背景场误差的结构特征及其对三维变分同化影响的研究
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摘要
在变分同化方法中，背景误差协方差矩阵对保证变分问题解的唯一性及分析的平滑性，反映不同变量之间的关系有着非常重要的作用。构造合理的背景误差协方差矩阵对于同化系统至关重要，甚至会决定同化分析的好坏。
目前我国的变分同化研究和国外比起步较晚，在背景误差协方差统计结构研究方面尚没有取得可以实际应用的成果，背景误差协方差统计结构研究成为当前数值预报业务与研究工作的一个亟待解决的问题。本文主要研究背景误差协方差结构的统计特征及其对三维变分同化系统的影响。
本文主要利用观测余差方法用T213模式的12小时、24小时预报资料和无线电探空观测资料统计出背景误差协方差样本，对单层的背景误差协方差样本进行高斯相关函数拟合，得到水平特征尺度与背景误差方差、观测误差方差：对于各层间的背景误差协方差结构进行分析时，分别用直接方法和厚度方法，得到各层间的背景误差协方差近似函数；在垂直方向用二阶自回归相关函数和垂直距离变换方法研究垂直背景误差的结构；最终获得水平和垂直可以分离的三维背景误差协方差空间分布模型。对于不同的相关函数模型对背景误差协方差的拟合也做了相关分析对比。
利用以上估计的背景误差和水平特征尺度，本文替换了GRAPES三维变分同化系统中原背景误差和水平特征尺度方案，并用GRAPES系统进行了台风同化预报试验。通过比较发现，同时改进GRAPES中水平特征尺度和背景误差后，改善了涡旋分析系统的风压平衡，提高了分析的质量。另外，对台风的强度和路径于预报也有一定的改善。
Background error covariance is very important to assure exclusive result, to govern the amount of smoothing of the observed information and to decide relationships between different variables in variational data assimilation. To a large extent, the form of this background error covariance governs the resulting objective analysis.
Because the research of variational data assimilation in our country is not advanced, there is little result in research of background error covariance, which is becoming a desiderating problem in present numerical weather prediction (NWP) operation and research work. The statistical structure of background error covariance and its impact on three-dimension variational data assimilation system are studied in this paper.
In order to get the height-height background error covariance, the innovation vector method is used in this paper. The data consisted of innovation data (12 h and 24 h predicted height of T213 model minus radiosonde measurements) at times 00 UTC and 12 UTC. Horizontal characteristic length, prediction error variance and observation error variance are obtained using Gauss correlation function in a particular level. The straightforward way and the empirical thickness method are used to get approximate function in interlevel values. In vertical direction, vertical covariance approximation is obtained by the second-order autoregressive (SOAR) correlation function and distance transformation method. The resulting three-dimensional approximation function is partially separable, being the product of the horizontal covariance function and the vertical correlation function. Different correlation functions fitting background error covariance are investigated and the results are given.
With new statistic background errors and horizontal characteristic length, the impact of background error covariance has been checked by comparing and analyzing the result of assimilation. With the NWP initial field attained by the assimilation, the process of typhoon has been forecasted through the GRAPES model. It was found that new statistic background errors and horizontal characteristic length have the potential to improve the quality of analysis field and the accuracy of track and precipitation forecast of tropical cyclone.
目前我国的变分同化研究和国外比起步较晚，在背景误差协方差统计结构研究方面尚没有取得可以实际应用的成果，背景误差协方差统计结构研究成为当前数值预报业务与研究工作的一个亟待解决的问题。本文主要研究背景误差协方差结构的统计特征及其对三维变分同化系统的影响。
本文主要利用观测余差方法用T213模式的12小时、24小时预报资料和无线电探空观测资料统计出背景误差协方差样本，对单层的背景误差协方差样本进行高斯相关函数拟合，得到水平特征尺度与背景误差方差、观测误差方差：对于各层间的背景误差协方差结构进行分析时，分别用直接方法和厚度方法，得到各层间的背景误差协方差近似函数；在垂直方向用二阶自回归相关函数和垂直距离变换方法研究垂直背景误差的结构；最终获得水平和垂直可以分离的三维背景误差协方差空间分布模型。对于不同的相关函数模型对背景误差协方差的拟合也做了相关分析对比。
利用以上估计的背景误差和水平特征尺度，本文替换了GRAPES三维变分同化系统中原背景误差和水平特征尺度方案，并用GRAPES系统进行了台风同化预报试验。通过比较发现，同时改进GRAPES中水平特征尺度和背景误差后，改善了涡旋分析系统的风压平衡，提高了分析的质量。另外，对台风的强度和路径于预报也有一定的改善。
Background error covariance is very important to assure exclusive result, to govern the amount of smoothing of the observed information and to decide relationships between different variables in variational data assimilation. To a large extent, the form of this background error covariance governs the resulting objective analysis.
