Vol.23, NO.2, 2012
Turn off MathJax
Article Contents
Article Navigation >  Journal of Applied Meteorological Science  > 2012  >  23(2): 129-138
Wang Ruichun, Gong Jiandong, Zhang Lin. Statistical estimation of dynamic balance constraints in GRAPES variational data assimilation system. J Appl Meteor Sci, 2012, 23(2): 129-138.
Citation: Wang Ruichun, Gong Jiandong, Zhang Lin. Statistical estimation of dynamic balance constraints in GRAPES variational data assimilation system. J Appl Meteor Sci, 2012, 23(2): 129-138.
shu

Statistical Estimation of Dynamic Balance Constraints in GRAPES Variational Data Assimilation System

  • 1.

    School of Atmospheric Sciences, Nanjing University of Information Science & Technology, Nanjing 210044

  • 2.

    National Meteorological Center, Beijing 100081

  • Received Date: 2011-07-20
  • Rev Recd Date: 2012-01-09
  • Publish Date: 2012-04-30
    Abstract
  • Dynamic balance constraints that govern the atmospheric circulation play very important roles in the analysis of atmospheric state. These constraints indicate how it might be possible to determine one variable from another. As a result, they could help to avoid noise caused by gravity waves, and enable maximum information to be extracted from the observations.The existing GRAPES three-dimensional variational data assimilation system, which is defined on sigma coordinates, uses linear balance equation to ensure that mass and wind analysis increments to be geostrophically coupled. In this formulation, to deal with difficulties in solving the balance equation at sigma levels, analysis variables need to be interpolated to a series of auxiliary isobaric surface to calculate balanced components. A new formulation of estimating dynamic balance constraints is developed in the variation assimilation system. In the new scheme, regression coefficients between stream function and dimensionless pressure (Exner function), instead of the geostrophic balance equation in the original scheme, is used to describe the balance relationship between rotational wind and mass field. In addition, the balance relationship between rotational wind and divergent wind is similarly described by regression coefficients between stream function and velocity potential. Compared to the old scheme, the new formulation avoids repeated interpolations along the vertical direction, which would make the estimation simpler and more accurate.In the new formulation, the balanced coefficients are computed using NMC method, which is found to produce a useful approximation to the true balance constraints in atmosphere. Based on 24 h, 48 h GRAPES forecast differences, linear regression is carried out for each level and for each latitude. By doing this an implied latitude-dependent structure in the dimensionless pressure is directly included in the analysis. Statistical results show that the explained variance of dimensionless pressure is primarily in the extratropics with the variance best explained below 100 hPa in this new formulation. And the explained velocity potential ratio has a maximum in the middle and high latitudes near the surface. Results of randomization and single-observation experiments indicate that, in regions where geostrophic balance is appropriate, the new formulation behaves similarly to the original scheme. However, in regions where geostrophic balance is not appropriate, the new formulation could allow for a smooth decoupling of stream function and dimensionless pressure, while the original scheme can not. Such properties of the new formulation could help variational data assimilation system get more reasonable analysis results in tropics and tropopause. Moreover, by adding the balance relationship between rotational wind and divergent wind, the new formulation could derive a more reasonable wind field in boundary layer.
    • FullText(HTML)
    References(25)

  • Fig. 1  Zonal average of the explained variance ratios of velocity potential (a) and dimensionless pressure (b)

    DownLoad: Full-Size Img PowerPoint

    Fig. 2  Zonal average of simulated background error standard deviations of dimensionless pressure in the original scheme (a) and the new scheme (b)(unit: 10-4)

    DownLoad: Full-Size Img PowerPoint

    Fig. 3  Zonal average of simulated background error standard deviations of velocity potential (a) and its balance part (b) in the new scheme (unit: 106m2·s-1)

    DownLoad: Full-Size Img PowerPoint

    Fig. 4  Dimensionless pressure increments generated by a simulated u component wind observation on the 12th model level at 45.5°N, 125.5°E which is 5 m·s-1stronger than background wind (unit: 10-5)

    (a) horizontal distribution of the original scheme, (b) horizontal distribution of the new scheme, (c) meridional section of the original scheme, (d) meridional section of the new scheme

    DownLoad: Full-Size Img PowerPoint

    Fig. 5  Dimensionless pressure increments generated by a simulated u component wind observation on the 24th model level at 45.5°N, 125.5°E which is 5 m·s-1stronger than background wind (unit: 10-5)

    (a) horizontal distribution of the original scheme, (b) horizontal distribution of the new scheme

    DownLoad: Full-Size Img PowerPoint

    Fig. 6  Dimensionless pressure increments generated by a simulated u component wind observation on the 12th model level at 5.5°N, 125.5°E which is 5 m·s-1stronger than background wind (unit:10-6)

    (a) horizontal distribution of the original scheme, (b) horizonal distribution of the new scheme

    DownLoad: Full-Size Img PowerPoint

    Fig. 7  Wind increments generated by a simulated pressure observation on the first model level at 45.5°N, 125.0°E which is 1 hPa higher than the background (unit:m·s-1)

    (a)u increment of the original scheme, (b)u increment of the new scheme, (c)v increment of the original scheme, (d)v increment of the new scheme

    DownLoad: Full-Size Img PowerPoint

    Table  1  Roughly corresponding pressure values of GRAPES model levels in Dec, Jan and Feb

