| 21 Oct 2025
Tipping interactions and cascades on multimillennial time scales in a model of reduced complexity
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.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Earth System Dynamics.
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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 2oC and 6oC, but a best estimate at 3oC 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 2.7oC, though after 2100? Please also note the revised figure (according to Climate Action Tracker, 2025) is 2.6oC.
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: “0,5oC” -> “0.5oC”
L841: “13,3” -> “13.3”