General comments

This paper presents a thorough and rigorous method for producing calibrated projections of sea level rise from the Amundsen Sea sector of West Antarctica, using a multistep process to consider and constrain uncertainty from a wide range of sources, by combining both a numerical ice flow model and a statistical surrogate model. The resulting sea level contributions by 2100 under RCP8.5 and Paris2C are at the lower end of the range of estimates from previous studies and similar between the two scenarios. They also extended some simulations to 2250 and found the two scenarios diverged after 2100 due to differences in snow accumulation.

In general, the study is very well presented (save a few consistency errors – see technical corrections below) and structured clearly, with a lot of methodological detail. However, I think certain later sections could benefit from further discussion and interpretation, e.g. Section 4, in particular, is very brief and offers no real interpretation, which is a bit of a shame – see specific comments for more detail.

Specific comments

There are several places where statements are made without supporting citations:

• L83-84: give examples of studies that use a mixed sliding law
• L114-115: reference for 50% figure?
• L148: reference for melt due to GHF?
• L537: reference for observed rate

L106: what is the threshold for the limit on superimposed ice, and where does this come from? How sensitive is runoff to this threshold – couldn’t this also feed into the Bayesian inference?

L113-114: This sentence implies that there are no other contributors to basal melt of grounded ice – perhaps worth clarifying that this is referring to your model rather than reality. For example, geothermal heat flux is mentioned later on as being of less importance, but this sentence implies it doesn’t contribute to melt at all.

Figure 2: caption could include more detail, e.g. define the colormaps. In the main text, are you able to offer any physical interpretation of what these PCs are showing?

L369: is the assumption that observational errors are spatially uncorrelated robust? E.g. velocity errors (in magnitude and direction) are dependent on flow speed.

L446 / Section 4: the interpretation and discussion in this section could be expanded. For example, why do think that the weight given to surface elevation change in the inversion (along with other inversion parameters) is the biggest contributor to uncertainty? Does this indicate that the model is most sensitive to C and A, or are the inversion parameter priors simply considerably wider than those of other parameters? Given the sensitivity, what is the implication therefore of keeping the C and A fields constant throughout century-scale forward simulations (I realise this is the way it’s done, but interested if your results give further insight into whether this can really be justified)? How do the various inversion parameters translate to variation in C and A, in magnitude and spatially? Do these fields differ a lot between the 1996 and 2021 initialisation?

For some parameters there is a big difference in the Sobol indices between RCP8.5 and Paris2C (e.g. basal mass balance parameters) – could you comment on this?

L478: perhaps worth noting that this rate is very similar to the present day observed rate for the sector.

L485-486: “Secondly, using adaptive mesh refinement…” – many of the studies cited above use BISICLES, which also uses AMR, with a resolution of 250 m at the grounding line, so this sentence is a bit misleading. In general, this paragraph could be developed further – e.g. the inclusion of a plume model rather than a very simple melt rate forcing used by some of the others could be discussed.

L561-564: It seems strange to introduce the concept of testing the reversibility in the final paragraph of the conclusions. Perhaps it would be better suited to the discussion, along with the relevant citations.

L580-581: I think limiting ocean driven melt to strictly ungrounded nodes is a sensible and widely used approach, but here or elsewhere, perhaps it is worth commenting on recent modelling and observational work that indicates that ocean water intrusions far upstream of the grounding “line” could be contributing significantly to melt? E.g. Bradley and Hewitt (2024, 10.1038/s41561-024-01465-7), Rignot et al. (2024, 10.1073/pnas.2404766121).

Appendix B: perhaps I missed this, but how do you sample the parameter space for the Ua-obs ensemble used to train the surrogate?

Technical corrections

Please ensure that all abbreviations/acronyms are defined at point of first use (e.g. SLR, line 22; RNN, figure 1).

Table 1: check inversion parameter symbols vs names

Check formatting of citations, e.g. years not in brackets (e.g. L151), use of et al. vs and others.

L348: thinnning -> thinning

L390: remove extra “model”

Fig. 4: E_dhdt -> hdot_e?

Fig. 7: hdot_E -> hdot_e (probably worth checking consistency of symbols throughout)

L440: colormap for GLs is brown (as indicated by the figure 6 caption) not red.

