Climate Dynamics

, Volume 37, Issue 11–12, pp 2437–2453

Changing climate states and stability: from Pliocene to present

  • V. N. Livina
  • F. Kwasniok
  • G. Lohmann
  • J. W. Kantelhardt
  • T. M. Lenton
Article

Abstract

We present a recently developed method of potential analysis of time series data, which comprises (1) derivation of the number of distinct global states of a system from time series data, and (2) derivation of the potential coefficients describing the location and stability of these states, using the unscented Kalman filter (UKF). We test the method on artificial data and then apply it to climate records spanning progressively shorter time periods from 5.3 Myr ago to the recent observational record. We detect various changes in the number and stability of states in the climate system. The onset of Northern Hemisphere glaciation roughly 3 Myr BP is detected as the appearance of a second climate state. During the last ice age in Greenland, there is a bifurcation representing the loss of stability of the warm interstadial state, followed by the total loss of this state around 25 kyr BP. The Holocene is generally characterized by a single stable climate state, especially at large scales. However, in the historical record, at the regional scale, the European monthly temperature anomaly temporarily exhibits a second, highly degenerate (unstable) state during the latter half of the eighteenth century. At the global scale, temperature is currently undergoing a forced movement of a single stable state rather than a bifurcation. The method can be applied to a wide range of geophysical systems with time series of sufficient length and temporal resolution, to look for bifurcations and their precursors.

