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Vakulenko N. V., Ivashenko N. N., Kotljakov V. M., Sonechkin D. M. On the period-multiplying bifurcation of glacial cycles in the pliocene – pleistocene. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 2, pp. 88-112. DOI: 10.18500/0869-6632-2013-21-2-88-112

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On the period-multiplying bifurcation of glacial cycles in the pliocene – pleistocene

Vakulenko N. V., P.P Shershov Institue of Oceanology
Ivashenko Nadezhda Nazarovna, Hydrometeorological Research Centre of Russian Federation
Kotljakov Vladimir Mihajlovich, Institute of Geography of Russian Academy of Sciences
Sonechkin Dmitrij Mihajlovich, Hydrometeorological Research Centre of Russian Federation

In the Pliocene (about five – two million years before present) global climate fluctuated with a period corresponding well 41-thousand-year cycle of changes in the Earth’s axis inclination to the ecliptic plane. Then, this period has disappeared, despite the fact that the 41-thousand-year cycle even slightly increased its scope and, therefore, the response to it would have only strengthened. By analyzing paleoclimatic series covering the Pliocene and subsequent Pleistocene, we show that the response of the climate system simply became unstable and therefore unobservable. At the same time, through perioddoubling bifurcation, a well-known in the theory of nonlinear dynamical systems, new stable and observable climatic oscillations have been excited. Further, they experienced several secondary bifurcations, at which their periods alternately tripled and doubled again.

  1. Hays JD, Imbrie J, Shackelton NJ. Variations in the Earth’s orbit: Pacemaker of the Ice Ages? Science. 1976;194(4270):1121–1132. DOI: 10.1126/science.194.4270.1121
  2. Ashkenazy Y. The role of phase locking in a simple model for glacial dynamics. Climate Dynamics. 2006;27(4):421–431. DOI:10.1007/s00382-006-0145-5.
  3. Ashkenazy Y, Tziperman E. Are the 41 kyr glacial oscillations a linear response to Milankovitch forcing? Quat. Sci. Rev. 2004;23(18):1879–1890. DOI:10.1016/j.quascirev.2004.04.008.
  4. Crowley TJ, Hyde WT. Transient nature of late Pleistocene climate variability. Nature. 2009;456(7219):226–230. DOI:10.1038/nature07365
  5. Drysdale RN, Hellstrom JC, Zanchetta G. et al. Evidence for obliquity forcing of glacial termination II. Science. 2009;325(5947):1527–1531. DOI:10.1126/science.1170371
  6. Huybers P, Wunsch C. Obliquity pacing of the late Pleistocene glacial terminations. Nature. 2005;434(7032):491–494. DOI:10.1038/nature03401
  7. Raymo ME, Huybers P. Unlocking the mysteries of the ice ages. Nature. 2008;451(7176):284–285. DOI:10.1038/nature06589
  8. Raymo ME, Nisancioglu K. The 41 kyr world: Milankovitch’s other unsolved mystery. Paleoceanology. 2003;18(1):1–6. DOI: 10.1029/2002PA000791.
  9. Tziperman E, Raymo ME, Huybers P. et al. Consequences of pacing the Pleistocene 100 kyr ice ages by nonlinear phase locking to Milankovitch forcing. Paleoceanology. 2006;21(4):PA4206. DOI:10.1029/2005PA001241.
  10. Huybers P. Antarctics’s orbital beat. Science. 2009;325(5944):1085–1086. DOI: 10.1126/science.1176186
  11. Huybers P. Early Pleistocene glacial cycles and the integrated summer insolation forcing. Science. 2006;313(5786):508–511. DOI:10.1126/science.1125249
  12. Berger A. Long-term variations of daily insolation and Quaternary climatic changes. J. Atmos. Sci. 1978;35(12):2362–2367. DOI:10.1175/1520-0469(1978)035<2362:LTVODI>2.0.CO;2
  13. Berger A, Loutre MF. Insolation values for the climate of the last 10 million years. Quat. Sci. Rev. 1991;10(4):297–317. DOI:10.1016/0277-3791(91)90033-Q
  14. Berger A, Melice JL, Loutre MF. On the origin of the 100-kyr cycles in the astronomical forcing. Paleoceanology. 2005;20(4):PA4019. DOI:10.1029/2005PA001173.
