This study by Van Breedam et al. analyses the hystheresis of the Antarctic Ice Sheet during the Eocene-Oligocene Transition. They use an ice sheet model (AISMPALEO) forced by fields provided by an emulator (CLISEMv1.0), that in turn uses outputs from HadSM3 to produce such forcings (temperature and precipitation). By carrying experiments where oribtal parameters (or directly insolation in some cases), CO2 levels, and the choice of bedrock topography are varied, they determine thresholds in CO2 and eccentricity that are able to drive a complete deglaciation (glaciation) starting from a continental-scale ice sheet (ice free land). 

They find a hystheresis behaviour for the ice sheet, where the difference between CO2 levels necessary drive the ice sheet from a fully glaciated to an ice free state and vice versa is 170~180 ppmv. The absolute levels, however, vary according to the choice of prescribed bedrock topography, due to an interplay between bedrock elevation and snowline elevation. They further show that much of this hystheresis behaviour is due to the isostatic adjustment of the bedrock to ice (de)loading, as a fixed bedrock topography reduced this difference by more than a factor of 4. Finally, by performing tests under different constant CO2 levels and varying orbital parametres, they find that eccentricity plays an important role in modulating the summer insolation values necessary to reach the threshold that will drive the ice sheet to a different state.

Overall, the quality of the work seems sound. The study offers good insights into the ice sheet hystheresis during a period where several geological changes were taking place (thus driving a substantial reorganisation of the climate system), and when several tipping points were crossed. Furthermore, it helps understand (and to a certain extent quantify) the drivers of permanent glaciation in Antarctica. I do think, however, that several technical aspects of the modelling approach need to be substantially clarified before the study's experimental design can be properly assessed and deemed publishable (which I think will be, don't get me wrong). Furthermore, some substantial reorganisation of the sections should be done, which would make it easier for the reader (and me as a reviewer) to follow the reasoning, methods used, and simulation ensembles carried out. These main concerns are outined below as "Major comments", while further suggestions to improve readability, as well as some minor corrections, are presented afterwards as "minor suggestions", "line by line comments", and "figure suggestions".

Major comments

Several technical aspects of the model are missing or unclear, and need to be clarified in the paper. How many vertical levels does the ice sheet model have? Are they uniformly spaced, or refined closer to the base? What is the basal slding law used? How do you determine the sliding coefficients? The dependence of ice deformation on its temperature is mentioned (L453-544), but there is no reference to how this interaction occurs in the model. How is ice deformation computed? Are any enhancement factors used? Is there any geothermal heat flux applied? Depending on how the parameters stated above are prescribed, they might strongly affect the results obtained. While I think performing extensive sensitivity tests to those parameters would make the paper even longer (and they are fairly unconstrained for the target period), the authors should discuss how their choice of model parameters might have influenced their results. Also, the ocean forcing seems to be completely ignored throughout the paper, except for a brief mention of marine-based ice sheets (L198-199). There is only a brief mention of ice shelves and the treatment of grounding lines, which is not clear at all (some of these concerns are listed further down in the line-by-line comments). How is basal melting of ice shelves prescribed? How is sea level prescribed? Even if the ocean plays a minor role in the EOT, this needs to be explicitly stated, and these aspects of the model still need to be described. From Fig. 6, there are indeed some ice shelves simulated. Finally, I would strongly suggest expanding more on how AISMPALEO and HadSM3 interact with CLISEMv1.0 (in section 2.3), including how/why it properly captures the ice-albedo feedback. As it is right now, it is not clear what is simulated and what is emulated. Since there's a lot of discussion on how the ice-albedo and elevation-mass balance feedbacks control the ice sheet response (and this is an important point of the study), it is crucial that the reader has at least a basic understanding of how the three model components interact without having to consult another publication.

