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## Ensemble variational data assimilation method based on regional successive analysis scheme

Wu Zhu-Hui, Han Yue-Qi, Zhong Zhong, Du Hua-Dong, Wang Yun-Feng
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• #### 摘要

集合变分数据同化方法的同化效果对集合样本容量具有很强的依赖性，研究发现此问题的出现是因为其计算过程中分析增量被表示为集合扰动向量或其展开正交基向量的线性组合. 这样的处理方法虽然避免了计算梯度而引入伴随模式，但是因为物理控制变量个数远大于集合样本容量，就会导致物理量的同化分析值对集合样本容量很敏感. 根据此原因，提出了区域逐步分析方法，减小了同化分析区域内物理变量个数与集合样本容量数之间的比值，使问题得到解决. 利用浅水方程模式进行资料同化数值试验表明，基于区域逐步分析的集合变分资料同化方法可以得到较好的结果，能明显提高同化的精度.

#### Abstract

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.

#### 作者及机构信息

###### 1. 金陵科技学院, 南京 211169; 2. 解放军理工大学, 电磁环境效应与光电工程重点实验室, 南京 211101; 3. 解放军理工大学气象海洋学院, 南京 211101
• 基金项目: 江苏省自然科学基金（批准号：BK20131065）、中国博士后科学基金（批准号：20110490185）、国家自然科学基金（批准号：41175090，41375106，41105065，41205073）和气象海洋学院基础理论研究基金资助的课题.

#### Authors and contacts

###### 1. Jinling Institute of Technology, Nanjing 211169, China; 2. Institute of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China; 3. National Key Laboratory on Electromagnetic Environmental Effects and Electro-optical Engineering, PLA University of Science and Technology, Nanjing 211101, China
• Funds: Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20131065), the China Postdoctoral Science Foundation (Grant No. 20110490185), the National Natural Science Foundation of China (Grant Nos. 41175090, 41375106, 41105065, 41205073), the Basic Theory Research Program of Institute of Meteorology and Oceanography, China.

#### 参考文献

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#### 施引文献

•  [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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##### 出版历程
• 收稿日期:  2013-11-09
• 修回日期:  2013-12-17
• 刊出日期:  2014-04-05

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