Summary of Review

Miles et al. put forth a compelling study of ice rumple history on the Totten ice shelf over the past century. By analyzing the formation of repeated surface undulations that are likely due to interaction with seafloor topography, these authors suggest that a period in the absence of undulations is likely due to variation in basal melt rate. Additionally, they compute interannual and decadal velocities, both of which do not show a significant trend and have large anomalies. I think that after answering the following questions, the authors can greatly strengthen their case through analytical rigor and clarity. However, without these added changes, their arguments remain speculative and claims are overreaching.

Major Points

1. What actually are these undulations from?
1. For the first half of the paper, I wasn’t convinced that the undulations you show were not large basal crevasses/channels generated from flow past the pinning point. The main reason I thought of this is that there is the large (roughly stationary) pinning point that is several kilometers away from the location you analyze. I know you are aware of the phenomena of fractures propagating laterally beyond pinning points, as you have shown in Miles et al. 2024. However, the icesat2 time series that show surface growth flipped my opinion, as you would not expect surface raising of O(10m) from a basal crevasse. To not have other readers have this confusion, please put a map of bathymetry that explains how local topography may promote the observed undulations, rather than having them originate from the larger ice rumple. Additionally, mention that fractures can be generated downstream of pinning points, and suggest that the observed surface undulations are inconsistent with the surface signature of basal crevasses (e.g., Luckman et al., 2012; McGrath et al., 2012). I know bathymetry products like BedMachine are uncertain (and have associated uncertainty provided), and you cite some folks saying that, but I had to dig into bathymetry data to find that there is a tail or foot to the seamount inferred in that region that highly suggests that what you are looking at is formed locally due to regrounding. This will significantly strengthen your argument.
2. Is velocity downstream of a pinning point actually representative of grounding line velocity?
1. The observed velocity data is quite noisy - on long time scales there are fluctuations, and on short time scales there are similar or larger amplitude fluctuations (your Figure 5). I would expect this signature of noise in a stick-slip type system, which I would expect from the ungrounding, regrounding, and potentially fracturing that is generated by these seamounts. In a stick-slip system, I would not expect the velocity downstream of the stick-slip location to be similar to those upstream, aka the grounding line. Please provide a convincing explanation of why we would expect the velocities you measure to be representative of the grounding line, as I find lines 138-140 to be unconvincing and appear as too much extrapolation.
1. To help illustrate the point, the most extreme example of flow past a pinning point may be the Brunt ice shelf. If one tried to compute velocity downstream of the pinning point, then these would be dominated by the flowing/fracturing that occurs as ice moves past an obstacle, and the results may not be a sensible measure of the upstream or grounding line velocity. This is a more extreme case, where the buttressing provided by the pinning point significantly impacts the ice velocity both downstream and upstream of the obstacle. All in all, I am not convinced that the velocity measured is representative for the ice shelf as a whole, nor the grounding line, but mostly for the local region in which it is measured. Please update your phrasing where appropriate - statements about whether a glacier is “in balance” is a measure of grounding line flux versus snowfall integrated from the ice divide, so I would remove or strongly minimize these large-scale claims.
3. Can you definitively conclude that basal melt is the dominant signal by concluding that the changes in snowfall (thickening) and grounded ice thickness (H) and velocity (u, v) cannot correspond to the observed thickness variation? Currently, it is argued (e.g. line 18) but not sufficiently proven.
1. You show in Figure 1a that you get about 2 meters a year of thinning of grounded ice over a half century window. I imagine this is an average rate. You show in Figure 8 that there is +-3 meters a year of melting on the ice shelf. Finally, you show 20 meters surface elevation changes in Figure 7a within 2 years. The mechanism you propose, largely basal melt variation, needs to get cyclic variations of melt pulses causing 20 meters of variation, as a baseline. I’m with you in that I think this is from the ocean, but mostly because I don’t expect this to be from grounded ice thickness and velocity changes or from ice shelf snowfall. Given that basal melt rates may be challenging to measure, can you construct your argument in terms of ruling out the other two options?
2. The thin film mass balance equation is partial_t H + div (u H) = a - b, as you are likely familiar with the terms: thickness tendency, divergence of ice flux with (depth-averaged) horizontal velocity vector (u,v), and snowfall rate and melt rate on the opposite side of the equality. This is a more mathematical way of framing the above argument. Please incorporate this logic if possible to see if you can definitively conclude that the changes in partial_t H would be driven by -b and not by div (u H).