  15. Laskar J, Joutel F, Boudin F. Orbital, precessional, and insolation quantities for the earth from 20 myr to +10 myr. Astronomy and Astrophysics. 1993;270(1-2):522–533.
  16. Laskar J, Robutel P, Joutel F. et al. A long-term numerical solution for the insolation quantities of the Earth. Astronomy and Astrophysics. 2004;428(1):261–285. DOI:10.1051/0004-6361:20041335.
  17. Vernekar AD. Long-term global variations of incoming solar radiation. Meteorol. Monogr. 1972;34:21.
  18. Monin AS. Earth rotation and climate. Leningrad: Hydrometeoisdate; 1972. 112 p. (In Russian).
  19. Monin AS, Sonechkin DM. Climate fluctuations according to observations. Triple solar and other cycles. Moscow: Nauka; 2005. 191 p. (In Russian).
  20. Ghil M. Theoretical climate dynamics: an introduction. In: Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics. M. Ghil, R. Benzi and G. Parisi (eds.). New-York: North Holland; 1985. 347 p.
  21. Wunsch C. The spectral description of climate change including the 100 ky energy. Climate Dynamics. 2003;20(4):353–363. DOI:10.1007/s00382-002-0279-z
  22. Le Treut H, Ghil M. Orbital forcing, climatic interactions, and glacial cycles. J. Geophys. Res. 1983;88(C9):5167–5190. DOI:10.1029/JC088IC09P05167
  23. Imbrie J, Boyle EA, Clemens SC. et al. On the structure and origin of major glacial cycles. 1. linear responses to Milankovitch forcing. Paleoceanography. 1992;7(6):701–738. DOI:10.1029/92PA02253
  24. Imbrie J, Berger A, Boyle EA. et al. On the structure and origin of major glacial cycles. 2. The 100 000-year cycle. Paleoceanography. 1993;8(6):699–735. DOI:10.1029/93PA02751
  25. Yiou P, Genthon C, Ghil M. et al. High-frequency paleovariability in climate and CO2 levels from Vostok ice core records. J. Geophys. Res. 1991;96:20365–20378. DOI:10.1029/91JB00422
  26. Ghil M. Cryothermodynamics: the chaotic dynamics of paleoclimate. Physica D. 1994;77(1-3):130–159. DOI:10.1016/0167-2789(94)90123-6
  27. Rial JA. Pacemaking the Ice ages by frequency modulation of Earth’s orbital eccentricity. Science. 1999;285(5427):564–568. DOI: 10.1126/science.285.5427.564
  28. Rial JA, Anaclerio CA. Understanding nonlinear responses of the climate system to orbital forcing. Quaternary Science reviews. 2000;19(17-18):1709–1722.
  29. Winograd IJ, Coplen C, Landwehr JM. et al. Continuous 500000-year climate record from vein calcite in Devils Hole, Nevada. Science. 1992;258(5080):255–260. DOI:10.1126/science.258.5080.255.
  30. Raymo ME. The timing of major climate terminations. Paleoceanography. 1997;12(4):577–585. DOI:10.1029/97PA01169.
  31. Petit JR, Jouzel J. Raynaud D. et al. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature. 1999;399(6735):429–436. DOI:10.1038/20859.
  32. Kotlyakov VM. The glaciology of Antarctica. Moscow: Nauka; 2000. 432 p. (In Russian).
  33. Zachos J, Pagani M, Sloan L, Thomas E, Billups K. Trends, rhythms, and aberrations in global climate 65 ma to present. Science. 2001;292(5517):686–693. DOI:10.1126/science.1059412.
  34. Lowenstein TK, Demicco RV. Elevated Eocene atmospheric CO2 and its subsequent decline. Science. 2006;313(5795):1928–1928. DOI:10.1126/science.1129555
  35. Filander SG, Fedorov AV. Role of tropics in changing the response to Milankovitch forcing some three million years ago. Paleoceanology. 2003;18(2):1045. DOI:10.1029/2002PA000837.
  36. Lawrence KT, Zhonghui Liu, Herbert TD. Evolution of the Eastern Tropical Pacific through Plio-Pleistocene glaciation. Science. 2006;312(5770):79–83. DOI:10.1126/science.1120395
  37. Lunt DJ, Valdes PJ, Haywood A, Rutt IC. Closure of the Panama seaway during the Pliocene: implications for climate and Northern Hemisphere glaciation. Climate Dynamics. 2007;30(1):1–18. DOI:10.1007/s00382-007-0265-6.
