Synchronization phenomena observed in glacial-interglacial cycles simulated in an Earth system model of intermediate complexity

Mitsui, Takahito; Willeit, Matteo; Boers, Niklas

doi:https://doi.org/10.5194/esd-2023-16

Preprints

https://doi.org/10.5194/esd-2023-16

Preprints

05 Jun 2023

| 05 Jun 2023

Status: this preprint is currently under review for the journal ESD.

Synchronization phenomena observed in glacial-interglacial cycles simulated in an Earth system model of intermediate complexity

Takahito Mitsui, Matteo Willeit, and Niklas Boers

Abstract. The glacial-interglacial cycles of the Quaternary exhibit 41-kyr periodicity before the Mid-Pleistocene Transition (MPT) around 1.2–0.8 Myr ago and ~100-kyr periodicity after that. From the viewpoint of dynamical systems, proposed mechanisms generating these periodicities are broadly divided into two types: (i) nonlinear forced responses of a mono- or multi-stable climate system to the astronomical forcing, or (ii) synchronization of internal self-sustained oscillations to the astronomical forcing. In this study, we investigate the dynamics of glacial cycles simulated by the Earth system model of intermediate complexity CLIMBER-2 with a fully interactive carbon cycle, which reproduces the MPT under gradual changes in volcanic CO₂ degassing and regolith cover. We report that, in this model, the dominant frequency of glacial cycles is set in line with the principle of synchronization. It is found that the model exhibits self-sustained oscillations in the absence of astronomical forcing. Before the MPT, glacial cycles synchronize to the 41-kyr obliquity cycles because the self-sustained oscillations have periodicity relatively close to 41 kyr. After the MPT the time scale of internal oscillations becomes too long to follow every 41-kyr obliquity cycle, and the oscillations synchronize to the 100-kyr eccentricity cycles that modulate the amplitude of climatic precession. The latter synchronization occurs with the help of the 41-kyr obliquity forcing through a mechanism that we term vibration-enhanced synchronization. While we interpret the dominant periodicities of glacial cycles as the result of synchronization of internal self-sustained oscillations with the astronomical forcing, the Quaternary glacial cycles show facets of both synchronization and forced response.

Received: 16 May 2023 – Discussion started: 05 Jun 2023

Download & links

Preprint (PDF, 3091 KB)

Supplement (1601 KB)

Download & links

Takahito Mitsui et al.

Status: final response (author comments only)

RC1:
'Comment on esd-2023-16', Anonymous Referee #1, 04 Jul 2023

REVIEW OF ‘SYNCHRONIZATION PHENOMENA OBSERVED IN GLACIAL-INTERGLACIAL CYCLES SIMULATED IN AN EARTH SYSTEM MODEL OF INTERMEDIATE COMPLEXITY’ BY MITSUI ET AL.
Mitsui et al. scrutinize the results of the coupled climate/ice-sheet/vegetation/carbon-cycle model CLIMBER-2. In an earlier publication, this model was shown to be able to generate the Mid-Pleistocene Transition forced only by insolation, as a result of changing two boundary conditions over time: volcanic degassing and regolith cover. In this study, Mitsui et al. conduct several sensitivity experiments, changing the boundary conditions and the strength of the different Milankovitch parameters controlling the astronomical forcing.
They find that using pre-MPT boundary conditions, CLIMBER-X generates self-sustained ~50 kyr glacial cycles in the absence of astronomical forcing. These are a result of a negative feedback of glaciogenic dust on ice sheet growth. When astronomical forcing is included, these cycles synchronize to (41-kyr) obliquity. Using post-MPT boundary conditions, the time scale of the self-sustained cycles increases to >100 kyr and synchronizes to eccentricity when astronomical forcing is switched on. Importantly, synchronization to the 95-kyr eccentricity cycle, rather than the stronger 405-kyr cycle, occurs because the power of obliquity is ‘just right’. Weaker, and indeed the self-sustained cycles would synchronize to long-eccentricity; stronger, and the obliquity itself would become dominant.
I found this article a particularly nice read, it is well-structured and well-written. It is the kind of study that I hoped would spur from the paper by Willeit et al. (2019), so I deem it timely and interesting for the community. In fact, I have no major objections to it being published in its current form. I do have some recommendations to the authors for minor improvements, including technical ones, that I list below.
SPECIFIC COMMENTS
Page 1, lines 12-13:

I think it’s better to briefly describe the influence of obliquity than to name-drop ‘vibration-enhanced synchronization’ in the abstract.
Introduction:

The 100-kyr problem is described in some detail, but the 41-kyr problem is not mentioned at all. I find this odd, as the study is essentially about both problems.
Page 3, lines 48-49:

It would, if (and only if) it is in fact linked to eccentricity. If it is for example related to 2/3 obliquity cycles, or 4/5 precession cycles, it wouldn’t have to involve damping of the longer eccentricity period.
Page 3, lines 62-63:

Similar time scale, and amplitude as well?
Page 4, line 91:

I think you can remove this sentence, as a proper scientific discussion naturally involves giving caveats.
Page 5, lines 121-122:

Remove the brackets.
Page 5, lines 124-125: ‘the CLIMBER-2 is simulated’

The grammar is incorrect.
Page 5, lines 126-127:

Not sure if this information is really needed in a non-technical paper.
Page 6, lines 155-156:

It is further evidence that changes in the internal dynamics of the Earth system are necessary to explain the MPT in CLIMBER-2.
Page 6, line 157:

‘is’ should be ‘are’
Fig. S7:

Add a cyan line to panel B.
Page 9, line 172: ‘Among others’

Can this be changed to ‘chiefly’ (or a similar word)?
Page 9, lines 190-191:

What is different about a termination? Why is glaciogenic dust deposition sustained during the deglaciation when it wasn’t in the interstadials before?
Page 10, line 196:

A spurious imbalance?
Page 10, line 206: ‘oblquity’

Typo.
Page 12, line 225: ‘two sets of sensitivity experiments’

Add ‘additional’
Figs. 7 and 10:

I found myself drawing lines at x=1.0 (true conditions). Perhaps these can be included in the figures?
Page 14, lines 264-269:

I must admit this part is lost on me. I wonder if it is really necessary to compare this mechanism to others, without any further explanation or discussion.
Figure 11:

My compliments on this figure, it summarizes the paper perfectly.
Summary and discussion:

In general, I prefer separate discussion and summary sections. The latter can be quite short, just a paragraph. This works better when I just want to check the conclusions of a paper again.
Page 18, line 285: ‘suitable’

Perhaps change to ‘small’, ‘specific’, or ‘limited’.
Page 19, line 301:

What in particular is improved in CLIMBER-X, that makes this model more reliable?
Page 19, lines 303-313:

IcIES-MIROC is climatically forced using a matrix interpolation method with pre-run climate simulations. That’s an important difference to CLIMBER-2, which is a fully coupled model. This difference should be mentioned, as it could (in part) explain the difference in results.
Page 19, lines 312-313:

This is true for the post-MPT period mostly.
Page 19, line 319: ‘Introduction’

Should be ‘the introduction’.
Page 19, line 320-322:

What kind of model do Le Treut and Ghil (1983) use? Please briefly explain.
Page 19, lines 326-329:

Reading this, I can’t help but wondering what happens if the astronomical forcing as a whole (so obliquity and eccentricity/precession combined) is decreased. Maybe as an idea for a next study, as in principle this article describes enough experiments as it is.
Figure B1:

Perhaps, you could include a phase wheel of obliquity and precession during terminations, like Figure 4 (top panels) in Watanabe et al. (2023).

