Review of “Stabilizing feedbacks allow for multiple states of the Greenland Ice Sheet in a fully coupled Earth System Model” by M. Andernach et al.

This manuscript investigates the potential multi-stability of the Greenland Ice Sheet (GrIS) using a fully coupled climate–ice sheet model under pre-industrial climate conditions. The existence of multiple steady states of the GrIS is not new, but this study provides a fresh and valuable contribution by employing a fully coupled model configuration and identifying four distinct equilibrium states at approximately 100%, 48%, 28%, and 19% of the pre-industrial ice volume.

The paper is well written, clearly structured, and scientifically solid. It is thoroughly embedded in the existing literature and successfully highlights both the consistency with, and the departures from, earlier work. The study thus adds important nuance to our understanding of Greenland Ice Sheet stability and the role of climate–ice sheet feedbacks.

I recommend acceptance with minor revisions. The manuscript is already strong, and the suggestions below are primarily aimed at clarification, readability, and strengthening the framing around stabilizing feedbacks.

## General Comment ##

Focus on stabilizing feedbacks and suggested summary table: The title emphasizes stabilizing feedbacks as key mechanisms allowing for multiple steady states. Given this framing, the paper would benefit from a clearer and more systematic presentation of which feedbacks dominate and how they differ among the identified equilibria.

I suggest including a summary table (e.g. in Section 4) listing the four steady states and the corresponding stabilizing feedbacks that maintain each. If the same mechanisms apply across all states, this could be explicitly stated. Such a synthesis would align the manuscript with its title and improve clarity for readers.

## Specific Comments ##

L7–8: “These steady states are stabilized through several feedback processes, such as the melt-elevation and melt-albedo feedback.”

Please clarify whether the melt–elevation and melt–albedo feedbacks are indeed stabilizing. These processes are usually considered positive feedbacks (destabilizing). Are they stabilizing only in certain states, depending on basin of attraction? A brief explanation of when and how their sign changes would be useful.

L12: “highlight the importance of climate–ice sheet feedbacks”

Consider adding “fully coupled”, as this aspect is a major strength of the study.

L61–69: You mention stabilizing feedbacks via isostatic adjustment and freshwater release into the North Atlantic. Could you clarify whether these are active in your simulations and, if so, whether they appear among the feedbacks constraining your steady states? If they are not significant here, a short note acknowledging that would be helpful.

L85–86: You talk of previous studies neglecting interactions with components such as the AMOC, vegetation, and isostatic adjustment. Since these interactions were previously neglected, it would strengthen the discussion (in Section 4 and perhaps already here) to comment briefly on whether they are important in your results—e.g., does the AMOC play a stabilizing or destabilizing role for any of the steady states?

L95–96: “we identify which feedbacks or combination of feedbacks constrain each steady state of the GrIS.” This is central to your paper’s theme but remains somewhat implicit. A concise table summarizing which feedbacks constrain which state would help make this claim more concrete.

L127: “the asynchronous coupling method has no impact on the results.” This phrasing feels too strong. Consider softening it to something like “We find no significant impact on the results or conclusions from the asynchronous coupling method.”

L129–150 This paragraph is long and dense. Consider splitting it into smaller paragraphs to improve readability.

L130 “five simulations starting from different GrIS volumes (0%, 21%, 43%, 70%, and 100% of the PI value; Tab. 1).” The list of initial conditions does not match Table 1 (which lists 0%, 33%, 70%, 100%). This creates confusion. Either align the lists or move the table reference to where the consistent set appears.

L200–201: “the dynamic growth of grass and shrubs in the unglaciated areas, which leads to strongly positive melt-albedo feedback.” Please clarify whether vegetation expansion is itself what you refer to as the melt-albedo feedback. Typically, the melt-albedo feedback refers to darkening of snow/ice by melt rather than vegetation. If the vegetation effect is distinct, please rephrase accordingly.

L242–243: When describing how the _SG state becomes unstable and transitions to the M_G state (paraphrasing: Above a certain threshold it becomes unstable), consider mentioning which physical processes cause this instability.

L290: You mention “the inertia of the ice sheet.” Please clarify what is meant by “inertia.” In a physical sense, ice sheets have relatively slow response times but limited true dynamical inertia; a short explanation would avoid confusion.

L342: “Below 70–68%, even further parts of the GrIS are lost”. It is unclear where these threshold numbers (70 – 68%) come from. Please specify.

