基于一个全球谱模式的集合Kalman滤波同化系统研究
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摘要
自上世纪90年代末集合Kalman滤波(EnKF)方法开始应用于大气资料同化领域以来,无论是在理论研究方面,还是实际应用方面都有了较大进展,取得了许多有意义的研究成果。国内对中期数值天气预报的研究已逾二十余载,同时中期数值预报模式的资料同化研究工作也随之在进行,目前的同化方法为3D-Var,但是基于集合Kalman滤波的中期数值预报模式的资料同化研究工作还在探索阶段。本文主要围绕一个中期数值预报谱模式T106L19,通过同化实际的常规观测资料和实际的ATOVS卫星资料,探讨了在全球中期数值预报系统中集合Kalman滤波同化方法的可行性,发展了一个基于中期数值预报模式的集合Kalman滤波同化预报系统。论文主要结论如下：
1.基于一个全球中期数值预报模式,发展了一个同化常规观测资料和ATOVS卫星资料的集合Kalman滤波同化系统。
2.对于常规资料同化,EnKF同化使分析场明显向观测靠近,尤其在对流层效果更加明显；其分析误差主要集中在槽、脊线附近,南半球因观测稀少误差较大。将T106L19-EnKF同化/预报效果与T106L19模式原有的客观分析系统01 (T106L19-OI)的同化/预报效果相比较：从分析场看,在北半球中高纬(NH)地区和热带、副热带(TR)地区,T106L19-EnKF分析场误差比T106L19-OI的分析场误差小一些,而在南半球中高纬(SH)地区,T106L19-EnKF分析场误差与T106L19-OI的分析场误差基本相同；从预报场来看,随着预报时间的增长,预报场的误差一直在增加,在SH和NH地区差误增长较快,TR地区误差增长较慢；在TR和NH地区,T106L19-EnKF的预报效果要比T106L19-OI的预报效果好一些,但在SH地区未显出优势。
3.参照已有的TOVS和ATOVS偏差订正方法,结合本系统所用的卫星ATOVS辐射产品的特征,发展了一个适合T106L19模式的ATOVS偏差订正处理系统,该系统作用是在ATOVS卫星资料同化之前,对该资料进行偏差订正。偏差订正后,观测残差的分布形状更趋于高斯分布,其峰值更向零值靠近了。
4.在常规资料同化的基础上,加入经过偏差订正和质量控制的卫星资料之后不但在常规资料稀少的南半球,而且在常规资料相对较多的北半球分析场都有明显改善。T106L19-EnKF的同化效果在全球绝大部分区域明显好于T106L19-01的同化效果；从预报效果来看,在热带、副热带和北半球中高纬地区,T106L19-EnKF的预报效果要比T106L19-OI的预报效果好一些,在SH地区预报前三天未显出优势。
5.为了更好的检验T106L19-EnKF的同化/预报效果,将T106L19-EnKF同化用于台风“派比安”个例的路径预报。从对台风“派比安”个例的路径预报上来看,相对于T106L19-EnKF只同化常规资料,T106L19-OI只同化常规资料和T106L19-OI同化了常规资料和卫星资料三者,以T106L19-EnKF同化常规资料和卫星资料的分析场为初始场进行预报的台风路径与最佳观测路径吻合的最好,500 hPa环流场也与“真实场”较一致。
There have been many significant results and greater progress both in theory and in practical applications since Ensemble Kalman Filter (EnKF) was applied to atmospheric data assimilation in the late 1990's. There has been more than two decades that research on Numerical Weather Prediction at a medium-range resolution in our country, while data assimilation at a medium-range resolution is being researching at the same time. At present, the data assimilation scheme is 3D-Var (3-Dimentional Variational). However, there is in the developing stage that EnKF scheme is used at a medium-range resolution. In this paper, the applicability and feasibility of EnKF in real atmospheric model-the global medium range spectral model T106L19 are studied by assimilating real conventional observational data and real ATOVS (Advanced Television and Infrared Observation Satellite Operational Vertical Sounder) satellite data. And a reasonable EnKF data assimilation system with a global spectral model at a medium-range resolution is set up. The main results are as follows:
1. An EnKF data assimilation system is set up, which assimilates conventional observational data and ATOVS satellite data with a global spectral model at a medium-range resolution.
2. For conventional data assimilation, EnKF makes the analysis field close to observations, while errors still exist, which are mainly in the near of trough and ridge and more obvious in the southern hemisphere due to few conventional observations. Compared the effect of T106L19-EnKF assimilation/forecast with that of T106L19-OI (There is original in the model T106L19), the results show as following: (1) the errors of analysis field of T106L19-EnKF are smaller than those of T106L19-OI in the middle and high latitude region of northern hemisphere (NH) and tropical and subtropical region (TR), while they are almost same in the middle and high latitude region of southern hemisphere (SH). (2) The errors of forecast field increase with the time of the forecast growth, and the errors increase more rapidly in region of SH and NH than in region of TR. (3) In region of TR and NH, the results of T106L19-EnKF forecast are better than those of T106L19-OI, however, such superiority is not founded in region of SH.
