外强迫对Lorenz系统初值可预报性的影响

黎爱兵; 张立凤; 项杰

doi:10.7498/aps.61.119202

摘要

利用强迫Lorenz模型, 研究了外强迫对Lorenz系统混沌性质、映射结构及初值可预报性的影响, 并以海表温度为大气运动的外强迫, 用实际大气海洋资料分析了外强迫对大气可预报性的影响. 结果发现, 系统混沌现象的出现与外强迫有关, 外强迫改变了Lorenz系统的运动规律, 使围绕两奇怪吸引子运动的随机性减少. 考虑外强迫后, 系统运动轨迹的概率密度函数呈不对称的双峰结构, 且Lorenz映射由无外强迫时的一个尖点分离为两个尖点, 尖点的偏离方向和偏离位置分别与外强迫的正负和大小有关. 外强迫可减小Lorenz系统对初值的敏感性, 提高系统的初值可预报性, 尤其是外强迫越大, 可预报性提高的幅度也越大. 这些结果在不同强度海表温度强迫下的实际大气可预报性分析中得到了证实, 即海温异常越大, 实际大气变量的可预报性也越大.

关键词:

Abstract

The influence of external forcing on chaotic character, Lorenz map structure and the predictability is studied with the Lorenz system which has a forcing term, and the atmospheric predictability forced by sea surface temperature (SST) is also analyzed. The chaotic attractors are related to the forcing term that changes the moving rules of system and makes randomicity of attractors reduce. The probability distribution function of Lorenz system in the x-y plane has a bimodal structure with two clearly separated peaks. In the absence of forcing, both peaks are equally likely. When an external forcing introduced, the probability of state moving around two Lorenz attractors is changed, and it makes the two peaks asymmetric. It is found that the single cusp of Lorenz map obtained in the absence of forcing splits into two cusps that represent two branches of the Lorenz attractor when the forcing is introduced. On Lorenz map, the moving directions of two cusps and the difference between two cusps and single cusp are determined by the sign and the magnitude of forcing term. The predictability of Lorenz system is also deeply affected by external forcing. The predictability is increased by introducing forcing, and especially the range of increasing is larger when the absolute value of forcing term is bigger. It is also found that the higher potential predictability is obtained by forcing with the stronger SST which causes the larger external variance.

Keywords:

作者及机构信息

1.
中国人民解放军理工大学气象学院, 南京 211101

基金项目: 国家自然科学基金(批准号: 40975031)资助的课题.

Authors and contacts

1.
Institute of Meteorology, People's Liberation Army University of Science and Technology, Nanjing 211101, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 40975031).

参考文献

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[2]	Evans E N, Bhatti J K, Pann L, Pena M, Yang S C, Kalnay E, Hansen J 2004 Bull. Amer. Meteor. Soc. 85 520
[3]	Palmer T N 1993 Bull. Amer. Meteor. Soc. 74 49
[4]	Tsonis A A 1992 Chaos: From Theory to Applications (New York: Plenum press) p274
[5]	Palmer T N 1999 J. Clim. 12 575
[6]	Yadav R S, Dwivedi S, Mittal A K 2005 J. Atmos. Sci. 62 2316
[7]	Sikka D R, Gadgil S 1980 Mon. Wea. Rev. 108 1840
[8]	Christiansen B 2003 J. Clim. 16 3681
[9]	Shukla J 1998 Science 282 728
[10]	Palmer T N 1994 Ind. Natl. Sci. Acad. 60 57
[11]	Pal P K, Shan S 1999 Ind. J. Radio Space Phys. 28 271
[12]	Mittal A K, Dwivedi S, Pandey A C 2003 Ind. J. Radio Space Phys. 32 209
[13]	Mittal A K, Dwivedi S, Pandey A C 2005 Nonlin. Pro. Geophy. 12 707
[14]	Dwivedi S, Mittal A K, Pandey A C 2007 Atmoshpere-Ocean 45 71
[15]	He W P, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 969 (in Chinese) [何文平, 封国林, 董文杰, 李建平 2006 物理学报 55 969]
[16]	He W P, Feng G L, Gao X Q, Chou J F 2006 Acta Phys. Sin. 55 3175 (in Chinese) [何文平, 封国林, 高新全, 丑纪范 2006 物理学报 55 3175]
[17]	Ding R Q, Li J P 2007 Chin. J. Atmos. Sci. 31 571 (in Chinese) [丁瑞强, 李建平 2007 大气科学 31 571]
[18]	Chen B H, Li J P, Ding R Q 2006 Sci. Chin. D 36 1068 (in Chinese) [陈宝花, 李建平, 丁瑞强 2008 中国科学(D辑) 36 1068]
[19]	Ding R Q, Li J P 2007 Phys. Lett. A 364 396
[20]	Ding R Q, Li J P 2008 Chin. J. Geophy. 51 1007 (in Chinese) [丁瑞强, 李建平 2008 地球物理学报 51 1007]
[21]	Ding R Q, Li J P 2009 Acta Meteor. Sin. 67 241 (in Chinese) [丁瑞强, 李建平 2009 气象学报 67 241]
[22]	Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[23]	Shukla J, Gutzler D S 1983 Mon. Wea. Rev. 111 1273
[24]	Trenberth K E 1984 Mon. Wea. Rev. 112 2369
[25]	Wang J, Guo Y F 2004 J. Appl. Meteor. Sci. 15 291 (in Chinese) [王嘉, 郭裕福 2004 应用气象学报 15 291]

