试用Lyapunov指数探讨气候突变及其前兆信号

吴浩; 侯威; 王文祥; 颜鹏程

doi:10.7498/aps.62.129204

摘要

Lyapunov 指数是标志一个系统做规则运动还是混沌运动的一个重要物理量.鉴于此, 本文利用Lyapunov指数研究系统的混沌特性, 研究气候的突变.计算结果表明, 定义法求得的Lyapunov指数是一种可靠的突变检测方法, 无论是理想序列还是实际存在突变的序列, 利用该方法都能准确地找出突变位置; 而利用非线性局部Lyapunov指数的可预报期限从理论上佐证了基于临界慢化现象的气候突变前兆信号的可靠性, 通过计算各个时间段的最大Lyapunov指数能够反映系统的内在性质、研究其混沌特性. 研究结果为该方法在实际观测资料中的广泛应用提供了理论基础.

关键词:

Abstract

Lyapunov exponent is an important physical quantity indicating a system is in regular motion or in chaotic motion. In view of this, in this paper, we use the Lyapunov exponent to study the chaotic properties of the system, and the mutations in climate. The results show that the Lyapunov exponent is a reliable mutation detection method. For the ideal sequence or actual atmosphere sequence the method can be used to accurately find out the mutation position; the predictability of nonlinear local Lyapunov exponent is used to evidence the reliability of the early warning signals of abrupt climate change based on the phenomenon of critical slowing down, through calculating the largest Lyapunov exponent of each time the system intrinsic properties can be reflected and the chaos characteristics can be studied, thereby providing a theoretical basis for the wide applications of the present method in real observation data.

Keywords:

作者及机构信息

1.
扬州大学物理科学与技术学院, 扬州 225002;

2.
国家气候中心, 北京 100081;

3.
西北师范大学物理与电子工程学院, 兰州 730070

基金项目: 国家重点基础研究发展计划(批准号: 2012CB955902, 2013CB430204)和国家自然科学基金(批准号: 41175067, 41275074, 41105033)资助的课题.

Authors and contacts

1.
College of Physical Science and Technology, Yangzhou University, Yangzhou 225002, China;

2.
National Climate Center, Beijing 100081, China;

3.
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

Funds: Project supported by the National Basic Research Program of China (Grant Nos. 2012CB955902, 2013CB430204) and the National Natural Science Foundation of China (Grant Nos. 41175067, 41275074, 41105033).

参考文献

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[17]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Nonlinear Proc. Geoph. 15 601
[18]	Chen B H, Li J P, Ding R Q 2006 Sci. China D Earth Sci. 36 1068 (in Chinese) [陈宝花, 李建平, 丁瑞强 2006 中国科学 D辑地球科学 36 1068]
[19]	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]
[20]	Scheffer M, Bascompte J, Brock W A, Brovkin V, Carpenter S R, Dakos V, Held H, van Nes E H, Rietkerk M, Sugihara G 2009 Nature 461 53
[21]	Carpenter S R, Brook W A 2006 Ecol. Lett. 9 311
[22]	Guttal V, Jayaprakash C 2008 Ecol. Lett. 11 450
[23]	Wu H, Hou W, Yan P C, Feng G L 2012 Acta Phys. Sin. 61 209202 (in Chinese) [吴浩, 侯威, 颜鹏程, 封国林 2012 61 209202]
[24]	Wu H, Hou W, Yan P C 2013 Acta Phys. Sin. 62 039206 (in Chinese) [吴浩, 侯威, 颜鹏程2013 62 039206]
[25]	Wu H, Feng G L, Hou W, Yan P C 2013 Acta Phys. Sin. 62 059202 (in Chinese) [吴浩, 封国林, 侯威, 颜鹏程2013 62 059202]
[26]	Yan P C, Hou W, Hu J G 2012 Acta Phys. Sin. 61 189202 (in Chinese) [颜鹏程, 侯威, 胡经国 2012 61 189202]
[27]	He D R, Wang B H, Wang Y M, Niu J J 2001 The Dynamics Characteristics in Everywhere Smooth and Piecewise Smooth Systems (Xian: Shaanxi Science and Technology Press) pp72-75 (in Chinese) [何大韧, 汪秉宏, 汪颖梅, 牛建军 2001 非线性动力学引论(处处光滑与分段光滑系统的动力学特征) (西安: 陕西科学技术出版社)第72–75页]
[28]	Lü J H, Lu J A, Chen S H 2005 The Analysis and Applications of Chaotic Time Series (Wuhan: Wuhan University Press) pp72-85 (in Chinese) [吕金虎, 陆君安, 陈士华 2005 混沌时间序列分析及其应用 (武汉: 武汉大学出版社)第72–85页]
[29]	He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 60 049202]
[30]	Xiao D, Li J P 2007 Chin. J. Atmos. Sci. 31 839 (in Chinese) [肖栋, 李建平 2007 大气科学 31 839]
[31]	Zeng H L, Gao X Q, Dai X G 2002 Plateau Meteor. 21 66 (in Chinese) [曾红玲, 高新全, 戴新刚 2002 高原气象 21 66]

