Please find the review attached.

Summary

The authors present a new diagnostic they call "sea-level potential" that represents the amount of mass lost from the ice sheet when a particular location first becomes free of ice. The underlying idea is that the combination with sub-ice drilling at specific locations could constrain past sea-level contributions from the ice sheet if recovered basal material allows identification and dating of ice-free conditions some time in the past.

In my view, the schematic forcing used renders the presented results as a proof-of-concept rather than an actually usable framework. If it could be applied in practice hinges on large uncertainties in climate forcing in the past, which remain to be resolved. In any case, uncertainties would need to be fully accounted for and/or shortcomings better acknowledged. I suggest mayor revisions are needed to resolve the conceptional problems and reframe the paper. 

General comments

While constraining ice sheet contributions to sea level in the past could in principle give some indication for future behaviour, I believe the presented method and experiments are not suited to give direct information about the future. The climatic forcing for the future would be different from what is prescribed here and consequently would be the spatial pattern of retreat. I would suggest to refrain from making statements about the future (e.g. l48, l398, l412, l415, l442) based on the presented method.

A similar problem arises for specific periods of the past, e.g. the last interglacial. Examples of ice sheet modelling results show a very large range of possible retreat scenarios, largely explained by uncertainties in the climatic boundary conditions, but not only (e.g. Plach et al., 2018). Going further back in time does not improve the constraints either. It is not clear to me how this large uncertainty somehow disappears when using the forcing applied in the presented work. I strongly reject the notion that the forcing and therefore the retreat is generic and independent of a specific deglaciation (e.g. l390 and l411).  

The results are obtained from a schematic, continuously increasing forcing, which promotes continuous retreat. How does the method cope with past deglaciations that include periods of intermediate cooling and re-advance? I believe this possibility needs to be discussed as it means a non-uniqueness for the mapping of sea-level contribution to location. 

The proposed "sea-level potential" diagnostic maps ice free conditions around the ice sheet to its global sea-level contribution. In some sense this is similar to "time of retreat", except that time then maps non-linearly to sea-level contribution. The declared advantage of the presented approach is that the time dependence is collapsed and any ice sheet trajectory can be mapped onto the same potential axis. My concern is that this would only work if the retreat was independent of the specific climate forcing, which is clearly not the case. Considering this, what is the advantage of conflating different uncertainties by determining "sea-level when ice-free" rather than finding time of retreat (with uncertainty) and then mapping to sea-level?     

I can see that for one specific ice sheet trajectory (and ignoring the non-uniqueness above for now) the method could indeed be used to identify relevant drilling sites or argue for certain sea-level constraints in the past. However, the uncertainty of climate and ice sheet model reconstructions for the past (e.g. the last interglacial) remains so large that any practical application is seriously hampered. If this method should indeed serve as the basis for determining best locations of multi-million dollar drill campaigns a full understanding of the uncertainties would be needed, rather than trying to minimise them. A discussion and (where possible) quantification of the full range of uncertainties entering the results should be added. Another alternative for this paper could be to present the approach as a proof-of-concept and acknowledge limitations better.      

    

The idea to determine where the next meter of SLR comes from occurs at several places in the manuscript. I would argue that this is a flawed concept and it is not possible to answer this question with the proposed method. Most importantly, ice loss from the GrIS may happen everywhere along the margin, whether or not a region becomes ice free. At a particular moment during the deglaciation, mass loss has not only happened in all the places that have become ice free until then, but also possibly everywhere else. Remember, ice is flowing! In other words, mass loss does not happen by removing entire columns of ice. This framing reveals a flawed understanding of the physical system. In addition, problems with specific future climate forcing also apply here. 

Specific comments

Page: 1

l16. There is no direct link between ice sheet response to past changes and future warming. This should be reflected in the sentence. 

l18. "direct information"?

I seem to understand that exposure dating so far has not given these tight constraints.

l19. "sea-level potential"

Is often used to refer to the total sea-level contribution of an ice sheet if entirely melted. Consider a different term.

l20. "the amount the GIS has contributed to sea level when a particular location in Greenland is ice-free"

See later for redefinition within an ensemble. Maybe this should be updated already here. 

l25. "Our framework allows us to quantify the local and regional uncertainty in sea-level potential"

Not clear what the local and regional refer to here.

Page: 2

l48. "the questions of when, at what rate, and from where will the next meter of global SLR"

Wrong question. See general comment.

l45. "the ice sheet remained extensive and continuous across the island despite >8ºC of warming"

Note that finding interglacial ice alone could not have possibly constrained that. The conclusion was drawn based on modelling experiments not referenced in the paper (Helsen et al. 2013).

l61. "more-or-less its present configuration for the duration of the Pleistocene"

I am confused about this sentence. The GrIS during MIS11 was likely substantially smaller. Even with Dye-3 intact, one could imagine large retreat. 

