Review of “Importance of ice elasticity in simulating tide-induced grounding line variations along prograde bed slopes” by Ross et al.
This revision has greatly improved the manuscript’s structure, helping readers understand the importance of your work in the context of tidal grounding line variations. There are still a few major structural points that we think would strengthen the manuscript. Below, we list these points along with minor corrections to consider as you revise.
Major Comments
1. The current organization of §2 and §3 makes your workflow opaque. For example, we expect the DInSAR measurements from §2.2.3 to be used as model inputs rather than validation because the section is squeezed between a section describing model inputs and a section describing the model. We think that a flowchart or schematic describing what data is used as input into the model, what outputs the model produces, and how DInSAR measurements are used to validate the model will help readers parse the manuscript.
2. Your revision to Figure 5 looks great and helps us visualize what is important between the models as grounding zone width changes. You do a great job summarizing these points in your reply to both reviewers, but the description of how glacier thickness, velocity, and bed slope impact the grounding zone in §4.2 is confusing as written. We think it would be beneficial to include the main points in your reply to reviewers in addition to the specific examples given with numbers.
Minor Comments [Line number of manuscript v3 given in brackets if applicable]
General comments:
● Unit abbreviations are inconsistent; please choose m/yr or m/year
● Supplement and figures should be cited in the order of first appearance (e.g., Table S6 is first mentioned on line 162, before Tables S2-S5 and Figure 6 is first referenced on line 185, before Figures 3-5)
[13] What type of tides does each region have? Does having more time for viscous components of the model to equilibrate matter (e.g., if tides are primarily diurnal versus semidiurnal)?
[19-20] Word choice: what error is considered a match of the model to measurements? ~74% more accurate is not meaningful without context from §4.3.
[21] Underscore the critical role played by ice elasticity in continuum mechanics-based glacier models *on daily tidal time scales*.
[37] This sentence does not explain the cool science you have done to make your short-term model include viscous components and better match data! It just seems like you are following the status quo of short term models.
[56] full Navier-Stokes
[60-64] This line seems overly specific for the intro — these are methods and should be moved to the appropriate location.
[71] "determine" is a strong word here that might imply the development of closed form parameterizations. A word like "assess" or similar is probably better here.
[76] Figure 1 shows locations, not relative locations
[82-84] This context on mass balance cites a paper that is over a decade old. There are much more up to date assessments of mass balance that should be provided.
[84-85] Just being grounded below sea level does *not* make a glacier potentially susceptible to collapse. It requires a reverse slope bed and TOT has ~ 40 km of prograde slope ("This means that the main trunk of TG will not be retreating on a retrograde bed and be prone to a marine instability in the coming years" from Li et al., 2015). Please revise accordingly
[89-92] Again, Pritchard et al. (2012) is 13 years old and multiple new, higher fidelity, longer-term estimates of basal melt have been published. It is important to look to the full body of literature when appropriate, but for specific values and assessments of stability, we should be using the most up-to-date perspectives.
[95] How do you choose the 69 profiles? They obviously do not matter much if your results are similar to when you used the nonphysical profiles in the first draft, so maybe mention that exact profile choice only saw ± x% error? You do not choose areas with negative or near-zero grounding zone widths (e.g., the gap between contours 25 and 26 on MU). Why? This looks like an interesting region as no GZ migration is observed. (This issue comes up again on line 102 where it says flow lines “were spaces 500 to 600 m apart” when there is a larger gap on MU)
[98-99] Rignot et al. (2017) has been superceded by the Mouginot et al. (2019) phase-based velocity map, which is considerably higher fidelity. Is there a reason here to use a somewhat out-dated velocity product?
[101] The expression "arctan(v_x/v_y)" can only provide direction across 180°, so we hope this was calculated not directly as the quotient, but rather as a two-argument function.
[101-102] The phrasing here is a little confusing. “Flow lines were selected along the flow direction” makes it sound like each flow line is selected along flow (which does not make sense since it would just select the same flow line over and over again). Did you mean they were selected across the direction of flow and generated for XX km along flow, centered on the grounding line (or something similar)?
[104] Parallel --> perpendicular. Also, some of the lines on, e.g., MU are indeed parallel to the grounding line. Crossflow heterogeneity is mentioned as impacting your analysis in lines 103-104, but there is no further mention of what possible errors it may introduce or how you might address those errors in future work.
[109] Figures 1 and 2 still have confusing colorbars. For example, the Figure 1 colorbar has two yellows and two pinks that look nearly the same. We had a hard time determining that Totten is up to 400 m/y faster than Moscow University from a quick look at the figure (until we saw the contour lines).
[122-123] "linearly approximating extracted bed elevation values": does this mean you fit a linear polynomial to the full profile and positive indicates prograde (i.e., higher upflow)? This is a little counterintuitive as we would reflexively think in an upflow-to-downflow frame, so a prograde slope should be a negative number), which just highlights that the reference frame should be defined and how this bedrock slope estimate is calculated should have a bit more clarity. Moreover, there seems to be a bit of a mismatch between the Figure 2 and Table S1 in that there appear to be some retrograde bed slopes (i.e., negative), particularly along the right side of MU, yet Table S1 indicates there are no negative bed slopes. This also plays back into the comment on lines 84-85, where the majority of these grounding line bed slopes are prograde, not retrograde, indicating there is *not* a substantial concern (at least in the chosen locations) of instability.
