Snowball Earth transitions from Last Glacial Maximum conditions provide an independent upper limit on Earth&rsquo;s climate sensitivity

Renoult, Martin; Sagoo, Navjit; Hörner, Johannes; Mauritsen, Thorsten

doi:10.5194/egusphere-2024-2981

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https://doi.org/10.5194/egusphere-2024-2981

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02 Oct 2024

| 02 Oct 2024

Snowball Earth transitions from Last Glacial Maximum conditions provide an independent upper limit on Earth’s climate sensitivity

Martin Renoult, Navjit Sagoo, Johannes Hörner, and Thorsten Mauritsen

Abstract. Geological evidence of a snowball Earth state indicate persistent tropical sea ice cover during the Neoproterozoic (> 635 million years ago). Current theory is that a strengthening of the positive surface albedo feedback with cooling temperatures, eventually exceeding the sum of all other feedbacks, leads to a global climate instability. Several recent high sensitivity climate models with strongly positive cloud feedbacks have not been able to simulate the much warmer Last Glacial Maximum state, suggestive that they cool excessively in response to a modest decrease in atmospheric carbon dioxide levels and therefore enter the snowball instability by this mechanism. Using a coupled Earth system model, MPI-ESM1.2, we show that clouds accelerate the transition to a snowball Earth state and reduce the radiative forcing required to trigger the climate instability. Positive cloud feedbacks over tropical oceans and ahead of the sea-ice edge act to cool down the oceans and promote sea ice formation. Regardless, when approached slowly the snowball Earth transitions appear to occur around a global mean temperature of zero degree Celsius, simultaneously with the sea ice edge advancing into the sub-tropics thereby strengthening the surface albedo feedback. This temperature threshold, if supported by several climate models, could be used as a novel and independent constraint on the upper bound of climate sensitivity. Currently, using the results from MPI-ESM1.2, we find it is implausible that Earth's climate sensitivity exceeds 5.5 K (4.4–6.6, 90 percent confidence).

Received: 23 Sep 2024 – Discussion started: 02 Oct 2024

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17 Mar 2026

Snowball Earth transitions from Last Glacial Maximum conditions provide an independent upper limit on Earth's climate sensitivity

Martin Renoult, Navjit Sagoo, Johannes Hörner, and Thorsten Mauritsen

Earth Syst. Dynam., 17, 303–318, https://doi.org/10.5194/esd-17-303-2026,https://doi.org/10.5194/esd-17-303-2026, 2026

Short summary

Martin Renoult, Navjit Sagoo, Johannes Hörner, and Thorsten Mauritsen

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-2981', Anonymous Referee #1, 11 Oct 2024
Review for manuscript "Snowball Earth transitions from Last Glacial Maximum conditions provide an independent upper limit on Earth's climate sensitivity"
Authors: Martin Renoult, Navjit Sagoo, Johannes Hörner, Thorsten Mauritsen
General comments
In the presented manuscript, the authors study relevant climate feedbacks during the initiation of a snowball Earth from pre-industrial (PI) or Last Glacial Maximum (LGM) conditions using Earth system model (ESM) simulations. Furthermore, the authors present a novel way of contraining an upper bound of the Earth's equilibrium climate sensitivity (ECS), by deriving a relationship between an Earth system model's ECS and the simulated global mean (sea surface) temperature anomaly of the LGM compared to PI conditions. While I am not sure about the novelty and relevance of the analysis of climate feedbacks during snowball Earth initiation, the attempted contraint of ECS is very interesting and seems scientifically relevant. The chosen tool (ESMs) are a good way to approach this problem. However, there are some issues with the manuscript in its current state that, in my eyes, need to be resolved before publication of this work.
All potential issues are listed below under "specific comments", but I highlight the main ones here:
The introduction and the method sections are a bit too short in my opinion: Some existing research about climate feedbacks during snowball Earth initiation is not discussed, the introduction fails to explain the reasoning behind the ECS constraint and the method section should go into a bit more detail about the used methods, instead of mostly referring to existing articles.

It does not at all become clear, how the global mean temperature at which snowball Earth inception occurs is being derived from the individual simulations.

My main concern is that the assumption that all models and setups would have a "snowball Earth inception temperature" of roughly 0 °C is too far fetched. This goes together with the above point that the derivation of this temperature is not clearly described and that even the results of the presented setup point to quite some uncertainty in my eyes (although a different derivation method could give a more precise, but model-specific number, as discussed below). This is especially worrying, as it seems that the uncertainty around the value of the inception temperature does not enter the calculation of the ECS constraint. If it would enter, the confidence on the reported value should be reduced significantly, unfortunately also reducing the significance of the findings reported in this manuscript.

Overall, the scientific idea, the chosen approach and the considerable amount of effort that went into conducting the simulations, make this manuscript a suitable contribution to ESD. However, the long list of issues and the potentially reduced certainty of the main finding of this work make me suggest that this manuscript should only be reconsidered after major revision.
Specific comments
The analysis of what feedbacks are important in the snowball Earth transition is not something completely new. For example, the contribution of Pierrehumbert et al. (2011) in the "Snowmip" activity is not mentioned at all (which is odd considering that the authors write about scientifc discussions with Raymond Pierrehumbert and other involved persons in their acknowledgements). Pierrehumbert et al. (2011) specifically discuss that snow and sea-ice albedos together with clouds and atmospheric circulation have a major control of the models behaviour during snowball Earth initiation. There is a short introduction to the topic in the very first paragraph, but I would strongly suggest to add more discussion of the existing literature here.

l. 31: After the introduction, it is still not clear how the logic behind the ECS constraint works. I would suggest to elaborate on the approach, i.e. that you constrain ECS ultimately by fitting a line for the relationship between a models ECS and the simulated LGM temperature anomaly, and then assume that there is a fixed value of the anomaly at which a snowball Earth would be initiated (in all models). Since a snowball Earth did not happen, you have a new and independent limit on ECS. This reasoning is completely missing in the introduction, so the reader has to guess how this should work. I would suggest to add a bit more explanation in the abstract too, since this is the main point of the paper.

l. 47-50: How is the growing sea ice problem then treated in MPI-ESM? The reasoning behind having the limit is to avoid numerical artefacts or model crashes as the surface layer runs dry. After reading the rest of the manuscript, it seems like this is just ignored and only the 50 ppm-simulation crashes after 1848 years because of this problem. But why is this not a problem earlier and in the other simulations? This limiter was included, because even pre-industrial states sometimes got too thick ice and crashed. Why are your much colder simulations not crashing quickly?

Methods generally: The authors refer to other papers for their methods, but I think some more explanation should enter also here, to let the reader understand what is being done without having to read up in other papers.

Table 1: It does not really become clear why all the different runs are being done. A bit more thourough explanation of why the individual sets of simulations are being done would make it easier to understand from the beginning, and not after reading the whole manuscrpt.

When first looking at Fig. 1, I assumed all dots correspond to stable climate states, but later it became clear that these were taken out of transient simulations that are in the middle of approaching a snowball Earth. Over which time periods where they averaged and should these numbers really be produced from non-equlibrium climate states? There generally needs to be more explanation which goes together with the fact that the method section is quite short. There is a similar issue with Fig. 2. These maps are all from one simulation, so over which time periods were they created? A figure with some simple time series of the runs would be very helpful.

l. 106-108: First, it is said that positive cloud feedbacks at the sea-ice edge decrease the temperature of instability, then it is said that cloud feedbacks substantially increase the threshold CO2 level, which are opposing statements. I can imagine this dicrepancy comes from comparing local to global effects of the cloud feedback or because neglecting the cloud feedback would decrease global mean temperatures at a reference CO2 level, but please explain in more detail what is the cause of the discrepancy here.

Fig. 3 description: Terming some phrases "stable climate" even though some of the runs are in the middle of a transition towards a snowball Earth seems incorrect to me. Please elaborate and be more specific about what is actually meant here.

l. 115: To me Fig. 3 does not really show that the different runs transit towards a snowball Earth at roughly the same (transient) global mean temperature. Again, a simple figure with time series of global mean temperature in all the runs would be helpful to support these kind of statements.

Fig. 4: Generally, schematics are nice, but this one is hardly telling a story. Could it be a bit more elaborate or just left out? If you want to keep this in, I am not going to oppose.

