MM5－卫星数据变分同化方法及气象预报应用研究
|
摘要
海洋气象研究中，特别是业务预报中使用各种非常规观测数据和各种迅速发展的大气数据同化方法，已经在全世界引起了越来越大的关注和重视。充分利用非常规资料，提高对非常规资料的同化能力已成为迫在眉睫的问题。“十·五”国家重点科技攻关项目“海洋环境预报与减灾技术”中把海洋气象数值预报及资料同化方法的研究列入重点内容。本论文的任务正是基于此背景，而开展对卫星气象数据同化方法及其应用的研究，寻求同MM5中尺度气象模式业务预报相结合的数据同化方法，为海洋环境预报服务。提高非常规资料的同化质量及应用水平关系到气象预报的未来，而非常规资料的同化利用也是未来数值天气预报的希望所在。很明显，本论文的研究具有重大的实用价值和现实意义。
本论文建立了基于Sasaki增广Lagrange算子算法并和MM5中尺度模式相结合的二维变分同化系统。地球同步卫星(Geostationary Meteorological Satellite(GMS-5))的红外和水汽轨迹风数据及来自NOAA极轨卫星的TOVS(TIROS Operational Vertical Sounder)温、湿数据作为观测资料，经过MM5模式的质量控制而最终进入该同化系统。使用该二维变分同化系统，对2002年发生的三个台风进行了同化卫星数据的数值模拟实验，并对模拟结果同三维观测松弛逼近等数据同化方法对台风路径影响做了比较分析。同时也对各同化方法同化不同卫星数据对台风的影响进行了比较分析。结果表明：所发展建立的二维变分同化系统发挥了应有的作用，也不同程度的改善了台风路径的数值模拟结果。选用现有不同卫星数据进行同化对台风路径的影响不同，但都在一定程度上改善了模拟的结果。虽然二维变分数据同化系统同化各卫星数据对台风模拟实验的结果，不如使用三维观测松弛逼近同化方法的效果好。但就所有的同化实验整体而言，台风路径误差在模式积分24时和48时分别减小约5％和10.5％，对单个台风路径误差可减少30％-50％。另外，即使只是使用很简单的同化方案，如卫星资料仅作为观测资料而被吸收到模式的初始场中，都会对模拟结果产生正面的影响。值得一提的是所发展建立的二维数据同化方法原理简单，计算快捷而稳定，而且易于应用到各种相关领域数据同化的研究中。
本论文接着改进和发展了由国家数值预报中心引进的，基于增量法和Delpha工作站平台的三维变分同化系统。所发展的三维变分同化系统以MICAPS(气象信息综合分析处理系统，由中国国家气象局和中国气象科学研究院共同研制)
T213为背景场并同入D涯5模式相结合。该同化系统有同化GMS一5的红外和水汽
轨迹风数据和TOVS温湿数据的能力并可在PC机的Linux系统下顺利运行。使
用所改进的同ND涯5模式相结合的三维变分同化系统，对以台风为代表的天气现
象进行了数值模拟实验，并检验了该同化系统的同化能力。对文中所用N伍15数
值模式所产生的初始场和三维变分同化系统生成的初始场进行了比较和分析。分
析比较初始风场、初始位势高度场、初始相对湿度场和台风周围分布的探空站的
探空曲线后的结果表明:在三维变分同化后各模式物理量之间更加协调，更加符
合实际观测。三维变分数据同化系统同化卫星数据后，所形成的初值场是合理和
正确的。
在初始场形成的较详细地比较和分析的基础之上，最后本论文进行了三维变
分数据同化系统同化卫星数据对台风影响的数值模拟实验结果的比较分析研究。
在对三维变分实验与对应控制实验的风场、位势高度场、相对湿度场和几个探空
站探空曲线的模拟结果，及对所模拟的台风路径和路径的偏差比较分析研究的基
础上，得到如下结果:各模式物理量之间在三维变分数据同化后的分布，在动力
上和物理上都更加协调和合理，更加符合实际观测。三维变分数据同化方法能明
显减小台风路径的模拟偏差，即使模式积分48小时台风路径的偏差改善也多达
50%。平均而言，同控制实验相比，台风路径偏差改善在模式积分24时为49%，
48时达到了56%。对单个台风，路径误差的改善更大。对台风路径的预报来说，
这是很令人鼓舞的消息。值得注意的是即使所模拟的台风是发生转向的台风，其
路径的改善也是明显的。同时使用该三维变分同化系统，比较分析了使用三维变
分同化方法仅同化常规观测数据的模拟结果和使用文中所用Nl五遭5模式同化方法
进行数值模拟的结果，分析结果表明在其它条件相同的情况下，前一种实验的模
拟效果远好于后一种实验，这也证实了变分方法的确比一般的客观分析方法优
越。
本论文发展、改进和建立的二维和三维变分数据同化方法有很普遍的适用
性。把二维变分和三维变分同化方法应用到类似M入15中尺度模式的模式系统中
也具有比较现实的意义。这两种数据同化系统中增加新类型的数据是极其方便和
快捷的;适用于海洋上发生的各种海洋天气现象的数值预报和模拟研究;而且就
计算量和所需的计算时间而言，在数值业务预报所容忍的范围之内。在地方级气
象台所能获取的卫星等非常规数据种类和数量都逐渐增加的前提和背景下，使用
本论文所建立的基于入D涯5模式的三维变分数据同化系统，对科研投资有限而无
法购买昂贵的高
Greater and greater concern and attention in the whole world has focused on using all kinds of non-routinely observed data and data assimilation methods that have developed very quickly in marine atmospheric research, especially in operational forecast. It has become a very urgent problem to use asynoptic data and improve the capability to assimilate data. The research on marine atmospheric numerical forecast and data assimilation methods are very important parts in the project of "marine environmental forecasting and natural disasters reducing technology", which belongs to the national key scientific projects of tenth five-year. The study of the thesis is based on such background to carry out the satellite data assimilation methods connected with MM5 mesoscale meteorology model operational forecast, and to serve for the marine environmental forecast and prediction. It is very clearly that the study of the thesis has important practical value and realistic meaning.
A two-dimensional variational (2DVar) data assimilation system connected with MM5 model is set up which based on the augmented Lagrangian algorithm of Sasaki. The Geostationary Meteorological satellite (GMS-5) derived wind data from infrared and water vapor images and TIROS Operational Vertical Sounder (TOYS) temperature and humidity data enter the assimilation system after the quality control of MM5 model. Then, the numerical simulation experiments with satellite assimilation are launched on three typhoons in 2002 using the 2DVar data assimilation system. The comparison analysis with other data assimilation methods, such as Nudging, is also going on the simulation results to typhoon track influence. The assimilation influence on typhoon track with different satellite data is also compared. The results show that the 2DVar assimilation scheme really takes effect and improves the numerical simulation results more or less. The typhoon track errors at model integral 24 hours and 48 hours reduce about 5% and 10.5%, respectively. Though numerical simulation experiments of typhoon processes using 2DVar data assimilation system is not so good as that of the Nudging method. In addition, even using very simple assimilation methods to assimilate satellite data, the positive influence will happen to the simulation results. The 2DVar assimilation scheme used here with
simple theory and numerical stability can be very easily applied to many relevant data assimilation fields.
