The work of Lecavalier and Tarasov assesses uncertainties in the solid Earth's response to loading and unloading of ice (and consequently the oceans) in the Antarctic. The authors show that there is a much larger uncertainty and different spatial patterns than previously estimated by the more popular Glacial Isostatic Adjustment (GIA) models, which are used to estimate the present-day AIS mass balance. Their assessment is done by history-matching a large ensemble of simulations using the Glacial Systems Model (GSM), producing a Not-Ruled-Out-Yet (NROY) subset that is further used as input to adhoc simulations of GIA using a more faithful solid-Earth model. The GSM ensemble is the same presented in a companion paper. They further use the NROY ensemble results to discuss implications for the climate and GIA (including when that means a limitation of the used forcings or solid-Earth models and parameter ranges).

Overall, the paper structure is mostly clear and easy to follow with just some points where the text could be improved, sometimes by rewriting confusing paragraphs, sometimes by clarifying some technical parts. Below I make some general remarks with suggestions to improve the overall state of the paper before it can be published, provide technical/editorial suggestions line by line, and finally comment on how to improve some of the figures presented.

I hope the authors find my comments useful, and I look forward to seeing a revised and improved version of this manuscript.

General remarks

1. The introduction adequately provides the background necessary to contextualise the paper, but it lacks a proper ending pointing the reader to what research question(s) the study aims to address. Please add a final paragraph or a couple of sentences framing how the present study fits into the picture provided, and what its goals are.
2. As per TC's guidelines, papers that are submitted or in prep (i.e., not yet available and without a DOI) cannot be cited. This needs to be rectified before the manuscript can be published. I suggest acting on it now instead of waiting for the same issue to be pointed out by the typesetting or copy-editing teams.
3. Considering I am no GIA expert, and that this paper is likely targeted at paleoglaciologists and ice sheet modellers as well, I personally feel that the GIA model description part is quite confusing and a bit unstructured, and could be improved. It would be beneficial to this manuscript if the authors invested some time in improving the flow of the model description section (especially the last two paragraphs), rearranging some of the sentences to make the sequence of information presented more logical (e.g., not going back and forth between the GIA and ice sheet components) and adding some clarifications to the more technical terms (e.g., PREM structure). I believe such changes would provide a much better context for the results, and aid the non-GIA experts who would likely be interested in this paper. 
4. The authors offload most of the explanation regarding scoring the simulations to two other papers: One that is "in prep", and another that is an exceedingly lengthy pre-print which was never accepted for publication. The "in prep" manuscript is provided as part of the review process, which is much appreciated (I actually found it very interesting and look forward to seeing it eventually published). Still, it is very much in preparation, and I could only get a general grasp of how the scoring was done. Considering that details regarding the scoring are not the focus of the manuscript under review, and "in prep" manuscripts cannot be cited, I would only ask that the authors explain slightly better why NROY simulations (or the entire ensemble, actually) do not bracket some observations, as evident in Figs 2 and 3. Is it because by choosing e.g., 3.5 or 4sigma means the "allowed variability" is actually larger than the ensemble variability itself? And what does the sigma refer to? Is it simply the standard deviation of the metric(s) being shown in the graphs?
5. The GLAC3 chronology comes totally out of the blue, being mentioned only in the abstract and conclusions. All I can gather is that it stems from the NROY ensemble, but no other context is provided. It would be worth contextualising it and saying why it is relevant, so the reader can appreciate how the NROY ensemble relates to it.

Line-by-line comments

L29-34: This feels more like a sequence of bullet points written in-line instead of proper text. Please rewrite and give it a proper flow for the reader, as it is hard (even if still possible) to follow the implications of one to another

L37: Please add a comma after "that" so the sentence actually states that it was your study that adequately explored the uncertainties, and not the previous studies.

L58: There's an extra ":" at the end of the line

L63: Is the author's last name really "A"? I could not find it in the reference list

L128-129: "ensemble parameter controlled three shell viscosity structure": some hyphenation needs to be done here so the reader can properly understand what is going on...

L186: Either "Antarctica" or "the Antarctic"

L195: A full stop works better than a comma after "matching"

L263: It is not clear which criteria were used to choose the HVSS. What counts as "High Variance" in this subset?

L323: Please change "Although" for "However"

L397: There's an extra "is" that does not make sense in this sentence

L438-440: It would be useful for the reader if this sentence was discussed more in terms of climate than "degrees of freedom", i.e., what kind of atmospheric, ocean, and basal conditions not captured in GSM would be necessary to fit the vertical motion estimates at sites 8426 and 8502?

