Application of nonlinear dynamical methods in abrupt climate change detection

Liu Qun-Qun; He Wen-Ping; Gu Bin

doi:10.7498/aps.64.179201

Abstract

The research of abrupt climate change is an important field in the climate change. The rapid and accurate detection of the abrupt climate change has important practical significance and major economic-social costs, which will help us understand climate change and forecast the future evolutionary trend of the climate system. The detection results of most traditional abrupt climate change depend on the selection of the time scale concerned, which may result in the fact that we cannot identify an abrupt climate change until the event has been past for a long time. Moreover, these detection methods cannot extract the dynamical changes from the observational data of the climate system. As the rapid development in nonlinear science, the abrupt climate change detection technology has also been improved gradually. This article briefly reviews several new progresses in abrupt dynamical detection methods developed on the basis of recent nonlinear technologies, and some applications in the real observational data. These new methods mainly contain the technologies based on the long-range correlation of climate systems, such as moving detrended fluctuation analysis, moving cut data-detrended fluctuation analysis, moving cut data-R/S analysis, degenerate fingerprinting, and red noise. Moreover, some abrupt dynamical detection methods developed by the complexity of the time series, namely, entropy, such as approximate entropy, moving cutting data-approximate entropy, Fisher information, and wavelet Fisher's information measure. Furthermore, there are some other abrupt dynamical detection methods based on the theory of phase space, such as the dynamics exponent Q. Climate system is a complex dynamical system with nonlinear and interactive nature, which has long-range persistence in spatio-temporal variation, thus the abrupt detection method on spatial field change is pointed out to be a promising direction for further research in future. Because the spatial field contains abundance of information about the evolution of climate system which is much more than that in a time series in single meteorological station, the detecting methods on spatial field will greatly help us detect an abrupt climate change as soon as possible. And then we will have enough time to take action and make preparations for the new challenges due to the abrupt climate change.

Keywords:

Authors and contacts

1.
College of Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China;
2.
Institute of Space Weather, Nanjing University of Information Science and Technology, Nanjing 210044, China;
3.
National Climate Center, China Meteorological Administration, Beijing 100081, China;
4.
The Key Laboratory for Aerosol-Cloud-Precipitation of CMA-NUIST, Nanjing 210044, China

Corresponding author: He Wen-Ping, wenping_he@163.com

Funds: Project supported by the National Basic Research Program of China (Grant No. 2012CB955902), the National Natural Science Foundation of China (Grant Nos. 41275074, 41175067), the Program of the Key Laboratory for Aerosol-Cloud-Precipitation of CMA-NUIST (Grant No. KDW1304).