L585: “is draft” -> “ice draft”?

The following is a review of “Calibrated sea level contribution from the Amundsen Sea sector, West Antarctica, under RCP8.5 and Paris 2C scenarios”, by S. H. R. Rosier et al.

General Comments:

In this discussion, the authors introduce a new methodology for comprehensively determining uncertainty of ice sheet model projections.  The study focuses on modeling ice sheet change in the Amundsen Sea sector of Antarctica under two different future emission pathways through 2100 and then through 2250, using the ice sheet model Úa. The authors design a method to derive uncertainty in their projections by training a surrogate model and then using Bayesian calibration to down select the most reasonable parameter space for their set of historical simulations.  They then sample the calibrated parameter distributions, running an ensemble of future projections, which are in turn used to train a new, time-dependent surrogate model to exhaustively cover the possible parameter space.  Results allow the authors to quantify uncertainty for every year of their projection and attribute uncertainty to each of their various parameters.  They conclude that uncertainty is dominated by parameters related to initialization of basal sliding and ice rigidity for both scenarios followed by parameters related to ice flow and basal melting.  Finally, the authors extend a subset of simulations in time through 2250 and find that mass loss accelerates through the year 2200, returning to a sea-level contribution similar to today’s by the end of the simulation, for both scenarios similarly. Results are compared against projections from previous Bayesian-based studies, concluding that the sea-level projections for this study are more conservative than others, especially considering that the simulations presented include a MICI mechanism for ice shelf collapse.

This manuscript is well written and of high quality.  The work is novel, and the figures are well designed, easy to read, and support the stated conclusions.  The experiments themselves required a significant amount of work and thoughtful effort toward their design. The authors take an organized approach to describing the complex workflow, including a helpful schematic figure and extensive appendices. For these reasons, I support the publication of this manuscript in The Cryosphere.

However, from a scientific point of view, I think the authors could expand upon their discussion of the results more.  I realize that the main point of the paper is to introduce the novel workflow to quantify uncertainty in ice sheet model projections, but the authors do make a point to compare their projection results against other published projections for the region.  They also conclude that their projections are more conservative than others, showing very little signs of instability (even though MICI processes were invoked during the simulations).  Because of this, I believe that the authors should do more than just show the end states of their projection ensembles; it would greatly enhance the manuscript if they also discussed why the simulations are tracking on the low end of sea-level contribution.  This includes expanding the discussion to investigate why the simulations do not match present-day sea-level contribution until 2200 and why the simulations for both scenarios increase so distinctly in the extended simulations (at year 2100).  I also think it would improve the manuscript if the authors noted some implications for their stated results and conclusions. Finally, I find that in some cases, the method description lacks detail and is vaguely described; it would aid the reader to have them clarified and/or quantified before publication. More specific comments are noted below.

Specific comments:

Fig. 1:  From my understanding, both the historical runs and the forward runs simulate the year 2021.  Is that correct?  If not, please clarify this throughout the text.

Table 1:  I suggest that you also include the ranges for these parameters in the table. That would be very handy information for the reader to have for reference.

Lines 78-79: … along “with” other sliding laws.  Additionally, please quantify “some time”.  It would also be helpful to the reader if other key sliding laws were explicitly listed (i.e. Coulomb and Weertman).

Line 94: Since you discuss the bias-corrected aspect later in the paper, it would be helpful if you noted that the correction later described (and perhaps reference the section) for the reader.

Line 106: Please include what this threshold is in the text.

Line 148: “which is at least two orders of magnitude larger than basal melting due to geothermal heat flux.” Is there a reference that can be added here for a noted estimate of geothermal heat flux magnitude?

Line 210: Please quantify what qualifies as “large” spatial gradients.

Line 216: Please specify mass balance, surface+basal mass balance?

Line 219: “after which all model forcing terms evolve based on the ERA5 outputs for the period 1996-2021.”  This statement is somewhat confusing, because if I understand correctly, the ocean forcing does not rely on ERA5. Similarly, my understanding is that the other (atmospheric) historical forcing is not dictated by ERA5 either (but corrected CESM1?). Please rephrase this section for clarity.  Also, ERA5 or the historical forcings have not yet been introduced at this point in the paper, so it is unclear what you mean by “ERA5 outputs”. Please either introduce (reference) it here or make a reference to Section 2.2 to help guide the reader.

