Tipping interactions and cascades on multimillennial time scales in a model of reduced complexity

Couplet, Victor; Crucifix, Michel

doi:10.5194/egusphere-2025-4959

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https://doi.org/10.5194/egusphere-2025-4959

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21 Oct 2025

| 21 Oct 2025

Tipping interactions and cascades on multimillennial time scales in a model of reduced complexity

Victor Couplet and Michel Crucifix

Abstract. A tipping cascade refers to a sequence of tipping events in the Earth system, where transitions in one subsystem can trigger subsequent transitions in other subsystems. These cascades represent a significant concern for the future, as the tipping of a single element could induce the tipping of interconnected elements that would not have otherwise crossed their thresholds. This chain reaction could lead to substantial and potentially irreversible changes in the Earth's system, even under low-emission scenarios. However, tipping cascades, particularly those involving ice sheets, may unfold over millennial timescales and are therefore rarely captured in state-of-the-art Earth system models, which typically run only until the end of the 21st century. In this study, we extend the simple climate model SURFER v3.0 to incorporate a network of interacting tipping elements and other nonlinear components. Using this extended model, we systematically investigate the occurrence of tipping events and cascades over multi-millennial timescales and under a range of realistic emission scenarios. We show that interactions among tipping elements generally increase their tipping risks, consistent with findings from previous studies. Furthermore, our results suggest that meeting the Paris Agreement target of limiting warming below 2 °C could lower the risk of observing tipping events and cascades by roughly an order of magnitude compared to current-policy pathways, underscoring the urgency of stronger climate action.

Received: 07 Oct 2025 – Discussion started: 21 Oct 2025

Competing interests: At least one of the (co-)authors is a member of the editorial board of Earth System Dynamics.

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Victor Couplet and Michel Crucifix

Status: final response (author comments only)

RC1: 'Comment on egusphere-2025-4959', Anonymous Referee #1, 08 Dec 2025

The manuscript ‘Tipping interactions and cascades on multimillennial time scales in a model of reduced complexity’ evaluates the tipping risk for six interconnected tipping elements of the climate system for different for a range of emission scenarios. Specifically, the authors consider how the tipping risk changes for including coupling between elements and feedbacks to the climate. The authors show that interactions between tipping elements generally increase the risk of tipping via cascades that can unfold over multi-millennial timescales. This result is consistent with previous studies; however, the authors also find the AMOC to be the main initiator of tipping cascades as opposed to the Greenland ice sheet. The authors attribute this to assuming a flux (derivative) coupling between the Greenland ice sheet and the AMOC instead of a coupling that is proportional to the remaining ice sheet. The manuscript is generally well written and easy to follow, but I have some general and specific comments that I would like to see the authors address before supporting publication.

General comments:
Further clarification on the classification of cascades is required. For instance, in Figure 9 there appears to be more than 1,000 cumulative counts (the number of different parameter setups) of destabilising GRIS events. Presumably this is because of stabilisation cascades and so the same parameter setup can be counted multiple times. For example, for a single parameter setup that must be scenarios, where GRIS tips for the first time at scenario j, then stabilises at scenario k (i.e. due to AMOC tipping) and then tips again in scenario l for j < k < l. Is this indeed the case? Similarly, for the same parameter set up if only GRIS changed tipping status at scenario j and only WAIS changed tipping status at scenario k for j \neq k then these would be represented by a single red dot for GRIS (first bar) and a single red dot for WAIS (third bar)? It appears counter-intuitive that not every (in particular) stabilising cascade has an initiator (Figure 11). As suggested by L530-531 for there to be no initiator in a stabilising cascade, there must be a change in the permafrost or sea ice that causes an element such as the AMOC to tip that then stabilises GRIS. If correct, this needs to be highlighted more clearly.

For the Latin Hypercube Sampling the authors employ a uniform distribution for all parameters, but with little apparent justification. For the critical temperature thresholds and transition timescales not only are the minimum and maximum estimates provided, but also a best estimate, which appears to get overlooked. For example, the EASB has an estimated temperature threshold between 2^oC and 6^oC, but a best estimate at 3^oC so arguably more weight should be applied to lower threshold values. By using a uniform distribution would therefore underestimate the tipping risk. Further, it is not a linear transform between the transition timescale and \tau_{-}, which has greater sensitivity for low values so further justification needs to be given for choosing a uniform distribution over \tau_{-} as opposed to the transition timescale.

