Verbitsky, Mikhail Y.
Crucifix, Michel
[UCL]
Volobuev, Dmitry M.
Variations in Northern Hemisphere ice volume over the past 3 million years have been described in numerous studies and well documented. These studies depict the mid-Pleistocene transition from 40kyr oscillations of global ice to predominantly 100kyr oscillations around 1 million years ago. It is generally accepted to attribute the 40kyr period to astronomical forcing and to attribute the transition to the 100kyr mode to a phenomenon caused by a slow trend, which around the mid-Pleistocene enabled the manifestation of nonlinear processes. However, both the physical nature of this nonlinearity and its interpretation in terms of dynamical systems theory are debated. Here, we show that ice-sheet physics coupled with a linear climate temperature feedback conceal enough dynamics to satisfactorily explain the system response over the full Pleistocene. There is no need, a priori, to call for a nonlinear response of the carbon cycle. Without astronomical forcing, the obtained dynamical system evolves to equilibrium. When it is astronomically forced, depending on the values of the parameters involved, the system is capable of producing different modes of nonlinearity and consequently different periods of rhythmicity. The crucial factor that defines a specific mode of system response is the relative intensity of glaciation (negative) and climate temperature (positive) feedbacks. To measure this factor, we introduce a dimensionless variability number, V. When positive feedback is weak (V ∼ 0), the system exhibits fluctuations with dominating periods of about 40kyr which is in fact a combination of a doubled precession period and (to smaller extent) obliquity period. When positive feedback increases (V ∼ 0.75), the system evolves with a roughly 100kyr period due to a doubled obliquity period. If positive feedback increases further (V ∼ 0.95), the system produces fluctuations of about 400kyr. When the V number is gradually increased from its low early Pleistocene values to its late Pleistocene value of V ∼ 0.75, the system reproduces the mid-Pleistocene transition from mostly 40kyr fluctuations to a 100kyr period rhythmicity. Since the V number is a combination of multiple parameters, it implies that multiple scenarios are possible to account for the mid-Pleistocene transition. Thus, our theory is capable of explaining all major features of the Pleistocene climate, such as the mostly 40kyr fluctuations of the early Pleistocene, a transition from an early Pleistocene type of nonlinear regime to a late Pleistocene type of nonlinear regime, and the 100kyr fluctuations of the late Pleistocene. When the dynamical climate system is expanded to include Antarctic glaciation, it becomes apparent that climate temperature positive feedback (or its absence) plays a crucial role in the Southern Hemisphere as well. While the Northern Hemisphere insolation impact is amplified by the outside-of-glacier climate and eventually affects Antarctic surface and basal temperatures, the Antarctic ice-sheet area of glaciation is limited by the area of the Antarctic continent, and therefore it cannot engage in strong positive climate feedback. This may serve as a plausible explanation for the synchronous response of the Northern and Southern Hemisphere to Northern Hemisphere insolation variations. Given that the V number is dimensionless, we consider that this model could be used as a framework to investigate other physics that may possibly be involved in producing ice ages. In such a case, the equation currently representing climate temperature would describe some other climate component of interest, and as long as this component is capable of producing an appropriate V number, it may perhaps be considered a feasible candidate.
- Abe-Ouchi Ayako, Saito Fuyuki, Kawamura Kenji, Raymo Maureen E., Okuno Jun’ichi, Takahashi Kunio, Blatter Heinz, Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume, 10.1038/nature12374
- Ashkenazy Yosef, Tziperman Eli, Are the 41 kyr glacial oscillations a linear response to Milankovitch forcing?, 10.1016/j.quascirev.2004.04.008
- Ashwin Peter, Ditlevsen Peter, The middle Pleistocene transition as a generic bifurcation on a slow manifold, 10.1007/s00382-015-2501-9
- Berger A., Loutre M.F., Insolation values for the climate of the last 10 million years, 10.1016/0277-3791(91)90033-q
-
Berger, W. H. and Wefer, G.: On the Dynamics of the Ice Ages: Stage-11 Paradox, Mid-Brunhes Climate Shift, and 100-Ky Cycle, in: Earth's Climate and Orbital Eccentricity: The Marine Isotope Stage 11 Question, Geophysical Monograph-American Geophysical Union, Washington, DC, 41–59, 2003.
