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EnKF中误差协方差优化方法及在资料同化中应用

梁晓 郑小谷 戴永久 师春香

梁晓, 郑小谷, 戴永久, 等. EnKF中误差协方差优化方法及在资料同化中应用. 应用气象学报, 2014, 25(4): 397-405..
引用本文: 梁晓, 郑小谷, 戴永久, 等. EnKF中误差协方差优化方法及在资料同化中应用. 应用气象学报, 2014, 25(4): 397-405.
Liang Xiao, Zheng Xiaogu, Dai Yongjiu, et al. A method of improving error covariances in EnKF and its application to data assimilation. J Appl Meteor Sci, 2014, 25(4): 397-405.
Citation: Liang Xiao, Zheng Xiaogu, Dai Yongjiu, et al. A method of improving error covariances in EnKF and its application to data assimilation. J Appl Meteor Sci, 2014, 25(4): 397-405.

EnKF中误差协方差优化方法及在资料同化中应用

资助项目: 

公益性行业 (气象) 科研专项 GYHY201206013,GYHY201306045

国家国际科技合作专项 2011DFG23150

详细信息
    通信作者:

    梁晓, email: liangx@cma.gov.cn

A Method of Improving Error Covariances in EnKF and Its Application to Data Assimilation

  • 摘要: 集合卡尔曼滤波 (the Ensemble Kalman Filter,简称EnKF) 中将预报集合的统计协方差作为预报误差协方差,但该估计可能严重偏离真实的预报误差协方差,影响同化精度。基于极大似然估计理论,发展了一种优化预报误差协方差矩阵的实时膨胀方法,即MLE (the Maximum Likelihood Estimation) 方法。利用蒙古国基准站Delgertsgot (简称DGS站) 观测资料,基于EnKF方法和MLE方法,在通用陆面模式 (the Common Land Model,简称CoLM) 中同化了地表温度和10 cm土壤温度观测资料,建立了土壤温度同化系统。结果表明:MLE方法对地表温度和各层土壤温度 (尤其深层土壤温度) 的估计比EnKF方法准确。考虑到浅层和深层土壤温度的差别,在实施MLE方法时对浅层和深层土壤温度采用了不同的膨胀因子。对比膨胀因子为单一标量时的结果,多因子膨胀能缓解深层土壤温度的不合理膨胀,改善同化效果。
  • 图  1  2003年9月1—30日地表温度 (a) 和3 cm土壤温度 (b) 观测场、模拟场和同化场平均日变化

    Fig. 1  The diurnal variation of observed, simulated and assimilated soil temperature at 0 cm (a) and 3 cm (b) averaged from 1 Sep to 30 Sep in 2003

    图  2  2003年9月1—30日10 cm (a) 和40 cm (b) 土壤温度观测场、模拟场和同化场变化

    Fig. 2  The observed, simulated and assimilated soil temperature at 10 cm (a) and 40 cm (b) from 1 Sep to 30 Sep in 2003

    图  3  MLE1方法和MLE2方法分别同化得到2003年9月1—30日40 cm (a) 和100 cm (b) 土壤温度

    Fig. 3  Soil temperature at 40 cm (a) and 100 cm (b) assimilated by MLE1 and MLE2 from 1 Sep to 30 Sep in 2003

    图  4  2003年9月1—30日3 cm土壤湿度观测场、模拟场和同化场

    Fig. 4  The observed, simulated and assimilated soil moisture at 3 cm from 1 Sep to 30 Sep in 2003

    表  1  2003年9月1—30日土壤温度模拟场和同化场平均的均方根误差 (单位:K)

    Table  1  Root mean square error of the simulated and assimilated soil temperature from 1 Sep to 30 Sep in 2003(unit:K)