Page: 3

l65. "short enough magnitude and/or duration (e.g. < 1ka) cause changes that are broadly reversible"

Not sure these are still arguments for a GrIS more or less the present size during the entire Pleistocene, but just to clarify: MIS11 lasted for how long? And reversible does not exclude a strong retreat!

l75. Again, not sure 'direct' is the right word here.

l96. "not tied to a particular interglacial"

I don't think it is possible to do that. See also general comment.

       

Page: 4

l118. "that have been established"

Reference or further data needed.

l119. "represent the major uncertainties"

A bit too confident here. What about the temperature lapse rate, for example? Can you confidently say that you have sufficiently sampled climate uncertainty, when your forcing isn't even specific for a given period?

Page: 6

l153. "Thickness differences are shown"

Should also show red where there is no ice observed but modelled. Contour the observed (BM) ice sheet extent rather than masking the results with it.

l156. "Figure 2 shows the method that we apply to calculate sea-level potential"

This is also described in 2.3. why split the description between here and there?

   

Page: 7

l178. "most sensitive to HTM climate"

Not sure what that means. Most sensitive compared to what? How can this be used to constrain the ensemble?

 

Page: 8

l184. Some more modelling information is needed.

How does the model solve for the thermal state? What geothermal heat flux and surface boundary conditions are used. How is isostatic adjustment calculated? Does the model have a name?

Grid resolution could also be mentioned here.

l190. "sliding to reduce the mismatch between the modelled and observed ice-sheet geometry"

Is this done here? How does that work for an initial state at LGM?

l204. "exist continuously for the last 21 kyr"

Reference needed. At what spatial and temporal resolution? How do these compare to state-of-the-art regional climate model simulations for the present?

l206. "the precise patterns"

Are you sure you know the precise pattern after 21 ka? Clarify and compare to RCMs at present.

l211. "Both forcings come from a blended model-data reconstruction"

A bit more detail would be good here beyond just adding the reference. What data and models are involved here?

Page: 9

l213. "Lapse rate applied to precipitation"

Is there no SMB-height feedback parametersed? This may be an important feedback as well.

l214. "periods can be volumetrically by increased"

Word missing?

l222. "not applying precipitation lapse-rate correction, because there is no compensation for increasing melt."

Not clear what is meant here.

l233. "an interglacial warming ramp"

So the forcing is schematic? Maybe better not to call it interglacial?

Also, ice sheet shrinking during the LIG and MIS11 was substantial during peak interglacial conditions, where the forcing is stabilised or even already decreasing. See also main comment on realism of ramping up forcing and possible implications. 

l239. "use two mantle relaxation times"

What kind of bedrock model is used here? More detail needed.

Page: 10

l257. "an evolving climatology for 21kyr"

This needs more details. What models and data are used? This is described in Buizert et al. but the most important basics should become clear without visiting the reference.

l258. "ice sheets differ in their geometry"

Add reference to 1b?

l261. "sea-level potential, defined"

The first definition would be correct for one specific ice sheet trajectory. Say so! 

The second definition holds for an ensemble of runs. Say so! 

Would it be possible to have just one definition instead?

A bit awkward to evoke the width of the histogram for this definition. Isn't it just the ensemble median value?

l265. "or the x-axis of Figure 2b"

What does the 'or' link to here? The parameter, the Greenland contribution? In either case, the x-axis is not the same as those items. Reformulate!

l265. "the parameter that the GIS responds most sensitively to"

This obviously depends on the range the parameter is sampled at, which makes this whole concept problematic. Even more so for parameters that are categorical. The parameters are not sampled in a statistically meaningful way, which makes these inferences difficult. 

l266. "dividing the width of the histogram"

Can this be formulated in statistical terms, rather than using the image of the histogram? Isn't this just the (sub-)ensemble spread of the potential?

Page: 11

l278. "the distribution of ice volume estimates"

The term doesn't speak to me (see elsewhere), but for consistency: refer to the potential here?

l283. "the first regions to deglaciate in our ensemble"

Difficult to imagine that wouldn't be the case in any other ensemble. Did an ice sheet ever deglaciate starting from the centre?

l284. "the last regions to deglaciate in our ensemble"

Can the behaviour of the ensemble be illustrated in some form? Maybe a figure like 2a for the entire ice sheet volume and 2d maps for a high, medium and a low sensitivity member of a few time slices.

