海洋流场数据同化方法与应用的研究
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摘要
本文以三维陆架海模型(HAMSOM)作为数据同化系统的模型部分，深入研究了数据同化的理论方法和在海洋流场数据处理中的应用，对海洋场的数据同化方法提出了行之有效的改进，并将中国黄、东海区域内的TOPEX／POSEIDON(T／P)数据和理论模式的计算结果相结合，进行同化处理，获得了更接近于真实的结果。
对数据同化问题的研究，尤其针对目前我国海区的数据同化应用研究较少这一情况。本文在前人文献的基础上，进行了方法及应用上的研究。这些成果包括：建立考虑了时间相关的方差矩阵和时空相关的最优插值算法；对卡尔曼滤波算法进行了SVD简化以及建立了显式的状态转移矩阵；将T／P实时卫星数据进行调和分析并与数值模型进行同化处理。具体内容为如下几个方面：
1 建立时间相关的协方差矩阵处理方法
在估值类的同化方法中，观测数据与理论模型结合的桥梁是各自的协方差矩阵。在确定协方差矩阵的时候，以往的做法是将所有不同观测时刻的数据当作同一时刻的数据应用；本文在形成协方差矩阵时，不仅考虑空间相关，而且应用了时间相关，对观测数据的应用依照其得到时间的不同分别处理到协方差矩阵的建立中，并根据其在时间上的相关强弱给予不同的权重值，使得对观测数据的应用更接近实际情况。
2 应用动态最优插值算法进行渤海海表温度同化
传统的最优插值算法没有考虑观测数据的时间错位。本文首先推导了既考虑空间相关，又考虑时间相关的最优插值算法，由于应用了时间相关的协方差矩阵，就使这个算法具有动态处理时间错位的观测数据的能力。随后，本文应用理论模型数据和模拟观测数据进行了并行试验，将动态插值算法应用到渤海海表温度场的计算中，同化结果兼顾理论模型结果和模拟观测结果，在方差意义上显示出最优特性，验证了本文所提出的方法改进的正确性。
浙江人学博十学位论文
全文摘要
3应用SVD分解，推导了简约形式的卡尔曼滤波方法，并直接建立了
显式的状态转移矩阵
卡尔曼滤波法无法直接应用于海洋，其主要原因是增益矩阵的计算
量太大。本文根据“最大限度保留原来的主要信息，尽可能地简化计算”
的原则，应用‘SVD分解推导了简约形式的卡尔曼滤波方法，得到了该方
法的简约表达公式，同时，还得到了截断误差部分的伴随发展公式，它
可用于探讨截差本身的动态发展。
另外，本文成功应用反向量表述的方法将通常需要迭代得到的卡尔
曼状态转移矩阵表述为可直接计算的显式表达形式。
上述两个方面的改进节省了数据同化卡尔曼滤波法的计算量，提高
了效率，对时效性很强的海洋预报计算很有意义。
4对T/P数据进行调和分析，并将其结果与理论模型数据进行同化处理，
使结果更接近于真实值
对卫星数据如何进行处理和应用是一个重要的课题。本文首先使用
黄、东海沿岸60个验潮站实际观测得到的调和常数进行同化处理，有效
地’改进了理论模式的结果。随后，本文将美国T/P卫星数据集的第1一第
150周期的数据进行调和分析，获得了黄、东海区域的10条轨道上的
MZ分潮的调和常数。在此基础上，本文进一步应用最优插值算法，将理
论模型结果和卫星数据调和结果进行同化处理。获得了更接近于真实值
的同化结果。
In this thesis, studies were carried out on the theoretical schemes of data assimilation and their applications on sea fluid field, the three-dimensional baroclinic primitive equation model-Hamburg Shelf Ocean Model (HAMSOM)-being one part of the three ones that constitute the data assimilation (DA) system. Effective modification on schemes of DA were obtained and applications on TOPEX/POSEIDON (T/P) data results that covering the area of Yellow Sea and East Sea were done. The final results became closer to the objective nature.
Studies on DA schemes and their applications were detailed on the basis of existed literatures, the studies of applications on China Sea being rather poor at the moment. The final results obtained in this paper contained that the optimal interpolation scheme highlighted by the covariance that the correlation between different time and the correlation between different place being considered; that the simplification of Kalman Filter with the singular-value decomposition (SVD) and the direct construction of state transition matrix pfeceded with "inverse vector expression"; and that the analysis of T/P data and its blending with theoretical model. They are detailed as follows:
1. To construct covariance matrix with time correlation and distance correlation.
Both observational data and theoretical model results has its respective errors, upon which both covariance matrix being produced. The matrices are the bridge that linkedd the observational data with the theoretical model results together. When made covariance matrix, the observational data were always treated as one group without considering the time misfit, which did not match the true situation. In this thesis not only the distance, but also the time correlation was taken into account when constructed the covariance matrix, the observational data being treated differently according to its obtaining time and the weight, big or small, being assigned to differently according to its time correlation, strong or weak. All that done mentioned above made the application of data be closer to practical situation.
2. Applied the dynamic optimal interpolation to Bohai SST.
There is no consideration of time misfit in traditional optimal interpolation. In this thesis, some researches were done on the methodology of optimal interpolation, in which a new form of the formulae was developed that named dynamic optimal interpolation, the time correlation being introduced. With the applications of the new method, the weight matrix of observations can be dealt with dynamically while without losing the merits of the traditional ones, and the time correlation can be taken into account in real time when computing the weight matrix, which overcome the problem of time misfit between observations and forecasts. A test arranged to check lately and the result indicates that the
new method can work efficiently, that the results were closer to the objective nature.
3. To produce a new reduced KF scheme with SVD, and construct the state transition matrix directly.
Many researchers have employed Kalman Filter (KF) scheme to data assimilation, which manifests its validity in blending the model results and data. However, the major difficulty in applying the KF scheme to data assimilation is its enormous size of the system, which leads to the suboptimum in practical applications. Nowadays, many extended KF schemes have been proposed to solve the manipulation of large size of matrix. All the simplifications of KF scheme followed the same rule, that is, kept the major information most possibly and simplified the calculation possibly. In our study, we adopt another new method to reduce the dimensions of state space variables and then obtain a new way to simplify the calculation of KF gain. With the new method, we not only obtain the results that have the same expression forms as those of literatures existed, but also deduce the new equations that can be used to evaluate the abandoned parts quantitatively, which expanded the application of KF and mad
对数据同化问题的研究，尤其针对目前我国海区的数据同化应用研究较少这一情况。本文在前人文献的基础上，进行了方法及应用上的研究。这些成果包括：建立考虑了时间相关的方差矩阵和时空相关的最优插值算法；对卡尔曼滤波算法进行了SVD简化以及建立了显式的状态转移矩阵；将T／P实时卫星数据进行调和分析并与数值模型进行同化处理。具体内容为如下几个方面：
1 建立时间相关的协方差矩阵处理方法
在估值类的同化方法中，观测数据与理论模型结合的桥梁是各自的协方差矩阵。在确定协方差矩阵的时候，以往的做法是将所有不同观测时刻的数据当作同一时刻的数据应用；本文在形成协方差矩阵时，不仅考虑空间相关，而且应用了时间相关，对观测数据的应用依照其得到时间的不同分别处理到协方差矩阵的建立中，并根据其在时间上的相关强弱给予不同的权重值，使得对观测数据的应用更接近实际情况。
2 应用动态最优插值算法进行渤海海表温度同化
传统的最优插值算法没有考虑观测数据的时间错位。本文首先推导了既考虑空间相关，又考虑时间相关的最优插值算法，由于应用了时间相关的协方差矩阵，就使这个算法具有动态处理时间错位的观测数据的能力。随后，本文应用理论模型数据和模拟观测数据进行了并行试验，将动态插值算法应用到渤海海表温度场的计算中，同化结果兼顾理论模型结果和模拟观测结果，在方差意义上显示出最优特性，验证了本文所提出的方法改进的正确性。
浙江人学博十学位论文
全文摘要
3应用SVD分解，推导了简约形式的卡尔曼滤波方法，并直接建立了
显式的状态转移矩阵
卡尔曼滤波法无法直接应用于海洋，其主要原因是增益矩阵的计算
量太大。本文根据“最大限度保留原来的主要信息，尽可能地简化计算”
的原则，应用‘SVD分解推导了简约形式的卡尔曼滤波方法，得到了该方
法的简约表达公式，同时，还得到了截断误差部分的伴随发展公式，它
可用于探讨截差本身的动态发展。
另外，本文成功应用反向量表述的方法将通常需要迭代得到的卡尔
曼状态转移矩阵表述为可直接计算的显式表达形式。
上述两个方面的改进节省了数据同化卡尔曼滤波法的计算量，提高
了效率，对时效性很强的海洋预报计算很有意义。
4对T/P数据进行调和分析，并将其结果与理论模型数据进行同化处理，
使结果更接近于真实值
对卫星数据如何进行处理和应用是一个重要的课题。本文首先使用
黄、东海沿岸60个验潮站实际观测得到的调和常数进行同化处理，有效
地’改进了理论模式的结果。随后，本文将美国T/P卫星数据集的第1一第
150周期的数据进行调和分析，获得了黄、东海区域的10条轨道上的
MZ分潮的调和常数。在此基础上，本文进一步应用最优插值算法，将理
论模型结果和卫星数据调和结果进行同化处理。获得了更接近于真实值
的同化结果。
In this thesis, studies were carried out on the theoretical schemes of data assimilation and their applications on sea fluid field, the three-dimensional baroclinic primitive equation model-Hamburg Shelf Ocean Model (HAMSOM)-being one part of the three ones that constitute the data assimilation (DA) system. Effective modification on schemes of DA were obtained and applications on TOPEX/POSEIDON (T/P) data results that covering the area of Yellow Sea and East Sea were done. The final results became closer to the objective nature.
