Ritchie et al. use a conceptual/mathematical framework to quantify which tipping elements would tip when overshooting 1.5°C global warming on different timescales. The article is concise and well-written, and the methods are clear and well-established. The topic of climate overshoots is obviously very relevant and well-suited for ESD. However, I have some concerns regarding the framing of the results, especially given the expected broad readership, and the lack of an assessment of uncertainties, which should however be straightforward to implement.

General/major comments

1. Novelty: This may of course be due to the length constraints, but the idea does not strike me as particularly “innovative” per the description of the “ESD Ideas” format. For example, overshoots of the Paris Agreement have previously been explored in a more comprehensive setup (including idealized interactions between different tipping elements) by Wunderling et al. (2023), which is not cited. In my view, this does not preclude publication of the present manuscript, but the authors should motivate the need for this piece more explicitly and position it better within the existing literature. One option would be to target a broader/policy-oriented audience. In this case, the following point would be especially relevant.

2. Policy message: Since this is a short article which I expect to be accessible to a rather wide audience, it would be important to both consider and explicitly acknowledge its policy implications and applicability.

Most importantly, the article should be very clear upfront that some (many?) of the underlying overshoot trajectories are neither physically nor socio-economically plausible. For example, a 4–5°C overshoot before a 1.5°C global warming stabilization within 100 years seems clearly unfeasible, but the avoidance of tipping under such unrealistic scenarios could a give a false sense of security that strong warming in the medium term would not be as dangerous. The recent paper by Schleussner et al. (2024) is worth a read (and maybe a cite) in this regard. They conclude: “[T]echnical, economic and sustainability considerations may limit the realization of carbon dioxide removal deployment at such scales [of several hundred gigatonnes]. Therefore, we cannot be confident that temperature decline after overshoot is achievable within the timescales expected today.”

To prevent any misinterpretation by readers or decision-makers, I think it is essential that this article cautions which of the results might be applicable to current global warming and which are not.

3. Minimal assessment of uncertainties: Overshoot timescales of the order of a human lifespan (Fig. 1b) are probably most interesting and relevant for a broad readership. However, assessing overshoots on these timescales in a non-probabilistic way could give a distorted view of the associated risks. In addition, the article is currently not clear about this omission: for example, “three are likely to tip” in L41-42 suggests that some probabilistic assessment might have taken place.

Since Armstrong McKay et al. (2022) provide confidence intervals for all GW level estimates and for most timescale estimates, it should be straightforward to turn the deterministic Fig. 1b into a probabilistic one, which could show a probability distribution (e.g., as a violin plot) of the number of tipped elements for each global warming level when taking into account parameter uncertainty. This would mean that it could not be shown which elements would tip in each case, but I would deem that an acceptable trade-off since the current Fig. 1b is already a part of Fig. 1c. I think it is ok to keep Fig. 1c as it is, but to remind the reader in the text that uncertainties are neglected here.

Specific and minor comments:

L2–3: “as is often assumed”: please provide one or two references that this is indeed the case – maybe from the scientific literature, or from media or the policy sphere. This is an important point because the entire article addresses an alleged common misconception that tipping would be instantaneous, but it is not shown that this misconception actually exists.

L16: The number calculated by the Climate Action Tracker refers to 2100 and the websites explicitly states “Temperatures continue to rise after 2100” (https://climateactiontracker.org/publications/the-climate-crisis-worsens-the-warming-outlook-stagnates/). Since you are discussing stabilization values in this paragraph, could you contextualize this?

Fig. 1: Some tipping elements are hard to distinguish just by color, maybe use colors in combination with different hatching patterns?

Fig. 1c: I am unsure if the current choice of the logarithmic axis is ideal. An overshoot of 10^5 years may at most be relevant for paleoclimate if we frame interglacials as “overshoots” to a glacial background climate, but probably not for the current anthropogenic global warming. This does not mean that the figure needs to be extensively modified, but the large range of overshoot durations should be pointed out (and put in context) explicitly in the text and/or caption. And maybe consider cutting off the axis at (some) 1000 years?

