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Chaotic signature of climate extremes

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Abstract

Understanding the dynamics of climate extremes is important in its prediction and modelling. In this study, linear trends in percentile, threshold, absolute, and duration-based temperature and precipitation extremes indicator were obtained from 1979 to 2012 using the ETCCDI data set. The pattern of trend was compared with nonlinear measures (Entropy, Hurst exponent, recurrence quantification analysis) of temperature and precipitation. Regions which show positive trends in temperature-based extremes were found to be areas with low entropy and chaotic values. Complexity measures also revealed that the dynamics of the Southern Hemisphere differs from that of the Northern Hemisphere.

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References

  • Abatan AA, Abiodun BJ, Gutowski WJ Jr, Rasaq-Balogun SO (2017) Trends and variability in absolute indices of temperature extremes over Nigeria: linkage with NAO. International Journal of Climatology In Press. https://doi.org/10.1002/joc.5196

    Google Scholar 

  • Abiodun BJ, Lawal KA, Salami AT, Abatan AA (2013) Potential influences of global warming on future climate and extreme events in Nigeria. Reg Environ Chang 13(3):477–491

    Google Scholar 

  • Abiodun BJ, Adegoke J, Abatan AA, Ibe CA, Egbebiyi TS, Engelbrecht F, Pinto I (2017) Potential impacts of climate change on extreme precipitation over four African coastal cities. Clim Change 143:399–413

    Google Scholar 

  • Ahn JH, Kim HS (2005) Nonlinear modeling of El Nino/southern oscillation index. J Hydrol Eng 10(1):8–15

    Google Scholar 

  • Aijain CM (1998) Characterizing ENSO with nonlinear dynamics. Msc., University of Rhode Island

  • Alexander L, Arblaster JM (2017) Historical and projected trends in temperature and precipitation extremes in Australia in observations and CMIP5. Weather Clim Extremes 15:34–56

    Google Scholar 

  • Alexander LV, Zhang X, Peterson TC, Caesar J, Gleason B, Klein Tank AMG, Haylock M, Collins D, Trewin B, Rahimzadeh F, Tagipour A, Rupa Kumar K, Revadekar J, Griffiths G, Vincent L, Stephenson DB, Burn J, Aguilar E, Brunet M, Taylor M, New M, Zhai P, Rusticucci M, Vazquez-Aguirre JL (2006) Global observed changes in daily climate extremes of temperature and precipitation. J Geophys Res: Atmos 111(D5):D05,109. https://doi.org/10.1029/2005JD006290

    Article  Google Scholar 

  • An X, Jiang D, Zhao M, Liu C (2012) Short term prediction of wind power using EMD and chaotic theory. Commun Nonlinear Sci Numer Simul 17:1036–1042

    Google Scholar 

  • Binder P, Wilches CA (2012) Absence of determinism in El Nino southern oscillation. Phys Rev E 65:055,207

    Google Scholar 

  • Boo K, Kwon W, Baek H (2006) Change of extreme events of temperature and precipitation over Korea using regional projection of future climate change. Geophys Res Lett 33:L01,701

    Google Scholar 

  • Chang P, Ji L, Li H, Flugel M (1996) Chaotic dynamics versus stochastic processes in El Nino - southern oscillation in coupled ocean-atmosphere models. Physica D 98:301–320

    Google Scholar 

  • Chou SC, Lyra A, Mourão C, Dereczynski C, Pilotto I, Gomes J, Bustamante J, Tavares P, Silva A, Rodrigues D et al (2014) Evaluation of the eta simulations nested in three global climate models. Am J Clim Change 3(5):438–454

    Google Scholar 

  • Christidis N, Stott PA (2016) Attribution analyses of temperature extremes using a set of 16 indices. Weather Clim Extremes 14:24–35. http://www.sciencedirect.com/science/article/pii/S2212094716300640

    Google Scholar 

  • Collins DA, Della-Marta PM, Plummer N, Trewin BC (2000) Trends in annual frequencies of extreme temperature events in Australia. Aust Met Mag 49:277–292

    Google Scholar 

  • de Vrese P, Hagemann S, Claussen M (2016) Asian irrigation, African rain: remote impacts of irrigation. Geophys Res Lett 43(8):3737–3745

    Google Scholar 

  • Dee DP, Uppala SM, Simmons AJ, Berrisford P, Poli P, Kobayashi S, Andrae U, Balmaseda MA, Balsamo G, Bauer P, Bechtold P, Beljaars ACM, Berg LVD, Bidlot J, Bormann N, Delsol C, Dragani R, Fuentes M, Geer AJ (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137(656):553–597. https://doi.org/10.1002/qj.828