Minor Points

1. Lines 16-17: Out of mass balance - insert the word mass.
2.  Line 48: define inland thinning - I presume you mean the thinning of grounded ice, as in Figure 1a, but you don’t define it
3. Lines 60-61: I would modify this sentence to say outlet glaciers lose mass through a flux imbalance, whereby ice mass loss aka discharge outweighs mass gain via snowfall and basal accretion under ice shelves.
4. Lines 61-63: What is the point of this sentence? It seems unnecessary if you are focusing on building a story about Totten in EAIS.
1. Lines 65-67: Part of the issue with the above sentence (61-63) is that it is used in a misleading manner, by tying mass loss in WAIS to a lack of acceleration of Totten Glacier in EAIS. You need to say in East Antarctica, since your last sentence is about West Antarctica and those conditions are different. CDW on the continental shelf does not imply the same environmental conditions.
5. Lines 67-68: The reason that glaciers accelerate is due to a loss of buttressing. If you can't show that there has been a change in buttressing, then you won't get acceleration. Please revise your framing of the problem.
6. Line 69: Acceleration of the ASB or the ice shelf or grounding line retreat? Which acceleration are you focused on?
7. Lines 70-71: Out of mass balance is a catch-all term, as technically glaciers are basically never actually balanced in an integrated sense given some environmental noise (Robel et al., 2018; Sergienko and Wingham, 2024; Sergienko and Haseloff, 2023). I think it is unreasonable to expect that glaciers would be in a steady state before the anthropocene in how you frame this statement.
8. Line 80: The surface elevation change is presumably an average rate. Can you say it is monotonic, or provide the reader with more relevant information for the thin film mass balance equation (see major comment 3)?
9. Lines 81-82: State that the rates of grounding line retreat are shown in red text in figure 1a. 
1. More Figure 1 aesthetics: Make the a and b labels more visible the font is too small, same from the text in the images.
10. Figure 2
1. Can you make the red circles wider or provide a border to them to help them stand out against the background?
2. Subfigure c, phrase “formed through interaction with ice rumple” - please do much more to justify this and explain in the caption what you mean: local interaction with a seamount or lateral effects from the major surface elevation change that we can clearly visibly see to the right of the undulation train you are analyzing. I got quite lost thinking about how ice rumples can modify elevation patterns of nearby ice flow through a basal crevasse forming and/or basal channel melting to alter surface topography. See major point 1.
11. Section 2.2 Ice speed, first paragraph - great argument!
12. Lines 135-138: either provide a hypothesis for what this feature is/how it formed, or state that it is of unknown formation. Your readers, who are scientists that enjoy problem-solving and oddities, may lose focus and try to figure it out for themselves.
13. Lines 138-141: I am unconvinced with this statement, see major point 2. I would appreciate more reasoning in your response rather than citing precedent.
14. Lines 158-161: This seems interesting, but you don’t include any figures/tables on this topic. Can you provide some more information via quantitative comparison, or remove this sentence?
15. Line 169: Is the channel along or perpendicular to the grounding line? This was unclear to me.
16. Lines 211-212: This statement added to my confusion around major point 1, as clearly fractures become a major feature of Totten ice shelf.
17. Lines 212-214: See major point 3, please use the full mass balance equation, and mention that the ice thickness at the grounding line is changing due to grounded ice thinning and grounding line movement.
18. Figure 4: please improve this schematic, it is nearly identical to the simple schematic in Miles et al., 2024. Make it 3D, and provide surface and basal topography variations (currently you only have one). Could greatly strengthen your argument about cyclic melt cycles later on. Additionally, provide some CDW arrows or something to make the ocean distinct between warm periods and cooler periods, with grounding line melting. The ocean circulation, heat and stratification are key players in your argument.
19. Lines 223-224: You should tie this point to the idea that there hasn’t been a major loss of buttressing, and thus there isn’t a major force change and subsequent ice acceleration change.
20. Lines 225-226: This sentence strengthens major point 2, and suggests that the decadal anomalies have such low signal-to-noise ratio (e.g. high frequency short term events) that your results for the decadal predictions might be a strong function of when the images were actually taken.
21. Lines 240-242: Doesn’t the gradual eastern channel widening through all of your time periods provide a different story compared to the hiatus in surface undulation formation that you claim in the abstract and conclusion are indicative of warmer periods (more CDW entry) in the past? Please elaborate.
22. Figure 7
1. Looking at the REMA elevation map with no axis units, labels, or flow orientation: I wish you had the star in every image, and noted whether the images are all properly aligned. It is hard to tell where the small inset is in a compared with b. Please label the flow direction if it's downwards in all images.
2. Please align subfigure 1a with bathymetry data such as BedMachine. The ICESat-2 imagery is very convincing that this is not a basal channel or crevasse, and I would have appreciated seeing this much earlier in the paper. See major point 1.
3. Subfigure b: fonts are too small
23. Lines 290-293: Having a large difference in grounding line ice velocity compared with these downstream ice velocity measurements can be evidence for my major point 2.
24. Lines 321-326: You should do way more with these coastal oceanography studies that show roughly 3 and 7 year melt cycles. Please explain what causes the separation, or what those authors suggest. I think that if you did more with the data of those other studies, you would draw a larger audience from the oceanography community for citing your work.
25. Lines 332-334: either provide a citation or reference a figure where you can easily show this claim.
26. Lines 361-363: Initial comment: Wasn't there an important ENSO in the 40s that was thought of as a trigger for Thwaites retreat? During paper review: You mention some papers later on that discuss this (lines 432-434), but you could bring the discussion or a reference of WAIS up to here.
27. Figure 8
1. This melt rate is similar to the elevation change from thinning of grounded ice. Supports my arguments in major point 3.
2. Why is the shelf getting thicker upstream? You are leaving the reader guessing/confused - for your argument, what really is important is grounding line thickness, and the melt rates downstream of the pinning point can’t be that large as the features you track stay around for many years.
28. Lines 371-373: Another case of bathymetry being important, uncertain, but meanwhile there have been no maps of bathymetry in the entire paper, yet they are crucial to your surface undulation formation mechanism. This supports my major point 1. Bathymetry products often come with uncertainty - you can include this as well.
29. Lines 403-405: Why not make more of a point of mentioning this as an aside in your abstract and/or conclusion? This is good to know and is fully tucked away deep in a paper that doesn’t highlight it.
30. Figure 9 - How are you drawing that ice shelf boundary? Is it land-fast sea ice, or glacial ice, or a mix?
31. Lines 444-445: see minor points 1, 3, and 7 for the same idea - I think it is unreasonable to assume that a glacier is ever truly “in balance” with respect to grounding line flux, which will oscillate the observed mass loss (and SLR for marine-terminating glaciers).
32. Lines 450-454: same idea as line above, and accelerating the detachment is very confusing language. Just say decoupling or losing contact.