    方法土壤温度
    0 cm3 cm10 cm40 cm100 cm
    COLM模拟3.7053.7041.0683.61812.907
    EnKF3.6553.4850.6981.8364.217
    MLE13.3343.2150.7522.4105.574
    MLE23.1483.1680.6521.2893.493
    下载: 导出CSV
  • [1] Evensen G.Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics.J Geophys Res, 1994, 99(C5):10143-10162. doi:  10.1029/94JC00572
    [2] Burgers G, Leeuwen P J V, Evensen G.Analysis scheme in the Ensemble Kalman Filter.Mon Wea Rev, 1998, 126:1719-1724. doi:  10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2
    [3] Evensen G.The ensemble Kalman filter:Theoretical formulation and practical implementation.Ocean Dynam, 2003, 53(4):343-367. doi:  10.1007/s10236-003-0036-9
    [4] Senegas J, Wackernagel H H, Rosenthal W, et al.Error covariance modeling in sequential data assimilation.Stoch Env Res Risk A, 2001, 15:65-86. doi:  10.1007/PL00009788
    [5] Daley R.Atmospheric Data Analysis.Cambridge:Cambridge University Press, 1991.
    [6] Kalnay E.Atmospheric Modeling, Data Assimilation, and Predictability.Cambridge:Cambridge University Press, 2002.
    [7] Anderson J L, Anderson S L.A Monte Carlo implementation of the non-linear filtering problem to produce ensemble assimilations and forecasts.Mon Wea Rev, 1999, 127:2741-2758. doi:  10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2
    [8] Constantinescu E M, Sandu A, Chai T, et al.Ensemble-based chemical data assimilation.I:General approach.Q J R Meteorol Soc, 2007, 133:1229-1243. doi:  10.1002/(ISSN)1477-870X
    [9] Dee D P.On-line estimation of error covariance parameters for atmospheric data assimilation.Mon Wea Rev, 1995, 123(4):1128-1145. doi:  10.1175/1520-0493(1995)123<1128:OLEOEC>2.0.CO;2
    [10] Dee D P, da Silva A M.Maximum-likelihood estimation of forecast and observation error covariance parameters.Part Ⅰ:Methodology.Mon Wea Rev, 1999, 127:1822-1834. doi:  10.1175/1520-0493(1999)127<1822:MLEOFA>2.0.CO;2
    [11] Dee D P, Gaspari G, Redder C, et al.Maximum-likelihood estimation of forecast and observation error covariance parameters.Part Ⅱ:Applications.Mon Wea Rev, 1999, 127:1835-1849. doi:  10.1175/1520-0493(1999)127<1835:MLEOFA>2.0.CO;2
    [12] Wang X, Bishop C H.A comparison of breeding and ensemble transform Kalman filter ensemble forecast schemes.J Atmos Sci, 2003, 60:1140-1158. doi:  10.1175/1520-0469(2003)060<1140:ACOBAE>2.0.CO;2
    [13] Li H, Kalnay E, Miyoshi T.Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter.Q J R Meteorol Soc, 2009, 135(639):523-533. doi:  10.1002/qj.v135:639
    [14] Miyoshi T.The gaussian approach to adaptive covariance inflation and its implementation with the Local Ensemble Transform Kalman Filter.Mon Wea Rev, 2011, 139:1519-1535. doi:  10.1175/2010MWR3570.1
    [15] Zheng X G.An adaptive estimation of forecast error covariance parameters for Kalman filtering data assimilation.Adv Atmos Sci, 2009, 26:154-160. doi:  10.1007/s00376-009-0154-5
    [16] Liang X, Zheng X G, Zhang S P, et al.Maximum likelihood estimation of inflation factors on error covariance matrices for ensemble Kalman filter assimilation.Q J R Meteorol Soc, 2011, 138:263-273, doi: 10.1002/qj.912.
    [17] Huang C L, Li X, Lu L.Retrieving soil temperature profile by assimilating MODIS LST products with ensemble Kalman filter.Rem Sens Environ, 2008, 112:1320-1336. doi:  10.1016/j.rse.2007.03.028
    [18] Yang K, Koike T, Kaihotsu I, et al.Validation of a dual-pass microwave land data assimilation system for estimating surface soil moisture in semiarid regions.J Hydrometeorology, 2009, 10(3):780-793. doi:  10.1175/2008JHM1065.1
    [19] 杨晓峰, 陆其峰, 杨忠东.基于AMSR-E土壤湿度产品的LIS同化试验.应用气象学报, 2013, 24(4):435-445. doi:  10.11898/1001-7313.20130406
    [20] 吴统文, 宋连春, 刘向文, 等.国家气候中心短期气候预测模式系统业务化进展.应用气象学报, 2013, 24(5):533-543. doi:  10.11898/1001-7313.20130503
    [21] 王莉, 黄嘉佑.Kalman滤波的试验应用研究.应用气象学报, 1999, 10(3):276-282. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=19990370&flag=1
    [22] 赵晓琳, 朱国富, 李泽椿.基于TIGGE资料识别适应性观测敏感区的应用研究.应用气象学报, 2010, 21(4):405-415. doi:  10.11898/1001-7313.20100403
    [23] Whitaker J S, Hamill T H.Ensemble data assimilation without perturbed observations.Mon Wea Rev, 2002, 130:1913-1924. doi:  10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2
    [24] Dai Y J, Zeng X B, Dickinson R E, et al.The common land model.Bull Amer Meteor Soc, 2003, 84:1013-1023. doi:  10.1175/BAMS-84-8-1013
    [25] 孟春雷, 张朝林.路面气象数值预报模型及性能检验.应用气象学报, 2012, 23(4):451-458. doi:  10.11898/1001-7313.20120408
    [26] Koike T.Coordinated Enhanced Observing Period (CEOP)-An initial step for integrated global water cycle observation.World Meteorological Organization Bulletin, 2004, 53(2):115-121.
    [27] 龚建东, 赵刚.全球资料同化中误差协方差三维结构的准确估计与应用:背景误差协方差调整与数值试验分析.气象学报, 2006, 64(6):669-682. doi:  10.11676/qxxb2006.065
    [28] 曹小群, 黄思训, 张卫民, 等.区域三维变分同化中背景误差协方差的模拟.气象科学, 2008, 28(1):8-14. http://www.cnki.com.cn/Article/CJFDTOTAL-QXKX200801004.htm
    [29] 马旭林, 庄照荣, 薛纪善, 等.GRAPES非静力数值预报模式的三维变分资料同化系统的发展.气象学报, 2009, 67(1):50-60. doi:  10.11676/qxxb2009.006
    [30] 王曼, 李华宏, 段旭, 等.WRF模式三维变分中背景误差协方差估计.应用气象学报, 2011, 22(4):482-492. doi:  10.11898/1001-7313.20110411
    [31] Jin R, Li X.Improving the estimation of hydrothermal state variables in the active layer of frozen ground by assimilating in situ observations and SSM/I data.Sci China Ser D:Earth Sci, 2009, 39(9):1220-1231. http://en.cnki.com.cn/Article_en/CJFDTOTAL-JDXG200911007.htm
    [32] Anderson J L.Spatially and temporally varying adaptive covariance inflation for ensemble filters.Tellus, 2009, 61:72-83. doi:  10.1111/tea.2008.61.issue-1
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出版历程
  • 收稿日期:  2014-01-06
  • 修回日期:  2014-05-05
  • 刊出日期:  2014-07-31

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