3. Based on the characteristic of ATOVS radiance data and the existing bias correction methods of TOVS and ATOVS, a bias correction system for model T106L19 is set up for bias correction and quality control of ATOVS data, which are done before satellite data assimilation. The distribution of observation residual is more similar to Gaussian distribution than that without bias correction and its peak is shifted to zero after bias correction.
4. There is a significant improvement for the analysis field, not only in the southern hemisphere that conventional data is sparse but also in the northern hemisphere that conventional data is relative abundance after assimilating ATOVS with bias correction and quality control based on conventional data assimilation. The results of assimilation show that T106L19-EnKF are better than T106L19-OI in majority of the global. For results of forecast, T106L19-EnKF are better than T106L19-OI in region of TR and NH, however, there is no superiority in the first three days in region of SH.
5. To investigate the effect of T106L19-EnKF assimilation/forecast further, T106L19-EnKF assimilation is used to the Typhoon "Prapiroon" track prediction. For the Typhoon "Prapiroon" track prediction, four test are done, including T106L19-EnKF or T106L19-OI assimilating conventional data only, and T106L19-OI or T106L19-EnKF assimilating conventional data and ATOVS satellite data. The results show that the Typhoon track is predicted by the analysis field of T106L19-EnKF that assimilate conventional data and ATOVS data as the initial fields matches best with the observed best track and its circulation at 500 hPa matches better with "the real field".
1.基于一个全球中期数值预报模式,发展了一个同化常规观测资料和ATOVS卫星资料的集合Kalman滤波同化系统。
2.对于常规资料同化,EnKF同化使分析场明显向观测靠近,尤其在对流层效果更加明显；其分析误差主要集中在槽、脊线附近,南半球因观测稀少误差较大。将T106L19-EnKF同化/预报效果与T106L19模式原有的客观分析系统01 (T106L19-OI)的同化/预报效果相比较：从分析场看,在北半球中高纬(NH)地区和热带、副热带(TR)地区,T106L19-EnKF分析场误差比T106L19-OI的分析场误差小一些,而在南半球中高纬(SH)地区,T106L19-EnKF分析场误差与T106L19-OI的分析场误差基本相同；从预报场来看,随着预报时间的增长,预报场的误差一直在增加,在SH和NH地区差误增长较快,TR地区误差增长较慢；在TR和NH地区,T106L19-EnKF的预报效果要比T106L19-OI的预报效果好一些,但在SH地区未显出优势。
3.参照已有的TOVS和ATOVS偏差订正方法,结合本系统所用的卫星ATOVS辐射产品的特征,发展了一个适合T106L19模式的ATOVS偏差订正处理系统,该系统作用是在ATOVS卫星资料同化之前,对该资料进行偏差订正。偏差订正后,观测残差的分布形状更趋于高斯分布,其峰值更向零值靠近了。
4.在常规资料同化的基础上,加入经过偏差订正和质量控制的卫星资料之后不但在常规资料稀少的南半球,而且在常规资料相对较多的北半球分析场都有明显改善。T106L19-EnKF的同化效果在全球绝大部分区域明显好于T106L19-01的同化效果；从预报效果来看,在热带、副热带和北半球中高纬地区,T106L19-EnKF的预报效果要比T106L19-OI的预报效果好一些,在SH地区预报前三天未显出优势。
5.为了更好的检验T106L19-EnKF的同化/预报效果,将T106L19-EnKF同化用于台风“派比安”个例的路径预报。从对台风“派比安”个例的路径预报上来看,相对于T106L19-EnKF只同化常规资料,T106L19-OI只同化常规资料和T106L19-OI同化了常规资料和卫星资料三者,以T106L19-EnKF同化常规资料和卫星资料的分析场为初始场进行预报的台风路径与最佳观测路径吻合的最好,500 hPa环流场也与“真实场”较一致。
There have been many significant results and greater progress both in theory and in practical applications since Ensemble Kalman Filter (EnKF) was applied to atmospheric data assimilation in the late 1990's. There has been more than two decades that research on Numerical Weather Prediction at a medium-range resolution in our country, while data assimilation at a medium-range resolution is being researching at the same time. At present, the data assimilation scheme is 3D-Var (3-Dimentional Variational). However, there is in the developing stage that EnKF scheme is used at a medium-range resolution. In this paper, the applicability and feasibility of EnKF in real atmospheric model-the global medium range spectral model T106L19 are studied by assimilating real conventional observational data and real ATOVS (Advanced Television and Infrared Observation Satellite Operational Vertical Sounder) satellite data. And a reasonable EnKF data assimilation system with a global spectral model at a medium-range resolution is set up. The main results are as follows:
1. An EnKF data assimilation system is set up, which assimilates conventional observational data and ATOVS satellite data with a global spectral model at a medium-range resolution.
