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https://doi.org/10.5194/egusphere-2025-14
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/egusphere-2025-14
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
21 Jan 2025
| 21 Jan 2025
A Saddle-Node Bifurcation is Causing the AMOC Collapse in the Community Earth System Model
Abstract. Recently, a collapse of the Atlantic Meridional Overturning Circulation (AMOC) was found in the Community Earth System Model (CESM) under constant pre-industrial greenhouse gas forcing conditions. To determine the stability changes of the AMOC with changing (freshwater) parameters in models, it is important to determine the origin of the collapse behavior. In this paper, we argue that the classical picture of a saddle-node bifurcation holds for the AMOC collapse in the CESM. We provide specific supporting arguments by showing results of additional pre-industrial CESM simulations and by comparison with a conceptual model. Theoretical arguments are also provided showing that the essential dynamics of the CESM can be reduced to a low-dimensional model in which a saddle-node bifurcation causes the AMOC collapse. The underlying physical reason is that the AMOC behaviour in CESM is controlled by a small set of dominant feedback processes. This has important consequences for the value of conceptual AMOC models, for assessing the effect of model biases on the AMOC stability, and for the interpretation of the AMOC behaviour under climate change scenario's.
How to cite. van Westen, R. M., Vanderborght, E., and Dijkstra, H. A.: A Saddle-Node Bifurcation is Causing the AMOC Collapse in the Community Earth System Model, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2025-14, 2025.
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Journal article(s) based on this preprint
20 Nov 2025
A saddle-node bifurcation may be causing the AMOC collapse in the Community Earth System Model
René M. van Westen, Elian Vanderborght, and Henk A. Dijkstra
Earth Syst. Dynam., 16, 2063–2085, https://doi.org/10.5194/esd-16-2063-2025, https://doi.org/10.5194/esd-16-2063-2025, 2025
Short summary
Short summary
The Atlantic Meridional Overturning Circulation (AMOC) is a tipping element in the fully-coupled Community Earth System Model (CESM). Under varying freshwater flux forcing parameters or climate change, the AMOC may collapse from a relatively strong state to a substantially weaker state. It is important to understand the dynamics of the AMOC collapse in the CESM. We show that the stability of the AMOC in the CESM is controlled by only a few feedback processes.
Interactive discussion
Status: closed
Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor
| : Report abuse
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RC1: 'Comment on egusphere-2025-14', Anonymous Referee #1, 22 Jun 2025
-
AC1: 'Reply on RC1', René van Westen, 31 Aug 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-14/egusphere-2025-14-AC1-supplement.pdf
-
AC1: 'Reply on RC1', René van Westen, 31 Aug 2025
-
RC2: 'Comment on egusphere-2025-14', Anonymous Referee #2, 06 Aug 2025
Summary:
This manuscript puts forward a number of arguments supporting AMOC collapse in the CESM model following the saddle-node bifurcation behaviour. The key arguments are that: there is a strict boundary of stability, a slower rate of quasi-equilibrium will lead to a faster tipping in forcing space, and that a simplified model shows the saddle-node bifurcation behaviour. The paper also demonstrates that warming under climate change can lead to tipping or lower levels of freshwater forcing for tipping. Finally, the paper demonstrates the sensitivity of the E-CCM model to locations of freshwater forcing.
The results are used to justify the continued importance of simplified and analytical model of the AMOC and provide guidance for the importance of model biases and the use of freshwater and climate forcing for AMOC tipping. I believe the paper may be suitable for publication in Earth System Dynamics providing the following comments are addressed.
Major Comments:
- The square root dependence needs more exploration. In the manuscript it is listed as the most important determinant of the saddle-node bifurcation but is then never discussed or justified to be ignored, and in Section 4 it is stated that Section 3.1 has shown it can’t be demonstrated with these models, but Section 3 doesn’t discuss the square root dependence at all. The manuscript needs to discuss the square root dependence, how it would be analysed using these models, whether any information can be gained (i.e. are the current runs at least consistent with the square root behaviour within error, or are there reasons why the equilibrium runs wouldn’t be expected to follow this behaviour?). How many runs would be required? Presumably 5 or 6 equilibrium runs near the threshold would be sufficient to analyse the shape?
