“The impact of regional-scale upper mantle heterogeneity on glacial isostatic adjustment in West Antarctica” by Erica M. Lucas, Natalya Gomez, and Terry Wilson

In this study the authors investigate lateral heterogeneity in upper mantle viscosity below West Antarctica. They compare three different viscosity profiles based on three different seismic models, two that are able to distinguish higher resolution features. They use the viscosity profiles to investigate the effect on GIA in the region using three ice histories: extended modern, modern and future. The results are compared to GPS vertical and horizontal rates. The main findings are that there is up to 20% difference in sea-level change near the grounding line of Thwaites and Pine Island glaciers over the next 300 years. Showing that including higher resolution 3D variations in upper mantle viscosity is important for these crucial and highly dynamic areas.

General Comment:

Overall, the paper is interesting, and the science is solid. However, my main concern is that the impact is lost in the sheer length of the paper, with already a lot of figures in the supplementary material. My comments are geared towards simplifying this paper to allow the science to be more impactful.

Specific Comments:

• Scales: Abstract line ~18 and introduction. It becomes a bit confusing with the mention of scales here. You mention continental, regional, local scale, and then >150km, 50-100km, and 50-200km separately. It would be useful to clearly define the spatial scale in km of each of the continental, regional and local scale – perhaps lines on 78 and 80. Furthermore, “local scale” is then not mentioned in the results – they are either CONT or REG. Is the regional scale actually representative of regional and local combined? Please clarify and simplify. Line 86, again clarify the scale in km.
• Section 2.1: I think this section is too long.
  • 1D model – This is introduced as if there will be lots of comparisons between the 1D and 3D, but I can only see it in Figure 6 of the main paper. This is fine, and I’m more interested in the differences between the 3D models anyway, but perhaps state on line 132 that most 1D results are in supp info.
  • Line 162: why is this 1D viscosity profile different to that mentioned earlier? It is a global average? If so, I would suggest to delete the end of the sentence “consistent with previous GIA modelling…. In west Antarctica” as this makes it sound like previous modelling shows UM viscosity in West Ant to be 5x10^20
  • Line 175 to 181: Suggestion - I think you can simplify this to: “…47degS (Fig 1a). [delete the next bit] Global viscosity variations are estimated from GLAD because it offers improved structure compared to S326ANI that was used in Gomez 2024”
  • Paragraphs starting line 217 and 234: I think most of this detail should be moved to supp info, particularly (all of?) the second paragraph.
  • I’m interested to know how you join the regional models into the ANT20 model – in terms of the edge effects. Do you have to do smoothing where these two datasets are joined together? Or are they referenced to the same background model so its not an issue? Perhaps include in the supp information with (d).
  • Line 294: “error” feels a bit harsh. Change to limitations? Maxwell is still valid! Could you return to this in the discussion – any idea what might the impact be if the experiments were repeated with a transient viscosity?
• Section 2.2:
  • just on terminology here – modern/extended modern ICE-25/ICE-125. Later on ICE-125 is also referred to as “modern ice mass change” e.g. section 3.2 title. Either change “modern” to “extended modern” where referring to ICE-125, or state that there are two version of modern in this section, and then be clear which modern you’re talking about.
  • Figure 2 caption – some of this description is repeating what is in the main text on how the ice histories are constructed. Not needed in the caption. Panel b – over what area or drainage basic is this calculated?
• Section 4.1: comparison to horizontal rates. I question the inclusion of comparing to horizontal GPS rates (line 656 to 685; Figure 7b and c). As the authors state, the horizontal GPS are not corrected for any kind of background GIA rate, and so already the comparison between the model and GPS observed rates in 7b is not going to match. I think this whole section could be removed or put into supplementary information.

Minor Comments:

Line 51: Change to “Accurate modelled predictions” since empirical estimates of GIA do not rely on Earth properties.

Line 111: remove “the”  > according to Wan

Line 175: put the transition zone depth in brackets here to help the reader, and also for the Moho on line 216

Line 194: something has happened with the end of this sentence – “how to correct”.

Figure S1: the scale of 200km looks like a label, a bit confusing as I thought I was looking at two slices at 200km depth

Line 388: modern or extended modern?

Line 416: Super picky – but can you change the reference to Fig 3a where PSK is also labelled? To save a lot of going backwards and forwards to different figures.