A three-dimensional variation (SDVar) system is successfully combined with MM5, which based on the original version of National numerical prediction center. The present version runs smoothly on a PC with Linux operation system rather than on Delpha workstation and using MICAPS (Meteorological Information Composite Analysis Processing system, by CNMC and CAMPS) T213 data as background. The 3DVar data assimilation system has the ability to assimilate GMS-5 cloud drifted winds and TOYS data. The numerical simulation experiments of typhoon processes are carried out using the 3DVar data assimilation system. After comparing the initial wind, geopential height, relative humidity and the sounding profiles of temperature and humidity at several sounding stations between the original MM5 assimilation scheme and the 3DVar assimilation system, some conclusions are drawn: the relationship among model variables becomes more harmony and more close to observations. The initial field formed by 3DVar system is right and reasonable. The study on the numerical simulation experiments to typhoon processes using 3DVar assimilation system also carries out. The conclusions are drawn after comparing the wind field, geopential height, relative humidity and several sounding profiles at sounding stations between control experiment and 3DVar data assimilation experiments. The results show that the model variables are more harmony in dynamic and physics to the experiments of 3DVAR assimilation. The simulated track errors obviously reduce using the 3DVar assimilation scheme, even to recurvature typhoon.
The 2DVar a
本论文建立了基于Sasaki增广Lagrange算子算法并和MM5中尺度模式相结合的二维变分同化系统。地球同步卫星(Geostationary Meteorological Satellite(GMS-5))的红外和水汽轨迹风数据及来自NOAA极轨卫星的TOVS(TIROS Operational Vertical Sounder)温、湿数据作为观测资料，经过MM5模式的质量控制而最终进入该同化系统。使用该二维变分同化系统，对2002年发生的三个台风进行了同化卫星数据的数值模拟实验，并对模拟结果同三维观测松弛逼近等数据同化方法对台风路径影响做了比较分析。同时也对各同化方法同化不同卫星数据对台风的影响进行了比较分析。结果表明：所发展建立的二维变分同化系统发挥了应有的作用，也不同程度的改善了台风路径的数值模拟结果。选用现有不同卫星数据进行同化对台风路径的影响不同，但都在一定程度上改善了模拟的结果。虽然二维变分数据同化系统同化各卫星数据对台风模拟实验的结果，不如使用三维观测松弛逼近同化方法的效果好。但就所有的同化实验整体而言，台风路径误差在模式积分24时和48时分别减小约5％和10.5％，对单个台风路径误差可减少30％-50％。另外，即使只是使用很简单的同化方案，如卫星资料仅作为观测资料而被吸收到模式的初始场中，都会对模拟结果产生正面的影响。值得一提的是所发展建立的二维数据同化方法原理简单，计算快捷而稳定，而且易于应用到各种相关领域数据同化的研究中。
本论文接着改进和发展了由国家数值预报中心引进的，基于增量法和Delpha工作站平台的三维变分同化系统。所发展的三维变分同化系统以MICAPS(气象信息综合分析处理系统，由中国国家气象局和中国气象科学研究院共同研制)
T213为背景场并同入D涯5模式相结合。该同化系统有同化GMS一5的红外和水汽
轨迹风数据和TOVS温湿数据的能力并可在PC机的Linux系统下顺利运行。使
用所改进的同ND涯5模式相结合的三维变分同化系统，对以台风为代表的天气现
象进行了数值模拟实验，并检验了该同化系统的同化能力。对文中所用N伍15数
值模式所产生的初始场和三维变分同化系统生成的初始场进行了比较和分析。分
析比较初始风场、初始位势高度场、初始相对湿度场和台风周围分布的探空站的
探空曲线后的结果表明:在三维变分同化后各模式物理量之间更加协调，更加符
合实际观测。三维变分数据同化系统同化卫星数据后，所形成的初值场是合理和
正确的。
在初始场形成的较详细地比较和分析的基础之上，最后本论文进行了三维变
分数据同化系统同化卫星数据对台风影响的数值模拟实验结果的比较分析研究。
在对三维变分实验与对应控制实验的风场、位势高度场、相对湿度场和几个探空
站探空曲线的模拟结果，及对所模拟的台风路径和路径的偏差比较分析研究的基
础上，得到如下结果:各模式物理量之间在三维变分数据同化后的分布，在动力
上和物理上都更加协调和合理，更加符合实际观测。三维变分数据同化方法能明
显减小台风路径的模拟偏差，即使模式积分48小时台风路径的偏差改善也多达
50%。平均而言，同控制实验相比，台风路径偏差改善在模式积分24时为49%，
48时达到了56%。对单个台风，路径误差的改善更大。对台风路径的预报来说，
这是很令人鼓舞的消息。值得注意的是即使所模拟的台风是发生转向的台风，其
路径的改善也是明显的。同时使用该三维变分同化系统，比较分析了使用三维变
分同化方法仅同化常规观测数据的模拟结果和使用文中所用Nl五遭5模式同化方法
进行数值模拟的结果，分析结果表明在其它条件相同的情况下，前一种实验的模
拟效果远好于后一种实验，这也证实了变分方法的确比一般的客观分析方法优
越。
本论文发展、改进和建立的二维和三维变分数据同化方法有很普遍的适用
性。把二维变分和三维变分同化方法应用到类似M入15中尺度模式的模式系统中
也具有比较现实的意义。这两种数据同化系统中增加新类型的数据是极其方便和
快捷的;适用于海洋上发生的各种海洋天气现象的数值预报和模拟研究;而且就
计算量和所需的计算时间而言，在数值业务预报所容忍的范围之内。在地方级气
象台所能获取的卫星等非常规数据种类和数量都逐渐增加的前提和背景下，使用
本论文所建立的基于入D涯5模式的三维变分数据同化系统，对科研投资有限而无
法购买昂贵的高
Greater and greater concern and attention in the whole world has focused on using all kinds of non-routinely observed data and data assimilation methods that have developed very quickly in marine atmospheric research, especially in operational forecast. It has become a very urgent problem to use asynoptic data and improve the capability to assimilate data. The research on marine atmospheric numerical forecast and data assimilation methods are very important parts in the project of "marine environmental forecasting and natural disasters reducing technology", which belongs to the national key scientific projects of tenth five-year. The study of the thesis is based on such background to carry out the satellite data assimilation methods connected with MM5 mesoscale meteorology model operational forecast, and to serve for the marine environmental forecast and prediction. It is very clearly that the study of the thesis has important practical value and realistic meaning.