Chapter 4: I am having a hard time believing that the temperature at which the climate transits to a snowball Earth state is similar across CO2 forcings, setups and even supposedly climate models (l. 118). First of all, what temperature is even meant here? These are all transient simulations, so I assume it is not the global mean temperature of the last stable pre-snowball equilibrium climate (which would surely be highly dependent on the climate model). Is it the (global mean) temperature at which the TOA radiative imbalance starts to grow over time again, as marked by the different phases in Figs. 3 and A1? But then, this is all but a clearly defined temperature range, as can be seen from the large ranges where the imbalance goes sideways in some runs, and even if taking the shown different colors as markers, there is still a range of ~10 K between the different runs. Does this count as "broadly similar"? Especially the statement that this temperature will still be the same even with other climate models seems dubios to me. Again, some of this issue could potentially be resolved by simply explaining more thourougly the procedure that was taken.

l. 127: Now it sounds like the "inception temperature" is actually the global mean temperature of the last stable pre-snowball climate state? A clear definition of what you mean by this temperature is highly desirable. Also, the final global mean temperature of the 50 ppm run (assuming it reached climatic equilibrium and that a further lowering of CO2 would drive the climate into a snowball state) IS probably the "inception temperature", when defined as above. I don't think that the other transient simulations can give any more reliable input. Hence, simply finding the last stable pre-snowball climate by iteratively changing the CO2 concentration of individual runs would give a more reliable and more precise estimate of the "inception temperature" for a given model setup.

l. 142: I find it very problematic to make such statements. First of all, what is the uncertainty range here? It seems to be in the order of at least 5 K. Second, it should be made clear that if this would be a sound statement, it would only be valid for the modern arrangement of continents and not for the setup during the Neoproterozoic, where the snowball Earth actually occurred. This needs to be specified. Lastly, this temperature is in fact highly model dependent. From personal experience, I can say that parameterisations like the sea-ice and snow albedos or even small changes in parameters of sea-ice dynamics can shift the transition towards snowball Earth inception substantially.

l. 151: how does Fig. 5 show that the instability is around 0°C?

l. 162: How are the critical ECS and the confidence interval computed? It seems like the values just come from the fit of the regression line in Fig. 6. But how does this account for the uncertainty in the "inception temperature", which surely has an uncertainty range of several degrees, maybe up to 5 K or more. This would substantially increase the uncertainty in the calculated upper limit of ECS.

l. 179: Point 3 is not really part of the recipe from the points above, but rather a general proposal, hence it doesn't really fit into the list.

Overall text:
Quite often simply the term temperature is used for "global mean temperature", which could lead to confusion. I'd suggest to be more precise with the wording.

The sentence structure is not always sensible (e.g. l. 15: it is not the geological evidence that supports the formation of sea ice within tropical regions, but there is geological evidence that supports the hypothesis that there was sea ice in tropical regions).

Sometimes unclear and weak use of the english language, like in l.127: "...the inception temperature happens at a temperature...". Not the inception temperature happens at a specific temperature, but snowball Earth inception does.

Technical corrections
- l.15 and other locations: To my knowledge, it should generally be "sea ice" without the hyphen, but then "sea-ice albedo", i.e. including a hyphen when combined with a following noun.
- l. 18 "referred to as"
- l.38 bad punctuation around MPI-ESM1.2
- l. 69-70: Example of weak language, making it hard to follow the text. "... the highest value of the Earth's ECS that does not lead to an unstable LGM state represents an upper limit..."
- l. 93 "snow ball"?
- l. 125: 50 ppm is rather 1/5 to 1/6 and not 1/4 of PI CO2, why not be precise?
- l. 140: "involve"
- l. 150 "as MPI-ESM1.2"
- l. 156-158: bad punctuation or sentence structure
- l.176 "surface"
- l. 184 "...model Earth's climate sensitivity." What does this man?
- l. 290: The doi in the reference does not go to the actual article, but to an eossar link. Please link the actual article.

References
Pierrehumbert, R. T., Abbot, D. S., Voigt, A., & Koll, D. (2011). Climate of the Neoproterozoic. Annual Review of Earth and Planetary Sciences, 39(1), 417-460, doi: 10.1146/annurev-earth-040809-152447
Citation: https://doi.org/10.5194/egusphere-2024-2981-RC1
- AC1: 'Reply on RC1', Martin Renoult, 16 Dec 2024
  
  Our response is attached as a pdf document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2981-AC1
RC2:
'Comment on egusphere-2024-2981', Anonymous Referee #2, 22 Oct 2024
The study addresses the role of cloud feedback in the transition to a snowball Earth state, and provides an upper bound on equilibrium climate sensitivity (ECS).
The authors use a suite of MPI-ESM simulations with negative CO2 forcing, including one set of simulations where feedbacks are locked by hiding changes in cloud/humidity/albedo fields from the radiation code. They show that while ice albedo feedback is the one that causes the snowball runaway, clouds play a crucial role in initiating this process. With additional support from CESM simulations, the authors argue that a transition to snowball Earth occurs around 0 degrees Celsius. They use this to develop an emergent constraint for an upper limit to ECS, which they quantify to be around 5.5 K. The justification for this emergent constraint arises from the fact that the Earth was not completely frozen during the LGM. The authors furthermore call upon modeling centers to replicate reduced-CO2 simulations to find thresholds for the transition to a snowball Earth in other models.
Overall, I find the simulations and the reported results enlightening, and I have learned interesting aspects from the paper. In particular, I enjoyed learning about the results from the feedback-locked simulations, which I think are well designed. However, I think that the study lacks rigor in important points, and I do not buy some of the main conclusions because of hand-wavy arguments.
Major comments

There are a few inconsistencies and a lack of clarity related to the transition temperature, which I summarize here:

How is the transition temperature defined? I assume when the feedback becomes zero?

If my interpretation is correct, how is the value and the uncertainty determined? E.g. looking at Fig. 3A in the 1/64 x CO2 line, I could see why one would argue the transition temperature to be at -20 K, but at the same time -33 K also seems reasonable. Similar reasonable ranges seem to exist for many other simulations.

How does this uncertainty affect the uncertainty of the emergent constraint?

My second set of comments refers to the emergent constraint:

Fig. 6: Taking out all the CESM-2 points (the blue ones and, as I read from the text, the upper left white one) leaves no relationship at all. In fact, the authors write that “the relationship lacks robustness” (caption Fig. 6). Considering only the remaining PMIP models, there seems to be no linear relationship at all, which seems to indicate that all the emergent constraint actually comes from CESM2.

The instability threshold was previously argued to be around 0 degC, in this figure it starts around -8 K SST anomaly relative to preindustrial. Given that pre-industrial SST were around 15 degC or so, how does this go together?

How is the emergent constraint different from simply excluding models that freeze over in the LGM when estimating ECS on the grounds that they would be too sensitive? Would that method lead to the same results?

The third set of comments refers to the threshold of snowball transition at 0 degC:

Some arguments are very hand-wavy. For example, the argument that this supposedly generalizes across models (l. 118-119) and the “geometric argument” in l.122-124.

In particular, I am not sure that the transition temperature would be 0 degC across all models. Already in Fig. 3A) I can see a transition temperature range of ~ 15 K across simulations performed with the same model. Similarly, in Fig. 5, the transition temperature seems to be at or below -20 K anomaly to pre-industrial, which would be well below 0 degC, too. The statement that all models share a similar transition temperature to snowball Earth also seems to be at odds with the statement in l. 28-29, which points towards different models having different transition temperatures. Also the statement in l. 147-148 points toward different transition types and temperatures even within the CESM model family.

l. 28 – 29: I found this surprising, and from skimming through Zhu et al. 2021a, I didn’t find that information. From my understanding, they look at only one climate model family (CESM), albeit in different configurations. While CESM2 definitely goes to a snowball state, I can’t see at what temperature the transition would happen, as their Gregory plot (Fig. 2 (d)) seems to indicate a stable regime throughout (with small, but nevertheless negative feedback). Furthermore, I was under the impression that cloud feedback accelerates the transition to the snowball state, or, as stated in l.95-97, doesn’t change the transition temperature. All of these statements seem to be inconsistent with each other. A similar statement is found in l.107. How do these conflicting statements go together?

l. 32: independent from what? If the intended meaning is “independent from models”, then I think independence is a strong claim, which should be further justified

l. 99-100: This is almost exactly the same finding as in Abbot 2014 (https://doi.org/10.1175/JCLI-D-13-00738.1), please cite

l. 145: “universal”: I suggest rewording, given that it was tested on only two selected models

Why is there no summary, conclusions, or discussions section? I don’t want to insist on the traditional structure, but some wrap-up and putting-into-context at the end of the paper might be helpful.

Minor comments

The authors did a great job motivating the study in the introduction. A few additional sentences about ECS and its uncertainty would be helpful, since the emergent constraint on ECS is one of the main purposes of the study. Also, the emergent constraint could already be clearly set as a goal for the paper, as well as the logic that is behind it.

l.99 I suggest “locked clouds” rather than “locked cloud feedbacks”. I find “locked cloud feedbacks” not wrong but misleading, because with locked clouds there is actually zero cloud feedback.

l. 130: “state” here refers to temperature, not CO2 concentration, I guess? If so, then I suggest making this clearer, since the CO2 concentration technically belongs to the state.

l.156-158: I am not sure the sentence is correct grammatically, at least it’s hard to digest

l. 171 and following: I suggest to implement the call for the new experiments to the abstract.