Citation: https://doi.org/10.5194/esd-2023-16-RC1
- AC1: 'Reply on RC1', Takahito Mitsui, 12 Jul 2023
  
  First of all, thank you very much for reviewing our manuscript in detail and giving us very useful feedback. In what follows, we respond to your comments and questions, point by point, and propose several changes to the manuscript. We consider that these changes will substantially improve the quality and clarity of our manuscript.
  
  In order to improve the readability of our replies we applied a color/type coding to discriminate our replies from the referee’s comments. We have attached our replies as a pdf document since color coding is not available in the browser based text editor.
  
  Citation: https://doi.org/10.5194/esd-2023-16-AC1
CC1:
'Comment on esd-2023-16', Andrey Ganopolski, 13 Jul 2023

The authors acknowledged my comments on their work. However, these comments were made on an early version of the manuscript which did not include the important finding of the manuscript published in ESDD, namely, the existence of self-sustained oscillations in the CLIMBER-2 model. This is why I would like to use an opportunity to provide additional comments on this aspect of the manuscript by Mitsui et al.
The manuscript is based on the version of the CLIMBER-2 model which was used in Willeit et al. (2019) (hereafter W19), and which is very similar to the version used in Ganopolski and Brovkin (GB17) but with somewhat different values of several model parameters. Similar to W19, the GB17 version of CLIMBER-2 simulates self-sustained oscillations with the constant orbital forcing and CO₂ for regolith covering all continents (as in REG simulation in Ganopolski and Calov, 2011), although, in a rather narrow range of CO₂ concentrations (220-240 ppm). However, the GB17 model does not simulate any appreciable (more than several meters in sea level equivalent) self-sustained oscillations for the present regolith cover neither with constant CO₂ for the entire range of CO₂ concentration from 180 to 300 ppm nor with the interactive CO₂ for a wide range of orbital parameters. In principle, such a difference between similar model versions is not very surprising – CLIMBER-2 is a strongly nonlinear model, and even small changes in model parameter values can cause the appetence or disappearance of some dynamical regimes. Moreover, the time-dependent regolith map used in W19 is slightly different at time 0K from that was used in GB17. Two questions arise in this regard: (i) What are the mechanisms of long self-sustained oscillations seen in the W19 (but not in GB17) model, and (ii) whether these oscillations with a typical periodicity of several hundred kiloyears arising under constant orbital parameters (Fig. 2c) are related to the strongly asymmetric glacial cycles with the periodicity close 100 kyr simulated in CLIMBER-2 under the influence of real orbital forcing (Fig. 2d)?
1. The appearance of very long glacial cycles (in the case of the orbital parameters corresponding to 21 ka, the periodicity reaches 500 kyr) is puzzling since none of the climate components of CLIMBER-2 has such a long time scale. The only suspect is the negative silicate weathering feedback with just the right time scale. The parameters of the carbon cycle model in CLIMBER-2 are selected in such a way that the average during glacial cycle weathering compensates for volcanic outgassing. However, under interglacial (warm) climate conditions, weathering exceeds volcanic outgassing and CO₂ drifts down, while under glacial (cold) climate conditions, weathering is smaller than volcanic outgassing and CO₂ rises slowly, which, of course, is opposite to what is observed during real glacial cycles. A combination of several strong positive feedbacks with the slow negative weathering feedback, in principle, can give rise (but not in the GB17 version) to the oscillations with periodicities order of several hundred thousand years. Fig. 6 in Mitsui et al. provides some support for this hypothesis.
2. Whatever the mechanism of such long self-sustained oscillations, more important is whether the existence of these oscillations is relevant for the 100-kyr glacial cycles simulated in CLIMBER-2 under realistic orbital forcing. I do not believe that this is the case. First, the shape and typical periodicity of these self-sustained oscillations are very different from the forced 100-kyr cycles. Second, the GB17 version does not possess such oscillations but simulates strong 100 kyr periodicity both with constant (sufficiently low) CO₂ concentrations and with interactive CO₂ (Ganopolski and Calov, 2011; GB17). Moreover, other models, which, unlike CLIMBER-2, do not include glaciogenic dust feedback and thus unlikely to possess similar self-sustained oscillations, also simulate 100-kyr cycles (e.g. Berger and Loutre, 2010; Abe-Ouchi et al. 2013). Thus, although the existence of self-sustained oscillations within a certain range of external boundary conditions may amplify nonlinear system response to orbital forcing at some frequencies, they are not essential for reproducing the main features of the late Quaternary glacial cycles.
Berger, A., and Loutre, M. F.: Modeling the 100-kyr glacial-interglacial cycles, Global and Planetary Change, 72, 275-281, 2010.