- Chalikov D.V., Verbitsky M.Ya., Modeling the Pleistocene Ice Ages, Advances in Geophysics Volume 32 (1990) ISBN:9780120188321 p.75-131, 10.1016/s0065-2687(08)60427-6
- Clark Peter U., Pollard David, Origin of the Middle Pleistocene Transition by ice sheet erosion of regolith, 10.1029/97pa02660
- Clark Peter U., Archer David, Pollard David, Blum Joel D., Rial Jose A., Brovkin Victor, Mix Alan C., Pisias Nicklas G., Roy Martin, The middle Pleistocene transition: characteristics, mechanisms, and implications for long-term changes in atmospheric pCO2, 10.1016/j.quascirev.2006.07.008
- Crucifix M., Why could ice ages be unpredictable?, 10.5194/cp-9-2253-2013
- Daruka István, Ditlevsen Peter D., A conceptual model for glacial cycles and the middle Pleistocene transition, 10.1007/s00382-015-2564-7
- DeConto Robert M., Pollard David, Contribution of Antarctica to past and future sea-level rise, 10.1038/nature17145
- Ellis Ralph, Palmer Michael, Modulation of ice ages via precession and dust-albedo feedbacks, 10.1016/j.gsf.2016.04.004
- Fretwell P., Pritchard H. D., Vaughan D. G., Bamber J. L., Barrand N. E., Bell R., Bianchi C., Bingham R. G., Blankenship D. D., Casassa G., Catania G., Callens D., Conway H., Cook A. J., Corr H. F. J., Damaske D., Damm V., Ferraccioli F., Forsberg R., Fujita S., Gim Y., Gogineni P., Griggs J. A., Hindmarsh R. C. A., Holmlund P., Holt J. W., Jacobel R. W., Jenkins A., Jokat W., Jordan T., King E. C., Kohler J., Krabill W., Riger-Kusk M., Langley K. A., Leitchenkov G., Leuschen C., Luyendyk B. P., Matsuoka K., Mouginot J., Nitsche F. O., Nogi Y., Nost O. A., Popov S. V., Rignot E., Rippin D. M., Rivera A., Roberts J., Ross N., Siegert M. J., Smith A. M., Steinhage D., Studinger M., Sun B., Tinto B. K., Welch B. C., Wilson D., Young D. A., Xiangbin C., Zirizzotti A., Bedmap2: improved ice bed, surface and thickness datasets for Antarctica, 10.5194/tc-7-375-2013
- Ganopolski Andrey, Roche Didier M., On the nature of lead–lag relationships during glacial–interglacial climate transitions, 10.1016/j.quascirev.2009.09.019
- Ganopolski A., Calov R., Claussen M., Simulation of the last glacial cycle with a coupled climate ice-sheet model of intermediate complexity, 10.5194/cp-6-229-2010
- Grinsted A., Moore J. C., Jevrejeva S., Application of the cross wavelet transform and wavelet coherence to geophysical time series, 10.5194/npg-11-561-2004
- Herbert T. D., Peterson L. C., Lawrence K. T., Liu Z., Tropical Ocean Temperatures Over the Past 3.5 Million Years, 10.1126/science.1185435
- Honisch B., Hemming N. G., Archer D., Siddall M., McManus J. F., Atmospheric Carbon Dioxide Concentration Across the Mid-Pleistocene Transition, 10.1126/science.1171477
- Huybers P., Early Pleistocene Glacial Cycles and the Integrated Summer Insolation Forcing, 10.1126/science.1125249
- Huybers P., Pleistocene glacial variability as a chaotic response to obliquity forcing, 10.5194/cp-5-481-2009
- Imbrie J., Imbrie J. Z., Modeling the Climatic Response to Orbital Variations, 10.1126/science.207.4434.943