Summary
In summary, when looking at the abstract:
l. 1-5 are intro

l. 6-8 seem sound and could be an interesting contribution, but I am genuinely not sure about their novelty.

l. 9-13: These statements are unconvincing.
I suggest major revisions in which the authors provide more rigorous arguments addressing the comments. In case that in the revision no convincing arguments for the constancy of the transition temperature and the justification of the emergent constraint can be made, and if the findings about the role of cloud feedback in the transition to a snowball Earth are not novel, I recommend rejection of the paper; otherwise it should be accepted.
Citation: https://doi.org/10.5194/egusphere-2024-2981-RC2
- AC2: 'Reply on RC2', Martin Renoult, 16 Dec 2024
  
  Our response is attached as a pdf document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2981-AC2
RC3:
'Comment on egusphere-2024-2981', Anonymous Referee #3, 20 Nov 2024

The concept of the manuscript content is novel. I think that the central scientific concepts (e.g. snowball Earth, climate sensitivity, and exploration of forcings) can be described more clearly so that the value of this approach to the community can be fully understood. The manuscript considers a model response that is somewhat unphysical and is perhaps related to model-deficiencies (e.g., falling into a snowball Earth state during a Quaternary glacial stage), so I think more clarity here would encourage other modelling groups to maybe take onboard these concepts. Similarly, I question whether new insights can be attained on Earth’s climate sensitivity using climate model runs with boundary conditions that are not temporally coincident in this extreme case (e.g. fixed LGM and PI boundary conditions with Precambrian levels of solar insolation or CO2).
Nevertheless, there is a lot of good work here. I believe that if these points are addressed, the manuscript has the potential to expand upon the derivation of climate sensitivity and could also provide insight into the role of climate feedbacks (e.g. surface albedo and clouds) during Precambrian Snowball Earth states.
General Comments (by line number).
L15 The authors state “During the Neoproterozoic (>635 million years ago) …”, here the Neoproterozoic ran from ca. 1000 - 538 Mya, and the Cryogenian stage (encompassed the two episodes of the Snowball Earth) ran from ca. 720 – 635 Mya. Your phrasing just needs to be tightened as this would get picked up by someone working in the Precambrian.
What defines your snowball Earth State? The definition of Snowball Earth generally falls into two camps, the Hard Snowball Earth in which the ocean is fully glaciated with marine terminating tropical glaciers, and a Soft Snowball Earth scenario in which sea ice reached into and perhaps beyond the sub-tropics (extending to approx. 10 - 25 degree latitude, sometimes referred to as waterbelt or slushbelt ). Within the manuscript is snowball Earth inception when the tropical ocean has >0% sea ice fraction (as shown in Figure B3). My apologies if I have missed your definition of snowball Earth inception.
L25-29 If some PMIP4 models do indeed attain a snowball Earth state in the modelling of the LGM, is this more likely due to deficiencies in model parameterisations? If so, are we really deriving insight into the Earth’s climate sensitivity? If my thinking here is logical, this needs a brief discussion in the text.
L15 geological evidences
L28 what models are you referring to when you say these models start transitioning to a snowball state (the PMIP4 models that fail to model the LGM?)
L38-40. You state that you are using an ESM. It would be beneficial to the reader if you briefly described which sub-models are included (e.g., is there an interactive Ice Sheet Model incorporated? If so is it a global model or just GIS & AIS domains) or are you referring to an atmosphere-ocean coupled model. I assume the latter. I would also write a sentence or two on the sea ice model as the physics and parameterisations would be important to a reader looking to understand and compare your modelling results with their own. It is also relevant to discuss the snow-albedo parametrisation within the model (e.g., deep snow albedo), I am assuming in these simulations that year-round persistent terrestrial snow cover advances equatorward, so a discussion of snow cover within the model is pertinent.
L41-43 You state that you use the “coarse” T31 truncated model for PI and the “low resolution” T63 model for LGM. I would be more consistent with your description of resolution, as T63 is higher resolution that T31. Or drop the terms “coarse resolution” and “low resolution” and use “low resolution” and “higher resolution”.
Are there any differences in other relevant parameterisations between MPI-ESM1.2-CR (T31 31L) and MPI-ESM1.2-LR (T63 47L) that could impact the outcomes of the study? For example, do both models share the same ocean model (in terms of spatial resolution and sea ice model parameters)?
It would be useful for the study if the same run (of Table 1.) was conducted for both CR and LR versions of the model. I understand from Table 1 that some of this is an opportunistic ensemble, and so I understand if this isn't possible in a reasonable time frame.
L47 A bit unclear here for the reader – are you saying that the act of limiting sea ice growth generates latent heat or does thick sea ice itself generate latent heat?
Table 1. 1/2056x CO2 should be 1/2048x CO2?
L56 Why does the length of the run vary with forcing? Could you have run each simulation long enough so that you didn’t have to use (linear?) regression of TOA radiation imbalance.
L55–57 This is a little bit unclear so needs clarifying- are you computing the climate feedback by determining the change in TOA imbalance over a 5 C temperature change?
L59-60 It would be helpful to the reader if you could succinctly describe how these are locked (1-2 sentences) L60 mentions that these are imposed on the radiation parameterization, but this is still not that clear to someone not experienced in locking feedbacks.
L64-69 So are you saying that you are comparing the snowball transition state to the modelled LGM state to derive the Equilibrium climate state?
L81 be slightly more specific here and say these all relate to global mean surface air temperature.
L91 “southern sea ice edge” I think you mean something like “equatorward sea ice edge” unless you are just considering the northern hemisphere sea ice extent here.
L114 It is not entirely clear from Fig 3. how the climate transition is broadly similar. What feature am I looking at in Figure 3? (is this where TOA radiative imbalance is most +ve?). Do you need to show on Fig 3 the global temperature in which your criteria for snowball Earth is met?
Figures 3 and A1 have the 2X CO2 in the upper right quadrant extending beyond the numbered parts of the y-axis. I would adjust the x- and y-axis numbering so that they extend into the +ve values.
L115 Appendix A should this instead be Figure A1
L125 50 ppm is closer to 1/6 of pre-industrial than ¼
L144 I believe this statement depends upon how tightly you are defining the transition / inception into a snowball Earth state, definition of this transition would clarify this.
L161. I am a little uncertain how this 5.5 K (4.4 -6.6, 90% confidence interval) statement relates to the data within Figure 6 – I guess this where your linear fit intercepts with the upper bounds of your instability threshold. Could this be identified within Figure 6.
L301, You state that your model is numerically unstable at low CO2 concentrations and so compare solar-forced snowball Earth transitions instead. Given that you are running at low CO2 levels, has this numerical instability impacted your work?
In the text, be consistent with the term “snow ball” or “snowball”
Some instances of informal scientific language used. 36 “notoriously difficult” or L145 “notoriously performed” are not scientific terms (notorious often means something bad or unfavourable that is somewhat common knowledge). Modify also L46 “few simulations” and L88 “All in all”.
Equilibrium climate sensitivity (ECS) is the temperature change to a doubling of CO2 once the atmosphere and ocean (including deep ocean) has equilibrated to that change in energy. I believe here you are in fact just considering only atmospheric changes. I think you therefore need to reconcile this ECS with your definition of climate sensitivity. Here also the definition of your snowball Earth is important (sea ice at the equator? I assume you are holding terrestrial boundary conditions fixed – no expansion of terrestrial glaciation).

Citation: https://doi.org/10.5194/egusphere-2024-2981-RC3
- AC3: 'Reply on RC3', Martin Renoult, 16 Dec 2024
  
  Our response is attached as a pdf document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2981-AC3

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-2981', Anonymous Referee #1, 11 Oct 2024
Review for manuscript "Snowball Earth transitions from Last Glacial Maximum conditions provide an independent upper limit on Earth's climate sensitivity"
Authors: Martin Renoult, Navjit Sagoo, Johannes Hörner, Thorsten Mauritsen
General comments
In the presented manuscript, the authors study relevant climate feedbacks during the initiation of a snowball Earth from pre-industrial (PI) or Last Glacial Maximum (LGM) conditions using Earth system model (ESM) simulations. Furthermore, the authors present a novel way of contraining an upper bound of the Earth's equilibrium climate sensitivity (ECS), by deriving a relationship between an Earth system model's ECS and the simulated global mean (sea surface) temperature anomaly of the LGM compared to PI conditions. While I am not sure about the novelty and relevance of the analysis of climate feedbacks during snowball Earth initiation, the attempted contraint of ECS is very interesting and seems scientifically relevant. The chosen tool (ESMs) are a good way to approach this problem. However, there are some issues with the manuscript in its current state that, in my eyes, need to be resolved before publication of this work.
All potential issues are listed below under "specific comments", but I highlight the main ones here:
The introduction and the method sections are a bit too short in my opinion: Some existing research about climate feedbacks during snowball Earth initiation is not discussed, the introduction fails to explain the reasoning behind the ECS constraint and the method section should go into a bit more detail about the used methods, instead of mostly referring to existing articles.

It does not at all become clear, how the global mean temperature at which snowball Earth inception occurs is being derived from the individual simulations.

My main concern is that the assumption that all models and setups would have a "snowball Earth inception temperature" of roughly 0 °C is too far fetched. This goes together with the above point that the derivation of this temperature is not clearly described and that even the results of the presented setup point to quite some uncertainty in my eyes (although a different derivation method could give a more precise, but model-specific number, as discussed below). This is especially worrying, as it seems that the uncertainty around the value of the inception temperature does not enter the calculation of the ECS constraint. If it would enter, the confidence on the reported value should be reduced significantly, unfortunately also reducing the significance of the findings reported in this manuscript.