Specific comments:
L87: “… neither exhibits signs of bistability,…” do not show signs of bistability in an ESM or the conceptual model? Also, explicity state again here that this is for Arctic sea ice and boreal permafrost.
L95-100: Is the sea level rise just an output of the model or does S_{gl} explicitly feed into the tipping dynamics somewhere that I’ve missed? i.e. what is the motivation for including it here? Maybe nearer the end of the section a small comment stating that sea level rise can be determined with a reference to the model paper would be sufficient. Additionally, why is there no contribution from ice sheets and only the mountain glaciers (also noted on L75)? If ice sheets are included in mountain glaciers, then this is confusing with mountain glaciers typically being treated as their own tipping element.
L180: The parameter x_{+} is also fixed…?
L186-187: Presumably SSP1-2.6 does not go until year 100000 CE so what happens to methane emissions at the end of SSP1-2.6, are they assumed to be zero?
L210-211: The authors claim that the choice of T_{-} does not affect the results of the “forward tipping points”. However, as the authors previously state specifying T_{-} determines x_{-}, which determines all the coefficients (Egns 5-8) in Eqn 3. Therefore, does this not affect characteristics such as the curvature of the fold at T_{+} and thus the overshoot behaviour?
L222 & L227: Where do the values for \tau_{+} come from and what transition timescales do these correspond to? Arguably these are less important than T_{-} and x_{-}, i.e. the results seem less dependent on the choice of \tau_{+}?
L397 & L399: “below” and “above” appear to be the wrong way round?
L404-405: Many readers will associate the “tipping threshold” with the critical global warming threshold, rather than the threshold that separates tipping from not. So, a comment to emphasise this is important.
L407-408: Specifically, what assumptions?
L504-505: However, the peak temperature can still be above 2.7^oC, though after 2100? Please also note the revised figure (according to Climate Action Tracker, 2025) is 2.6^oC.
L509: Maybe use “probability” instead of “risk” when referring to a stabilizing cascade.
L600: As previously mentioned, arguably the choice of T_{-} and the corresponding value for x_{-} already matters for “forward tipping points” and not just “back tipping” points.
L650: Presumably, the first term in the denominator should be F(2024) to give E(t) = E(2024) when t=2024 in Equation (A1)?

Technical comments:
L40: “several thousand of years” -> “several thousands of years”
L51: “from Amazon” -> “from the Amazon”
L92: “greenhouse gas.” -> “greenhouse gas emissions.”
L216: Add space between “\tau_{+}” and “in”
Figs 5 & G2 legends: “Rictchie” -> “Ritchie”
L566: “(Deutloff et al., 2025)” -> “Deutloff et al. (2025)”
L575: “imitator” -> “initiator”
L593: “he” -> “the”
L797: please correct “increase of increase”
L812: “0,5^oC” -> “0.5^oC”
L841: “13,3” -> “13.3”

Citation: https://doi.org/10.5194/egusphere-2025-4959-RC1
RC2:
'Comment on egusphere-2025-4959', Anonymous Referee #2, 15 Dec 2025
This study uses SURFER, a low-complexity ESM with six tipping elements and two nonlinear elements as well as important climate feedbacks, to assess the risk of tipping cascades. It is well structured and largely well-written. Within the limits of this framework, the analysis is carefully executed and has clear didactic value, particularly in demonstrating transient tipping behaviour under overshoot scenarios. Overall, this publication is a next logical step within a series of simple network models of tipping elements by adding transient feedbacks to the climate system, such that I generally support its publication.

However, a major concern is that the simplified risk metric based on Monte Carlo occurrence counts, combined with large uncertainties in tipping thresholds and highly idealised interactions, makes it difficult to draw conclusions about real-world risk and may lead to over- or understatement when taken out of context. This is a common limitation of these simple models (beyond this study) but should be addressed more transparently by elaborating more on how to interpret the results, and which conclusions about the real world can not be done, or only in limited fashion. In particular when stating that risk may be overestimated, it is on the authors to provide more reflections on how the limitations of this approach also limits the extent to which such statements can be done. Especially the limitations of the expert-based parametrisation of the interactions should be expanded on. Apart from this, there is a range of minor and major specific comments below.

