A risk assessment framework for interacting tipping elements

Bara, Jacques; Wunderling, Nico; Barfuss, Wolfram

doi:10.5194/egusphere-2025-4077

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https://doi.org/10.5194/egusphere-2025-4077

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02 Sep 2025

| 02 Sep 2025

A risk assessment framework for interacting tipping elements

Jacques Bara, Nico Wunderling, and Wolfram Barfuss

Abstract. Tipping elements, such as the Greenland Ice Sheet, the Atlantic meridional ocean circulation (AMOC) or the Amazon rainforest, interact with one another and with other non-linear systems such as the El-Nino Southern Oscillation (ENSO). In doing so the risk of any one element collapsing into a degraded state can be drastically affected, typically increasing due to the interactions. In this work, therefore, we propose a fully probabilistic network model for risk assessment of interacting tipping elements that coherently incorporates literature-based belief assessments of intra-element interactions. We provide analytic results for the equilibrium risks of nine interacting tipping elements, the existence and stability of their stationary distributions and convergence times to the equilibrium solution. Moreover we simulate their tipping risks until 2350 using emission pathways from the shared socio-economic pathways (SSP 1-1.9, 1-2.6, 2-4.5, 3-7.0, and 5-8.5). Compared to the hypothetical no-interactions case, we find that interactions tend to destabilise the climate system, for instance the coral reefs are likely to have collapsed by 2100 even under the most optimistic scenario (SSP1-1.9). The effects of interactions, however, are most noticeable after 2100, especially for the highest shared socio-economic pathways (SSP3-7.0 and SSP5-8.5). In summary, our comprehensive risk assessment framework for tipping elements indicates that rapid mitigation is essential to keep temperatures as close as possible to 1.5 °C in the short term and below 1 °C in the longer run.

Received: 20 Aug 2025 – Discussion started: 02 Sep 2025

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Journal article(s) based on this preprint

15 Apr 2026

A risk assessment framework for interacting tipping elements

Jacques Bara, Nico Wunderling, and Wolfram Barfuss

Earth Syst. Dynam., 17, 333–352, https://doi.org/10.5194/esd-17-333-2026,https://doi.org/10.5194/esd-17-333-2026, 2026

Short summary

Jacques Bara, Nico Wunderling, and Wolfram Barfuss

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4077', Anonymous Referee #1, 10 Sep 2025

Please see attached PDF

Citation: https://doi.org/10.5194/egusphere-2025-4077-RC1
- AC1: 'Reply on RC1', Jacques Bara, 18 Nov 2025
  