Overall, the scientific idea, the chosen approach and the considerable amount of effort that went into conducting the simulations, make this manuscript a suitable contribution to ESD. However, the long list of issues and the potentially reduced certainty of the main finding of this work make me suggest that this manuscript should only be reconsidered after major revision.
Specific comments
The analysis of what feedbacks are important in the snowball Earth transition is not something completely new. For example, the contribution of Pierrehumbert et al. (2011) in the "Snowmip" activity is not mentioned at all (which is odd considering that the authors write about scientifc discussions with Raymond Pierrehumbert and other involved persons in their acknowledgements). Pierrehumbert et al. (2011) specifically discuss that snow and sea-ice albedos together with clouds and atmospheric circulation have a major control of the models behaviour during snowball Earth initiation. There is a short introduction to the topic in the very first paragraph, but I would strongly suggest to add more discussion of the existing literature here.

l. 31: After the introduction, it is still not clear how the logic behind the ECS constraint works. I would suggest to elaborate on the approach, i.e. that you constrain ECS ultimately by fitting a line for the relationship between a models ECS and the simulated LGM temperature anomaly, and then assume that there is a fixed value of the anomaly at which a snowball Earth would be initiated (in all models). Since a snowball Earth did not happen, you have a new and independent limit on ECS. This reasoning is completely missing in the introduction, so the reader has to guess how this should work. I would suggest to add a bit more explanation in the abstract too, since this is the main point of the paper.

l. 47-50: How is the growing sea ice problem then treated in MPI-ESM? The reasoning behind having the limit is to avoid numerical artefacts or model crashes as the surface layer runs dry. After reading the rest of the manuscript, it seems like this is just ignored and only the 50 ppm-simulation crashes after 1848 years because of this problem. But why is this not a problem earlier and in the other simulations? This limiter was included, because even pre-industrial states sometimes got too thick ice and crashed. Why are your much colder simulations not crashing quickly?

Methods generally: The authors refer to other papers for their methods, but I think some more explanation should enter also here, to let the reader understand what is being done without having to read up in other papers.

Table 1: It does not really become clear why all the different runs are being done. A bit more thourough explanation of why the individual sets of simulations are being done would make it easier to understand from the beginning, and not after reading the whole manuscrpt.

When first looking at Fig. 1, I assumed all dots correspond to stable climate states, but later it became clear that these were taken out of transient simulations that are in the middle of approaching a snowball Earth. Over which time periods where they averaged and should these numbers really be produced from non-equlibrium climate states? There generally needs to be more explanation which goes together with the fact that the method section is quite short. There is a similar issue with Fig. 2. These maps are all from one simulation, so over which time periods were they created? A figure with some simple time series of the runs would be very helpful.

l. 106-108: First, it is said that positive cloud feedbacks at the sea-ice edge decrease the temperature of instability, then it is said that cloud feedbacks substantially increase the threshold CO2 level, which are opposing statements. I can imagine this dicrepancy comes from comparing local to global effects of the cloud feedback or because neglecting the cloud feedback would decrease global mean temperatures at a reference CO2 level, but please explain in more detail what is the cause of the discrepancy here.

Fig. 3 description: Terming some phrases "stable climate" even though some of the runs are in the middle of a transition towards a snowball Earth seems incorrect to me. Please elaborate and be more specific about what is actually meant here.

l. 115: To me Fig. 3 does not really show that the different runs transit towards a snowball Earth at roughly the same (transient) global mean temperature. Again, a simple figure with time series of global mean temperature in all the runs would be helpful to support these kind of statements.

Fig. 4: Generally, schematics are nice, but this one is hardly telling a story. Could it be a bit more elaborate or just left out? If you want to keep this in, I am not going to oppose.

Chapter 4: I am having a hard time believing that the temperature at which the climate transits to a snowball Earth state is similar across CO2 forcings, setups and even supposedly climate models (l. 118). First of all, what temperature is even meant here? These are all transient simulations, so I assume it is not the global mean temperature of the last stable pre-snowball equilibrium climate (which would surely be highly dependent on the climate model). Is it the (global mean) temperature at which the TOA radiative imbalance starts to grow over time again, as marked by the different phases in Figs. 3 and A1? But then, this is all but a clearly defined temperature range, as can be seen from the large ranges where the imbalance goes sideways in some runs, and even if taking the shown different colors as markers, there is still a range of ~10 K between the different runs. Does this count as "broadly similar"? Especially the statement that this temperature will still be the same even with other climate models seems dubios to me. Again, some of this issue could potentially be resolved by simply explaining more thourougly the procedure that was taken.

l. 127: Now it sounds like the "inception temperature" is actually the global mean temperature of the last stable pre-snowball climate state? A clear definition of what you mean by this temperature is highly desirable. Also, the final global mean temperature of the 50 ppm run (assuming it reached climatic equilibrium and that a further lowering of CO2 would drive the climate into a snowball state) IS probably the "inception temperature", when defined as above. I don't think that the other transient simulations can give any more reliable input. Hence, simply finding the last stable pre-snowball climate by iteratively changing the CO2 concentration of individual runs would give a more reliable and more precise estimate of the "inception temperature" for a given model setup.

l. 142: I find it very problematic to make such statements. First of all, what is the uncertainty range here? It seems to be in the order of at least 5 K. Second, it should be made clear that if this would be a sound statement, it would only be valid for the modern arrangement of continents and not for the setup during the Neoproterozoic, where the snowball Earth actually occurred. This needs to be specified. Lastly, this temperature is in fact highly model dependent. From personal experience, I can say that parameterisations like the sea-ice and snow albedos or even small changes in parameters of sea-ice dynamics can shift the transition towards snowball Earth inception substantially.

l. 151: how does Fig. 5 show that the instability is around 0°C?

l. 162: How are the critical ECS and the confidence interval computed? It seems like the values just come from the fit of the regression line in Fig. 6. But how does this account for the uncertainty in the "inception temperature", which surely has an uncertainty range of several degrees, maybe up to 5 K or more. This would substantially increase the uncertainty in the calculated upper limit of ECS.

l. 179: Point 3 is not really part of the recipe from the points above, but rather a general proposal, hence it doesn't really fit into the list.

Overall text:
Quite often simply the term temperature is used for "global mean temperature", which could lead to confusion. I'd suggest to be more precise with the wording.

The sentence structure is not always sensible (e.g. l. 15: it is not the geological evidence that supports the formation of sea ice within tropical regions, but there is geological evidence that supports the hypothesis that there was sea ice in tropical regions).

Sometimes unclear and weak use of the english language, like in l.127: "...the inception temperature happens at a temperature...". Not the inception temperature happens at a specific temperature, but snowball Earth inception does.

Technical corrections
- l.15 and other locations: To my knowledge, it should generally be "sea ice" without the hyphen, but then "sea-ice albedo", i.e. including a hyphen when combined with a following noun.
- l. 18 "referred to as"
- l.38 bad punctuation around MPI-ESM1.2
- l. 69-70: Example of weak language, making it hard to follow the text. "... the highest value of the Earth's ECS that does not lead to an unstable LGM state represents an upper limit..."
- l. 93 "snow ball"?
- l. 125: 50 ppm is rather 1/5 to 1/6 and not 1/4 of PI CO2, why not be precise?
- l. 140: "involve"
- l. 150 "as MPI-ESM1.2"
- l. 156-158: bad punctuation or sentence structure
- l.176 "surface"
- l. 184 "...model Earth's climate sensitivity." What does this man?
- l. 290: The doi in the reference does not go to the actual article, but to an eossar link. Please link the actual article.

References
Pierrehumbert, R. T., Abbot, D. S., Voigt, A., & Koll, D. (2011). Climate of the Neoproterozoic. Annual Review of Earth and Planetary Sciences, 39(1), 417-460, doi: 10.1146/annurev-earth-040809-152447
Citation: https://doi.org/10.5194/egusphere-2024-2981-RC1
- AC1: 'Reply on RC1', Martin Renoult, 16 Dec 2024
  
  Our response is attached as a pdf document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2981-AC1
RC2:
'Comment on egusphere-2024-2981', Anonymous Referee #2, 22 Oct 2024
The study addresses the role of cloud feedback in the transition to a snowball Earth state, and provides an upper bound on equilibrium climate sensitivity (ECS).
The authors use a suite of MPI-ESM simulations with negative CO2 forcing, including one set of simulations where feedbacks are locked by hiding changes in cloud/humidity/albedo fields from the radiation code. They show that while ice albedo feedback is the one that causes the snowball runaway, clouds play a crucial role in initiating this process. With additional support from CESM simulations, the authors argue that a transition to snowball Earth occurs around 0 degrees Celsius. They use this to develop an emergent constraint for an upper limit to ECS, which they quantify to be around 5.5 K. The justification for this emergent constraint arises from the fact that the Earth was not completely frozen during the LGM. The authors furthermore call upon modeling centers to replicate reduced-CO2 simulations to find thresholds for the transition to a snowball Earth in other models.
Overall, I find the simulations and the reported results enlightening, and I have learned interesting aspects from the paper. In particular, I enjoyed learning about the results from the feedback-locked simulations, which I think are well designed. However, I think that the study lacks rigor in important points, and I do not buy some of the main conclusions because of hand-wavy arguments.
Major comments

There are a few inconsistencies and a lack of clarity related to the transition temperature, which I summarize here:

How is the transition temperature defined? I assume when the feedback becomes zero?

If my interpretation is correct, how is the value and the uncertainty determined? E.g. looking at Fig. 3A in the 1/64 x CO2 line, I could see why one would argue the transition temperature to be at -20 K, but at the same time -33 K also seems reasonable. Similar reasonable ranges seem to exist for many other simulations.

How does this uncertainty affect the uncertainty of the emergent constraint?