Studies on DA schemes and their applications were detailed on the basis of existed literatures, the studies of applications on China Sea being rather poor at the moment. The final results obtained in this paper contained that the optimal interpolation scheme highlighted by the covariance that the correlation between different time and the correlation between different place being considered; that the simplification of Kalman Filter with the singular-value decomposition (SVD) and the direct construction of state transition matrix pfeceded with "inverse vector expression"; and that the analysis of T/P data and its blending with theoretical model. They are detailed as follows:
1. To construct covariance matrix with time correlation and distance correlation.
Both observational data and theoretical model results has its respective errors, upon which both covariance matrix being produced. The matrices are the bridge that linkedd the observational data with the theoretical model results together. When made covariance matrix, the observational data were always treated as one group without considering the time misfit, which did not match the true situation. In this thesis not only the distance, but also the time correlation was taken into account when constructed the covariance matrix, the observational data being treated differently according to its obtaining time and the weight, big or small, being assigned to differently according to its time correlation, strong or weak. All that done mentioned above made the application of data be closer to practical situation.
2. Applied the dynamic optimal interpolation to Bohai SST.
There is no consideration of time misfit in traditional optimal interpolation. In this thesis, some researches were done on the methodology of optimal interpolation, in which a new form of the formulae was developed that named dynamic optimal interpolation, the time correlation being introduced. With the applications of the new method, the weight matrix of observations can be dealt with dynamically while without losing the merits of the traditional ones, and the time correlation can be taken into account in real time when computing the weight matrix, which overcome the problem of time misfit between observations and forecasts. A test arranged to check lately and the result indicates that the
new method can work efficiently, that the results were closer to the objective nature.
3. To produce a new reduced KF scheme with SVD, and construct the state transition matrix directly.
Many researchers have employed Kalman Filter (KF) scheme to data assimilation, which manifests its validity in blending the model results and data. However, the major difficulty in applying the KF scheme to data assimilation is its enormous size of the system, which leads to the suboptimum in practical applications. Nowadays, many extended KF schemes have been proposed to solve the manipulation of large size of matrix. All the simplifications of KF scheme followed the same rule, that is, kept the major information most possibly and simplified the calculation possibly. In our study, we adopt another new method to reduce the dimensions of state space variables and then obtain a new way to simplify the calculation of KF gain. With the new method, we not only obtain the results that have the same expression forms as those of literatures existed, but also deduce the new equations that can be used to evaluate the abandoned parts quantitatively, which expanded the application of KF and mad
引文
1 Ekman,V.W.,On the influence of the earth's rotation on ocean currents. Arch. Math. Astron. Phys.,1905,2(11) .
2 Sevrdrup,H.V.,M.W. Johnson and R.H. Fleming, The Oceans:Their Physics,Chemistry and General Biology. Prentice Hall,Upper Saddle River,N.Y. 1942,pp1087．
3 Stommel,H. The Gulf stream,2nd ed. University of California press, Berkeley, 1965, pp248．
4 von Schwind,J.J. Geophysical Fluid Dynamics for Oceanographers. Prentice Hall, Upper Saddle River,N.Y. 1980,pp307．
5 Wunsch.C. Trasient tracers as a problem in control theory. J. Geophys . Res. 1988, 93: 8099-8110．
6 Bennett,A.F. Inverse Methods in Physical Oceaography. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press, Cambridge. 1992． pp346．
7 Martel. F. and C. Wunsch, Combined inversion of a finite difference model and altimeter sea surface topography. Man. Geod. 1993b, 18(4) : 219-226．
8 Fisher,M. and M.Latif, Assimilstion of temperaure and sea level observations into a primitive equation model of the tropical Pacific. J.Mar. Syst., 1995, 6: 31-46．
9 Bengtsson,L.M. Ghil and E.Kallen eds.DYNAMIC METEOROLGY: DATA ASSIMILATION METHOD.Springer-Verlag,Berlin,1981,pp330．
10 M.Ghil. Meteorological data assimilation for oceanography: decription and theoretical framework. Dynamic Atomsphere, Ocean, specil issue: Data assimilation.Vol 1 3,Nos.3/4,171-218．
11 Lorenz,E.N., Deterministic nonperiodic flow. J. Atmos. Sci., 1963, 20, 130-141．
12 Lorenz,E.N.,Climate predictability:the physical basis of climate modelling. WMO, GARP Publi.Ser., 1975,16,132-136．
13 Palmer,T.N.,Extended-range atmospheric prediction and the Lorenz mode.Bull. Am.Meterol.Soc.1993,74(1) :49-65
14 Sheinin,D.A. and G.L.Mellor,Predictability studies with a coastal forecast system for the U. S. east coast. EOS, Trans. Am. Geophys. Union, Spring Meet, 1994, 75(16), April 19, Suppl. pp197.
15 Houghton, J. The Bahesian Lecture: The predictability of weather and climate. Philos. Trans. R. Soc. London A. 1991, 337: 521-572.
16 Carton, J. A. How prediatable are the geostrophic currents in the recieculation zone. J. Phys. Oceanogr., 1987,17(6):751-762.
17 Adamec, D. Predictability of quasi-geostrophic ocean flow: sensitivity to varying model vertical resolution. J. Phys. Oceanogr., 1989, 19(11): 1753-1764.
18 Allan R. Robinson and Pierre F. J. Lermusiaux, Overview of Data Assimilation. Harvard Reports in Physical/Interdisciplinary Ocean Science. Number 62. August, 2000. pp17.
19 冯培悌，系统辨识，杭州，浙江大学出版社，1999，pp179
20 Andrew C. Lorenc, Atomospheric Data Assimilation. Forecasting Research Division Scientific Paper. No. 34, 1995.
21 韩桂军：伴随法在潮汐和海温数值计算中的应用研究，中国科学院博士学位论文，2001。
22 Bennett, F. and M. A. Thorburn.1992, The generalized inverse of a nonlinear quasigeostrophic ocean circulation model. J.Phys. Oceanogr., 1992, 22: 213-230.
23 张洪钺，陈新海，现代控制理论—最佳估计理论。北京：北京航空学院出版社，1987。
24 靳尚来，随机控制，清华大学出版社，2001。
25 数学手册编写组，数学手册，科学出版社，2001
26 Ghil, M. and P. Malanotte-Rizzoli, Data Assimilation in Meteorology and Oceanography, Adv. Geophys., 1991, 33, 141-266.
27 Berry, P. J. and J. C. Marshall, Ocean modeling studies in support of altimetry, Dyn. Atmos. Oceans, 1989, 13, 269-300.
28 De Mey, P. and A. R. Robinson, Assimilation of Altimeter Eddy Fields Into a Limited-Area Quasi-Geostrophic Model, J. Phys. Oceanogr., 1987, 17(12), 2280-2293.
29 De Mey, P. and Y, Menard, Synoptic Analysis and Dynamical Adjustment of Geos 3 and Seasat Altimeter Eddy Fields in the Northwest Atlantic, J. Geophys. Res., 1989, 94, 6221-6230.
30 Hurlburt, H.E., D.N. Fox and J.Metzger, Statistical inference of weakly correlated subthermocline fields from satellite altimeter data, J. Geophys. Res., 1990,95, 11375-11409．
31 陈上及，马继瑞，海洋数据处理分析方法及其应用，北京：海洋出 版社， 1991．
32 Robinson, A.R., L.J. Walstad, J. Caiman, E.B. Dobson, D.W. Denbo, S.M. Glenn, D.L. Porter and J. Goldhirsh, Frontal Signals East of Iceland from the Geosat Altimeter, Geophys. Res. Lett., 1989,116, 77-80．
33 Haines, K., A Direct Method of Assimilating Sea Surface Height Data into Ocean Models with Adjustments to the Deep Circulation, J. Phys. Oceanogr., 1991,21(6) , 843-868．
34 Holland, W. and P. Malanotte-Rizzoli, Assimilation of Altimeter Data into Ocean Circulation Model: Space Versus Time Resolution Studies, J. Phys. Oceanogr., 1989,19(10) , 1507-1534．
35 Verron, J., Altimeter Data Assimilation Into Ocean Model: Sensitivity to Orbital Parameters, J. Geophys. Res., 1990,95, 11443-11459．
36 Verron, J., Nudging Satellite Altimeter Data into Quasi-Geostrophic Ocean Models, J. Geophys. Res., 97(C5) , 7479-7492, 1992．
37 Verron, J., J.-M. Molines, and E. Blayo, Assimilation of Geosat Data into a Quasi-geostrophic Model of the North Atlantic between 20 and 50 N: Preliminary Results, Oceanologica Acta. 1992,15(5) , 575-583．
38 Holland, W.R., V. Zlotnicki and L.-L. Fu, Modelled time dependent flow in the Agulhas retroflection region as deduced from altimeter data assimilation, S. African J. Marine Sci., 1991,10, 407-427．
39 Blayo, E., J. Verron, and J.M. Molines, Assimilation of TOPEX /POSEIDON altimeter data into a circulation model of the North Atlantic, J. Geophys. Res., 1994,99, 24691-24705．
40 Smedstad, O.M. and D.N. Fox, Assimilation of Altimeter data in a two-layer primitive equation model of the Gulf Stream, J. Phys. Oceanogr., 1994,24, 305-325．
41 White, W.B., N. Graham and C.-K. Tai, Reflection of Annual Rossby Waves at the Maritime Western Boundary of the Tropical Pacific, J. Geophys. Res., 1990a,95(C3) , 3101-3116．
42 White, W.B., C.-K. Tai and J. DiMento, Annual Rossby Wave
Characteristics in The California Current Region from the Geosat Exact Repeat Mission, J. Phys. Oceanogr., 1990b,20(9) , 1297--1311．
43 White, W.B., C.-K. Tai and W.R. Holland, Continuous Assimilation of Geosat Altimetric Sea Level Observations into a Numerical Synoptic Ocean Model of the California Current, J. Geophys. Res., 1990c,95(C3) , 3127--3148．
44 Dombrowski, E. and P. De Mey, Continuous assimilation in an open domain of the northeast Atlantic 1． Methodology and application to AthenA-88, J. Geophys. Res., 1992,97, 9719-9731,.