- 127-160: The overshoot under half-rate forcing seems statistically indistinguishable to that in the full-rate, so discussing the larger rate seems unrelated. The discussion of the feedbacks also seems unrelated as the comparison of feedbacks is not made between the rates. Finally, the key result drawn out in this section is that the collapse takes approximately 100 years each time, which is unrelated to the feedbacks. I think the relationship of the times and the forcing should be explored further while the feedbacks either need more explanation of their relevance or should be removed. Should the feedback analysis simply all be moved to section 4, where the importance of the feedbacks and their links to the simplified models is discussed in more detail.
- Greater discussion of the theory behind the analysis is needed. While other papers can be cited to justify arguments, more explanation is needed on why the saddle-node should follow a square-root behaviour, why the rates should lead to different rates of transition.
- Section 3.2 seems unrelated to the rest of the manuscript. The saddle-node behaviour in E-CCM has already been shown in a previous paper and can be referenced here. The response of the E-CCM model to the position of the freshwater forcing is interesting, but not discussed in the abstract, introduction, or summary of this paper and could be removed without impacting the rest of the paper. I suggest removing this section, potentially combining it with additional runs of the CESM model to compare the freshwater sensitivity and producing a separate manuscript discussing the sensitivity to location of freshwater forcing. Alternatively, the relevance of this section to the rest of the manuscript should be justified.
- Why was the region 20 and 50N chosen for the freshwater forcing when presumably the freshwater should be coming from further North? Is this a particularly sensitive area for freshwater forcing? This should be explained and justified as opposed to other regions. ? I believe this goes back to Stefan Rahmstorf’s 1995 paper where the 20-50N region gives a clearer bifurcation than the Greenland forcing, but it would be helpful to clarify this here. (e.g. lines 57-59)
Minor Comments:
- Title: I am not entirely convinced the strength of the title is justified and so could alter this to something weaker “A Saddle-Node Bifurcation may be causing the AMOC Collapse in the Community Earth System Model”?
- 10: no apostrophe needed in “scenario’s”?
- 13: Citation for the CMIP6 project/ models?
- 19-20: Rephrase this sentence “The existence of the salt advection feedback is why the AMOC is labelled as a tipping point in the climate system”
- 37: “Whether this behaviour is also caused”
- 77: Why the “E-CCM”? Could you explain this to the reader otherwise it seems to appear out of nowhere, is it the extended-Cimatoribus climate model?
- Figure 2: The text and the Figures are very small, if they could be combined with shared axes or split perhaps with panels a and b at the top and the other 9 figures below them to allow more space.
- I am confused by the relation between the steady states in panels a and b of Figure 2 and the right hand panels. Why is there no steady state behaviour for the 0.51 Sv case? Was this not left to equilibriate or were there other issues? Could you run a few steady state runs around 0.50 and 0.505 to specify the range of the bifurcation in more detail? Would this provide useful additional information
- 112: Given this range of 0.495-0.510 does this significantly change later results, some of the changes are quite close to this? (see Major comment 2)
- 119: Could you give more detail here about how the “tipping” is determined as the exact position seems very important and worth including in this manuscript even if discussed in more detail in another paper. (See Major comment 3)
- Line 125: Uncertainty ranges on these numbers would be very helpful, there is clearly a lot of uncertainty in the reference value and probably also a large amount of uncertainty in where the AMOC collapses and so these values seem likely to be statistically indistinguishable. (See Major comment 2)
- Figure 4: If the comparison is trying to understand why the slower rate overshoots more than the faster overshoot, the faster overshoot should be included in this figure. This would allow clearer comparison
- Lines 145-147: Does this suggest that 0.465 is a potential point at which the tipping might be initiated and that the other values are simply overshoots and the runs were not conducted enough times/ for long enough to find this tipping at the lower levels? Maybe the basic levels and overshoots discussed earlier in the manuscript should be adjusted to account for this.
