Statistical precursor signals for Dansgaard-Oeschger cooling transitions

Mitsui, Takahito; Boers, Niklas

doi:https://doi.org/10.31223/X54S90

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https://doi.org/10.31223/X54S90

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27 Jun 2023

| 27 Jun 2023

Statistical precursor signals for Dansgaard-Oeschger cooling transitions

Takahito Mitsui and Niklas Boers

Abstract. Given the likely bistability of the Atlantic Meridional Overturning Circulation (AMOC) and its recently inferred weakening, it is important to investigate the capability of identifying robust precursor signals for a possible future AMOC collapse as well as its collapses in the past. Dansgaard-Oeschger (DO) events, manifested most clearly as abrupt Northern-Atlantic temperature jumps during glacial conditions, likely reflect past switches between strong and weak AMOC modes. In general, the variance and the autocorrelation with a small lag increase in a system approaching a co-dimension one bifurcation point. Some previous studies find such statistical precursor signals for the DO warming transitions associated with a strengthening AMOC. On the other hand, statistical precursor signals for the abrupt DO cooling transitions, presumably associated with AMOC transitions from the strong to the weak mode, have not been identified. Here we identify robust and statistically significant precursor signals for several DO cooling transitions in Greenland ice core records. The important source of the statistical precursor signals stems from so-called rebound event, humps in the temperature observed at the end of interstadial, some decades to centuries prior to the transition. We propose several dynamical mechanisms that give rise to such rebound events and statistical precursor signals.

Received: 10 Jun 2023 – Discussion started: 27 Jun 2023

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Journal article(s) based on this preprint

22 Mar 2024

Statistical precursor signals for Dansgaard–Oeschger cooling transitions

Takahito Mitsui and Niklas Boers

Clim. Past, 20, 683–699, https://doi.org/10.5194/cp-20-683-2024,https://doi.org/10.5194/cp-20-683-2024, 2024

Short summary

Takahito Mitsui and Niklas Boers

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1267', Anonymous Referee #1, 21 Aug 2023
The paper examines statistical indicators for Dansgaard-Oeschger (DO) events in the Greenland ice core records and argues that these indicators can serve as signals for a potential weakening of the Atlantic Meridional Overturning Circulation (AMOC). I believe this is an excellent study that contributes significantly to our understanding of the tipping behaviour of the AMOC and is very well presented. While I think the paper can be published as it is, I suggest a few minor points that could improve the presentation of the results:
The authors have used Dansgaard-Oeschger (DO) events as indicators of tipping in the AMOC. They briefly mention this in the abstract (line 5) and later provide some references in the introduction (lines 48-51). However, if the main message of the paper is to propose "robust precursor signals for a possible future AMOC collapse," I think further discussion is required to establish a clear connection between DO events and the transition from a strong to a weak AMOC. I think the paper could benefit from a new section that addresses this point.

It is well established that changes in variance and autocorrelations are good indicators of critical slowing down (occurring during codimension one bifurcations). However, does this approach work as effectively for more complex tipping mechanisms, such as excitability (suggested in section 4 as a possible mechanism)?

I would like to draw attention to the rate-induced mechanism, where an excessively rapid change in forcing can tip the system even before reaching the bifurcation point. This mechanism could arise from mechanism 3 (the Hopf bifurcation), where the system can cross the unstable limit cycle (regular threshold) and tip. It could also be relevant to mechanism 4, where the rate of forcing might push the system to cross an irregular threshold in the form of a maximal canard. Please see (Wieczorek et al. 2023) and (O'Sullivan et al. 2023), for more details:

Wieczorek, Sebastian, Chun Xie, and Peter Ashwin. "Rate-induced tipping: Thresholds, edge states, and connecting orbits." Nonlinearity 36.6 (2023): 3238.

