Articles | Volume 16, issue 6
https://doi.org/10.5194/esd-16-1989-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-16-1989-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Milankovitch theory “as an initial value problem”: Implications of the long memory of ice advection
Mikhail Y. Verbitsky
CORRESPONDING AUTHOR
Gen5 Group, LLC, Newton, MA, USA
UCLouvain, Earth and Life Institute, Louvain-la-Neuve, Belgium
Dmitry Volobuev
The Central Astronomical Observatory of the Russian Academy of Sciences at Pulkovo, Saint Petersburg, Russia
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The cause of the MPT- period shift is generally thought to be a change within the Earth System, since the orbital insolation forcing does not change its pattern through the event. Here we propose that the MPT could be a dominant-period relaxation process that is strongly dependent on the initial state of the system and this sensitivity to the initial state is enabled by the orbital forcing.
Mikhail Y. Verbitsky, Michael E. Mann, and Dmitry Volobuev
Earth Syst. Dynam., 15, 1015–1017, https://doi.org/10.5194/esd-15-1015-2024, https://doi.org/10.5194/esd-15-1015-2024, 2024
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It was recently suggested that global warming can be explained by the non-anthropogenic factor of seismic activity. If that is the case, it would have profound implications. We have assessed the validity of the claim by using a statistical technique that evaluates the existence of causal connections between variables, finding no evidence for any causal relationship between seismic activity and global warming.
Mikhail Y. Verbitsky and Michel Crucifix
Clim. Past, 19, 1793–1803, https://doi.org/10.5194/cp-19-1793-2023, https://doi.org/10.5194/cp-19-1793-2023, 2023
Short summary
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Are phenomenological dynamical paleoclimate models physically similar to Nature? We demonstrated that though they may be very accurate in reproducing empirical time series, this is not sufficient to claim physical similarity with Nature until similarity parameters are considered. We suggest that the diagnostics of physical similarity should become a standard procedure before a phenomenological model can be utilized for interpretations of historical records or future predictions.
Mikhail Verbitsky
EGUsphere, https://doi.org/10.5194/egusphere-2022-758, https://doi.org/10.5194/egusphere-2022-758, 2022
Preprint archived
Short summary
Short summary
Phenomenological models may be impressive in reproducing empirical time series but this is not sufficient to claim physical similarity with nature until comparison of similarity parameters is performed. We illustrated such a process of diagnostics of physical similarity by comparing a phenomenological dynamical paleoclimate model with a more physically explicit dynamical model.
Mikhail Y. Verbitsky
Earth Syst. Dynam., 13, 879–884, https://doi.org/10.5194/esd-13-879-2022, https://doi.org/10.5194/esd-13-879-2022, 2022
Short summary
Short summary
Reconstruction and explanation of past climate evolution using proxy records is the essence of paleoclimatology. In this study, we use dimensional analysis of a dynamical model on orbital timescales to recognize theoretical limits of such forensic inquiries. Specifically, we demonstrate that major past events could have been produced by physically dissimilar processes making the task of paleo-record attribution to a particular phenomenon fundamentally difficult if not impossible.
Mikhail Verbitsky and Michael Mann
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2021-87, https://doi.org/10.5194/esd-2021-87, 2021
Revised manuscript not accepted
Short summary
Short summary
In this study, we highlight a component of global warming variability, a scaling law that is based purely on fundamental physical properties of the climate system.
Mikhail Y. Verbitsky and Michel Crucifix
Earth Syst. Dynam., 12, 63–67, https://doi.org/10.5194/esd-12-63-2021, https://doi.org/10.5194/esd-12-63-2021, 2021
Short summary
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We demonstrate here that a single physical phenomenon, specifically, a naturally changing balance between intensities of temperature advection and diffusion in the viscous ice media, may influence the entire spectrum of the Pleistocene variability from orbital to millennial timescales.
Cited articles
Abe-Ouchi, A., Saito, F., Kawamura, K., Raymo, M. E., Okuno, J. I., Takahashi, K., and Blatter, H.: Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume, Nature, 500, 190–194, 2013.
Bahr, D. B., Pfeffer, W. T., and Kaser, G.: A review of volume-area scaling of glaciers, Rev. Geophys., 53, 95–140, https://doi.org/10.1002/2014RG000470, 2015.
Barenblatt, G. I.: Scaling, Cambridge University Press, Cambridge, ISBN 0 521 53394 5, 2003.
Berger, W. H.: On the Milankovitch sensitivity of the Quaternary deep-sea record, Clim. Past, 9, 2003–2011, https://doi.org/10.5194/cp-9-2003-2013, 2013.
Buckingham, E.: On physically similar systems; illustrations of the use of dimensional equations, Phys. Rev., 4, 345–376, 1914.
Crucifix, M.: Oscillators and relaxation phenomena in Pleistocene climate theory, Philos. T. Roy. Soc. A, 370, 1140–1165, 2012.
Crucifix, M.: Why could ice ages be unpredictable?, Clim. Past, 9, 2253–2267, https://doi.org/10.5194/cp-9-2253-2013, 2013.
Ganopolski, A.: Toward generalized Milankovitch theory (GMT), Clim. Past, 20, 151–185, https://doi.org/10.5194/cp-20-151-2024, 2024.