References

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[2]	Liu S D, Liu S K, Liang S, Ren K, Fu Z T 2002 Prog. Nat. Sci. 12 1 (in Chinese) [刘式达, 刘式适, 梁爽, 任奎, 付遵涛 2002 自然科学进展 12 1]
[3]	Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta. Phys. Sin 58 2853 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉 2009 物理学报 58 2853]
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[5]	Feng G L, Dong W J 2003 Chin. Phys. 12 1072
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[12]	Kendall M G 1970 Rank Correlation Methods (London: Charles Griffin)
[13]	Mann H B, Whitney D R 1947 Annals of Mathematical Statistics 18 50
[14]	Lepage 1971 Biometrika 58 213
[15]	He W P, Wan S Q, Jiang Y D, Jin H M, Zhang W, Wu Q, He T 2013 Int. J. Climatol. 33 2713
[16]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geophys. 15 601
[17]	He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604
[18]	He W P, Deng B S, Wu Q, Zheng 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 物理学报 59 8264]
[19]	Sun D Y, Zhang H B, Huang Q 2014 Acta Phys. Sin. 63 209203 (in Chinese) [孙东永, 张洪波, 黄强 2014 物理学报 63 209203]
[20]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1996 (in Chinese) [王启光, 张增平 2008 物理学报 57 1996]
[21]	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 物理学报 60 049202]
[22]	Held H, Kleinen T 2004 Geophysical Research Letters 31 L23207
[23]	Fisher R A 1922 Philos. Trans. R. Soc. Lond. Ser. A 222 309
[24]	Savit R, Green M 1991 Phys. D 50 95
[25]	Abaimov S G, Turcotte D L, Shcherbakov R, Rundle J B 2007 Non. Proc. Geophys. 14 455
[26]	Blender R, Fraedrich K, Sienz F 2008 Non. Proc. Geo. 15 557
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[28]	Bunde A, Eichner J F, Kantelhardt J W, Havlin S 2005 Phys. Rev. Lett. 94 048701
[29]	Bunde E K, Bunde A, Havlin S, Roman H E, Goldreich Y, Schellnhuber H J 1998 Phys. Rev. Lett. 81 729
[30]	Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 8 046133-1
[31]	Govindan R B, Vjushin D, Brenner S, Bunde A, Havlin S, Schellnhuber H J 2001 Phys. A 294 239
[32]	He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou Unibersity) p13 (in Chinese) [何文平 2008 博士论文 (兰州: 兰州大学) p13]
[33]	Peng C K, Buldyrev S V 1993 Phys. Rev. E 49 1685
[34]	Shiesinger M F, West B J, Klafter J 1987 Phys. Rev. Lett. 58 1100
[35]	Costas A Varotsos, Christian L E Franzke, Maria N Efstathiou, Andrei G Degermendzhi 2014 Theor. Appl. Climatol. 116 51
[36]	Chen Z, Ivanov P, Hu K, Stanley H E 2002 Physical Review E 65 041107
[37]	Hurst H 1951 Transactions of the American society of civil engineers 116 770
[38]	Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econometrics 112 265
[39]	He W P, Liu Q Q, Jiang Y D, Lu Y 2015 Chin. Phys. B 24 049205
[40]	Daniel L R, Russ E D 2003 Deep-Sea Reaearch Part I 50 691
[41]	Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[42]	Pincus S M 1995 J. Chaos 5 110
[43]	Pincus S M, Goldberger A L 1994 Am. J. Physiol. 266 H1643
[44]	Jin H M, He W P, Hou W, Zhang D Q 2012 Acta Phys. Sin. 61 069201 (in Chinese) [金红梅, 何文平, 侯威, 章大全 2012 物理学报 61 069201]
[45]	Jin H M, He W P, Zhang W, Feng A X, Hou W 2012 Acta Phys. Sin. 61 129202 (in Chinese) [金红梅, 何文平, 张文, 冯爱霞, 侯威 2012 物理学报 61 129202]
[46]	Frieden B R 1998 Physics from Fisher Information: A Unification (Cambridge: Cambridge University Press) pp319
[47]	Brian D F, Heriberto C, Christopher W P 2003 J. Theor. Biol. 222 517
[48]	Audrey L M, Christopher W P, Heriberto C 2006 Ecological Modelling 95 72
[49]	Julio R P, Deni T R, Luis R D, Joel T S, Francisco M P 2011 Entropy 13 1648
[50]	Yrulla L L, Giuliant A, Zbilut J P 1996 Phys. Lett. A 223 255
[51]	Gao J B, Cai H Q 2000 Phys. Lett. A 270 75
[52]	Provenzale A, Smith L A, Vio R, Murante G 1992 Physica D 58 31
[53]	Yu D J, Lu W P, Harrison R G 1999 J. Chaos 9 865
[54]	Schreiber T 1994 Phys. Rev. Lett. 78 843
[55]	Savit R, Green M 1991 Phys. D 50 95
[56]	Sauer T 1994 Phys. Rev. Lett. 72 3811
[57]	Grassberger P 1983 Phys. D 9 189
[58]	58 Li C G, Pei L Q 2003 Acta Phys. Sin. 52 2114 (in Chinese) [李春贵, 裴留庆 2003 物理学报 52 2114]
[59]	Wan S Q, Feng G L, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5487 (in Chinese) [万仕全, 封国林, 董文杰, 李建平 2005 物理学报 54 5487]
[60]	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]
[61]	Santer B D, Taylor K E, Wigley T M L, Penner J E, Jones P D, Cubasch U 1995 Clim. Dynam. 12 77
[62]	Santer B D, Taylor K E, Wigley T M L, Johns T C, Jones P D, Karoly D J, Mitchell J F B, Oort A H, Penner J E, Ramaswamy V, Schwarzkopf M D, Stouffer R J, Tett S 1996 Nature 382 39
[63]	Bernacchia A, Naveau P 2008 Nonlin. Processes Geophys. 15 159
[64]	Bernacchia A, Naveau P, Vrac M, Yiou P 2008 Nonlin. Processes Geophys. 15 169
[65]	Mocenni C, Facchini A, Vicino A 2010 Proceedings of the National Academy of Sciences of the United States of America 107 8097
[66]	Feng G L, Gong Z Q, Dong W J, Li J P 2005 Acta. Phys. Sin 54 5494 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉 2005 物理学报 54 5494]
[67]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林, 戴新刚, 王爱慧, 丑纪范 2001 物理学报 50 606]
[68]	Feng G L, Dong W J, Jia X J 2004 Chin. Phys. 13 413