Citation: https://doi.org/10.5194/esd-2023-16-CC1
- AC2: 'Reply on CC1', Takahito Mitsui, 01 Aug 2023
  
  Thank you very much for these very valuable comments. We respond to them, point by point, and propose several according changes to our manuscript. We consider that these changes will substantially improve the quality and clarity of our manuscript.
  
  In order to improve the readability of our replies we applied a color/type coding to discriminate our replies from your comments. We have attached our replies as a pdf document since color coding is not available in the browser based text editor.
  
  Citation: https://doi.org/10.5194/esd-2023-16-AC2
RC2:
'Comment on esd-2023-16', Anonymous Referee #2, 21 Jul 2023

This paper presents glacial cycle simulations from the intermediate complexity CLIMBER-2 model, discussing phase locking (synchronization) of the 40 kyr and 100 kyr glacial cycles with Milankovitch forcing. The authors discuss how Milankovitch forcing interacts with these ice ages: does it only set the phase (say, the time of terminations), or is it responsible for the existence of these oscillations? I enjoyed reading the paper; it deals with the important problem of understanding these ice ages, it presents an interesting, carefully done, and well-informed analysis, and the model used is more detailed than used for similar purposes in previous works. This is an interesting contribution; I make some comments below and am recommending publishing the paper with minor revisions.

Comments:
* Introduction, the results sections 4.1 and 4.2, conclusions, and more: the authors need to clarify what's new. The synchronization of ice ages by Milankovitch forcing has been repeatedly discussed in the literature, including the effects of summer insolation vs. obliquity or precession, the effects of noise, the dynamics before and after the MPT, etc. There is no question that there are many new and very valuable results here. Yet, when providing a result consistent with previous results, it would be helpful to note this; if it differs from previous results, explain the reason for the difference.
* As an example of the last issue: the first lines of the conclusions write: "We ... have explained the rhythms of simulated glacial cycles from the perspective of the synchronization principle": I think this was explained multiple times before. What was done here is to demonstrate this issue with a more detailed model and to perform an analysis of the model results that definitely adds to our understanding.
* The authors should show all model results in terms of equivalent sea level rather than delta18O. We have a good idea of what the amplitude of ice ages was in terms of sea level, while the isotopic signal is a complex and uncertain mix of temperature and ice volume that is difficult to decipher. The model delta18O curves could be shown in the appendix/supplementary if the authors feel strongly that the model does an excellent job producing the processes involved and that the model proxy record, therefore, contains valuable information.
* line 41: the phase locking/synchronization between insolation and ice volume was discussed by Tziperman et al. (2006) and Crucifix (2013) in much simpler models than those used here, but exploring the same issues.
* lines 292-292: nice analysis. I am not sure the oscillations pre-MPT are self-sustained, but the authors are making an interesting case for this. The alternative is oscillations driven by obliquity (more accurately, by integrated insolation with a low threshold that filters out precession, see Huybers paper on integrated insolation) with some role for nonlinearity that can be seen by the asymmetry in the oscillations and noted by some of the papers cited here already. Verbitsky, Crucifix, and Volobuev (2018) also discuss the mechanism of the mid-Pleistocene transition and the role of Milankovitch forcing.
* line 50: the need for brevity is understood, but the mention of the different mechanisms here seems a bit superficial; what, very briefly, are the dynamics of the mechanisms in each of these papers? How confident are we whether the oscillations produced in each of these papers represent internal oscillations or not?
* 73: mode-> model
* lines 205-210: Why would it be eccentricity and not precession times 4 or 5; or obliquity time 2 or 3? While eccentricity clearly modulates precession, it has such small power in insolation that it typically does not matter (hence the "Milankovitch paradox"). This issue has also been explored previously using simpler models that might help put things in perspective here rather than relying on the general (Pikovsky et al., 2003) reference alone.
* Page 11 and many other places: the difference between 107 kyr and 95 kyr is so small, given observational uncertainty, that it is not clear that there is justification for explaining a presumed 107 kyr signal in terms of a 95 kyr forcing (Rial paper). It seems worth mentioning this issue.
* Figure 6: I agree with the public comment question asking what model component leads to a time scale of 250 kyr here. Perhaps plotting additional model diagnostics might reveal this.
* Section 4.1: I admittedly felt there might be too much material here. The authors may want to attempt to decide what's important and reduce the number of figures. When every statement is followed by a reference to 3 or 4 figures (e.g., Figs S9, 7a, and 7b), this reader was a bit lost in the detail :-)
* Around Line 250: how would you reconcile this with the Huybers and Wunsch results on the synchronization with obliquity?
* Bottom of page 14: the new "vibration" terminology was mentioned in the abstract very prominently, and the authors finally get to it at this point and discuss it very briefly. I did not exactly understand what the message is and what the authors attempted to explain. The explanation was very brief, and I am not convinced that this justifies a new terminology. Also, what is the chaotic equivalent hinted at, and why is it relevant here?