A two-dimensional variational (2DVar) data assimilation system connected with MM5 model is set up which based on the augmented Lagrangian algorithm of Sasaki. The Geostationary Meteorological satellite (GMS-5) derived wind data from infrared and water vapor images and TIROS Operational Vertical Sounder (TOYS) temperature and humidity data enter the assimilation system after the quality control of MM5 model. Then, the numerical simulation experiments with satellite assimilation are launched on three typhoons in 2002 using the 2DVar data assimilation system. The comparison analysis with other data assimilation methods, such as Nudging, is also going on the simulation results to typhoon track influence. The assimilation influence on typhoon track with different satellite data is also compared. The results show that the 2DVar assimilation scheme really takes effect and improves the numerical simulation results more or less. The typhoon track errors at model integral 24 hours and 48 hours reduce about 5% and 10.5%, respectively. Though numerical simulation experiments of typhoon processes using 2DVar data assimilation system is not so good as that of the Nudging method. In addition, even using very simple assimilation methods to assimilate satellite data, the positive influence will happen to the simulation results. The 2DVar assimilation scheme used here with
simple theory and numerical stability can be very easily applied to many relevant data assimilation fields.
A three-dimensional variation (SDVar) system is successfully combined with MM5, which based on the original version of National numerical prediction center. The present version runs smoothly on a PC with Linux operation system rather than on Delpha workstation and using MICAPS (Meteorological Information Composite Analysis Processing system, by CNMC and CAMPS) T213 data as background. The 3DVar data assimilation system has the ability to assimilate GMS-5 cloud drifted winds and TOYS data. The numerical simulation experiments of typhoon processes are carried out using the 3DVar data assimilation system. After comparing the initial wind, geopential height, relative humidity and the sounding profiles of temperature and humidity at several sounding stations between the original MM5 assimilation scheme and the 3DVar assimilation system, some conclusions are drawn: the relationship among model variables becomes more harmony and more close to observations. The initial field formed by 3DVar system is right and reasonable. The study on the numerical simulation experiments to typhoon processes using 3DVar assimilation system also carries out. The conclusions are drawn after comparing the wind field, geopential height, relative humidity and several sounding profiles at sounding stations between control experiment and 3DVar data assimilation experiments. The results show that the model variables are more harmony in dynamic and physics to the experiments of 3DVAR assimilation. The simulated track errors obviously reduce using the 3DVar assimilation scheme, even to recurvature typhoon.
The 2DVar a
引文
[1] Achtemeier, G.C. On the initialization problem: a variational adjustment method. Mon. Wea. Rev., 1975, 103: 1089-1103
[2] Aitken, A. Statistical Mathematics. Oliver and Boyd Ltd., Edinburgh, 7 edition. 1939
[3] Andersson, E., J. Haseler, P. Unden, P. Courtier et. al. The ECMWF implementation of three dimensional variational assimilation(3D-Var). Ⅲ: experimental results. Q. J. Roy. Meteorol. Soc. 1998, 124: 1831-1860
[4] Andersson, E., J. Pailleux, J.-N. Thepaut, J. R. Eyre, A. P. McNally, G. A. Kelly, and P.Coutier. Use of cloud cleared radiances in three/four-dimensional variational data assimilation. Q. J. Roy. Meteorol. Soc. 1994, 120: 627-653
[5] Barnes, S. L. Mesoscale objective analysis using weighted time-series observations. NOAA technical Memorandum ERL NSSL-62． Environmental Research Laboratories, National Severe Storms Laboratory, Norman, Okla.1973, 60pp
[6] Bergthorsson, P. and Doos, B. Numerical weather map analysis. Tellus, 1955, 7: 329-340
[7] Bouttier, F. Kalman filtering. Meteorological training course lecture series, ECMWF. 1997
[8] Charney, J. The use of the primitive equations of motion in numerical prediction. Tellus, 1955, 7: 22-26
[9] Charney,J.,M. Halem and R. Jastrow. Use of incomplete historical data to infer the present state of the atmosphere. J. Atmos. Sci., 1969, 26: 1160-1163
[10] Cohn S., A. DA Silva, J. GUO. M. Sienkiewicz and D. lamicah. Assessing the effects of data selection in the DAO Physical-Space Statistical Analysis System. Mon. Wea. Rev., 1998, 126: 2913-2926
[11] Cohn S. E, Parrish D. P. The behavior of forecast error covariances for a Kalman filter in two dimensions. Mon. Wea. Rev., 1991,119: 1757-1785
[12] Courtier, P. Dual formulation of 4d-var assimilation. Q. J. R. Meteorol. Soc, 1997, 123: 2449-2461
[13] Courtier, P, E. Andersson, W. Heckley, G. Kelly, J. Pailleux, F. Rabier, J.-N. Thepaut, P. Unden, D. Vasiljevic, C. Cardinali, J. Eyre, M. Hamrud, J. Haseler, A. Hollingsworth, A. McNally,and A. Stoffelen. Variational assimilation at ECMWF. ECMWF Tech. Mem. 1993, 194
[14] Courtier P. E. Andersson, W. Heckley, J. Pailleux, D. Vasiljevic, M. Hamrud, Hollingsworth, A., Rabier, F. and Fisher, M. The ECMWF implementation of three dimensional variational assimilation (3D-Var). I: Formulation. Q. J. R. Meteorol. Soc., 1998,124: 1783-1807
[15] Courtier, P., Thepaut, J.-N. and Hollingsworth, A. A strategy for operational implementation of 4D-Var, using an incremental approach. Q. J. R. Meteorol. Soc., 1994,120:1367-1387
[16] Cressman. An operational objective analysis system. Mon. Wea. Rev., 1959, 87: 367-374
[17] Daley R. Atmospheric data analysis. Cambridge: Cambridge university press, 1991．
[18] Dee D P. Simplification of the Kalman filter for meteorological data assimilation. Q. J. R. Meteorol. Soc, 1991, 117: 365-384
[19] Derber, J. Variational four-dimensional analysis using quasi-geostrophic constraints. Mon. Wea. Rev., 1987,115: 998-1008
[20] Desroziers, G., Pouponneau, B., Thepaut, J., Janiskova, M., and Veerse, F. Four-dimensional variational anlayses of faster situations using special observations. Q. J. R. Meteorol. Soc., 1999,125:3339-3358
[21] Ehrendorfer M. Four-dimensional data assimilation: comparison of variational and sequential algorithms. Q. J. R. Meteorol. Soc., 1992,118: 673-713
[22] Ehrendorfer, M. and Tribbia, J. Optimal prediction of forecast error covariances through singular vectors. J. Atmos. Sci., 1997,54: 286-313
[23] Eliassen A. Provisional report on calculation of spatial covariance and autocorrelation of the pressure field. Rep. No. 5, 1954．
[24] Errico, F. M. What is an adjoint modei. Bull. Amer. Meteorol. Soc., 1997,2577-2591．
[25] Errico, R., T. Vukicevic and K. Raeder. Examination of the accuracy of a tangent linear model. Tellus, 1993, 45A: 462-477
[26] Errico, R. and T. Vukicevic. Sensitivity Analysis using an Adjoint of the PSU-NCAR Mesoscale Modei. Mon. Wea. Rev., 1992,120: 1644-1660
[27] Evensen G, Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model. J. Geophys. Res., 1992,97: 17 905-17 904
[28] Evensen G. Sequential data assimilation with a nonlinear quasigeostrophic modei using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 1994,99(C5) : 10 143-10 612
[29] Evre. J. R. Inversion of cloud satellite sounding radiances by nonlinear optimal estimation. Ⅰ; Theory and simulation of TOVS. Q. J. R Meteorol. Soc. 1989a, 115: 1001-1026
[30] Eyre. J. R. Inversion of cloud satellite sounding radiances by nonlinear optimal estimation. Ⅱ: Application to TOVS data. Q. J. R. Meteorol. Soc. 1989b, 115: 1027-1037
[31] Eyre, J. R. G. Kelly, A. P. McNally, E. Andersson, and A. Persson. Assimilation of TOVS radiances through one-dimensional variational analysis. Q. J. Roy. Meteorol. Soc., 1993, 119: 1427-1463
[32] Fisher, M. Development of a simplified kalman filter. Meteorological training course lecture
series, ECMWF. 1998
[33] Gaffard, C., and H.Roquet. Impact of the ERS-1 scatterometer wind data on the ECMWF 3D-VAR assimilation system. ECMWF Research Department Tech. Memo. 1995,217, 21pp.