References

1. Luckman, A., Jansen, D., Kulessa, B., King, E. C., Sammonds, P., and Benn, D. I.: Basal crevasses in Larsen C Ice Shelf and implications for their global abundance, The Cryosphere, 6, 113–123, https://doi.org/10.5194/tc-6-113-2012, 2012.
2. McGrath, Daniel, Konrad Steffen, Ted Scambos, Harihar Rajaram, Gino Casassa, and Jose Luis Rodriguez Lagos. 2012. “Basal Crevasses and Associated Surface Crevassing on the Larsen C Ice Shelf, Antarctica, and Their Role in Ice-Shelf Instability.” Annals of Glaciology 53 (60): 10–18. https://doi.org/10.3189/2012AoG60A005.
3. Robel, Alexander A., Gerard H. Roe, and Marianne Haseloff. 2018. “Response of Marine-Terminating Glaciers to Forcing: Time Scales, Sensitivities, Instabilities, and Stochastic Dynamics.” Journal of Geophysical Research: Earth Surface 123 (9): 2205–27. https://doi.org/10.1029/2018JF004709.
4. Sergienko, Olga, and Duncan John Wingham. 2024. “Diverse Behaviors of Marine Ice Sheets in Response to Temporal Variability of the Atmospheric and Basal Conditions.” Journal of Glaciology 70 (January):e52. https://doi.org/10.1017/jog.2024.43.
5. Sergienko, Olga, and Marianne Haseloff. 2023. “‘Stable’ and ‘Unstable’ Are Not Useful Descriptions of Marine Ice Sheets in the Earth’s Climate System.” Journal of Glaciology 69 (277): 1483–99. https://doi.org/10.1017/jog.2023.40.
6. Miles, B.W.J., Bingham, R.G. Progressive unanchoring of Antarctic ice shelves since 1973. Nature 626, 785–791 (2024). https://doi.org/10.1038/s41586-024-07049-0 

Miles et al. presents an interesting history of ice flow on the Totten Ice Shelf from the early 1970s to the present day, reconstructed from feature tracking in historical Landsat imagery. They also produce a history of ice surface undulations that they ascribe to varying degrees of interaction between the ice shelf and a hypothetical pinning point. They interpret this as a qualitative history of decadal variations in ice thickness that also suggests decadal variations in basal melt rates. Overall, they conclude that Totten Glacier was likely losing mass at a similar rate in 1970s, but that a period of high melting in the 1940s to 1960s may have initiated that mass loss.  