Keywords

Potential analysis Bifurcations Time series analysis Climate states 

References

  1. Alley et al (2003) Abrupt climate change. Sci Agric 299:2005–2010Google Scholar
  2. Barriendos M, Llasat MC (2003) The case of the ’Malda’ anomaly in the western Mediterranean basin (1760–1800): an example of a strong climatic variability. Clim Change 61:191–216CrossRefGoogle Scholar
  3. Bartoli G, Sarnthein M, Weinelt M, Erlenkeuser H, Garbe-Schoenberg D, Lea D (2005) Final closure of Panama and the onset of northern hemisphere glaciation. Earth Planet Sci Lett 237:33–44CrossRefGoogle Scholar
  4. Benzi R, Parisi G, Sutera A, Vulpiani A (1983) Theory of stochastic resonance in climatic change. SIAM J Appl Math 43(3):565CrossRefGoogle Scholar
  5. Binford M, Kolata A, Brenner M, Janusek J, Seddon M, Abbott M, Curtis J (1997) Climate variation and the rise and fall of an Andean civilization. Quat Res 47(2):235–248CrossRefGoogle Scholar
  6. Black DE, Peterson L, Overpeck J, Kaplan A, Evans M, Kashgarian M (1999) Eight centuries of North Atlantic ocean-atmosphere variability. Sci Agric 286:1709–1713Google Scholar
  7. Braun H, Ditlevsen P, Chialvo DR (2008) Solar forced Dansgaard-Oeschger events and their phase relation with solar proxies. Geophys Res Lett 35:L06703CrossRefGoogle Scholar
  8. Dima M, Lohmann G (2008) Conceptual model for millennial climate variability: a possible combined solar-thermohaline circulation origin for the 1,500-year cycle. Clim Dyn 32(2–3):301–311Google Scholar
  9. Ditlevsen P (1999) Anomalous jumping in a double-well potential. Phys Rev E 60(1):172CrossRefGoogle Scholar
  10. Ditlevsen P, Kristensen MS, Andersen KK (2005) The recurrence time of Dansgaard-Oeschger events and limits on the possible periodic component. J Clim 18:2594CrossRefGoogle Scholar
  11. Fuhrer K, Neftel A, Anklin M, Maggi V (1993) Continuous measurement of hydrogen-peroxide, formaldehyde, calcium and ammonium concentrations along the new GRIP Ice Core from Summit, Central Greenland. Atmos Environ Sect A 27: 1873–1880Google Scholar
  12. Gammaitoni L (1998) Stochastic resonance. Rev Modern Phys 70(1):223CrossRefGoogle Scholar
  13. Ganopolski A, Rahmstorf S (2001) Rapid changes of glacial climate simulated in a coupled climate model. Nature 409:153–158CrossRefGoogle Scholar
  14. Ganopolski A, Rahmstorf S (2002) Abrupt glacial climate changes due to stochastic resonance. Phys Rev Lett 88(3):038501CrossRefGoogle Scholar
  15. Gardiner CW (2004) Handbook of stochastic methods: 3rd. edn . Springer, New York, p 415Google Scholar
  16. Ghil M (2000) Is our climate stable? Bifurcations, transitions and oscillations in climate dynamics. In: Keilis-Borok VI, Sorondo M~Sanchez (eds) Science for survival and sustainable development. Pontifical Academy of Sciences, Vatican City, p 163Google Scholar
  17. Ghil M (2002) Natural climate variability. In: MacCracken M, Perry J (eds) Encyclopedia of global environmental change: vol. 1. Wiley , Chichester/New York, p 544Google Scholar
  18. Hansen J et al (2001) A closer look at United States and global surface temperature. J Geophys Res Ocean 106(D20):23,947–23,963CrossRefGoogle Scholar
  19. Hasselmann K (1976) Stochastic climate models. Tellus 6(XXVIII):473CrossRefGoogle Scholar
  20. Hasselmann K (1999) Climate change: linear and nonlinear signature. Nature 398:755CrossRefGoogle Scholar
  21. Haug GH, Hughen KA, Peterson LC, Sigman DM, Röhl U (2001) Southward migration of the intertropical convergence zone through the Holocene. Sci Agric 293:1304–1308Google Scholar
  22. Held H, Kleinen T (2004) Detection of climate system bifurcations by degenerate fingerpinting. Geophys Res Lett 31:L23207CrossRefGoogle Scholar
  23. Jouzel J et al (2007) Orbital and millennial Antarctic climate variability over the past 800,000 years. Sci Agric 317(5839):793–796Google Scholar
  24. Julier SJ, Uhlmann JK (2004) Unscented filtering and nonlinear estimations. Proc IEEE 92(3):401CrossRefGoogle Scholar
  25. Kravtsov S, Kondrashov D, Ghil M (2005) Multilevel regression modeling of nonlinear processes: derivation and applications to climatic variability. J Clim 18(21):4404CrossRefGoogle Scholar
  26. Kwasniok F, Lohmann G (2009) Deriving dynamical models from paleoclimatic records: application to glacial millennial-scale climate variability. Phys Rev E 80:066104CrossRefGoogle Scholar
  27. Kwasniok F, Lohmann G (2010) A stochastic nonlinear oscillator model for glacial millennial-scale climate transitions derived from ice-core data. Nonlin Proc Geophys: submittedGoogle Scholar
  28. Lenton TM, Held H, Kriegler E, Hall J, Lucht W, Rahmstorf S, Schellnhuber HJ (2008) Tipping elements in the earth system. Proc Nat Acad Sci USA 105(6):1786–1793CrossRefGoogle Scholar
  29. Lisiecki LE, Raymo ME (2005) A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O records. Paleoceanography 20, Article no: PA1003Google Scholar
  30. Livina VN, Lenton T (2007) A modified method for detecting incipient bifurcations in a dynamical system. Geophys Res Lett 34:L03712CrossRefGoogle Scholar
  31. Livina VN, Kwasniok F, Lenton TM (2010) Potential analysis reveals changing number of climate states during the last 60 kyr. Clim Past 6:77–82CrossRefGoogle Scholar
  32. Livina VN, Ditlevsen PD, Lenton TM (submitted) An independent test of methods of detecting and anticipating bifurcations in time-series data. Nonlin Proc GeophysGoogle Scholar
  33. Lohmann G, Rimbu N, Dima M (2004) Climate signature of solar irradiance variations: analysis of long-term instumental, historical, and proxy data. Int J Climatol 24:1045–1056CrossRefGoogle Scholar
  34. Lohmann G (2009) Abrupt climate change. In: Meyers R (ed) Encyclopedia of complexity and systems science, vol. 1. Springer, New York, pp 1–21Google Scholar
  35. Luterbacher J, Dietrich D, Xoplaki E, Grosjean M, Wanner H (2004) European seasonal and annual temperature variability, trends and extremes since 1500. Sci Agric 303:1499–1503Google Scholar
  36. Maraun D, Kurths J (2004) Cross wavelet analysis. Significance testing and pitfalls. Nonlin Proc Geoph 11:505–514CrossRefGoogle Scholar
  37. New M, Hulme M, Jones P (2000) Representing twentieth-century space-time climate variability. Part II: development of 1901–1996 monthly grids of terrestrial surface climate. J Clim 13:2217–2238CrossRefGoogle Scholar
  38. Niels Bohr Institute archive of paleodata. http://www.glaciology.gfy.ku.dk
  39. Paillard D (1998) The timing of Pleistocene glaciations from a simple multiple-state climate model. Nat Biotechnol 391:378–381CrossRefGoogle Scholar
  40. Palmer T (1999) A nonlinear dynamical perspective on climate prediction. J Clim 12:575CrossRefGoogle Scholar
  41. Scheffer M, Bascompte J, Brock WA, Brovkin V, Carpenter SR, Dakos V, Held H, van Nes EH, Rietkerk M, Sugihara G (2009) Early-warning signals for critical transitions. Nature 461: 53–59Google Scholar
  42. Silverman BW (1986) Density estimation of statistics and data analysis. Chapman & Hall, LondonGoogle Scholar
  43. Sitz A, Schwarz U, Kurths J, Voss HU (2002) Estimation of parameters and unobserved components for nonlinear systems from noisy time series. Phys Rev E 66:016210CrossRefGoogle Scholar
  44. Smith T, Reynolds R, Peterson T, Lawrimore J (2008) Improvements to NOAA’s historical merged land-ocean surface temperature analysis (1880–2006). J Clim 21:2283Google Scholar
  45. Steffensen J et al (2008) High-resolution Greenland Ice Core data show abrupt climate change happens in few years. Sci Agric 321:680–684Google Scholar
  46. Voss H, Timmer J, Kurths J (2004) Nonlinear dynamical system identification from uncertain and indirect measurements. Int J Bifurcat Chaos 14(6):1905–1933CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • V. N. Livina
    • 1
  • F. Kwasniok
    • 2
  • G. Lohmann
    • 3
  • J. W. Kantelhardt
    • 4
  • T. M. Lenton
    • 1
  1. 1.School of Environmental SciencesUniversity of East AngliaNorwichUK
  2. 2.College of Engineering, Mathematics and Physical SciencesUniversity of ExeterExeterUK
  3. 3.Alfred Wegener Institute for Polar and Marine ResearchBremerhavenGermany
  4. 4.Institute of Physics, Theory groupMartin-Luther-Universität Halle-WittenbergHalleGermany

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