L480: What is the difference between the minimum score and the joint minimum score? Is the GPS score not included in the former? If so, please clarify that in the text.

L515: I believe it should be "reliance on three reference..."

L562: Here you state that the ensemble comprises 9,292 simulations, whereas in L16 and L255 it is stated 9,293. Please double check which one is correct

L571-579: I struggle to see how this paragraph fits in the Conclusions section. It reads much better without it, but I do understand that this relevant information. I'd suggest the authors to either rewrite it, or to move this to the previous section, making the appropriate changes so it fits in the text. This is related to my general comment #4

Figures

Figure 1: Please add to the caption what the abbreviations in the legend mean (paleoExt, paleoH, paleoRSL). In the text, only paleoH is explained

Figure 4 and all others in similar style: It looks like the grounding line shown is that of present day. I would recommend changing to that of one of the reference simulations, so the figures can better illustrate the solid-Earth response to changes in ice loading/unloading

Figs 4 and S3: What is the significance of a RSL value where ice is grounded? If nothing, wouldn't it be clearer to mask out values where the ice is grounded in all ensemble members for each of the time slices? I would imagine this can be addressed in combination with a solution to my comment above.

This study presents an ensemble of coupled ice sheet–2D Glacial Isostatic Adjustment (GIA) simulations applied to the Antarctic Ice Sheet over the last two glacial cycles. The authors conducted 9,292 simulations and employs history matching techniques using Markov Chain Monte Carlo (MCMC) sampling and Bayesian Artificial Neural Networks (BANNs) to efficiently explore parameter space and refine model estimates. They selected a sub-ensemble of 82 simulations that best align with the bounds of past and present GIA and relative sea-level (RSL) observations. The selected sub-ensemble aims to provide improved constraints on past and present ice sheet evolution and the associated GIA response, contributing valuable insights into uncertainties in Antarctic mass balance assessments. The results indicate that the uncertainty in present-day GIA is greater than previously estimated by IJ05_R2 (Ivins and James, 2005), W12a (Whitehouse et al., 2012b), and ICE-6G_D (Peltier et al., 2015), particularly in the Amundsen Sea Embayment.

General Remarks

This study holds significant value for the scientific community. The analysis is well executed, and the figures are effectively presented. However, the methodology section is too concise and the section often refers to manuscripts in preparation and a preprint. Therefore, additional methodological details should be described within this manuscript. The interpretation of specific areas requiring additional explanation are outlined in the detailed comments below.

The sensitivity test often cited to explain differences between the model ensemble and the dataset examines the effect of lateral Earth structure. However, using 2D structures with a relatively low mantle viscosity results in significantly different ice sheet evolution, bedrock uplift and sea level change than using 3D Earth structures (Gomez et al., 2018; van Calcar et al., 2023). Additionally, the test employs an uncoupled GIA model, where lower viscosity affects ice sheet dynamics differently than in a coupled model, as the stabilizing GIA effect is absent. This likely leads to an overestimation of uplift between 15 and 5 ka due to stronger ice mass loss in the uncoupled model compared to a coupled model. Since the test does not fully assess the impact of lateral structure in the original coupled model ensemble but rather the effect of globally lower viscosity in an uncoupled model, its limitations should be acknowledged. While coupled 3D GIA–ice sheet simulations are not expected, the methods section should clarify these constraints, and the results should discuss potential uplift overestimation and its implications.

Last, the conclusion now consist of a short summary of what has been done and of recommendations for future work. This section would be improved by including more detail on the performance of the NROY subset and the 2sigma subset. Conclude which subset performs best in which region and the corresponding uncertainty ranges.

Line-by-Line Comments

L123: The expanded climate forcing scenarios are known to be of high influence on the ice sheet model and is later in this manuscript mentioned as an important source of uncertainty. It would therefore be useful mention which expanded climate forcing scenarios have been applied.

L126-128: Please explain how the PREM density structure is applied to the layers of in the model.

L130-131: Please mention explicitly what the GIA component in post-processing modelled ice sheet chronologies is.

L135-136: Explain in detail what is meant by zeroth order geoidal approximation and how this is applied.

L136-138: At this point in the text, it is not clear what is meant by “full transient simulation” and why the simulations in section 4 are different from the simulations in the other sections. Please elaborate in the text which method is used for which simulations exactly. It would be useful to end the introduction with a short overview of which simulations are discussed in which section so that the reader has got an overview to which you can refer to lines 136-138.

