General Comments

The manuscript, “Resolving GIA in response to modern and future ice loss at marine grounding lines in West Antarctica” by Wan et al., addresses what computational grid is required to resolve the local sea level changes caused by solid-earth responses to changes in cryospheric loading, and how those compare to uncertainties in the solid-earth mechanisms (e.g., elastic vs. viscoelastic, poorly constrained viscosities). These questions are particularly salient for those engaged in describing and forecasting the sea level effects of changes in the cryosphere, particularly in areas, like West Antarctica, where such solid-earth feedbacks on the future dynamics of the ice are a significant source of uncertainty.

The authors find that the limiting factor for spatial resolution is the representation of the load, rather than the smoother solid-earth response, and provide a useful rule of thumb for determining what resolution is necessary to compute the elastic response of certain loads. They additionally show how uncertainties in the behavior of the mantle (in particular, the possibility of a low viscosity zone underlying parts of West Antarctica) can generate signal differences far exceeding errors caused by resolution, emphasizing how critical it is to include these processes in modeling and to encourage observational constraints of the mantle rheology. 

The manuscript is well presented and I have only a handful of rhetorical suggestions to help with cohesion and flow, and one requested additional model run to resolve an apparent inconsistency in the comparison of the 3D rheologies with the 1D average rheology.

Finally, I would like to encourage the authors to release their model code source publicly, in accordance with the journal’s data policy, to “guarantee integrity, transparency, reuse, and reproducibility.”

Specific comments

Comment on the 1D Viscosity: The vertically averaged GIA model you use to compare with the 3D viscosity models is for the whole of Antarctica and therefore not reflective of the viscosity underlying your region of interest (the Amundsen Sea). It makes it difficult for me to evaluate claims like the one made in Line 378 that there is a dependence on the 3D structure within the Amundsen Sea domain or in Line 404 that a 1D viscosity, rather than one with simply a long relaxation time, is closer to the purely elastic model. I appreciate that you quantify the importance of GIA from outside the Amundsen Sea (L313 and Supplemental S1) as being about 6% of the central response, and so might be hesitant to apply a lower viscosity 1D average to the globe. However, if you were to focus only on load changes in the Amundsen Sea, is there not any 1D viscosity profile or relaxation spectrum that, within other uncertainties, reproduces? This would greatly strengthen the cited arguments and the comparison you make in Figure 8.

Comment on ice dynamics and grounding lines: Though the paper’s technical scope is focused on modeling local sea level changes due to solid-earth processes, part of the justification is that these sea level processes will affect the dynamics of the ice’s grounding line, and are therefore necessary to model in tandem. I think a good place for this discussion could be surrounding the location of the grounding line under different resolutions and physical assumptions (e.g., elastic or viscoelastic mantle). And yet the final grounding lines in Figure 2, 4, 6, and 7 doesn’t appear to change at all from case to case - the variation in the sea level (almost 20 m near the grounding line in Figures 2i,f) doesn’t seem to affect where ice is floating. Is that right? In contrast, when we included the ice dynamics, we found a lag in a grounding line position of about 30 km after 100 years for a similar amount of sea level fall at Pine Island (Figure 3b in Kachuck et al., 2020). Considering this will significantly affect the resolution error near the grounding line that you show in Figure 9, and I think is worth discussing.

Line-by-line

L35: Instead of “consists of… and…”, you might indicate that a viscoelastic material’s response begins as that of an instantaneous elastic solid, and transitions to a longer-timescale viscous-like relaxation. For heuristic and analytic purposes we sometimes treat them as separable and additive.

L60: “Viscous effects due to ongoing ice loss … ​​have not been included in recent high resolution coupled projections”: You could cite Kachuck et al (2020), Coulon et al. (2021), or De Conto et al. (2021) as recent examples of coupling ice dynamics to viscous vertical land motion in projections. The first has high spatial resolution, with 500 m grid spacing near the grounding line, for projections with viscoelastic feedback of Pine Island Glacier in the Amundsen Sea Embayment. The others are Antarctic-wide and determine that the ELRA model, and modifications thereof, are satisfactory for constraining large-scale sea levels.

L246: An image of the ice load and topography would really help in understanding this description.

L255: The Scaling Factor used in Figure 3b is not introduced in the main body text and doesn’t appear again in the results focused on the Amundsen Sea. I would recommend integrating it more (see next note). Additionally, "scaling factor" is used previously to refer to the construction of viscosity profiles from seismic data (e.g., L179), muddling the usage. Another term might make this clearer.

L322: I could use more elaboration here on the differences between representing the ice load and computing the elastic response, and maybe some tie-in with the Idealized Experiments results. Is the idea that we need finer resolution for better representation of the grounding line (i.e, where the ice load disappears), but not necessarily for the smoother earth response, which is consistent with your findings in the idealized experiment? If so, could you use the Scaling Factor from Figure 3b to explain this? In those earlier experiments, though, am I right in understanding that you didn’t have any ice-ocean interaction? Does the ocean load smooth that boundary?

L353: It is hard for me to visually evaluate this statement across the different scales of the colorbars.

L369: “A viscous process” is vague. Could you specify that this is a result of assuming viscous incompressibility, or whatever other viscous consequence you are referring to?

L423: This would lead me to conclude that high resolution is not important for coupling viscoelastic deformation to grounding line motion. Do you believe that to be so? Are there conditions you can foresee in which resolution would play a larger role?

L465: Although this feedback on grounding line dynamics is not addressed in this study.

L489: see comment to L322. Clarification there will also clarify here.