Because the research of variational data assimilation in our country is not advanced, there is little result in research of background error covariance, which is becoming a desiderating problem in present numerical weather prediction (NWP) operation and research work. The statistical structure of background error covariance and its impact on three-dimension variational data assimilation system are studied in this paper.
In order to get the height-height background error covariance, the innovation vector method is used in this paper. The data consisted of innovation data (12 h and 24 h predicted height of T213 model minus radiosonde measurements) at times 00 UTC and 12 UTC. Horizontal characteristic length, prediction error variance and observation error variance are obtained using Gauss correlation function in a particular level. The straightforward way and the empirical thickness method are used to get approximate function in interlevel values. In vertical direction, vertical covariance approximation is obtained by the second-order autoregressive (SOAR) correlation function and distance transformation method. The resulting three-dimensional approximation function is partially separable, being the product of the horizontal covariance function and the vertical correlation function. Different correlation functions fitting background error covariance are investigated and the results are given.
With new statistic background errors and horizontal characteristic length, the impact of background error covariance has been checked by comparing and analyzing the result of assimilation. With the NWP initial field attained by the assimilation, the process of typhoon has been forecasted through the GRAPES model. It was found that new statistic background errors and horizontal characteristic length have the potential to improve the quality of analysis field and the accuracy of track and precipitation forecast of tropical cyclone.
引文
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[2] 王跃山．客观分析和四维同化—站在新世纪的回望(Ⅱ)客观分析的主要方法(1)．气象科技，2001，1：1—9
[3] F.Vandenberghe, Y.-H.Kuo. Introduction to the MM5 3D-VAR data assimilation system: Theoretical basis. NCAR. Technical Note, 1999, 1-38
[4] 沈桐立，田永祥等．数值天气预报．北京：气象出版社．2003．237-240
[5] 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(5)
[6] 薛纪善，庄世宇，朱国富，张华．GRAPES 3D-Var系统的科学设计方案(内部交流)．中国气象科学研究院数值预报研究中心，2001
[7] Drozdov O., Shepelevskii A. The theory of interpolation in a stochastic field of meteorological elements and its application to meteorological map and network rationalization problems. Trudy Niu Gugrns Series, 1946, 1: 13
[8] Rutherford I. Data assimilation by statistical interpolation of forecast error fields. J. Atmos. Sci, 1972, 29: 809-15
[9] Hollingsworth A., 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
[10] Lonnberg P., Hollingsworth A. The statistical structure of short-range forecast errors as determined from radiosonde data. Part Ⅱ The covariance of height and wind errors. Tellus, 1986, 38A: 137-61
[11] Richard Franke. Three-Dimensional Covariance Functions for NOGAPS Data. Monthly Weather Review, 1999, 127: 2293-2308
[12] Xu Qin, Li Wei, Andrew Van Tuyl, Barker Edward H. Estimation of Three-Dimensional Error Covariances.Part Ⅰ:Analysis of Height Innovation Vectors. Monthly Weather Review, 2001, 129: 2126-2135
[13] Schlatter T. Some experiments with a multivariate statistical objective analysis scheme. Mon.Wea.Rev., 1975, 103: 246-257
[14] Bengtsson L., Gustavsson N. An experiment in the assimilation of data in dynamic analysis. Tellus, 1971, 23: 328-336
[15] Ghil M., Cohn S., Tavantzis J., Bube K., Issacson E. Applications of estimation theory to numerical weather prediction. In Dynamic meteorology: data assimilation methods. Bengtsson L., Ghil M., Kallen E. New York:Springerverlag, 1981, 139-224
[16] Dee D., Gaspari G. Development of anisotropic correlation models for atmospheric data assimilation. The 11th conference on numerical weather prediction, Norfolk, Va, USA, American Meteorological Society, 1996, 249-251