Cited By

[1]	Liu S D, Liu S K 1997 Chin. Sci. Bull. 42 1565 (in Chinese) [刘式达, 刘式适 1997 科学通报 42 1565]
[2]	Liu S D, Liu S K, Liang S, Ren K, Fu Z T 2002 Prog. Nat. Sci. 12 1 (in Chinese) [刘式达, 刘式适, 梁爽, 任奎, 付遵涛 2002 自然科学进展 12 1]
[3]	Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta. Phys. Sin 58 2853 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉 2009 物理学报 58 2853]
[4]	Fu C B, Wang Q 1992 Chinese J. Atmos. Sci. 16 483 (in Chinese) [符淙斌, 王强 1992 大气科学 16 483]
[5]	Feng G L, Dong W J 2003 Chin. Phys. 12 1072
[6]	Feng G L, Dong W J, Li J P 2004 Chin. Phys. 13 1582
[7]	Li J P, Chou J F, Shi J E 1996 Journal of Beijing Meteorological college 2 16 (in Chinese) [李建平, 丑纪范, 史久恩 1996 北京气象学院 2 16]
[8]	Li J P, Shi J E 1993 Chinese J. Atmos. Sci. 17 132 (in Chinese) [李建平, 史久恩 1993 大气科学 17 132]
[9]	Xiao D, Li J P 2007 J. Geophys. Res. 112 D24S22
[10]	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: Metrological press) p27-89 [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 27–第89页]
[11]	Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静, 曹鸿兴 2002 物理学报 51 1181]
[12]	Kendall M G 1970 Rank Correlation Methods (London: Charles Griffin)
[13]	Mann H B, Whitney D R 1947 Annals of Mathematical Statistics 18 50
[14]	Lepage 1971 Biometrika 58 213
[15]	He W P, Wan S Q, Jiang Y D, Jin H M, Zhang W, Wu Q, He T 2013 Int. J. Climatol. 33 2713
[16]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geophys. 15 601
[17]	He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604
[18]	He W P, Deng B S, Wu Q, Zheng 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 物理学报 59 8264]
[19]	Sun D Y, Zhang H B, Huang Q 2014 Acta Phys. Sin. 63 209203 (in Chinese) [孙东永, 张洪波, 黄强 2014 物理学报 63 209203]
[20]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1996 (in Chinese) [王启光, 张增平 2008 物理学报 57 1996]
[21]	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 物理学报 60 049202]
[22]	Held H, Kleinen T 2004 Geophysical Research Letters 31 L23207
[23]	Fisher R A 1922 Philos. Trans. R. Soc. Lond. Ser. A 222 309
[24]	Savit R, Green M 1991 Phys. D 50 95
[25]	Abaimov S G, Turcotte D L, Shcherbakov R, Rundle J B 2007 Non. Proc. Geophys. 14 455
[26]	Blender R, Fraedrich K, Sienz F 2008 Non. Proc. Geo. 15 557
[27]	Bunde A, Havlin S, Kantelhardt J W, Penzel T T, Peter J H, Voigt K 2000 Phys. Rev. Lett. 85 3736
[28]	Bunde A, Eichner J F, Kantelhardt J W, Havlin S 2005 Phys. Rev. Lett. 94 048701
[29]	Bunde E K, Bunde A, Havlin S, Roman H E, Goldreich Y, Schellnhuber H J 1998 Phys. Rev. Lett. 81 729
[30]	Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 8 046133-1
[31]	Govindan R B, Vjushin D, Brenner S, Bunde A, Havlin S, Schellnhuber H J 2001 Phys. A 294 239
[32]	He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou Unibersity) p13 (in Chinese) [何文平 2008 博士论文 (兰州: 兰州大学) p13]
[33]	Peng C K, Buldyrev S V 1993 Phys. Rev. E 49 1685