The experimental design for the ice sheet model comes much later than the model description, and several experiments are only mentioned down the line. I would suggest to change the order where the models are presented in section 2 (e.g., leaving the ice sheet model description as 2.3, right before delving into the different experiments), and clearly state all experiments shown in sections 3 and 4 already in section 2. The way the experiments are presented in the manuscript right now is too scattered, making it hard to follow. A good way to solve this issue would be by having a single summarising table, with the experiments grouped by "goals". This would make it easier for the reader to have an overview of what has been tested (as opposed to having 3 tables - are the experiments in Figs. 12-15 in them? this is not clear). In that way, it would be easy to refer to this table (and to which group of simulations is being evaluated) throghout the different sections, so the reader can easily follow which parameters are being kept fixed, and which are being varied (especially when changes in CO2 and orbital parametres are being discussed). This might require a substantial ammount of rewriting of some sections, but it will greatly improve the flow of the manuscript.

The discussion is very concise and easy to follow, but I miss a bit more of detail on what these thresholds mean to the current state of Antarctica, if anything at all. If not, in what do they differ so that such high CO2 levels can still sustain continental-scale ice sheets? One thing that strikes me is the the fact that no attention has been given to the ocean at all, both in the description of the model (already stated above) and when discussing the results. Is that because there are barely any ice shelves? If that is the case, why? Could this be because of how the model simulates them? The technical aspects of the model need to be clarified (as stated above). If ice shelves are present and play some role, how much would the fact that the climate component uses a slab-ocean model affect the results?

Minor suggestions

- Although potential tipping-point triggers for the EOT are mentioned early in the introduction, it is not clear from the start why this study focuses on this period. The reasoning is only made explicit at the very last sentence of the introduction. It would be good to highlight much earlier why this period was chosen, so the reader can be more engaged.

- The description of hystheresis in L42-47 and the definition stated L442 are not quite the same. How can they be reconciled?

- For an easier reading, I strongly suggest to explicitly say "mean surface temperatures" as opposed to "MAT_sur". Similarly for "MAT_clim"

- The solid Earth interaction with the ice sheet is defined in several different ways. "solid Earth rebound (feedback)", "isostatic adjustment (feedback)", "isostatic rebound", "isostasy". Please stick to one way for consistency, unless appropriate for that specific context/explanation.

Line by line comments

L62: "deform" is a more appropriate term than "deflect"

L67: It is not clear what is meant with "surface type". Is it ice/bare rock/snow? It needs to be clarified.

L69: "potentially significant impact"

L70-73: What would be a "constant curve"? In the following sentence, it is not clear which parameters are kept constant and which are not. Do you mean that you vary 2 orbital parameters while CO2 and a third orbital parameter is kept constant? Or you vary one orbital parameter and CO2? It is quite hard to follow.

L89-90: Do you mean that you are solving for the full-stokes equations, or a combination of SSA/SIA? I assume the "transition zone" is the grounding line, but this needs to be explicitly described.

L90-91: Does that mean that you have a fixed mask to determine "the coast"? Or how is that defined?

L91: by mass balance I assume you refer to surface mass balance? Please update accordingly

L91 and 94: PPD and DDF are acronyms that are not defined. Not every reader of the journal is familiar with glaciology technical terms, so these should be explicitly defined.

L95: As in the comment above, please define "m i.e." the first time it is used. It might be straightforward for the glaciological community, but CP is a journal that targets a wider audience, and therefore not everybody would be used to these more specific units

L98-100: What are the values for the lithosphere rigidity and viscosity? All values should be clearly stated somewhere, so that results can be reproducible

L107: What anomalous heat convergence? Due to what? This really comes out of the blue here

L111-112: what is the resolution of the bedrock dataset? This might not be the appropriate section to mention it. As far as I understand, this is part of the ice sheet model setup, not the climate model.

L120-122: How were these initial geometries created? Are they also the ones used as initial conditions for the hystheresis experiments?

L123: does the ice sheet model not receive any ocean field?

L126: "every 500 years" reads better

L134: "only ice" -> "ice is present only"?