2. For conventional data assimilation, EnKF makes the analysis field close to observations, while errors still exist, which are mainly in the near of trough and ridge and more obvious in the southern hemisphere due to few conventional observations. Compared the effect of T106L19-EnKF assimilation/forecast with that of T106L19-OI (There is original in the model T106L19), the results show as following: (1) the errors of analysis field of T106L19-EnKF are smaller than those of T106L19-OI in the middle and high latitude region of northern hemisphere (NH) and tropical and subtropical region (TR), while they are almost same in the middle and high latitude region of southern hemisphere (SH). (2) The errors of forecast field increase with the time of the forecast growth, and the errors increase more rapidly in region of SH and NH than in region of TR. (3) In region of TR and NH, the results of T106L19-EnKF forecast are better than those of T106L19-OI, however, such superiority is not founded in region of SH.
3. Based on the characteristic of ATOVS radiance data and the existing bias correction methods of TOVS and ATOVS, a bias correction system for model T106L19 is set up for bias correction and quality control of ATOVS data, which are done before satellite data assimilation. The distribution of observation residual is more similar to Gaussian distribution than that without bias correction and its peak is shifted to zero after bias correction.
4. There is a significant improvement for the analysis field, not only in the southern hemisphere that conventional data is sparse but also in the northern hemisphere that conventional data is relative abundance after assimilating ATOVS with bias correction and quality control based on conventional data assimilation. The results of assimilation show that T106L19-EnKF are better than T106L19-OI in majority of the global. For results of forecast, T106L19-EnKF are better than T106L19-OI in region of TR and NH, however, there is no superiority in the first three days in region of SH.
5. To investigate the effect of T106L19-EnKF assimilation/forecast further, T106L19-EnKF assimilation is used to the Typhoon "Prapiroon" track prediction. For the Typhoon "Prapiroon" track prediction, four test are done, including T106L19-EnKF or T106L19-OI assimilating conventional data only, and T106L19-OI or T106L19-EnKF assimilating conventional data and ATOVS satellite data. The results show that the Typhoon track is predicted by the analysis field of T106L19-EnKF that assimilate conventional data and ATOVS data as the initial fields matches best with the observed best track and its circulation at 500 hPa matches better with "the real field".
引文
Anderson, J. L. An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 2001,129:2884～2903.
Anderson, J. L. A local least-squares framework for ensemble filtering. Mon. Wea. Rev.,2003, 131:634-642.
Bishop, C. H., B. J. Etherton and S. J. Majumdar. Adaptive sampling with the ensemble transform Kalman filter. Part Ⅰ:Theoretical aspects. Mon. Wea. Rev.,2001,129:420～436.
Bouttier, F. and Kelly, G. Observing-system experiments in the ECMWF 4DVar data assimilation system. Q. J. Roy. Meteorol. Soc.,2001,127:1469～1488.
Bowler, N. E. Comparison of error breeding, singular vectors, random perturbations and ensemble Kalman filter perturbation strategies on a simple model. Tellus,2006,58A:538～548.
Burgers, G., P. J. van Leeuwen, and G. Evensen. Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev.,1998,126:1719～1724.
Cui L. M., J. H. Sun and L. L. Qi. Two bias correction schemes for ATOVS radiance data. J. Trop. Meteor.,2010,16(1):71～76.
Cohn, S. E., and D. F. Parrish. The behavior of forecast error covariances for a Kalman filter in two dimensions. Mon. Wea. Rev.,1991,119:1757～1785.
Courtier P. Variational methods. J. Meteor. Soc. Japan,1997,75, 1B:211～217.
Daley, R. Estimating model-error covariances for applications to atmospheric data assimilation. Mon. Wea. Rev.,1992,120:1735～1746.
Dee, D. P. On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Rev.,1995,123:1128～1145.
Blanchet, I., C. Frankignoul, and M. A. Cane. A comparison of adaptive Kalman filters for a tropical Pacific ocean model. Mon. Wea. Rev.,1997,125:40～58.
Eliassen, A. Provisional report on calculation of spatial covariance and autocorrelation of the pressure field. Inst. Weather and Climate Research, Acad. Sci., Oslo,1954, Report No.5
Epstein. E. S. Stochastic dynamic prediction. Tellus. Ser. A.1969,21:739～759.