    模式面 全球平均气压/hPa
    第4层 900
    第8层 740
    第12层 566
    第16层 403
    第20层 262
    第24层 153
    第28层 69
    第32层 26
    第36层 8.8
    DownLoad: Download CSV
  • [1]
    Daley R. Atmospheric Data Analysis. Cambridge: Cambridge University Press, 1991: 2-6; 107-118.
    [2]
    Kalnay E. Atmospheric modeling, data assimilation and predictability. Cambridge: Cambridge University Press, 2003: 186-190.
    [3]
    Lönnberg 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: 137-161. doi:  10.1111/tela.1986.38A.issue-2
    [4]
    Courtier P, Talagrand O. Variational assimilation of meteorological observations with direct and adjoint shallow-water equations. Tellus, 1990, 42A: 531-549. doi:  10.3402/tellusa.v42i5.11896
    [5]
    薛纪善.新世纪初我国数值天气预报的科技创新研究.应用气象学报, 2006, 17(5): 602-610. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=200605103&flag=1
    [6]
    曾智华, 马雷鸣, 梁旭东, 等. MM5数值预报引入GRAPES三维变分同化技术在上海地区的预报和检验.应用气象学报, 2004, 15(5): 534-542. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20040566&flag=1
    [7]
    Parrish D F, Derber J C. The national meteorological center's spectral statistical interpolation analysis system. Mon Wea Rev, 1992, 120: 1747-1763. doi:  10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2
    [8]
    Lorenc A. A global three-dimensional multivariate statistical interpolation scheme. Mon Wea Rev, 1981, 109: 701-721. doi:  10.1175/1520-0493(1981)109<0701:AGTDMS>2.0.CO;2
    [9]
    Derber J, Bouttier F. A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus, 1999, 51A: 195-221. doi:  10.1034/j.1600-0870.1999.t01-2-00003.x/citedby
    [10]
    Wu W S, Purser R J, Parrish D F. Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon Wea Rev, 2002, 130: 2905-2916. doi:  10.1175/1520-0493(2002)130<2905:TDVAWS>2.0.CO;2
    [11]
    Barker M D, Huang W, Guo Y R, et al. A three-dimensional variational data assimilation system for MM5: Implementation and initial results. Mon Wea Rev, 2004, 132: 897-914. doi:  10.1175/1520-0493(2004)132<0897:ATVDAS>2.0.CO;2
    [12]
    Lorenc A, Ballard S P, Bell R S, et al. The Met. Office global three-dimensional variational data assimilation scheme. Q J R Meteorol Soc, 2000, 126: 2991-3012. doi:  10.1002/(ISSN)1477-870X
    [13]
    朱乾根, 林景瑞, 寿绍文, 等.天气学原理和方法.北京:气象出版社, 2000: 22-59.
    [14]
    庄世宇, 薛纪善, 朱国富, 等. GRAPES全球三维变分同化系统——基本设计方案与理想试验.大气科学, 2005, 29(6): 872-884. http://www.cnki.com.cn/Article/CJFDTOTAL-DQXK200506003.htm
    [15]
    马旭林, 庒照荣, 薛纪善, 等. GRAPES非静力数值预报模式的三维变分同化系统的发展.气象学报, 2009, 67(1): 50-60. doi:  10.11676/qxxb2009.006
    [16]
    陈德辉, 杨学胜, 张红亮, 等.多尺度非静力通用模式框架的设计策略.应用气象学报, 2003, 14(4): 452-461. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20030456&flag=1
    [17]
    黄丽萍, 伍湘君, 金之雁. GRAPES模式标准初始化方案设计与实现.应用气象学报, 2005, 16(3): 374-384. doi:  10.11898/1001-7313.20050312
    [18]
    陈德辉, 沈学顺.新一代数值预报系统GRAPES研究进展.应用气象学报, 2006, 17(6): 773-777. doi:  10.11898/1001-7313.20060614
    [19]
    Bannister R N. A review of forecast error covariance statistics in atmospheric variational data assimilation. Ⅱ: Modelling the forecast error covariance statistics. Q J R Meteorol Soc, 2008, 134: 1971-1996. doi:  10.1002/qj.v134:637
    [20]
    薛纪善, 陈德辉.数值预报系统GRAPES的科学设计与应用.北京:气象出版社, 2008: 6-11.
    [21]
    Bannister R N. A review of forecast error covariance statistics in atmospheric variational data assimilation. Ⅰ: Characteristics and measurements of forecast error covariances. Q J R Meteorol Soc, 2008, 134: 1951-1970. doi:  10.1002/qj.v134:637
    [22]
    成秋影.天气分析和诊断方法.北京:气象出版社, 1992: 152-156.
    [23]
    沈桐立, 田永祥, 葛孝贞, 等.数值天气预报.北京:气象出版社, 2003: 267-293.
    [24]
    Ingleby N B. The statistical structure of forecast errors and its representation in the met office global 3-D variational data assimilation scheme. Q J R Meteorol Soc, 2001, 127: 209-231. doi:  10.1002/(ISSN)1477-870X
    [25]
    Andersson E, Fisher M, Munro R, et al. Diagnosis of background errors for radiances and othe observable quantities in a variational data assimilation scheme, and the explanation of case of poor convergence. Q J R Meteorol Soc, 2000, 126: 1455-1472. doi:  10.1256/smsqj.56511
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中
  • -->

Catalog

    Figures(7)  / Tables(1)

    Get Citation
    PDF
    XML
    Article views (4108) PDF downloads(1627) Cited by()
    • Received : 2011-07-20
    • Accepted : 2012-01-09
    • Published : 2012-04-30
    Journal Online
    Contact

    © 2020 Journal of Applied Meteorological Science   京ICP备15006967号-1

    Supported by Beijing Renhe Information Technology Co. Ltd

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return