L137: "land inwards" -> inland?

L133-L142: reads like results?

L147-149: I find it curious that the ice sheet grows to a continental scale at 550 ppmv. What were the initial conditions for this ice sheet growth experiment? As the paper highlights, the initial conditions are quite important for the resulting ice sheet (see comment above on L120-122)

L149: "ppm" is used, as opposed to ppmv, which is the one used throughout most of the paper.

L155: By "control parameters", do you mean that they were kept constant?

L156: What are these values?

L160: You state in L144 that all experiments span 10 Myr, yet here you state that some are only 2.4 Myr long. It would be easier to follow the description if the experiment duration was added to the table of experiments as well.

L165: "minimum and maximum topography estimates"

L167: "linearly decreased" - but from which value to whch value?

L168: This (partly) answers my question raised above for L120-122! I think some reorganisation of the experimental design and methodology would make the experimental design much easier to follow

L180: "In section 3.1 we test the sensitivity of the Antarctic ice sheet hysteresis to the bedrock topography dataset" reads much better

L184: "chosen" or "prescribed" would fit better than "applied".

L189-190: I am not sure I understand the use of "except" in this sentence

L191: what do you mean by "lower above the ice sheet because the elevation is higher"? Are you not talking about the surface temperature? Or do you mean further inland?

L226: this is the first mention of "rebounded topography". Is it because you are referring to the deglaciated runs? If so, it should also be stated for the minimum bedrock topography as well. If not, does it mean that the other deglaciation experiments mentioned had no isostatic model included?

L228: I would suggest to use another word rather than "march", so that it is not mistaken with the month of March. One alternative is to use "range" instead

L231 and 232 (and throughout): maximum and minimum topographies, as you are referring to more than one

L243: I suggest use "deform" instead of "deflect" again

L243-244: I am not sure I follow the reasoning behind the lowering of the snowline being delayed. The atmospheric cooling is the responsible for lowering the snowline, and with a delayed increase in ice sheet elevation, what happens is that it will take longer for the same extent of the ice sheet to be above the snowline. These are not quite the same thing (relative vs. absolute points of reference)

L244-245: Again, new experiments are being introduced... Please summarise all in a single table as stated in the major comments.

L279: the use of "or" here is confusing. If you are defining/naming MAT_clim as the mean temperature at sea level, state explicitly that this is how you are defining it. Or are they two completely different things?

L281-283: The reasoning here is not quite clear. I would suggest you more explicitly explain it as in L283-285 for the initial difference in temperature

L294: This sentence does not read well. You can start with either "there is a CO2 threshold to..." or "A CO2 threshold to continental-scale glaciation exists". Also, "for a certain" makes me wonder if you are talking about your experiments or not. I suggest "for each tested bedrock topography" instead. If that is what you mean, it might be good to highlight in the sentence that these thresholds are different for each of the tested bedrock topographies.

L297-299: I am not sure I follow the explanation here. How does the time indicate the change in sensitivity of the ice sheet? do you mean the time when the tipping point is crossed? In the panretheses, are you stating that in each experiment the initial conditions are representative of the ice sheet at a certain point in time (in which case it would have been through a different number of precession cycles)? This bit needs to be rewritten for clarity.

L304-305: This is a very interesting statement, and would be good to have a figure to illustrate it. It would be of great support to understanding Fig. 10 (maybe as a second panel?)

L317: I find it odd to use "remarkable" here. Isn't that exactly what hystheresis is about, as you state later in L442? Also, the dependence of the ice sheet response on initial conditions (both geometry and thermal state) is something quite actively discussed and not a surprise.

L351-352: isn't that true for the 'intermediate' case as well?

L375: While the 40kyr time presented in L346-347 is within the bounds stated here, it makes me wonder what configuration yields the 40 kyr time used as justification in L346-347? It would be good to state that for clarity when comparing these two statements

L384: Is that only due to the high pressure area? The high pressure area at the poles exists even in the most idealised (e.g., "water planet") Earth atmopsheric circulation scenarios. I suggest it might also be due to an orographic effect caused by the ice sheet growth itself, which acts as a barrier to weather systems and restricts them to the margin (where most accumulation occurs).