Evensen, G. Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res.,1994,99(C5):10143～10162.
Evensen, G. and P. J. van Leeuwen. An Ensemble Kalman Smoother for nonlinear dynamics. Mon. Wea. Rev.,2000,128:1852～1867.
Evensen, G. The ensemble Kalman filter:Theoretical formulation and practical implementation. Ocean Dyn.,2003,53:343～367.
Evensen, G. Sampling strategies and square root analysis schemes for the EnKF. Ocean Dyn., 2004,54:539～560.
Eyre, J. R. A bias correction scheme for simulated TOVS brightness temperatures. Technical Memorandum,1992,176:81～109.
Farrell, B. F. and P. J. Ioannou. State estimation using a reduced-order Kalman filter. J. Atmos. Sci.,2001,58:3666～3680.
Fisher, M. Assimilation Techniques (5):Approximate Kalman Filters and Singular Vectors. ECMWF Meteorological Training Course Lecture Series,2001, [Available from ECMWF: http://www.ecmwf.int]
Gandin, L. S. Objective Analysis of Meteorological Fields. Leningrad:Hydromet Press,1963: 56～60
Gaspari, G., and S. Cohn,1999:Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc,125:723～757.
Hamill, T. M. and C. Snyder. A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon. Wea. Rev.,2000,128:2905-2919.
Hamill, T. M., J. S. Whitaker, and C. Snyder. Distance-dependent filtering of background-error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev.,2001,129:2776～2790.
Harris, B. A. and Kelly, G. A satellite radiance bias correction scheme for data assimilation. Quart. J. Roy. Meteor. Soc.,2001,127:1453～1468.
Hong Li, Improved analyses and foreeasts with AIRS retrievals using the Local ensemble Transform Kalman Filter.2007:PPT.
Hollingsworth, A. and P. Lonnberg. The statistical structure of short-range forecast errors as determined from radiosonde data. I:the wind field. Tellus,1986,38A:111～136.
Houtekamer, P. L. and H. L. Mitchell. Data assimilation using an ensemble Kalman filter technique. Mon Wea Rev,1998,126:796～811.
Houtekamer, P. L. and H. L. Mitchell. A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation. Mon. Wea. Rev.,2001,129:123～137.
Houtekamer, P. L. and H. L. Mitchell. Ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc, 2005,131:3269～3289.
Hunt, B. R., E. Kalnay, E. J. Kostelieh, E. ott, D. J. Patil, T. Sauer, I., Szunyogh, J.A. Yorke, and A.V. Zimin. Four dimensional ensemble Kalman filtering.Tellus,2004,56A:273～277.
Hunt, B. R., E. Kostelich, and I. Szunyogh. Efficient data assimilation for spatiotemporal chaos:A local ensemble transform Kalman filter,2007,230(1-2):112～126.
Kalman, R. E. A New Approach to Linear Filtering and Prediction Problems. Transaction of the ASME-J. Basic. Eng.,1960:35～45.
Kalnay, E. Atmospheric modeling, data assimilation and predictability. Cambridge University Press,2003.341.
Keppenne, C. L. Data assimilation into a primitive equation model with a parallel ensemble Kalman filter. Mon. Wea. Rev.,2000:128:1971～1981.
Keppenne, C. L., and M. M. Rienecker. Initial testing of a massively parallel ensemble Kalman filter with the Poseidon isopycnal ocean general circulation model. Mon. Wea. Rev., 2002,130:2951～2965.
Keppenne C. L, M. M. Rienecker Assimilation of temperature into an isopycnal ocean general circulation model using a parallel ensemble Kalman filter. J Marine Sys 2003:40～41.
Kuo H. L. Further studies of the parameterization of the influence of cumulus convection on large-scale flow. J. Atmos. Sci.1974,31:1232～1240
Lonnberg, P. and A. Hollingsworth. The statistical structure of short-range forecast errors as determined from radiosonde data. Ⅱ:the covariance of height and wind errors. Tellus,1986, 38A:137～161.
Lorenc, A. C. A global three-dimensional multivariate statistical analysis scheme. Mon. Weather Rev.,1981,109:701～721.
Lorenz, E. N. A study of the predictability of a 28-variable atmospheric model. Tellus,1965,17: 321～333.
Lu, C. and G. L. Browning. Four-Dimensional Variational Data Assimilation for Limited-Area Models:Lateral Boundary Conditions, Solution Uniqueness, and Numerical Convergence. J. Atmos. Sci.,2000,57:1341～1353.
Meng, Z., and F. Zhang,2007:Test of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part Ⅱ:Imperfect model experiments. Mon. Wea. Rev.,135:1403～1423.