    Article  Google Scholar 

  • Elsner JB, Tsonis AA (1993) Nonlinear dynamics established in the ENSO. Geophys Res Lett 20(2):213–216

    Google Scholar 

  • Faranda D, Messori G, Alvarex-Castro MC, Yiou P (2017) Dynamical properties and extremes of northern hemisphere climate fields over the past 60 years. Nonlin Processes Geophys 24:713– 725

    Google Scholar 

  • Feulner G, Rahmstorf S, Levermann A, Volkwardt S (2013) On the origin of the surface air temperature difference between the hemispheres in Earth’s present-day climate. J Climate 26(18):7136–7150. https://doi.org/10.1175/JCLI-D-12-00636.1

    Article  Google Scholar 

  • Franzke C (2011) Nonlinear trends, long-range dependence, and climate noise properties of surface temperature. J Climate 25:4172

    Google Scholar 

  • Fuwape IA, Ogunjo ST (2016) Quantification of scaling exponents and dynamical complexity of microwave refractivity in a tropical climate. J Atmos Solar-Terrestrial Phys 150-151:61–68. https://doi.org/10.1016/j.jastp.2016.10.010

    Article  Google Scholar 

  • Fuwape IA, Ogunjo ST, Oluyamo SS, Rabiu AB (2017) Spatial variation of deterministic chaos in mean daily temperature and rainfall over Nigeria. Theor Appl Climatol 130(1):119–132. https://doi.org/10.1007/s00704-016-1867-x

    Article  Google Scholar 

  • Gautama T, Mandic DP, Hulle MMV (2004) The delay vector variance method for detecting determinism and nonlinearity in time series. Phys D 190:167–176. https://doi.org/10.1016/j.physd.2003.11.001

    Article  Google Scholar 

  • Gille ST (2002) Warming of the Southern Ocean since the 1950s. Science 295 (5558):1275–1277. https://doi.org/10.1126/science.1065863. http://science.sciencemag.org/content/295/5558/1275

    Article  Google Scholar 

  • Gonzalez J, de Faria E, Albuquerque MP, Albuquerque MP (2011) Nonadditive Tsallis entropy applied to the Earth’s climate. Phys A Stat Mech its Appl 390(4):587–594. https://doi.org/10.1016/j.physa.2010.10.045

    Article  Google Scholar 

  • Gottwald GA, Melbourne I, A PRSL (2004) A new test for chaos in deterministic systems, pp 603–611. https://doi.org/10.1098/rspa.2003.1183

    Google Scholar 

  • Hall AD, Skalin J, Terasvirta T (2001) A nonlinear time series model of El Nino. Environ Modell Softw 16:139–146

    Google Scholar 

  • Hansen J, Ruedy R, Sato M, Lo K (2010) Global surface temperature change. Rev Geophys 48 (4):n/a–n/a. https://doi.org/10.1029/2010RG000345

    Article  Google Scholar 

  • Hunt BG, Dix MR (2017) Stochastic implications for long-range rainfall predictions. Climate Dynamics, https://doi.org/10.1007/s00382-017-3572-6

    Google Scholar 

  • Jin Y, Kawamura A, Jinno K, Berndtsson R (2005) Nonlinear multivariate analysis of SOI and local precipitation and temperature. Nonlinear Processes Geophys 12:67–74

    Google Scholar 

  • Kalimeri M, Papadimitriou C, Balasis G, Eftaxias K (2008) Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy. Phys A Stat Mech its Appl 387(5-6):1161–1172. https://doi.org/10.1016/j.physa.2007.10.053

    Article  Google Scholar 

  • Kantelhardt JW, Koscielny-Bunde E, Rybski D, Braun P, Bunde A, Havlin S (2006) Long-term persistence and multifractality of precipitation and river runoff records. J Geophys Res Atmos 111(1):D01,106. https://doi.org/10.1029/2005JD005881

    Google Scholar 

  • Kantz H (1994) A robust method to estimate the maximal Lyapunov exponent of a time series. Phys Lett A 185(1):77–87

    Google Scholar 

  • Kawachi T, Maruyama T, Singh VP (2001) Rainfall entropy for delineation of water resources zones in Japan. J Hydrol 246(1–4):36–44

    Google Scholar 

  • Kawamura A, McKerchar AI, Spigel RH, Jinno K (1998) Chaotic characteristics of the southern oscillation index time series. J Hydrol 204:168–181