L399: I believe you meant "as noted earlier"

L399-401: I suggest breaking up this sentence in two for an easier flow

L401: I suggest rewriting to "Fig. 14 also illustrates this hystheresis behaviour...". As it is now, it's as if the figure itself had some type of hystheresis...

L429: This sentence construction is weird. I suspect you meant "either an ice-free continent (bare bedrock) or from an ice sheet"

L432: "gradually increases when lowering..."

L443: This sentence is hard to follow, with "to allow", "to develop", and "to initiate" one after the other. I suggest breaking up or rephrasing as "... topography and initiate ice build up" or alternatively "... topography, initiating ice build up"

L446: I would refrain from using terms such as "very" or "very much". You state the same thing without including them here, the study already demonstrates that.

L451: I would state "depending on the choice of/chosen bedrock topography" instead, to avoid the reading mistaking it for a local topographic dependency. I would also remove "slightly", as the experiments demonstrate it is exactly due to the different topographies.

L457: "This is mainly because"

L461: "Conversely" reads better than "oppositely"

L485-486: For an easier reading, I suggest rephrasing as "the amplitude of the precession cycle becomes important, and is governed by the eccentricity."

L488: I suggest rephrasing as "important in order to keep"

L493: This is a bold statement, as these results are based only the model results from this study. It is more honest to state that this is what your model/experiments show, especially because there has been no comparison to geological constraints, neither an assessment of the robustness of the ice sheet model to unconstrained model parametres.

L494: "these thresholds [...] depend" - correct for plural

L496: why is "ice sheets" in plural? So far the AIS has been treated as a single ice sheet

L512: I suggest rephrasing to "The role of eccentricity is especially important" for easier reading

L515: I suspect you mean 180 ppmv? This is the first time the number 80 comes in the story, and is at the closing sentence of the paper!

References

Baatsen et al. (2020) is cited, but not in the references

Payne et al. (2005) is in the references but not cited

Zeitz et al. (2021) is in the references but not cited

There might be other references that are cited but are not listed in the references. I would strongly advise the use of a reference manager to help keeping track of the citations.

Figure comments

Figure 2: a thrid panel showing the difference between both topographies would be beneficial to highlight in which areas they differ the most (and how uniform that difference is). This would help quite a bit when discussing the effect of the chosen bedrock topography and the mass balance-elevation feedback

Figure 3: I think it is confusing to mention 2x Pre-Industrial CO2 in the caption. Since you discuss all results in terms of the absolute values, it would make more sense to state 560 ppmv instead.

Figure 4: What was the window used for the running mean mentioned in the caption? The period between 34.2 and 31.8 is very hard to see in the figure. I suggest adding a background shaded box to properly highlight it.

Figure 6: what elevation to the contour lines represent in panels (a) and (c)?

Figure 10: I do not understand what you meant with the statement on the experiment duration. Are you using the resulting geometry as initial conditions to another experiment? Based on the figure's description in the main text and in the caption before that statement, I suggest labelling x axis to "time to reach threshold" and y axis to "eccentricity threshold". You clearly state in the methods that your experiments last for 10 Myr, so this labeling is quite confusing.

Figure 11: This is a very nice and illustrative figure - it gets the point across very easily. I just wonder what the red boxes around the dots mean?

Figures 13 and 14: "Simulations starting from bare bedrock" reads better, without the article. Note in Fig. 13 that you are referring to 2 simulations, so the caption should be in the plural as well.

Figure 15: I really like this figure and think it is very illustrative. As in Fig. 6, it would be good to state in the caption what intervals the elevation contours represent.

REVIEW OF ‘HYSTERESIS AND ORBITAL PACING OF THE EARLY CENOZOIC ANTARCTIC ICE SHEET’ BY VAN BREEDAM ET AL.