  Thank you for all of your thorough feedback and comments, please find our full response attached as a pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4077-AC1
RC2:
'Comment on egusphere-2025-4077', Gideon Futerman, 04 Nov 2025
General Comments
I generally think this is an interesting paper. It is well within the scope of the journal. The approach seems novel, and to be build on appropriately cited literature. However, there should be better clarity in the conclusion as to exactly what is novel, and how substantial the contributions of this paper are - this is currently a little unclear. The assumptions informing the model are generally valid, although in a few places could be laid out better, the methods should be better justified, and the extent to which the conclusions are dependent on particular uncertain parameter values/ranges should be laid out in more depth. Similarly, the limitations of the model created could be better justified.
I have a number of key specific issues with the paper that I think should be addressed (Specific Comments), and less significant suggestions/concerns which I leave addressing up to the authors discretion (Minor Comments).
Major Comments
Abstract
The abstract suggests the paper presents a “comprehensive risk assessment framework”. The paper does not do this, and should be revised to suggest this.
Methods
These are my overall comments regarding the model itself.
In your methods section, you do not have the recovery probability as influenced by GMST. However, recovery clearly is influenced by GMST, and this is especially relevant if we are either dealing with overshoot scenarios (which are discussed later in the paper with SSP1-1.9) or scenarios where certain forms of Solar Radiation Modification are used. One justification is that timescales can be long enough that we can think of the tipping elements as irreversible over human relevant timescales, and this appears to be the justification in Appendix A and Table 1. However, this isn’t correct for all the tipping elements, as noted about REEF in the paper. For other tipping elements, it isn’t implausible that they have decadal recovery times, even if you have assumed they have longer recovery times in this paper. Not having any GMST dependence for recovery probability reduces the utility of your model if you use different parameters for recovery time such that it can’t be ignored. To me therefore, at the very least you need to justify why you don’t have the recovery probability influenced by the GMST in the main body of the text. Likely ideally, you would actually incorporate GMST dependence.
I also think it's important to discuss what role GMST is playing in this model more broadly. In general, in the tipping literature, anthropogenic drivers of tipping tends to be collapsed into a discussion of GMST and critical (temperature) thresholds. However, for a number of tipping points, especially Amazon Dieback and Coral Reefs, there are other anthropogenic drivers that are not correlated with GMST. Similarly, for most other tipping points, the drivers are caused by GMST rise, but aren’t necessarily entirely linked. If we could decouple GMST rise from the rest of the climate system, as an intervention like Solar radiation Modification could do, this would change a number of these factors. I think, therefore, noting the exact role that GMST is playing in the model would be helpful. There are a two clear ways you can do this. The first is that you can simply clarify this as a limitation of your model. The second is that you can argue that GMST is a useful proxy for all anthropogenic influence (since it is currently by a very long margin the most dominant - and likely would be even under SRM deployment), and include all the other complexity under your beta term. Since the uncertainty is so large, my guess is this is simply dwarfed by your already existent uncertainty, so would not change your results.
Results
The presentation of the results of the “short term” case is misleading by the choice of the two dates to discuss: 2100 and 2350. Looking at Figure 4, it is clear that much of the increase in the tipped probability across the tipping elements happens in the 2100s, which means the choice of these two dates might give the impression that the tipping will happen later than it in fact does. I know 2100 is a very common date used in the climate literature, and therefore I might use three dates in the discussion: 2100, 2150 and 2350 for example, to illustrate this massive increase in tipping probability soon after 2100.
You almost exclusively discuss the arguably two least likely projections, SSP 1-1.9 and SSP 5-8.5. At least a small amount of discussion of the more “middle of the road” scenarios would be helpful to give the readers a more complete picture.
It seems very strange to me that S3 is not in the main paper. This seems to be one of the key results for the paper. I also think this needs to be discussed in a fair amount of depth in the results or conclusions, as its a really important take away. This better comparison to the no-interactions case seems particularly important given your mentioning of a similar point in the abstract.
Conclusions
I think I would like considerably more discussion on the limitations of your approach, which seem only minorly discussed. This will be important to how people should interpret your results, since it is such a simplified model. Moreover, this will be helpful for people building on your results.
Like all models, your model is, in large part, a consequence of the assumptions going into it. I however, don’t know the degree to which your results are dependent on your parameters, which are highly uncertain, so some discussion of this would be very helpful. Moreover, I’d like to get a sense if any results were surprising given the inputs used, and whether such a simplified set up has the capacity to provide novel explanatory power. This is all unclear to me, and at least should be gestured towards in the conclusion.
Minor Comments
Introduction - please define tipping element
Methods/Discussion: I’d like a bit more explanation as to the role of timescales of tipping and how these play a role in tipping interactions. This seems to be a limitation of your model, albeit currently somewhat small given high uncertainty. As you model this as a 2-step Markov process, the timescale is just the timescale it takes to tip from one state to another. There is no intermediate state. However, intermediate states do exist (even if tipping processes are at this stage self-perpetuating), and its not clear at which stage in the process of tipping the interactions are most prominent. This may mean the timescale of tipping underestimates when interactions can occur. Of course, this is subsumed under the other uncertainties already present in your model, but is probably worth briefly discussing.
Lines 38-45: Whilst I agree with the positives of expert elicitation, I still think some discussion of the serious problems with it in this context would be informative to readers. Namely, very poor process understanding and a lack of useful historical observations, whilst weighing heavily against the use of GCMs, also suggest a lack of reliability for expert elicitation.
Line 286: I think it should be stressed here that “short term” risks are still, in this paper, seen as multi-centennial. This will be good to push back against some of the more catastrophist thinking about tipping elements.
Figure 4 should be edited for clarity. Namely:
You need to mention that not all the scales are the same for each of the graphs

The scales are not actually quite the same even for a to f, which all go from 0-100% on the y axis. Please edit them so they all go only from 0-100% (some go above 100%), and that they are all scaled the same

I should have the same scale as a to f. I don’t really think there is a good justification for why it stops at roughly 95% on the y axis.