施引文献

[1]	Fu C B, Wang Q 1992 Chin. J. Atmos. Sci. 16 482 (in Chinese) [符淙斌, 王强 1992 大气科学 16 482]
[2]	Alley R B, Marotzke J, Nordhaus W D, Overpeck J T, Peteet D M, Pielke R A, Pierrehumbert R T, Rhines P B, Stocker T F, Talley L D, Wallace J M 2005 Science 299 5615
[3]	Fu C B 1994 Chin. J. Atmos. Sci. 18 373 (in Chinese) [符淙斌 1994 大气科学 18 373]
[4]	Wang S W, Ye J L 1995 Chin. J. Atmos. Sci. 19 545 (in Chinese) [王邵武, 叶瑾琳 1995 大气科学 19 545]
[5]	Chou J F 1997 Bull. Chin. Acad. Sci. 5 325 (in Chinese) [丑纪范 1997 中国科学院院刊 5 325]
[6]	He W P, Wu Q, Zhang W, Wang Q G, Zhang Y 2009 Acta Phys. Sin. 58 2862 (in Chinese) [何文平, 吴琼, 张文, 王启光, 张勇 2009 58 2862]
[7]	He W P, Deng B S, Wu Q, Zhang W, Cheng H Y 2010 Acta Phys. Sin. 59 8264 (in Chinese) [何文平, 邓北胜, 吴琼, 张文, 成海英 2010 59 8264]
[8]	He W P, Wu Q, Cheng H Y, Zhang W 2011 Acta Phys. Sin. 60 029203 (in Chinese) [何文平, 吴琼, 成海英, 张文 2011 60 029203]
[9]	Wei F Y 1999 The Technologies of Statistics Diagnosis and Forecast in Modern Climate (Beijing: the Weather Publishing Company) pp63-76 (in Chinese) [魏凤英 1999 现代气候统计诊断与预测技术(北京: 气象出版社)第63–76页]
[10]	Babak A S, Krishnaprasad P S 2004 EURASIP J. Appl. Signal Proc. 15 2295
[11]	Feng G L, Gong Z Q, Zhi R 2008 Acta Meteorol. Sin. 66 892 (in Chinese) [封国林, 龚志强, 支蓉 2008 气象学报 66 892]
[12]	Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear Theories and Methods on Spatial-Temporal Distribution of the Obserbational Data (Beijing: the Weather Publishing Company) pp5-8 (in Chinese) [封国林, 董文杰, 龚志强, 侯威, 万仕全, 支蓉 2006 观测数据非线性时空分布理论和方法(北京: 气象出版社)第5–8页]
[13]	Feng G L, Gong Z Q, Dong W J 2005 Acta Phys. Sin. 54 5494 (in Chinese) [封国林, 龚志强, 董文杰 2005 54 5494]
[14]	Wan S Q, Feng G L, Dong W J 2005 Acta Phys. Sin. 54 5487 (in Chinese) [万仕全, 封国林, 董文杰 2005 54 5487]
[15]	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 55 3180]
[16]	He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604
[17]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Nonlinear Proc. Geoph. 15 601
[18]	Chen B H, Li J P, Ding R Q 2006 Sci. China D Earth Sci. 36 1068 (in Chinese) [陈宝花, 李建平, 丁瑞强 2006 中国科学 D辑地球科学 36 1068]
[19]	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]
[20]	Scheffer M, Bascompte J, Brock W A, Brovkin V, Carpenter S R, Dakos V, Held H, van Nes E H, Rietkerk M, Sugihara G 2009 Nature 461 53
[21]	Carpenter S R, Brook W A 2006 Ecol. Lett. 9 311
[22]	Guttal V, Jayaprakash C 2008 Ecol. Lett. 11 450
[23]	Wu H, Hou W, Yan P C, Feng G L 2012 Acta Phys. Sin. 61 209202 (in Chinese) [吴浩, 侯威, 颜鹏程, 封国林 2012 61 209202]
[24]	Wu H, Hou W, Yan P C 2013 Acta Phys. Sin. 62 039206 (in Chinese) [吴浩, 侯威, 颜鹏程2013 62 039206]
[25]	Wu H, Feng G L, Hou W, Yan P C 2013 Acta Phys. Sin. 62 059202 (in Chinese) [吴浩, 封国林, 侯威, 颜鹏程2013 62 059202]
[26]	Yan P C, Hou W, Hu J G 2012 Acta Phys. Sin. 61 189202 (in Chinese) [颜鹏程, 侯威, 胡经国 2012 61 189202]
[27]	He D R, Wang B H, Wang Y M, Niu J J 2001 The Dynamics Characteristics in Everywhere Smooth and Piecewise Smooth Systems (Xian: Shaanxi Science and Technology Press) pp72-75 (in Chinese) [何大韧, 汪秉宏, 汪颖梅, 牛建军 2001 非线性动力学引论(处处光滑与分段光滑系统的动力学特征) (西安: 陕西科学技术出版社)第72–75页]
[28]	Lü J H, Lu J A, Chen S H 2005 The Analysis and Applications of Chaotic Time Series (Wuhan: Wuhan University Press) pp72-85 (in Chinese) [吕金虎, 陆君安, 陈士华 2005 混沌时间序列分析及其应用 (武汉: 武汉大学出版社)第72–85页]
[29]	He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 60 049202]
[30]	Xiao D, Li J P 2007 Chin. J. Atmos. Sci. 31 839 (in Chinese) [肖栋, 李建平 2007 大气科学 31 839]
[31]	Zeng H L, Gao X Q, Dai X G 2002 Plateau Meteor. 21 66 (in Chinese) [曾红玲, 高新全, 戴新刚 2002 高原气象 21 66]

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