O’Sullivan, Eoin, Kieran Mulchrone, and Sebastian Wieczorek. "Rate-induced tipping to metastable zombie fires." Proceedings of the Royal Society A 479.2275 (2023): 20220647.
Citation: https://doi.org/10.5194/egusphere-2023-1267-RC1
- AC1: 'Reply on RC1', Takahito Mitsui, 06 Sep 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 changes to the manuscript in accordance. We think that these changes will 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/egusphere-2023-1267-AC1
RC2:
'Comment on egusphere-2023-1267', Anonymous Referee #2, 28 Sep 2023

This paper by Mitsui and Boers looks at Dansgaard-Oeschger (DO) transitions, which are examples of abrupt transitions in the Earth's past. The authors identify statistical precursor signals (SPS) in the transition from the warm to the cold state, which is evidence of DO transitions being caused by a loss of stability rather than stochastic variability. The Authors propose some dynamical mechanisms to explain this. I thought this was a good paper: the authors have clearly taken time to carefully analyse their results, although I was sad to see the code used in this paper was not shared 'by default'.
The authors may want to consider the following comments.
Broad Comments:
There are lots of time series here: 2 proxy variables, 2 early warning signals, 3 cores, 12 interstadials, 5 window sizes and 6 smoothing spans leading to 3480 analysed time series (when accounting for the fact that not all cores have all interstadials in them), although relatively few give SPS (31%). If there is a common mechanism at work, why is this the case? Can the authors be sure the results are not down to chance? The authors argue that more SPS are observed than would be expected by chance, but none of the time series for each interstadial are truly independent, and there being a false positive in one time series would increase the chance of there being a false positive in another. Furthermore, looking at figure 4d, different cores give different results for the same interstadial, e.g. in GI-20 only 4 cores give any SPS and only one 'robustly'. Different interstadials give different amounts of SPS, for example GI-14 gives many robust SPS but GI-19.2 doesn't. How do the authors account for this?
When looking for SPS, the time series must be decomposed into an slowly changing equilibrium state and fluctuations about that state. As a lot of the signal in this case for SPS comes from 'rebound events' the authors are assuming that the rebound events represent fluctuations rather than changes in the equilibrium state. What is the justification for this?
The authors may want to discuss mechanisms that can lead to changes in variance and autocorrelation not due to changing stability but due other factors. For example, due to changes in the properties of the climate forcing. Furthermore, changes in the statistical properties in the measurement process may also affect the results. For example, measurements in the ice cores further in the past may be more uncertain and therefore noisier, but measurements closer to the present may be less noisy and therefore more correlated.
Specific Comments:
Line 11: Should be rebound events not rebound event
Line 15: This tipping definition excludes N-tipping, which has no thresholds. Different authors define tipping differently but as there is disagreement over whether DO events are N or B tipping I wonder if it is better to adopt a definition compatible with the Ashwin 2012 typology?
Line 91 "R^2 = 0.95", what fit is this measuring?
Line 114: The autocorrelation is different to that in Bury et al who have C(tau) = (cos (omega tau)) exp(mu |tau|)
Line 115: Should be "increase or decrease"
Line 117: How do the authors know tau is sufficiently small, especially as omega may also be changing?
Line 120: Is a linear fit suitable if half of the interstadial is used i.e. 500+ years? Could the stable state be changing nonlinearly in this period?
Line 187: makes reference to interstadials shorter than 1000 years but Line 106 implies the authors are excluding interstadials shorter than 1000 years. Have I misunderstood?
Line 295-298: "can be shown to be 0.05". I think it would be helpful to show this. When I run the authors code I do not get any output like 0.044 or 0.042, but I may be running the code incorrectly. Is this calculation included in the shared code?
Figure 4d: Could the colormap used in this figure be changed to a diverging colormap, with its centre at 15, so that it is easy to see if an SPS is robust. Currently it is difficult to know if the colours correspond to values larger than or smaller than 15.
Bibliography:

Ashwin 2012 https://doi.org/10.1098/rsta.2011.0306

Citation: https://doi.org/10.5194/egusphere-2023-1267-RC2
- AC2: 'Reply on RC2', Takahito Mitsui, 25 Oct 2023
  
  First of all, 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 changes to the manuscript in accordance. We think that these changes will 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/egusphere-2023-1267-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1267', Anonymous Referee #1, 21 Aug 2023
The paper examines statistical indicators for Dansgaard-Oeschger (DO) events in the Greenland ice core records and argues that these indicators can serve as signals for a potential weakening of the Atlantic Meridional Overturning Circulation (AMOC). I believe this is an excellent study that contributes significantly to our understanding of the tipping behaviour of the AMOC and is very well presented. While I think the paper can be published as it is, I suggest a few minor points that could improve the presentation of the results:
The authors have used Dansgaard-Oeschger (DO) events as indicators of tipping in the AMOC. They briefly mention this in the abstract (line 5) and later provide some references in the introduction (lines 48-51). However, if the main message of the paper is to propose "robust precursor signals for a possible future AMOC collapse," I think further discussion is required to establish a clear connection between DO events and the transition from a strong to a weak AMOC. I think the paper could benefit from a new section that addresses this point.