    Google Scholar 

  • Khan S, Ganguly AR, Bandyopadhyay S, Saigal S, Erickson DJ III, Protopopsescu V, Ostrouchov G (2006) Nonlinear statistics reveals stronger ties between ENSO and the tropical hydrological cycle. Geophys Res Lett 33:L24,402

    Google Scholar 

  • Klein Tank AMG, Konnen GP (2003) Trends in indices of daily temperature and precipitation extremes in Europe, 1946-99. J Climate 16:3665

    Google Scholar 

  • Klein Tank AMG, Zwiers FW, Zhang X (2009) Guidelines on analysis of extremes in a changing climate in support of informed decisions for adaptation, climate data and monitoring. Tech Rep WCDMP-No 72, World Meteorological Organization, wMO-TD No. 1500

  • Kunkel KE, Andsageer K, Easterling DR (1999) Long term trends in extreme precipitation events over the conterminous United States and Canada. J Climate 12:2515–2528

    Google Scholar 

  • Kyoung MS, Kim HS, Sivakumar B, Singh VP, Ahn KS (2011) Dynamic characteristics of monthly rainfall in the Korean Peninsula under climate change. Stoch Environ Res Risk Assess 25(4):613–625. https://doi.org/10.1007/s00477-010-0425-9

    Article  Google Scholar 

  • Manton M, Della-Marta P, Haylock M, Hennessy K, Nicholls N, Chambers L, Collins D, Daw G, Finet A, Gunawan D, Inape K, Isobe H, Kestin T, Lefale P, Leyu C, Lwin T, Maitrepierre L, Ouprasitwong N, Page C, Pahalad J, Plummer N, Salinger M, Suppiah R, Tran V, Trewin B, Tibig I, Yee D (2001) Trends in extreme daily rainfall and temperature in Southeast Asia and the South Pacific: 1961–1998. Int J Climatol 21(3):269–284. https://doi.org/10.1002/joc.610

    Article  Google Scholar 

  • Marwan N, Romano MC, Thiel M, Kurths J (2007) Recurrence plots for the analysis of complex systems. Phys Rep 438(5–6):237– 329

    Google Scholar 

  • Millán H, Ghanbarian-Alavijeh B, Garcia-Fornaris I (2010) Nonlinear dynamics of mean daily temperature and dewpoint time series at Balolsar, Iran, 1961 - 2005. Atmos Res 98(1):89–101. https://doi.org/10.1016/j.atmosres.2010.06.001

    Article  Google Scholar 

  • Ogunjo S (2015) Effect of data transformation on long term memory of chaotic time series. African Rev Phys 10:219– 224

    Google Scholar 

  • Ogunjo ST, Adediji AT, Dada JB (2017) Investigating chaotic features in solar radiation over a tropical station using recurrence quantification analysis. Theor Appl Climatol 127(1-2):421–427. https://doi.org/10.1007/s00704-015-1642-4

    Article  Google Scholar 

  • Panagoulia D, Vlahogianni EI (2014) Nonlinear dynamics and recurrence analysis of extreme precipitation for observed and general circulation model generated climates. Hydrol Process 28(4):2281–2292. https://doi.org/10.1002/hyp.9802

    Google Scholar 

  • Potter KW (1979) Annual precipitation in the northeast United States: long memory, short memory or no memory? Water Resour Res 15(2):340–347

    Google Scholar 

  • Reason CJC (2000) . Multidecadal climate variability in the subtropics/mid-latitudes of the Southern Hemisphere oceans 52A:203–223

    Google Scholar 

  • Rind D (1999) Complexity and climate. Science 284(5411):105– 107

    Google Scholar 

  • Rosenstein MT, Collins JJ, de Luca CJ (1993) A practical method for calculating largest Lyapunov exponents from small data sets. Phys D Nonlinear Phenom 65(1–2):117–134. http://www-anw.cs.umass.edu/mtr/papers/RosensteinM93.pdf%5Cnpapers3://publication/uuid/B61A1922-225A-4FC2-8CC9-D5147B26022D

    Google Scholar 

  • Samet H, Marzbani F (2014) Quantizing the deterministic nonlinearity in wind speed time series. Renew Sustain Energy Rev 39:1143–1154. https://doi.org/10.1016/j.rser.2014.07.130

    Article  Google Scholar 

  • Sano M, Sawada Y (1985) Measurement of the Lyapunov spectrum from a chaotic time series. Phys Rev Lett 55(10):1082–1085. https://doi.org/10.1103/PhysRevLett.55.1082