Mitchell, H. L., and P. L. Houtekamer. An. adaptive ensemble Kalman filter. Mon. Wea. Rev., 2000,128:416～433.
Mitchell, H. L. and P. L. Houtekamer. Ensemble Size, Balance, and Model-Error Representation in an Ensemble Kalman Filter. Mon. Wea. Rev.,2002,130:2791～2808.
Miyoshi T.2005. Ensemble Kalman Filter Experiments with a Primitive-Equation Global Model. Ph.D. thesis, University of Maryland.
Miyoshi, T. and S. Yamane. Local Ensemble Transform Kalman Filtering with an AGCM at a T159/L48 Resolution.SOLA,2007,3:037-040.
Moinn, A. S. and A. M. Obukhov. Basic laws of turbulent mixing in the atmosphere near the ground. Trakad Nuak SSSR Geofiz Inst,1954,24(151):161～187.
Okamoto K., M. Kazumori and H. Owada. The assimilation of ATOVS radiances in the JMA global analysis system. Journal of the Meteorological Society of Japan,2005,83(2):201～217.
Oke, P.R., P. Sakov, S. P. Corney. Impacts of localisation in the EnKF and EnOI:experiments with a small model. Ocean Dynamics,2007,57:32～45.
Oliver D. S. Moving Averages for Gaussian Simulation in Two and Three Dimensions. Mathematical Geology,1995,27(8):940～959.
Ott, E., B. R. Hunt, I. Szunyogh, A.V. Zimin, E. J. Kostelieh, M.Corazza, E.Kalnay, D.J. Patil, and J.A.Yorke. A local ensemble Kalman filter for atmospheric assimilation.Tellus,2004:56A, 415～428.
Pham, D. T. Stochastic methods for sequential data assimilation in strongly nonlinear systems. Mon. Wea. Rev.,2001,129:1194～1207.
Sakov, P. and P. Oke. Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters. Mon. Wea. Rev.,2008,136:1042～1053.
Szunyogh, I., E. J. Kostelich, G. Gyarmati, D. J. Patil, B. R. Hunt, E. Kalnay, E. Ott, and J. A. Yorke. Assessing a local ensemble Kalman filter:Perfect model experiments with the National Centers for Environmental Prediction global model. Tellus,2005,57A:528～545.
Talagrand O. Assimilation of observations, an introduction. J. Met. Soc. Japan.1997, Special Issue 75, 1B:191～209.
Tippett M. K., J. L. Anderson, C. H. Bishop, T. M. Hamill and J. S. Whitaker. Ensemble square-root filters. Mon. Wea. Rev.,2003,131:1485～1490.
Whitaker, J. S., G. P. Compo, X. Wei, and T. M. Hamill. Reanalysis without radiosondes using ensemble data assimilation. Mon. Wea. Rev.,2004,132:1190～1200.
Whitaker, J. S. and T. M. Hamill. Ensemble data assimilatrion without perturbed observations. Mon. Wea. Rev.,2002,130:1913～1924.
Zhang, F. Q. and C. Snyder. Ensemble-based data assimilaton. Bull. Amer. Meteor. Soc.,2007, 88:565-568.
Zhang, F. Q., M. Zhang, and J. A. Hansen. Coupling ensemble Kalman filter with four-dimensional variational data assimilation. Adv. Atmos. Sci.,2009:26(1),1～8, doi: 10.1007/s00376-009-0001-8.
Zheng, F., and J. Zhu. A multivariate empirical orthogonal function based scheme for balanced initial ensemble generation of an ensemble Kalman filtering. Adv. Atmos. Sci.,2009. (submitted)
Zhi, J. L. and I. M. Navon. Optimality of variational data assimilation and its relationship with the Kalman filter and smoother. Quart. J. Roy. Meteor. Soc.,2001,127: 661～684.
Zhu J, Kamachi M. An adaptive variational method for data assimilation with imperfect models. Tellus,2000,52A:265～279.
Zupanski, D. and F. Mesinger. Four-Dimensional Variational Assimilation of Precipitation Data. Mon. Weather Rev.,1995,123:1112～1127.
Eugenia Kalnay大气模式、资料同化和可预报性.北京,气象出版社,2005,8.
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.地球科学进展.2000,15：571～575.
高拴柱.集合Kalman滤波资料同化技术及研究现状.气象,2005,6：3～8.
刘成思,薛纪善.关于集合Kalman滤波的理论和方法的发展.热带气象学报,2005,21(6)：628～633.
刘志权,张凤英,吴雪宝,等.区域极轨卫星ATOVS辐射偏差订正方法研究.气象学报,2007, 65(1)：113～123.
黄小刚,费建芳,陆汉城.基于集合Kalman滤波数据同化的热带气旋路径集合预报研究.大气科学,2007,31(3)：468～478.
