a quasi-geostrophic open ocean model of the Gulf Stream region using the adjoint method. Journal of Physical Oceanography, 1991, 21: 398~427
[120]Yu L S, O'Brien J J. On the initial condition parameter estimation. Journal of Physical Oceanography, 1992, 22: 1361~1364
[121]Gunson J R, Malanotte-Rizzoli P. Assimilation studies of open-ocean flows, Part I: Estimation of initial and boundary conditions, Journal of Geophysical Research, 1996a, 101: 28457~28472
[122]Gunson J R, Malanotte-Rizzoli P. Assimilation studies of open-ocean flows, Part II: Error measures with strongly nonlinear dynamics. Journal of Geophysical Research, 1996b, 101: 28473~28488
[123]Greiner E, Perigaud C. Assimilation of Geo-sat altimetric data in a nonlinear reduced-gravity model of the Indian Ocean, Part I: adjoint approach and model-data consistency. Journal of Physical Oceanography, 1994, 24(8): 1783~1804
[124]Greiner E, Perigaud C. Assimilation of Geo-sat altimetric data in a nonlinear reduced-gravity model of the Indian Ocean, Part II: Some Validation and Interpretation of the assimilated results. Journal of Physical Oceanography, 1996, 26: 1735~1746
[125]Greiner E, Arnault S, Morliaère A. Twelve-monthly experiments of 4D-variational assimilation in the tropical Atlantic during 1987, Part 1: Method and statistical results. Progress in Oceanography, 1998a, 41: 141~202
[126]Greiner E, Arnault S, Morliaère A. Twelve-monthly experiments of 4D-variational assimilation in the tropical Atlantic during 1987, Part 2: Oceanographic interpretation. Progress in Oceanography, 1998b, 41: 203~247
[127]马继瑞,韩桂军,李冬.变分伴随数据同化在海表面温度预报中的应用研究.海洋学报,2002,24(5):1～7
[128]Seiler U. Estimation of open boundary conditions with the adjoint method. Journal of Geophysical Research, 1993, 98: 22855~22870
[129]Lardner R W. Optimal control of an open boundary conditions for a numerical tidal model. Computer Methods in Applied Mechanics and Engineering, 1993, 102: 367~387
[130]Mewis P, Holz KP. Inverse boundary value estimation for a shallow water model. Computational Methods in Water Resources XI, Cancun, Volume 2, Computational Methods in Surface Flow and transport Problems, 1996: 223~230
[131]朱江,曾庆存,郭冬建,刘卓.利用伴随算法从岸边潮位站资料估计近岸模式的开边界条件.中国科学(D辑),1997,27(5):462～468
[132]Marotzke J, Giering R, Zhang Q K, Stammer D, Hill C N, Lee T. Construction of the adjoint MIT ocean general circulation model and application to Atlantic heat transport sensitivity. Journal of Geophysical Research, 1999, 104: 29529~29548
[133]吕咸青,张杰.如何利用水位资料反演开边界条件(1).水动力学研究与进展,1999,14:92～102
[134]韩桂军,何柏荣,马继瑞,刘克修,李冬.利用伴随法优化非线性潮汐模型的开边界条件I:伴随方程的建立及“孪生”数值试验.海洋学报,2000,22(6):134～140
[135]韩桂军,何柏荣,马继瑞,刘克修,李冬.利用伴随法优化非线性潮汐模型的开边界条件II:黄海、东海潮汐资料的同化试验.海洋学报,2001,23(2):25～31
[136]Zhang A J, Wei E, Parker B B. Optimal estimation of tidal open boundary conditions using predicted tides and adjoint data assimilation technique. Continental Shelf Research, 2003, 23: 1055~1070
[137]吕咸青,吴自库,殷忠斌,田纪伟.渤、黄、东海潮汐开边界的1种反演方法.青岛海洋大学学报,2003a,33(2):155～172
[138]尹训强,杨永增,乔方利.浅水潮波模式变分同化共轭码技术研究.海洋科学进展,2003,21(4):413～423
[139]Peng S Q, Xie L. Effect of determining initial conditions by four-dimensional variational data assimilation on storm surge forecasting. Ocean Modelling, 2006, 14: 1~18