My second set of comments refers to the emergent constraint:

Fig. 6: Taking out all the CESM-2 points (the blue ones and, as I read from the text, the upper left white one) leaves no relationship at all. In fact, the authors write that “the relationship lacks robustness” (caption Fig. 6). Considering only the remaining PMIP models, there seems to be no linear relationship at all, which seems to indicate that all the emergent constraint actually comes from CESM2.

The instability threshold was previously argued to be around 0 degC, in this figure it starts around -8 K SST anomaly relative to preindustrial. Given that pre-industrial SST were around 15 degC or so, how does this go together?

How is the emergent constraint different from simply excluding models that freeze over in the LGM when estimating ECS on the grounds that they would be too sensitive? Would that method lead to the same results?

The third set of comments refers to the threshold of snowball transition at 0 degC:

Some arguments are very hand-wavy. For example, the argument that this supposedly generalizes across models (l. 118-119) and the “geometric argument” in l.122-124.

In particular, I am not sure that the transition temperature would be 0 degC across all models. Already in Fig. 3A) I can see a transition temperature range of ~ 15 K across simulations performed with the same model. Similarly, in Fig. 5, the transition temperature seems to be at or below -20 K anomaly to pre-industrial, which would be well below 0 degC, too. The statement that all models share a similar transition temperature to snowball Earth also seems to be at odds with the statement in l. 28-29, which points towards different models having different transition temperatures. Also the statement in l. 147-148 points toward different transition types and temperatures even within the CESM model family.

l. 28 – 29: I found this surprising, and from skimming through Zhu et al. 2021a, I didn’t find that information. From my understanding, they look at only one climate model family (CESM), albeit in different configurations. While CESM2 definitely goes to a snowball state, I can’t see at what temperature the transition would happen, as their Gregory plot (Fig. 2 (d)) seems to indicate a stable regime throughout (with small, but nevertheless negative feedback). Furthermore, I was under the impression that cloud feedback accelerates the transition to the snowball state, or, as stated in l.95-97, doesn’t change the transition temperature. All of these statements seem to be inconsistent with each other. A similar statement is found in l.107. How do these conflicting statements go together?

l. 32: independent from what? If the intended meaning is “independent from models”, then I think independence is a strong claim, which should be further justified

l. 99-100: This is almost exactly the same finding as in Abbot 2014 (https://doi.org/10.1175/JCLI-D-13-00738.1), please cite

l. 145: “universal”: I suggest rewording, given that it was tested on only two selected models

Why is there no summary, conclusions, or discussions section? I don’t want to insist on the traditional structure, but some wrap-up and putting-into-context at the end of the paper might be helpful.

Minor comments

The authors did a great job motivating the study in the introduction. A few additional sentences about ECS and its uncertainty would be helpful, since the emergent constraint on ECS is one of the main purposes of the study. Also, the emergent constraint could already be clearly set as a goal for the paper, as well as the logic that is behind it.

l.99 I suggest “locked clouds” rather than “locked cloud feedbacks”. I find “locked cloud feedbacks” not wrong but misleading, because with locked clouds there is actually zero cloud feedback.

l. 130: “state” here refers to temperature, not CO2 concentration, I guess? If so, then I suggest making this clearer, since the CO2 concentration technically belongs to the state.

l.156-158: I am not sure the sentence is correct grammatically, at least it’s hard to digest

l. 171 and following: I suggest to implement the call for the new experiments to the abstract.

Summary
In summary, when looking at the abstract:
l. 1-5 are intro

l. 6-8 seem sound and could be an interesting contribution, but I am genuinely not sure about their novelty.

l. 9-13: These statements are unconvincing.
I suggest major revisions in which the authors provide more rigorous arguments addressing the comments. In case that in the revision no convincing arguments for the constancy of the transition temperature and the justification of the emergent constraint can be made, and if the findings about the role of cloud feedback in the transition to a snowball Earth are not novel, I recommend rejection of the paper; otherwise it should be accepted.
Citation: https://doi.org/10.5194/egusphere-2024-2981-RC2
- AC2: 'Reply on RC2', Martin Renoult, 16 Dec 2024
  
  Our response is attached as a pdf document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2981-AC2
RC3:
'Comment on egusphere-2024-2981', Anonymous Referee #3, 20 Nov 2024

The concept of the manuscript content is novel. I think that the central scientific concepts (e.g. snowball Earth, climate sensitivity, and exploration of forcings) can be described more clearly so that the value of this approach to the community can be fully understood. The manuscript considers a model response that is somewhat unphysical and is perhaps related to model-deficiencies (e.g., falling into a snowball Earth state during a Quaternary glacial stage), so I think more clarity here would encourage other modelling groups to maybe take onboard these concepts. Similarly, I question whether new insights can be attained on Earth’s climate sensitivity using climate model runs with boundary conditions that are not temporally coincident in this extreme case (e.g. fixed LGM and PI boundary conditions with Precambrian levels of solar insolation or CO2).
Nevertheless, there is a lot of good work here. I believe that if these points are addressed, the manuscript has the potential to expand upon the derivation of climate sensitivity and could also provide insight into the role of climate feedbacks (e.g. surface albedo and clouds) during Precambrian Snowball Earth states.
General Comments (by line number).
L15 The authors state “During the Neoproterozoic (>635 million years ago) …”, here the Neoproterozoic ran from ca. 1000 - 538 Mya, and the Cryogenian stage (encompassed the two episodes of the Snowball Earth) ran from ca. 720 – 635 Mya. Your phrasing just needs to be tightened as this would get picked up by someone working in the Precambrian.
What defines your snowball Earth State? The definition of Snowball Earth generally falls into two camps, the Hard Snowball Earth in which the ocean is fully glaciated with marine terminating tropical glaciers, and a Soft Snowball Earth scenario in which sea ice reached into and perhaps beyond the sub-tropics (extending to approx. 10 - 25 degree latitude, sometimes referred to as waterbelt or slushbelt ). Within the manuscript is snowball Earth inception when the tropical ocean has >0% sea ice fraction (as shown in Figure B3). My apologies if I have missed your definition of snowball Earth inception.
L25-29 If some PMIP4 models do indeed attain a snowball Earth state in the modelling of the LGM, is this more likely due to deficiencies in model parameterisations? If so, are we really deriving insight into the Earth’s climate sensitivity? If my thinking here is logical, this needs a brief discussion in the text.
L15 geological evidences
L28 what models are you referring to when you say these models start transitioning to a snowball state (the PMIP4 models that fail to model the LGM?)
L38-40. You state that you are using an ESM. It would be beneficial to the reader if you briefly described which sub-models are included (e.g., is there an interactive Ice Sheet Model incorporated? If so is it a global model or just GIS & AIS domains) or are you referring to an atmosphere-ocean coupled model. I assume the latter. I would also write a sentence or two on the sea ice model as the physics and parameterisations would be important to a reader looking to understand and compare your modelling results with their own. It is also relevant to discuss the snow-albedo parametrisation within the model (e.g., deep snow albedo), I am assuming in these simulations that year-round persistent terrestrial snow cover advances equatorward, so a discussion of snow cover within the model is pertinent.
L41-43 You state that you use the “coarse” T31 truncated model for PI and the “low resolution” T63 model for LGM. I would be more consistent with your description of resolution, as T63 is higher resolution that T31. Or drop the terms “coarse resolution” and “low resolution” and use “low resolution” and “higher resolution”.
Are there any differences in other relevant parameterisations between MPI-ESM1.2-CR (T31 31L) and MPI-ESM1.2-LR (T63 47L) that could impact the outcomes of the study? For example, do both models share the same ocean model (in terms of spatial resolution and sea ice model parameters)?
It would be useful for the study if the same run (of Table 1.) was conducted for both CR and LR versions of the model. I understand from Table 1 that some of this is an opportunistic ensemble, and so I understand if this isn't possible in a reasonable time frame.
L47 A bit unclear here for the reader – are you saying that the act of limiting sea ice growth generates latent heat or does thick sea ice itself generate latent heat?
Table 1. 1/2056x CO2 should be 1/2048x CO2?
L56 Why does the length of the run vary with forcing? Could you have run each simulation long enough so that you didn’t have to use (linear?) regression of TOA radiation imbalance.
L55–57 This is a little bit unclear so needs clarifying- are you computing the climate feedback by determining the change in TOA imbalance over a 5 C temperature change?
L59-60 It would be helpful to the reader if you could succinctly describe how these are locked (1-2 sentences) L60 mentions that these are imposed on the radiation parameterization, but this is still not that clear to someone not experienced in locking feedbacks.
L64-69 So are you saying that you are comparing the snowball transition state to the modelled LGM state to derive the Equilibrium climate state?
L81 be slightly more specific here and say these all relate to global mean surface air temperature.
L91 “southern sea ice edge” I think you mean something like “equatorward sea ice edge” unless you are just considering the northern hemisphere sea ice extent here.
L114 It is not entirely clear from Fig 3. how the climate transition is broadly similar. What feature am I looking at in Figure 3? (is this where TOA radiative imbalance is most +ve?). Do you need to show on Fig 3 the global temperature in which your criteria for snowball Earth is met?
Figures 3 and A1 have the 2X CO2 in the upper right quadrant extending beyond the numbered parts of the y-axis. I would adjust the x- and y-axis numbering so that they extend into the +ve values.
L115 Appendix A should this instead be Figure A1
L125 50 ppm is closer to 1/6 of pre-industrial than ¼
L144 I believe this statement depends upon how tightly you are defining the transition / inception into a snowball Earth state, definition of this transition would clarify this.
L161. I am a little uncertain how this 5.5 K (4.4 -6.6, 90% confidence interval) statement relates to the data within Figure 6 – I guess this where your linear fit intercepts with the upper bounds of your instability threshold. Could this be identified within Figure 6.
L301, You state that your model is numerically unstable at low CO2 concentrations and so compare solar-forced snowball Earth transitions instead. Given that you are running at low CO2 levels, has this numerical instability impacted your work?
In the text, be consistent with the term “snow ball” or “snowball”
Some instances of informal scientific language used. 36 “notoriously difficult” or L145 “notoriously performed” are not scientific terms (notorious often means something bad or unfavourable that is somewhat common knowledge). Modify also L46 “few simulations” and L88 “All in all”.
Equilibrium climate sensitivity (ECS) is the temperature change to a doubling of CO2 once the atmosphere and ocean (including deep ocean) has equilibrated to that change in energy. I believe here you are in fact just considering only atmospheric changes. I think you therefore need to reconcile this ECS with your definition of climate sensitivity. Here also the definition of your snowball Earth is important (sea ice at the equator? I assume you are holding terrestrial boundary conditions fixed – no expansion of terrestrial glaciation).