45 Mellor, G.L. and T. Ezer, A Gulf Stream Model and an Altimetry Assimilation Scheme, J. Geophys. Res., 1991,96 8779-8795．
46 Ezer, T. and G.L. Mellor, Continuous assimilation of Geosat altimeter data into a three-dimensional primitive equation Gulf Stream model, J. Phys. Oceanogr., 1994,24, 832-847．
47 朱江，徐迎春，王赐震等，海温数值预报资料同化试验 I，客观分析 的最优插值法试验，海洋学报，1995, 17 (6) : 9-20
48 Chavent,G.,Dupuy,M. and Lemommier,P. Histroy matching by use of optimal theory,.Soc Petroleum Engrs.,J. 1975,15,74-86．
49 Marchuk,G.I. Numerical solution of the problems of the dynamics of the atmosphere and ocean,Gidrometeoizadat,Leningrad,U.S.S.R., 1974．
50 Le Dimet,F.X. and Talagrand,O. Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects, Tellus, 1986, 38A, 97-110．
51 Talagrand,O. and Courtier,P. Variational assimilation of meteorological abservations with the adjoint vorticity equation.I: theory, Q.J.R. Meteorol Soc., 1987,113,1,311-328．
52 Courtier,P, and Talagrand,O. Variational assimilation of meteorological abservations with the direct and adjoint shallow water equations, Tellus,1990,42A, 531-549．
53 Derber,J.C. A Variational continuous data assimilation technique. Mon. Wea. Rev. 1989,117,2437-2446．
54 Talagrand,O. and Courtier,P. Variational assimilation of meteorological abservations with the adjoint vorticity equation.II: numerival results,Q.J.R. Meteorol.Soc., 1987,113,1329-1347．
55． Chao,W.C. and Chang,L.P. Development of a four-dimensional
variational analysis system using th eadjoint method at GLA. Part I:Dynamics,Mon. Wea.Rev. 1992,120,1661-1673．
56 Courtier,P., Derber,J. ERRico,R.,Louis,J-F and Vukicevic,T. Important literature on the use of adjoint,variational methods and kalman filter in meteorology,rellus,1993,45A,342-357．
57 Bennett,A.F.,Chua,B.S. and Leslie,L.M. Generalized inversion of a global numerical weather prediction model . Meteor. Atmos. Phys., 1996． 60, 165-178．
58 Bennett,A.F.,Chua,B.S. and Leslie,L.M. Generalized inversion of a global numerical weather prediction model,II: analysis and implementation. Meteor. Atmos. Phys., 1997,62,129-140．
59 Thacker,W.C. and Long,R.B. Fitting dynamics to data, J. Geophys. Res., 1988, 93, 1227-1240．
60 Panchang,V.G. and O'Brien,J.J. On the determination of hydraulic model parameters using the adjoint state formulation, Modelling Marine system ,A.M. davies(ed.),CRC Press,Boca Rayon,FL,1989．
61 Schroter, J. Driving of non-linear-dependent ocean models by observation of transient tracer-a problem of constrained optimisation, in: Oceanic Circulation Models: Combining Data and Dynamics, 1989, pp257-285．
62 张爱军：最优变分伴随方法及在近岸水位资料同化中的应用，中国 科学院海洋研究所博士学位论文， 2000．
63 Miller, R.N., Direct Assimilation of Altimetric Differences Using the Kalman Filter, Dyn. Atmos. Oceans, 1989,13,317-333,
64 Gaspar, P. and C. Wunsch, Estimates from Altimeter Data of Barotropic Rossby Waves in the Northwestern Atlantic Ocean, J. Phys. Oceanogr-, 1989,19(12) , 1821-1844．
65 Fukumori, I., J. Benveniste, C. Wunsch and D. Haidvogel, Assimilation of sea surface topography into an ocean circulation model using a steady-state smoother, J. Phys. Oceanogr. 1993,23, 1831--1855
66 Fukumori I, Assimilation of TOPEX sea level measurements with a reduced-gravity, shallow water model of the tropical Pacific Ocean[J]. J.Geophys.Res., 1995,100(c4) :25027-25039．
67 Fukumori, I. and P. Malanotte-Rizzoli, An approximate Kalman filter for ocean data assimilation: a reduced-dimension, static, linearized
Kalman filter, J. Geophys. Res., 1995, 100(c4) ,6779-6793．
68 Dee,D.P.,S.E.Cohn,A.Dalcher,and M.Ghil, An effient algorithm for estimating noise covariances in distributed systems. IEEE Trans. Control., 1985: AC-30, 1057-1065．
69 D.P.,Simplified adaptive Kalman filtering for large-scale geophysical models.Realization and Modelling in System Theory, M.A.Kaashoek, J.H.van Schuppen, and A.C.M.Ran, Eds., 1990:Proceedings of the International Symposium MTNS-89, Vol.1,Birkhauser,561-574．
70 Daley,R.,Forecast-error statistics for homogeneous and inhomogeneous observation networks.Mon.Wea.Rev., 1992b, 120,627-643．
71 Daley,R., Atmospheric Data Analysis.Cambridge University Press, 1991,457pp.
72 Jiang,S.,and M.Ghil, Dynamical properties of error statistics in a shallow-water model. J.Phys.Oceanogr., 1993:23,2541-2566．
73 Parrish,D:F..,andS.E.Cohn, A Kalman filter for a two-dimensional shallow-water model: Formulation and preliminary experiments. Office Note304, 1985, NOAA/NWS/NMC,64pp.
74 Evensen,G.,:Open boundary conditions for the extended Kalman filter with a quasi geostrophic ocean model. J. Geophys. Res., 1993, 98, 16529-16546．
75 Evensen,G., Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 1994a: 99 (C5) ,10143-10162．
76 Evensen,G., Inverse methods and data assimilation in nonlinear ocean models. Physical, 1994b:77,108-129．
77 Miller,A.J.,M.Ghil,and F.Gauthier, Data assimilation in strongly non-linear dynamical systems.J.Atmos.Sci., 1994:51,1037-1056．
78 Ehrendorfer,M.,and R.M.Errico, Mesoscale predictability and the spectrum of optimal perturbations..J..Atmos.Sci, 1995:52, 3475-3500．
79 Toth,Z.,andE.Kalnay, Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer.Meteor.Soc., 1993:74,2317-2330．
80 Press,W.H., B.P. Flannery,S.A. Teukolsky and W.T.Vetterling, Numerical Recipes: The Art of Scientific Compting. Cambridge University Press,Cambridge. 1989．
81 Aart,E.H.L. and J.H.M.Korst.Boltzmann machines as a model for
parallel annealing. Algorithmica, 1991, 6(3): 437-465
82 Barth,N.H.,Oceanographic experiment design. Ⅱ. Genetic algorithms., J. Atmos. Ocean. Technol., 1992, 9, 434-443.
83 Barth, N.H. and C. Wunsch, Oceanographic experiment design by simulated annealing., J. Phys. Oceanogr., 1990, 20, 1249-1263.
84 Allan R.R.,P.F.J.Lermusiaux and N.Quincy Sloan Ⅲ., CHAPTER 20 DATA ASSIMILATION, The Sea, Volume 10, pp541-595. John Wiley &Sons, Inc. 1998.
85 Allan R.R.,P.F.J.Lermusiaux and N.Quincy Sloan Ⅲ.,CHAPTER 12 DATA ASSIMILATION FOR MODELLING AND PREDICTING COUPLED PHYSICAL BIOLOGICAL INTERACTIONS IN THE SEA, The Sea, Volume 12, pp475-536. John Wiley & Sons, Inc. 2002.
86 王东晓，施平，杨昆，等。南海TOPEX海面高度资料的混合同化试验[J]。海洋与湖沼，2001，32(1)：101-108。
87 P. Malanotte-Rizzoli. Modern Approches to data assimilation in ocean modeling,. Elsevier oceanography series, New York, 2002, pp455.