[140]Tziperman E, Thacker W C. An Optimal Control/Adjoint equations approach to studying the oceanic general circulation. Journal of Physical Oceanography, 1989, 19: 1471~1485
[141]Tziperman E, Thacker W C, Bryan K. Computing the steady state oceanic circulation using an optimization approach. Dynamics of Atmospheres and Oceans, 1992, 16(5): 379~404
[142]Bergamasco A, Malanotte-Rizzoli P, Thacker W C, Long R B. The seasonal steady circulation of the Eastern Mediterranean determined with the adjoint method. In Topical Studies in Oceanography: Physical Oceanography of the Eastern Mediterranean Sea, special issue of Deep Sea Research II, 1993, 40(6): 1269~1298
[143]Marotzke J, Wunsch C. Finding the steady state of a general circulation model through data assimilation: application to the North Atlantic Ocean. Journal of Geophysical Research, 1993, 98: 20149~20167
[144]Schlitzer R. Determining the mean, large-scale circulation of the Atlantic with adjoint method. Journal of Physical Oceanography, 1993, 23: 1935~1952
[145]Griffin D A, Thompson K R. The adjoint method of data assimilation used operationally for shelf circulation. Journal of Geophysical Research, 1996, 101(C2): 3457~3478
[146]Yu L S, Malanotte-Rizzoli P. Analysis of the North Atlantic climatologies using the combined OGCM/adjoint approach. Journal of Marine Research, 1996, 54: 867~913
[147]Yu L S, Malanotte-Rizzoli P. Inverse modeling of the seasonal variations in the North Atlantic Ocean. Journal of Physical Oceanography, 1998, 28: 902~922
[148]王东晓,兰健,吴国雄,朱江.一个海洋环流模式伴随系统的初步实验.自然科学进展,1999,9(9):824～833
[149]王东晓,吴国雄,朱江,兰健.大洋风生环流观测优化的伴随分析.中国科学(D),2000,30(1):97～106
[150]Roquet H, Planton S. Determination of Ocean Heat Fluxes by a Variational Method. Journal of Geophysical Research, 1993, 98: 10211~10221
[151]Schiller A. The mean circulation of the Atlantic Ocean north of 30S determined with the adjoint method applied to an ocean general circulation model. Journal of Marine Research, 1995, 53(3): 453~497
[152]Yu L S, O'Brien J J. Variational data assimilation for determining the seasonal net surface heat flux using a tropical Pacific Ocean model. Journal of Physical Oceanography, 1995, 25: 2319~2343
[153]Yuan D L, Rienecker M M. Inverse estimation of sea surface heat flux over the equatorial Pacific Ocean: Seasonal cycle. Journal of Geophysical Research, 2003, 108(C8): 3247
[154]Lawson L M, Spitz Y H, Hofmann E E, Long R B. A data assimilation technique applied to a predator-prey model. Bulletin of Mathematical Biology, 1995, 57: 593~617
[155]Lawson L M, Hofmann E E, Spitz Y H. Time series sampling and data assimilation in a simple marine ecosystem model. Deep-Sea Research II, 1996, 43: 625~651
[156]Spitz Y H, Moisan J R, Abbort M R, Richman J G. Data assimilation and a pelagic ecosystem model: parameterization using time series observations. Journal of Marine Systems, 1998, 16: 51~68
[157]Spitz Y H, Moisan J R, Abbort M R. Configuration an ecosystem model using data from the Bermuda, Atlantic Time Series (BATS). Deep-Sea Research II, 2001, 48: 1733~1768
