the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Feb 2026
Highlighting processes underlying the stability and hysteresis of the Antarctic Ice Sheet
Abstract. Previous studies assessed that the Antarctic Ice Sheet (AIS) is subject to hysteresis, which means that if ice is lost due to an increase of temperature, a comparatively larger decrease is needed to recover the original state. This implies that the ice-sheet volume is multistable with respect to temperature and that ice loss can be abrupt and largely irreversible. This was simulated throughout a variety of modelling setups by using forcing ramps or steps which are prescribed offline. In contrast, the present study relies on an online, adaptive forcing technique in which the temperature anomalies are only increased when the rate of ice volume is below a tolerance that is significantly smaller than the present-day ice volume loss. Thus, previously unidentified bifurcations of the AIS are captured. We herein highlight the processes underlying such bifurcations. First, we show that the marine ice sheet instability (MISI) is an important driver of the numerous self-sustained retreats experienced by the East-Antarctic Subglacial Basins. Second, we highlight that the merger of two ice caps is an important driver of self-sustained regrowth. We refer to this as the perimeter feedback to generalise the interplay between ice-sheet geometry, ice flow, surface mass balance and thermodynamics which was partially described in studies considering the merger/collapse of ice saddles in different glaciological applications. We emphasise, for the first time to our knowledge, that the perimeter feedback applies beyond the case of a saddle merger/collapse and represents an important positive feedback on the mass balance of marine ice sheets, both at retreat and regrowth. Furthermore, by using a glacial isostatic adjustment (GIA) model of intermediate complexity, we highlight that, although GIA locally acts as a negative feedback on ice-sheet dynamics, it crucially eases other positive feedbacks on the continental scale and modulates the ice-ocean interaction. Finally, we show that the magnitude of the hysteresis might be larger than previously assessed in a similar modelling framework. We explain this by the increased sensitivity to the ocean of the present setup, which results from including a more marked nonlinearity of the basal friction law and an enhanced melt at the grounding zone due to tidal water intrusion, as suggested by recent publications.
Competing interests: A.R. is a member of the editorial board of The Cryosphere.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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RC1: 'Comment on egusphere-2025-6566', Anonymous Referee #1, 16 Mar 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-6566/egusphere-2025-6566-RC1-supplement.pdfReplyCitation: https://doi.org/
10.5194/egusphere-2025-6566-RC1 -
RC2: 'Comment on egusphere-2025-6566', Anonymous Referee #2, 20 Mar 2026
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This is a novel and comprehensive study of tipping and hysteresis for the Antarctic Ice Sheet (AIS). The authors introduce a new technique, adaptive quasi-equilibrium forcing (AQEF), which improves on step- and ramp-based methods and is efficient and easy to implement. They show that marine ice sheet instability (MISI) is fundamental to AIS retreat in a warming climate for both the West Antarctic Ice Sheet (WAIS) and (at higher temperatures) the East Antarctic Ice Sheet (EAIS). They also quantify the role of glacial isostatic adjustment (GIA). They find that the ocean is the main driver of retreat for global mean warming up to about 5 K, while the atmosphere dominates for high levels of warming. They show that the EAIS does not have a single bifurcation point, but multiple bifurcations in different basins. Also, they highlight the importance of perimeter feedback, not only for land-based saddles but also for marine-based ice.
The paper is original, well organized, and clearly written. I liked the physical explanations describing the interplay of ice dynamics, geometry, and climate forcing. I also appreciated the discussions of relevance to future sea-level rise. I found AQEM to be an elegant method that could enable other groups to do similar experiments.
My critiques fall into two main categories. First, the paper could be clearer about the differences between equilibrium and transient experiments (with the latter being a closer analog of AIS retreat in the next few centuries. Second, it is unclear to what extent some of the results – including the limited role of atmospheric forcing for lower levels of warming and the long delay in marine-ice formation during regrowth – might depend on model simplifications. The authors discuss the influence of some model choices, such as the basal sliding law and grounding-zone melt parameterization, but they say little about other choices, such as ice-shelf hydrofracture and calving.
Specific suggestions follow, with some minor corrections at the end.