Citation: https://doi.org/10.5194/egusphere-2024-2981-RC3
- AC3: 'Reply on RC3', Martin Renoult, 16 Dec 2024
  
  Our response is attached as a pdf document.
  
  Citation: https://doi.org/10.5194/egusphere-2024-2981-AC3

Peer review completion

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

ED: Reconsider after major revisions (16 Dec 2024) by Claudia Timmreck

AR by Martin Renoult on behalf of the Authors (20 Jan 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (24 Jan 2025) by Claudia Timmreck

RR by Anonymous Referee #2 (30 Jan 2025)

Suggestions for revision or reasons for rejection

First of all, I appreciate the authors’ great efforts to address the concerns I raised. The manuscript has greatly improved because the authors took the time to clarify the open points with great care. In particular, the new Fig. 1 and the revised Fig. 7 (previously Fig. 6) add a lot of aid for understanding, as well as precision. I now see the merit of the paper more clearly and recommend publication under the condition of addressing a few minor remarks that I still have.

Line numbers refer to the tracked-changes pdf.

Minor

- Fig. 7: As mentioned before, I find this much more convincing now. Still, I wonder how much the relationship would change if the upper left point (CESM2) were left out. Specifically, what are the central values and uncertainty intervals for the upper limit of ECS (assuming inception temperatures of 0 degC and 5 degC, respectively) if this model is discarded? If they change substantially, this would imply that the relationship relies a lot on one model, and then this should be reported in the text. If not, it’s fine.
As a tangent to this: I interpret “whether CESM2.1 is included or not” from l. 143 such that you experimented with including/excluding the single model-family ensemble, but not the simulation that is part of PMIP4 (i.e., the upper left point in Fig. 7). Is that correct? If that is not correct, then ignore my previous remark.

- Methods section: I failed to make this point in the previous review: In the methods section it should be stated in isolation that the emergent constraint is derived from the PMIP4 multi-model ensemble, and how many models this includes. Right now, the fact that PMIP is used only clearly stated in the caption of Fig. 7, and PMIP is mentioned in a side note in the methods section.

- l. 143 – 146: I don’t understand the statement because CESM2 is a *high*-ECS model (and CESM2.1 too, I assume?), so I don’t understand how the fact that the relationship is robust against adding or leaving out CESM2.1 shows “that the *lower*-ECS CESM models are not necessary to preserve the quality of the relationship”.

Very minor

- l. 227: “a temperature of -24 K” is not correct, either temperature anomaly, or degC.
- l. 253-255: grammar error in first half-sentence

Suggestions, but I don’t require these to be addressed:

- in the authors’ response letter, an important point was raised:
“We emphasise that we are constraining the upper bound of ECS here. Much larger values on the upper bound are often given, and with some lines of evidence the upper bound is basically infinite. Therefore, even providing a value of 10 K with uncertainty brings valuable information to the
community effort of constraining ECS.”
I very much agree with this statement and believe that the paper would profit if this statement were included with the same clarity.

l. 138 – 146: The paragraph is now structured in a way that first advocates adding the CESM large ensembles to the PMIP ensemble, and then justifies why they were not added. It could be left out altogether.

Hide

RR by Anonymous Referee #1 (09 Feb 2025)

Suggestions for revision or reasons for rejection

General comments

In their revised article, the authors implemented a range of changes based on the reviewers comments. The most important ones are a more detailed introduction and method section, an additional figure with a helpful schematic, and a range of clarifications in the text. I appreciate these changes, as they improve the clarity of the manuscript to some extent. I also still think that this work is generally interesting and suitable for publication in ESD. However, there are a range of issues that have to be resolved before I can recommend the acceptance of the manuscript, and the full list can be found below. My two remaining major concerns can be summarized as the following:

1. There is still a missing link between the presented simulations and how the authors arrive at an "inception temperature" of 0°C. From looking at the figures, one can see how this ROUGHLY matches, but nowhere in the manuscript do the authors present the actually derived values. The text always simply concludes with something like "Therefore this supports an inception temperature close to 0°C". In order to combat this, the authors should clearly indicate in Figs. 4, 6 and A1 the dots from which the inception temperature is derived and present the derived values, e.g. in a table. Furthermore, the 50ppm run should be added in Fig. 4, to actually show how this run shows "instability" around 0°C.

There are a range of further issues related to this. The main one being that the actual uncertainty around the inception temperature is not communicated well enough, e.g. in the abstract, which still does not include the uncertainty in the presented range for the ECS upper limit, or e.g. in the new schematic figure, which makes a strong statement that the "True" inception point is exactly at 0°C. It feels a bit like the authors try to downplay the uncertainty around the limit on the upper bound of climate sensitivity, which I do not think is necessary. As the authors point out in their response to reviewers comments, any constraint is helpful for the scientific community, even if there is quite some uncertainty. I think a proper representation of the uncertainty around the constraint would actually improve the impact of this work, as it puts the estimate one a more sound basis.

2. The general scientific quality of the written text is sometimes low. At several occasions the formulations are missing precision, which is fundamental in a scientific publication. Some arguments are not well founded. There are several sentences with a weak use of the English language, which sometimes make it hard to understand what is meant. I list most of them in the specific comments below, which is hopefully helpful to combat this issue. Lastly, including a clearly defined conclusion section would improve the quality of the manuscript in my eyes.

To conclude, this is an interesting work, which simply needs some more effort to bring it into a shape that is adequate for publication in ESD.

Specific comments

- Abstract l. 10: Please specify "... approximately zero degree Celsius in MPI-ESM1.2 and CESM,...".

- Abstract l. 13: The authors still do not account for the uncertainty in the inception point temperature in their main estimate of the upper bound of ECS. This has to enter somehow. Please, at least add one more sentence about the limitation and indicate that the range could be different when using another inception temperature.

- Introduction: Please add the main motivation behind constraining the upper bound of ECS here. This was written in the response to reviewers only, which I found quite useful (see below). Then, please add references to the statements made in the response.
"We emphasise that we are constraining the upper bound of ECS here, not the best estimate value, which is necessarily lower. Much larger values on the upper bound are often given, and with some lines of evidence the upper bound is basically infinite. Therefore, even providing a value of 10 K brings valuable information to the community wide effort of constraining ECS."

- l.70: You can add you argument here (or already in the introduction), that this is necessary because not all modelling centers share their failed LGM experiments. This would give a nice justification for your claim at the end of the manuscript.

- Table 1 and text: The name "abrupt50ppm" stands in contrast to the other runs called e.g. "1/8xCO2". But actually all runs use an abrupt change in CO2 at the start of the simulation, if I understand correctly. I would suggest to remove the "abrupt" from the simulation name, as otherwise the reader is misled to believe that a different procedure was taken in this run.

- Figure 1: I like this schematic, but please indicate that there is uncertainty in the "True point of snowball Earth inception", for example as a note in the figure caption. Currently, the schematic makes a very strong statement that 0°C is the one and only ("True") snowball Earth inception point, which is misleading.

- l. 98-99: The formulation of this sentence is a bit unclear. As I do not see the added value of this sentence, I would suggest to remove it.

- l. 100 - 105: The fact that you get a different inception point in different runs, tells us that there is quite some uncertainty. You then go on to say that, therefore, you need additional experiments. But this still doesn't help the reader to understand HOW you used those additional runs. Right now, to me it seems that you have just taken the inception point of the run with the slowest transition to a snowball Earth. Which is okay, it just has to be clarified, and the remaining uncertainty has to be discussed.
You could simply continue this paragraph with a few more sentences here. Which requires further clarification, is that the new schematic in Fig. 1 hints to an approach, where the authors fitted a line through the points of lowest feedback and then calculate where that line crosses 0. I don't think this is what is done. Again, this is just an issue of missing detail on how the overall inception temperature of the model is derived from all of the runs.