Specific comments
Overall
Highlight novelty of the study more clearly, and its limitations

Provide summary figure(s) and table(s) that help the reader dissect the different parts of the paper better (see comments below)

Revise section 2 to make sure all expressions and terms are introduced in the right order (in the current version the reader needs to scroll back and forth to make sense of this).

Make sure that the figure and table captions contain all necessary information to read them. If there are too many acronyms or terms that don’t fit the caption, refer to one of the glossary tables requested above

Adapt figure sizes, especially font size, to make them more readable.

Abstract
Introduce with a sentence explaining what tipping is. Also, “chain reaction could lead to substantial and possibly irreversible changes in the Earth’s system” → this is already true for a single tipping element.

From the abstract, the novelty of the study is not clear. It is certainly building confidence that it is consistent with previous studies, but it is not clear how this study differs from previous ones in its approach.

Introduction
Please overall check that tipping-related terms are carefully defined. E.g. distinguish climate tipping points (Lenton et al 2008; Armstrong McKay et al 2022) from Earth system tipping points (Lenton et al, 2023); also tipping elements and tipping systems. Cite IPCC where appropriate (e.g. at “may be abrupt and/or irreversible”)

On critical slowing down / early warning signals: Please group the references by system, and also include recent literature. For the different systems, criticism of the (in parts very simplified) EWS analyses has been published in the last years – to my understanding not fully refuting EWS, but justifying that statements on critical slowing down should be done in a weaker way (e.g. “...exhibit signals that are consistent with critical slowing down, which is however debated…”)

I stumbled over interactions and feedbacks, and had to go back to recent reviews (e.g. Wunderling et al 2024) to confirm that “interactions between tipping elements” indeed does only include direct influences (e.g. via precip pattern changes, FW release, regional circulation changes etc.). A reader (myself included) might think that the Amazon “interacts” with the ice sheets too via release of carbon (and subsequent global warming) when it tips. It gets clearer when reading on, that the latter kind of “interaction” is labelled climate feedback here, and is not included in “interactions between tipping elements”. Maybe it would help to make this more clear in the beginning, by explicitly stating that tipping elements can interact directly (e.g. freshwater discharge from GRIS destabilises the AMOC) and can impact each other indirectly, via modification of the global climate, also providing examples for each.

The summary of recent work using simple climate models in this context was well done. I believe the paper could greatly benefit from a conceptual overview figure here, including

A map of all considered tipping elements, sketching their interactions and feedback to the global climate

A global temperature curve as in figure 4a, conceptually sketching a “prescribed” overshoot (as in Wunderling et al 2023, Möller et al 2024) vs one that includes the temperature feedbacks on the global climate, e.g. an overshoot curve that includes the warming induced by an AMAZ collapse

Methods
SURFER model
Although brevity is appreciated, some more background on SURFER would be good in the beginning; at least statements on how it performs against observations and CMIP (i.e. some more context for “reliably estimates …. in response to anthropogenic GHG emissions”)

Representation of tipping elements
There are many symbols defined somewhere in the text (sometimes not directly around the corresponding equation). Readers would greatly benefit from a table in the appendix with all introduced symbols. Please revise section 2.2, making sure that all the terms are introduced in a logical order and explained (e.g. T_U in eq 1, which is only later introduced in line 152). Same with equation 16, where a sum over j and \delta L_j are introduced but only explained quite a bit later.

Not critical, but \delta q usually suggests a small deviation from a state (perturbation), but in this context it is meant to be the anomaly wrt to a preindustrial state, which is “large” in the sense that it is not a perturbation to a system but fundamentally changes the stability landscape. So \Delta q would be more appropriate, reserving \delta q for small variations e.g. for EWS / resilience studies. Also, there is some inconsistency, as most expressions involve \delta q, but e.g in line 118 and in equation 3, there is also q (without \delta). And then q_max in eq 35 should also be a \Delta q_max.