  38. Ravelo AC, Andreasen DH, Lyle M, Lyle AO, Wara MW. Regional climate shifts caused by gradual global cooling in the Pliocene epoch. Nature. 2004;429(6989):263–267. DOI: 10.1038/nature02567.
  39. Sosdian S, Rosenthal Y. Deep-sea temperature and ice volume changes across the Pliocene-Pleistocene climate transitions. Science. 2009;325(5938):306–310. DOI:10.1126/science.1169938.
  40. Vakulenko NV, Kotlyakov VM, Sonechkin DM. Evidence of the proactive role of the ocean in the cyclicity of the ice ages of the late Pleistocene. Doklady Academii Nauk. 2008;421(3):402–405.
  41. Vakulenko NV, Kotlyakov VM, Lambert F, Sonechkin DM. On the role of the ocean in climate change Pleistocene. Doklady Academii Nauk. 2010;432(2):260–263.
  42. Bolton EW, Maasch KA, Lilly JM. A wavelet analysis of Plio-Pleistocene climate indicators: A new view of periodicity evolution. Geoph. Res. Lett. 1995;22(20):2753–2756. DOI:10.1029/95GL02799.
  43. Han-Shou Liu, Chao BF. Wavelet spectral analysis of the Earth’s orbital variations and paleoclimatic cycles. J. Atmos. Sci. 1998;55(2):227–236. DOI:10.1175/1520-0469(1998)055<0227:WSAOTE>2.0.CO;2.
  44. Press WH, Teukolsky SA, Vetterling WT. et al. Numerical Recipes in FORTRAN, nded. Cambridge: Cambridge University Press; 1992. 963 p.
  45. Schulz M, Stattegger K. Spectrum: Spectral analysis of unevenly spaced paleoclimatic time series Computers & Geosciences. 1997;23(9):929–945. DOI:10.1016/S0098-3004(97)00087-3.
  46. Sonechkin DM. Substantiation of four-dimensional (continuous) assimilation of meteorological observations based on a dynamic-stochastic approach. Meteorology and Hydrology. 1973;4:13–20.
  47. Vakulenko NV, Ivashchenko NN, Kotlyakov VM, Sonechkin DM. On the bifurcation of the multiplication of the period of glacial cycles at the beginning of the Pleistocene. Doklady Academii Nauk. 2011;436(4):541–544.
  48. Shackleton NJ, Hall MA, Pate D. Pliocene stable isotope stratigraphy of ODP site 846. Proc. Ocean Drill. Program Sci. Results. 1995;138:337–355. DOI: 10.2973/
  49. Shackleton NJ, Crowhurst S, Hagelberg T, Pisias NG, Schneider DA. A new late Neogene time scale: Application to Leg 138 sites. Proc. Ocean Drill. Program Sci. Results. 1995;138:73–101. DOI:10.2973/
  50. Lisiecki LE, Raymo ME. A Pliocene-Pleistocene stack of 57 globally distributed bentic δ18O records. 2005;20(1). DOI:10.1029/2004PA001071.
  51. Vakulenko NV, Kotlyakov VM, Monin AS, Sonechkin DM. Significant features of the calendar of the late Pleistocene glacial cycles. Izvestiya. Atmospheric and Oceanic Physics. 2007;43(6):713-721. DOI 10.1134/S0001433807060059.
  52. Arnold VI, Afraimovich VS, Ilyashenko US, Shilnikov PL. Bifurcation theory, Dynamical systems – 5, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 5. Moscow: VINITI; 1986. 218 p.
  53. Sonechkin DM. Stochasticity in models of general atmospheric circulation. Leningrad: Hydrometeoisdat; 1984. 280 p. (In Russian).
  54. Andronov AA, Witt AA, Haikin SE. Vibration theory. Moscow: Fizmatgiz; 1959. 918 p. (In Russian).
  55. Afraimovich VS, Shilnikov LP. Invariant two-dimensional tori, their destruction and stochasticity. Collection: Methods of qualitative theory of differential equations. Gorky: GNU; 1983. 23 p. (In Russian).
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