L148-149: Please indicate why these ranges for viscosity and lithospheric thickness have been chosen and discuss the implications of this choice on the results. As mentioned later in the manuscript, it has been shown that the upper mantle viscosity can regionally be orders of magnitude lower than 0.1*10^21 pa s (e.g. Barletta et al., 2018). Furthermore, it has been shown that using a uniform upper mantle viscosity of, for example, 10^19 pa s better represents a laterally varying Earth structure than a uniform viscosity of 10^21 pa s because most ice mass changes have occurred over the West Antarctic Ice Sheet and the average viscosity of the West Antarctic Ice Sheet is an order of magnitude lower than 10^21 pa s (van Calcar et al. 2023).

L212-216: It is not clear how the 5% error estimate for RSL was chosen. Additionally, the range of bias error for present-day uplift rates needs further clarification. Is this range site-dependent, and if so, what parameters influence its variation?

L220: The concept of multi-million-point Markov Chain Monte Carlo (MCMC) sampling should be explained.

L220: Please also mention how many simulations were included in the original Glacial Systems Model (GSM) ensemble.

L221-226: For improved readability, consider moving the sentence "The BANN targets… for data-model comparison" to line 222 before "The BANNs were trained…"

L226-227: The term "MCMC converged sampling chains" requires further explanation. How was convergence assessed? Additionally, more context is needed on the role of the Bayesian Artificial Neural Network (BANN) architectures prior to this sentence.

L245-247: What measures have been taken to address the potential issue of overfitting? Could the discrepancies be due to deficiencies in the climate model rather than model overfitting? Please provide a discussion on overfitting control.

L248: Clarify which previous ensembles of simulations are being referred to.

L255: The selection process for the 9,293 simulations is unclear. Additionally, where did the 30,000 model simulations originate? Are there references supporting this methodology? A step-by-step description of how simulations were filtered and refined would be beneficial.

L263-267: Define how "high variance" is measured in the subset. What parameters exhibit high variance? What criteria were used for selection? List all key metrics of interest and the minimum scores to which relevant data types.

L268: Clarify how the repeated GIA post-processing has been done.

L269: Also include the upper limits for lithospheric thickness and upper mantle viscosity, as well as the step size used in the sensitivity analysis.

L271: Figures S1 and S2 are referenced but not discussed. A brief summary of their implications should be included in the main text to guide the reader.

L289-290: Please elaborate on how GPS measurements are elastically corrected. Could this correction method contribute to the discrepancies in the model fit for West Antarctica? A brief discussion on the limitations of the elastic correction approach would be valuable.

L322: Can the required upper mantle viscosity for data consistency in this region be quantified?

L323-324: The manuscript lacks a clear definition of “lateral structure” and whether is or is not a lateral structure in a certain region. Lateral variations in viscosity depend on spatial scale, and the sensitivity of RSL measurements depends on the extent of ice (un)loading. For example, at the Syowa Coast, viscosity varies by one to two orders of magnitude over 300 km (e.g. Ivins et al., 2023). The inferred average viscosity of ~10^20 Pa·s for this region appears reasonable. Additionally, while inconsistencies could stem from climate forcing, the possibility of errors in the Earth structure model should not be dismissed.

L454-455: Provide a clearer explanation of the distinction between nominal ranges and Gaussian confidence intervals.

L455-456: Briefly justify why the reader should consider the complete NROY sub-ensemble. How do the results of the full NROY sub-ensemble compare to those within the nominal 2σ range? A short discussion on the added insights from the complete sub-ensemble would be beneficial.

L466-467: The phrasing suggests that uncertainties in regional RSL measurements are large. However, given the relatively small error bars in Figure 2, the uncertainty appears to stem from the model fit to all Antarctic RSL measurements rather than the measurements themselves. The sentence should be reworded to emphasize model uncertainty sources, including the choice of climate and GIA models (2D instead of 3D).

L469-471: Provide examples of specific regions where this effect occurs. Do these correspond to areas with the largest RSL uncertainty ranges?

L570: GLAC3 is mentioned for the first time here. Please include an explanation in the method section.

Figure 1: The caption should briefly define the abbreviations used in the legend (e.g., paleoExt, paleoH, paleoRSL).

Figure S1 & S2: Ensure consistency between the legend and caption regarding viscosity values. The notation should be clarified, and redundant legends should be removed for clarity. The caption states that UMV varies from 5·10^21 to 0.005·10^21 Pa·s, but the legend lists values of 0.05 and 0.005, presumably referring to 5·10^19 and 5·10^18 Pa·s. Clarify this discrepancy and ensure consistency in notation.

References E. R. Ivins, W. van der Wal, D. A. Wiens, A. J. Lloyd, L. Caron, 2023. "Antarctic upper mantle rheology," The Geochemistry and Geophysics of the Antarctic Mantle, A. P. Martin, W. van der Wal.