[34] Gandin, L. (1963) . Objective analysis of meteorological fields(Leningrad: Gridromet). English translation (Jerusalem: Israel Program for Scientific Translation), 1965．
[35] Ghil, M. Meteorological Data Assimilation for Oceanographers. Part Ⅰ: Description and Theoretical Framework. Dyn. of Atmos. Oceans, 1989, 13: 171-218
[36] Ghil, M. and Malanotte-Rizzoli, P. Data assimilation in meteorology and oceanography. Advances in Geophysics, 1991, 33: 141-266．
[37] Gichrist B, Cressman G. An experiment in objective analysis. Tellus, 1954, 6: 309-318
[38] Gordin, V. A. Variational adjustment of meteorological fields. Soviet Meteorology and Hydrology. 1977, 12: 95-96
[39] Goerss, J S. The impact of multispectral GOES-8 wind information on Atlantic tropical cyclone track forecasts in 1995． Part Ⅱ: NOGAPS forecast. Mon. Wea. Rev., 1998, 126: 1219-1227
[40] Griffith, A. Data Assimilation for Numerical Weather Predicition using Control Theory. Ph.D. thesis, University of Reading. 1997
[41] Hestenes, M. R. and Stieffel. Methods of conjugate-gradients for solving linear systems. J. Res. Natl. Bur. Stand., 1952, 48: 409-436
[42] Hestenes, M. R. Conjugate directions methods in optimization. Applications of Mathematics, 1980, 12: Springer-Verlag, 325 pp.
[43] Hayden, C. M. and R J. Purser. Recursive filter objective analysis of meteorological fields: applications to NESDIS operational processing. J. Appl. Meteorol., 1995,34: 3-15
[44] Hinkelmann k. Ein numerisches experiment mit den primitiven gleichungen. New York: Rockefeller Institute Press, 1959,486-500
[45] Hoffman, R. N. A four-dimensional analysis exactly satifying equations of motion. Mon. Wea. Rev., 1986,114: 388-397
[46] Hollingsworth, A. and Lonnberg, P.The statistical structure of short-range forecast errors as determined from radiosonde data. part i: the wind field. Tellus, 1986, 38A: 111-136
[47] Jazwinski, A. Stochastic Processes and Filtering Theory. Academic Press. 1970．
[48] Jones R H. Optimal estimation of initial conditions for numerical prediction. J. Atmos. Sci., 1965,22: 658-663
[49] Julian, P. and Thiebaux, H. On some properties of correlation functions used in optimum interpolation schemes. Mon. Wea. Rev., 1975,103: 605-616
[50] Kalman R. E. A new approach to linear filtering and prediction problems. Transaction of the ASME, J. of Basic Engineering, 1960, 82D: 34-45
[51] Kalman R. E, Bucy R. New results in linear filtering and prediction. Transaction of the ASME, J. of Basic Engineering, 1961, 83D: 95-108
[52] Kistler, R. E. A study of data assimilation techniques in an autobarotropic primitive equation channel model. M.S. thesis, The Pennsylvania State University, 1974, 84pp.[Available from the Dept. of Meteorology, The Pennsylvanin State University,Univeristy Park, PA 16802]
[53] LeDimet, F. and Talagrand, O. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus, 1986,38A: 97-110
[54] Le Marshall, J. E, L. M. Leslie and A. F. Bennett. Tropical cyclone Beti-an example of the benefits of assimilation hourly satellite wind data. Aust. Meteor. Mag., 1996,45: 275-278
[55] Le Marshall, J. F. Cloud and water motion vectors in tropical cyclone track Forecasting-A Review. Meteorol., Atmos. Phys., 1998, 65(3-4) : 141-151
[56] Lewis J. M. Dynamical adjustment of 500mb vorticity using P. D. Thompson's scheme: a case study. Tellus, 1980,32: 511-524
[57] Lorenc, A. Analysis methods for numerical weather prediction. Q. J. Roy. Meteorol. Soc., 1986, 112: 1177-1194
[58] Lorenc, A. C. Iterative analysis using covariance functions and filters. Q. J. R. Meteorol. Soc.,1992, 118:569-591．
[59] Lorenc, A. C., R. S. Bell and B. MacPherson. The meteorological office analysis correction data assimilation scheme. Q. J. R. Meteorol. Soc., 1991, 117: 59-89
[60] Lorenc, A. C., S. P. Ballard, R. S. Bell, N. B. Ingleby, P. L. F. Andrews, D. M. Barker, J. R. Bray, A. M. Clayton, T. Dalby, D. Li, T. J. Payne, and F. W. Saunders. The Met. Office global three-dimensional variational data assimilation scheme. Q. J. R. Meteorol. Soc., 2000, 126: 2991-3012
[61] Mahfouf, J.-F. Analysis of soil moisture from near-surface paramenter: a feasibility study. J Appl. Meteorol. 1991, 30: 1534-1547
[62] Monin, A. Obukhov. A note on the general classification of motions in a baroclinic atmosphere. Tellus, 1959, 11: 159-162
[63] Nuss, Titley. Use of multiquadric interpolation for meteorological objective analysis. Mon. Wea. Rev., 1994,122: 1611-1631
[64] O'Brien, J. J. Alternative solution to the classical vertical velocity problem. J. Appl. Metrorol., 1970,9: 197-203
[65] Philips N A. The spatial statistics of random geostrophic modes and first-guess errors. Tellus, 1986, 38A: 314-322
[66] Parrish, D. and Derber, J. The national meteorological center's spectral statistical-interpolation analysis system. Mon. Wea. Rev., 1992,120: 1747-1763
[67] Phillips N A. The spatial statistics of random geostrophic modes and first-guess errors. Tellus, 1986, 38A: 314-322
[68] Rabier, F. and P. Bernardet. Variational analysis of orographic waves. Beitr. Phys. Atmos. 1991, 64: 207-217
[69] Rabier, E, McNally, A., Andersson, E., Courtier, P, Unden, P, Eyre, J., Hollingsworth, A., and Bouttier, F. The ECMWF implementation of three dimensional variational assimilation (3D-Var). Ⅱ: structure functions. Q. J. R. Meteorol. Soc., 1998, 124: 1809-1829
[70] Rabier, F., Thepaut, J., and Courtier, P. Extended assimilation and forecast experiments with a 4d var assimilation system. Q. J. R. Meteorol. Soc., 1998, 124: 1861-1887
[71] Rutherford, I.. Experiments in the updating of P. E. forecasts with real wind and geopotential data. Preprint, Third Conference on probability and Statistics in Atmospheric Science. Boston, Amer. Meteorol. Soc., 1973, 198-201
[72] Sasaki, Y. An objective analysis based on the variational method. J. Meteorol. Soc. Japan, 1958,36: 77-88
[73] Sasaki, Y. Some basie formalisms in numerical variational analysis. Mon. Wea. Rev., 1970, 98: 875-883
[74] Sasaki, Y. Numerical variational analysis formulated under the constraints as determined by longwave equations and a low-pass filter. Mon. Wea. Rev., 1970, 98: 884-898
[75] Sasaki. Y. Numerical variational analysis with weak constraint and application to surface analysis of severe storm gust. Mon. Wea. Rev., 1970,98: 899-910
[76] Shiryaev, A. Kolmogorov:life and creative activities. The Annals of Probability, 1989, 17(3) : 866-944
[77] Soden, B J, Velden, C. S. and Tuleya R E. The impact of satellite winds on experimental GFDL hurricane modei forecasts. Mon. Wea. Rev., 2001, 129: 835-852
[78] Stephens J. J. A varaitional approach to numerical weather prediction. Rep. No. 3, Atmos. Sci., Group, The University of Texas, Austin, USA, 1965,243pp.
