In the manuscript, van den Linden et al. use linear response functions from Levermann et al. (2020) which were derived from ice sheet model responses in sea-level contribution to perturbations by uniform sub-shelf melt rate increases. Sea-level projections are updated by using CMIP6 instead of CMIP5 models and by recalibrating the sensitivity of melt rates to ocean temperature changes using observed mass changes. The authors conclude that with the new calibration, sea-level projections are lowered in comparison to LARMIP2 (Levermann et al., 2020) and ISMIP6 (Seroussi et al. 2020; Edwards et al. 2021).

First of all, I want to thank the authors for this well written manuscript which is easy to understand and follow. Unfortunately, I think that the approach presented in the manuscript cannot be applied this way. However, the approach could be interesting and informing further studies, so I suggest two possible modifications that would make it applicable in a methodologically correct way.

Major comment:

The central issue is that the calibration factor gamma, which relates ocean temperature changes at depth to sub-shelf melt rates changes, is fitted over the historic period in the Weddell Sea, Ross Sea and in East Antarctica, all three regions where very little mass gains or losses have been observed (see Rignot et al. 2019; Figure A1 in the manuscript), in particular in comparison to the overall volume of the regions (if the methodology can be applied to the Antarctic Peninsula should also be checked). This makes a sound calibration with changes in ocean temperatures from CMIP6 models over the historic period basically impossible, due to a number of issues: (1) the changes in mass in the respective region might not even be causally linked to ocean forcing but explainable through, e.g., surface mass balance changes; (2) changes in ocean temperatures in CMIP6 models show a wide spread and how close they are to real changes and if they can actually capture subtleties in the historic record that can be linked to the small changes in ice discharge, is questionable.

This means that the calibration factor is fitted between two numbers that are zero or quite small, but have large uncertainties, so that in the end the calibration factor is not really constrained. And this is physically correct, because if there is no enhanced ice discharge due to changes in ocean forcing in the historic record, as for example in the Weddell Sea, the melt sensitivity to ocean forcing cannot be deduced from observations. This problem shows for example in the result that most calibration parameters are zero in many ice-sheet-ocean-model combinations (section 3.1). And that, even if the parameters are fitted to represent past discharge, they largely underestimate the observed mass loss (Fig. 6).

Two suggestions to avoid this problem are:

1) focus the study on the Amundsen Sea (potentially also the AP), where actually enhanced ice discharge has been documented extensively and linked to enahnced ocean-driven melting. This would allow you to derive a sound fit for that region. Then you could compare the projections for the Amundsen Sea with ISMIP6 and LARMIP2 for that region. Alternatively,

2) if you want to include the whole of Antarctica, you could use your proposed method to fit gamma in the Amundsen Sea (and AP), where substantial discharge occurred, and assume an uncertainty distribution of gamma (based on LARMIP, your fit, ISMIP6 calibration,..) for the other regions.



Since these would mean major changes to the manuscript and potentially the central findings, in the following I mostly omitted comments on the methodology and results that will be affected by the major comment above:

Minor comments:

• the study uses “discharge” in some places, but what it actually means is “changes in discharge”, as the latter should in principle be associated to changes in sub-shelf melt. Please check and correct.
• page 1, line 24: specify “long-term”
• page 2, line 53-55: ISMIP6 used more than the quadratic calibration, and those were two options for calibration (not done at the same time)
• page 3, line 69, line 85: this is discussed as if the scaling factor in LARMIP only has disadvantages, but it actually has the advantage that also uncertainties in the global mean temperature changes (and not only the CMIP trajectories) were included in the uncertainty estimate
• page 5, line 100; Table 2: the sub-surface temperatures used as ocean forcing look too shallow for me. The relevant water masses are those at depth of the continental shelf that drive the melting close to the grounding lines. I would expect these more around 800 to 1000m depth.
• page 6, line 118-120: why do you not correct for individual model biases but by the ensemble mean?
• Fig. 3 caption: change to “Annual… time series of the CMIP6 multi-model mean (green) , model drift and bias-adjusted, and the GREP ensemble mean (orange). Both are smoothed by a five year running average filter.”
• page 7, line 121: this sounds weird, the water is not warmed in the cavities, but it’s the change in the pressure that lowers the freezing point and increases the thermal driving
• page 6, line 137: that T_f is a constant for each region is a very coarse assumption, could be discussed in the discussion.
• page 9, line 171-174: why this condition for the “unbounded”? Would you get a better fit for the Amundsen Sea if you would remove this?
• section 3.2: LARMIP2 did not calibrate the melt-factor with observed changes in ice discharge, but it did compare the obtained mass losses over the historic period, which actually look like a much better fit than your results (Fig 6, Levermann et al. 2020).
• section 3.1: do you have an estimate on the uncertainty of your calibrated melt factors for each combination?
• figure 5: instead show the sensitivity in m/a/K, your legend is hard to see, maybe increase the intensity of the colors?
• page 13, line 239: but they should, by construction. This indicated the underlying problem with the methodology.
• discussion: you could add Payne et al. 2021 for a comparison between CMIP5 and CMIP6 effects on AIS sea-level projections; you should discuss the errors that arise through not including surface mass balance changes in your fitting procedure.