- l. 142-143: This statement is only true for a slight range between -5 and -10 K temperature anomaly, so this condition must also be written in the text. I assume you want to highlight that the maximum (positive) values for the cloud feedback are achieved for the strongest forcings. So please be precise.

- l. 148: The surface albedo feedback "starts to exceed" the combined other feedbacks at -15 to -20 K. If you only write "exceeds", it sounds like this only true during that temperature range. But it actually starts at these temperatures and becomes even stronger at colder temperatures.

- Fig. 4: The table here shows the years of the first instability. I don't know why, as this year is never again referred to in the text. It would be much more interesting to show the inception temperature you calculate from each of the runs in this table.

- l. 172: The authors write that the "temperature at which the climate transits towards a snowball Earth state is broadly similar across the different CO2 forcing", but they never actually show these temperatures anywhere, and from Fig. 4 it seems like there is a spread of at least 10 K among the runs. Again, simply showing the numbers for each of the run would be helpful for the argument.

- l. 180: I agree with one of the other reviewers that the geometric argument is very hand-wavy. Furthermore, this line of argument presumes that the snowball Earth instability would be reached when the sea-ice edge enters the sub-tropics in every model (and the real world). As this is not proven here (in other models the instability could be reached earlier or later), the line of argument is flawed and I would suggest to remove this sentence.

- l. 183ff: I would still suggest that the final global mean temperature of the 50 ppm run is very close to the inception temperature that the authors are looking for. Indeed, it is stated that the run shows signs of instability around 0°C of global mean temperature. But this is not shown anywhere, and just stated in the text so the reader simply has to believe what the authors say. This has to be shown! I also do not understand, why the 50 ppm run is not included in Fig. 4, as it would be very helpful. The 50 ppm run together with the 1/8xCO2 run are probably the most insightful runs, when it comes to defining the inception temperature.

- l. 183: the authors responded to my and one of the other authors previous comment that 50 ppm is rather 1/6 of pre-industrial CO2 and not 1/4, by saying that they choose to stick with 1/4, because it fits better with their other runs. This is not a "choice" the authors can make! 50/284 = 0.176, which is roughly 1/6 and only 70% of what is actually 1/4 of pre-industrial CO2. Given the logarithmic nature of CO2, this is not an insignificant difference. The authors should not defy the actual numbers, just because it fits better into the list of other runs, especially since there seems to be no other real reason for doing that.

-l. 199-200: Does this mean that you take the value for the slowest run that transitions to a snowball Earth? And what exactly is this value? Again, "close to 0°" is not precise. Please provide the actual number that was used as the transition temperature. And if the authors simply used zero instead of deriving the number from their runs, then this should also be clarified.

- Fig. 6: The authors responded to my previous comment on Fig. 5 ("How does Fig. 5 show that the instability is around 0°C?) that they added an explanation on how to read a Gregory plot in the Method section. This was not the point of the comment. The authors should ideally add a graphical derivation of the inception point for these simulations. In their response they write that it is approximately -5°C in Fig. 6, but in line 209, they write that it is at -24 K, which translates to approximately -10°C. So what is true? From looking at Fig. 6, it seems the latter is the correct number. Again, my main concern is the missing scientific clarity and detail in explaining and showing how these numbers are derived.

- l.209: Please specify in the text how exactly you go from -24 K to -14 K (or from -10°C to 0°C) for deriving the actual inception temperature in CESM1.2. This will let the reader get a better chance in building their own opinion on how reliable this estimate is. Please also discuss the uncertainty in this approach in more detail! CESM is not MPIESM, and it is not at all given that the instability temperature would progress to higher values in exactly the same way as it does for MPIESM.

- l. 221: "close to" or actually 0°C? Why not be precise? You must have used a specific value.

- l. 228: The formulation is not accurate. You do not "apply an uncertainty", but rather test the outcome of using another value for the inception temperature.

- l. 229-231: I do not agree that this is a modest change, especially since you only tested one additional value. Furthermore, even in this example the difference is quite significant, as the lower bound of the 90% confidence interval for -5°C as inception temperature (4.7 K) is much less critical for CMIP6 models than the default lower bound (3.9 K). As written above, this uncertainty has to also enter the abstract, as this is probably the main outcome that readers will take away from this work.

- I agree with one of the other reviewers that there should be a conclusion section. Especially since the last section also still includes some results. There is a lot of value in the standard structure of a scientific paper, and I think that also here it would be useful to summarize and conclude in a separate section.

- General: Please consistently use either "inception temperature" or "transition temperature". Otherwise this will only confuse the reader. Ideally, also describe how this relates to the "temperature of instability".

l. 379-381: Should also include what greenhouse gas concentrations are used in Voigt et al. (2011), I think they used pre-industrial values.

Technical corrections

- l. 9: remove "Regardless"; comma after "slowly"; "transition appears"
- l. 100: remove "Unfortunately"
- l. 102: remove "kind of"
- l. 137: "break down"
- l. 138 and at other locations: "..anomalies to pre-industrial" is poor use of the English language. I know it requires more words each time, but correct would be e.g. "We report anomalies of the global mean temperature compared to pre-industrial values in units of K." Or "We report global mean temperature anomalies with respect to the pre-industrial value in units of K."
- l. 130 "considered to be the main driver"
- l. 151: "diagnostic ... is" or "diagnostics ... are"
- l. 168: "Whereas" -> "While"
- l. 177-180: Sentence very long and hard to understand. Please rewrite.
- l. 189: time-dependent
- l. 190: " we believe to be due to the..." -> "we speculate/hypothesize that this is due to the".
- l. 195: "... shown in Appendix ..."
- l. 198: "hardly" -> "not"
- l. 210-211: Sentence poorly formulated
- l. 233: "This" -> "The"
- l. 235: remove "to"
- l. 250: Remove "model". This was raised already in my previous review.
- Fig. A1.: The second sentence in the caption is poorly formulated.

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RR by Anonymous Referee #3 (11 Feb 2025)

Suggestions for revision or reasons for rejection

I appreciate the response to my review and the systematic alteration of the manuscripts text and figures. I feel the authors have addressed my main concern that questioned the insight that can be attained from modelling a snowball earth state that did not happen - by demonstrating awareness of this to the reader and describing how this work provides an upper bound to ECS. With the additional text and figures I feel also that the manuscript provides insight into snowball earth dynamics. Note Line numbers refer to the manuscript with tracked changes.

I would omit the phrase “And as it happens” from the start of this sentence at L183. Similarly, L245 avoid starting a sentence with the word “Because”. L251 rephrase the start of this sentence “ This here proposed approach” possibly to “The described approach to provide an upper bound…”

When referring to anomalies, where the authors use temperatures in K, I am uncomfortable with statements in which temperatures are reported with negative temperatures (in units of Kelvin) without reference to the temperature being an anomaly relative to pre-industrial, e.g., L227 “.. which at 1/128x CO2 is around a temperature of -24K.”. Wherever the author presents a negative temperature & Kelvin unit please insert the word “anomaly” or words to that effect, e.g., L227 “.. which at 1/128x CO2 is around a temperature anomaly of -24K.”. Address also L168 and L173. Personally, I would use the same temperature unit throughout and rely upon appropriate text to notify the reader that an anomaly is being presented.

Please also clarify if the land surface is held fixed in these experiments or if a dynamic vegetation model is used. I ask as the authors use an ESM (GCM with additional earth system components ) and they acknowledge that ECS includes changes in atmosphere, ocean, and vegetation. Mauritsen et al., 2019, which they cite for model description, states that MPI-ESM1.2-LR (and I assume -CR) has a dynamically computed vegetation distribution. If vegetation is held fixed then this could be corrected at L71 , for example “Continental configuration, land surface, non-CO2 greenhouse gasses and orbital configurations are held fixed as in PI or LGM”. If a dynamic vegetation model is implemented what extent is this coupled with an interactive carbon cycle (one-way coupling?) and what happens to the vegetated part of the land surface in these simulations? (interesting to think what would happen to plant photosynthesis and leaf water vapor conductance at low CO2 values) – could this cause the ESM to fail? If the land surface is held fixed then this needs to be specified as it would be useful for other modelling groups that would like to follow up on this work.

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ED: Reconsider after major revisions (25 Feb 2025) by Claudia Timmreck

AR by Martin Renoult on behalf of the Authors (07 Apr 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (10 Apr 2025) by Claudia Timmreck

RR by Anonymous Referee #2 (11 Apr 2025)

Suggestions for revision or reasons for rejection

Complete Report in attached pdf.

The point cloud in Fig. 7 without the CESM model looks so scattered to me, that I decided to read out the data with an online tool (plotdigitizer.com) and perform the regression myself. When excluding the upper left point in Fig. 7 I find an r-value of only 0.12, and a p-value of 0.74, contradicting the authors’ claim that the relationship is statistically significant without including the outlier model. From this quick analysis, I infer that LGM TS and ECS are uncorrelated or only very weakly correlated among models when excluding the CESM model, in contrast to what the authors asserted. Only when including the CESM model does the relationship pass basic tests of significance (r=-0.76, and p=0.01). Furthermore, the slope changes drastically when including (slope=-0.29 K/K) vs. excluding (slope=-0.05) the outlier. Finally, the data seems to be different from what is shown in Fig. 13 of Renoult et al. 2023, where the statistically significant relationship in PMIP4 is obvious to me.