[79] Stephens J. Variational initialization with the balance equation. J. Appl. Meteorol., 1970, 9: 732-739
[80] Stephens J. J. and K. W. Johnson. Middle-large-scale variational adjustment of atmospheric fields in mesoscale diagnostic numerical variational analysis models. Final report, Deparment of meteorology, Florida State Univ., 1978,1-38
[81] Stauffer, D. R. and N. L. Seaman. Use of four-dimensional data assimilation in a limited-area mesoscale modei. Part I: Experiments with synoptic-scale data. Mon. Wea. Rev., 1990, 118:
1250-1277
[82] Stauffer, D. R., N. L. Seaman and F. S. Binkowski. Use of four-dimensional data assimilation in a limited-area mesoscale modei. Part Ⅱ: Effects of data assimilation within the planetary boundary layer. Mon. Wea. Rev., 1991, 119: 734-754
[83] Thompson P A dynamical method of analyzing meteorological data. Tellus, 1969, 13: 334-349
[84] Thepaut, J., Courtier, P, Belaud, G., and Lemaitre, G. Dynamical structure functions in 4d variational assimilation: A case study. Q. J. R. Meteorol. Soc., 1996,122: 535-561
[85] Thepaut, J., Hoffman, R., and Courtier, P. Interactions of dynamics and observations in a 4d variational assimilation. Mon. Wea. Rev., 1993, 121: 3393-3414
[86] Todling, R. and Cohn, S. Suboptimal schemes for atmospheric data assimilation based on the kalman filter. Mon. Wea. Rev., 1994, 122: 2537-2557
[87] Tomassini, M. D. LeMeur, and R. W. Saunders. Near-surface satellite wind observations of hurricane and their impact on ECMWF modei analysis and forecasts. Mon. Wea. Rev., 1998,126: 1274-1286
[88] Z. Li and I. Navon. Optimality of 4d var and its relationship with the kalman filter and smoother. Q. J. R. Meteorol. Soc., 2001,127(572) : 661-683
[89] Velden, C.S., Winds Derived from geostationary satellite moisture channel observations: applications and impact on numerical weather prediction. Meteorol., Atmos. Phys., 1996, 60: 37-46
[90] Velden, C.S., C. Hayden, S. Nieman, W. P. Menzel, S. Wanzong and J Goerss. Upper-tropospheric winds derived from geostationary satellite water observations. Bull. Amer. Meteorol. Soc., 1997, 77: 173-195
[91] Velden, C. S., Olander, T L and Wanzong S. The impact of multispectral GOES-8 wind information on Atlantic tropical cyclone track forecasts in 1995． Part Ⅰ: dataset methodology, description, and case analysis. Mon. Wea. Rev., 1998, 126: 1202-1218
[92] Washington, W. A note on the adjustment towards geostrophic equilibrium in a simple fluid system. Tellus, 1964,16, 530-534
[93] Wahba, G. and J. Wendelberger. Some new mathematical methods for variational analysis using splines and cross-validation. Mon. Wea. Rev., 1980, 108: 1122-1143
[94] Wergen,W. The effect of modei errors in variational assimilation.Tellus, 1992, 44A: 297-313
[95] Wiener, N. Extrapolation, interpolation and smoothing of stationary time series: with engineering applications. MIT Press and John Wiley and Sons.,1949
[96] Williamson, D. and A. Kasahara, 1971:Adaptation of meteorological variables forced by updating. J. Atmos. Sci., 28, 1313-1324
[97]Wunsch, C. The Ocean Circulation Inverse Problem. Cambridge University Press., 1996
[98]陈子通，沈桐立等．中尺度数值模式的资料同化系统——(一)伴随模式的设计，南京气象学院学报，1998，21(2)：165-172
[99]丑纪范．天气数值预报中使用过去资料的问题．中国科学，1974，6：635-644
[100]冯伍虎，邱崇践．变分四维同化方法若干问题的数值试验．高原气象，1999，18(2)：138-146
[101]高山红，吴增茂，谢红琴．Kalman滤波在气象数据同化中的发展与应用．2000，15(5)：571-575
[102]高山红．Kalman滤波与松弛逼近法在大气数据同化中的应用研究．青岛海洋大学，2001，1-115。
[103]郜吉东，丑纪范．数值天气预报中的两类反问题及一种数值解法——理解试验，气象学报，1994，52(2)：129-137
[104]郜吉东，丑纪范等．数值模式的初值敏感性程度对四维同化的影响——基于Lorentz系统的研究，气象学报，1995，53(4)：471-479
[105]顾建峰，殷鹤宝，徐一鸣等．MM5在上海区域气象中心数值预报中的改进和应用．2000，应用气象学报，11(2)，189-198
[106]龚建东，王强．区域四维变分资料同化的数值试验，气象学报，1999，57(2)：131-142
[107]李晓莉，沈桐立．四维伴随模式变分同化简介．气象教育与科技．2002，22(1)：1-5
[108]潘宁，董超华，张文捷等．变分同化及卫星资料同化．气象科技，2001，No2：29-36
[109]蒲朝霞，丑纪范．对中尺度遥感资料进行同化的共轭方法及其数值研究．高原气象．1994，13(4)：419-429
[110]邱崇践．变分同化中使用背景场时尺度匹配的数值研究．大气科学，2001，25(1)：103-110
[111]沈桐立，陈子通等．中尺度数值模式的资料同化系统——(二)伴随模式系统的检验和试验，南京气象学院学报，1998，21(2)：173-180
[112]杨学联，季晓阳，黄润恒等．卫星遥感资料在台风数值预报中的应用．海洋预报，2001，8(4)：1-8
[113]张守峰，王诗文．在台风业务系统中使用卫星云导风资料的实验．气象，1999，25(8)：22-25
[114]张昕，王斌等．“98·7”武汉暴雨模拟中的三维变分资料同化研究．自然科学进展，2002，12(2)：156-160
[115]朱江．观测资料的四维质量控制，气象学报，1995，53(4)：480-487
[116]朱江，Masafumikamachi等．含有开关参数化物理过程的模式变分资料同化的非光滑优化的方法：几个理论问题．大气科学进展：英文版，2002，19(3)：405-424
[117]朱宗申，马清云等．区域资料同化试验．应用气象学报，1995，6(1)：1-8
[118]朱宗申，胡铭．一种区域格点三维变分分析方案——基本框架和初步试验．大气科学，2002，26(5)：684-694
[2] Aitken, A. Statistical Mathematics. Oliver and Boyd Ltd., Edinburgh, 7 edition. 1939
[3] Andersson, E., J. Haseler, P. Unden, P. Courtier et. al. The ECMWF implementation of three dimensional variational assimilation(3D-Var). Ⅲ: experimental results. Q. J. Roy. Meteorol. Soc. 1998, 124: 1831-1860