Line 380-384: You discuss exogenous stabilisation of particular tipping elements. I think it is useful to not skirt around the subject, and explicitly state what you mean here. Whilst there are local geoengineering interventions, these are fairly nascent. I suspect this is mostly referring to either localised or global Solar Radiation Modification. If this is so, then I would make this explicit, and cite some of the emerging analysis of how SRM interacts with different tipping elements. One interesting point here, that is the flip side of the point you raise, is that it is feasible that global SRM reduces the risk of tipping for many tipping elements, whilst leaving a few without much risk reduction. AMOC looks amongst the most uncertain tipping elements as to whether SRM can reduce its risk of tipping or not, which is an interesting counterpoint to the discussion. It is not clear to me a more extensive discussion of such exogenous stabilisation is needed in the paper, but given the (useful) discussion, I think a few more lines to give the reader more context on the state of the literature on that would be helpful.
Line 385: Update citation to reflect the publication of the 2025 Global Tipping Point Report
Citation: https://doi.org/10.5194/egusphere-2025-4077-RC2
- AC1: 'Reply on RC1', Jacques Bara, 18 Nov 2025
  
  Thank you for all of your thorough feedback and comments, please find our full response attached as a pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4077-AC1

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-4077', Anonymous Referee #1, 10 Sep 2025

Please see attached PDF

Citation: https://doi.org/10.5194/egusphere-2025-4077-RC1
- AC1: 'Reply on RC1', Jacques Bara, 18 Nov 2025
  