88 叶安乐，李凤歧，物理海洋学，青岛海洋大学出版社，1992。
89 Orlanski, A simple Boundary condition for unbounded hyperbolic flow, Journal of Computation Physics 21, pp251-269(1976).
90 Munk W. H. and E. R. Anderson, Notes on a theory of the thermocline. J. Mar. Res., 1948, Vol.7.No.3, pp276～295.
91 Pacanowiski, R. C. and S.G.H. Philander, 1981: Parameterization of vertical mixing in numerical models of tropic oceans, Journal of Physical Oceanography, 1981, Vol. 11. pp. 1443～1451.
92 黄大吉，渤海正压和斜压动力过程的数值研究，青岛海洋大学博士相位论文，1995，10。
93 Bouttier F and Courtier P, Data Assimilation Concept and Methods training course. Notes of ECMWF. 2001.
94 盛华，纪立人。三维多元最优插值的区域性试验，气象学报，1991，49(5)：151-161。
95 李立，吴日升，李燕初等。TOPEX／POSEIDON高度计浅海潮汐混淆的初步分析，海洋学报，1999，21(3)：7-14。
96 懂晓军：利用TOPEX／POSEIDON卫星高度计资料提取黄海、东海潮汐的研究，交流资料。
97 Mike Fisher, Meteorological Training Course Lecture Series:
Assimilation techniques(3): 3dVar,2001,4,pp11.
98 Mike Fisher, Meteorological Training Course Lecture Series: Assimilation techniques(4): 4dVar, 2001, 4, pp9.
99 R.Delay. Atmospheric data analysis. Cambridge university press.1991.
100 Thiebaux, H.J.Anisotropic correction functions for objective analysis. Mon. Wea. Rev. 1976,104:994～1002
101 P.F.J. Lermusiaux, D.G.M. Anderson and C.J. Lozano. On the mapping of multivariate geophysical fields:Error and variability subspace estimates. (personal communication materials.), 1999,pp58.
102 Bennett. A.F.,B.S.Chua et al. Generalized inversion of a global numerical weather predication model. Meteorol. Atmos. Phys. 1995, 60 (1-3), 165-178.
103 张贤达，信号处理中的线性代数。北京：科学出版社，1997。
104 彭玉华，小波变换与工程应用．科学出版社，1999。
105 L.S.Gandian. The problem of optimal interpolation. Trudy Main Geophys. Obs. 1959,55,69-76.
106 L.S.Gandian. On optimal interpolation and extrapolation of meteorological fields. Trudy Main Geophys. Obs. 1960,114,75-89.
107 F.P.Bretheerton, J.C.McWilliams. Estimations from irregular array. Rev. Geophys. Space Phys. 1980,18,789-812.
108 J.Segschneider, J.Alves, D.Anderson, et al. Asssimilation of TOPEX/POSEIDON data into a seasonal forcast system. Phys. Chem. Earth(A). 1999, 24(4): 369-374.
109 杨晓霞，沈桐立，徐文金等。最优插值客观分析，南京气象学院学报，1991，14(4)：566-574。
110 潘晓斌，魏绍远，马华平等。逐次最优插值方案及其试验，气象科学，1996，16(1)：30-39
111 屠伟铭，张跃堂。全球最优插值客观分析，气象学报，1995，53(2)：148-156。
112 R.A.Akmaev. Aprototype upper-atmospheric data assimilation scheme based on optomal interpolation: 1. Theoty. Journal of Atmospheric and Solar-Terrestrial Physics. 1999, 61,491-504.
113 R.A.Akmaev. Aprototype upper-atmospheric data assimilation scheme based on optomal interpolation: 1. Numerical experiments. Journal of Atmospheric and Solar-Terrestrial Physics. 1999, 61, 505-517.
114 贾沛璋，朱征桃，最优估计及其应用，科学出版社，1984。
115 Thiebaux, H.J.Anisotropic correction functions for objective analysis. Mon. Wea. Rev. 1976,104:994～1002
116 李庆扬，王能超，易大义，数值分析，华中理工大学出版社，1982．
117 ROBINSON A R, LERMUSIAUX P F J , SLOAN N Q. Data Assimilation. The Global Coastal Ocean: Process and Methods. BRINK K.H , ROBINSON A R, Vol 10 of The Sea, Wiley New York, pp541-594.
118 黄大吉，陈宗镛，苏纪兰。三维陆架海模式在渤海中的应用Ⅰ。潮流、风生环流及其相互作用。海洋学报，1996，18(5)：1-13。
119 黄大吉，苏纪兰，陈宗镛。三维陆架海模式在渤海中的应用Ⅱ。温度的季节性变化。海洋学报，1996，18(6)：8-18。
120 马寨璞，黄大吉，章本照。应用SVD分解简化卡尔曼增益计算的理论研究。浙江大学学报(工学版)(已录用，待发表)。
121 PARRISH D P, COHN S.1985: A kalman filter for a two-dimensional shallow water model :formulation and preliminary experiments. Office Notes 304, washington, D.C.,National Meteorolcgical Center,64pp
122 徐士良。FORTRAN常用算法程序集。北京：清华大学出版社，1997。
123 S.Hoang, R.Baraille, O.Talagrand, X.Carton, P.De Mey. Adaptive filtering: application to satellite data assimilation in oceanography. Dynamics of Atmospheres and Oceans. 1997, 27,257-281.
124 Hoteit, D.Pham, J.Blum. A semi-evolutive partially local filter for data assimilation. Marine Pollution Bullrtin. 2001, 43(7-12), 164-174.
125 R.Canizares, H.Madsen, H.R.Jensen, H.J.Vested. Developments in operational shelf sea modeling in Danish waters. Estuarine, Coastal and Shelf Science. 2001, 53, 595-605.
126 A.R.Robinson, J.Sellschop, A.Warm-Varnas et al. The Atlantic lonian stream. Journal of Marine System. 1999, 20, 129-156.
127 P.F.J.Lermusiaux, A.R.Robinson. Data assimilation via error subspace statistical estimation Part Ⅰ: Theory and schemes. Monthly Weather Review. 1999, 127(7), 1385-1407
128 P.F.J.Lermusiaux, A.R.Robinson. Data assimilation via error subspace statistical estimation Part Ⅰ: Middle atlantic bight shelf break front simulations and ESSe validation. Monthly Weather Review. 1999, 127(7), 1408-1432.
129 P.F.J.Lermusiaux, D.G.M.Anderson, C.J.Lozano. On the mapping of multivariate geophysical fields error and variability subspace estimates. Personal communication materials. 1999,9 ,pp58．
130 P.F.J.Lermusiaux, Evoluing the subspace of the three dimansional multiscale ocean variability Massachasetts Bay. Journal of Marine System, 2000． Personal communication materials, pp56．
131 P.F.J.Lermusiaux, A.R.Robinson. Features of dominant mesoscale variability circulation patterns and dymnamics in the straight of Sicily. Deep Sea Reasearch. 2000,11, Personal communication materials, pp58．
132 P.F.J.Lermusiaux, Estimation and study of mesoscale variability in the straight of Sicily. Dynamics of Atmospheres and Ocean, 1999, 29,255-303．
133 A.R.Robinson, P.F.J.Lermusiaux, N.Q.Sloan, CHAPTER 20 :DATA ASSIMILATION, The Sea, Volume 10, pp541-595． John Wiley & Sons, Inc. 1998．
134 P.Barasseur, J.Ballabrera-Poy, J.Verron. Assimilation of altimetric data in the mid-latitude oceans using the singular evolutive extended kalman filter with an eddy-resolving primitive equation model. Journal of the Marine System. 1999, 22, 269-294．
135 J.Verron, J.Gourdeau, L.Pham, D.T.Murtugvdde, et al. An extended kalman filter to assimilate satellite aitimeter data into a non-linear numerical model of the tropical pacific: mode and validation. Journal of Geophysical Research,1999, 104(3) , 5441-5458．
136 V.Carmillet, J.M.Brankart. P.Barasseur, et al. A singular evolutive extended kalman filter to assimilate ocean color data in a coupled physical-biochemical model of the north Atlantic ocean. Ocean Modelling. 2001, 3, 167-192．
137 D.T.Pham, J.Verron, M.C.Roubaud. A singular evolutive edxtended kalman filter for data assimilation in oceanography. Journal of Marine System, 1998, 16, 323-340．
138 A.C.Vorrips, A.W.Hermink. G.J.Komen. Wave data assimilation with the kalman filter. Journal of Marine System. 1999, 19, 267-291．
139 Verlaan, M.Hermink, Data assimilation scheme for non-linear shallow water models in Rahman Brebbia. Personal communication materials,
1996．
140 Verlaan, M.Hermink, Tidal flow forecasting using reduced rank square root filters. Stochastic Hydr. Hydraul. 1997, 11, 249-368．
141 L.Bertino, G.Evensen, H.Wackernagel. Combining geostatistics and kalman filter for data assimilation in an estuarine system. Inverse Problems, 2002,18, 1-23
142 N.Hirore, I.Fukumori, J.H.Yoon. Assimilation of TOPEX/POSEIDON altimeter data with a reduced gravity model of the Japan Sea. Journal of Oceanography. 1999, 55, 53-64．
143 A.C. Mark, A.Kaplan, Miller R N et al, Mapping tropical Pacific sea level: Data assimilation via a reduced state space Kalman filter. J.Geophys.Res. 1996,101(c4) : 22599-22617．
144 K.A. Myers, B.D. Tapley. Adaptive sequential estimation with unknown noise statics, IEEE, Trans. Autom. Control, 1976,21(5) : 520-523．
145 D.P. Dee. Simplification of the Kalman filter for meteorological data assimilation, Q.J.R.Meterol. Soc, 1991, 117(4) : 365-384．
146 J.D. Annan, Hargreaves J C, Sea surface temperature assimilation for a three-dimensional baroclinic model of shelf sea. Continental shelf Research. 1999,19(3) : 1507-1520．
147 K.P. Belyaev, J.J. OBrien, P.A.Nobre. A data assimilation method used with an ocean circulation model and its application to the tropical Atlantic data analysis. Journal of Mathematical science. 2001, 106(2) , 2792-2802．
148 K.P. Belyaev, C.A.S.Tanajura, J.J. OBrien. A data assimilation used with an ocean circulation model and its application to the tropical Atlantic. Applied Mathematical Modelling. 2001, 25, 655-670．
149 S.Cohn, D.F.Parrish. The behavior of frocast error covariance foe a kalman filter in two dimensions. Monthly Weather Review. 1991, 119(8) , 1757-1785．
150 R.N.Miller, M.A.Cane. A kalman filter analysis of sea level height in the tropical Pacific. Journal of Physical Oceanography. 1989, 19(6) , 773-790．
151 L.L.Fu. I.Fukumori, R.N.Miller. Fitting dynamic models to the great sea level observations in the tropical Pacific Ocean, Part II: A linear
wind-driven model. Journal of Physical Oceanography, 1993, 23, 2162-2168.