Ganopolski, A. and Calov, R.: The role of orbital forcing, carbon dioxide and regolith in 100 kyr glacial cycles, Clim. Past, 7, 1415–1425, https://doi.org/10.5194/cp-7-1415-2011, 2011.
Gowan, E. J.: Bayesian analysis and paleo ice sheet modelling: a commentary on the proposal by Tarasov and Goldstein, RC2, https://doi.org/10.5194/egusphere-2022-1410-RC2, 2023.
Huybers, P.: Early Pleistocene glacial cycles and the integrated summer insolation forcing, Science, 313, 508–511, https://doi.org/10.1126/science.1125249, 2006.
Huybers, P.: Pleistocene glacial variability as a chaotic response to obliquity forcing, Clim. Past, 5, 481–488, https://doi.org/10.5194/cp-5-481-2009, 2009.
Huybers, P.: Combined obliquity and precession pacing of late Pleistocene deglaciations, Nature, 480, 229–232, https://doi.org/10.1038/nature10626, 2011.
Huybers, P. and Wunsch, C.: Obliquity pacing of the late Pleistocene glacial terminations, Nature, 434, 491–494, https://doi.org/10.1038/nature03401, 2005.
Lisiecki, L. E. and Raymo, M. E.: A Pliocene-Pleistocene stack of 57 globally distributed benthic δ18O records, Paleoceanography, 20, PA1003, https://doi.org/10.1029/2004PA001071, 2005.
Omta, A. W., van Voorn, G. A. K., Rickaby, R. E. M., and Follows, M. J.: On the potential role of marine calcifiers in glacial-interglacial dynamics, Glob. Biogeochem. Cyc., 27, 692–704, oi:10.1002/gbc.20060, 2013.
Omta, A. W., Kooi, B. W., van Voorn, G. A. K., Rickaby, R. E. M., and Follows. M. J.: Inherent characteristics of sawtooth cycles can explain different glacial periodicities, Clim. Dynam. 46, 557–569, https://doi.org/10.1007/s00382-015-2598-x, 2016.
Saltzman, B.: Finite amplitude free convection as an initial value problem, Journal of atmospheric sciences, 19, 329–341, 1962.
Saltzman, B.: Dynamical paleoclimatology: generalized theory of global climate change, in: Vol. 80, Academic Press, San Diego, CA, ISBN 0126173311, 2002.
Talento, S. and Ganopolski, A.: Reduced-complexity model for the impact of anthropogenic CO2 emissions on future glacial cycles, Earth Syst. Dynam., 12, 1275–1293, https://doi.org/10.5194/esd-12-1275-2021, 2021.
Tziperman, E., Raymo, M. E., Huybers, P., and Wunsch, C.: Consequences of pacing the Pleistocene 100 kyr ice ages by nonlinear phase locking to Milankovitch forcing, Paleoceanography, 21, PA4206, https://doi.org/10.1029/2005PA001241, 2006.
Verbitsky, M. Y.: Equilibrium ice sheet scaling in climate modeling, Climate Dynamics, 7, 105–110, https://doi.org/10.1007/BF00209611, 1992.
Verbitsky, M. Y.: Inarticulate past: similarity properties of the ice–climate system and their implications for paleo-record attribution, Earth Syst. Dynam., 13, 879–884, https://doi.org/10.5194/esd-13-879-2022, 2022.
Verbitsky, M. Y. and Crucifix, M.: π-theorem generalization of the ice-age theory, Earth Syst. Dynam., 11, 281–289, https://doi.org/10.5194/esd-11-281-2020, 2020.
Verbitsky, M. Y. and Crucifix, M.: Do phenomenological dynamical paleoclimate models have physical similarity with Nature? Seemingly, not all of them do, Clim. Past, 19, 1793–1803, https://doi.org/10.5194/cp-19-1793-2023, 2023.
Verbitsky, M. Y., Crucifix, M., and Volobuev, D. M.: A theory of Pleistocene glacial rhythmicity, Earth Syst. Dynam., 9, 1025–1043, https://doi.org/10.5194/esd-9-1025-2018, 2018.
Volobuev, D. and Verbitsky, M.: Supplementary Code and Data to Earth System Dynamics Paper “Milankovitch Theory “as an Initial Value Problem”: Implications of the Long Memory of Ice Advection” by Mikhail Y. Verbitsky and Dmitry Volobuev, Zenodo [code], https://doi.org/10.5281/zenodo.17272864, 2025.
Chief editor
Broadly, there are two schools of thought with regards to the relationship between orbital cycles and Ice Ages: either the orbital cycles directly force the Ice Ages or the Ice Ages are an oscillation within the climate system that is phase-locked to the orbital cycles. Both of these schools of thought implicitly assume that the orbital forcing makes the climate system "forget" its initial state. Here, Verbitsky & Volobuev perform idealized ice-sheet simulations and show that the system doesn't "forget" its initial state. Furthermore, this system exhibits spontaneous periodicity changes. The authors argue that this behaviour depends on the memory duration of the climate system. Therefore, this work opens an important avenue to be addressed by future research, focusing on the length of the memory of the climate system.
Broadly, there are two schools of thought with regards to the relationship between orbital...
Short summary
We describe a so far unrecognized physical phenomenon of orbital forcing modifying the terrestrial physics in such a way that instead of erasing the memory of initial conditions this memory is extended and initial values become major governing parameters.
We describe a so far unrecognized physical phenomenon of orbital forcing modifying the...
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