3: When I first read “This was simulated”, I was unclear on whether the reference was to this study or earlier studies. Please reword for clarity (e.g., “Earlier studies have simulation AIS hysteresis through …”)
6: I suggest rewording slightly, e.g. “are only increased when the rate of ice volume loss is below a magnitude significantly smaller than the present-day rate of ice volume loss.”
36: MISI is defined here in terms of retrograde bedrock. Some authors (e.g. Schoof 2007) have described MISI in the context of 1D flow without buttressing from lateral margins or pinning points. There are studies (e.g., Gudmundsson et al. 2012) showing that marine ice sheets on retrograde slopes are not necessarily unstable in two dimensions. Please say a few words about this.
Also, I suggest adding that MISI can also play a role in EAIS retreat. The next paragraph refers to two studies identifying melt–elevation feedback as the main driver of EAIS mass loss, but ice dynamics and ice–ocean interactions are also important for the EAIS.
56: This is a good explanation of the drawbacks of step and ramp experiments. I suggest stating explicitly in the first sentence what quantities are typically stepped or ramped: T_atm, T_ocn, CO2, etc.
72: This and the following paragraphs briefly describe the model setup and parameterizations. I realize that you don’t want to get bogged down in technical details. However, some of the details are pertinent to later results and should be stated explicitly, perhaps in appendices so as not to break the flow of the text. Here are several examples:
- The calving parameterization is described in one short sentence with a reference to Lipscomb et al. (2019). That paper simulates calving for Greenland, which is very different from Antarctica. Please describe the calving algorithm and calving law used in your simulations. (The CalvingMIP wiki has a good discussion of the distinction between laws and algorithms.) I am surprised that a simple stress-based parameterization in a coarse-resolution model can reproduce observed AIS calving fronts, as suggested by Fig. A2. Were any masks used to fit the observed present-day calving margin? How do ice shelves evolve under warming? Does the calving rate increase as the ice thins, or does the calving front retreat only when the surface or basal mass balance is sufficient to melt the column from the top or bottom?
- Is there any treatment of lateral melting at grounded marine termini?
- The FastIsostasy model is said to account for sea-surface changes resulting from gravitational anomalies. Were gravitational effects included in any of the experiments? The later sections refer to isostatic rebound but not gravitational changes.
- The effective pressure N is based on a local basal till model. What is the value of the parameter delta, which determines the minimum N as a fraction of overburden? Similarly, what is the range of cb values? It might be worth mentioning that the inferred taub is probably too large for the Siple coast, leading to a thick bias as shown in Fig. A2. Also, I would be curious to know what fraction of the bed is thawed at the end of the spin-up; this could be illustrated with a plot.
- How is the basal geothermal heat flux determined?
- Which datasets provide the thickness and velocity targets for the inversion? Is the spun-up state (mostly) free of drift?
- Why was hydrofracture not considered as a possible source of shelf breakup under atmospheric warming?
120: Please briefly describe the PDD method. How well does the resulting SMB agree with the RACMO-simulated SMB?
124: When using the Jourdain et al. (2020) dataset and the Favier et al. (2019) non-local quadratic law, did you do any tuning, either basin-scale or local? For instance, did you adjust values of K or deltaT in Eq. (1) of Jourdain et al. (2019)? Tuning is often necessary to get a good match to the observed grounding line.
Table 1: If the GIA model includes ice sheet self-gravity, please indicate how this is handled for UPL and DPR.
126: When running the REF experiment using AQEF, how many model years elapse during the bifurcation periods with fixed forcing, as compared to the periods with slow, steady warming? It would be informative to add a table showing the number of model years elapsed during each of the major bifurcation periods. This would show whether MISI events tend to be of similar duration, or if some are much longer than others.
141: I would suggest dividing the current Section 3 into Sections 3, 4 and 5 corresponding to the current 3.1, 3.2 and 3.3.
Figure 1: I suggest rewording the second sentence of the caption to something like “The coloured curves ATM, OCN and DPR show the equilibrium retreat when oceanic warming, atmospheric warming and GIA are deactivated, respectively.” On the first reading, I wasn’t sure whether OCN referred to ocean on or ocean off.