[34]	Shiesinger M F, West B J, Klafter J 1987 Phys. Rev. Lett. 58 1100
[35]	Costas A Varotsos, Christian L E Franzke, Maria N Efstathiou, Andrei G Degermendzhi 2014 Theor. Appl. Climatol. 116 51
[36]	Chen Z, Ivanov P, Hu K, Stanley H E 2002 Physical Review E 65 041107
[37]	Hurst H 1951 Transactions of the American society of civil engineers 116 770
[38]	Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econometrics 112 265
[39]	He W P, Liu Q Q, Jiang Y D, Lu Y 2015 Chin. Phys. B 24 049205
[40]	Daniel L R, Russ E D 2003 Deep-Sea Reaearch Part I 50 691
[41]	Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[42]	Pincus S M 1995 J. Chaos 5 110
[43]	Pincus S M, Goldberger A L 1994 Am. J. Physiol. 266 H1643
[44]	Jin H M, He W P, Hou W, Zhang D Q 2012 Acta Phys. Sin. 61 069201 (in Chinese) [金红梅, 何文平, 侯威, 章大全 2012 物理学报 61 069201]
[45]	Jin H M, He W P, Zhang W, Feng A X, Hou W 2012 Acta Phys. Sin. 61 129202 (in Chinese) [金红梅, 何文平, 张文, 冯爱霞, 侯威 2012 物理学报 61 129202]
[46]	Frieden B R 1998 Physics from Fisher Information: A Unification (Cambridge: Cambridge University Press) pp319
[47]	Brian D F, Heriberto C, Christopher W P 2003 J. Theor. Biol. 222 517
[48]	Audrey L M, Christopher W P, Heriberto C 2006 Ecological Modelling 95 72
[49]	Julio R P, Deni T R, Luis R D, Joel T S, Francisco M P 2011 Entropy 13 1648
[50]	Yrulla L L, Giuliant A, Zbilut J P 1996 Phys. Lett. A 223 255
[51]	Gao J B, Cai H Q 2000 Phys. Lett. A 270 75
[52]	Provenzale A, Smith L A, Vio R, Murante G 1992 Physica D 58 31
[53]	Yu D J, Lu W P, Harrison R G 1999 J. Chaos 9 865
[54]	Schreiber T 1994 Phys. Rev. Lett. 78 843
[55]	Savit R, Green M 1991 Phys. D 50 95
[56]	Sauer T 1994 Phys. Rev. Lett. 72 3811
[57]	Grassberger P 1983 Phys. D 9 189
[58]	58 Li C G, Pei L Q 2003 Acta Phys. Sin. 52 2114 (in Chinese) [李春贵, 裴留庆 2003 物理学报 52 2114]
[59]	Wan S Q, Feng G L, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5487 (in Chinese) [万仕全, 封国林, 董文杰, 李建平 2005 物理学报 54 5487]
[60]	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]
[61]	Santer B D, Taylor K E, Wigley T M L, Penner J E, Jones P D, Cubasch U 1995 Clim. Dynam. 12 77
[62]	Santer B D, Taylor K E, Wigley T M L, Johns T C, Jones P D, Karoly D J, Mitchell J F B, Oort A H, Penner J E, Ramaswamy V, Schwarzkopf M D, Stouffer R J, Tett S 1996 Nature 382 39
[63]	Bernacchia A, Naveau P 2008 Nonlin. Processes Geophys. 15 159
[64]	Bernacchia A, Naveau P, Vrac M, Yiou P 2008 Nonlin. Processes Geophys. 15 169
[65]	Mocenni C, Facchini A, Vicino A 2010 Proceedings of the National Academy of Sciences of the United States of America 107 8097
[66]	Feng G L, Gong Z Q, Dong W J, Li J P 2005 Acta. Phys. Sin 54 5494 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉 2005 物理学报 54 5494]
[67]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林, 戴新刚, 王爱慧, 丑纪范 2001 物理学报 50 606]
[68]	Feng G L, Dong W J, Jia X J 2004 Chin. Phys. 13 413

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