It is well established that changes in variance and autocorrelations are good indicators of critical slowing down (occurring during codimension one bifurcations). However, does this approach work as effectively for more complex tipping mechanisms, such as excitability (suggested in section 4 as a possible mechanism)?

I would like to draw attention to the rate-induced mechanism, where an excessively rapid change in forcing can tip the system even before reaching the bifurcation point. This mechanism could arise from mechanism 3 (the Hopf bifurcation), where the system can cross the unstable limit cycle (regular threshold) and tip. It could also be relevant to mechanism 4, where the rate of forcing might push the system to cross an irregular threshold in the form of a maximal canard. Please see (Wieczorek et al. 2023) and (O'Sullivan et al. 2023), for more details:

Wieczorek, Sebastian, Chun Xie, and Peter Ashwin. "Rate-induced tipping: Thresholds, edge states, and connecting orbits." Nonlinearity 36.6 (2023): 3238.

O’Sullivan, Eoin, Kieran Mulchrone, and Sebastian Wieczorek. "Rate-induced tipping to metastable zombie fires." Proceedings of the Royal Society A 479.2275 (2023): 20220647.
Citation: https://doi.org/10.5194/egusphere-2023-1267-RC1
- AC1: 'Reply on RC1', Takahito Mitsui, 06 Sep 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 changes to the manuscript in accordance. We think that these changes will 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/egusphere-2023-1267-AC1
RC2:
'Comment on egusphere-2023-1267', Anonymous Referee #2, 28 Sep 2023

This paper by Mitsui and Boers looks at Dansgaard-Oeschger (DO) transitions, which are examples of abrupt transitions in the Earth's past. The authors identify statistical precursor signals (SPS) in the transition from the warm to the cold state, which is evidence of DO transitions being caused by a loss of stability rather than stochastic variability. The Authors propose some dynamical mechanisms to explain this. I thought this was a good paper: the authors have clearly taken time to carefully analyse their results, although I was sad to see the code used in this paper was not shared 'by default'.
The authors may want to consider the following comments.
Broad Comments:
There are lots of time series here: 2 proxy variables, 2 early warning signals, 3 cores, 12 interstadials, 5 window sizes and 6 smoothing spans leading to 3480 analysed time series (when accounting for the fact that not all cores have all interstadials in them), although relatively few give SPS (31%). If there is a common mechanism at work, why is this the case? Can the authors be sure the results are not down to chance? The authors argue that more SPS are observed than would be expected by chance, but none of the time series for each interstadial are truly independent, and there being a false positive in one time series would increase the chance of there being a false positive in another. Furthermore, looking at figure 4d, different cores give different results for the same interstadial, e.g. in GI-20 only 4 cores give any SPS and only one 'robustly'. Different interstadials give different amounts of SPS, for example GI-14 gives many robust SPS but GI-19.2 doesn't. How do the authors account for this?
When looking for SPS, the time series must be decomposed into an slowly changing equilibrium state and fluctuations about that state. As a lot of the signal in this case for SPS comes from 'rebound events' the authors are assuming that the rebound events represent fluctuations rather than changes in the equilibrium state. What is the justification for this?
The authors may want to discuss mechanisms that can lead to changes in variance and autocorrelation not due to changing stability but due other factors. For example, due to changes in the properties of the climate forcing. Furthermore, changes in the statistical properties in the measurement process may also affect the results. For example, measurements in the ice cores further in the past may be more uncertain and therefore noisier, but measurements closer to the present may be less noisy and therefore more correlated.
Specific Comments:
Line 11: Should be rebound events not rebound event
Line 15: This tipping definition excludes N-tipping, which has no thresholds. Different authors define tipping differently but as there is disagreement over whether DO events are N or B tipping I wonder if it is better to adopt a definition compatible with the Ashwin 2012 typology?
Line 91 "R^2 = 0.95", what fit is this measuring?
Line 114: The autocorrelation is different to that in Bury et al who have C(tau) = (cos (omega tau)) exp(mu |tau|)
Line 115: Should be "increase or decrease"
Line 117: How do the authors know tau is sufficiently small, especially as omega may also be changing?
Line 120: Is a linear fit suitable if half of the interstadial is used i.e. 500+ years? Could the stable state be changing nonlinearly in this period?
Line 187: makes reference to interstadials shorter than 1000 years but Line 106 implies the authors are excluding interstadials shorter than 1000 years. Have I misunderstood?
Line 295-298: "can be shown to be 0.05". I think it would be helpful to show this. When I run the authors code I do not get any output like 0.044 or 0.042, but I may be running the code incorrectly. Is this calculation included in the shared code?
Figure 4d: Could the colormap used in this figure be changed to a diverging colormap, with its centre at 15, so that it is easy to see if an SPS is robust. Currently it is difficult to know if the colours correspond to values larger than or smaller than 15.
Bibliography:

Ashwin 2012 https://doi.org/10.1098/rsta.2011.0306

Citation: https://doi.org/10.5194/egusphere-2023-1267-RC2
- AC2: 'Reply on RC2', Takahito Mitsui, 25 Oct 2023
  
  First of all, 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 changes to the manuscript in accordance. We think that these changes will 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/egusphere-2023-1267-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Reconsider after major revisions (06 Nov 2023) by Bjørg Risebrobakken

AR by Takahito Mitsui on behalf of the Authors (18 Dec 2023) Author's response

ED: Referee Nomination & Report Request started (19 Dec 2023) by Bjørg Risebrobakken

RR by Anonymous Referee #2 (03 Jan 2024)

RR by Anonymous Referee #3 (26 Jan 2024)

Suggestions for revision or reasons for rejection

General comments

This paper is analysing the so-called Doeschgaard-Oeschger (DO) events recorded in numerous proxies from Greenland ice core records. The authors use those reconstruction to test some statistical early warning indicators, to see if they are able to provide any alarm in advance of the occurrence of those events when they move to cold state. Results show that this is the case when the interstadial is long enough and show a slight rebound before the cooling events.

This is an interesting paper, well-written, and provided interesting insights on the question of early warning signal. The paper is not overstating the results and provide balanced discussion of the results. It is also providing a quite long discussion on potential mechanism, which remains quite theoretical but still of great interest.

Thus, I support the publication of this paper and I do not have any major comments against it. However, I do have a number of mandatory suggestions, which might help to further improve its clarity.

Specific comments

• Line 5: “co-dimension one bifurcation” is far too technical for an abstract, and is not well defined in the manuscript. Please provide more insights for non-experts.
• Line 5: “variance and the autocorrelation” of what? Of the time series of a variable representing the system analysed, I assume, but please clarify.
• Line 54: SPS is not defined here, and its definition only appears later on.
• Line 75: “with sufficient data length”. Indeed, and in this respect the work of Michel et al. (2022) certainly deserves to be cited on top of Boers (2021) paper…
• Line 84: “20-year resolution” is quite coarse. What might be the implication of this for the utility of those data for present-day? It might be worth to discuss this caveat later on
• Line 95: typo on “stadial”
• Line 119: “codimension-one”: please explain what it is.
• Line 121: “numerical studies” is a bit unclear. Do you mean “studies using numerical climate models”?

Reference:
Michel S., et al. Early warning signal for a tipping point suggested by a millennial Atlantic Multidecadal Variability reconstruction. Nature Communications 13, 5176 (2022).

Hide

EF by Svenja Lange (22 Dec 2023) Author's tracked changes

EF by Svenja Lange (22 Dec 2023) Manuscript

ED: Publish subject to minor revisions (review by editor) (26 Jan 2024) by Bjørg Risebrobakken

AR by Takahito Mitsui on behalf of the Authors (05 Feb 2024) Author's response Author's tracked changes Manuscript

ED: Publish as is (08 Feb 2024) by Bjørg Risebrobakken

AR by Takahito Mitsui on behalf of the Authors (09 Feb 2024) Author's response Manuscript

Journal article(s) based on this preprint

22 Mar 2024

Statistical precursor signals for Dansgaard–Oeschger cooling transitions

Takahito Mitsui and Niklas Boers

Clim. Past, 20, 683–699, https://doi.org/10.5194/cp-20-683-2024,https://doi.org/10.5194/cp-20-683-2024, 2024

Short summary

Takahito Mitsui and Niklas Boers

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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

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Short summary

In general, the variance and the autocorrelation with small lag increase in a system approaching a bifurcation point. Using these indicators, we identify statistical precursor signals for the Dansgaard-Oeschger cooling events recorded in two climatic proxies of three Greenland ice core records. We then provide a dynamical systems theory that bridges the gap between observing statistical precursor signals and the physical precursor signs empirically known in paleoclimate research.


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