Review of van der Linden et al. “Calibration of basal melt on past ice discharge lowers projections of Antarctica’s sea level contribution”.

General Comments:

In this paper, the authors use linear response functions of ice sheet models from LARMIP-2 to estimate contributions to sea level in three future emissions scenarios.  Forcing is derived from ocean conditions in CMIP6 models and is further bias-adjusted and corrected for model drift.  Their methodology resembles that of LARMIP-2, however the key difference is that instead of calibrating basal melt rates on observed melt rates (as in ISMIP6), basal melt rates were calibrated on observation-based estimates of ice discharge (Rignot et al., 2019).  The authors use two different forms of melt rate parameterization (linear and quadratic) and then use their derived values for gamma to update sea level rise projections under three SSP projections out to 2100.  They conclude that their method results in lower projections of Antarctic sea level contribution that the other main methods used in IPCC AR6 (ISMIP6 and LARMIP-2).

I want to thank the authors for this work, and their new approach in calibrating to a different observational dataset than has been typically used in the community so far.   They have recognized and tried to address a need to better-constrain gamma values.  That said, I have a few broad-brush concerns about the paper.

First, the calibration of basal melt rate is based on past ice discharge in regions (e.g. Ross, Weddell) where very little ice loss was taking place.  As a result, gamma values are often equal to zero, and so future contributions to sea level from these regions is inevitably muted despite the potential for actual increases in thermal forcing.  My concern here is that it is hard to derive a meaningful value for gamma in regions where there is minimal mass loss, and therefore hard to deduce the actual sensitivity of the region to changes in ocean temperature.  The uncertainty around CMIP6 ocean warming coupled with the lack of historical mass loss in some of these key regions makes finding a valid range of gamma very difficult. This problem is manifested when the authors find that ESM-RF pairs underestimate the magnitude of observed Antarctic sea level response despite being tuned to match it. Furthermore, after picking the top 10% of ESM-RF pairs, some regional hindcasts do not capture the observed sea level response (Figs A1 & A2). As a result, I’m concerned that the conclusions drawn about the future contributions to sea level, and their uncertainty analysis, are rendered less credible.  

Second (and this is a correctable issue) I felt that the rational/motivation for doing the calibration on ice discharge rather than basal melt rate was not well-articulated.  I think the authors could add stronger language for why this method is worthwhile.  This should also be put in the context of ISMIP6 and LARMIP-2 methodologies, and what potential issues calibrating to basal melt rate could create.

Specific Comments:

L41:  UK-ESM has included an evolving ice sheet in a GCM framework.  And there are other efforts currently in the works in other groups to include an evolving Antarctic ice sheet in a ESM.  So not sure what is meant by ‘short-term’ here I guess.

L69: Please specify why GSAT is a less desirable metric than subsurface temp. Or alternatively, why is it a more useful metric? Easier to derive?

L72:  How is future loss consistent with past loss? Please elaborate on pros/cons of ISMIP6 calibration methodology and your methodology here. What makes your useful? Motivation needed.

Table 2: Is this the mean grounding line depth? I believe so, but if it is, shouldn’t Amundsen GL depth be closer to ~500m?

L108 – L114:  Could rearrange this to start with the motivation first (ocean T bias will affect magnitude of basal melt rate in quadratic estimate, therefore these are the steps we take to deal with it).  Currently this feels like you don’t know why you’re dealing with bias correction until after it is explained.

L118:  Why remove the mean bias, which may even have the opposite sign to the model-specific bias? Why not just remove the bias for each model?