Line 224: Please give a value for the initial coarse resolution.

Lines 239-241: This statement is confusing to the reader because RCP4.5 is noted as running through 2080, but the obs simulations only run through 2021, is that correct?  Also it not clear what “that most closely matches observed atmospheric conditions in the model domain” means.  Please rephrase.

Line 243: Please add a reference for the CESM1 simulations used here, as well as the ensemble simulations.  This part of your method discussing the inclusion of climate variability is quite vaguely described.

Line 252:  Is the bias correction done monthly (for temp and precip)?  Is the temperature correction spatially varying as well?  Please add a more precise description of this method.

Lines 257-258: Please clarify if the bias correction is done on all precipitation and temperature forcing, even the fwd simulations.  In this case, if the historical bias correction for precipitation was used on the future forcing, then the larger precipitation values grow, the larger the correction (because a scaling factor is applied)?  In this case, couldn’t the surface mass balance future trend be altered by the precipitation scaling?  Could you comment on whether or not that is a concern?

Line 265: Please specify how this is done.  Point by point on the forcing grid?  Is it for temperature only, or also for the ocean modeling?  I am curious about whether this affects your trend when you restart your simulations, as it is not clear why both emissions begin increasing in sea level contribution starting right at 2100 (Figure 9).  The RCP8.5 in particular changes from a downward trend to an upward trend almost instantaneously.  Have you diagnosed what causes the sudden retread based on your simulation ensemble?  This is an example of a curious model response that could be explained and discussed in more detail in the paper.

Lines 276-277: “Thus, the simulation start dates of 1996 and 2021 were chosen to ensure that the velocity and surface elevation change data were approximately aligned in time, but the precise timing is not well defined.”  This sentence is awkward, and I am not sure what it means, please rephrase.

Lines 311-312 and Fig. 2/3: My understanding is that you are focused on change of surface elevation and change in surface speed during your obs period.  However, I have found that the wording to describe these terms throughout the manuscript is confusing.  Sometimes you refer to just surface speed (i.e. Fig 2 is labeled surface elevation and velocity – a side note, in this case, perhaps velocity should be changed to speed?).  The Fig 2 caption also specifies that you are plotting variable change: i.e., “surface ice speed (top row) and surface elevation change (bottom row)”, but this sounds like you are considering only change with respect to the surface elevation, not surface speed.  This is similarly confusing in Fig. 3, since the plot labels include a delta, but the caption is not clear that it is delta speed being shown. In general, speed seems to be referenced in many sections of the paper, but I do not find it explicitly stated in each instance that the benchmark of interest is “change” in speed.  This just might be a question of wording and can be fixed easily. Please try to make this clear and consistent all throughout the manuscript.

Line 326: Please note what the resulting k values are in the main text for this analysis and Fig. 3.

Fig. 2: In my understanding, your calibration is based on the change of speed and the change of thickness over the observational period of interest. Do you think there are implications to choosing these diagnostics and how do you think it affects your results?  For instance, you are testing for a linear change but change in this area is temporally variable and non-linear.  Even the clear strong trend captured by the PC1’s (responsible for a significant portion of the changes) are in reality much more complex temporally. What are the repercussions of this assumption?  Mentioning these caveats in the manuscript and discussing on how these constraints were decided upon (or computationally forced) would be a very interesting addition to the paper.  This is especially the case because difficult decisions and concessions like these are likely why many others have not attempted an assessment of this magnitude. 

Lines 347-348:  With respect to capturing the trend and magnitude of these constraints spatially, do you think that PC2+ play an important factor in capturing the variability despite the lower dimensionality?  Having done all the work to assess the presented method, how reasonable do you think this method of calibration is, considering mass loss in this area is so non-linear?

Lines 359-360:  Please note or reference these physically plausible values, or reference where it is discussed (e.g. Appendix C).

Line 413: Quantify “large”.