Citation: https://doi.org/10.5194/esd-2023-16-RC2
- AC3: 'Reply on RC2', Takahito Mitsui, 01 Aug 2023
  
  Thank you very much for reviewing our manuscript in detail and giving us very valuable feedback. We respond to your comments and questions, point by point, and propose several changes to the manuscript in accordance. We think that these changes will substantially improve the quality and clarity of our manuscript.
  
  In order to improve the readability of our replies we applied a color/type coding to discriminate our replies from the referee’s comments. We have attached our replies as a pdf document since color coding is not available in the browser based text editor.
  
  Citation: https://doi.org/10.5194/esd-2023-16-AC3

Takahito Mitsui et al.

Supplement

https://doi.org/10.5194/esd-2023-16-supplement

Takahito Mitsui et al.

Viewed

Total article views: 629 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	Supplement	BibTeX	EndNote
524	84	21	629	28	7	6

HTML: 524
PDF: 84
XML: 21
Total: 629
Supplement: 28
BibTeX: 7
EndNote: 6

Views and downloads (calculated since 05 Jun 2023)

Month	HTML	PDF	XML	Total
Jun 2023	176	45	9	230
Jul 2023	199	26	7	232
Aug 2023	126	9	4	139
Sep 2023	23	4	1	28

Cumulative views and downloads (calculated since 05 Jun 2023)

Month	HTML	PDF	XML	Total
Jun 2023	176	45	9	230
Jul 2023	199	26	7	232
Aug 2023	126	9	4	139
Sep 2023	23	4	1	28

Viewed (geographical distribution)

Total article views: 597 (including HTML, PDF, and XML) Thereof 597 with geography defined and 0 with unknown origin.

Country	#	Views	%

Latest update: 21 Sep 2023

Download

Preprint (3091 KB)
Metadata XML

Short summary

The glacial-interglacial cycles of the Quaternary exhibit 41-kyr periodicity before the Mid-Pleistocene Transition (MPT) around 1.2–0.8 Myr ago and ~100-kyr periodicity after that. The mechanism generating these periodicities remains elusive. Through an analysis of an Earth system model of intermediate complexity CLIMBER-2, we show that the dominant periodicities of glacial cycles can be explained from the viewpoint of synchronization theory.


Total:	0
HTML:	0
PDF:	0
XML:	0