[17] Yaglom A. Stationary random functions.1962, English edition, New York: Dover, 1973
[18] Buell C. Correlation functions for wind and geopotential on isobaric surfaces. J. Appl. Meteor, 1972a, 11: 51-59
[19] Julian P., Thiebau H.J.On some properties of correlation functions used in optimun interpolation schemes. Mon. Wea. Rev., 1975, 103: 605-616
[20] Thiebaux H. J. Anisotrophic correlation functions for objective analysis. Mon. Wea. Rev., 1976, 104: 994-1002
[21] Seaman R. A systematic description of the spatial variability of geopotential and temperature in the Australian region. Aust. Met. Mag, 1982, 30: 133-141
[22] Buell C., Seaman R. The "scissors effect": anisotropic and ageostrophic influences on wind correlation coefficients. Aust. Met. Mag, 1983, 31: 77-83
[23] Bouttier F. A dynamical estimation of forecast error covariances in an assimilation system. Mon. Wea. Rev., 1994, 122: 2376-2390
[24] Benjamin S. G. An isentropic meso α-scale analysis system and its sensitivity to aircraft and surface observations. Mon. Wea. Rev., 1989, 117: 1586-1603
[25] Lars peter Rhshθjgaard. A direct way of specifying flow-dependent background error correlations for meteorological analysis systems. Tellus, 1998, 51A: 42-57
[26] Hollingsworth A. Objective analysis for numerical weather prediction. In: Short and medium range numerical weather prediction, collected papers presented at WMO/IUGG NWP symposium, Tokyo, August 1986, Matsuno T., ed. Special volume of the J.Meteor.Soc.Japan: 11-59
[27] 陈德辉等．新一代多尺度数值预报系统(区域)技术手册(内部交流)．北京．2002．
[28] Lorenc A. C. A global three-dimensional multivariate statistical interpolation scheme. Mon. Wea. Rev., 1981, 109: 701-721
[29] Bouttier F., Courtier P. Data Assimilation Concepts and Methods March 1999. Meteorological Training Course Lecture Series, ECMWF, 2002.
[30] Courtier Ph.J.N., Thepaut, Hollingworth A. A strategy for operational implementation of 4D-VAR using an incremental approach. Quart.J.R.Met.Soc, 1994, 120: 1367-1387
[31] Dale Barker. A General Formulation for 3DVAR Control Variables. NCAR Technical Note, 1999, 1-22
[32] Lorenc A. C. Iterative analysis using covariance functions and filters. Q. J. R. Meteorol. Soc, 1992, 118: 569-591
[33] Hayden C. M., Purser R. J. Recursive filter objective analysis of meteorological fields: application to NESDIS operational processing. J. Appl. Meteo, 1995, 34: 3-15
[34] Gal-chen T, Somerville R. C. J. On use of a coordinate transformation for the resolution of the Navier-Stokes equation. J. Comput. Phys, 1975, 17: 209-228
[35] Bubnova R. Integration of the fully elastic equations cast in the hydrostatic pressure terrain—following coordinate in the frame work of the ARPEGE/ALADIN NWP system.
Mon. Wea. Rev., 1995, 123: 515—535
[36] Laprise R. The Euler equations of motion with hydrostatic pressure as an independent variable. Mon. Wea. Rev., 1992, 120: 197—207
[37] Gottlieb D., Orszag S. A. Numerical Analysis of Spectral Methods: Theory and Application, CBMS—NSF, Regional Conference Series in Applied Math., 1977, 26
[38] 蒋伯诚等．计算物理中的谱方法—FFT及其应用．湖南科学技术出版社，1989
[39] 廖洞贤等．数值天气预报中的若干新技术．北京：气象出版社，1995
[40] 廖洞贤，朱艳秋．Tschebycheff函数在大气模式垂直离散问题中的应用．应用气象学报，1995，6(2)：213—219
[41] Liao Dongxian, Hu ming. Design of a 3-dimensional global adiabatic spectral primitive equation model. Acta Meteor. Sinica, 1997, 11(4): 414—431
[42] 胡志晋，邹光源．大气非静力平衡模式和弹性适应．中国科学，1991，B辑(5)：550—560
[43] Cote J., Gravel S., Methot A., Patoine A., Roch M., Staniforth A. The operational CMC-MRB Global Environmental Multiscale (GEM) Model. Part Ⅰ: Design consideration and formulation. Mon. Wea. Rev., 1998, 126: 1373-1395
[44] Grell G. A. A description of the fifth—generation Penn. State/NCAR mesoscale model (MM5). NCAR Technical Note, NCAR/TN—398+STR. 1994
[45] Lynch P., Huang X. Y. Initialization of the HIRLAM model using a digital filter. Mon. Wea. Rev., 1992, 120: 1019—1034
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