## Editorial and Typographical Comments ##

L193: Suggest to revise to: “Only in the mountains are temperatures cold enough…”

L263–264: Revise to: “does an ice cover in the northwest become stable”

L273:“disintegrates” (add final s)

Review of Andernach et al. 2025

In this paper, Andernach et al. explore with an advanced fully coupled model potential multistable states of the Greenland Ice Sheet. The authors find four ice sheet steady states under pre-industrial greenhouse gas forcing, and illustrate ice-climate feedbacks and climate processes responsible for ice sheet regrowth or failure to regrow. Andernach et al. also illustrate that including an active Antarctic Ice Sheet in their model has an impact on the timing and magnitude of Greenland changes.

This paper represents a very nice contribution to the modelling community, particularly for those involved in coupled Earth system/ice sheet modelling efforts, and it’s a great fit for The Cryosphere. I surely recommend publication, after some (minor) comments are dealt with. I have two general comments regarding the way methodology and results are presented, which I hope the authors will find useful. More detailed specific comments follow, suggesting changes that I hope will improve readability and clearness.

General comments

1. I think that the section where ice sheet climate feedbacks are introduced is a bit hard to follow, and the paper would benefit from a more organized structure - perhaps where (a) first, all positive and negative feedback are introduced, and (b) then, the main studies illustrating the impact of these feedbacks are cited. Finally, it would be good to state clearly which processes and feedbacks are accounted for in your studies.
2. You mention that your model is coupled with a solid Earth model (VILMA), but there is no mention of how this coupling is affecting the results of your simulations. Maybe there is no large impact compared to other ice-climate feedback and processes, but it would be good to have some text dedicated to that. Similar for the vegetation - it would be very interesting to learn what’s happening in ice-free Greenland, especially in regions where the ice sheet can’t regrow.

Specific comments

Abstract

L2-3: I think the introduction should introduce the concept of multistability - maybe emphasizing that studies suggesting the existence of abrupt thresholds an no multistability often neglect important feedbacks (in contrast with Gregory et al. 2020).

L4: Maybe mention explicitly that your model includes active GrIS and AIS?

L4-5: Maybe provide some examples of what these feedbacks are?

L6: Not sure it is immediate for the reader what the GrIS PI state is... you mean an ice sheet state similar to a present-day state with PI climate?

Introduction

L23: When you mention sea level, I would also include a reference to the latest ISMIP paper for Greenland, Goelzer et al. 2020.

L25: Some more recent papers simulating GrIS tipping point are Bochow et al. 2023 and Petrini et al. 2025. Might be worth mentioning those.

L26-29: For clarity I would mention immediately that your ice sheet model coupling is bi-polar (also, it is a pretty cool feature!). Something like ‘...coupled to an ice sheet model (ISM) over Greenland and Antarctic domains...’. Also, I think you should mention here which are the models you are using.

L32: As in the abstract: I think it would be good to clearly introduce the concept of multistability (hence monostability) before the first mention.

L35-36: Perhaps it would be good to quickly mention the complexity/resolution of GCM used in these studies.

L42-48: You don’t mention the melt-albedo feedback here, and it’s is a bit strange, since you mention it in the abstract. Also, might be worth mentioning precipitation changes due to orographic changes (see General comment 1).

L52: Missing 'side’? 

L63: Maybe important to mention that glacial rebound operates on millennial timescales , as opposed to some of the ice-climate feedbacks mentioned above (see also Petrini et al. 2025).

L64: Is instead of has? Or perhaps I am not understanding the phrasing.

L72-75: The sentence about ice sheet-ocean feedback in Antarctica feels a bit off-topic (and overly simplified) at this point, perhaps there is no need to mention it?

L88: ...one study of the stability of the GrIS exists that accounts accounts... . Also, I think that you should mention that the resolution of the model used in Vizcaino et al. 2008 is quite coarse.

Methods

L104: Maybe add ‘with a non-evolving Antarctic ice sheet’.

L113: ...was is calculated during runtime... I think that you should also add more detalils on how the SMB is downscaled in your model, considering that there is a large gap between atmospheric resolution (3deg) and ice sheet model resolution (10 km).

L124: What happens with the freshwater fluxes at the end of the 100 years-long ISM cycle? Is the ocean receiving an averaged amount or an integrated amount of freshwater fluxes?

L130: Again, how the PI value for GrIS volume and extent compares to the present-day value? Or PI = PD? Same for AIS at L134.