- Lines 150-153: If all transitions take the same amount of time and the overshoot is just related to the rate of forcing vs the duration, surely this might be a general feature of other transitions? What transitions are we ruling out through this analysis? This is only helpful to determine a saddle-node bifurcation if it does not characterise other transitions
- 158-159: For the FovS, the variance increases up to the tipping but continues increasing after this, presumably if it actually tips in the saddle-node behaviour, the variance should decrease after the tipping and after settling in to the new behaviour? Is this true and should we expect this?
- Line 249-251: Why is it reasonable to ignore the sea-ice melt term when it is clearly one of the dominant terms in the model? Surely we want this reduced model to represent CESM not a box model and leaving out key terms such as this mean it is a poor representation when we know they are important.
- Equation 7: Could some of the freshwater not be stored in the Atlantic freshwater content rather than the variation terms? This assumes the Atlantic freshwater content must immediately return to equilibrium.
- Figure 8: Referring to the results as “Observations” seems unclear, the analysis is based on observed values but is not actual observations, the label in the legend could be changed for clarity.
- 316-326: This paragraph justifies multiple times that making these estimates is not useful or unrealistic. This paragraph should be removed or rephrased to emphasise that in the real world there are key differences which would lead to lower freshwater fluxes (e.g. the value of the FovS) but that there are other factors such as climate change and the location of forcing that make this unreliable.
- 386-388: You did not really show that this is not feasible for the CESM and need to justify this. (See Major comment 1)
- 391: “parameters somehow tuned”, probably just drop the word “somehow” here
- 414-417: there is no section 4b, change this reference
Citation: https://doi.org/10.5194/egusphere-2025-14-RC2 -
AC2: 'Reply on RC2', René van Westen, 31 Aug 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-14/egusphere-2025-14-AC2-supplement.pdf
Interactive discussion
Status: closed
Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor
| : Report abuse
-
RC1: 'Comment on egusphere-2025-14', Anonymous Referee #1, 22 Jun 2025
General Comments: This paper investigates the mechanisms behind Atlantic Meridional Overturning Circulation (AMOC) collapse in the Community Earth System Model (CESM). The paper aims to demonstrate that the classical picture of a saddle-node bifurcation, as exhibited by box models, also holds for the AMOC collapse in the CESM. This is done by analyzing pre-industrial CESM simulations and comparing them with a conceptual model (E-CCM). The authors use physical arguments to demonstrate that the complex behavior of AMOC in the CESM can be approximated by a reduced-order model, in which a saddle-node bifurcation drives the AMOC collapse.
These results underscore the utility of idealized AMOC models and may help evaluate the effect of model biases on the AMOC stability landscape and for understanding AMOC responses under various climate change projections. The careful experimental design and related analyses, for simulations in CESM and E-CCM, are commendable. I think the paper may be suitable for publication after the following issues are satisfactorily addressed.
Specific Comments
- The paper needs a discussion of the normal form of a saddle-node bifurcation and its properties (this could be in the appendix), given that the central aim of the work is to establish that the AMOC, as represented in CESM, has a saddle-node bifurcation. The strongest evidence for this is the square root dependence of the AMOC strength on the freshwater hosing in the reduced-order model developed from physical arguments. However, the paper does not explain why one should expect to see this square-root dependence.
- Lines 391-394: Is the second argument in support of the existence of a saddle-node bifurcation in CESM qualitative? Does the `two-times' faster transition in the `half-rate' hosing experiment have any quantitative significance? Isn't this related to the inertia associated with the system? Lines 150-151 claim that this is a typical characteristic of transitions near saddle-node bifurcations. Could you explain this in more detail? I was unable to verify this claim by going through Kuehn 2011. In summary, I think the authors need to precisely clarify how this observation constitutes evidence for the existence of a saddle-node bifurcation.