  Thank you for all of your thorough feedback and comments, please find our full response attached as a pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4077-AC1
RC2:
'Comment on egusphere-2025-4077', Gideon Futerman, 04 Nov 2025
General Comments
I generally think this is an interesting paper. It is well within the scope of the journal. The approach seems novel, and to be build on appropriately cited literature. However, there should be better clarity in the conclusion as to exactly what is novel, and how substantial the contributions of this paper are - this is currently a little unclear. The assumptions informing the model are generally valid, although in a few places could be laid out better, the methods should be better justified, and the extent to which the conclusions are dependent on particular uncertain parameter values/ranges should be laid out in more depth. Similarly, the limitations of the model created could be better justified.
I have a number of key specific issues with the paper that I think should be addressed (Specific Comments), and less significant suggestions/concerns which I leave addressing up to the authors discretion (Minor Comments).
Major Comments
Abstract
The abstract suggests the paper presents a “comprehensive risk assessment framework”. The paper does not do this, and should be revised to suggest this.
Methods
These are my overall comments regarding the model itself.
In your methods section, you do not have the recovery probability as influenced by GMST. However, recovery clearly is influenced by GMST, and this is especially relevant if we are either dealing with overshoot scenarios (which are discussed later in the paper with SSP1-1.9) or scenarios where certain forms of Solar Radiation Modification are used. One justification is that timescales can be long enough that we can think of the tipping elements as irreversible over human relevant timescales, and this appears to be the justification in Appendix A and Table 1. However, this isn’t correct for all the tipping elements, as noted about REEF in the paper. For other tipping elements, it isn’t implausible that they have decadal recovery times, even if you have assumed they have longer recovery times in this paper. Not having any GMST dependence for recovery probability reduces the utility of your model if you use different parameters for recovery time such that it can’t be ignored. To me therefore, at the very least you need to justify why you don’t have the recovery probability influenced by the GMST in the main body of the text. Likely ideally, you would actually incorporate GMST dependence.
I also think it's important to discuss what role GMST is playing in this model more broadly. In general, in the tipping literature, anthropogenic drivers of tipping tends to be collapsed into a discussion of GMST and critical (temperature) thresholds. However, for a number of tipping points, especially Amazon Dieback and Coral Reefs, there are other anthropogenic drivers that are not correlated with GMST. Similarly, for most other tipping points, the drivers are caused by GMST rise, but aren’t necessarily entirely linked. If we could decouple GMST rise from the rest of the climate system, as an intervention like Solar radiation Modification could do, this would change a number of these factors. I think, therefore, noting the exact role that GMST is playing in the model would be helpful. There are a two clear ways you can do this. The first is that you can simply clarify this as a limitation of your model. The second is that you can argue that GMST is a useful proxy for all anthropogenic influence (since it is currently by a very long margin the most dominant - and likely would be even under SRM deployment), and include all the other complexity under your beta term. Since the uncertainty is so large, my guess is this is simply dwarfed by your already existent uncertainty, so would not change your results.
Results
The presentation of the results of the “short term” case is misleading by the choice of the two dates to discuss: 2100 and 2350. Looking at Figure 4, it is clear that much of the increase in the tipped probability across the tipping elements happens in the 2100s, which means the choice of these two dates might give the impression that the tipping will happen later than it in fact does. I know 2100 is a very common date used in the climate literature, and therefore I might use three dates in the discussion: 2100, 2150 and 2350 for example, to illustrate this massive increase in tipping probability soon after 2100.
You almost exclusively discuss the arguably two least likely projections, SSP 1-1.9 and SSP 5-8.5. At least a small amount of discussion of the more “middle of the road” scenarios would be helpful to give the readers a more complete picture.
It seems very strange to me that S3 is not in the main paper. This seems to be one of the key results for the paper. I also think this needs to be discussed in a fair amount of depth in the results or conclusions, as its a really important take away. This better comparison to the no-interactions case seems particularly important given your mentioning of a similar point in the abstract.
Conclusions
I think I would like considerably more discussion on the limitations of your approach, which seem only minorly discussed. This will be important to how people should interpret your results, since it is such a simplified model. Moreover, this will be helpful for people building on your results.
Like all models, your model is, in large part, a consequence of the assumptions going into it. I however, don’t know the degree to which your results are dependent on your parameters, which are highly uncertain, so some discussion of this would be very helpful. Moreover, I’d like to get a sense if any results were surprising given the inputs used, and whether such a simplified set up has the capacity to provide novel explanatory power. This is all unclear to me, and at least should be gestured towards in the conclusion.
Minor Comments
Introduction - please define tipping element
Methods/Discussion: I’d like a bit more explanation as to the role of timescales of tipping and how these play a role in tipping interactions. This seems to be a limitation of your model, albeit currently somewhat small given high uncertainty. As you model this as a 2-step Markov process, the timescale is just the timescale it takes to tip from one state to another. There is no intermediate state. However, intermediate states do exist (even if tipping processes are at this stage self-perpetuating), and its not clear at which stage in the process of tipping the interactions are most prominent. This may mean the timescale of tipping underestimates when interactions can occur. Of course, this is subsumed under the other uncertainties already present in your model, but is probably worth briefly discussing.
Lines 38-45: Whilst I agree with the positives of expert elicitation, I still think some discussion of the serious problems with it in this context would be informative to readers. Namely, very poor process understanding and a lack of useful historical observations, whilst weighing heavily against the use of GCMs, also suggest a lack of reliability for expert elicitation.
Line 286: I think it should be stressed here that “short term” risks are still, in this paper, seen as multi-centennial. This will be good to push back against some of the more catastrophist thinking about tipping elements.
Figure 4 should be edited for clarity. Namely:
You need to mention that not all the scales are the same for each of the graphs

The scales are not actually quite the same even for a to f, which all go from 0-100% on the y axis. Please edit them so they all go only from 0-100% (some go above 100%), and that they are all scaled the same

I should have the same scale as a to f. I don’t really think there is a good justification for why it stops at roughly 95% on the y axis.

