<i>π</i>-theorem generalization of the ice-age theory

Verbitsky, Mikhail Y.; Crucifix, Michel

doi:https://doi.org/10.5194/esd-11-281-2020

Articles | Volume 11, issue 1

https://doi.org/10.5194/esd-11-281-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/esd-11-281-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 11, issue 1

Research article

|

17 Mar 2020

Research article |

| 17 Mar 2020

π-theorem generalization of the ice-age theory

Mikhail Y. Verbitsky and Michel Crucifix

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Final revised paper (published on 17 Mar 2020)
Preprint (discussion started on 23 Oct 2019)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Review for Π-theorem generalization of the ice-age theory', Anonymous Referee #1, 30 Nov 2019
- AC1: '“Π-theorem generalization of the ice-age theory” by Mikhail Y. Verbitsky and Michel Crucifix - Response to Anonymous Referee 1', Mikhail Verbitsky, 16 Dec 2019
RC2: 'Π-theorem generalization of the ice-age theory', Anonymous Referee #2, 04 Dec 2019
- AC2: '“Π-theorem generalization of the ice-age theory” by Mikhail Y. Verbitsky and Michel Crucifix - Response to Anonymous Referee 2', Mikhail Verbitsky, 16 Dec 2019
- AC3: '“Π-theorem generalization of the ice-age theory” by Mikhail Y. Verbitsky and Michel Crucifix - Response to Anonymous Referee 2', Mikhail Verbitsky, 16 Dec 2019
RC3: 'Reviewer Comments on esd-2019-65. Π-theorem generalization of the ice-age theory', Anonymous Referee #3, 17 Dec 2019
- AC4: '“Π-theorem generalization of the ice-age theory” by Mikhail Y. Verbitsky and Michel Crucifix - Response to Anonymous Referee 3', Mikhail Verbitsky, 24 Dec 2019

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (10 Jan 2020) by Gabriele Messori

AR by Mikhail Verbitsky on behalf of the Authors (11 Jan 2020) Author's response Manuscript

ED: Referee Nomination & Report Request started (15 Jan 2020) by Gabriele Messori

RR by Anonymous Referee #3 (17 Jan 2020)

RR by Anonymous Referee #1 (26 Jan 2020)

RR by Anonymous Referee #2 (30 Jan 2020)

ED: Publish subject to minor revisions (review by editor) (31 Jan 2020) by Gabriele Messori

Dear Authors,

I have now received a second set of comments from the reviewers of your study, which I provide below. You will see that whilst they are positive about your revision, they suggest the paper requires some minor additional edits before it can be considered suitable for publication.

Reviewer #2
I appreciate the authors' effort in addressing my comments. I am happy with the responses and edits, except regarding my first comment.

At this point, the text that is added to lines 15-18 of Page 6 seems contradictory to what is discussed in lines 13 and 14. If changing one parameter (\epsilon) leads to the expression shown at the end of Line 18, then why would not you except that this expression to hold in general? What matters in dimensional analysis is the change in the dimensionless groups, not a specific parameter. It would be helpful if you further clarify the text that follows Eq. 13.

Reviewer #3
In my first review I wrote:
"Nonetheless, the robustness of the V number, at least when subject to a simple forcing, is impressive. Therefore, in order to strengthen the paper, and add more new material, my suggestion is that the authors will take this model and add several potential feedback mechanisms to obtain different variation of dynamical systems. Then they will have different V numbers for the different models. If for the same value of the different V numbers, for the different models, the dynamic response of the different models will be similar this will be highly cool and much more robust. This will mean that what truly matters is the ratio between positive to negative feedback mechanisms, not only within the same model but also with similar models of the same family."

I think that the authors' response for this suggestion is only partial and not truly satisfying to evaluate the robustness of the V number in different models.

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AR by Mikhail Verbitsky on behalf of the Authors (03 Feb 2020) Author's response Manuscript

ED: Publish as is (11 Feb 2020) by Gabriele Messori

AR by Mikhail Verbitsky on behalf of the Authors (11 Feb 2020) Manuscript

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Short summary

Using the central theorem of dimensional analysis, the π theorem, we show that the relationship between the amplitude and duration of glacial cycles is governed by a property of scale invariance that does not depend on the physical nature of the underlying positive and negative feedbacks incorporated by the system. It thus turns out to be one of the most fundamental properties of the Pleistocene climate.