- The addition of tables would be helpful for readers to keep track of the many simulations (CESM, E-CCM, and reduced-order model) used in this work. Please include details such as type (QE, branched from QE, steady state), duration, forcing characteristics, etc.
- For completeness, I would suggest including a brief discussion of the 5-box model (Section 2.2), such as a short description of the different boxes.
- Line 125: In theory, would it have been better to run the half-rate forcing experiment, branching off from a much lower value of freshwater forcing? Is a shorter overshoot (in $F_H$) the only difference you would expect to see, compared to existing results?
Technical Comments
- Figures 2 and 5: The font size of the text in the subfigures is too small.
- Figure 5 (a,b): What causes the large overshoot in the backward quasi-equilibrium simulations after tipping back to the AMOC-on state?
- Line 10: Typo: Should it be `scenarios' (without the apostrophe)?
- Line 37: `whether also this behavior' reads a bit awkward.
- Lines 166-167: Missing a `to' in 'lower compared the'
- Line 387: Should it be `built'?
- Line 391: What do you mean by 'with parameters somehow tuned'?
Citation: https://doi.org/10.5194/egusphere-2025-14-RC1 -
AC1: 'Reply on RC1', René van Westen, 31 Aug 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-14/egusphere-2025-14-AC1-supplement.pdf
-
RC2: 'Comment on egusphere-2025-14', Anonymous Referee #2, 06 Aug 2025
Summary:
This manuscript puts forward a number of arguments supporting AMOC collapse in the CESM model following the saddle-node bifurcation behaviour. The key arguments are that: there is a strict boundary of stability, a slower rate of quasi-equilibrium will lead to a faster tipping in forcing space, and that a simplified model shows the saddle-node bifurcation behaviour. The paper also demonstrates that warming under climate change can lead to tipping or lower levels of freshwater forcing for tipping. Finally, the paper demonstrates the sensitivity of the E-CCM model to locations of freshwater forcing.
The results are used to justify the continued importance of simplified and analytical model of the AMOC and provide guidance for the importance of model biases and the use of freshwater and climate forcing for AMOC tipping. I believe the paper may be suitable for publication in Earth System Dynamics providing the following comments are addressed.
Major Comments:
- The square root dependence needs more exploration. In the manuscript it is listed as the most important determinant of the saddle-node bifurcation but is then never discussed or justified to be ignored, and in Section 4 it is stated that Section 3.1 has shown it can’t be demonstrated with these models, but Section 3 doesn’t discuss the square root dependence at all. The manuscript needs to discuss the square root dependence, how it would be analysed using these models, whether any information can be gained (i.e. are the current runs at least consistent with the square root behaviour within error, or are there reasons why the equilibrium runs wouldn’t be expected to follow this behaviour?). How many runs would be required? Presumably 5 or 6 equilibrium runs near the threshold would be sufficient to analyse the shape?
- 127-160: The overshoot under half-rate forcing seems statistically indistinguishable to that in the full-rate, so discussing the larger rate seems unrelated. The discussion of the feedbacks also seems unrelated as the comparison of feedbacks is not made between the rates. Finally, the key result drawn out in this section is that the collapse takes approximately 100 years each time, which is unrelated to the feedbacks. I think the relationship of the times and the forcing should be explored further while the feedbacks either need more explanation of their relevance or should be removed. Should the feedback analysis simply all be moved to section 4, where the importance of the feedbacks and their links to the simplified models is discussed in more detail.
- Greater discussion of the theory behind the analysis is needed. While other papers can be cited to justify arguments, more explanation is needed on why the saddle-node should follow a square-root behaviour, why the rates should lead to different rates of transition.