[126] Remove "relief"
[145-146] Horizontal flow velocity is also not uniform even on tidal timescales – what error is introduced by assuming the double difference interferogram cancels out the horizontal deformation (e.g., Rack et al., 2017; Wild et al., 2019)?
[158-161] Why is the IBE correction applied here? Doesn’t IBE contribute to grounding line motion as well?
[166] Why can you assume that the grounding line position observed in the interferogram corresponds to the largest tidal level among the acquisitions? Does this mean you cannot image low tide very well and are missing important information about GL migration near low tide?
[170-172] Thank you for including the table of height changes from DInSAR measurements for each glacier (though we note these are results, not methods, so should probably be moved). We noticed there is only one set of measurements (high and low tide) for each glacier (as a result of tasking constraints we presume), which do not always span a representative range of tides. Because this is tasked and there does not seem to be more available data, some discussion of the limitations of the analysis given the limited dataset is critical later in the manuscript.
[202] You do an excellent job explaining model variables as they appear, so we think having Table 1 in the main text now detracts from the read-through. We would put it in an appendix or the supplement for easy reference.
[205] Do you want to use (x,z) to be consistent with Stubblefield et al., (2021)?
[211] Line 211 and equations 3,4,5 should replace “f(x)” with “b(x)” to be consistent with Figure 4 and Equation 41 (or use β(x) as in Stubblefield et al., 2021).
[234] We might use η(D) rather than η(ν) in equations 8 and 10 (local η should only depend on invariants of D). This is also consistent with using η(τ) in equation 13.
[250] Shouldn’t this definition come after eq. 12 and not eq. 13?
[279.5] Why do you jump around from indicial to tensor notation in equation 30?
[319] Does adding additional tidal constituents change the results?
[322] Thank you for clarifying that the data-model comparison is not one-to-one. We interpret the comparison as selecting points from the model at the same tidal level as the interferogram, but the wording is confusing. We suggest revising this section with an emphasis on the precise comparison made. Also, if you are modeling 1 m tides, then are subselecting, is this a fair comparison if the tidal range is different from 2 m here? In other words, the model is missing the maximum stresses if the modeled tide range is different from the actual tide range at these glaciers (which is important for the viscous component).
[376] “%” --> “m/yr”
[382-383] The statement, "MU introduces some variability, particularly due to its wide grounding zones exceeding 6km", is confusing. On Figure S1, there does not appear to be any MU grounding zones that exceed 6 km in width at all. In fact only Totten has grounding zone widths that exceed 6 km.
[393-394] Why is this assumption being made? The data collection time from 1996 should be available and therefore the tide stand of that grounding line can be explicitly estimated
[438] Y-axis does not show evolution, but rather the size of GZ for different chosen ice speeds.
[442] What does “where the results for different inflow speeds are averaged by glacier thickness” mean?
[501] "confirms" is not a great word choice here. It is certainly consistent with your observations, but other processes can account for this apparent sensitivity.
[502] Figure 7: What justification do you have for the glacier thickness/flow speed/GZ length dependence? We could draw a line with a positive or negative slope within the error bars presented in Figure 5c.
[530-532] This line is off the mark. Plenty of people have used pure elastic models successfully to model flexure over tidal timescales and compare to observations. Yes, you will not fully capture all glaciological processes, but you can certainly investigate individual processes with elastic models.
Table S1: Including standard deviation would be helpful for a reader to understand variability across the glacier.
Figure S2: Why is only the lower boundary the smaller mesh size? Did you try a run with all small mesh sizes to see if there are different results? The monotonic decrease in GZ width with decrease in mesh size in Figure S1 is interesting. How do you know it evens out in the viscoelastic model? Wouldn’t you expect scatter in GZ width once it is not mesh size dependent?
Table S2: The r squared values of 1.0 are suspicious. How many data points are in the regression?
Figure S4: Clarify if these are bar plots or histograms. If they are histograms, the bar width should encompass the full range of values in each bin. (e.g., In panel b, if the first bar is all profiles with a glacier thickness between 2.0 and 2.1 km, then it should stretch all the way to 2.1 km).
References (that do not appear in the manuscript reference list)
Li, X., E. Rignot, M. Morlighem, J. Mouginot, and B. Scheuchl (2015). Grounding line retreat of Totten Glacier, East Antarctica, 1996 to 2013, Geophys. Res. Lett., 42, 8049–8056, doi:10.1002/2015GL065701.
Mouginot, J., Rignot, E. & Scheuchl, B. (2019). MEaSUREs Phase-Based Antarctica Ice Velocity Map. (NSIDC-0754, Version 1). [Data Set]. Boulder, Colorado USA. NASA National Snow and Ice Data Center Distributed Active Archive Center, doi: 10.5067/PZ3NJ5RXRH10.
Rack, W., King, M. A., Marsh, O. J., Wild, C. T., and Floricioiu, D. (2017). Analysis of ice shelf flexure and its InSAR representation in the grounding zone of the southern McMurdo Ice Shelf, The Cryosphere, 11, 2481–2490, doi: 10.5194/tc-11-2481-2017.
Wild, C. T., Marsh, O. J., and Rack, W. (2019). Differential interferometric synthetic aperture radar for tide modelling in Antarctic ice-shelf grounding zones, The Cryosphere, 13, 3171–3191, doi: 10.5194/tc-13-3171-2019. |