Overall, the paper investigates an important question - the long-term history of mass loss in one of East Antarctica’s most dynamic areas. However, the study cannot directly measure the variables of interest: flux across the grounding line and basal melt rates. What can be measured is the velocity of a single feature in the middle of the ice shelf and the presence or absence of surface undulations at certain locations. I think the paper’s argument could be much stronger with more attention to giving quantitative, data-supported, or physics-based explanations that strongly link these proxy records to the variables of interest.

Major Comments:

[1] More detail is needed on the manual feature tracking for velocity estimates. To what degree of precision can the exact same point on a feature be detected 10 years later? Is 1 pixel of error for the feature tracking a sufficient uncertainty bound given changes in features shape, illumination conditions, etc over time? How reproducible is this tracking? (e.g., if someone else were to do the tracking with the same imagery, would they get the same numbers.)

A supplementary or appendix figure showing all the features that were tracked in each image pair and the specific points that were tracked would go a long way towards increasing confidence in these results. I’m imagining something like an expanded Figure 3.

[2] I am not entirely convinced by the argument that velocity variations within the feature tracking box should reflect velocity variations across the grounding line. Since the feature tracking box is directly downstream of the ice rumple, it seems like it would be more indicative of flow as modulated by interactions with that pinning point, including fracture processes as the ice flows around or over a barrier. Can you show, using the MEASURES velocity record in the modern era, that velocity changes within this box are correlated with velocities changes across the grounding line in both relative magnitude and phasing?

[3] Line 189 – this argument is not convincing to me. I generally understand how undulations might form as ice passes over a pinning point, but from Figure 1, it seems like these undulations are forming to the left side of the ice rumple, not directly down flow from it. Is there some submarine bedrock high or pinning point directly upstream of these undulations that is not marked on the maps or visible in the imagery? If not, what is the theory for undulations forming next to the pinning point? The 2D schematic in Figure 4 does not seem to capture the real geometry of the Totten Ice Shelf and would be more useful and convincing in 3D. I know that sub-ice shelf bathymetry is always highly uncertain, but if you are using BedMachine or some other project to infer the presence of a potential pinning point, it would greatly strengthen your argument to show that bathymetry.

On further digging in the literature, it seems that perhaps there is a lot of reliance on the conclusions from Roberts et al. (2017) when ascribing the origin of these undulations? If that is the basis for these conclusions, the paper would be strengthened by some review of their arguments for the reader who is not as informed about the history of these research on Totten.

Minor Comments:

Line 34 – “…detachment of the ice shelf from pinning points…” Which ice shelf is being discussed here? This is confusing since the sentence seems to refer to the entire ASB sector.

Line 60 – surface mass balance would be better than snowfall here. I suppose on Totten that SMB is dominated by snowfall, but since the sentence is general one about outlet glaciers, I would recommend using SMB.

 Line 64 – I don’t see where Kim et al. (2024) ascribes the mass loss they measure to the thinning of ice shelves. Ice shelves are barely mentioned in the paper, which to my reading it is more focused on measuring the partitioning between SMB and discharge.

Figure 1 – the label text is quite small, and the images are low dpi which makes the labels hard to read even when zoomed in on the pdf. Ground line retreat rates are given as distance, not rates. The timescale needs to be specified. If the black line in panel b is the MODIS 2009 grounding line, why are there multiple discontinuous black lines in many places? It looks like multiple grounding line estimates are overlaid?

Figure 2 – the purple and green “feature tracking vectors” need more explanation. What are they and what do the different colors represent? What should the reader take from their presence on the figure?

Line 159 – this difference between MEASURES and ITS_LIVE seems significant. Do your results compare favorably with one or the other, or present a third interpretation?  Why are there such stark differences between the products?

Line 210 – would be very helpful to have this flowline on a map somewhere. In general, having flow vectors for velocity on one of the maps would help a lot with interpreting much of the discussion on how features are related to one another along the shelf.

Figure 6 – this figure needs a locator map showing the whole ice shelf and where these individual sections fall.

Line 288 – this seems to counteract your argument that the velocity anomalies within your feature tracking area should be indicative of the velocity across the grounding line.

Line 321 – this is so key to your argument, it could use more development. Can you discuss more the drivers of these melt cycles, whether they apply over the whole ice shelf, how they would impact ice thickness at the grounding line, etc? What are typical basal melt rates on the Totten Ice Shelf from this study and magnitude of the change over the cycle? Could these variations in that melt rate reasonably explain the 25 m variations in surface elevation? Is it possible to directly align these modeled melt cycles with the undulation wavelengths like in Figure

Line 376 – this seems somewhat speculative given that a clear physical mechanism for the formation of these undulations to the side of the ice rumple has not been clearly presented.

Line 389 – What is the decadal variability in melt rates? Does it align with the scale of melt rates that would be needed to observe or not observe the formation of these undulations?