Lines 541-551 and the next paragraph: I’m not sure I follow here. Does “higher relative sea level” mean “less sea level fall”? So the CONT model predicts more sea level fall than the REG models? Might be worth just clarifying here and relating to the colours on the graph.

Figure 6: Is this figure really needed?

Figure 7: The symbols are hard to see because they are so small. In fact, the statement on line ~650 “introducing regional variations in viscosity reduces differences between predicted and observed crustal rates at a number of sites” is really hard to see in this figure. It looks like the opposite is true. I wonder if REG_P ICE-25 should be removed, REG_S colour could be changed to group it in with REG_P, leaving CONT and 1D in blue/green.

Section 4.1: Is there also an elastic correction made to the GPS rates for SMB?

Line 716: What is this “O” in O(100m)? Please define

Line 720: alter the amount of uplift by 20% impacting the strength of the feedback…. Which way does this go – does it increase or decrease the strength of the feedback, i.e., is it stabilising or destabilising/less stabilising by including regional scale 3D variations in viscosity?

Code availability: It’s great to see that this code is on its way to being made publicly available.

General Comments:

The submitted manuscript investigates the impact of regional-scale (50-100 km) lateral variations in mantle viscosity on GIA model predictions in Antarctica. Understanding heterogeneity in mantle viscosity is important for interpreting geophysical data and modeling ice sheet-solid Earth feedbacks, and has critical implications for the future of the Antarctic Ice Sheet. 

The authors employ two previously published regional tomography models for their work. They stitch these models into continental- and global-scale topography models and convert the velocity anomaly to a viscosity anomaly. Their final models show similar features to previously published work, however, they highlight shorter wavelength variability, particularly in the Amundsen Sea. 

Model predictions of solid Earth deformation, gravitational potential change, and relative sea-level change with the regional viscosity structure show significant differences from the continental and 1D models. The authors highlight the importance of these findings by comparing their deformation estimates with GPS data from across West Antarctica. While they do not find that the regional model improves the overall fit to the data, they show convincingly that these differences are significant and warrant further exploration. 

This work presents a specific and important scientific problem and investigates it with sound methods. I find the work to be robust and believe it will make a solid contribution to our understanding of GIA in Antarctica. That said, I have outlined some issues below that should be addressed. 

Major Points:

In isolation, the parameter choices for the 1D viscosity model are well justified, as is the justification for the 1-D reference profile from which 3D anomalies are calculated. However, I find it confusing to use two different 1D profiles in the same study. It would be much easier to interpret the differences between the 1D and CONT/REG_P/REG_S models if those 3D models used the same reference 1D case. As written, it is unclear to what degree differences between 1D and 3D are due to the actual anomalies in the 3D model or due to the difference in the mean viscosity value (approximately an order of magnitude). 

I think the issue of vertical smearing in body wave tomography identified in Lucas et al. (2020) is overlooked. The authors explain that the checkerboard tests determine the amplitude recovery values, but do not explain how this is related to vertical smearing of the velocity anomaly. This limits the vertical resolution of their REG_X models and certainly has an impact on the GIA results they obtain so it should be discussed. It might also be noted that their vertical resolution is quite different to the ANT-20 model.

It is unclear to me how the regional models are inserted into the ANT-20 model. The relative travel time models should only provide velocity perturbations, while the ANT-20 adjoint model provides absolute velocities. It seems that to insert the regional model would require making some correction based on the ANT-20 mean over the same spatial domain. Could the authors please explain their methods and reasoning here?

The investigation of the 125 versus 25 year ice forcings is very thorough, however, since this paper is focused on the spatial pattern of solid Earth deformation rather than the ice reconstructions, I think including a lengthy discussion of both of these in the main text is unnecessary and detracts from the most important findings of the study. The main takeaway from Figure 4 is that there is more deformation in the region of load change in the longer loading scenario, which is not surprising and does not add much additional information in terms of how regional- versus continental-scale viscosity models behave. I suggest moving this figure to the supplement and focusing mainly on the 125 yr history in the main text. 

I suggest moving the discussion of specific features in the Earth models (section 2.1.3) to the results section. These features are a product of the conversion from velocity to viscosity and thus belong in the results. I think this will also improve the readability to have these features highlighted closer to where they are discussed in detail at the end of the paper. A sentence in the beginning of the results section (lines 379-380) actually indicates that this was the intention, but for some reason it was placed in the methods. 

