the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Dec 2024
100-kyr ice age cycles as a timescale matching problem
Abstract. The dominant periodicity of the late Pleistocene glacial cycles is roughly 100 kyr, rather than other major astronomical periods such as 19, 23, 41, and 400 kyr. Various models explain this fact through distinct dynamical mechanisms, including synchronization of self-sustained oscillations and resonance in mono- or multi-stable systems. However, the variety of proposed models and dynamical mechanisms could obscure the essential factor for realizing the 100-kyr periodicity. We propose the hypothesis that the ice-sheet climate system responds to astronomical forcing at the ~100-kyr periodicity because the intrinsic timescale of the system is closer to 100 kyr than to other major astronomical periods. We support this idea with analyses and sensitivity studies of several simple ice age models with contrasting mechanisms.
Competing interests: One of the co-authors, Michel Crucifix, is a member of the editorial board of Earth System Dynamics. The authors declare no other competing financial interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.- Preprint
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CC1: 'Some thoughts regarding Mitsui et al paper “100-kyr ice age cycles as a timescale matching problem”', Mikhail Verbitsky, 04 Jan 2025
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AC1: 'Reply on CC1', Takahito Mitsui, 21 Jan 2025
Thank you very much for reading our manuscript in detail and providing us with valuable feedback. We have addressed your comments point by point and proposed several changes to the manuscript. We believe these revisions will significantly enhance the quality and clarity of our work.
To improve the readability of our responses, we have applied type coding to distinguish our replies from your comments. For precise formatting and clarity, we have prepared our responses using LaTeX and attached them as a PDF document.
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CC2: 'Reply on AC1', Mikhail Verbitsky, 23 Jan 2025
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CC3: 'Illustration of CC2', Mikhail Verbitsky, 25 Jan 2025
I hope the enclosed figure S5 with comments is helpful.
- AC3: 'Reply on CC2 and CC3', Takahito Mitsui, 13 Feb 2025
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CC3: 'Illustration of CC2', Mikhail Verbitsky, 25 Jan 2025
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CC2: 'Reply on AC1', Mikhail Verbitsky, 23 Jan 2025
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AC1: 'Reply on CC1', Takahito Mitsui, 21 Jan 2025
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RC1: 'Comment on esd-2024-39', Holger Kantz, 09 Jan 2025
The authors pose the hypothesis that out of the many models
for glacial cycles those which when driven with proper insolation data produce
particularly good matching with observations are those which possess an
intrinsic time scale close to 100kyr. This is a very interesting hypothesis.
The authors demonstrate this in detail for 3 models which represent very
different classes:
One with self-sustained oscillations, one which effectively is a
damped oscillator which without driving relaxes to a fixed point,
and one which is a bistable system where switches in either direction
involve some transition times the sum of which again is approximately 100kyr.
In order to verify the relevance of these intrinsic times, the authors
rescale time in all models while keeping the driving unaltered, thereby
showing that the models only exhibit the approximate 100kyr periodicity when
their intrinsic time scales are close to this. For about 10 more models they
check for their intrinsic time scales as well and show that all of these
satisfy their hypothesis. A relevant conclusion is that while the
existence of some intrinsic 100kyr time scale seems to be the key for good
performance, the dynamical mechanism by which this time scale is created can
be quite different.I consider this paper to be a very novel, interesting and relevant
contribution to the 100kyr problem.I missed (or may have overlooked the discussion of) only one aspect
in this issue of the 100kyr cycles: The lack of spectral power at 100kyr in the
65N insolation time series means that the driving signal lacks this frequency
component. Nonetheless they state in line 60 that 'proximity of the intrinsic
time scale .... to the 100kyr periodicity of the eccentricity cycles' is
relevant, i.e., they consider the 100kyr period of the driver to be due to
eccentricity. This seems to be in contradiction to the fact that in the PSD
of 65N insolation there is no enhanced power in this frequency band, and they
also cite Berger who proposed a kind of beating frequency
of the 23.7 and 19kyr modes to be responsible for the 100kyr cycle.