    Google Scholar 

  • Schoof JT, Robeson SM (2016) Projecting changes in regional temperature and precipitation extremes in the United States. Weather Clim Extremes 11:28–40

    Google Scholar 

  • Sillman J, Kharin VV, Zhang X, Zwiers FW, Bronaugh D (2013) Climate extremes indices in the CMIP5 multimodel ensemble: part 1. Model evaluation in the present climate. J Geophys Res: Atmos 118:1716–1733

    Google Scholar 

  • Singh VP (1997) The use of entropy in hydrology and water resources. Hydrol Process 11:587–626

    Google Scholar 

  • Sivakumar B (2004) Chaos theory in geophysics: past, present and future. Chaos Solitons & Fractals 19 (2):441–462. https://doi.org/10.1016/s0960-0779(03)00055-9

    Article  Google Scholar 

  • Sivakumar B (2005) Correlation dimension estimation of hydrological series and data size requirement: myth and reality. Hydrol Sci 50(4):591–603. https://doi.org/10.1623/hysj.2005.50.4.591

    Article  Google Scholar 

  • Sivakumar B, Wallender WW, Horwath WR, Mitchell JP, Prentice SE, Ba Joyce (2006) Nonlinear analysis of rainfall dynamics in California’s Sacramento Valley. Hydrol Process 20:1723–1736. https://doi.org/10.1002/hyp.5952

    Article  Google Scholar 

  • Sivakumar B, Jayawardena AW, Li WK (2007) Hydrologic complexity and classification: a simple data reconstruction approach. Hydrol Process 21:2713–2728

    Google Scholar 

  • Stone L, Saparin PI, Huppert A, Price C (1998) El Nino chaos: the role of noise and stochastic resonance on the ENSO cycle. Geophys Res Lett 25(2):175–178

    Google Scholar 

  • Tang Y, Deng Z (2010) Low dimensional nonlinearity of ENSO and its impact on predictability. Physica D 239:258–268

    Google Scholar 

  • Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD (1992) Testing for nonlinearity in time series: the method of surrogate data. Physica D 58:77–94

    Google Scholar 

  • Tsallis C (1988) Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 52:479

    Google Scholar 

  • Tsonis AA (2009) Dynamical changes in the ENSO system in the last 11000 years. Climate Dynam 33:1069

    Google Scholar 

  • Tziperman E, Stone L, Cane MA, Jarosh H (1994) El Nino chaos: overlapping of resonances between the seasonal cycle and the pacific ocean-atmosphere oscillator. Science 264:72–74

    Google Scholar 

  • Ubilava D, Helmers CG (2013) Forecasting ENSO with a smooth transition autoregressive model. Environ Modell Softw 40:181–190

    Google Scholar 

  • Vallis GK (1986) El Nino: a chaotic dynamical system? Science 232:243

    Google Scholar 

  • Vose RS, Easterling DR, Gleason B (2005) Maximum and minimum temperature trends for the globe: an update through 2004. Geophys Res Lett 32(23):n/a–n/a. https://doi.org/10.1029/2005GL024379

    Article  Google Scholar 

  • Wolf A, Swift JB, Swinney HL, Vastano Vastano JA (1985) Determining Lyapunov exponents from a time series. Phys D Nonlinear Phenom 16(3):285–317. https://doi.org/10.1093/rof/rfs003

    Article  Google Scholar 

  • Zbilut JP, Webber CL (2006) Recurrence quantification analysis. In: Wiley Encycl. Biomed. Eng. https://doi.org/10.1002/9780471740360.ebs1355. Wiley, Hoboken

  • Zbilut JP, Webber CL (2015) Recurrence quantification analysis. https://doi.org/10.1007/978-3-319-07155-8

  • Zivkovic T, Rypdal K (2013) ENSO dynamics: low dimensional chaotic or stochastic? J Geophys Res 118:2161–2168

    Google Scholar 

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Acknowledgments

Part of this research was carried out at the Max Planck Institute for the Physics of Complex Systems, Dresden, Germany by Ogunjo Samuel. The authors also acknowledge the Expert Team on Climate Change Detection and Indices (ETCCDI) for providing data which are available from http://www.cccma.ec.gc.ca/data/climdex/.

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Correspondence to Samuel Ogunjo.

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Fuwape, I., Oluyamo, S., Rabiu, B. et al. Chaotic signature of climate extremes. Theor Appl Climatol 139, 565–576 (2020). https://doi.org/10.1007/s00704-019-02987-6

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