I attach my code and screenshots of how I picked out the data so that the authors can reproduce what I did. I would like to ask from the authors to point out where I am wrong (e.g., by sharing code), and how they come to the conclusion that the relationship between LGM TS and ECS is significant, “not sensitive to the inclusion of CESM2”, and that “the inclusion (or non-inclusion) or CESM2 and/or the CESM model family leads to the same slope and intercept for the emergent constraint relationship”, beyond a reference to Renoult et al. 2023.

The remaining points of mine were addressed in a way that I am satisfied with.

I included my code and some more information on how I obtained the data in the more complete pdf report that is attached (unfortunately the EGU system does not allow for non-pdf attachments).

Referee Report: PDF

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RR by Anonymous Referee #1 (16 Apr 2025)

Suggestions for revision or reasons for rejection

I am content with the modfications made by the authors and suggest that the manuscript can be accepted after some minor issues are resolved. Below I provide a short response to some of the authors' replies ("general comments") and the two modifications that I think are necessary before acceptance ("specific comments").

General comments

- I admit that saying that the drift in inception temperature for the different simulations is the source of uncertainty was misformulated. What I had in mind was rather the uncertainty in the inception temperature of each simulation, i.e. the curves being pretty flat around the minimum forcing point. Furthermore, more uncertainty is coming from the method how the snowball inception temperature of "close to 0°C" was derived from this and, more importantly, that this is probably model dependent. That said, I appreciate the clarifications added to the manuscript.

- The reason why I suggested that the 50ppm run together with the 1/8xCO2 run are the most insightful runs is the following: The "true" inception temperature of this model must be somewhere between the inception temperature derived from the 1/8xCO2 run and the final equilibrium temperature in the 50 ppm run. That is, these two temperatures set the upper and lower bound for the inception temperature of the model. Therefore, I think that taking the mid point of these two temperatures is potentially a better estimate of the model's inception temperature than simply taking the derived inception temperature of the 50ppm run. From Fig. 4A) it seems like that would give an inception temperature of around 1°C, assuming that the value of -14.7°C temperature change translates to -0.3°C in absolute temperature. My recommendation would be to add this information in a sentence, but since I haven't made this clearer in my earlier reviews, I will not insist.

Specific comments

- The inception temperature anomaly of -14.7 K compared to PI would translate to an absolute inception temperature of -1.05°C, when taking a standard PI temperature of 13.65°C. How do the authors arrive at the -0.3°C value mentioned in their response? Is it because the PI of MPI-ESM1.2 has a warmer PI mean temperature (i.e. 14.4°C)? Please clarify in the manuscript. It is fine to stick with "close to 0°C " for the rest of the manuscript, but I believe the actual numbers should be clarified at least once. This would also give a better reference for other modelling center that might try to reproduce the runs.

- Table 1: The added column for the inception temperature has values given as anomalies with respect to pre-industrial conditions, but neither the column header, nor the table caption specify this, making it seem like these are absolute temperatures. This is especially confusing, as later in the text and e.g. in Fig.1 the inception temperature is not referred to as an anomaly, but as an absolute temperature. Please make it clear in this table that this is a temperature anomaly, or (even better) give the values in absolute temperatures here as well

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ED: Reconsider after major revisions (24 Apr 2025) by Claudia Timmreck

AR by Martin Renoult on behalf of the Authors (02 Jun 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (10 Jun 2025) by Claudia Timmreck

RR by Anonymous Referee #2 (11 Jun 2025)

Suggestions for revision or reasons for rejection

I suggest to reject the paper for two reasons, each of which alone is sufficient for rejection.

First, the scientific essence of the paper relies on the emergent constraint established in Fig. 7. I have come to the conclusion that there is no linear relationship between LGM TS anomaly and ECS across models unless either CESM2 or the other CESM models are added (for further details see my last review comments). It is not scientifically sound to claim a robust relationship when in fact all of it stems from one model (family). I have given the authors ample opportunity to convince me of the opposite, but they have not. I have received a lot of comments about different PMIP generations, differences between global and tropical SST, and more. What remains is the fact that Fig. 7 shows a linear relationship, which entirely falls apart as soon as the upper left point is left out. The authors’ main argument to refute this is that one could replace the CESM2 point by other points from the CESM family, which however does not change the fact that the relationship rests on one model (family). As a side note to this: I reject the notion raised in the authors’ last response that “the method is not invalid”. Of course, the method of emergent constraints is not invalid in general. But it is invalid in this particular application because there is no sufficiently robust inter-model relationship.

Secondly, on a higher level, I find the authors’ response to my comments unsatisfactory. To make my point clear, this is the question I asked in the second round of revision: “I wonder how much the relationship would change if the upper left point (CESM2) were left out. Specifically, what are the central values and uncertainty intervals for the upper limit of ECS (assuming inception temperatures of 0 degC and 5 degC, respectively) if this model is discarded?” This question has a very clear answer that the authors could have provided by repeating an analysis with just one data point less, a task I later completed with minimal effort. Instead, I received a long answer asserting that “The relationship is not sensitive to the inclusion of CESM2” and that “the inclusion (or non-inclusion) of CESM2 and/or the CESM model family leads to the same slope and intercept for the emergent constraint relationship”. I then showed both of these statements to be false. Excluding CESM2 and the CESM model family does lead to a different slope and intercept. I want to stress that this was not a side point, but the core of my very specific question. When I reiterated this point, the authors responded in the third round by stating that they “wished to describe that CESM2 and the CESM-family ensemble are exchangeable, meaning the relationship is significant as long as one of the two is present”. This response appears inconsistent with their previous statements, which suggested otherwise. I am concerned about the shifting nature of the responses. In particular, had I not questioned the statements made in the second round of the revision and simply accepted the authors’ assertions, the problem I raised in the first paragraph of this review would have remained unnoticed.

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RR by Anonymous Referee #1 (16 Jun 2025)

RR by Maria Rugenstein (27 Oct 2025)

Suggestions for revision or reasons for rejection

I was asked to look over the reasoning for reviewer #2 to reject the paper. They raise two arguments: 1) the constraint in Fig.6 (former Fig. 7) is not robust and 2) the answers to the issues brought up before are not satisfactory.

I do not think the paper has to be rejected because of the potential non-robustness of Fig.6, as the rest of the paper seems valid and adds to an understudied problem and presents the findings well. Even if the relationship in Fig.6 was not robust, laying out the reasoning of the transition temperature being able to constrain ECS is worthwhile and the recipe the authors provided, might motivate some modeling centers to invest into paleo or LGM simulations in general. It’s not the authors’ fault that not many climate models take part in the LGM experiments and many paleo studies rely on relationships between even fewer models and even relying on outliers from one model family is (unfortunately) common for emergent constraints.

However, the reviewer has a point in that this needs to be discussed more clearly. Currently, around line 75 there is a tight mentioning on the subject of “model families” and Fig.6 is also barely explained. I suggest to add *one paragraph* around Fig. 6 (on page 9, 10 or 11) which states a) the issue of having only few simulations available, as is already mentioned in paragraph 165, b) the regression slope sensitivity to the CESM model family and other models, *quantitatively*, as reviewer #2 demands; leave-one-out seems meaningful to me.

Even if these changes are really minor (one paragraph, all content is there, the sensitivity/robustness analyses will take 30min), I would demand major and mandatory revisions if I was the editor. This is to address reviewer #2’s point that responses should be taken very seriously to honor the reviewers' effort going into this, which is a huge service. The whole wait and discussion here could have been easily avoided by more carefully responding to the issues in the first round or two and the paper and readers will profit from this.

I hope I followed the different versions correctly and didn’t miss anything, as the several rounds of reviews were indeed a little confusing. Maria Rugenstein

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ED: Reconsider after major revisions (28 Oct 2025) by Claudia Timmreck

AR by Martin Renoult on behalf of the Authors (19 Dec 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (07 Jan 2026) by Claudia Timmreck

ED: Publish as is (21 Feb 2026) by Claudia Timmreck

AR by Martin Renoult on behalf of the Authors (24 Feb 2026) Manuscript

Journal article(s) based on this preprint

17 Mar 2026

Snowball Earth transitions from Last Glacial Maximum conditions provide an independent upper limit on Earth's climate sensitivity

Martin Renoult, Navjit Sagoo, Johannes Hörner, and Thorsten Mauritsen

Earth Syst. Dynam., 17, 303–318, https://doi.org/10.5194/esd-17-303-2026,https://doi.org/10.5194/esd-17-303-2026, 2026

Short summary

Martin Renoult, Navjit Sagoo, Johannes Hörner, and Thorsten Mauritsen

Data sets

Simulation outputs for the manuscript "Snowball Earth transitions from Last Glacial Maximum conditions provide an independent upper limit on Earth's climate sensitivity" Martin Renoult https://doi.org/10.5281/zenodo.8117483

Martin Renoult, Navjit Sagoo, Johannes Hörner, and Thorsten Mauritsen

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Geological evidence indicate persistent tropical sea-ice cover in the deep past, often called Snowball Earth. Using a climate model, we show here that clouds substantially cool down the tropics and facilitate the advance of sea-ice into lower latitudes. We identify a critical threshold temperature of 0 °C from where cooling down the Earth is accelerated. This value can be used as a constraint on Earth's sensitivity to CO₂, as recent cold paleoclimates never entered Snowball Earth.


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