L26 and following: Are the values in Armstrong McKay et al. really derived from an equilibrated climate (as suggested by Fig. 1a) or from transient simulations? If they are derived from transient runs, wouldn’t this lead to a systematic bias when they are used in an equilibrium view?

L29: It would be more reader-friendly to include the Supplement directly within the article (e.g., as an Appendix), if this is allowed by the Editors.

L30 and Suppl. L38: It is not entirely clear how the choice \alpha=1 for all TEs is motivated. Could you check the validity of this assumption, for example, in one or two commonly used conceptual models of some tipping elements (e.g., Stommel model for the AMOC)?

Recently, some overshoot studies have been performed with state-of-the-art numerical models, notably Bochow et al. (2023) for the Greenland ice sheet (see their Fig. 3 for different overshoot durations). It would be very valuable to benchmark (e.g., in the Supplement) your estimates from Fig. 1c against their results to see if the results hold when compared to a comprehensive model.

”Climate Action Tracker” reference should be updated to the most recent version (and equipped with a URL).

Suppl. L23: “as expecting” -> “as expected”

Bochow, N., Poltronieri, A., Robinson, A., Montoya, M., Rypdal, M., & Boers, N. (2023). Overshooting the critical threshold for the Greenland ice sheet. Nature, 622, 528–536. https://doi.org/10.1038/s41586-023-06503-9

Schleussner, C.-F., Ganti, G., Lejeune, Q., Zhu, B., Pfleiderer, P., Prütz, R., et al. (2024). Overconfidence in climate overshoot. Nature, 634, 366–373. https://doi.org/10.1038/s41586-024-08020-9

Wunderling, N., Winkelmann, R., Rockström, J., Loriani, S., Armstrong McKay, D. I., Ritchie, P. D. L., et al. (2023). Global warming overshoots increase risks of climate tipping cascades in a network model. Nature Climate Change, 13, 75–82. https://doi.org/10.1038/s41558-022-01545-9

This Idea makes the relevant point that climate tipping elements do not tip instantly upon crossing a critical threshold in global mean temperature – the tipping risk depends on the duration of the overshoot as well as the peak exceedance value. The authors illustrate this statement by calculating whether various proposed tipping elements tip for different combinations of exceedance duration and peak warming, based on a simplified formula (Ritchie et al. 2019) and threshold/timescale estimates of Armstrong McKay et al. (2022).

The text is clearly written, and the results coherently support the main argument. I agree with the authors that it is crucial to consider the timescales of the forcing relative to the internal timescales of the tipping element for assessing tipping risk, an aspect sometimes ignored in the broader debate. However, I am concerned that the article oversimplifies the problem of climate tipping under overshoots and is therefore misleading particularly for a non-specialist audience. Without additional contextualization, there is a risk that the article perpetuates misunderstandings about tipping points rather than correcting them. I believe this can be solved by replacing some of the descriptive text with a brief, yet critical discussion of the assumptions, uncertainties and real-world complexities involved.

Major comment

My main critique is that the results described in this work convey a deceptive sense of certainty. The presentation suggests that whether a tipping element will tip can be determined with certainty from knowledge of the peak warming level and duration above 1.5 degrees C, independently of the other tipping elements. This depiction neglects that

• The warming threshold and timescale estimates in Armstrong McKay et al. (2022) have considerable uncertainty ranges.
• A sharp critical threshold may not exist for all tipping elements.
• Besides peak and duration, the shape of the forcing protocol may matter.
• For a given forcing protocol, tipping may be sensitive to the initial condition (see e.g. Romanou et al. 2023, Mehling et al. 2024).
• The climate tipping elements interact (Wunderling et al. 2024). The fact that interactions are neglected here is only mentioned in the Supplementary Material.
• Global warming levels are a climate response to forcing themselves and may not be an appropriate control parameter for all tipping elements considered.

This implies that the results in Fig. 1 have a significant uncertainty themselves and should be viewed probabilistically. While I think the results are still interesting in their current form, I ask the authors to better clarify in the main text that the results are simply the outcome of combining the best estimates of Armstrong McKay et al. (2022) with the adapted inverse-square law under multiple simplifying assumptions, and to highlight the inherent uncertainties.