孟智勇、徐祥德、陈联,寿.卫星亮温资料四维同化方案及其对“7.20”武汉特大暴雨的模拟试验.大气科学,2002,26(5)：663～677.
潘宁、董超华、张文建ATOVS辐射率资料的直接变分同化试验研究.气象学报,2003,61(2)：226～236.
王宗皓、毛建平、黄继红,等.卫星探测数据对B～模式分析预报系统性误差的影响.气象学报,1993；51(1)：21～33.
王子厚、王宗皓、张凤英HIRS/2亮温直接应用于数值预报的试验研究.应用气象学报,1995,6(3)：273～280.
王超、万丰.数值预报/卫星反演/数据同化循环试验.气象学报,1997,55(6)：740～749.
翁永辉、徐祥德TOVS资料的变分处理方法在青藏高原地区的数值试验.大气科学,1999,23(6)：703～712.
张红华,沈桐立,王桂臣,朱琳.集合Kalman滤波同化理论及数值试验.中国气象学会2008年年会复杂地形影响下的天气与气候分会场论文集.2008.
张华,丑纪范,邱崇践.西北太平洋威马逊台风结构的卫星观测同化分析.科学通报,2004,49(5)：493～498.
庄照荣.集合Kalman滤波资料同化系统的设计及其在集合预报中的应用.中国科学院研究生院博士学位论文.2007.5.
Anderson, J. L. A local least-squares framework for ensemble filtering. Mon. Wea. Rev.,2003, 131:634-642.
Bishop, C. H., B. J. Etherton and S. J. Majumdar. Adaptive sampling with the ensemble transform Kalman filter. Part Ⅰ:Theoretical aspects. Mon. Wea. Rev.,2001,129:420～436.
Bouttier, F. and Kelly, G. Observing-system experiments in the ECMWF 4DVar data assimilation system. Q. J. Roy. Meteorol. Soc.,2001,127:1469～1488.
Bowler, N. E. Comparison of error breeding, singular vectors, random perturbations and ensemble Kalman filter perturbation strategies on a simple model. Tellus,2006,58A:538～548.
Burgers, G., P. J. van Leeuwen, and G. Evensen. Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev.,1998,126:1719～1724.
Cui L. M., J. H. Sun and L. L. Qi. Two bias correction schemes for ATOVS radiance data. J. Trop. Meteor.,2010,16(1):71～76.
Cohn, S. E., and D. F. Parrish. The behavior of forecast error covariances for a Kalman filter in two dimensions. Mon. Wea. Rev.,1991,119:1757～1785.
Courtier P. Variational methods. J. Meteor. Soc. Japan,1997,75, 1B:211～217.
Daley, R. Estimating model-error covariances for applications to atmospheric data assimilation. Mon. Wea. Rev.,1992,120:1735～1746.
Dee, D. P. On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Rev.,1995,123:1128～1145.
Blanchet, I., C. Frankignoul, and M. A. Cane. A comparison of adaptive Kalman filters for a tropical Pacific ocean model. Mon. Wea. Rev.,1997,125:40～58.
Eliassen, A. Provisional report on calculation of spatial covariance and autocorrelation of the pressure field. Inst. Weather and Climate Research, Acad. Sci., Oslo,1954, Report No.5
Epstein. E. S. Stochastic dynamic prediction. Tellus. Ser. A.1969,21:739～759.
Evensen, G. Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res.,1994,99(C5):10143～10162.
Evensen, G. and P. J. van Leeuwen. An Ensemble Kalman Smoother for nonlinear dynamics. Mon. Wea. Rev.,2000,128:1852～1867.
Evensen, G. The ensemble Kalman filter:Theoretical formulation and practical implementation. Ocean Dyn.,2003,53:343～367.
Evensen, G. Sampling strategies and square root analysis schemes for the EnKF. Ocean Dyn., 2004,54:539～560.
Eyre, J. R. A bias correction scheme for simulated TOVS brightness temperatures. Technical Memorandum,1992,176:81～109.
Farrell, B. F. and P. J. Ioannou. State estimation using a reduced-order Kalman filter. J. Atmos. Sci.,2001,58:3666～3680.
Fisher, M. Assimilation Techniques (5):Approximate Kalman Filters and Singular Vectors. ECMWF Meteorological Training Course Lecture Series,2001, [Available from ECMWF: http://www.ecmwf.int]
Gandin, L. S. Objective Analysis of Meteorological Fields. Leningrad:Hydromet Press,1963: 56～60
Gaspari, G., and S. Cohn,1999:Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc,125:723～757.
Hamill, T. M. and C. Snyder. A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon. Wea. Rev.,2000,128:2905-2919.