Technical corrections

L136: “structure. which”

L475: “reflecting” -> “reflect”

L481: missing word in “over time our simulations”

Comments on Supplemental material

L36: The referenced plot is titled “ASE_10km-ASE_1km” rather than “ANT_10km-ASE_ANT.”

Caption to Figure S1. The grounding line appears to be a shade of green rather than the red as described in the text (which will probably be very difficult for individuals with red-green color-blindness).

Figure S2.2a) It looks like the recorded minimum of -3.21 m sea level occurs outside the domain, given the scalebar.

Figure S2.2b) max and min are written as negatives, but look on the scalebar as positive.

Summary

“Resolving GIA in response to modern and future ice loss at marine grounding lines in West Antarctica” by Wan et al.

In this study the authors seek to find out what GIA model resolution is required to accurately capture viscoelastic deformation in response to present-day and future ice loss in the Amundsen Sea Embayment of West Antarctica. They conduct several experiments to determine this: 1) the elastic response to an idealised cylindrical load; 2) the elastic response to realistic ice loss; 3) viscoelastic response to realistic ice loss with a 1D earth structure and three 3D earth models. The results are given in terms of percentage error for each grid resolution tested and the authors find that errors converge at a resolution of 3.75 km, or three times the radius for the idealised experiment. Furthermore, the results show that the error from neglecting viscoelastic deformation over short time scales, or from adopting different 3D earth models, is far larger than the error from grid resolution.

This topic is timely given the efforts within the GIA community to improve models. High-resolution models are very computationally expensive, prohibitively so for most, and quantifying the error for different grid resolutions is very valuable. The paper is well written and clearly organised but would benefit from some small amendments to the text as suggested below.

General Comments

1) The main conclusions from this study state that the GIA model grid resolution needed for an isolated cylindrical load is three times its radius, and that for realistic ice loading in the ASE a grid resolution of 3.75 km is required to achieve an error of 2%. I think the paper could be improved by adding a qualitative discussion of how these findings might apply in other areas. Line 344 states “for most applications, errors of less than 5% can be achieved with a 7.5 km grid, and errors of less than 2% with a 3.75 km grid”. It would be beneficial to have a short section in the discussion expanding on this, discussing whether this rule of thumb is limited to ASE, or marine grounding lines, whether it might apply in other areas of Antarctica where present-day ice change is occurring, or how different spatial scale of ice loading change might affect this general rule.

2) In this study the authors find that representation of the ice load on the GIA model grid leads to higher error than the grid resolution itself, however, there is no discussion of how representation of the Earth structure within the model grid might impact the results. Particularly in Section 2.2 and 2.3, what is the resolution of the seismic tomography data that is used? How does this compare with the vertical resolution of the grid with depth, how much is it being down sampled? Perhaps the results from the tests mentioned on line 158/159 could be included in the supplementary information.

Specific Comments

Line 21: The authors repeatedly refer to a “spatially isolated load”. The use of this term is particularly important since once of the main conclusions of the paper – a grid resolution needed of 3 times the radius of the load – only holds for cylindrical loads. For clarity, consider changing this term to “spatially isolated disc/cylindrical load”.

Line 57: please quantify short spatial scales, e.g. 10s of km, or 100s of km.

Figure 1c: is the white area saturated? Please add to colour bar

Figure 1d: scale bar in the figure is not clear. The choice of colour bar makes it difficult to see the regional variation in viscosity.

Line 151: 70 radial layers – Are these radial layers where properties are assigned, or is this the vertical resolution of the grid? On line 153 it says layer boundaries at 12, 25, and 43km, again are these the boundaries of material properties or grid resolution?

Line 157: 29 million nodes is a lot! It would be interesting to add here what the run time of this model is.

Figure 3a:  consider adding solid/dotted/dashed lines to the key for the 2/5/10km ice, or perhaps label.

Figure 3b:  x-axis label - Grid Resolution km, not m?

Figure 3b-e:  y-axis would look better labelled at 2km intervals rather than 2.5 km intervals.

Line 260: “grid points” do you mean nodes? Is the load applied at the nodes or the centre of the elements?

Line 292: “serve as a guide…. appropriate grid resolution for a given problem” I think its important to include here that this guide is restricted to isolated cylindrical loads.

Line 335-344: There is reference to Figure 5(a) and 5(b) in this paragraph but there are no corresponding panels in figure 5. Fig 5 caption also only states (a).

Figure 6: (and 2/4/7) it would be useful to include the acronyms ICE_SH etc referred to in the text in the column headings of these figures.

Line 397: This reference is missing from the list.

Figure 8: panels b and c need y-axis labels; the grey colour showing ice thickness in the lower panels is washed out and hard to see. In the caption for panel a) this is not identical to figure 3c, perhaps figure 2 instead.

Line 402: It is confusing to label these two sites A/B since the panels in the figure are labelled b and c. Perhaps change to 1/2 or X/Y, since I think this is the only time they are referred to anyway.  

Line 403: it is not clear what the authors mean by “spin up time”.

Figure 9: the hollow diamonds don’t show up very well on this figure.

Line 560: add “in the ASE” to the first sentence to clarify the region the conclusions apply to.

Line 564: would be useful to quote the percentage error in conclusion (1)

The following paper is relevant and worth citing:

Blank, B., Barletta, V., Hu, H., Pappa, F., & van der Wal, W. (2021). Effect of lateral and stress-dependent viscosity variations on GIA induced uplift rates in the Amundsen Sea Embayment. Geochemistry, Geophysics, Geosystems. https://doi.org/10.1029/2021GC009807

Technical Comments

Line 158: missing word “limited to the surface (and?) a few layers down to 10km”

Line 211: incorrect spelling of adopted

Line 475: reflect rather than reflecting