the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
25 Feb 2021
25 Feb 2021
Abrupt climate change as rate-dependent cascading tipping point
- 1Physics of Ice, Climate and Earth, Niels Bohr Institute, University of Copenhagen, Denmark
- 2Institute for Marine and Atmospheric Research, Utrecht University, The Netherlands
- 1Physics of Ice, Climate and Earth, Niels Bohr Institute, University of Copenhagen, Denmark
- 2Institute for Marine and Atmospheric Research, Utrecht University, The Netherlands
Abstract. We propose a conceptual model comprising a cascade of tipping points as a mechanism for past abrupt climate changes. In the model, changes in a control parameter, which could for instance be related to changes in the atmospheric circulation, induce sequential tipping of sea-ice cover and the ocean's meridional overturning circulation. The ocean component, represented by the well-known Stommel box model, is shown to display so-called rate-induced tipping. Here, an abrupt resurgence of the overturning circulation is induced before a bifurcation point is reached due to the fast rate of change of the sea-ice. During the rate-induced transition, the system is attracted by the stable manifold of a saddle. This results in a significant delay of the tipping if the system spends longer periods of time in the vicinity of the saddle before escaping towards the alternative state of a vigorous overturning circulation. The delay opens up the possibility for an early warning of the impending abrupt transition by detecting the change in linear stability. We propose early warning by estimating properties of the Jacobian from the noisy time series, which are shown to be useful as a generic precursor to detect rate-induced tipping.
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Johannes Lohmann et al.
Status: final response (author comments only)
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RC1: 'Comment on esd-2021-7', Anonymous Referee #1, 09 Mar 2021
This well written work proposes a conceptual model coupling ocean dynamics with sea-ice cover dynamics. Their model exhibits rate-induced bifurcations in the ocean dynamics and their results suggest that cascading bifurcations may be a general mechanism in inducing abrupt transitions in climate systems. The authors nicely illustrate the influence of noise on the bifurcation behaviour with convincing numerical simulations. The authors further show that the critical slowing down experienced during rate-induced bifurcations may be difficult to detect using the standard variance indicator (but is readily detected in the sea-ice dynamics which experiences a “classical” bifurcation) and propose a simple indicator based on estimating the elements of the associated Jacobian.
I enjoyed reading the paper and believe that its results — both on the particular role of rate-induced bifurcations on cascading transitions and on warning indicators — are valuable for the community, and I recommend publication subject to some comments the authors may want to take on board.
The authors identify the importance of sea-ice for the occurrence of abrupt climate changes and couple its dynamics into a Stommel box model. The authors may want to put their model with its inherent dynamic mechanisms in context to other similar attempts highlighting the different implied dynamical mechanisms; for example the conceptual models considered by Boers et al, Proc Natl Acad Sci 115(47):E11005–E11014 and by Gottwald, Clim Dyn (2021) 56:227-243.
The authors tune the parameter h in (5) to allow for what they coin smooth bifurcations. Are there observations suggesting that transitions are smooth or non-smooth? Also, it might be helpful to show the two cases of non-smooth and smooth in Figure 3 (and also for the Stommel model). This would clarify what the authors mean by smooth and non-smooth bifurcations; depending on the background of the reader these terms may invoke different associations. Might also be worthwhile defining this in the manuscript.
It was not clear to me how their model allows for the succession of abrupt climate changes such as the DO events mentioned in the introduction. The model seems to capture only single transitions. Can the authors comment on this?Regarding the new proposed warning indicator J. Am I correct in thinking that the reason why looking at the individual elements of the Jacobian rather than at the eigenvalues of the Jacobian is that the estimation of each element is done via finite-differencing (which is a bad estimator for noisy data) and calculating the eigenvalues exacerbates this via multiplication?
Typos and minor comments:Figure 1. What are the values of \eta_3 in (b) and of \eta_1 in (c)Line 266: andBoers —> and Boers-
AC1: 'Reply on RC1', Johannes Lohmann, 03 May 2021
The comment was uploaded in the form of a supplement: https://esd.copernicus.org/preprints/esd-2021-7/esd-2021-7-AC1-supplement.pdf
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AC1: 'Reply on RC1', Johannes Lohmann, 03 May 2021
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RC2: 'Comment on esd-2021-7', Anonymous Referee #2, 05 Apr 2021
This paper presents and analyzes a dynamical system where the Stommel model is coupled to a zero-dimensional sea-ice model. The sea-ice model exhibits a fold bifurcation. Since there is a separation of time scales between the ice dynamics and the ocean dynamics, as the ice model's tipping point is crossed, there is an almost instantaneous "parameter change" in the Stommel model. The change in ocean dynamics may hence be described as a rate-induced tipping point.
The paper is well written, but I still find it difficult to read. I encourage the authors to present a clearer "take-home-message."
I have a few suggestions and questions that the authors may use in their revision:
- Why not present and analyze the coupled model (Eq. 6) before discussing rate-induced tipping in the Stommel model? I feel that a "standard analysis" of the model in Eq. 6 is missing? You have a relatively simple dynamical system and one control parameter (R). Don't you have a simple saddle-node bifurcation in the three-dimensional system?
- As you go into more detail, is it possible to be more precise? I feel that it becomes very descriptive.
- How important is it that the Stommel model has a bistable regime? What would happen if you just coupled the sea-ice model to a simpler model with a smooth transition between "modes".
- I would like to see a discussion of how your proposed EW indicator would work in a "real-data setting".
There are a few typos in the manuscript. You'll find them when you read through it carefully. I am looking forward to reading a revised version.
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AC2: 'Reply on RC2', Johannes Lohmann, 03 May 2021
The comment was uploaded in the form of a supplement: https://esd.copernicus.org/preprints/esd-2021-7/esd-2021-7-AC2-supplement.pdf
Johannes Lohmann et al.
Johannes Lohmann et al.
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