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The ensemble variational data assimilation method may be subject to significant uncertainties due to the size of forecast ensemble. We found that this problem occurs because the analysis increment of this method is expressed as a linear combination of ensemble perturbation vectors or expansion of the orthogonal basis vectors. Though this method avoids introducing adjoint model while calculating the gradient of object function, the number of physical control variables is much larger than the sample size of forecast ensemble, which causes the assimilation results to be sensitive to the number of ensemble members. For this reason, the regional successive analysis scheme of ensemble variational method is proposed. By this scheme, the ratio between the number of physical control variables in analysis region and the sample size is decreased, so that it is expected that the problem can be solved. The results of numerical experiments using shallow water model show that the regional successive analysis scheme can give better assimilation results than traditional method, and the analysis precision is improved appreciably.
[1] Huang X Y, Xiao Q, Barker D M 2009 Mon. Wea. Rev. 137 299
[2] Cao X Q, Huang S X, Du H D 2008 Acta Phys. Sin. 57 1984 (in Chinese)[曹小群, 黄思训, 杜华栋2008 物理学报 57 1984]
[3] Cao X Q, Zhang W M, Song J Q 2012 Acta Phys. Sin. 61 020507 (in Chinese)[曹小群, 张卫民, 宋君强2012 物理学报61 020507]
[4] Evensen G 1994 J. Geophys. Res. 99 10143
[5] Houtekamer P L, Mitchell H L 2001 Mon. Wea. Rev. 129 123
[6] Lorenc A C 2003 Q. J. R. Meteorol. Soc. 129 3183
[7] VanLeeuwen P J 2010 Q. J. R. Meterorol. Soc. 136 1991
[8] Leng H Z, Song J Q, Cao X Q 2012 Acta Phys. Sin. 61 070501 (in Chinese)[冷洪泽, 宋君强, 曹小群2012 物理学报61 070501]
[9] Du Z C, Tang B, Li K 2006 Acta Phys. Sin. 55 999 (in Chinese)[杜正聪, 唐斌, 李可2006 物理学报55 999]
[10] Snyder C, Zhang F 2003 Mon. Wea. Rev. 131 1663
[11] Kalnay E, Li H, Miyoshi T 2007 Tellus Ser. A 59 758
[12] Cao X Q, Song J Q, Zhang W M 2011 Acta Phys. Sin. 60 070511 (in Chinese)[曹小群, 宋君强, 张卫民2011 物理学报60 070511]
[13] Wang S C, Li Y, Zhang W M 2011 Acta Phys. Sin. 60 099203 (in Chinese)[王舒畅, 李毅, 张卫民2011 物理学报 60 099203]
[14] Qiu C J, Zhang L, Shao A M 2007 Sci. China D 50 1232
[15] Chou J F, Li J P, Gao L 2006 Chin. Phys. 15 882
[16] Liu C S, Xiao Q, Wang B 2008 Mon. Wea. Rev. 136 3363
[17] Zupanski M, Navon I M, Zupanski D 2008 Q. J. R. Meteorol. Soc. 134 1039
[18] Han Y Q, Zhong Z, Wang Y F 2013 Acta Phys. Sin. 62 049201 (in Chinese)[韩月琪, 钟中, 王云峰2013 物理学报 62 049201]
[19] Wang B, Zhao Y 2005 Acta Meteo. Sin. 63 694 (in Chinese)[王斌, 赵颖2005 气象学报63 694]
[20] Zhang F Q, Zhang M, James A 2009 Adv. Atmos. Sci. 26 1
[21] Zhang L, Qiu C J, Zhang S W 2009 Acta Meteo. Sin. 67 1124 (in Chinese) [张蕾, 邱崇践, 张述文2009 气象学报67 1124]
[22] Shao A M, Qiu X B, Qiu C J 2011 Plateau Meteo. 30 583 (in Chinese)[邵爱梅, 邱晓滨, 邱崇践2011 高原气象 30 583]
[23] Jazwinski A H 1970 Stochastic Processes and Filtering Theory (1st Ed.) (New York: Academic Press) p376
[24] Lorenc A C 1992 Q. J. R. Meteorol. Soc. 118 569
[25] Liu D C, Nocedal J 1989 Math. Programming 45 503
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[1] Huang X Y, Xiao Q, Barker D M 2009 Mon. Wea. Rev. 137 299
[2] Cao X Q, Huang S X, Du H D 2008 Acta Phys. Sin. 57 1984 (in Chinese)[曹小群, 黄思训, 杜华栋2008 物理学报 57 1984]
[3] Cao X Q, Zhang W M, Song J Q 2012 Acta Phys. Sin. 61 020507 (in Chinese)[曹小群, 张卫民, 宋君强2012 物理学报61 020507]
[4] Evensen G 1994 J. Geophys. Res. 99 10143
[5] Houtekamer P L, Mitchell H L 2001 Mon. Wea. Rev. 129 123
[6] Lorenc A C 2003 Q. J. R. Meteorol. Soc. 129 3183
[7] VanLeeuwen P J 2010 Q. J. R. Meterorol. Soc. 136 1991
[8] Leng H Z, Song J Q, Cao X Q 2012 Acta Phys. Sin. 61 070501 (in Chinese)[冷洪泽, 宋君强, 曹小群2012 物理学报61 070501]
[9] Du Z C, Tang B, Li K 2006 Acta Phys. Sin. 55 999 (in Chinese)[杜正聪, 唐斌, 李可2006 物理学报55 999]
[10] Snyder C, Zhang F 2003 Mon. Wea. Rev. 131 1663
[11] Kalnay E, Li H, Miyoshi T 2007 Tellus Ser. A 59 758
[12] Cao X Q, Song J Q, Zhang W M 2011 Acta Phys. Sin. 60 070511 (in Chinese)[曹小群, 宋君强, 张卫民2011 物理学报60 070511]
[13] Wang S C, Li Y, Zhang W M 2011 Acta Phys. Sin. 60 099203 (in Chinese)[王舒畅, 李毅, 张卫民2011 物理学报 60 099203]
[14] Qiu C J, Zhang L, Shao A M 2007 Sci. China D 50 1232
[15] Chou J F, Li J P, Gao L 2006 Chin. Phys. 15 882
[16] Liu C S, Xiao Q, Wang B 2008 Mon. Wea. Rev. 136 3363
[17] Zupanski M, Navon I M, Zupanski D 2008 Q. J. R. Meteorol. Soc. 134 1039
[18] Han Y Q, Zhong Z, Wang Y F 2013 Acta Phys. Sin. 62 049201 (in Chinese)[韩月琪, 钟中, 王云峰2013 物理学报 62 049201]
[19] Wang B, Zhao Y 2005 Acta Meteo. Sin. 63 694 (in Chinese)[王斌, 赵颖2005 气象学报63 694]
[20] Zhang F Q, Zhang M, James A 2009 Adv. Atmos. Sci. 26 1
[21] Zhang L, Qiu C J, Zhang S W 2009 Acta Meteo. Sin. 67 1124 (in Chinese) [张蕾, 邱崇践, 张述文2009 气象学报67 1124]
[22] Shao A M, Qiu X B, Qiu C J 2011 Plateau Meteo. 30 583 (in Chinese)[邵爱梅, 邱晓滨, 邱崇践2011 高原气象 30 583]
[23] Jazwinski A H 1970 Stochastic Processes and Filtering Theory (1st Ed.) (New York: Academic Press) p376
[24] Lorenc A C 1992 Q. J. R. Meteorol. Soc. 118 569
[25] Liu D C, Nocedal J 1989 Math. Programming 45 503
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