Fig 4:  As you mention in Appendix B3, for instance, values for n have been questioned recently.  Your calibrated ranges for m and n are interesting to see, and they are a nice result in themselves.  It would be great to see some discussion on this result added to the text.

Line 424: Instead of using “~”, please specify the exact number of simulations.  Also, please note here that it is 2000 simulations in total (not for each of the scenarios as I understand it).

Fig 5: This is a really nice figure, with a significant amount of information portrayed.  While it is clear that the sea-level projections are conservative, and this is amply noted in the manuscript, it would improve the text if you discussed the reasoning for why the trend of sea level contribution is lower than the past observed long-term trend, and much lower than the present-day trend. I would be curious to know what is happening dynamically to slow down the sea-level contribution, and an interpretation of what those results mean (i.e., line 532 suggests that by 2100 the rate of ice loss is ½ of the present-day rate, which is a quite surprising behavior – what is stabilizing the model projections?). For instance, it might be that the majority of your simulations are generally stuck on their current grounding line (but it is surprising that it would happen to be for all of them), or there is something about the initialization constraints that do not allow the transient fwd simulations to contribute as much sea-level as is observed at their start (present-day).  Whatever is the cause, an analysis of the simulations could reveal a general conservative trend that many of ensemble members (ice sheet model runs) seem to be following. 

Line 455: It would be interesting for you to comment in the paper if you think this happens because of the type of inversion method being used for this study?  That is, there are larger degrees of freedom than if you just inverted for one parameter?  Do you think this uncertainty would be as strong if only basal sliding was inverted for, for instance?  Could you make a statement in the discussion about the implication for this and choices for model initialization impacting not only future projections but their uncertainty?

Line 494: The Sun et al., 2014 is based on Bedmap2 uncertainties, perhaps you could add some additional references for more recent papers that support this hypothesis using BedMachine or similar.

Lines 536-537: As discussed above, please add some assessment of why this is the case and what the implications are for these results, including the sudden increase in sea-level contribution in the extended projections. In addition, do you know what causes what looks like another stabilization (and even possible downtrend in sea-level contribution in Paris 2C) around year 2200?  Fig. 6 is very helpful to see that grounding lines do significantly retreat during the extended simulations, but have you seen any reasoning for why when analyzing the results?

Line 541: Please make a statement about what it means that these two scenarios are so similar. (In some ways this does make sense with the attribution analysis presented, that model setup and initialization is more important than forcing).  Does this mean that ice sheet modelers should take particular caution in initializing their models, especially as computational ability allows for a more complex method and therefore possibly more unknows?

Fig 9: Could you add a line where the current (or historical) sea-level rate of change is for comparison?

Line 552:  Could you make a statement about the implication of these results?  

Line 553: Do you think that your historical being linear and calving/climate variability being partly stochastic drives this result in any way?

Fig E1: This is a nice, and very helpful, plot to include.  It suggests that the pdf for your simulations should not be that different from what the surrogate model outputs.  Is that correct?  For the values of this plot, I think this is accumulated sea-level contribution at the end of each year.  Please clarify what the values of the axes are in the caption, to prevent confusion.

Technical corrections:

Fig. 1: Please define RNN, GMSL, and LSTM for this figure.  Some are defined in other parts of the text, but it would be helpful for the reader to have it spelled out here too.

Line 83: “popular” => I suggest using more formal wording here, like “used more frequently by the community”, or something similar that invokes a scientific backing.

Lines 89-91: “Note that other contributions to changes in precipitation (and hence accumulation) …”  This sentence is difficult to understand.  Please rephrase.

Line 100: Please make sure symbols are clearly defined (i.e. σ_M , T_cesm )

Line 154: Please make sure symbols are defined (i.e. r , r_c)

Line 200: Bedmachine => BedMachine

Line 234: “this study” sounds like your study, but I think you mean the Naughten study?  Please specify.

Line 330: “changed” => change

Fig. 3:  Caption should have elevation as the top row and speed as the bottom row.

Fig 7: On the x axis: h_E => h_e

Appendix A2: Please update the title so it reflects that this is specifically for ocean-induced melt

Line 742: “an Long” => “a Long”

Line 752: This statement does not need to be approximate.  Please include the exact number of simulations used.