Hamill, T. M., J. S. Whitaker, and C. Snyder. Distance-dependent filtering of background-error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev.,2001,129:2776～2790.
Harris, B. A. and Kelly, G. A satellite radiance bias correction scheme for data assimilation. Quart. J. Roy. Meteor. Soc.,2001,127:1453～1468.
Hong Li, Improved analyses and foreeasts with AIRS retrievals using the Local ensemble Transform Kalman Filter.2007:PPT.
Hollingsworth, A. and P. Lonnberg. The statistical structure of short-range forecast errors as determined from radiosonde data. I:the wind field. Tellus,1986,38A:111～136.
Houtekamer, P. L. and H. L. Mitchell. Data assimilation using an ensemble Kalman filter technique. Mon Wea Rev,1998,126:796～811.
Houtekamer, P. L. and H. L. Mitchell. A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation. Mon. Wea. Rev.,2001,129:123～137.
Houtekamer, P. L. and H. L. Mitchell. Ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc, 2005,131:3269～3289.
Hunt, B. R., E. Kalnay, E. J. Kostelieh, E. ott, D. J. Patil, T. Sauer, I., Szunyogh, J.A. Yorke, and A.V. Zimin. Four dimensional ensemble Kalman filtering.Tellus,2004,56A:273～277.
Hunt, B. R., E. Kostelich, and I. Szunyogh. Efficient data assimilation for spatiotemporal chaos:A local ensemble transform Kalman filter,2007,230(1-2):112～126.
Kalman, R. E. A New Approach to Linear Filtering and Prediction Problems. Transaction of the ASME-J. Basic. Eng.,1960:35～45.
Kalnay, E. Atmospheric modeling, data assimilation and predictability. Cambridge University Press,2003.341.
Keppenne, C. L. Data assimilation into a primitive equation model with a parallel ensemble Kalman filter. Mon. Wea. Rev.,2000:128:1971～1981.
Keppenne, C. L., and M. M. Rienecker. Initial testing of a massively parallel ensemble Kalman filter with the Poseidon isopycnal ocean general circulation model. Mon. Wea. Rev., 2002,130:2951～2965.
Keppenne C. L, M. M. Rienecker Assimilation of temperature into an isopycnal ocean general circulation model using a parallel ensemble Kalman filter. J Marine Sys 2003:40～41.
Kuo H. L. Further studies of the parameterization of the influence of cumulus convection on large-scale flow. J. Atmos. Sci.1974,31:1232～1240
Lonnberg, P. and A. Hollingsworth. The statistical structure of short-range forecast errors as determined from radiosonde data. Ⅱ:the covariance of height and wind errors. Tellus,1986, 38A:137～161.
Lorenc, A. C. A global three-dimensional multivariate statistical analysis scheme. Mon. Weather Rev.,1981,109:701～721.
Lorenz, E. N. A study of the predictability of a 28-variable atmospheric model. Tellus,1965,17: 321～333.
Lu, C. and G. L. Browning. Four-Dimensional Variational Data Assimilation for Limited-Area Models:Lateral Boundary Conditions, Solution Uniqueness, and Numerical Convergence. J. Atmos. Sci.,2000,57:1341～1353.
Meng, Z., and F. Zhang,2007:Test of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part Ⅱ:Imperfect model experiments. Mon. Wea. Rev.,135:1403～1423.
Mitchell, H. L., and P. L. Houtekamer. An. adaptive ensemble Kalman filter. Mon. Wea. Rev., 2000,128:416～433.
Mitchell, H. L. and P. L. Houtekamer. Ensemble Size, Balance, and Model-Error Representation in an Ensemble Kalman Filter. Mon. Wea. Rev.,2002,130:2791～2808.
Miyoshi T.2005. Ensemble Kalman Filter Experiments with a Primitive-Equation Global Model. Ph.D. thesis, University of Maryland.
Miyoshi, T. and S. Yamane. Local Ensemble Transform Kalman Filtering with an AGCM at a T159/L48 Resolution.SOLA,2007,3:037-040.
Moinn, A. S. and A. M. Obukhov. Basic laws of turbulent mixing in the atmosphere near the ground. Trakad Nuak SSSR Geofiz Inst,1954,24(151):161～187.
Okamoto K., M. Kazumori and H. Owada. The assimilation of ATOVS radiances in the JMA global analysis system. Journal of the Meteorological Society of Japan,2005,83(2):201～217.
Oke, P.R., P. Sakov, S. P. Corney. Impacts of localisation in the EnKF and EnOI:experiments with a small model. Ocean Dynamics,2007,57:32～45.
Oliver D. S. Moving Averages for Gaussian Simulation in Two and Three Dimensions. Mathematical Geology,1995,27(8):940～959.