152 R.N.Miller. Tropical data assimilation experiments with simulated data: The impact of the tropical ocean and global atmosphere thermal array for the ocean. Journal of Geophysical Research. 1990, 95(7), 11461-11482.
153 张占海，吴辉碇。渤海潮汐和潮流数值计算，海洋预报，1994，11(2)：48～54。
154 孙洪亮，黄卫民。广西近海潮汐和海流的观测分析与数值研究——Ⅰ．观测与分析，黄渤海海洋，2001，19(4)：1～11。
155 孙洪亮，黄卫民。广西近海潮汐和海流的观测分析与数值研究——Ⅱ．数值研究，黄渤海海洋，2001，19(4)：12～21。
156 孙洪亮，黄卫民。北部湾潮汐潮流的三维数值模拟，海洋学报，2001，23(2)：1～8。
157 赵保仁，曹德明，李徽翡，王其茂。渤海的潮混合特征及潮汐锋现象，海洋学报，2001，23(4)：113～120
158 方国洪，杨景飞。渤海潮运动的一个二维数值模型。海洋与湖沼，1985，16(5)：337～346。
159 赵保仁，方国洪，曹德明。渤、黄、东海三维潮波运动数值模拟。海洋与湖沼，1998，29(6)：611～616。
160 杨陇慧，朱建荣，朱首贤。长江口杭州湾及邻近海区潮汐潮流场三维数值模拟，华东师范大学学报，2001，3，74～84。
161 朱玉荣。末次冰消期以来渤、黄、东海陆架潮汐、潮流演变过程模拟研究，青岛海洋大学学报，2002，32(2)：279～286。
162 林楚平。海山潮汐能的综合开发利用，水利水电技术，1999，30(1)。
163 邵守良，张锦文。港口工程设计中的一些潮汐计算问题，港工技术，2001，4，4～5，31。
164 熊绍隆，胡玉棠。潮汐河口悬移质动床实物模型的理论与实践，泥沙研究，1999，1。
165 华祖林，褚克坚。基于三角形网格的潮汐水域水流水质的一种计算模式，河海大学学报，2001，29(4)：31～37。
166 王东晓，朱江。伴随方法在海洋数值模式中的应用，地球物理进展，1997，12(1)：98～107。
167 兰健。资料同化中的伴随方法及其在海洋中的应用，青岛海洋大学学报，1998，28(2)：174～178。
168 吕咸青，刘文剑。数据同化中的伴随方法及其有关问题的研究，海洋科学，2001，25(3)：44～50。
169 马刚，邱崇践，王强。用变分法修正边界层资料的数值试验，气象学报，2001，59(1)：107～113。
170 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)：13～19。
171 吕咸青，方国洪。渤海开边界潮汐的伴随法反演，海洋与湖沼，2002，33(2)：113～120。
172 韩桂军，何柏荣，马继瑞，刘克休，李冬。利用伴随法优化非线性潮汐模型的开边界条件Ⅰ：伴随方程的建立及其“孪生”数值试验，海洋学报，2000，22(6)：134～140。
173 韩桂军，方国洪，马继瑞，刘克休，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。
174 朱江，曾庆存，郭冬建，刘卓。利用伴随算子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。
175 李培良，左军成，李磊，黄娟。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。
176 暴景阳，晁定波，李建成，邓晓丽。由T／P卫星测高数据建立南中国海潮汐模型的初步研究，武汉测绘科技大学学报，1999，24(4)：
177 董晓军，马继瑞，黄珹，范振华，韩桂军，许崇金。利用TOPEX／Poseidon卫星高度计资料提取黄海、东海潮汐信息的研究，海洋与湖沼，2002，33(4)：386～392。
178 毛庆文，施平，齐义泉。运用调和分析方法分离卫星高度计资料中的潮汐信息。海洋工程，2002，20(1)：41～45。
179 李立，吴日升，李燕初，甘子钧。TOPEX／POSEIDON高度计浅海潮汐混淆的初步分析，海洋学报，1999，21(3)：7～14。
180 暴景阳，晁定波，李建成。南中国海TOPEX／POSEIDON轨迹交叉点测高数据的潮汐调和分析，测绘学报，2000，29(1)：17～23。
181 刘克休，马继瑞，韩桂军，范振华，许崇金。引入差比法分析西北太平洋TOPEX／POSEIDON卫星高度计测高数据。海洋学报，2002，24(4)：1～10。
2 Sevrdrup,H.V.,M.W. Johnson and R.H. Fleming, The Oceans:Their Physics,Chemistry and General Biology. Prentice Hall,Upper Saddle River,N.Y. 1942,pp1087．
3 Stommel,H. The Gulf stream,2nd ed. University of California press, Berkeley, 1965, pp248．
4 von Schwind,J.J. Geophysical Fluid Dynamics for Oceanographers. Prentice Hall, Upper Saddle River,N.Y. 1980,pp307．
5 Wunsch.C. Trasient tracers as a problem in control theory. J. Geophys . Res. 1988, 93: 8099-8110．
6 Bennett,A.F. Inverse Methods in Physical Oceaography. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press, Cambridge. 1992． pp346．
7 Martel. F. and C. Wunsch, Combined inversion of a finite difference model and altimeter sea surface topography. Man. Geod. 1993b, 18(4) : 219-226．
8 Fisher,M. and M.Latif, Assimilstion of temperaure and sea level observations into a primitive equation model of the tropical Pacific. J.Mar. Syst., 1995, 6: 31-46．
9 Bengtsson,L.M. Ghil and E.Kallen eds.DYNAMIC METEOROLGY: DATA ASSIMILATION METHOD.Springer-Verlag,Berlin,1981,pp330．
10 M.Ghil. Meteorological data assimilation for oceanography: decription and theoretical framework. Dynamic Atomsphere, Ocean, specil issue: Data assimilation.Vol 1 3,Nos.3/4,171-218．
11 Lorenz,E.N., Deterministic nonperiodic flow. J. Atmos. Sci., 1963, 20, 130-141．
12 Lorenz,E.N.,Climate predictability:the physical basis of climate modelling. WMO, GARP Publi.Ser., 1975,16,132-136．
13 Palmer,T.N.,Extended-range atmospheric prediction and the Lorenz mode.Bull. Am.Meterol.Soc.1993,74(1) :49-65
14 Sheinin,D.A. and G.L.Mellor,Predictability studies with a coastal forecast system for the U. S. east coast. EOS, Trans. Am. Geophys. Union, Spring Meet, 1994, 75(16), April 19, Suppl. pp197.
15 Houghton, J. The Bahesian Lecture: The predictability of weather and climate. Philos. Trans. R. Soc. London A. 1991, 337: 521-572.
16 Carton, J. A. How prediatable are the geostrophic currents in the recieculation zone. J. Phys. Oceanogr., 1987,17(6):751-762.
17 Adamec, D. Predictability of quasi-geostrophic ocean flow: sensitivity to varying model vertical resolution. J. Phys. Oceanogr., 1989, 19(11): 1753-1764.
18 Allan R. Robinson and Pierre F. J. Lermusiaux, Overview of Data Assimilation. Harvard Reports in Physical/Interdisciplinary Ocean Science. Number 62. August, 2000. pp17.
