Please find detailed referee comments in the file attached.

This manuscript assesses how different sub-shelf melting schemes used to spin up ice-sheet models lead to similar but not identical initial ice-sheet states. This impacts considerably projections of the Antarctic ice sheet’s contribution to future sea-level rise. The issue of initialization was treated in part by initMIP-Antarctica but given that different models with different setups were used within that project, the specific effect of different initial conditions was not isolated. This study is interesting because it represents a further step in this direction. A better characterization of initial conditions should help to reduce uncertainties in projections. I think this result deserves to be conveyed.  However, I have a few major issues that prevent me from accepting this paper at this stage.

First, the methodological approach needs to be explained in more detail. Right now it is unclear to me what experiments have been done: have the authors used the data from Lowry et al (2021) for their comparison or  have they redone simulations using the same basal melting scheme as in that study? This is critical because to be sure that the results shown are only due to the different sub-shelf melting initialization the experiments would need to be redone with exactly the same model version and configuration. 

Also, the basal melting scheme used in the projections is not clearly described. The authors should clarify this and also show how the basal melting fields evolve smoothly from the spinup into the projections.

Finally, the section on “Model Projection Results” lacks proper illustration of some of the results that are discussed, including the comparison to LOW21 and the descriptions of relevant physical mechanisms that are described but are not illustrated, so that they remain speculative. 

Another less critical issue is that several figures do not appear in the order in which they are cited.

Specific comments (numbers indicate the lines to which the comments refer)

Title: “Antarctica ice sheet” should be “the Antarctic ice sheet” here and everywhere below. 

Abstract: 

15: “impedes” sounds too strong; I suggest “brakes” o “reduces”. Also, what does “the state of sub ice-shelf melting” refer to?

16: replace “inaccuracies” by “uncertainties”

17-18: “we adopt a single ice sheet model (PISM) and investigate two different sub-ice shelf melt rate schemes during model spin-ups” - to me this implies the authors have performed experiments with two different sub-shelf melt schemes, but this is unclear in the experimental setup and results sections.

21, 25: “ice sheet regions” should be “ice-sheet regions”, and “ice sheet mass changes” should be “ice-sheet mass changes”. This should be modified throughout the paper (see eg lines 29

Introduction

27: “discharge” should be “discharges”

30-31: “The exposure of ice shelves to warm seawater causes basal melting, combined with their near-flotation elevations,  resulting in high susceptibility to oceanic forcing” - this sentence does not seem grammatically correct. Also, “vulnerability” seems more appropriate than “susceptibility”

34: “grounding line retreat” should be “groundingl-line retreat” here and elsewhere

36-37: I don’t think Rignot et al (2008) is so explicit about MISI

38: I think these two papers rather focus on MICI, not MISI (even if MISI is present too)

39: should be “ice-sheet model”; same in line 47, 50, 53

40: should be “parameterizations”  (plural). Also, the authors could refer here to Favier et al (2019), who provide a review of sub-shelf  melting parameterizations (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) , Geosci. Model Dev., 12, 2255–2283, https://doi.org/10.5194/gmd-12-2255-2019, 2019.).

44: You should refer here specifically to initMIP-Antarctica. Also “ice sheet models exhibit significant divergence” - I guess you mean projections or ice-sheet model responses in experiments

50: I understand that this is an attempt to explain how this manuscript contributes beyond the results of initMIP-Antarctica. If so, please make this more explicit.

56: “the identical ice sheet model” seems to refer to CISM which is not the case. I suggest writing “a single ice-sheet model and initialization method”

58: I would rephrase question (2) as “How does this initial state affect long-term Antarctic ice sheet projections” - because I assume the basal melting scheme in the projections is the same as in LOW21 (see below).

60: “Therefore, in this paper, we consider two different sub-ice shelf melt rate approaches” - it seems to me here you mean you will do experiments with both but this is not clear after. Also, write “Parallel Ice Sheet Model, (PISM)” before “ice-sheet model”

61: “the Antarctica ice sheet” should be “Antarctic ice sheet”

Model and Methods

72: LOW21 appears here for the first time. I understand that it refers to Lowry et al (2021). This should be stated clearly. More importantly, it is unclear to me if the authors have used the data from Lowry et al (2021) here or if they have redone the simulations using the same basal melting scheme as in that study. In this section and throughout the manuscript the authors refer to the results using the prescribed basal melting of Rignot et al (2013) (S1) as “our approach”, or “our simulations” so it seems the simulations with parameterized melting scheme (S2) have not been done here. This is critical because it seems to me that in order to be sure the results shown are only due to the different sub-shelf melting and initialization the experiments need to be redone with exactly the same model version and configuration. 

73: Figure 2 is referred to here before referring to Figure 1. 

74: “and other datasets” is vague, please be more specific.

80: Maybe I am missing something but I don’t fully understand how the basal temperatures are being used if the basal melting rates are imposed.

104: What does “evolutionary” mean here?

107: Importantly: Please explain how sub-shelf melting is handled in the projections.  I assume S2 is being used for both initializations but I did not see it written explicitly.