- Imbrie John Z., Imbrie-Moore Annabel, Lisiecki Lorraine E., A phase-space model for Pleistocene ice volume, 10.1016/j.epsl.2011.04.018
- Le Brocq A. M., Payne A. J., Vieli A., An improved Antarctic dataset for high resolution numerical ice sheet models (ALBMAP v1), 10.5194/essd-2-247-2010
- Levitus S., Antonov J. I., Boyer T. P., Baranova O. K., Garcia H. E., Locarnini R. A., Mishonov A. V., Reagan J. R., Seidov D., Yarosh E. S., Zweng M. M., World ocean heat content and thermosteric sea level change (0-2000 m), 1955-2010 : WORLD OCEAN HEAT CONTENT, 10.1029/2012gl051106
- Lisiecki Lorraine E., Raymo Maureen E., A Pliocene-Pleistocene stack of 57 globally distributed benthic δ18O records : PLIOCENE-PLEISTOCENE BENTHIC STACK, 10.1029/2004pa001071
- MacAyeal D. R., Binge/purge oscillations of the Laurentide Ice Sheet as a cause of the North Atlantic's Heinrich events, 10.1029/93pa02200
- Marshall Shawn J., Clark Peter U., Basal temperature evolution of North American ice sheets and implications for the 100-kyr cycle : GLACIAL TERMINATIONS, 10.1029/2002gl015192
- Mitsui Takahito, Aihara Kazuyuki, Dynamics between order and chaos in conceptual models of glacial cycles, 10.1007/s00382-013-1793-x
- Omta Anne Willem, Kooi Bob W., van Voorn George A. K., Rickaby Rosalind E. M., Follows Michael J., Inherent characteristics of sawtooth cycles can explain different glacial periodicities, 10.1007/s00382-015-2598-x
- Paillard Didier, The timing of Pleistocene glaciations from a simple multiple-state climate model, 10.1038/34891
- Paillard Didier, Quaternary glaciations: from observations to theories, 10.1016/j.quascirev.2014.10.002
- Paillard Didier, Parrenin Frédéric, The Antarctic ice sheet and the triggering of deglaciations, 10.1016/j.epsl.2004.08.023
-
Past Interglacial Working Group of PAGES: Interglacials of the last 800,000 years, Rev. Geophys., 54, 162–219, 2016.
-
Paterson, W. S. B.: The physics of glaciers, Pergamon Press, Oxford, 1981.
- Pattyn F., Schoof C., Perichon L., Hindmarsh R. C. A., Bueler E., de Fleurian B., Durand G., Gagliardini O., Gladstone R., Goldberg D., Gudmundsson G. H., Huybrechts P., Lee V., Nick F. M., Payne A. J., Pollard D., Rybak O., Saito F., Vieli A., Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP, 10.5194/tc-6-573-2012
- Pattyn Frank, Perichon Laura, Durand Gaël, Favier Lionel, Gagliardini Olivier, Hindmarsh Richard C.A., Zwinger Thomas, Albrecht Torsten, Cornford Stephen, Docquier David, Fürst Johannes J., Goldberg Daniel, Gudmundsson G. Hilmar, Humbert Angelika, Hütten Moritz, Huybrechts Philippe, Jouvet Guillaume, Kleiner Thomas, Larour Eric, Martin Daniel, Morlighem Mathieu, Payne Anthony J., Pollard David, Rückamp Martin, Rybak Oleg, Seroussi Hélène, Thoma Malte, Wilkens Nina, Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison, 10.3189/2013jog12j129
-
Payne, A. J.: Limit cycles in the basal thermal regime of ice sheets, J. Geophys. Res.-Solid Ea., 100, 4249–4263, 1995.