19 冯培悌，系统辨识，杭州，浙江大学出版社，1999，pp179
20 Andrew C. Lorenc, Atomospheric Data Assimilation. Forecasting Research Division Scientific Paper. No. 34, 1995.
21 韩桂军：伴随法在潮汐和海温数值计算中的应用研究，中国科学院博士学位论文，2001。
22 Bennett, F. and M. A. Thorburn.1992, The generalized inverse of a nonlinear quasigeostrophic ocean circulation model. J.Phys. Oceanogr., 1992, 22: 213-230.
23 张洪钺，陈新海，现代控制理论—最佳估计理论。北京：北京航空学院出版社，1987。
24 靳尚来，随机控制，清华大学出版社，2001。
25 数学手册编写组，数学手册，科学出版社，2001
26 Ghil, M. and P. Malanotte-Rizzoli, Data Assimilation in Meteorology and Oceanography, Adv. Geophys., 1991, 33, 141-266.
27 Berry, P. J. and J. C. Marshall, Ocean modeling studies in support of altimetry, Dyn. Atmos. Oceans, 1989, 13, 269-300.
28 De Mey, P. and A. R. Robinson, Assimilation of Altimeter Eddy Fields Into a Limited-Area Quasi-Geostrophic Model, J. Phys. Oceanogr., 1987, 17(12), 2280-2293.
29 De Mey, P. and Y, Menard, Synoptic Analysis and Dynamical Adjustment of Geos 3 and Seasat Altimeter Eddy Fields in the Northwest Atlantic, J. Geophys. Res., 1989, 94, 6221-6230.
30 Hurlburt, H.E., D.N. Fox and J.Metzger, Statistical inference of weakly correlated subthermocline fields from satellite altimeter data, J. Geophys. Res., 1990,95, 11375-11409．
31 陈上及，马继瑞，海洋数据处理分析方法及其应用，北京：海洋出 版社， 1991．
32 Robinson, A.R., L.J. Walstad, J. Caiman, E.B. Dobson, D.W. Denbo, S.M. Glenn, D.L. Porter and J. Goldhirsh, Frontal Signals East of Iceland from the Geosat Altimeter, Geophys. Res. Lett., 1989,116, 77-80．
33 Haines, K., A Direct Method of Assimilating Sea Surface Height Data into Ocean Models with Adjustments to the Deep Circulation, J. Phys. Oceanogr., 1991,21(6) , 843-868．
34 Holland, W. and P. Malanotte-Rizzoli, Assimilation of Altimeter Data into Ocean Circulation Model: Space Versus Time Resolution Studies, J. Phys. Oceanogr., 1989,19(10) , 1507-1534．
35 Verron, J., Altimeter Data Assimilation Into Ocean Model: Sensitivity to Orbital Parameters, J. Geophys. Res., 1990,95, 11443-11459．
36 Verron, J., Nudging Satellite Altimeter Data into Quasi-Geostrophic Ocean Models, J. Geophys. Res., 97(C5) , 7479-7492, 1992．
37 Verron, J., J.-M. Molines, and E. Blayo, Assimilation of Geosat Data into a Quasi-geostrophic Model of the North Atlantic between 20 and 50 N: Preliminary Results, Oceanologica Acta. 1992,15(5) , 575-583．
38 Holland, W.R., V. Zlotnicki and L.-L. Fu, Modelled time dependent flow in the Agulhas retroflection region as deduced from altimeter data assimilation, S. African J. Marine Sci., 1991,10, 407-427．
39 Blayo, E., J. Verron, and J.M. Molines, Assimilation of TOPEX /POSEIDON altimeter data into a circulation model of the North Atlantic, J. Geophys. Res., 1994,99, 24691-24705．
40 Smedstad, O.M. and D.N. Fox, Assimilation of Altimeter data in a two-layer primitive equation model of the Gulf Stream, J. Phys. Oceanogr., 1994,24, 305-325．
41 White, W.B., N. Graham and C.-K. Tai, Reflection of Annual Rossby Waves at the Maritime Western Boundary of the Tropical Pacific, J. Geophys. Res., 1990a,95(C3) , 3101-3116．
42 White, W.B., C.-K. Tai and J. DiMento, Annual Rossby Wave
Characteristics in The California Current Region from the Geosat Exact Repeat Mission, J. Phys. Oceanogr., 1990b,20(9) , 1297--1311．
43 White, W.B., C.-K. Tai and W.R. Holland, Continuous Assimilation of Geosat Altimetric Sea Level Observations into a Numerical Synoptic Ocean Model of the California Current, J. Geophys. Res., 1990c,95(C3) , 3127--3148．
44 Dombrowski, E. and P. De Mey, Continuous assimilation in an open domain of the northeast Atlantic 1． Methodology and application to AthenA-88, J. Geophys. Res., 1992,97, 9719-9731,.
45 Mellor, G.L. and T. Ezer, A Gulf Stream Model and an Altimetry Assimilation Scheme, J. Geophys. Res., 1991,96 8779-8795．
46 Ezer, T. and G.L. Mellor, Continuous assimilation of Geosat altimeter data into a three-dimensional primitive equation Gulf Stream model, J. Phys. Oceanogr., 1994,24, 832-847．
47 朱江，徐迎春，王赐震等，海温数值预报资料同化试验 I，客观分析 的最优插值法试验，海洋学报，1995, 17 (6) : 9-20
48 Chavent,G.,Dupuy,M. and Lemommier,P. Histroy matching by use of optimal theory,.Soc Petroleum Engrs.,J. 1975,15,74-86．
49 Marchuk,G.I. Numerical solution of the problems of the dynamics of the atmosphere and ocean,Gidrometeoizadat,Leningrad,U.S.S.R., 1974．
50 Le Dimet,F.X. and Talagrand,O. Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects, Tellus, 1986, 38A, 97-110．
51 Talagrand,O. and Courtier,P. Variational assimilation of meteorological abservations with the adjoint vorticity equation.I: theory, Q.J.R. Meteorol Soc., 1987,113,1,311-328．
52 Courtier,P, and Talagrand,O. Variational assimilation of meteorological abservations with the direct and adjoint shallow water equations, Tellus,1990,42A, 531-549．
53 Derber,J.C. A Variational continuous data assimilation technique. Mon. Wea. Rev. 1989,117,2437-2446．
54 Talagrand,O. and Courtier,P. Variational assimilation of meteorological abservations with the adjoint vorticity equation.II: numerival results,Q.J.R. Meteorol.Soc., 1987,113,1329-1347．
55． Chao,W.C. and Chang,L.P. Development of a four-dimensional
variational analysis system using th eadjoint method at GLA. Part I:Dynamics,Mon. Wea.Rev. 1992,120,1661-1673．
56 Courtier,P., Derber,J. ERRico,R.,Louis,J-F and Vukicevic,T. Important literature on the use of adjoint,variational methods and kalman filter in meteorology,rellus,1993,45A,342-357．
57 Bennett,A.F.,Chua,B.S. and Leslie,L.M. Generalized inversion of a global numerical weather prediction model . Meteor. Atmos. Phys., 1996． 60, 165-178．
58 Bennett,A.F.,Chua,B.S. and Leslie,L.M. Generalized inversion of a global numerical weather prediction model,II: analysis and implementation. Meteor. Atmos. Phys., 1997,62,129-140．
59 Thacker,W.C. and Long,R.B. Fitting dynamics to data, J. Geophys. Res., 1988, 93, 1227-1240．
60 Panchang,V.G. and O'Brien,J.J. On the determination of hydraulic model parameters using the adjoint state formulation, Modelling Marine system ,A.M. davies(ed.),CRC Press,Boca Rayon,FL,1989．
61 Schroter, J. Driving of non-linear-dependent ocean models by observation of transient tracer-a problem of constrained optimisation, in: Oceanic Circulation Models: Combining Data and Dynamics, 1989, pp257-285．
62 张爱军：最优变分伴随方法及在近岸水位资料同化中的应用，中国 科学院海洋研究所博士学位论文， 2000．
63 Miller, R.N., Direct Assimilation of Altimetric Differences Using the Kalman Filter, Dyn. Atmos. Oceans, 1989,13,317-333,
64 Gaspar, P. and C. Wunsch, Estimates from Altimeter Data of Barotropic Rossby Waves in the Northwestern Atlantic Ocean, J. Phys. Oceanogr-, 1989,19(12) , 1821-1844．
65 Fukumori, I., J. Benveniste, C. Wunsch and D. Haidvogel, Assimilation of sea surface topography into an ocean circulation model using a steady-state smoother, J. Phys. Oceanogr. 1993,23, 1831--1855
66 Fukumori I, Assimilation of TOPEX sea level measurements with a reduced-gravity, shallow water model of the tropical Pacific Ocean[J]. J.Geophys.Res., 1995,100(c4) :25027-25039．
67 Fukumori, I. and P. Malanotte-Rizzoli, An approximate Kalman filter for ocean data assimilation: a reduced-dimension, static, linearized
Kalman filter, J. Geophys. Res., 1995, 100(c4) ,6779-6793．
68 Dee,D.P.,S.E.Cohn,A.Dalcher,and M.Ghil, An effient algorithm for estimating noise covariances in distributed systems. IEEE Trans. Control., 1985: AC-30, 1057-1065．
69 D.P.,Simplified adaptive Kalman filtering for large-scale geophysical models.Realization and Modelling in System Theory, M.A.Kaashoek, J.H.van Schuppen, and A.C.M.Ran, Eds., 1990:Proceedings of the International Symposium MTNS-89, Vol.1,Birkhauser,561-574．
70 Daley,R.,Forecast-error statistics for homogeneous and inhomogeneous observation networks.Mon.Wea.Rev., 1992b, 120,627-643．
71 Daley,R., Atmospheric Data Analysis.Cambridge University Press, 1991,457pp.
72 Jiang,S.,and M.Ghil, Dynamical properties of error statistics in a shallow-water model. J.Phys.Oceanogr., 1993:23,2541-2566．
73 Parrish,D:F..,andS.E.Cohn, A Kalman filter for a two-dimensional shallow-water model: Formulation and preliminary experiments. Office Note304, 1985, NOAA/NWS/NMC,64pp.
