Predictability of forced Lorenz system

Li Bao-Sheng; Ding Rui-Qiang; Li Jian-Ping; Zhong Quan-Jia

doi:10.7498/aps.66.060503

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:

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).

References

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[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]
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[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

Cited By

[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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Vol. 66, Issue 6 - 2017-03-20

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