强迫Lorenz系统的可预报性研究

李保生; 丁瑞强; 李建平; 钟权加

doi:10.7498/aps.66.060503

摘要

根据非线性局部Lyapunov指数方法，分别以常数强迫Lorenz系统和准周期强迫Lorenz系统为例，研究了在外强迫存在的条件下混沌系统可预报性的改变.结果表明：外强迫会影响混沌系统的可预报性，两种不同类型的强迫Lorenz系统的可预报期限都随着外强迫的增强而增加，但是大小相等方向相反的外强迫对系统可预报性的影响不同，其中正值强迫比负值强迫作用下的可预报期限更长，并且这种差异随着强度的增加而增大；不同形式的外强迫对可预报性的影响也不同，常数强迫的影响主要体现在误差增长的线性阶段，准周期强迫的影响除了线性阶段还必须考虑到非线性阶段；当强度相等的常数强迫和准周期强迫驱动Lorenz系统时，常数强迫作用下的系统可预报性更高.本文基于混沌理论模型的研究，对于实际大气的可预报性研究具有一定的启示意义.

关键词:

Abstract

In recent years, the actual atmospheric predictability has attracted widespread attention. Improving our understanding of weather predictability is vital to developing numerical models and improving our forecast skill in weather and climate events. Given that the atmosphere is a complex and nonlinear system, taking the Lorenz system as an example is a better way to understand the actual atmosphere predictability. Up to now, some predictability problems of the Lorenz system have been investigated, such as the relative effects of the initial error and the model error. Previous advances in the research of predictability mainly focus on the relationship between the predictability limit and the initial error. As is well known, the external forcing can also result in the change of the predictability. Therefore, it is significant to investigate the predictability changing with the external forcing. The nonlinear local Lyapunov exponent (NLLE) is introduced to measure the average growth rate of the initial error of nonlinear dynamical model, which has been used for quantitatively determining the predictability limit of chaos system. Based on the NLLE approach, the influences of external forcing on the predictability are studied in the Lorenz system with constant forcing and Lorenz system with quasi-periodic forcing in this paper. The results indicate that for the Lorenz systems with constant and quasi-periodic forcings respectively, their predictability limits increase with forcing strength increasing. In the case of the same magnitude but different directions, the constant and quasi-periodic forcing both show different effects on the predictability limit in the Lorenz system, and these effects become significant with the increase of forcing strength. Generally speaking, the positive forcing leads to a higher predictability limit than the negative forcing. Therefore, when we consider the effects of positive and negative elements and phases in the atmosphere and ocean research, the predictability problems driven by different phases should be considered separately. In addition, the influences of constant and quasi-periodic forcings on the predictability are different in the Lorenz system. The effect of the constant forcing on the predictability is mainly reflected in the linear phase of error growth, while the nonlinear phase should also be considered additionally for the case of the quasi-periodic forcing. The predictability of the system under constant forcing is higher than that of the system under quasi-periodic forcing. These results based on simple chaotic model could provide an insight into the predictability studies of complex systems.

Keywords:

作者及机构信息

1.
中国科学院大气物理研究所, 大气科学和地球流体力学数值模拟国家重点实验室, 北京 100029;

2.
中国科学院大学地球科学学院, 北京 100049;

3.
成都信息工程大学, 高原大气与环境四川省重点实验室, 成都 610225;

4.
北京师范大学全球变化与地球系统科学研究院, 北京 100875;

5.
全球变化研究协同创新中心, 北京 100875

通信作者: 丁瑞强, drq@mail.iap.ac.cn

基金项目: 国家自然科学基金优秀青年科学基金（批准号：41522502）、全球变化与海气相互作用专项（批准号：GASI-IPOVAI-06）和国家重点研发计划（批准号：2016YFA0601801）资助的课题.

Authors and contacts

1.
State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;

2.
College of Earth Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;

3.
Plateau Atmosphere and Environment Key Laboratory of Sichuan Province, Chengdu University of Information Technology, Chengdu 610225, China;

4.
College of Global Change and Earth System Science(GCESS), Beijing Normal University, Beijing 100875, China;

5.
Joint Center for Global Change Studies, Beijing 100875, China

Corresponding author: Ding Rui-Qiang, drq@mail.iap.ac.cn

Funds: Project supported by the National Natural Science Foundation of China for Excellent Young Scholars (Grant No. 41522502), the National Programme on Global Change and Air-Sea Interaction, China (Grant No. GASI-IPOVAI-06), and the National Key Research and Development Plan of China (Grant No. 2016YFA0601801).