It is not clear to me if the inclusion of tipping elements into SURFER is an addition or a modification. E.g. a “non-tipping” SURFER version includes land (Fig 1) – is that the total global carbon X stored in non-marine vegetation and soil? If yes, how is the AMAZ represented in the modified model? Is then X = X_linear + X_AMAZ ? I.e. it would be enlightening to see what the state variables in the different SURFER versions are, and if the inclusion of tipping elements modifies the differential equations and/or adds additional state variables.

When discussing the stability structure, readers might benefit from additional links to literature such as textbooks by Dijkstra, Strogatz etc.

Eq 4: How does H_i change..?

On the comment in line 155ff: The critical temperature thresholds for tipping elements are (or intend to be) already accounting for “all” climate-related effects that might lead to tipping. Shouldn’t the global warming level already be a good proxy for all other climate-related forcings, especially different ocean temperatures? If you want to make the case that there are other forcing influences, then wouldn’t it be appropriate to also list other systems such as land use for AMAZ?

Related small caveat: If intermediate and deep ocean temperatures are not used in this work, please refrain from introducing more terms (bracket in line 157), especially since the I subscript is already used above for the inflexion point

Eq 16: Why is it needed to separate \epsilon_ij from \delta L_j rather than just having one \delta L_ij matrix?

Eq 17: why is q included in the forcing? I mean, why is the second term in the forcing not just a function of \delta L_ij ?

Table 1: In the caption, please add explainers for T_i etc

Overall, it would make more sense to me to have the calibration part directly after section 2.2, and have the experimental setup last in section 2 (i.e. switch the order of sections 2.3 and 2.4)

Up for the authors to decide (might be a matter of taste): To me, equations 3,4,16,17 are the important ones in section 2.2, and this section might be easier to read if it focussed on these (and expanded the explanation according to the other comments made here). Eqs 5-15 “only” describe how the parameters are inferred from data/literature, and could be deferred to the calibration section.

Experimental Setup
What is the reason for 100,000 years of simulation?

The CO2 and CH4 scenarios don’t seem too compatible, what is the reason to consider e.g. 5000PgC together with a SSP1-2.6 CH4 scenario?

Latin hypercube sampling appears to be the standard for these kind of studies. One could argue that with the amount of information that is available on critical thresholds, any sampling is as wrong as another. However, Armstrong McKay et al. provide expert-based best estimates for the critical threshold, which could be a good starting point for a sensitivity analysis that draws the MC samples not evenly from the full range but rather, say, from a normal distribution centered on that best estimate. Another option would be to do a conservative approach and only draw samples from the minimum to the central estimate, i.e. the lower range of the Armstrong McKay et al’s uncertainty ranges. It would be of great added value to see if an alternative sampling would lead to a qualitatively different result.

Calibration
Table 2: What is the justification for deviating from Armstrong McKay et al. (2022) for the EAIS timescales. A reference or more elaborated reason than “This provides a better estimation of committed sea level rise” is needed here.

Line 209 and 222: If the focus is primarily on “forward tipping points”, why are different “backwards-tipping” timescales included? This is a bit contradictory. I understand that estimations of backwards-tipping points are basically non-existent in the literature but the position of the backwards-tipping point does affect the unstable equilibrium and is therefore important as soon as overshoots are considered. This is also the reason why the different backwards-tipping timescales are included as I understand it. Please provide a consistent argumentation for the taken approach.

Equation 19 and 20: The numbers below the fractional line clearly indicate a unit conversion. However these should be included in the units of the quantities used. This would also make the formulae easier to understand.

Results
Next to the definition of “risks” please add a disclaimer of how to read “likelihoods” in the remainder of the paper

Individual tipping elements
Is there some intuition behind 4a_0^2\kappa? It seems to link somewhat to the slope of the stability landscape close to the critical point, but it would be nice to have some explanation

Similarly, is there an explanation why \tau_- plays a role in eq 38, but not \tau_+ ?

Figure 4: include T_max. t_over … in the figure

Confusing language: In the context of tipping points, transgression of a threshold == tipping. In lines 392ff “threshold” is used in the context of eq38, and suddenly being above the threshold == no tipping. Since that threads through the results chapter, I strongly suggest to find an alternative terminology. Actually Ritchie et al 2019 refer to this as the “boundary curve separating safe and unsafe overshoot”, which seems way more appropriate.