- Pollard D., DeConto R. M., Description of a hybrid ice sheet-shelf model, and application to Antarctica, 10.5194/gmd-5-1273-2012
- Pollard D., DeConto R. M., A simple inverse method for the distribution of basal sliding coefficients under ice sheets, applied to Antarctica, 10.5194/tc-6-953-2012
- Pollard David, DeConto Robert M., Alley Richard B., Potential Antarctic Ice Sheet retreat driven by hydrofracturing and ice cliff failure, 10.1016/j.epsl.2014.12.035
- Raymo M. E., The timing of major climate terminations, 10.1029/97pa01169
- Rohling E.J., Braun K., Grant K., Kucera M., Roberts A.P., Siddall M., Trommer G., Comparison between Holocene and Marine Isotope Stage-11 sea-level histories, 10.1016/j.epsl.2009.12.054
- Rohling E. J., Foster G. L., Grant K. M., Marino G., Roberts A. P., Tamisiea M. E., Williams F., Sea-level and deep-sea-temperature variability over the past 5.3 million years, 10.1038/nature13230
- Ruddiman W. F., Ice-driven CO2 feedback on ice volume, 10.5194/cp-2-43-2006
-
Saltzman, B.: Dynamical paleoclimatology: generalized theory of global climate change, in: Vol. 80, Academic Press, San Diego, CA, 2002.
- Saltzman Barry, Maasch Kirk A, A first-order global model of late Cenozoic climatic change II. Further analysis based on a simplification of CO2 dynamics, 10.1007/bf00210005
- Saltzman Barry, Verbitsky Mikhail Ya, Asthenospheric ice-load effects in a global dynamical-system model of the Pleistocene climate, 10.1007/bf00209339
- Saltzman Barry, Verbitsky Mikhail Ya, Multiple instabilities and modes of glacial rhythmicity in the plio-Pleistocene: a general theory of late Cenozoic climatic change, 10.1007/bf00208010
- Saltzman Barry, Verbitsky Mikhail Ya., The Late Cenozoic Glacial Regimes as a Combined Response to Earth-Orbital Variations and Forced and Free CO2 Variations, Ice in the Climate System (1993) ISBN:9783642850189 p.343-361, 10.1007/978-3-642-85016-5_20
- Saltzman Barry, Verbitsky Mikhail, Late Pleistocene climatic trajectory in the phase space of global ice, ocean state, and CO2: Observations and theory, 10.1029/94pa02289
- Saltzman Barry, Verbitsky Mikhail, C02 and glacial cycles, 10.1038/367419a0
- Schoof Christian, Ice sheet grounding line dynamics: Steady states, stability, and hysteresis, 10.1029/2006jf000664
-
Shumskiy, P. A.: On the flow law for polycrystalline ice, Trudy instituta mekhaniki MGU, 42, 54–68, 1975.
- Tzedakis P. C., Crucifix M., Mitsui T., Wolff E. W., A simple rule to determine which insolation cycles lead to interglacials, 10.1038/nature21364
- Tziperman Eli, Raymo Maureen E., Huybers Peter, Wunsch Carl, Consequences of pacing the Pleistocene 100 kyr ice ages by nonlinear phase locking to Milankovitch forcing : HOW TO PACE AN ICE AGE, 10.1029/2005pa001241
- Vakulenko N. V., Ivashchenko N. N., Kotlyakov V. M., Sonechkin D. M., On periods of multiplying bifurcation of early pleistocene glacial cycles, 10.1134/s1028334x11020115
-
Verbitsky, M. Y. and Chalikov, D. V.: Modelling of the Glaciers–Ocean–Atmosphere System, Gidrometeoizdat, Leningrad, 1986.
-
Verbitsky, M. Y. , Crucifix, M., and Volobuev, D. M.: Supplementary to ESD paper “A Theory of Pleistocene Glacial Rhythmicity” available at: https://github.com/DmitryVolobuev1973/Model-of-Pleistocene-Glacial-Cycles/, last access: 15 August 2018.
-
Vialov, S. S.: Regularities of glacial shields movement and the theory of plastic viscous flow, in: Physics of the movements of ice IAHS, International Association of Hydrological Sciences (IAHS), London, UK, 266–275, 1958.
- Zhang Y. G., Pagani M., Liu Z., Bohaty S. M., DeConto R., A 40-million-year history of atmospheric CO2, 10.1098/rsta.2013.0096
Référence bibliographique |
Verbitsky, Mikhail Y. ; Crucifix, Michel ; Volobuev, Dmitry M.. A theory of Pleistocene glacial rhythmicity. In: Earth System Dynamics, Vol. 9, no.3, p. 1025-1043 (2018) |
Permalien |
http://hdl.handle.net/2078.1/204290 |