L143: Please note why/how this assumption is flawed.

L148-149: Is there wide variability in salinity between far-field and sub-shelf? Ie. Please comment on whether using far-field salinity climatology is a fairly broad assumption, or not? Please discuss.  The same goes for T_f too.

L166: consider rephrasing this since but here you say sea level contributions are calibrated on ice discharge, but the rest of the paper states that basal melt rate is calibrated on ice discharge. I understand what you mean here, but this may be confusing for readers.

Section 2.3 in general requires more work to increase clarity for the reader.  Please describe the iterative process, how it works. And please expand on the rationale for why to do unbounded vs. bounded methods, as well as the discussion on how the ‘unbounded’ calibration range is determined. The final paragraph of this section also needs some more clarification.

L138:  Please define T₀ . It is not defined.

L227: What calibrated gamma values? All of them? The full range? The median? Mean? This is unclear to me.

L239-242: What is “reasonable extent”? Also, this seems fairly problematic to me. If the ESM-RF pairs cannot capture the magnitude of the observed Antarctic sea level response, even though they are calibrated to do so, what does this say about the methodology? This is assuming that the past conditions and sensitivities hold into the future as well, which may or may not be true, particularly when feedbacks become triggered (e.g. MICI).   This is illustrated by the observation that pre-2010 discharge is overestimated, and post-2010 discharge is underestimated.

Figure 6: What gamma is used? Median? Mean? Full range? Is the shaded area intermodal spread, are you using a spread in gamma too or just a singular gamma value? 

L407: Please spell out the argument that applies to ISMIP6 gamma-values.

In general I enjoyed the discussion, and thought that plenty of this type of language could have been used as motivation/context in the introduction. Just something to consider. 

Minor Comments:

L 7-8: Explicitly state all three SSP scenarios used.

L23-24: include references for model (ice sheet models, I assume?) and geological data being referred to.

L25: Moreover, melt of Antarctic land ice…

L32: Using similar methodologies to what? To each other, I assume…?

L32-35: Can you mention why uncertainties are increasing?

L36: Future projections are always based on modeling (not often).

L38 & L42: What do you mean “balanced by data from ESMs”? Please clarify.

L39: Is there a citation for claiming ice sheet-ESMs show undesirable/unrealistic trends ?

L46: Used as one basis for projections…

L56: In that study, the temperature…

L75-76:  What does it mean to arrive at an estimate of future mass loss that is consistent with observed mass loss over the past four decades?

L86: Reference Lambert et al (2021) here would be appropriate.

L91: Please state explicitly what Levermann et al calibrates to.

L97: What does “delayed ice sheet response” mean here?

Table 1:  What level does “subsurface ocean temperature” refer to here? I assume it is the mean depth of the grounding line (table 2), but please be clear.

L103: The ocean temperature time series…?

L107: Remove text: “For the quadratic melt parameterization”.

L123 & 142: Do any CMIP6 models represent cavities?

L126: Table 3 is referenced, but perhaps prematurely. I suggest T3 and T4 are swapped in order. 

L138: “See Table 4…” already noted earlier.

Figure 5: Increase font size here please.

L227: “as specified on top” à “as specified in the titles”

L281-285:  This text seems to be repeated again later on from L290-295.  Please give this another proofread to make sure there is no longer repetition and the flow works well.

L326: “The differences with ISMIP6 and LARMIP-2…”  I think you mean difference between this study’s results and these two studies, but this phrasing leaves this ambiguous.

Fig11&12: Label the x-axis please. And possibly increase fontsize.

L345: “is computed using forcing from state-of-the-art…”

L346: “CMIP6 applied to linear response functions…”

L364: Is there an appropriate reference for the comments made about ESM performance?

L373: By climate-state dependent do you mean time-evolving?

Table 7: Please state what the percentages refer to. Also add units.

L376: Please elaborate on the processes you refer to here.

L384: The better prediction of future mass loss you do achieve is for less physically defensible reasons, no?

L386: Elaborate on the advantages and disadvantages.

L395: Therefore, it is interesting…

L434-435: Please state what you mean by ‘highest’ and ‘lowest’ methods.

FigA1 & A2:  Font sizes of tick labels and axis labels could be increased for better readability.

In general, section headings could be more clear.  For example, “Magnitude and Rate” and “Best Estimate” could be more specific to help the reader understand what the section is about.