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https://doi.org/10.5194/egusphere-2026-3872
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/egusphere-2026-3872
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
10 Jul 2026
| 10 Jul 2026
Status: this preprint is open for discussion and under review for Earth System Dynamics (ESD).
ESD Ideas: A "Butterfly" on Orbital Timescales: Weak Millennial Forcing or “Brief” Human Impact May Dramatically Change the Rhythmicity of the Long-Memory Ice-Climate System
Abstract. We demonstrate that (a) the patterns of the Pleistocene climate history as different as classic reconstructions of Lisiecki and Raymo (2005) and the new one of Clark et al (2025) may both be produced by the same long-memory ice-climate system under different initial conditions or under slightly different millennial forcing, and (b) even single “brief” (on orbital timescales, i.e., a few hundred years) pulse-perturbation of the forcing, consistent with a possible human impact, may fundamentally change the dynamics of the global ice-climate system for hundreds of thousands years, making the time series we have not observed in the past.
How to cite. Verbitsky, M.: ESD Ideas: A "Butterfly" on Orbital Timescales: Weak Millennial Forcing or “Brief” Human Impact May Dramatically Change the Rhythmicity of the Long-Memory Ice-Climate System, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2026-3872, 2026.
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RC1: 'Comment on egusphere-2026-3872', Martin Claussen, 16 Sep 2026
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AC1: 'Reply on RC1', Mikhail Verbitsky, 20 Sep 2026
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My response is enclosed as a pdf file.
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AC1: 'Reply on RC1', Mikhail Verbitsky, 20 Sep 2026
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Gen5 Group, LLC, Newton, MA, USA
UCLouvain, Earth and Life Institute, Louvain-la-Neuve, Belgium
Short summary
We show that (a) the patterns of the climate history as different as reconstructions of Lisiecki and Raymo (2005) and of Clark et al (2025) may both be produced by the same long-memory climate system with different initial conditions or under different millennial forcing, and (b) a single brief perturbation of the forcing, consistent with a possible human impact, may change the dynamics of the global ice-climate system for million years, making the time series we did not observe in the past.
We show that (a) the patterns of the climate history as different as reconstructions of Lisiecki...
Comments on the manuscript
ESD Ideas: A “Butterfly” on Orbital Timescales: …
by
Mikhail Y. Verbitsky
Mikhail Verbitsky explores the idea that the dynamics of Pleistocene ice ages is an initial value problem. This idea was proposed by Verbitsky and Volobuev (2025) who developed a long-memory ice-climate system of reduced complexity in the sense of Saltzman (2002). In their model, the dynamics of large ice sheets is defined by the advection of mass and temperature. Because of the ice-climate system’s nonlinearity, the response of the surface mass balance of ice sheets to the orbital forcing is not symmetrical. This asymmetry may lead to a dynamics of the ice-climate system with a much longer memory of its initial conditions than previously supposed.
Mikhail Verbitsky applies this ice-climate model to three experiments. In a first experiment, the ice-climate model is forced by a pure obliquity period of 41 kyr to reproduce the results of Verbitsky and Volobuev (2025). The resulting time series of the area of glaciation is pretty close to the reconstruction by Lisiecki and Raymo (2005) with a pronounced 100 kyr peak and secondary, smaller 41 kyr and 23 kyr peaks. In a second experiment, the ice-climate model is driven by an additional forcing with a period of 5 kyr and an amplitude twice as large as the original orbital forcing, everything else being unchanged. Consistent with the initial-value hypothesis, the time series of the simulated glaciation area changes considerably with roughly equally strong peaks at periods of 80 kyr and 41 kyr. The later is reminiscent of the new reconstruction by Clark et al. (2025) – if one accepts that the Clark et al reconstruction captures the changes in global ice-sheet area. In a third experiment, the ice-climate model is run over the last 500 kyr into the future, but it is perturbed by a strong reduction in the glaciation area at t = 0 kyr. Interestingly the resultant time series of future glaciations shows a spectrum similar to the one of the second experiment, but with an even stronger 41 kyr signal. These results point at an intransitive response to orbital forcing which is at variance with other long-term paleoclimate simulations with more complex models by Ganopolski (2024), for example, who concludes that the pacing of orbitally driven glaciations is predictable.
Predictable vs chaotic, transitive vs intransitive? Can the hypothesis of intransitivity be validated, or better: be invalidated, in any way? Looking at the glaciation reconstructions by Lisiecki and Raymo (2005) and Clark et al.(2025), I find peaks at 41 kyr and 100 kyr in both time series, only the ratio of the amplitude of these peaks differ. Wouldn’t this speak against an initial-value problem, but in favor of predictable periods with, perhaps, only unpredictable amplitudes?
Besides addressing the issue of validation, the following comments should be considered in a revision: The idea that anthropogenic greenhouse gas emissions could push future glaciation dynamics away from its Pleistocene path was already proposed by Loutre and Berger (2000) or Ganopolski et al. (2016). In a keynote lecture at an ESF conference in Stockholm in early 2002, Andrè Berger even speaks of the end of Quaternary and the start of a new geological period, the Quinternary, with much less ice than the Quaternary. This change in dynamics is, however, not a consequence of intransitive ice sheet dynamics, but of a drastic change in the type of forcing which dominates over the next at least 10 or 20 millennia when the orbital forcing becomes negligibly small.
The ice-climate system model is forced by the 41 kyr obliquity period. But the spectrum of the insolation changes during the caloric half-year also shows a sizable contribution from the 23 kyr precession period. In the maximum summer insolation, the latter period is even the dominant one. Would this multi-period forcing have any effect on the question of whether the ice-climate system is an initial value problem?
References:
Clark, P. U., Shakun, J. D., Rosenthal, Y., Pollard, D., Hostetler, S. W., Köhler, P., Bartlein, P. J., Gregory, J. M., Zhu, C., Schrag, D. P., Liu, Z., and Pisias, N. G.: Global mean sea level over the past 4.5 million years, Science, 390, eadv8389, https://doi.org/10.1126/science.adv8389, 2025.
Ganopolski, A.: Toward generalized Milankovitch theory (GMT), Clim. Past, 20, 151–185, https://doi.org/10.5194/cp-20-151-2024, 2024.
Ganopolski, A., Winkelmann, R., and Schellnhuber, H. J.: Critical insolation–CO2 relation for diagnosing past and future glacial inception, Nature, 529, 200–203, https://doi.org/10.1038/nature16494, 2016.
Lisiecki, L. E. and Raymo, M. E.: A Pliocene‐Pleistocene stack of 57 globally distributed benthic δ18 O records, Paleoceanography, 20, 2004PA001071, https://doi.org/10.1029/2004PA001071, 2005.
Loutre, M. F. and Berger, A.: Future Climatic Changes: Are We Entering an Exceptionally Long Interglacial?, Clim. Change, 46, 61–90, https://doi.org/10.1023/A:1005559827189, 2000.
Saltzman, B.: Dynamical paleoclimatology: generalized theory of global climate change, Academic press, San Diego, 2002.
Verbitsky, M. Y. and Volobuev, D.: Milankovitch theory “as an initial value problem”: Implications of the long memory of ice advection, Earth Syst. Dyn., 16, 1989–2002, https://doi.org/10.5194/esd-16-1989-2025, 2025.