[4] Andersson, E., J. Pailleux, J.-N. Thepaut, J. R. Eyre, A. P. McNally, G. A. Kelly, and P.Coutier. Use of cloud cleared radiances in three/four-dimensional variational data assimilation. Q. J. Roy. Meteorol. Soc. 1994, 120: 627-653
[5] Barnes, S. L. Mesoscale objective analysis using weighted time-series observations. NOAA technical Memorandum ERL NSSL-62． Environmental Research Laboratories, National Severe Storms Laboratory, Norman, Okla.1973, 60pp
[6] Bergthorsson, P. and Doos, B. Numerical weather map analysis. Tellus, 1955, 7: 329-340
[7] Bouttier, F. Kalman filtering. Meteorological training course lecture series, ECMWF. 1997
[8] Charney, J. The use of the primitive equations of motion in numerical prediction. Tellus, 1955, 7: 22-26
[9] Charney,J.,M. Halem and R. Jastrow. Use of incomplete historical data to infer the present state of the atmosphere. J. Atmos. Sci., 1969, 26: 1160-1163
[10] Cohn S., A. DA Silva, J. GUO. M. Sienkiewicz and D. lamicah. Assessing the effects of data selection in the DAO Physical-Space Statistical Analysis System. Mon. Wea. Rev., 1998, 126: 2913-2926
[11] Cohn S. E, Parrish D. P. The behavior of forecast error covariances for a Kalman filter in two dimensions. Mon. Wea. Rev., 1991,119: 1757-1785
[12] Courtier, P. Dual formulation of 4d-var assimilation. Q. J. R. Meteorol. Soc, 1997, 123: 2449-2461
[13] Courtier, P, E. Andersson, W. Heckley, G. Kelly, J. Pailleux, F. Rabier, J.-N. Thepaut, P. Unden, D. Vasiljevic, C. Cardinali, J. Eyre, M. Hamrud, J. Haseler, A. Hollingsworth, A. McNally,and A. Stoffelen. Variational assimilation at ECMWF. ECMWF Tech. Mem. 1993, 194
[14] Courtier P. E. Andersson, W. Heckley, J. Pailleux, D. Vasiljevic, M. Hamrud, Hollingsworth, A., Rabier, F. and Fisher, M. The ECMWF implementation of three dimensional variational assimilation (3D-Var). I: Formulation. Q. J. R. Meteorol. Soc., 1998,124: 1783-1807
[15] Courtier, P., Thepaut, J.-N. and Hollingsworth, A. A strategy for operational implementation of 4D-Var, using an incremental approach. Q. J. R. Meteorol. Soc., 1994,120:1367-1387
[16] Cressman. An operational objective analysis system. Mon. Wea. Rev., 1959, 87: 367-374
[17] Daley R. Atmospheric data analysis. Cambridge: Cambridge university press, 1991．
[18] Dee D P. Simplification of the Kalman filter for meteorological data assimilation. Q. J. R. Meteorol. Soc, 1991, 117: 365-384
[19] Derber, J. Variational four-dimensional analysis using quasi-geostrophic constraints. Mon. Wea. Rev., 1987,115: 998-1008
[20] Desroziers, G., Pouponneau, B., Thepaut, J., Janiskova, M., and Veerse, F. Four-dimensional variational anlayses of faster situations using special observations. Q. J. R. Meteorol. Soc., 1999,125:3339-3358
[21] Ehrendorfer M. Four-dimensional data assimilation: comparison of variational and sequential algorithms. Q. J. R. Meteorol. Soc., 1992,118: 673-713
[22] Ehrendorfer, M. and Tribbia, J. Optimal prediction of forecast error covariances through singular vectors. J. Atmos. Sci., 1997,54: 286-313
[23] Eliassen A. Provisional report on calculation of spatial covariance and autocorrelation of the pressure field. Rep. No. 5, 1954．
[24] Errico, F. M. What is an adjoint modei. Bull. Amer. Meteorol. Soc., 1997,2577-2591．
[25] Errico, R., T. Vukicevic and K. Raeder. Examination of the accuracy of a tangent linear model. Tellus, 1993, 45A: 462-477
[26] Errico, R. and T. Vukicevic. Sensitivity Analysis using an Adjoint of the PSU-NCAR Mesoscale Modei. Mon. Wea. Rev., 1992,120: 1644-1660
[27] Evensen G, Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model. J. Geophys. Res., 1992,97: 17 905-17 904
[28] Evensen G. Sequential data assimilation with a nonlinear quasigeostrophic modei using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 1994,99(C5) : 10 143-10 612
[29] Evre. J. R. Inversion of cloud satellite sounding radiances by nonlinear optimal estimation. Ⅰ; Theory and simulation of TOVS. Q. J. R Meteorol. Soc. 1989a, 115: 1001-1026
[30] Eyre. J. R. Inversion of cloud satellite sounding radiances by nonlinear optimal estimation. Ⅱ: Application to TOVS data. Q. J. R. Meteorol. Soc. 1989b, 115: 1027-1037
[31] Eyre, J. R. G. Kelly, A. P. McNally, E. Andersson, and A. Persson. Assimilation of TOVS radiances through one-dimensional variational analysis. Q. J. Roy. Meteorol. Soc., 1993, 119: 1427-1463
[32] Fisher, M. Development of a simplified kalman filter. Meteorological training course lecture
series, ECMWF. 1998
[33] Gaffard, C., and H.Roquet. Impact of the ERS-1 scatterometer wind data on the ECMWF 3D-VAR assimilation system. ECMWF Research Department Tech. Memo. 1995,217, 21pp.