Van Breedam et al. quantify the CO2-thresholds for glaciation and deglaciation of the Early Cenozoic Antarctic ice sheet using an ice sheet model coupled to a climate model through a process emulator. They investigate the influence of the choice of bedrock topography, glacial isostatic adjustment, and orbital parameters (eccentricity and obliquity) on these thresholds. Their main findings are: 1) the choice of bedrock topography significantly affects both thresholds, but not the difference between them (hysteresis); 2) excluding glacial isostatic adjustment raises the CO2 level of glaciation but does not change the deglaciation threshold value; 3) the long eccentricity cycle has a significant impact on the timing of glaciation.

The topic of the study is interesting and timely, the methodology is sound, and the results are robust. My only concern is that the implications of the study are mostly left for the reader to deduce. In principle, the study achieves its stated aim of identifying the forcing needed to initiate and end a continental-scale glaciation, under various assumptions on bedrock topography, GIA and CO2. But what do the results actually mean for ephemeral glaciations prior to the EOT? What is the consequence of the hysteresis and orbital variations for the stability of the transiently evolving ice sheet? It could be worthwhile to include a (brief) discussion of proxy CO2 or ice volume data in this respect. The discussion section could be further improved for instance through a comparison, either present-day to Early Cenozoic Antarctica, or Antarctica to other ice sheets (the comparison to Greenland in the discussion section that is there, is a bit half-hearted). With some more discussion in this direction, the manuscript would in my opinion reach a wider audience. 

Furthermore, I have some recommendations to the authors for minor revisions to clarify the text and figures.

SPECIFIC COMMENTS PER SECTION:

§1 Introduction

L22-24:

The recent publication by Li et al. (2023) is also relevant here:

Li, Q., Marshall, J., Rye, C. D., Romanou, A., Rind, D., & Kelley, M. (2023). Global Climate Impacts of Greenland and Antarctic Meltwater: A Comparative Study. Jounrla of Climate, 1-40.

L27, L32: ‘favourable’ and ‘optimal’

The environmental conditions do not necessarily have to be favourable, and certainly not optimal, for glaciation to occur. They just have to be sufficient.

L55-64:

Also worthy to mention that Pollard and DeConto (2005) did not use early Cenozoic Antarctic bedrock topography.

L68:

Recent paleo-bedrock elevation reconstructions

§2 Model description and experimental set-up

§2.1:

Is ice-ocean interaction not important at all (i.e., no ice shelves)? How is the basal mass balance underneath the ice shelves calculated? And calving? Are sea level variations taken into account, if yes, how?

Which sliding law is used, and what about the grounding line physics? These are important factors, especially for deglaciation.

L90-91:

Influx of snow (from the atmosphere) and ice (from upstream), I think?

L92:

So the input consists of daily temperatures and precipitation rates?

L97-100:

Please mention the specifics of the GIA model.

L113-114:

The Wilson topographies are also used in the ISM, in higher resolution, I guess?

Figure 2:

It could be a valuable addition to show the difference between the two reconstructions.

L121-122:

What vegetation is used for ice-free land, tundra (L500 seems to suggest this) or bare bedrock, and what is the albedo?

L127-128:

Worthy to mention Herrington and Poulsen (2011) here:

Herrington, A. R., & Poulsen, C. J. (2011). Terminating the Last Interglacial: The role of ice sheet–climate feedbacks in a GCM asynchronously coupled to an ice sheet model, Journal of Climate 25(6), 1871-1882.

L137-139:

Winter precipitation may be lower, but judging from the temperatures summer precipitation will be almost all rain.

L147-149:

Mention that these CO2 bounds apply to this particular model set-up. You could add that these values are roughly in line with proxy data (see also my comment to L495-496).

Figure 4:

Please make the black lines bracketing 34.2 and 31.8 Ma a little thicker, or preferably highlight this period in some other manner.