152: The text refers to a phase of “relatively small sensitivity” to warming. I suggest writing this as “relatively small equilibrium sensitivity” and adding a caution that equilibrium sensitivity doesn’t necessarily correlate with transient sensitivity.
161: This is an important point about fragmented tipping, which I wish were more widely recognized.
179: “this ungrounding results in the formation of large ice shelves”. Please comment on how the calving scheme determines CF retreat. For example, does the calving front tend to remain in place as the grounding line retreats, allowing the formation of large ice shelves that can provide buttressing?
220: This sentence confused me at first because it uses two separate measures of hysteresis: delta_f for a given V and delta_V for a given f. Later (l. 417), these measures are defined as the hysteresis width and height. It might be helpful to introduce these definitions earlier in the paper.
Figure 4: I don’t see the ATM curve mentioned in the caption. Also, where the caption says “retreat”, should this be “regrowth”?
As mentioned above with respect to the retreat experiment, it would be informative to have a table showing the duration of the bifurcation events in simulated years.
231: This is indeed a major policy challenge. Again, it would be helpful to know the simulated collapse timescales for WAIS and WSB.
243: The failure of the EAIS to advance beyond the coastline between 8 and 3.8K is a striking result. At some point (maybe in the Discussion), please comment on whether you think this is realistic.
Specifically, one might expect that when a reasonably thick grounded ice column (say, 200+ m) reaches the coast, it keeps going. It doesn’t necessarily form a shelf, but it becomes grounded marine-based ice. Since it’s grounded, it doesn’t melt from below, so its advance is limited mainly by calving and lateral melting. Why doesn’t grounded marine ice form earlier in the model?
The answer depends on the model details, but I could suggest one possibility. Suppose that during a given timestep, 1 m of ice is advected from the last cell above sea level to the first cell below sea level. If the ocean is warm (say, 5 K warmer than PI) and the ice is considered to fill the cell uniformly, then the simulated melt rate could be tens of m/yr. This would immediately melt the ice, such that the ice margin cannot advance. But if the model has a subgrid calving scheme, a grounded column with Haf >> Ht could advance to fill a small fraction of the grid cell and experience little or no basal melting. Have you considered such possibilities and determined that the failure to form grounded marine-based ice is not a model artifact?
252: This is the first mention of the WAIS failure to regrow when temperatures return to PI values. This is an interesting result, but I wonder if it might depend on model simplifications (such as the lack of a subgrid calving scheme) or the equilibrium assumption. For instance, WAIS fails to regrow after a retreat period during which the bedrock equilibrates to the lighter load. What about a transient case in which the climate cools before the bedrock fully rebounds? Please comment on how the transient outcome might differ.
Also, can you extend the AQEM simulation and determine at what temperature the WAIS does, in fact, fully regrow?
260: Here and elsewhere, I suggest changing “bathymetry” to a more general term such as “basal topography” in cases where you’re considering both oceans and land.
271: What is the meaning of the initial time, t = 144 kyr? I’m not clear on how time is measured during AQEM experiments.
305: See the question above about the details of grounded ice advancing into a warm ocean. I can imagine that with a warm enough ocean, calving and/or lateral melting at grounded ice fronts could keep the grounding line shallow, but these processes aren’t explained in the text.
404: “when the ice sheet has already reached most coastlines but is incapable of advancing beyond” – see comments above.
466: The text says “melt–elevation feedback”. Should this be “melt–albedo feedback”?
475: With regard to the AIS being incapable of advancing over marine regions, please see the comments above. PMPT and the regularized Coulomb law might be part of the explanation, but other model choices might also be important.
486: The text says that including melt at the grounding zone implies larger hysteresis. If it turns out that the failure of grounded ice to advance into a warm ocean is in part a model artifact, then this statement would need to be qualified.
490: What is meant by a “realistic projection”? I’d suggest stating the temperature level and pointing out that this level is surpassed by most (or all?) of the SSPs, without commenting on the realism of the various SSPs, which is more of a socioeconomic judgment.
498: “the regrowth curve from an ice-free Antarctica is a quite good proxy for the AIS regrowth from intermediate stages.” That depends on how close the intermediate stages are to equilibrium. On timescales of a few centuries or less, the system likely won’t be in equilibrium.