Ott, E., B. R. Hunt, I. Szunyogh, A.V. Zimin, E. J. Kostelieh, M.Corazza, E.Kalnay, D.J. Patil, and J.A.Yorke. A local ensemble Kalman filter for atmospheric assimilation.Tellus,2004:56A, 415～428.
Pham, D. T. Stochastic methods for sequential data assimilation in strongly nonlinear systems. Mon. Wea. Rev.,2001,129:1194～1207.
Sakov, P. and P. Oke. Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters. Mon. Wea. Rev.,2008,136:1042～1053.
Szunyogh, I., E. J. Kostelich, G. Gyarmati, D. J. Patil, B. R. Hunt, E. Kalnay, E. Ott, and J. A. Yorke. Assessing a local ensemble Kalman filter:Perfect model experiments with the National Centers for Environmental Prediction global model. Tellus,2005,57A:528～545.
Talagrand O. Assimilation of observations, an introduction. J. Met. Soc. Japan.1997, Special Issue 75, 1B:191～209.
Tippett M. K., J. L. Anderson, C. H. Bishop, T. M. Hamill and J. S. Whitaker. Ensemble square-root filters. Mon. Wea. Rev.,2003,131:1485～1490.
Whitaker, J. S., G. P. Compo, X. Wei, and T. M. Hamill. Reanalysis without radiosondes using ensemble data assimilation. Mon. Wea. Rev.,2004,132:1190～1200.
Whitaker, J. S. and T. M. Hamill. Ensemble data assimilatrion without perturbed observations. Mon. Wea. Rev.,2002,130:1913～1924.
Zhang, F. Q. and C. Snyder. Ensemble-based data assimilaton. Bull. Amer. Meteor. Soc.,2007, 88:565-568.
Zhang, F. Q., M. Zhang, and J. A. Hansen. Coupling ensemble Kalman filter with four-dimensional variational data assimilation. Adv. Atmos. Sci.,2009:26(1),1～8, doi: 10.1007/s00376-009-0001-8.
Zheng, F., and J. Zhu. A multivariate empirical orthogonal function based scheme for balanced initial ensemble generation of an ensemble Kalman filtering. Adv. Atmos. Sci.,2009. (submitted)
Zhi, J. L. and I. M. Navon. Optimality of variational data assimilation and its relationship with the Kalman filter and smoother. Quart. J. Roy. Meteor. Soc.,2001,127: 661～684.
Zhu J, Kamachi M. An adaptive variational method for data assimilation with imperfect models. Tellus,2000,52A:265～279.
Zupanski, D. and F. Mesinger. Four-Dimensional Variational Assimilation of Precipitation Data. Mon. Weather Rev.,1995,123:1112～1127.
Eugenia Kalnay大气模式、资料同化和可预报性.北京,气象出版社,2005,8.
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.地球科学进展.2000,15：571～575.
高拴柱.集合Kalman滤波资料同化技术及研究现状.气象,2005,6：3～8.
刘成思,薛纪善.关于集合Kalman滤波的理论和方法的发展.热带气象学报,2005,21(6)：628～633.
刘志权,张凤英,吴雪宝,等.区域极轨卫星ATOVS辐射偏差订正方法研究.气象学报,2007, 65(1)：113～123.
黄小刚,费建芳,陆汉城.基于集合Kalman滤波数据同化的热带气旋路径集合预报研究.大气科学,2007,31(3)：468～478.
孟智勇、徐祥德、陈联,寿.卫星亮温资料四维同化方案及其对“7.20”武汉特大暴雨的模拟试验.大气科学,2002,26(5)：663～677.
潘宁、董超华、张文建ATOVS辐射率资料的直接变分同化试验研究.气象学报,2003,61(2)：226～236.
王宗皓、毛建平、黄继红,等.卫星探测数据对B～模式分析预报系统性误差的影响.气象学报,1993；51(1)：21～33.
王子厚、王宗皓、张凤英HIRS/2亮温直接应用于数值预报的试验研究.应用气象学报,1995,6(3)：273～280.
王超、万丰.数值预报/卫星反演/数据同化循环试验.气象学报,1997,55(6)：740～749.
翁永辉、徐祥德TOVS资料的变分处理方法在青藏高原地区的数值试验.大气科学,1999,23(6)：703～712.
张红华,沈桐立,王桂臣,朱琳.集合Kalman滤波同化理论及数值试验.中国气象学会2008年年会复杂地形影响下的天气与气候分会场论文集.2008.
张华,丑纪范,邱崇践.西北太平洋威马逊台风结构的卫星观测同化分析.科学通报,2004,49(5)：493～498.
庄照荣.集合Kalman滤波资料同化系统的设计及其在集合预报中的应用.中国科学院研究生院博士学位论文.2007.5.