74 Evensen,G.,:Open boundary conditions for the extended Kalman filter with a quasi geostrophic ocean model. J. Geophys. Res., 1993, 98, 16529-16546．
75 Evensen,G., Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 1994a: 99 (C5) ,10143-10162．
76 Evensen,G., Inverse methods and data assimilation in nonlinear ocean models. Physical, 1994b:77,108-129．
77 Miller,A.J.,M.Ghil,and F.Gauthier, Data assimilation in strongly non-linear dynamical systems.J.Atmos.Sci., 1994:51,1037-1056．
78 Ehrendorfer,M.,and R.M.Errico, Mesoscale predictability and the spectrum of optimal perturbations..J..Atmos.Sci, 1995:52, 3475-3500．
79 Toth,Z.,andE.Kalnay, Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer.Meteor.Soc., 1993:74,2317-2330．
80 Press,W.H., B.P. Flannery,S.A. Teukolsky and W.T.Vetterling, Numerical Recipes: The Art of Scientific Compting. Cambridge University Press,Cambridge. 1989．
81 Aart,E.H.L. and J.H.M.Korst.Boltzmann machines as a model for
parallel annealing. Algorithmica, 1991, 6(3): 437-465
82 Barth,N.H.,Oceanographic experiment design. Ⅱ. Genetic algorithms., J. Atmos. Ocean. Technol., 1992, 9, 434-443.
83 Barth, N.H. and C. Wunsch, Oceanographic experiment design by simulated annealing., J. Phys. Oceanogr., 1990, 20, 1249-1263.
84 Allan R.R.,P.F.J.Lermusiaux and N.Quincy Sloan Ⅲ., CHAPTER 20 DATA ASSIMILATION, The Sea, Volume 10, pp541-595. John Wiley &Sons, Inc. 1998.
85 Allan R.R.,P.F.J.Lermusiaux and N.Quincy Sloan Ⅲ.,CHAPTER 12 DATA ASSIMILATION FOR MODELLING AND PREDICTING COUPLED PHYSICAL BIOLOGICAL INTERACTIONS IN THE SEA, The Sea, Volume 12, pp475-536. John Wiley & Sons, Inc. 2002.
86 王东晓，施平，杨昆，等。南海TOPEX海面高度资料的混合同化试验[J]。海洋与湖沼，2001，32(1)：101-108。
87 P. Malanotte-Rizzoli. Modern Approches to data assimilation in ocean modeling,. Elsevier oceanography series, New York, 2002, pp455.
88 叶安乐，李凤歧，物理海洋学，青岛海洋大学出版社，1992。
89 Orlanski, A simple Boundary condition for unbounded hyperbolic flow, Journal of Computation Physics 21, pp251-269(1976).
90 Munk W. H. and E. R. Anderson, Notes on a theory of the thermocline. J. Mar. Res., 1948, Vol.7.No.3, pp276～295.
91 Pacanowiski, R. C. and S.G.H. Philander, 1981: Parameterization of vertical mixing in numerical models of tropic oceans, Journal of Physical Oceanography, 1981, Vol. 11. pp. 1443～1451.
92 黄大吉，渤海正压和斜压动力过程的数值研究，青岛海洋大学博士相位论文，1995，10。
93 Bouttier F and Courtier P, Data Assimilation Concept and Methods training course. Notes of ECMWF. 2001.
94 盛华，纪立人。三维多元最优插值的区域性试验，气象学报，1991，49(5)：151-161。
95 李立，吴日升，李燕初等。TOPEX／POSEIDON高度计浅海潮汐混淆的初步分析，海洋学报，1999，21(3)：7-14。
96 懂晓军：利用TOPEX／POSEIDON卫星高度计资料提取黄海、东海潮汐的研究，交流资料。
97 Mike Fisher, Meteorological Training Course Lecture Series:
Assimilation techniques(3): 3dVar,2001,4,pp11.
98 Mike Fisher, Meteorological Training Course Lecture Series: Assimilation techniques(4): 4dVar, 2001, 4, pp9.
99 R.Delay. Atmospheric data analysis. Cambridge university press.1991.
100 Thiebaux, H.J.Anisotropic correction functions for objective analysis. Mon. Wea. Rev. 1976,104:994～1002
101 P.F.J. Lermusiaux, D.G.M. Anderson and C.J. Lozano. On the mapping of multivariate geophysical fields:Error and variability subspace estimates. (personal communication materials.), 1999,pp58.
102 Bennett. A.F.,B.S.Chua et al. Generalized inversion of a global numerical weather predication model. Meteorol. Atmos. Phys. 1995, 60 (1-3), 165-178.
103 张贤达，信号处理中的线性代数。北京：科学出版社，1997。
104 彭玉华，小波变换与工程应用．科学出版社，1999。
105 L.S.Gandian. The problem of optimal interpolation. Trudy Main Geophys. Obs. 1959,55,69-76.
106 L.S.Gandian. On optimal interpolation and extrapolation of meteorological fields. Trudy Main Geophys. Obs. 1960,114,75-89.
107 F.P.Bretheerton, J.C.McWilliams. Estimations from irregular array. Rev. Geophys. Space Phys. 1980,18,789-812.
108 J.Segschneider, J.Alves, D.Anderson, et al. Asssimilation of TOPEX/POSEIDON data into a seasonal forcast system. Phys. Chem. Earth(A). 1999, 24(4): 369-374.
109 杨晓霞，沈桐立，徐文金等。最优插值客观分析，南京气象学院学报，1991，14(4)：566-574。
110 潘晓斌，魏绍远，马华平等。逐次最优插值方案及其试验，气象科学，1996，16(1)：30-39
111 屠伟铭，张跃堂。全球最优插值客观分析，气象学报，1995，53(2)：148-156。
112 R.A.Akmaev. Aprototype upper-atmospheric data assimilation scheme based on optomal interpolation: 1. Theoty. Journal of Atmospheric and Solar-Terrestrial Physics. 1999, 61,491-504.
113 R.A.Akmaev. Aprototype upper-atmospheric data assimilation scheme based on optomal interpolation: 1. Numerical experiments. Journal of Atmospheric and Solar-Terrestrial Physics. 1999, 61, 505-517.
114 贾沛璋，朱征桃，最优估计及其应用，科学出版社，1984。
115 Thiebaux, H.J.Anisotropic correction functions for objective analysis. Mon. Wea. Rev. 1976,104:994～1002
116 李庆扬，王能超，易大义，数值分析，华中理工大学出版社，1982．
117 ROBINSON A R, LERMUSIAUX P F J , SLOAN N Q. Data Assimilation. The Global Coastal Ocean: Process and Methods. BRINK K.H , ROBINSON A R, Vol 10 of The Sea, Wiley New York, pp541-594.
118 黄大吉，陈宗镛，苏纪兰。三维陆架海模式在渤海中的应用Ⅰ。潮流、风生环流及其相互作用。海洋学报，1996，18(5)：1-13。
119 黄大吉，苏纪兰，陈宗镛。三维陆架海模式在渤海中的应用Ⅱ。温度的季节性变化。海洋学报，1996，18(6)：8-18。
120 马寨璞，黄大吉，章本照。应用SVD分解简化卡尔曼增益计算的理论研究。浙江大学学报(工学版)(已录用，待发表)。
121 PARRISH D P, COHN S.1985: A kalman filter for a two-dimensional shallow water model :formulation and preliminary experiments. Office Notes 304, washington, D.C.,National Meteorolcgical Center,64pp
122 徐士良。FORTRAN常用算法程序集。北京：清华大学出版社，1997。
123 S.Hoang, R.Baraille, O.Talagrand, X.Carton, P.De Mey. Adaptive filtering: application to satellite data assimilation in oceanography. Dynamics of Atmospheres and Oceans. 1997, 27,257-281.
124 Hoteit, D.Pham, J.Blum. A semi-evolutive partially local filter for data assimilation. Marine Pollution Bullrtin. 2001, 43(7-12), 164-174.
125 R.Canizares, H.Madsen, H.R.Jensen, H.J.Vested. Developments in operational shelf sea modeling in Danish waters. Estuarine, Coastal and Shelf Science. 2001, 53, 595-605.
126 A.R.Robinson, J.Sellschop, A.Warm-Varnas et al. The Atlantic lonian stream. Journal of Marine System. 1999, 20, 129-156.