- Section 3.2 seems unrelated to the rest of the manuscript. The saddle-node behaviour in E-CCM has already been shown in a previous paper and can be referenced here. The response of the E-CCM model to the position of the freshwater forcing is interesting, but not discussed in the abstract, introduction, or summary of this paper and could be removed without impacting the rest of the paper. I suggest removing this section, potentially combining it with additional runs of the CESM model to compare the freshwater sensitivity and producing a separate manuscript discussing the sensitivity to location of freshwater forcing. Alternatively, the relevance of this section to the rest of the manuscript should be justified.
- Why was the region 20 and 50N chosen for the freshwater forcing when presumably the freshwater should be coming from further North? Is this a particularly sensitive area for freshwater forcing? This should be explained and justified as opposed to other regions. ? I believe this goes back to Stefan Rahmstorf’s 1995 paper where the 20-50N region gives a clearer bifurcation than the Greenland forcing, but it would be helpful to clarify this here. (e.g. lines 57-59)
Minor Comments:
- Title: I am not entirely convinced the strength of the title is justified and so could alter this to something weaker “A Saddle-Node Bifurcation may be causing the AMOC Collapse in the Community Earth System Model”?
- 10: no apostrophe needed in “scenario’s”?
- 13: Citation for the CMIP6 project/ models?
- 19-20: Rephrase this sentence “The existence of the salt advection feedback is why the AMOC is labelled as a tipping point in the climate system”
- 37: “Whether this behaviour is also caused”
- 77: Why the “E-CCM”? Could you explain this to the reader otherwise it seems to appear out of nowhere, is it the extended-Cimatoribus climate model?
- Figure 2: The text and the Figures are very small, if they could be combined with shared axes or split perhaps with panels a and b at the top and the other 9 figures below them to allow more space.
- I am confused by the relation between the steady states in panels a and b of Figure 2 and the right hand panels. Why is there no steady state behaviour for the 0.51 Sv case? Was this not left to equilibriate or were there other issues? Could you run a few steady state runs around 0.50 and 0.505 to specify the range of the bifurcation in more detail? Would this provide useful additional information
- 112: Given this range of 0.495-0.510 does this significantly change later results, some of the changes are quite close to this? (see Major comment 2)
- 119: Could you give more detail here about how the “tipping” is determined as the exact position seems very important and worth including in this manuscript even if discussed in more detail in another paper. (See Major comment 3)
- Line 125: Uncertainty ranges on these numbers would be very helpful, there is clearly a lot of uncertainty in the reference value and probably also a large amount of uncertainty in where the AMOC collapses and so these values seem likely to be statistically indistinguishable. (See Major comment 2)
- Figure 4: If the comparison is trying to understand why the slower rate overshoots more than the faster overshoot, the faster overshoot should be included in this figure. This would allow clearer comparison
- Lines 145-147: Does this suggest that 0.465 is a potential point at which the tipping might be initiated and that the other values are simply overshoots and the runs were not conducted enough times/ for long enough to find this tipping at the lower levels? Maybe the basic levels and overshoots discussed earlier in the manuscript should be adjusted to account for this.
- Lines 150-153: If all transitions take the same amount of time and the overshoot is just related to the rate of forcing vs the duration, surely this might be a general feature of other transitions? What transitions are we ruling out through this analysis? This is only helpful to determine a saddle-node bifurcation if it does not characterise other transitions
- 158-159: For the FovS, the variance increases up to the tipping but continues increasing after this, presumably if it actually tips in the saddle-node behaviour, the variance should decrease after the tipping and after settling in to the new behaviour? Is this true and should we expect this?
- Line 249-251: Why is it reasonable to ignore the sea-ice melt term when it is clearly one of the dominant terms in the model? Surely we want this reduced model to represent CESM not a box model and leaving out key terms such as this mean it is a poor representation when we know they are important.
- Equation 7: Could some of the freshwater not be stored in the Atlantic freshwater content rather than the variation terms? This assumes the Atlantic freshwater content must immediately return to equilibrium.
- Figure 8: Referring to the results as “Observations” seems unclear, the analysis is based on observed values but is not actual observations, the label in the legend could be changed for clarity.