L140: Are you isostatically adjusting the bedrock also for intermediate volumes?

L141: It’s not clear how you obtained intermediate initial GrIS volumes: aren’t all the simulations using constant PI GHGs concentration? Did you run your model at different CO2 concentrations to get the different initial states? For how long?  

L149: I suggest to mention that S_G means small Greenland and XS_G means very small Greenland, in the same way M_G and L_G stand for medium and  large Greenland. I see you do it at the beginning of subsection 3.1, but good to have it here too I think.

Results

L166: Missing m before SLE.

Fig.1: Based on the ice extent in L_g, it looks like there are several locations where Greenland is in contact with the ocean. It should be quickly clarified in the methodology section how marine-based ice is treated in Greenland and Antarctica.

L174: Isn’t the temperature shown in Fig. 3a and 3e DJF and JJA, respectively?

L175-176: If the section is about Results only, it feels somehow strange to see results from other studies. A sentence like ‘The high orography blocks synoptic storm systems approaching Greenland from the west (Andernach et al., 2025; Dethloff et al., 2004).’ belongs perhaps more to section 4 Summary and Discussion? It may be personal preference though. If you want to present results and discuss them immediately, maybe better to have section 3 Results and Discussion and section 4 Summary?  

L182-185: I would reference Figures to support these statements.

L196: Can you try to quantify this lapse rate effect?

Fig. 4: Would it be possible to zoom a bit more the figure around Greenland like in Figure 3?

L237: Not sure about the use of ‘reminiscent’ here.

L251-252: This reminds me of what happens in Petrini et al. 2025 (although with shorter timescales of 20,000-30,000 years), where central west margin remains stable for about 20,000 years and then enters self-sustained retreat all the way to the east. See Fig. 2, simulation +3.4 K. This is interesting as simulations in Petrini et al. 2025 include melt-elevation feedback only, as there is no climate coupling.

L276: Please include in the manuscript how you deal with ice-ocean interactions; I understand this is described elsewhere, but I think a paper should provide the essential information to the reader to be able to understand methodology and results.

L281: I understand that the paper is about Greenland, but some more information or figures about the processes leading to WAIS collapse would be useful.

L285: at ~3-degree resolution, is the ocean model ‘seeing’ that?

L299: same comment as before about Results/Discussions.

Summary & Discussion

L349: I am not sure about the relevance of this sentence, as the paper here explores very idealized scenarios and very long timescales.

L350: Are you referring here to model uncertainty?

L364-366: I would remove ‘including climate-ice sheet feedback’ to improve readability, I think it’s clear at this point in the manuscript that your simulations are doing that.

L371: While I can intuitively understand what the authors mean with ‘topographic pinning point’, it may be necessary to give a clearer explanation to facilitate the reader.

Conclusion

L424: Maybe add main drivers of this multistability?

L427: This sentence is a bit vague; of course, it is important to include all feedbacks, but can you mention which are the most important in your simulations?

References

Goelzer, H., Nowicki, S., Payne, A., Larour, E., Seroussi, H., Lipscomb, W. H., Gregory, J., Abe-Ouchi, A., Shepherd, A., Simon, E., Agosta, C., Alexander, P., Aschwanden, A., Barthel, A., Calov, R., Chambers, C., Choi, Y., Cuzzone, J., Dumas, C., Edwards, T., Felikson, D., Fettweis, X., Golledge, N. R., Greve, R., Humbert, A., Huybrechts, P., Le clec'h, S., Lee, V., Leguy, G., Little, C., Lowry, D. P., Morlighem, M., Nias, I., Quiquet, A., Rückamp, M., Schlegel, N.-J., Slater, D. A., Smith, R. S., Straneo, F., Tarasov, L., van de Wal, R., and van den Broeke, M.: The future sea-level contribution of the Greenland ice sheet: a multi-model ensemble study of ISMIP6, The Cryosphere, 14, 3071–3096, https://doi.org/10.5194/tc-14-3071-2020, 2020

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

Petrini, M., Scherrenberg, M. D. W., Muntjewerf, L., Vizcaino, M., Sellevold, R., Leguy, G. R., Lipscomb, W. H., and Goelzer, H.: A topographically controlled tipping point for complete Greenland ice sheet melt, The Cryosphere, 19, 63–81, https://doi.org/10.5194/tc-19-63-2025, 2025.