107-108:  “high” and “low” are not scenarios but different grounding-line parameterizations using sub-grid interpolation of basal melting at grounding lines or not; this should be better explained. Also, was this also used in LOW21? This is also critical to assess the differences.

Figure 1: Does “our simulations” mean S1? Also, the temperature field of Chambers et al (2021) should be referred to in the text.

Figure 2: Again, authors say “our study and LOW21” so it is unclear if they have performed simulations using S2. Also, the discussion in lines 205-208 below on the fact Rignot et al (2013)’s sub-shelf melting rates are higher than those used in S2/LOW21 should appear here, when the differences are shown (see comment below)

Model Initialization Results

114: Again, this sounds as if you have not done the simulations with S2.

115: Start a  new sentence to describe the RMSE differences (between S1 and S2/LOW21?)

118: “consistent” sounds weak - I guess you mean very similar between S1 and S2

118-121: Figure 7 is referred to here (before Figures 3-6). There is no need for this now, since you actually only describe these results later on.

122: Antarctica should be Antarctic and ice sheet should be ice-sheet

129: I think there is no need for a new paragraph here. Also, here and elsewhere, I would rather use the notation S1 and S2 rather than “our” and “LOW21”

145: replace “led” by “leads” (to have everything in the same verbal tense, present)

149: What complex ice-dynamic feedbacks?

152: Totton should be Totten

154-156: I am not sure about this mechanism. Thinning downstream causes thickening upstream? Can this be explained further via a reference or additional results showing the stronger lateral resistance invoked?

156: Replace “decreased” by “decreases”

174: replace “reduced” by “are reduced”

178-184: To what extent are these processes represented in the ice-sheet model? For example, sedimentary basins? Also,  replace “WAIS” by “the WAIS” and  “EAIS” by “the EAIS”

192: should be “ice-sheet destabilization”

195: The sentence starting with “This positive feedback…” seems grammatically incorrect

205: Should be “the” WAIS and “the susceptibility”

206-208: It seems to me this discussion on the fact Rignot et al (2013)’s sub-shelf melting rates are higher than those used in S2/LOW21 should appear earlier, at the end of Section 2 when the differences are shown

212: should be “ice-shelf buttressing”

Figure 3 and table 1: When are these fields exactly taken? At the end of the initialization procedure? Do they correspond to 2015?

Figure 4: Are you using the same color bar and levels for ice thickness and velocity? This strongly limits visualization of the ice-thickness anomalies so I would suggest to use different color bars and levels for each field

Figure 7: There is no discussion as to how isostasy is treated. Is the bedrock elevation identical at this stage for S1 and S2 or are you just showing the original data?

Model Projection Results

A general comment: Please describe how the thermal forcing is applied in these simulations (which basal melting scheme).

231-233: “Prognostic simulations from 2015 to 2100 revealed divergent ice mass changes compared to LOW21” - where is this shown? If it is just in Figure 8 this suggests the simulations for S2 have not been done again, is that the case? If so I think it would be very difficult to be able to guarantee that the model versions are identical (given that LOW21 was published four years ago) and the only difference is the initialization unless the simulations.

232: replace “ranging” by “range”

238-239: what does “relative to the hysteretic response of ice-sheet dynamics to climate forcing” mean here? Please reformulate to clarify.

242: 0.36 m is in the mean value, this should be stated.

261-268: The discussion starting with “This significant mass loss is propelled… “ describes what we think has been the main mechanism driving Antarctic ice mass loss in  the past decades, but it is discussed here as if it were also the relevant mechanism leading to ice-loss in the present simulations. There is however no support from figures to demonstrate that this indeed the case, so this is therefore speculative.

217-272: Similarly, the enhanced moisture transport is not illustrated so this remains speculative.

279-280: The same applies to the sentence “This transient pattern is tied to the intensification of polar westerly winds”

292: “the” WAIS

296: Please introduce the emulator the first time Edwards et al (2021) is mentioned to give a little more context.

309: I suggest writing “demonstrating its heightened vulnerability to ocean-induced melt rates at the initialization"

315, 318, 329, 331: should be “ice-sheet” 

321: Indeed, the AIS might not be in steady state for the present day, and if projections are very sensitive to initial conditions one has to think what the most realistic state would be. For instance, reaching that initial state (previous to projections) via long, transient spinups involving paleo-evolution could be critical because of the different dynamical state achieved in this way.  It would be nice if the authors could discuss how they think a better initial state can be achieved.

Table 2: I suppose the numbers in brackets correspond to  “high” and “low” projections and the individual numbers are averages but this should be stated in the table caption. Also, India should be Indian and Antarctica should be Antarctic.

Figure 8: I would have expected to see the same scenarios carried out with the alternative initial conditions. 

Figure 9: Similar to my comment above, I would have expected to see similar results for the alternative initial conditions. India should be Indian.

Also, I would like to see how a time series of ice volume for the spinup and its continuation into the projections, to make sure the transition is smooth. 

Conclusions

344, 345: should be “Antarctic”