[158]Friedrichs M A M. A data assimilative marine ecosystem model of the central equatorial Pacific: numerical twin experiments. Journal of Marine Research, 2001, 59: 859~894
[159]Friedrichs M A M. Assimilation of JGOFS EqPac and SeaWiFS data into a marine ecosystemmodel of the central equatorial Pacific Ocean. Deep-Sea Research II, 2002, 49: 289~319
[160]Kuroda H, Kishi M J. A data assimilation technique applied to estimate parameters for the NEMURO marine ecosystem model. Ecological Modelling, 2004, 172: 69~85
[161]Xu Q, Liu Y G, Lu X Q. Adjoint assimilation in marine ecosystem models and an example of application. Journal of Ocean University of China, 2005, 4(1): 14~20
[162]Zhao L, Wei H, Xu Y, Feng S Z. An adjoint data assimilation approach for estimating parameters in a three-dimensional ecosystem model. Ecological Modelling, 2005, 186: 234~249
[163]徐青,刘玉光,程永存,吕咸青.伴随同化技术在渤、黄海生态模式中的应用:控制变量的选取与孪生实验.高科技通讯,2006,16(1):78～83
[164]Yeh W W G. Review of parameter identification procedures in groundwater hydrology: The inverse problem. Water Resources Research, 1986, 22: 95~108
[165]Carrera J, Neuman S P. Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incorporating prior information. Water Resource Research, 1986a, 22(2): 199~210
[166]Carrera J, Neuman S P. Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability and solution algorithms. Water Resource Research, 1986b, 22(2): 211~227
[167]Carrera J, Neuman S P. Estimation of aquifer parameters under transient and steady state conditions: 3. Application to synthetic and field data. Water Resource Research, 1986c, 22(2): 228~242
[168]Courtier P, Talagrand O. Variational assimilation of meteorological observations with the adjoint vorticity equation Part II: Numerical result. Quarterly Journal of the Royal Meteorological Society, 1987, 113: 1329~1348
[169]Courtier P, Talagrand O. Variational assimilation of meteorological observations with the direct and adjoint shallow-water equation. Tellus, 1990, 42A: 531~549
[170]LeDimet F X, Navon I M. Variational and optimization methods in meteorology: a review. Technology Report FSU-SCRI-88-144, Florida State University, Tallahassee, Florida, 83pp, 1988
[171]Zou X, Navon I M, LeDimet F X. An optimal nudging data assimilation scheme using parameter estimation. Quarterly Journal of the Royal Meteorological Society, 1992, 118: 1163~1186
[172]Schroter J, Seiler U, Wenzel M. Variational Assimilation of Geo-sat Data into an Eddy-resolving Model of the Gulf Stream Extension Area. Journal of PhysicalOceanography, 1993, 23: 925~953
[173]Sirkes Z, Tziperman E. Finite Difference of Adjoint or Adjoint of Finite Difference? Monthly Weather Review, 1997, 125: 3373~3378
[174]韩桂军.伴随法在潮汐和海温数值计算中的应用研究:[博士学位论文].青岛:中国科学院海洋研究所,2001
[175]Segal M, Pielke R A. Numerical model simulation of human biometeorological heat load conditions - summer day case study for the Chesapeake Bay area. Journal of Applied Meteorology, 1981, 20: 735~749
[176]Barnes S L. A technique for maximizing details in numerical map analysis. Journal of Applied Meteorology, 1964, 3: 395~409