Line 380-384: You discuss exogenous stabilisation of particular tipping elements. I think it is useful to not skirt around the subject, and explicitly state what you mean here. Whilst there are local geoengineering interventions, these are fairly nascent. I suspect this is mostly referring to either localised or global Solar Radiation Modification. If this is so, then I would make this explicit, and cite some of the emerging analysis of how SRM interacts with different tipping elements. One interesting point here, that is the flip side of the point you raise, is that it is feasible that global SRM reduces the risk of tipping for many tipping elements, whilst leaving a few without much risk reduction. AMOC looks amongst the most uncertain tipping elements as to whether SRM can reduce its risk of tipping or not, which is an interesting counterpoint to the discussion. It is not clear to me a more extensive discussion of such exogenous stabilisation is needed in the paper, but given the (useful) discussion, I think a few more lines to give the reader more context on the state of the literature on that would be helpful.
Line 385: Update citation to reflect the publication of the 2025 Global Tipping Point Report
Citation: https://doi.org/10.5194/egusphere-2025-4077-RC2
- AC1: 'Reply on RC1', Jacques Bara, 18 Nov 2025
  
  Thank you for all of your thorough feedback and comments, please find our full response attached as a pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2025-4077-AC1

Peer review completion

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

ED: Reconsider after major revisions (23 Jan 2026) by Luke Kemp

AR by Jacques Bara on behalf of the Authors (27 Jan 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (02 Feb 2026) by Luke Kemp

RR by Anonymous Referee #1 (09 Feb 2026)

Suggestions for revision or reasons for rejection

The authors have satisfactorily addressed most of my previous comments. However, I still find the Conclusion to be overly long and insufficiently focused. I recommend a clearer separation between core findings, limitations, and future research directions, which would help sharpen the main take-home messages and improve readability.

More generally, while I find the methodological framework interesting, the conclusion places disproportionate emphasis on advocating it, at times extending beyond what can be supported by a probabilistic risk-assessment approach. In particular, the use of language implying physical prediction (e.g. 439-442) or methodological superiority over process/physics-based model studies (see comment below) should be tempered, with clearer emphasis on the stylised nature of the results when it comes to future predictions.

Specific comments:
Line 30:
The statement “most interactions are destabilizing and may cause tipping cascades” is too strong. A formulation such as “most interactions are destabilizing, increasing the likelihood of tipping cascades” would be more accurate and better aligned with the probabilistic nature of the framework.

Line 33:
As these references are cited repeatedly, the most recent and relevant work would be Sinet et al. (2025), Science Advances.

Line 35:
Jackson et al. (2015) does not directly state this claim. Rather, it shows a cooling over Greenland associated with AMOC weakening. The wording should be adjusted accordingly to better reflect the original result.

Line 65:
While I understand the intended point, the sentence involving N-tipping remains awkward. In particular, N-tipping is not an "example" of stochastic noise.

Line 121:
"Below in Eq. (1)" here is redundant.

Line 301:
I still do not understand the role or meaning of the phrase “far from being a neat theoretical result/exercise”. This expression appears vague.

Line 422:
In relation to the general comment above, if “refute” is understood in the academic sense, it is essentially synonymous with disproving. While I see that the conclusions of the cited studies and those of the present work are not compatible, I do not see how a probabilistic risk assessment can disprove results from a process-based model study, or vice versa.

450: remove "Particularly"

Hide

ED: Reconsider after major revisions (02 Mar 2026) by Luke Kemp

AR by Jacques Bara on behalf of the Authors (10 Mar 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (19 Mar 2026) by Luke Kemp

ED: Publish as is (24 Mar 2026) by Ira Didenkulova (Chief editor)

AR by Jacques Bara on behalf of the Authors (01 Apr 2026) Manuscript

Journal article(s) based on this preprint

15 Apr 2026

A risk assessment framework for interacting tipping elements

Jacques Bara, Nico Wunderling, and Wolfram Barfuss

Earth Syst. Dynam., 17, 333–352, https://doi.org/10.5194/esd-17-333-2026,https://doi.org/10.5194/esd-17-333-2026, 2026

Short summary

Jacques Bara, Nico Wunderling, and Wolfram Barfuss

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https://doi.org/10.5194/egusphere-2025-4077-supplement

Jacques Bara, Nico Wunderling, and Wolfram Barfuss

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When one tipping element collapses the likelihood of another collapsing may be significantly affected. Using our simplified network model, we find that on the whole these interactions destabilise the Earth system, both in the short term and at equilibrium, though the effects are most noticeable after the year 2100. We find that to minimise tipping risks, it is essential to keep temperatures as close as possible to 1.5 °C in the short term and below 1 °C in the longer run.


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