参考文献

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[2]	Chou J F 2002 Nonlinearity and Complexit in Atmospheric Sciences (Beijing: China Meteorological Press) p131 (in Chinese) [丑纪范 2002 大气科学中的非线性和复杂性 (北京: 气象出版社) 第131页]
[3]	Lorenz E N 1965 Tellus A 17 321
[4]	Lorenz E N, Palmer T N, Hagedorn R 1995 Proceedings of a Seminar Held at ECMWF on Predictability (I), 1995 p1
[5]	Li J P, Chou J F 2003 Chin. J. Atmos. Sci. 27 653 (in Chinese) [李建平, 丑纪范 2003 大气科学 27 653]
[6]	Duan W S, Mu M 2006 Chin. J. Atmos. Sci. 30 759 (in Chinese) [段晚锁, 穆穆 2006 大气科学 30 759]
[7]	Duan W S, Ding R Q, Zhou F F 2013 Climatic Environ. Res. 18 524 (in Chinese) [段晚锁, 丁瑞强, 周菲凡 2013 气候与环境研究 18 524]
[8]	Ding R Q, Li J P 2007 Phys. Lett. A 364 396
[9]	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]
[10]	Ding R Q, Li J P 2008 Acta Phys. Sin. 57 7494 (in Chinese) [丁瑞强, 李建平 2008 物理学报 57 7494]
[11]	Li J P, Ding R Q 2008 Chin. J. Atmos. Sci. 32 975 (in Chinese) [李建平, 丁瑞强 2008 大气科学 32 975]
[12]	Ding R Q, Li J P 2009 Acta Meteor. Sin. 67 343 (in Chinese) [丁瑞强, 李建平 2009 气象学报 67 343]
[13]	Ding R Q, Li J P, Seo K H 2010 Mon. Wea. Rev. 138 1004
[14]	Ding R Q, Li J P, Seo K H 2011 Mon. Wea. Rev. 139 2421
[15]	Ding R Q, Li J P 2011 Mon. Wea. Rev. 139 3265
[16]	Ding R Q, Li J P 2013 Int. J. Climatol. 33 1936
[17]	Ding R Q, Li J P, Zheng F, Feng J, Liu D Q 2015 Climate Dyn. 46 1563
[18]	Ding R Q, Li J P 2012 Adv. Atmos. Sci. 29 1078
[19]	Reichler T J, Roads J O 2003 Nonlinear Proc. Geoph. 10 211
[20]	Yang X Q, Xie Q, Huang T S 1992 Acta Meteor. Sin. 50 349 (in Chinese) [杨修群, 谢倩, 黄士松 1992 气象学报 50 349]
[21]	Li C Y, Zhu J H, Sun Z B 2002 Climatic Environ. Res. 7 209 (in Chinese) [李崇银, 朱锦红, 孙照渤 2002 气候与环境研究 7 209]
[22]	Li W J, Li Y, Chen L J, Zhao Z G 2013 J. Appl. Meteor. Sci. 24 385 (in Chinese) [李维京, 李怡, 陈丽娟, 赵振国 2013 应用气象学报 24 385]
[23]	Charles C D, Hunter D E, Fairbanks R G 1997 Science 277 925
[24]	Wang B, Wu R G, Fu X H 2000 J. Climate 13 1517
[25]	Zhang Z S, Hu P, Feng G L 2016 Acta Meteor. Sin. 74 165 (in Chinese) [张志森, 胡泊, 封国林 2016 气象学报 74 165]
[26]	Gong Z Q, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 3180 (in Chinese) [龚志强, 封国林, 董文杰, 李建平 2006 物理学报 55 3180]
[27]	Gong Z Q, Zhou L, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 5351 (in Chinese) [龚志强, 周磊, 支蓉, 封国林 2008 物理学报 57 5351]
[28]	Palmer T N 1994 Proceedings-Indian National Science Academy Part A 60 57
[29]	He W P, Feng G L, Gao X Q 2006 Acta Phys. Sin. 55 3175 (in Chinese) [何文平, 封国林, 高新全 2006 物理学报 55 3175]
[30]	Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[31]	Eckmann J P, Ruelle D 1985 Rev. Mod. Phys. 57 617
[32]	Lacarra J F, Talagrand O 1988 Tellus 40A 81
[33]	Mittal A K, Dwivedi S, Pandey A C 2005 Nonlin. Pro. Geophy. 12 707