[178]Egbert G D, Ray R D, Bills B G. Numerical modeling of the global semidiurnal tide in the present day and in the last glacial maximum. Journal of Geophysical Research, 2004, 109: C03003
[179]Zhao B R, Fang G H, Cao D M. Numerical modeling on the tides and tidal currents in the eastern China Seas. Yellow Sea Research, 1993, 5: 41~61
[180]Sannino G, Bargagli A, Artale V. Numerical modeling of the semidiurnal tidal exchange through the strait of Gibraltar. Journal of Geophysical Research, 2004, 109: C05011
[181]吕咸青,方国洪.渤海M2分潮的伴随模式数值实验.海洋学报,2002a,24(1):17～24
[182]吕咸青,方国洪.渤海开边界潮汐的伴随法反演.海洋与湖沼,2002b,33(2):113～120
[183]张继才,吕咸青.渤、黄、东海二维潮汐模式底摩擦系数的反演研究.计算力学学报,2007,22(3):214～219
[184]Fang G H, Wang Y G, Wei Z X, Choi B H, Wang X Y, Wang J. Empirical cotidal charts of the Bohai, Yellow, and East China Seas from 10 years of T/P altimetry. Journal of Geophysical Research, 2004, 109: C11006
[185]Choi B H. A fine-grid three-dimensional M2 tidal model of the East China Sea. In: Davies A M eds. Modelling Marine Systems. Boca Raton, Florida: CRC Press, 1989. 167~185
[186]Yanagi T, Inoue K. Tide and tidal current in the Yellow/East China Seas. Lamer, 1994, 32: 153~165
[187]Mofjeld H O. Depth Dependence of Bottom Stress and Quadratic Drag Coefficient for Barotropic Pressure-Driven Currents. Journal of Physical Oceanography, 1988, 18: 1658~1669
[188]Le Provost C, Genco M L, Lyard F, Vincent P, Canceil P. Spectroscopy of the world oceantides from a finite element hydrodynamic model. Journal of Geophysical Research, 1994, 99(C12): 24777~24798
[189]Aldridge J N, Davies A M. A high resolution three-dimensional hydrodynamic tidal model of the Eastern Irish Sea. Journal of Physical Oceanography, 1993, 23: 207~224
[190]孙丽艳.渤黄东海潮汐底摩擦系数的优化研究:[硕士学位论文].青岛:中国海洋大学海洋环境学院,2005
[191]Mazzega P, Berge M. Ocean tides in the Asian semienclosed seas from TOPEX/POSEIDON. Journal of Geophysical Research, 1994, 99(C12): 24867~24882
[192]Egbert G D, Bennett A F, Foreman M G. TOPEX/POSEIDON tides estimated using a global inverse model. Journal of Geophysical Research, 1994, 99(C12): 24821~24852
[193]Kantha L H. Barotropic tides in the global oceans from a nonlinear tidal model assimilating altimetric tides, 1, Model description and results. Journal of Geophysical Research, 1995, 100(C12): 25283~25308
[194]Kantha L H, Tierney C, Lopez J W, Desai S D, Parke M E, Drexler L. Barotropic tides in the global oceans from a nonlinear tidal model assimilating altimetric tides, 2, Altimetric and geophysical implications. Journal of Geophysical Research, 1995, 100(C12): 25309~25317
[195]Andersen O B, Woodworth P L, Flather R A. Intercomparison of recent ocean tide models. Journal of Geophysical Research, 1995, 100(C12): 25261~25282
[196]Yanagi T, Morimoto A, Ichikawa K. Co-tidal and co-range charts for the East China Sea and the Yellow Sea derived from satellite altimetric data. Journal of Oceanography, 1997, 53: 303~309
[197]张占海,吴辉碇.渤海潮汐和潮流数值计算.海洋预报,1994,11(1):48～54
[198]Leendertse J J, Alexander R C, Liu S K. A Three Dimensional Model for Estuaries and Coastal Seas, Vol. I: Principles of computations. Report R-1417-OWRR, Rand Corporation, Santa Monica, 1973.