The fact that the eccentricity period of 95kyr is
close to the 100kyr, is this essential or just by chance? Perhaps the authors
can comment on this.purely technical minor issues:
line 25, "Hencefore, the $\approx$ 100 glacial cycles...": kyr is missing
line 117: "... the VCV18 model CANNOT be qualified as ... synchronization"???
line 155: What is the difference between I(t) and f(t)? In line 86 it is said
"I(t) is the standardized summer solstice insolation anomaly at 65N", as well
as in line 107. f(t) is defined in line 128 as '65N summer solstice insolation
anomaly'. Perhaps the authors can invest one more line to clarify this (also
where the mean over the past 1Myr appears and what f_1, f_2 are).Citation: https://doi.org/10.5194/esd-2024-39-RC1 -
AC2: 'Reply on RC1', Takahito Mitsui, 21 Jan 2025
Thank you very much for reviewing our manuscript in detail and providing us with valuable feedback. We have addressed your comments and questions point by point and proposed several changes to the manuscript. We believe these revisions will significantly enhance the quality and clarity of our work.
To improve the readability of our responses, we have applied type coding to distinguish our replies from your comments. For precise formatting and clarity, we have prepared our responses using LaTeX and attached them as a PDF document.
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AC2: 'Reply on RC1', Takahito Mitsui, 21 Jan 2025
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RC2: 'Comment on esd-2024-39', Anonymous Referee #2, 07 Apr 2025
The preprint titled "100-kyr ice age cycles as a timescale matching problem" presents a compelling hypothesis that the dominant ~100-kyr periodicity of late Pleistocene glacial cycles arises from the proximity of the climate system's intrinsic timescale to the ~100-kyr eccentricity cycles. The study systematically analyzes three distinct ice age models—representing synchronization, resonance in a mono-stable system, and resonance in a multi-stable system—to demonstrate that the ~100-kyr periodicity emerges when the intrinsic timescale of the system aligns with the astronomical forcing. The manuscript is well-structured, clearly written, and addresses a long-standing question in paleoclimatology with a novel perspective. The manuscript makes a significant contribution to understanding the ~100-kyr problem by unifying diverse mechanisms under the timescale-matching hypothesis. With minor revisions—particularly expanding the discussion of the MPT and clarifying the generality of the results—the paper would be suitable for publication. I recommend acceptance after addressing the specific comments above.
The three models (SO, VCV18, G24-3) are well-chosen to represent distinct mechanisms, but their simplicity raises questions about whether the results generalize to more complex systems. For instance, how would the timescale-matching hypothesis hold in models incorporating additional feedbacks (e.g., carbon cycle, dust-albedo interactions)? A discussion on this limitation would be valuable.
The definition of "intrinsic timescale" varies across models (e.g., self-sustained oscillation period vs. relaxation timescales in bistable systems). The manuscript should clarify whether these differences affect the interpretation of timescale matching or if they represent fundamentally distinct dynamics.
The brief discussion of the MPT (Section 4) is insightful but underdeveloped. The authors suggest that the 41-kyr periodicity before the MPT could also result from timescale matching, but this is not explored in depth. Including a sensitivity analysis or model experiments addressing the MPT would significantly strengthen the paper.
The distinction between nonlinear resonance and synchronization is well-explained, but the manuscript could better highlight why this distinction matters for the ~100-kyr problem. For example, does the dominance of one mechanism over the other have implications for predicting future climate variability?
The power spectral density (PSD) analysis is robust, but the manuscript could include a more detailed comparison between model outputs and proxy records (e.g., time-domain metrics or phase relationships). This would help assess whether the models not only reproduce the ~100-kyr peak but also the timing of deglaciations.
Figures S1–S7 are cited in the text but are not included in the preprint. The authors should ensure all supplementary figures are accessible or provide descriptions in the main text.
Line 25: "Henceforth" should likely be "Previously."
Lines 70-75: It only briefly explains each chapter's general content, not the research purpose and main methods, making it hard for readers to grasp the research core at the start. Suggest the author supplement research objective and main method info. When explaining objectives, state key scientific problems to solve and expected results. When describing methods, detail model selection criteria, simulation experiment process, and data analysis methods and ideas to help readers understand the paper's core content and research context.
Line 204: The term "quasi-Arnold tongue" (Section 3.2) is introduced without a clear definition. A brief explanation or reference would aid readability.
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