施引文献

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[2]	Chou J F 2002 Nonlinearity and Complexit in Atmospheric Sciences (Beijing: China Meteorological Press) p131 (in Chinese) [丑纪范 2002 大气科学中的非线性和复杂性 (北京: 气象出版社) 第131页]
[3]	Lorenz E N 1965 Tellus A 17 321
[4]	Lorenz E N, Palmer T N, Hagedorn R 1995 Proceedings of a Seminar Held at ECMWF on Predictability (I), 1995 p1
[5]	Li J P, Chou J F 2003 Chin. J. Atmos. Sci. 27 653 (in Chinese) [李建平, 丑纪范 2003 大气科学 27 653]
[6]	Duan W S, Mu M 2006 Chin. J. Atmos. Sci. 30 759 (in Chinese) [段晚锁, 穆穆 2006 大气科学 30 759]
[7]	Duan W S, Ding R Q, Zhou F F 2013 Climatic Environ. Res. 18 524 (in Chinese) [段晚锁, 丁瑞强, 周菲凡 2013 气候与环境研究 18 524]
[8]	Ding R Q, Li J P 2007 Phys. Lett. A 364 396
[9]	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]
[10]	Ding R Q, Li J P 2008 Acta Phys. Sin. 57 7494 (in Chinese) [丁瑞强, 李建平 2008 物理学报 57 7494]
[11]	Li J P, Ding R Q 2008 Chin. J. Atmos. Sci. 32 975 (in Chinese) [李建平, 丁瑞强 2008 大气科学 32 975]
[12]	Ding R Q, Li J P 2009 Acta Meteor. Sin. 67 343 (in Chinese) [丁瑞强, 李建平 2009 气象学报 67 343]
[13]	Ding R Q, Li J P, Seo K H 2010 Mon. Wea. Rev. 138 1004
[14]	Ding R Q, Li J P, Seo K H 2011 Mon. Wea. Rev. 139 2421
[15]	Ding R Q, Li J P 2011 Mon. Wea. Rev. 139 3265
[16]	Ding R Q, Li J P 2013 Int. J. Climatol. 33 1936
[17]	Ding R Q, Li J P, Zheng F, Feng J, Liu D Q 2015 Climate Dyn. 46 1563
[18]	Ding R Q, Li J P 2012 Adv. Atmos. Sci. 29 1078
[19]	Reichler T J, Roads J O 2003 Nonlinear Proc. Geoph. 10 211
[20]	Yang X Q, Xie Q, Huang T S 1992 Acta Meteor. Sin. 50 349 (in Chinese) [杨修群, 谢倩, 黄士松 1992 气象学报 50 349]
[21]	Li C Y, Zhu J H, Sun Z B 2002 Climatic Environ. Res. 7 209 (in Chinese) [李崇银, 朱锦红, 孙照渤 2002 气候与环境研究 7 209]
[22]	Li W J, Li Y, Chen L J, Zhao Z G 2013 J. Appl. Meteor. Sci. 24 385 (in Chinese) [李维京, 李怡, 陈丽娟, 赵振国 2013 应用气象学报 24 385]
[23]	Charles C D, Hunter D E, Fairbanks R G 1997 Science 277 925
[24]	Wang B, Wu R G, Fu X H 2000 J. Climate 13 1517
[25]	Zhang Z S, Hu P, Feng G L 2016 Acta Meteor. Sin. 74 165 (in Chinese) [张志森, 胡泊, 封国林 2016 气象学报 74 165]
[26]	Gong Z Q, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 3180 (in Chinese) [龚志强, 封国林, 董文杰, 李建平 2006 物理学报 55 3180]
[27]	Gong Z Q, Zhou L, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 5351 (in Chinese) [龚志强, 周磊, 支蓉, 封国林 2008 物理学报 57 5351]
[28]	Palmer T N 1994 Proceedings-Indian National Science Academy Part A 60 57
[29]	He W P, Feng G L, Gao X Q 2006 Acta Phys. Sin. 55 3175 (in Chinese) [何文平, 封国林, 高新全 2006 物理学报 55 3175]
[30]	Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[31]	Eckmann J P, Ruelle D 1985 Rev. Mod. Phys. 57 617
[32]	Lacarra J F, Talagrand O 1988 Tellus 40A 81
[33]	Mittal A K, Dwivedi S, Pandey A C 2005 Nonlin. Pro. Geophy. 12 707

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