§3 Ice sheet hysteresis

L189-190:

It would be interesting to see what the difference in maximum ice thickness is between the two simulations (Wilson min and max), could you include a (supplemental) figure showing maps? And is the ice sheet in fact still land-terminating in this case (L198-199)?

Figure 6:

Why do you show this at 550 ppm CO2? I don’t get that.

Figure 7:

To aid comparison, it would be beneficial to have the same y-axis scales in both panels.

Figure 8:

Here as well, maps of maximum ice thickness (and maybe surface height) would be nice. I would think excluding GIA will lead to higher surface elevations, but only slightly because precipitation is depleted when the surface is raised. On the other hand, the ice will be less deep, because the bedrock topo remains higher.

L283-284:

I am not sure why the ice area is larger at the start of the no-GIA experiment.

§4 Threshold dependency on orbital forcing

§4.1

This paragraph is not so clear to me. Which experiments do you discuss here? Judging from the text you keep the CO2 constant but vary all the orbital parameters. If that is the case, why are these experiments not described in §2?

L308: ‘exceeding 0.03’

You mean below 0.03?

L298-299 (L317-318, L325)

Why has the ice sheet size changed after a few precessional cycles, is there a trend towards larger ice volume? Even at constant high CO2-levels?

Figure 10:

The duration of the experiment is the time passed since 34.2 Ma, and it affects the background ice sheet size, right? The main text explains it well, but I must say the figure remains hard to interpret: I cannot see a clear pattern, particularly not for the glaciation threshold.

L346-347:

The difference in timescale between glaciation and deglaciation mentioned later on (L375-376) is relevant here already, I believe.

Table 3:

You could add present-day values for comparison.

L363-365, L366-367

Add ‘not shown’.

Figure 12:

And here again, showing maps (e.g., like Fig. 15 does) would be nice.

L382-383:

So there is a double importance of ice area: the area itself (larger accumulation area), and the higher accumulation rate at the margins of the area. Moreover, the CO2 level affects the precipitation rates as well I think (warmer = more precip)?

L387-389:

One could also think of an ice-volume-CO2 feedback loop: initial ice volume increase leads to lower CO2, which stimulates further glaciation.

Figure 14:

Could you add a color scale?

§5 Discussion

L453-455:

Is colder ice flowing slower in fact a positive feedback? On the one hand, indeed, more ice will remain within the net accumulation zone. But on the other hand, expansion of the net accumulation zone due to surface uplift by inflowing ice is impeded.

L460-470:

Hysteresis behaviour of the AIS is also quantified (albeit for the Miocene) in the appendix of Gasson et al. (2016):

Gasson, E., DeConto, R. M., Pollard, D., & Levy, R. H. (2016). Dynamic Antarctic ice sheet during the early to mid-Miocene. PNAS 113(13), 3459-3464.

L471-480:

You could also compare to Abe-Ouchi et al. (2013), who found that instantaneous isostatic rebound obstructs deglaciation, in experiments of the Pleistocene Northern Hemisphere ice sheets.

Abe-Ouchi, A., Saito, F., Kawamura, K., Raymo, M. E., Okuno, J. I., Takahashi, K., & Blatter, H. (2013). Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume. Nature 500(7461), 190-193.

§6 Conclusions

L495-496:

It should be noted that these values are very model-dependent, see Gasson et al. (2014). Maybe you could include a (brief) comparison to proxy data from around the EOT?

Gasson, E., Lunt, D. J., DeConto, R., Goldner, A., Heinemann, M., Huber, M., ... & Valdes, P. J. (2014). Uncertainties in the modelled CO2 threshold for Antarctic glaciation. Climate of the Past 10(2), 451-466.

§ Code and data availability

Thank you for sharing the code of the emulator. I realize it is not required by the journal, but on a personal note I’d like to ask: Has the code of AISMPALEO also been made publicly available? If not, please do so. This facilitates transparency and reproducibility.