Figures 4 and 5 are very nice illustrations of the “Ritchie theory” and the consequences of coupling on safe overshoots. Since (to me) they are good takeaways of the paper, I suggest revising them to make sure they can serve as standalone explainers. E.g. rather than labelling 2000PgC, Tmax=4.2°C in 5b, explicitly label the boundary curve as “theoretical boundary for [overshoot scenario]” and hash out one side of the boundary with the label “unsafe overshoot”, the other one with “safe overshoot”. For the [overshoot scenario] either use the 2000PgC overshoot trajectory reaching Tmax=4.2°C, or put that info in the caption and in the (shareable) figure rather put the peak temperature, landing temperature and overshoot duration.

Line 400 → refer to Figure 5 (otherwise one might try and find this somewhere in Fig 4..)

Line 411 → Please add what landing climate reaching 2.9°C with 1000PgC correspond to and which overshoot duration, to make clear that 2.9°C and higher are only “safe” when the overshoot is short and has a low landing climate

Line 426 → simplify sentence; “...inevitable without AMOC influence, which can reduce the aggregated tipping risk when it has a stabilising effect.”

Line 441 → baseline should be called “decoupled”

Tipping cascades
I think it would greatly improve the understanding of the results if the definition of a tipping cascade was explained more thoroughly early on. The brief “technical” definition in line 456ff only somewhat starts making sense with the thoughts introduced only later in the discussion in lines 581ff.

Figure 9: Interesting representation of the results. Some comments on readability:

Write somewhere what the horizontal axis is supposed to be (the different combinations of tipping events)

Maybe visually rework the inset table to make more clear how to read it. E.g. “Single tipping events” is formatted exactly like “tipping events” and “percentage of…” and could be mistaken for a heading.

Figure 10: Add “from 2024” to the caption

Lines 526ff: I don’t quite understand “This can be verified by rerunning the model …”. Does that mean that if you want to know if AMOC is a potential initiator of a cascade occurring in run j, you compare run j to run j-1 in the uncoupled case? Or how should I understand “This can be verified by rerunning the model …” ? What does “with all other elements … held at their values from scenario j-1..” mean?

Discussion + Conclusion
I’d wish for a more critical assessment on the limitations of this study, and overall these kinds of studies (including Wunderling et al. etc). The (valid) points brought up mostly address the limitations from a technical side – calibration, bifurcation- vs. other types of tipping etc. But more fundamentally,
What are the epistemological limitations?

The claim tipping risk might be overestimated when just considering critical thresholds makes sense within the limitations of this study. However, what are potential downsides of these simplified risk assessments?

What is the merit of having 800000 model runs, if they’re based on uniform sampling of very broad uncertainty ranges for parameters?

Overall, more reflection here (and acknowledgement of the limitations) would provide the reader more confidence that the results should not be taken at face value in a risk assessment kind of way. Additionally, the limitation of the study with regards to the expert based calibration of most of the interactions should be highlighted.
Citation: https://doi.org/10.5194/egusphere-2025-4959-RC2

Victor Couplet and Michel Crucifix

Data sets

SURFER v3.0 + TEs output dataset for reproducing results in papers "Tipping interactions and cascades on multimillennial time scales in a model of reduced complexity" and "Tipping cascades may lock the Earth system on a pathway towards a melthouse" Victor Couplet and Michel Crucifix https://doi.org/10.5281/zenodo.17276820

Interactive computing environment

SURFER v3.0 + Tipping Elements: Model code for "Tipping interactions and cascades on multimillennial time scales in a model of reduced complexity" Victor Couplet and Michel Crucifix https://doi.org/10.5281/zenodo.17279674

Victor Couplet and Michel Crucifix

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Short summary

Some parts of the Earth system, like ice sheets or the Amazon rainforest, may start changing on their own once pushed past a limit, even if the original pressure stops. A major concern is whether these “tipping elements” can trigger one another, setting off domino-like cascades. Here we use a simple climate model to investigate this possibility. We show that strong emission cuts are needed to lower the risk of triggering such cascades.


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