500: The text states that following the regrowth scenario, sea level continues to rise even as temperature fall, because less snow is accumulating. I don’t know that this would this be true for a transient simulation. It would depend on the relative timescales for ice dynamics, snow accumulation, and GIA.
507: “cooling the climate below pre-industrial level is unlikely and would probably have other undesired impacts.” There are several issues with this statement: (1) I don’t think that equilibrium experiments, by themselves, give us confidence that a collapsed WAIS would not regrow under a return to a PI climate. (2) It’s hard to say whether cooling below PI levels will be unlikely or unfeasible given the technology and political systems of the distant future. (3) “Undesired impacts” is vague and subjective.
594: “ungrounding the major EASBs via MISI is relatively unlikely over the coming millennium.” The text hasn’t given a time scale for how long it would take to unground these ASBs with sustained high temperatures, so I don’t see how this statement is justified by what's gone before.
599: It’s appropriate to list model limitations at this point in the paper, but as indicated above, I would like to see more discussion in Section 3 of how particular limitations might influence particular results.
Two other limitations that could be mentioned are (1) a simplified treatment of calving and lateral melting and (2) the lack of ice-shelf hydrofracture.
608: I think this is the first mention that WAIS retreat is initiated in Thwaites. Earlier in the paper, could you add a few sentences about how WAIS retreat comes about? You could simply summarize what the videos show.
Figure A2: The letters in several panels don’t match the caption. Also, it’s hard to see the biases for key regions such as Thwaites. It would be useful to make the panels larger or add some some plots zooming in on WAIS.
Figure D2: The reference to Figure 1 k-l is not correct.
Minor corrections and suggestions:
- 30: “display” -> “have”
- 52: “melt-elevation” -> “melt-elevation feedback”
- 164: “amount” -> “number”
- 184 and elsewhere: “Gamburtsev” is misspelled.
- 352: “remoteness to” -> “distance from”
- 369: “We propose to further quantify” -> “We further quantify”
- 431: “We propose to compare” -> “We compare”
- 468: “the similar values” -> “similar values”
- 559: “eased” -> “aided” or “supported”. Also l. 562.
- 634: “might result much more complicated”. Please reword.
References:
Favier, L., Jourdain, N. C., Jenkins, A., Merino, N., Durand, G., Gagliardini, O., Gillet-Chaulet, F., and Mathiot, P.: Assessment of sub-shelf melting parameterisations using the ocean–ice-sheet coupled model NEMO(v3.6)–Elmer/Ice(v8.3), Geoscientific Model Development, 12, 2255–2283, https://doi.org/10.5194/gmd-12-2255-2019, 2019.
Gudmundsson, G. H., Krug, J., Durand, G., Favier, L., and Gagliardini, O.: The stability of grounding lines on retrograde slopes, The Cryosphere, 6, 1497–1505, https:// doi:10.5194/tc-6-1497-2012, 2012.
Jourdain, N. C., Asay-Davis, X., Hattermann, T., Straneo, F., Seroussi, H., Little, C. M., and Nowicki, S.: A protocol for calculating basal melt rates in the ISMIP6 Antarctic ice sheet projections, The Cryosphere, 14, 3111–3134, https://doi.org/10.5194/tc-14-3111-2020, 2020.
Schoof, C.: Ice sheet grounding line dynamics: Steady states, stability, and hysteresis, Journal of Geophysical Research, 112, F03S28, https://doi.org/10.1029/2006JF000664, 2007.
CalvingMIP wiki: https://github.com/JRowanJordan/CalvingMIP/wiki
Citation: https://doi.org/10.5194/egusphere-2025-6566-RC2
Model code and software
Yelmo A. Robinson et al. https://github.com/palma-ice/yelmo
Yelmox A. Robinson et al. https://github.com/palma-ice/yelmox
FastIsostasy J. Swierczek-Jereczek et al. https://github.com/palma-ice/FastIsostasy
Video supplement
Video supplements of "Highlighting processes underlying the stability and hysteresis of the Antarctic Ice Sheet" J. Swierczek-Jereczek et al. https://drive.google.com/drive/folders/1W-ZK7PSYJwAxL00RlqqAsOUDMEwAQLbO?usp=drive_link
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