[199]Backhaus J. A three-dimensional model for the simulation of shelf sea dynamics. Deutsche Hydrographische Zeitschrift, 1985, 38: 165~187
[200]Casulli V, Cheng R T. Semi-implicit finite difference methods for the three dimensional shallow water flow. International Journal for Numerical Methods in Fluids, 1992, 15: 629~648
[201]Casulli V. A semi-implicit finite difference method for the non-hydrostatic free-surface flow. International Journal for Numerical Methods in Fluids, 1999, 30: 425~440
[202]Yuan H L, Wu C H. An implicit three-dimensional fully non-hydrostatic model for free-surface flows. International Journal for Numerical Methods in Fluids, 2004, 46: 709~733
[203]Roache P J. Fundamentals of Computational Fluid Dynamics. New Mexico: Hermosa Publishers, Albuquerque, 1982
[204]方国洪,于克俊.斜压海洋动力学的一种三维数值模式Ⅰ.动力学方程数值格式.海洋与湖沼,1998,29(3):232~240
[205]于克俊,方国洪.斜压海洋动力学的一种三维数值模式Ⅱ.温度、盐度和垂直涡动粘性系数的计算.海洋与湖沼,1998,29(4):381~388
[206]Simons T J. Verification of numerical models of Lake Ontario, Part 1: circulation in spring and early summer. Journal of Physical Oceanography, 1974, 4: 507~523
[207]Bennett A F, McIntosh P C. Open ocean modeling as an inverse problem: tidal theory. Journal of Physical Oceanography, 1982, 12: 1004~1018
[208]Prevost C, Salmon R. A variational method for inverting hydrographic data. Journal of Marine Science, 1986, 44: 1~34
[209]孙文心,江文胜,李磊.近海环境流体动力学数值模型.北京:科学出版社,2004
[210]Winninghoff F J. On the adjustment toward a geostrophic balance in a simple primitive equation model with application to the problems of initialization and objective analysis: [Ph.D. Thesis]. Los Angeles: University of California, 1968. pp.161
[211]Chapman D C. Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model. Journal of Physical Oceanography, 1985, 15: 1060~1075
[212]肖庭延,于慎根,王彦飞.反问题的数值解法.北京:科学出版社,2003
[213]Lanseth A T. Sources and applications of integral equations. SIAM Review, 1977, 19: 241~278
[214]Baumeister J. Stable solution of inverse problems. Brauschweig: Vieweg, 1987
[215]Engl H W. Regularization methods for the stable solution of inverse problems. Surv. Math. Ind., 1993, 3: 71~143
[216]苏超伟.偏微分方程逆问题的数值解法及其应用.西安:西北工业大学出版社,1995
[217]Hadamard J. Lectures on the Cauthy problems in linear partial differential equations. New Haven: Yale university Press, 1923
[218]Tarantola A. Inverse problem theory: Methods for data fitting and model parameter estimation. Amsterdam: Elsevier, 613 pp., 1987
[219]Ayoub N. Estimation of boundary values in a North Atlantic circulation model using an adjoint method. Ocean Modelling, 2006, 12: 319~347
[220]Gejadze I Y, Copeland G J M, Navon I M. Open boundary control problem for Navier-Stokes equations including a free surface: data assimilation. Computers and Mathematics with Applications, 2006, 52: 1269~1288.
[221]Gejadze I Y, Copeland G J M. Open boundary control problem for Navier-Stokes equations including a free surface: adjoint sensitivity analysis. Computers and Mathematics with Applications, 2006, 52: 1243~1268
[222]Richardson J E, Panchang V G. A modified adjoint method for inverse eddy viscosity estimation in coastal circulation models. In: Spaulding M L, Bedford K, Blumberg A, Cheng R, Swanson C eds. Estuarine and Coastal Modeling. New York: Academic Press, 1992. 733~745
[223]Tikhonov A N. Solution of incorrectly formulated problems and the regularization method. Sov. Math. Dokl., 1963a, 4: 1035~1038
[224]Tikhonov A N. Regularization of incorrectly posed problems. Sov. Math. Dokl., 1963a, 4: 1624~1627
[225]Wang Z, Navon I M, LeDimet F X, Zou X L. The Second Order Adjoint Analysis: Theory and Application. Meteorology and Atmospheric Physics, 1992, 50: 3~20
[226]韩桂军,何柏荣,马继瑞,李冬.关于二阶伴随模型的理论研究.海洋学报,2000,22(3):16～20
[227]李守巨.基于计算智能的岩土力学模型参数反演方法及其工程应用:[博士学位论文].大连:大连理工大学工程,2004
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