127 P.F.J.Lermusiaux, A.R.Robinson. Data assimilation via error subspace statistical estimation Part Ⅰ: Theory and schemes. Monthly Weather Review. 1999, 127(7), 1385-1407
128 P.F.J.Lermusiaux, A.R.Robinson. Data assimilation via error subspace statistical estimation Part Ⅰ: Middle atlantic bight shelf break front simulations and ESSe validation. Monthly Weather Review. 1999, 127(7), 1408-1432.
129 P.F.J.Lermusiaux, D.G.M.Anderson, C.J.Lozano. On the mapping of multivariate geophysical fields error and variability subspace estimates. Personal communication materials. 1999,9 ,pp58．
130 P.F.J.Lermusiaux, Evoluing the subspace of the three dimansional multiscale ocean variability Massachasetts Bay. Journal of Marine System, 2000． Personal communication materials, pp56．
131 P.F.J.Lermusiaux, A.R.Robinson. Features of dominant mesoscale variability circulation patterns and dymnamics in the straight of Sicily. Deep Sea Reasearch. 2000,11, Personal communication materials, pp58．
132 P.F.J.Lermusiaux, Estimation and study of mesoscale variability in the straight of Sicily. Dynamics of Atmospheres and Ocean, 1999, 29,255-303．
133 A.R.Robinson, P.F.J.Lermusiaux, N.Q.Sloan, CHAPTER 20 :DATA ASSIMILATION, The Sea, Volume 10, pp541-595． John Wiley & Sons, Inc. 1998．
134 P.Barasseur, J.Ballabrera-Poy, J.Verron. Assimilation of altimetric data in the mid-latitude oceans using the singular evolutive extended kalman filter with an eddy-resolving primitive equation model. Journal of the Marine System. 1999, 22, 269-294．
135 J.Verron, J.Gourdeau, L.Pham, D.T.Murtugvdde, et al. An extended kalman filter to assimilate satellite aitimeter data into a non-linear numerical model of the tropical pacific: mode and validation. Journal of Geophysical Research,1999, 104(3) , 5441-5458．
136 V.Carmillet, J.M.Brankart. P.Barasseur, et al. A singular evolutive extended kalman filter to assimilate ocean color data in a coupled physical-biochemical model of the north Atlantic ocean. Ocean Modelling. 2001, 3, 167-192．
137 D.T.Pham, J.Verron, M.C.Roubaud. A singular evolutive edxtended kalman filter for data assimilation in oceanography. Journal of Marine System, 1998, 16, 323-340．
138 A.C.Vorrips, A.W.Hermink. G.J.Komen. Wave data assimilation with the kalman filter. Journal of Marine System. 1999, 19, 267-291．
139 Verlaan, M.Hermink, Data assimilation scheme for non-linear shallow water models in Rahman Brebbia. Personal communication materials,
1996．
140 Verlaan, M.Hermink, Tidal flow forecasting using reduced rank square root filters. Stochastic Hydr. Hydraul. 1997, 11, 249-368．
141 L.Bertino, G.Evensen, H.Wackernagel. Combining geostatistics and kalman filter for data assimilation in an estuarine system. Inverse Problems, 2002,18, 1-23
142 N.Hirore, I.Fukumori, J.H.Yoon. Assimilation of TOPEX/POSEIDON altimeter data with a reduced gravity model of the Japan Sea. Journal of Oceanography. 1999, 55, 53-64．
143 A.C. Mark, A.Kaplan, Miller R N et al, Mapping tropical Pacific sea level: Data assimilation via a reduced state space Kalman filter. J.Geophys.Res. 1996,101(c4) : 22599-22617．
144 K.A. Myers, B.D. Tapley. Adaptive sequential estimation with unknown noise statics, IEEE, Trans. Autom. Control, 1976,21(5) : 520-523．
145 D.P. Dee. Simplification of the Kalman filter for meteorological data assimilation, Q.J.R.Meterol. Soc, 1991, 117(4) : 365-384．
146 J.D. Annan, Hargreaves J C, Sea surface temperature assimilation for a three-dimensional baroclinic model of shelf sea. Continental shelf Research. 1999,19(3) : 1507-1520．
147 K.P. Belyaev, J.J. OBrien, P.A.Nobre. A data assimilation method used with an ocean circulation model and its application to the tropical Atlantic data analysis. Journal of Mathematical science. 2001, 106(2) , 2792-2802．
148 K.P. Belyaev, C.A.S.Tanajura, J.J. OBrien. A data assimilation used with an ocean circulation model and its application to the tropical Atlantic. Applied Mathematical Modelling. 2001, 25, 655-670．
149 S.Cohn, D.F.Parrish. The behavior of frocast error covariance foe a kalman filter in two dimensions. Monthly Weather Review. 1991, 119(8) , 1757-1785．
150 R.N.Miller, M.A.Cane. A kalman filter analysis of sea level height in the tropical Pacific. Journal of Physical Oceanography. 1989, 19(6) , 773-790．
151 L.L.Fu. I.Fukumori, R.N.Miller. Fitting dynamic models to the great sea level observations in the tropical Pacific Ocean, Part II: A linear
wind-driven model. Journal of Physical Oceanography, 1993, 23, 2162-2168.
152 R.N.Miller. Tropical data assimilation experiments with simulated data: The impact of the tropical ocean and global atmosphere thermal array for the ocean. Journal of Geophysical Research. 1990, 95(7), 11461-11482.
153 张占海，吴辉碇。渤海潮汐和潮流数值计算，海洋预报，1994，11(2)：48～54。
154 孙洪亮，黄卫民。广西近海潮汐和海流的观测分析与数值研究——Ⅰ．观测与分析，黄渤海海洋，2001，19(4)：1～11。
155 孙洪亮，黄卫民。广西近海潮汐和海流的观测分析与数值研究——Ⅱ．数值研究，黄渤海海洋，2001，19(4)：12～21。
156 孙洪亮，黄卫民。北部湾潮汐潮流的三维数值模拟，海洋学报，2001，23(2)：1～8。
157 赵保仁，曹德明，李徽翡，王其茂。渤海的潮混合特征及潮汐锋现象，海洋学报，2001，23(4)：113～120
158 方国洪，杨景飞。渤海潮运动的一个二维数值模型。海洋与湖沼，1985，16(5)：337～346。
159 赵保仁，方国洪，曹德明。渤、黄、东海三维潮波运动数值模拟。海洋与湖沼，1998，29(6)：611～616。
160 杨陇慧，朱建荣，朱首贤。长江口杭州湾及邻近海区潮汐潮流场三维数值模拟，华东师范大学学报，2001，3，74～84。
161 朱玉荣。末次冰消期以来渤、黄、东海陆架潮汐、潮流演变过程模拟研究，青岛海洋大学学报，2002，32(2)：279～286。
162 林楚平。海山潮汐能的综合开发利用，水利水电技术，1999，30(1)。
163 邵守良，张锦文。港口工程设计中的一些潮汐计算问题，港工技术，2001，4，4～5，31。
164 熊绍隆，胡玉棠。潮汐河口悬移质动床实物模型的理论与实践，泥沙研究，1999，1。
165 华祖林，褚克坚。基于三角形网格的潮汐水域水流水质的一种计算模式，河海大学学报，2001，29(4)：31～37。
166 王东晓，朱江。伴随方法在海洋数值模式中的应用，地球物理进展，1997，12(1)：98～107。
167 兰健。资料同化中的伴随方法及其在海洋中的应用，青岛海洋大学学报，1998，28(2)：174～178。
168 吕咸青，刘文剑。数据同化中的伴随方法及其有关问题的研究，海洋科学，2001，25(3)：44～50。
169 马刚，邱崇践，王强。用变分法修正边界层资料的数值试验，气象学报，2001，59(1)：107～113。
170 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)：13～19。
171 吕咸青，方国洪。渤海开边界潮汐的伴随法反演，海洋与湖沼，2002，33(2)：113～120。
172 韩桂军，何柏荣，马继瑞，刘克休，李冬。利用伴随法优化非线性潮汐模型的开边界条件Ⅰ：伴随方程的建立及其“孪生”数值试验，海洋学报，2000，22(6)：134～140。
173 韩桂军，方国洪，马继瑞，刘克休，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。
174 朱江，曾庆存，郭冬建，刘卓。利用伴随算子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。
175 李培良，左军成，李磊，黄娟。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。
176 暴景阳，晁定波，李建成，邓晓丽。由T／P卫星测高数据建立南中国海潮汐模型的初步研究，武汉测绘科技大学学报，1999，24(4)：
177 董晓军，马继瑞，黄珹，范振华，韩桂军，许崇金。利用TOPEX／Poseidon卫星高度计资料提取黄海、东海潮汐信息的研究，海洋与湖沼，2002，33(4)：386～392。
178 毛庆文，施平，齐义泉。运用调和分析方法分离卫星高度计资料中的潮汐信息。海洋工程，2002，20(1)：41～45。
179 李立，吴日升，李燕初，甘子钧。TOPEX／POSEIDON高度计浅海潮汐混淆的初步分析，海洋学报，1999，21(3)：7～14。
180 暴景阳，晁定波，李建成。南中国海TOPEX／POSEIDON轨迹交叉点测高数据的潮汐调和分析，测绘学报，2000，29(1)：17～23。
181 刘克休，马继瑞，韩桂军，范振华，许崇金。引入差比法分析西北太平洋TOPEX／POSEIDON卫星高度计测高数据。海洋学报，2002，24(4)：1～10。