- 316-326: This paragraph justifies multiple times that making these estimates is not useful or unrealistic. This paragraph should be removed or rephrased to emphasise that in the real world there are key differences which would lead to lower freshwater fluxes (e.g. the value of the FovS) but that there are other factors such as climate change and the location of forcing that make this unreliable.
- 386-388: You did not really show that this is not feasible for the CESM and need to justify this. (See Major comment 1)
- 391: “parameters somehow tuned”, probably just drop the word “somehow” here
- 414-417: there is no section 4b, change this reference
Citation: https://doi.org/10.5194/egusphere-2025-14-RC2 -
AC2: 'Reply on RC2', René van Westen, 31 Aug 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-14/egusphere-2025-14-AC2-supplement.pdf
Peer review completion
AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload
ED: Reconsider after major revisions (31 Aug 2025) by Gabriele Messori
AR by René van Westen on behalf of the Authors (15 Sep 2025)
Author's response
Author's tracked changes
Manuscript
ED: Referee Nomination & Report Request started (17 Sep 2025) by Gabriele Messori
RR by Jonathan Rosser (28 Sep 2025)
RR by Anonymous Referee #1 (03 Oct 2025)
ED: Publish subject to minor revisions (review by editor) (04 Oct 2025) by Gabriele Messori
AR by René van Westen on behalf of the Authors (08 Oct 2025)
Author's response
Author's tracked changes
Manuscript
ED: Publish as is (23 Oct 2025) by Gabriele Messori
AR by René van Westen on behalf of the Authors (23 Oct 2025)
Journal article(s) based on this preprint
20 Nov 2025
A saddle-node bifurcation may be causing the AMOC collapse in the Community Earth System Model
René M. van Westen, Elian Vanderborght, and Henk A. Dijkstra
Earth Syst. Dynam., 16, 2063–2085, https://doi.org/10.5194/esd-16-2063-2025, https://doi.org/10.5194/esd-16-2063-2025, 2025
Short summary
Short summary
The Atlantic Meridional Overturning Circulation (AMOC) is a tipping element in the fully-coupled Community Earth System Model (CESM). Under varying freshwater flux forcing parameters or climate change, the AMOC may collapse from a relatively strong state to a substantially weaker state. It is important to understand the dynamics of the AMOC collapse in the CESM. We show that the stability of the AMOC in the CESM is controlled by only a few feedback processes.
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Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, the Netherlands
Elian Vanderborght
Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, the Netherlands
Henk A. Dijkstra
Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, the Netherlands
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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
The Atlantic Meridional Overturning Circulation (AMOC) is a tipping element in the fully-coupled Community Earth System Model (CESM). Under varying freshwater flux forcing parameters or climate change, the AMOC may collapse from a relatively strong state to a substantially weaker state. It is important to understand the dynamics of the AMOC collapse in the CESM. We show that the stability of the AMOC in the CESM is controlled by only a few feedback processes.
The Atlantic Meridional Overturning Circulation (AMOC) is a tipping element in the fully-coupled...
General Comments: This paper investigates the mechanisms behind Atlantic Meridional Overturning Circulation (AMOC) collapse in the Community Earth System Model (CESM). The paper aims to demonstrate that the classical picture of a saddle-node bifurcation, as exhibited by box models, also holds for the AMOC collapse in the CESM. This is done by analyzing pre-industrial CESM simulations and comparing them with a conceptual model (E-CCM). The authors use physical arguments to demonstrate that the complex behavior of AMOC in the CESM can be approximated by a reduced-order model, in which a saddle-node bifurcation drives the AMOC collapse.
These results underscore the utility of idealized AMOC models and may help evaluate the effect of model biases on the AMOC stability landscape and for understanding AMOC responses under various climate change projections. The careful experimental design and related analyses, for simulations in CESM and E-CCM, are commendable. I think the paper may be suitable for publication after the following issues are satisfactorily addressed.
Specific Comments
Technical Comments