     

Page: 12

l296. "the mean amount"  

I think in 2.3 this was defined as the median?

l297. "width of the full histogram"

= ensemble spread?

l312. "(Figure 4a)"

A bit difficult to understand. Maybe best placed right, as it is a combination of b) and c). So we can try to understand those first as we visit the figure.

l312. "This map reveals"

Can you explain why this is an interesting target to look at? I understand looking for regions with low error, but why is it interesting to look at low potential? I would imagine high potential and low error to be an interesting target for constraining deglaciations in the past.

Page: 13

l319. "(Figure 3a)"

My understanding is that the result of this analysis is highly model dependent. Already the choice of parameters is subjective and may not be the same for another model. This should come out clearly in the discussion, but better be mentioned already here.

l335. "where ice-cover at that site is associated with a wide range of potential ice-sheet geometries"

I am not convinced about this point. What you are showing is the opposite: ice-free conditions associated with a wide range of potential. What makes you think the opposite is also true?

l337. "require a contribution of +1.4 m SLE"

Why not formulate this as potential of x and spread of y?

l338. "has contributed +5.6 m SLE (Christ et al. 2023)"

So this is not from your results? A bit confusing. Clarify.

l339. "by adding constraints on simultaneously ice-free conditions at more than one location"

Not sure I understand how that would work. Could you explain?

l339. "by considering a subset of our parameter space."

You have to distinguish between the actual uncertainty and the uncertainty produced by your ensemble.

Do you want to reduce uncertainty in your ensemble by removing ensemble members that disagree? Sure, you could remove a lot of uncertainty by just running one single representation. Then uncertainty is zero. But that doesn't change anything about the actual uncertainty.

Page: 14

l366. "the elevation-surface mass balance feedback" 

Not clear how that is included in the current modelling.

 

Page: 15

l390. "Our approach circumvents the need for direct reconstruction"

I don't believe that you have circumvented the problem. A different climate forcing will lead to a different deglaciation and therefore a different distribution of potential than what you are finding. You seem to assume that the two climatologies in combination with the Buizert forcing for the last deglaciation is sufficient to generate climate forcing that could represent any deglaciation? I don't think that is true. See also general comment.

l394. "may become dominant in the future as boundary conditions and forcings evolve"

More relevant for this study and its potential application (identifying drill sites) is whatever happened in the past during LIG and MIS11. I don't understand the focus on the future here. See also general comment.

l397. "correctly predicting the spatial patterns of climate over Greenland"

Again, not clear why this discussion point is about the future. We have methods to project future sea-level contributions that are far more advanced than this modelling approach. The need of subglacial observations is to constrain the past, not the future, I suppose.

l398. "first meter of future sea-level change"

This is the wrong question. See general comment.

       

Page: 16

l411. "the patterns that hold true regardless of the style of deglaciation"

I disagree with this statement. Ignoring the specific forcing does not render the results more general and true. The presented results are just the specific response to another specific forcing.

l412. "useful insight into the uncertain future of the GIS"

Again, not clear to me how this has strong implications for the future.

l414. "the first few meters of sea-level rise from Greenland are likely to originate"

Not clear to me how your method is providing that information. There is mass loss happening in places that deglaciate late or never in your simulations.

l425. "can provide robust estimates"

Robust against what? Are you accounting for all of the uncertainties in your modelling?

       

Page: 17

l442. "into information that can inform adaptation efforts"

Adaptation to sea-level rise? Not clear to me what the proposed translation does.

l443. "we expect that improved knowledge of the past spatial mass balance patterns and relationships between temperature and precipitation change will have the greatest impact"

If that is true, which I believe, your method is not general at all.

l453. "6 Code Availability"

If you want the described framework to be used by anyone else, this is the place to share the code. Making work reproducible by others is becoming a standard throughout the community. I strongly suggest to think about how to make your work accessible and reproducible.

l456. "7 Data Availability"

The same as for code availability above. What data is needed to reproduce these results of this paper?

References

Helsen, M. M., van de Berg, W. J., van de Wal, R. S. W., van den Broeke, M. R., and Oerlemans, J.: Coupled regional climate–ice-sheet simulation shows limited Greenland ice loss during the Eemian, Clim. Past, 9, 1773–1788, https://doi.org/10.5194/cp-9-1773-2013, 2013.

Plach, A., Nisancioglu, K. H., Le clec'h, S., Born, A., Langebroek, P. M., Guo, C., Imhof, M., and Stocker, T. F.: Eemian Greenland SMB strongly sensitive to model choice, Clim. Past, 14, 1463–1485, https://doi.org/10.5194/cp-14-1463-2018, 2018.