施引文献

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[2]	Evans E N, Bhatti J K, Pann L, Pena M, Yang S C, Kalnay E, Hansen J 2004 Bull. Amer. Meteor. Soc. 85 520
[3]	Palmer T N 1993 Bull. Amer. Meteor. Soc. 74 49
[4]	Tsonis A A 1992 Chaos: From Theory to Applications (New York: Plenum press) p274
[5]	Palmer T N 1999 J. Clim. 12 575
[6]	Yadav R S, Dwivedi S, Mittal A K 2005 J. Atmos. Sci. 62 2316
[7]	Sikka D R, Gadgil S 1980 Mon. Wea. Rev. 108 1840
[8]	Christiansen B 2003 J. Clim. 16 3681
[9]	Shukla J 1998 Science 282 728
[10]	Palmer T N 1994 Ind. Natl. Sci. Acad. 60 57
[11]	Pal P K, Shan S 1999 Ind. J. Radio Space Phys. 28 271
[12]	Mittal A K, Dwivedi S, Pandey A C 2003 Ind. J. Radio Space Phys. 32 209
[13]	Mittal A K, Dwivedi S, Pandey A C 2005 Nonlin. Pro. Geophy. 12 707
[14]	Dwivedi S, Mittal A K, Pandey A C 2007 Atmoshpere-Ocean 45 71
[15]	He W P, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 969 (in Chinese) [何文平, 封国林, 董文杰, 李建平 2006 物理学报 55 969]
[16]	He W P, Feng G L, Gao X Q, Chou J F 2006 Acta Phys. Sin. 55 3175 (in Chinese) [何文平, 封国林, 高新全, 丑纪范 2006 物理学报 55 3175]
[17]	Ding R Q, Li J P 2007 Chin. J. Atmos. Sci. 31 571 (in Chinese) [丁瑞强, 李建平 2007 大气科学 31 571]
[18]	Chen B H, Li J P, Ding R Q 2006 Sci. Chin. D 36 1068 (in Chinese) [陈宝花, 李建平, 丁瑞强 2008 中国科学(D辑) 36 1068]
[19]	Ding R Q, Li J P 2007 Phys. Lett. A 364 396
[20]	Ding R Q, Li J P 2008 Chin. J. Geophy. 51 1007 (in Chinese) [丁瑞强, 李建平 2008 地球物理学报 51 1007]
[21]	Ding R Q, Li J P 2009 Acta Meteor. Sin. 67 241 (in Chinese) [丁瑞强, 李建平 2009 气象学报 67 241]
[22]	Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[23]	Shukla J, Gutzler D S 1983 Mon. Wea. Rev. 111 1273
[24]	Trenberth K E 1984 Mon. Wea. Rev. 112 2369
[25]	Wang J, Guo Y F 2004 J. Appl. Meteor. Sci. 15 291 (in Chinese) [王嘉, 郭裕福 2004 应用气象学报 15 291]

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