Specific comments

• L. 53: The authors frame their Idea as a challenge of the “conventional wisdom” that tipping occurs instantaneously. However, the authors’ previous work (Ritchie et al. 2019, 2021) and related studies (Bochow et al. 2023, Wunderling et al. 2023) have already debunked this “wisdom” and established the idea in the field over the past years. This questions how innovative the idea is in this work. If the authors’ aim is thus to establish the concept among a wider audience, clarifying the underlying assumptions for obtaining Fig. 1 is especially important.
• Could the authors comment on how their results might depend on the specific shape of the forcing protocol, i.e. steepness, asymmetry, etc.?
• L. 17-19: In my opinion, counting the number of Earth system elements tipping is not very informative, as the tipping elements have highly heterogeneous impacts. Perhaps the cumulative impact of multiple elements tipping could be viewed in a different way?
• The reference list seems rather selective, perhaps owing to the short format of the Idea. I note that all scientific articles cited in the main text are led by the same institution. Additional references underlying the authors’ approach (e.g., Wunderling et al. 2021) are only cited in the Supplementary Material. If allowed by the format, adding further references to the main text would help putting this article into context.

Technical comments

• L. 16: Ref. Climate Action Tracker (2021) – is this a reference from the peer-reviewed literature and, if not, could the specific study be cited here?
• L. 1: The figure labels are almost too small to read.
• L. 25: …without tipping (Ritchie et al. 2021).
• L. 28: …of 1.5C. Our…
• L. 31-32: The relevance of the curvature of the equilibrium branch for tipping risk is not explained. Only in the Supplementary Material it is stated that a fold bifurcation is assumed for all tipping elements. This assumption may not hold for all tipping elements catalogued in Armstrong McKay et al. (2022).
• L. 39: No comma after Barents sea ice
• L. 44: Period missing after supplement)
• L. 46-47: The sentence “These fast tipping elements would…” seems redundant, especially given the final sentence (L. 55-56), and the space could be used to comment on limitations/uncertainties instead.

Supplementary Material

• L. 3: “…elements of the Earth system, and based…” – should the “and” be there?
• L. 23: change “expecting” to “expected”

Ritchie et al. describe the concept of overshooting tipping points in their ESD ideas. They state that crossing a tipping point is not an instantaneous event but rather emerges over a finite time. This allows, in theory, for the prevention of a tipping point by reversing the forcing, i.e., global warming, to previous levels. They demonstrate that restricting the time above 1.5°C above pre-industrial levels would reduce risks associated with tipping points. For this, they combine results from a recent review paper about tipping elements (McKay et al., 2022) and from an earlier conceptual study about the overshooting concept by Ritchie et al. (2021).

The manuscript is clearly written and understandable for a broader audience. I fully agree that the topic of overshooting tipping points and considering their timescales is generally important. I also agree with the authors that the notion of the instantaneousness of tipping points is no longer appropriate. At the same time, I struggle to see the novelty of the presented concepts/results, at least for the scientific community. While I see that this misconception of the instantaneousness of tipping points is very prevalent in the public media/opinion, I am not sure if this is also the case in recent scientific publications; at least some references would be needed to back up this claim. Alternatively, a reframing of the presented work in relation to the misconception in the public rather than the scientific community might need to be considered.

Additionally, I think the manuscript partly oversimplifies the tipping point/overshoot concept in a manner that could convey overconfidence in the results, especially for non-experts. This can be easily avoided by stating the limitations of the results and discussing uncertainties.

General comments:

• I struggle to see the novelty of the presented concept, as I do not agree with the authors that this is very new information. As I understand it, the ESD Ideas format is intended for novel ideas or concepts. However, the idea that tipping is not instantaneous is not new (e.g., their own paper Ritchie et al., 2021), and it is not surprising to me that tipping can be avoided in conceptual models when the overshoot temperature and time are limited. I could imagine this manuscript, including the supplement, being included as a section in a more detailed manuscript.
• It seems like uncertainties related to the threshold levels are not mentioned anywhere in the main text. I think it should at least be stated that there is considerable uncertainty related to tipping point thresholds, even in McKay et al. (2022). Generally, I feel that the manuscript is written in a way that takes the concept of tipping elements/points for granted without considering the uncertainties. This gives the impression that the results shown are considered to be absolute truth. I wonder if it is possible to repeat the analysis with upper and lower limits for the individual tipping point thresholds and show them in the supplementary information or in an extended figure.
• I do not see any mention in the main text that the results are based on a, arguably, very simple conceptual model.
• Generally, I think some more references are needed for some statements (see also specific comments).
• I don't think the supplementary information is easy enough to access/find. Additionally, the supplement is almost as long as the ESD Ideas itself. I wonder why this is not expanded upon and submitted as a regular research article.
• Coupling between the elements is ignored, but it is only stated in the supplement. It should at least be stated in the main text. Although, I wonder how much value the results have if coupling between the tipping elements is completely ignored, given that we know there is interaction between the individual elements (e.g. Wunderling et al., 2024).
• Given the broad target audience and policy relevance of the manuscript, I think it would be a good idea to comment on the feasibility of the presented overshoot scenarios. A recent study showed that there likely is an overconfidence in overshoot scenarios and temperature decline after an overshoot might not even be possible (Schleussner et al. 2024).

Specific comments

• L.1: "as is often assumed" — I would expect some references for that claim. In fact, there have been recent studies showing that tipping is generally not instantaneous (e.g., Bochow et al. (2023) or Höning et al. (2024)). I would almost claim that within the broad scientific community, it is known that tipping is not instantaneous.
• L.8: There is no reference for the Barents Sea ice threshold. Is this also taken from McKay et al. (2022)?
• L.47: I am not sure if defining "extremely short" as several decades is appropriate.
• L.53: Here again, I would expect references for the statement: "conventional wisdom that the commitment to tip occurs as soon as a critical threshold is crossed." I don't agree that this is "conventional wisdom" anymore.
• L.38 (supplement): How realistic is this choice of α, and what influence does it have on the results? I would guess that for some tipping elements, e.g., Antarctica (Garbe et al. (2020)) or Greenland (Bochow et al. (2023), Höning et al. (2023 and 2024)), the curvature parameter could be roughly estimated.
• The colors in the plot are a little bit hard to distinguish. I wonder if a different color palette would make the plot more accessible.

References

Garbe, J., Albrecht, T., Levermann, A. et al. The hysteresis of the Antarctic Ice Sheet. Nature 585, 538–544 (2020). https://doi.org/10.1038/s41586-020-2727-5

Dennis Höning et al 2024 Environ. Res. Lett. 19 024038, 10.1088/1748-9326/ad2129

Höning, D., Willeit, M., Calov, R., Klemann, V., Bagge, M., & Ganopolski, A. (2023). Multistability and transient response of the Greenland ice sheet to anthropogenic CO2 emissions. Geophysical Research Letters, 50, e2022GL101827. https://doi.org/10.1029/2022GL101827

Bochow, N., Poltronieri, A., Robinson, A. et al. Overshooting the critical threshold for the Greenland ice sheet. Nature 622, 528–536 (2023). https://doi.org/10.1038/s41586-023-06503-9

Ritchie, P.D.L., Clarke, J.J., Cox, P.M. et al. Overshooting tipping point thresholds in a changing climate. Nature 592, 517–523 (2021). https://doi.org/10.1038/s41586-021-03263-2

David I. Armstrong McKay et al., Exceeding 1.5°C global warming could trigger multiple climate tipping points.Science377, eabn7950(2022).DOI:10.1126/science.abn7950

Schleussner, CF., Ganti, G., Lejeune, Q. et al. Overconfidence in climate overshoot. Nature 634, 366–373 (2024). https://doi.org/10.1038/s41586-024-08020-9

Wunderling, N., von der Heydt, A. S., Aksenov, Y., Barker, S., Bastiaansen, R., Brovkin, V., Brunetti, M., Couplet, V., Kleinen, T., Lear, C. H., Lohmann, J., Roman-Cuesta, R. M., Sinet, S., Swingedouw, D., Winkelmann, R., Anand, P., Barichivich, J., Bathiany, S., Baudena, M., … Willeit, M. (2024). Climate tipping point interactions and cascades: A review. Earth System Dynamics, 15(1), 41–74. https://doi.org/10.5194/esd-15-41-2024