[34] Gandin, L. (1963) . Objective analysis of meteorological fields(Leningrad: Gridromet). English translation (Jerusalem: Israel Program for Scientific Translation), 1965．
[35] Ghil, M. Meteorological Data Assimilation for Oceanographers. Part Ⅰ: Description and Theoretical Framework. Dyn. of Atmos. Oceans, 1989, 13: 171-218
[36] Ghil, M. and Malanotte-Rizzoli, P. Data assimilation in meteorology and oceanography. Advances in Geophysics, 1991, 33: 141-266．
[37] Gichrist B, Cressman G. An experiment in objective analysis. Tellus, 1954, 6: 309-318
[38] Gordin, V. A. Variational adjustment of meteorological fields. Soviet Meteorology and Hydrology. 1977, 12: 95-96
[39] Goerss, J S. The impact of multispectral GOES-8 wind information on Atlantic tropical cyclone track forecasts in 1995． Part Ⅱ: NOGAPS forecast. Mon. Wea. Rev., 1998, 126: 1219-1227
[40] Griffith, A. Data Assimilation for Numerical Weather Predicition using Control Theory. Ph.D. thesis, University of Reading. 1997
[41] Hestenes, M. R. and Stieffel. Methods of conjugate-gradients for solving linear systems. J. Res. Natl. Bur. Stand., 1952, 48: 409-436
[42] Hestenes, M. R. Conjugate directions methods in optimization. Applications of Mathematics, 1980, 12: Springer-Verlag, 325 pp.
[43] Hayden, C. M. and R J. Purser. Recursive filter objective analysis of meteorological fields: applications to NESDIS operational processing. J. Appl. Meteorol., 1995,34: 3-15
[44] Hinkelmann k. Ein numerisches experiment mit den primitiven gleichungen. New York: Rockefeller Institute Press, 1959,486-500
[45] Hoffman, R. N. A four-dimensional analysis exactly satifying equations of motion. Mon. Wea. Rev., 1986,114: 388-397
[46] Hollingsworth, A. and Lonnberg, P.The statistical structure of short-range forecast errors as determined from radiosonde data. part i: the wind field. Tellus, 1986, 38A: 111-136
[47] Jazwinski, A. Stochastic Processes and Filtering Theory. Academic Press. 1970．
[48] Jones R H. Optimal estimation of initial conditions for numerical prediction. J. Atmos. Sci., 1965,22: 658-663
[49] Julian, P. and Thiebaux, H. On some properties of correlation functions used in optimum interpolation schemes. Mon. Wea. Rev., 1975,103: 605-616
[50] Kalman R. E. A new approach to linear filtering and prediction problems. Transaction of the ASME, J. of Basic Engineering, 1960, 82D: 34-45
[51] Kalman R. E, Bucy R. New results in linear filtering and prediction. Transaction of the ASME, J. of Basic Engineering, 1961, 83D: 95-108
[52] Kistler, R. E. A study of data assimilation techniques in an autobarotropic primitive equation channel model. M.S. thesis, The Pennsylvania State University, 1974, 84pp.[Available from the Dept. of Meteorology, The Pennsylvanin State University,Univeristy Park, PA 16802]
[53] LeDimet, F. and Talagrand, O. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus, 1986,38A: 97-110
[54] Le Marshall, J. E, L. M. Leslie and A. F. Bennett. Tropical cyclone Beti-an example of the benefits of assimilation hourly satellite wind data. Aust. Meteor. Mag., 1996,45: 275-278
[55] Le Marshall, J. F. Cloud and water motion vectors in tropical cyclone track Forecasting-A Review. Meteorol., Atmos. Phys., 1998, 65(3-4) : 141-151
[56] Lewis J. M. Dynamical adjustment of 500mb vorticity using P. D. Thompson's scheme: a case study. Tellus, 1980,32: 511-524
[57] Lorenc, A. Analysis methods for numerical weather prediction. Q. J. Roy. Meteorol. Soc., 1986, 112: 1177-1194
[58] Lorenc, A. C. Iterative analysis using covariance functions and filters. Q. J. R. Meteorol. Soc.,1992, 118:569-591．
[59] Lorenc, A. C., R. S. Bell and B. MacPherson. The meteorological office analysis correction data assimilation scheme. Q. J. R. Meteorol. Soc., 1991, 117: 59-89
[60] Lorenc, A. C., S. P. Ballard, R. S. Bell, N. B. Ingleby, P. L. F. Andrews, D. M. Barker, J. R. Bray, A. M. Clayton, T. Dalby, D. Li, T. J. Payne, and F. W. Saunders. The Met. Office global three-dimensional variational data assimilation scheme. Q. J. R. Meteorol. Soc., 2000, 126: 2991-3012
[61] Mahfouf, J.-F. Analysis of soil moisture from near-surface paramenter: a feasibility study. J Appl. Meteorol. 1991, 30: 1534-1547
[62] Monin, A. Obukhov. A note on the general classification of motions in a baroclinic atmosphere. Tellus, 1959, 11: 159-162
[63] Nuss, Titley. Use of multiquadric interpolation for meteorological objective analysis. Mon. Wea. Rev., 1994,122: 1611-1631
[64] O'Brien, J. J. Alternative solution to the classical vertical velocity problem. J. Appl. Metrorol., 1970,9: 197-203
[65] Philips N A. The spatial statistics of random geostrophic modes and first-guess errors. Tellus, 1986, 38A: 314-322
[66] Parrish, D. and Derber, J. The national meteorological center's spectral statistical-interpolation analysis system. Mon. Wea. Rev., 1992,120: 1747-1763
[67] Phillips N A. The spatial statistics of random geostrophic modes and first-guess errors. Tellus, 1986, 38A: 314-322
[68] Rabier, F. and P. Bernardet. Variational analysis of orographic waves. Beitr. Phys. Atmos. 1991, 64: 207-217
[69] Rabier, E, McNally, A., Andersson, E., Courtier, P, Unden, P, Eyre, J., Hollingsworth, A., and Bouttier, F. The ECMWF implementation of three dimensional variational assimilation (3D-Var). Ⅱ: structure functions. Q. J. R. Meteorol. Soc., 1998, 124: 1809-1829
[70] Rabier, F., Thepaut, J., and Courtier, P. Extended assimilation and forecast experiments with a 4d var assimilation system. Q. J. R. Meteorol. Soc., 1998, 124: 1861-1887
[71] Rutherford, I.. Experiments in the updating of P. E. forecasts with real wind and geopotential data. Preprint, Third Conference on probability and Statistics in Atmospheric Science. Boston, Amer. Meteorol. Soc., 1973, 198-201
[72] Sasaki, Y. An objective analysis based on the variational method. J. Meteorol. Soc. Japan, 1958,36: 77-88
[73] Sasaki, Y. Some basie formalisms in numerical variational analysis. Mon. Wea. Rev., 1970, 98: 875-883
[74] Sasaki, Y. Numerical variational analysis formulated under the constraints as determined by longwave equations and a low-pass filter. Mon. Wea. Rev., 1970, 98: 884-898
[75] Sasaki. Y. Numerical variational analysis with weak constraint and application to surface analysis of severe storm gust. Mon. Wea. Rev., 1970,98: 899-910
[76] Shiryaev, A. Kolmogorov:life and creative activities. The Annals of Probability, 1989, 17(3) : 866-944
[77] Soden, B J, Velden, C. S. and Tuleya R E. The impact of satellite winds on experimental GFDL hurricane modei forecasts. Mon. Wea. Rev., 2001, 129: 835-852
[78] Stephens J. J. A varaitional approach to numerical weather prediction. Rep. No. 3, Atmos. Sci., Group, The University of Texas, Austin, USA, 1965,243pp.
