一种基于复数域微分的资料同化新方法

曹小群; 宋君强; 张卫民; 赵延来; 刘柏年

doi:10.7498/aps.62.170504

摘要

提出了一种基于复数域微分的资料同化新方法. 针对变分资料同化中目标泛函梯度计算复杂和精度不高的问题, 首先利用复变量求导法把梯度分析过程转化为复变泛函的数值计算, 进而高效和高精度地获得梯度值; 然后结合经典的最优化方法, 给出了非线性物理系统资料同化问题的新求解算法; 最后对典型混沌系统和包含开关现象的单格点比湿发展方程进行了资料同化数值实验, 结果表明新方法能非常有效地估计出非线性动力预报模式的初始条件.

关键词:

Abstract

A new method for data assimilation is proposed using complex-variable differentiation (CVD), which can be used to estimate the initial conditions of the nonlinear physical system governed by the following equation:. Firstly, the gradient analysis of cost function in variational data assimilation is transformed into function numerical computation in complex domain, and the value of gradient is computed more efficiently and exactly. Secondly, the new algorithm of data assimilation is developed by combining an accurate gradient information from CVD with the classical optimization method. Finally, numerical simulations of typical chaotic systems and a humidity evolution equation with physical on-off process show that the new data assimilation method can reconstruct initial conditions of the nonlinear dynamical system very conveniently and accurately.

Keywords:

作者及机构信息

1.
国防科学技术大学计算机学院, 长沙 410073

基金项目: 国家自然科学基金(批准号: 41105063)资助的课题.

Authors and contacts

1.
School of Computer Science, National University of Defense Technology, Changsha 410073, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 41105063).

参考文献

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[28]	Zheng Q, Dai Y 2009 Progress in Natural Science 19 81
[29]	Han Y Q, Zhong Z, Wang Y F, Du H D 2013 Acta Phys. Sin. 62 049201 (in Chinese) [韩月琪, 钟中, 王云峰, 杜华栋 2013 62 049201]
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[33]	Dai D, Ma X K, Li F C, You Y 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤勇 2002 51 2459]
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施引文献

[1]	Zou X L 2009 Data Assimilation-Theory and Application (Vol. 1) (Beijing: Meteorology Press) p43 (in Chinese) [邹晓蕾 2009 资料同化-理论与应用(上册) (北京: 气象出版社) 第43页]
[2]	Huang S X, Wu R S 2001 Mathematical Physics Problems in Atmosphere Science (Beijing: Meteorology Press) (in Chinese) p460 [黄思训, 伍荣生 2001 大气科学中的数学物理问题(北京: 气象出版社) 第460页]
[3]	Evensen G 1994 J. Geophys. Res. 99 10143
[4]	Evensen G, Van Leeuwen P J 2000 Mon. Wea. Rev. 128 1852
[5]	Houtekamer P L, Mitchell H L 2001 Mon. Wea. Rev.129 123
[6]	Talagrand O, Courtier P 1987 Q. J. R. Meteorol. Soc. 113 1311
[7]	Lorenc A C 2003 Q. J. R. Meteorol. Soc. 129 3183
[8]	Andersson E, Coauthors 1998 Q. J. R. Meteorol. Soc. 124 1831
[9]	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 57 1984]
[10]	Zhang W M, Cao X Q, Song J Q 2012 Acta Phys. Sin. 61 249202 (in Chinese) [张卫民, 曹小群, 宋君强 2012 61 249202]
[11]	Rabier F, Jarvinen H, Klinker E, Mahfouf J F 2000 Q. J. R. Meteorol. Soc. 126 1148
[12]	He J H 2008 Int. J. Modern. Phys. B. 22 3487
[13]	He J H 2000 Appl. Math. Mech. 21 797
[14]	He J H 2001 Int. J. Nonlin. Sci. Numer. 2 309
[15]	He J H, Lee E W M 2009 Phys. Lett. A 373 1644
[16]	Wu G C 2012 Chin. Phys. B 21 120504
[17]	Wu G C, Dumitru B 2013 Appl. Math. Model. 37 6183
[18]	Giering R 1998 ACM Trans. On Math. Software 24 437
[19]	Cheng Q, Zhang H B, Wang B 2009 Math. Numer. Sin. 31 15 (in Chinese) [程强, 张海斌, 王斌 2009 计算数学 31 15]
[20]	Lyness J N, Moler C B 1967 SIAM J. Numer. Anal. 4 202
[21]	Martins J R R A 2002 A Coupled-adjoint method for highfidelity aero-structural optimization Ph. D. Dissertation. (Stanford: Stanford University)
[22]	Martins J R R A, Kroo I M, Alonso J J 2000 Proceedings of the 38th Aerospace Sciences Meeting, Reno, NV, January 2-5, AIAA Paper 2000-0689
[23]	Gao X W, Liu D D, Chen P C 2002 Comput. Mech. 28 40
[24]	Guo L, Gao X W 2008 Journal of Southeast Univerity (Natural Science Edition) 38 141 (in Chinese) [郭力, 高效伟 2008 东南大学学报 (自然科学版) 38 141]
[25]	Mu M, Zheng Q 2005 Mon Wea. Rev. 133 2711
[26]	Wang J F, Mu M, Zheng Q 2005 Tellus 57A 736
[27]	Zheng Q, Sha J X, Fang C L 2012 Sci. China Earth Sci. 42 458
[28]	Zheng Q, Dai Y 2009 Progress in Natural Science 19 81
[29]	Han Y Q, Zhong Z, Wang Y F, Du H D 2013 Acta Phys. Sin. 62 049201 (in Chinese) [韩月琪, 钟中, 王云峰, 杜华栋 2013 62 049201]
[30]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[31]	Liu F C, Liang X M 2005 Acta Phys. Sin. 54 4584 (in Chinese) [刘福才, 梁晓明 2005 54 4584]
[32]	Li L X, Peng H P, Lu H B, Guan X P 2001 Acta Phys. Sin. 50 629 (in Chinese) [李丽香, 彭海朋, 卢辉斌, 关新平 2001 50 629]
[33]	Dai D, Ma X K, Li F C, You Y 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤勇 2002 51 2459]
[34]	Gao F, Tong H Q 2006 Acta Phys. Sin. 55 577 (in Chinese) [高飞, 童恒庆 2006 55 577]
[35]	Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁, 黄娟娟 2006 55 3997]

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