Ideally, the authors would address the issue of future projections of GIA by running a fully coupled simulation with a dynamic ice model. This would be the only way to fully understand the impact that their REG_X viscosity models might have on groundline dynamics and GIA. Without coupled simulations, it is hard to interpret their results since these ice-loading models (ICE-FUT) are based on different viscosity structures. At a minimum, it would be helpful to plot the groundline evolution (as calculated by the floatation criterion in the Seakon) in Figure 6 for different models to assess the potential impact this viscosity structure might have on ice stability.

Comparing predicted and observed crustal rates is a nice way to highlight the importance of regional viscosity models. However, it is unclear to what degree either model performs better/worse than the 1D or CONT models in matching observed vertical rates overall.  For each model, I would suggest reporting an average residual between predicted and observed rates (for the vertical rates at least). This would provide context for the authors’ argument that regional models are necessary to accurately interpret the data (lines 687-690). 

In keeping with the central theme of the paper to investigate the impact of shorter wavelength features, I think it would be useful to have a paragraph in the discussion about whether the resolution of the adopted models are good enough. Should the GIA community strive for even higher resolution? What resolution is unnecessarily high? Is there evidence to suggest low/high viscosity zones may exist that these new models do not capture? I think the authors have valuable insight to contribute and could strengthen the overall impact of the paper by addressing these questions. 

Minor Points:

Line 80: Could you provide approximate length scales of ‘local’ and ‘regional’?

Line 87: Similarly it would be nice to define clearly what is exactly meant by regional and how much it differs from continental. 

Line 88: It would be useful to define ‘relative sea level’ here or somewhere in the introduction or at the beginning of the results section. This term can be confusing especially in studies like this where simulations are run both from the past to present and from present into the future. 

Line 194: Looks like something happened to part of a sentence here. 

Line 405: I would suggest changing “higher relative sea level” to “less relative sea level fall”. It may be confusing to some who are less familiar with GIA and thinking about ‘relative’ sea level to interpret this sentence. Saying “less sea level fall” more directly gets to the point that over the length of the simulation there is less change in RSL in the 1D model. (On a very technical level, the statement that RSL is ‘higher’ at present is also confusing since the final prediction of the Seakon (or any) GIA code in a historical/paleo simulation is that RSL=0.)

I might also change ‘lower magnitude vertical crystal rates’ to ‘lower magnitude modern-day vertical crustal rates’ if that is what is plotted. 

Line 416: Could you label the PSK region in Figure 3?

Figure 3: The label on the left for plots (a) (b) and (c), should more accurately be ‘change in relative sea level’ or ‘relative sea level at 125 ya’. 

Line 419-420: Following the comment about line 405, I would change the language to “less change in relative sea level”. 

Figure 4: It would be useful to readers to state which model is subtracted from the other in the figure caption. (Same with Figure S4)

Figure 5: I would add in the caption a line to aid the reader in interpreting the REG_P - CONT and REG_S - CONT plots. Something like: “positive values indicate overall less sea level fall in the regional model during the labeled time period”. 

Line 543-544: Here, I think it makes sense to say ‘higher relative sea level is predicted’ since RSL can vary between different models in the future. But I would clarify this in the sentence and also add a point about what this means for overall sea level change to aid the reader. I would correct this by changing:

“Compared to simulation with CONT, higher relative sea level (+1.31 m compared to CONT) is predicted in the central PIG basin with the REG_P model”

To something like: 

“In the central PIG basin, the REG_P predicts overall less sea level fall from 1950 to 2050 compared to CONT, resulting in 1.31 m higher relative sea level in 2050”

Line 543-548: I found this paragraph confusing. I would suggest revising to get at the really intriguing differences between the REG_G at 2050 (which predicts less sea level fall overall) and the REG_S (which has a northern region with more sea-level fall and a southern region near Thwaites with less). 

Figure 6: In panels A and B, could you also plot the viscosity anomalies along the profile for REG_P and REG_S? 

Figure 7: The symbols in the A and B are hard to read. I would suggest offsetting the symbols horizontally by a small amount and adding dashing lines to separate each station. REG_P (ICE-25) could also be in the supplement. 

Line 720: Could you say in which direction it would alter it? More or less?