[79] Stephens J. Variational initialization with the balance equation. J. Appl. Meteorol., 1970, 9: 732-739
[80] Stephens J. J. and K. W. Johnson. Middle-large-scale variational adjustment of atmospheric fields in mesoscale diagnostic numerical variational analysis models. Final report, Deparment of meteorology, Florida State Univ., 1978,1-38
[81] Stauffer, D. R. and N. L. Seaman. Use of four-dimensional data assimilation in a limited-area mesoscale modei. Part I: Experiments with synoptic-scale data. Mon. Wea. Rev., 1990, 118:
1250-1277
[82] Stauffer, D. R., N. L. Seaman and F. S. Binkowski. Use of four-dimensional data assimilation in a limited-area mesoscale modei. Part Ⅱ: Effects of data assimilation within the planetary boundary layer. Mon. Wea. Rev., 1991, 119: 734-754
[83] Thompson P A dynamical method of analyzing meteorological data. Tellus, 1969, 13: 334-349
[84] Thepaut, J., Courtier, P, Belaud, G., and Lemaitre, G. Dynamical structure functions in 4d variational assimilation: A case study. Q. J. R. Meteorol. Soc., 1996,122: 535-561
[85] Thepaut, J., Hoffman, R., and Courtier, P. Interactions of dynamics and observations in a 4d variational assimilation. Mon. Wea. Rev., 1993, 121: 3393-3414
[86] Todling, R. and Cohn, S. Suboptimal schemes for atmospheric data assimilation based on the kalman filter. Mon. Wea. Rev., 1994, 122: 2537-2557
[87] Tomassini, M. D. LeMeur, and R. W. Saunders. Near-surface satellite wind observations of hurricane and their impact on ECMWF modei analysis and forecasts. Mon. Wea. Rev., 1998,126: 1274-1286
[88] Z. Li and I. Navon. Optimality of 4d var and its relationship with the kalman filter and smoother. Q. J. R. Meteorol. Soc., 2001,127(572) : 661-683
[89] Velden, C.S., Winds Derived from geostationary satellite moisture channel observations: applications and impact on numerical weather prediction. Meteorol., Atmos. Phys., 1996, 60: 37-46
[90] Velden, C.S., C. Hayden, S. Nieman, W. P. Menzel, S. Wanzong and J Goerss. Upper-tropospheric winds derived from geostationary satellite water observations. Bull. Amer. Meteorol. Soc., 1997, 77: 173-195
[91] Velden, C. S., Olander, T L and Wanzong S. The impact of multispectral GOES-8 wind information on Atlantic tropical cyclone track forecasts in 1995． Part Ⅰ: dataset methodology, description, and case analysis. Mon. Wea. Rev., 1998, 126: 1202-1218
[92] Washington, W. A note on the adjustment towards geostrophic equilibrium in a simple fluid system. Tellus, 1964,16, 530-534
[93] Wahba, G. and J. Wendelberger. Some new mathematical methods for variational analysis using splines and cross-validation. Mon. Wea. Rev., 1980, 108: 1122-1143
[94] Wergen,W. The effect of modei errors in variational assimilation.Tellus, 1992, 44A: 297-313
[95] Wiener, N. Extrapolation, interpolation and smoothing of stationary time series: with engineering applications. MIT Press and John Wiley and Sons.,1949
[96] Williamson, D. and A. Kasahara, 1971:Adaptation of meteorological variables forced by updating. J. Atmos. Sci., 28, 1313-1324
[97]Wunsch, C. The Ocean Circulation Inverse Problem. Cambridge University Press., 1996
[98]陈子通，沈桐立等．中尺度数值模式的资料同化系统——(一)伴随模式的设计，南京气象学院学报，1998，21(2)：165-172
[99]丑纪范．天气数值预报中使用过去资料的问题．中国科学，1974，6：635-644
[100]冯伍虎，邱崇践．变分四维同化方法若干问题的数值试验．高原气象，1999，18(2)：138-146
[101]高山红，吴增茂，谢红琴．Kalman滤波在气象数据同化中的发展与应用．2000，15(5)：571-575
[102]高山红．Kalman滤波与松弛逼近法在大气数据同化中的应用研究．青岛海洋大学，2001，1-115。
[103]郜吉东，丑纪范．数值天气预报中的两类反问题及一种数值解法——理解试验，气象学报，1994，52(2)：129-137
[104]郜吉东，丑纪范等．数值模式的初值敏感性程度对四维同化的影响——基于Lorentz系统的研究，气象学报，1995，53(4)：471-479
[105]顾建峰，殷鹤宝，徐一鸣等．MM5在上海区域气象中心数值预报中的改进和应用．2000，应用气象学报，11(2)，189-198
[106]龚建东，王强．区域四维变分资料同化的数值试验，气象学报，1999，57(2)：131-142
[107]李晓莉，沈桐立．四维伴随模式变分同化简介．气象教育与科技．2002，22(1)：1-5
[108]潘宁，董超华，张文捷等．变分同化及卫星资料同化．气象科技，2001，No2：29-36
[109]蒲朝霞，丑纪范．对中尺度遥感资料进行同化的共轭方法及其数值研究．高原气象．1994，13(4)：419-429
[110]邱崇践．变分同化中使用背景场时尺度匹配的数值研究．大气科学，2001，25(1)：103-110
[111]沈桐立，陈子通等．中尺度数值模式的资料同化系统——(二)伴随模式系统的检验和试验，南京气象学院学报，1998，21(2)：173-180
[112]杨学联，季晓阳，黄润恒等．卫星遥感资料在台风数值预报中的应用．海洋预报，2001，8(4)：1-8
[113]张守峰，王诗文．在台风业务系统中使用卫星云导风资料的实验．气象，1999，25(8)：22-25
[114]张昕，王斌等．“98·7”武汉暴雨模拟中的三维变分资料同化研究．自然科学进展，2002，12(2)：156-160
[115]朱江．观测资料的四维质量控制，气象学报，1995，53(4)：480-487
[116]朱江，Masafumikamachi等．含有开关参数化物理过程的模式变分资料同化的非光滑优化的方法：几个理论问题．大气科学进展：英文版，2002，19(3)：405-424
[117]朱宗申，马清云等．区域资料同化试验．应用气象学报，1995，6(1)：1-8
[118]朱宗申，胡铭．一种区域格点三维变分分析方案——基本框架和初步试验．大气科学，2002，26(5)：684-694