the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Apr 2024
Importance of ice elasticity in simulating tide-induced grounding line variations along prograde bed slopes
Abstract. The grounding line, delineating the boundary where a grounded glacier goes afloat in ocean water, shifts in response to tidal cycles. Here we analyze COSMO-SkyMed Differential Interferometric Synthetic Aperture Radar data acquired in 2020 and 2021 over Totten, Moscow University, and Rennick glaciers in East Antarctica, detecting tide-induced grounding line position variations from 0.5 to 12.5 km along prograde slopes ranging from ~0 to 5 %. Considering a glacier as a non-Newtonian fluid, we provide two-dimensional formulations of the viscous and viscoelastic short-term behavior of a glacier in partial frictional contact with the bedrock, and partially floating on sea water. Since the models’ equations are not amenable to analytical treatment, numerical solutions are obtained using FEniCS, an open-source Python package. We establish the dependence of the grounding zone width on glacier thickness, bed slope, and glacier flow speed. The predictions of the viscoelastic model match ~93 % of all the DInSAR grounding zone measurements and are 71 % more accurate than those of the viscous model. The results of this study underscore the critical role played by ice elasticity in continuum mechanics-based glacier models, and being validated with the DInSAR measurements, can be used in other studies on glaciers.
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CC1: 'Comment on egusphere-2024-875', Tracy Moffat-Griffin, 17 Apr 2024
The paper cites Dempsey et al and Beldon & Mitchell, these papers are to do with atmospheric solar tide observations at ~80 - 100 km, it's not clear what, if any, relevance they have to the grounding line work done here.
Citation: https://doi.org/10.5194/egusphere-2024-875-CC1 -
AC1: 'Reply on CC1', Natalya Maslennikova, 19 Oct 2024
Thank you for your comment! These two citations were removed and the reference list was revised.
Citation: https://doi.org/10.5194/egusphere-2024-875-AC1
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AC1: 'Reply on CC1', Natalya Maslennikova, 19 Oct 2024
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RC1: 'Comment on egusphere-2024-875', Anonymous Referee #1, 20 Jun 2024
GENERAL COMMENT:
The preprint “Importance of ice elasticity in simulating tide-induced grounding line variations along prograde bed slopes” by Maslennikova et al. investigates the impact of viscoelastic processes to establish relations between grounding zone width and ice speed, ice thickness, and bed slope. The authors use a combination of SAR satellite data and a numerical model in their work.
This work presents significant and novel knowledge, building on recent efforts to better understand the impact of elasticity on processes occurring at the grounding zone. I have very few comments regarding the content and methodology of this paper, which I think is of high quality and surely required a lot of work. However, I have several concerns about how methods, findings are presented and discussed, which, in my opinion, need further work before this preprint can be published. Overall, my biggest concern is that this paper lacks a robust discussion regarding the physics of what is modeled, which is briefly mentioned in the conclusion section. There is also some discrepancy in the various sections, where methodology is provided in the results section and a proper discussion is only included in the conclusion section. I think a rearrangement of these sections would really be beneficial to this preprint.
I've made generic and specific comments below to this point, which, in my opinion, would further strengthen the manuscript.
INTRODUCTION
I find that the introduction contains a lot of information, but at times, it is unclear how this benefits the paper’s goals. The authors include many references after each statement, which makes the reading experience slow and confusing. I recommend citing only papers that are directly related to the context. Furthermore, a researcher outside of the peer review team even commented that a couple of citations (Dempsey et al. and Beldon & Mitchell) are completely off-topic. I looked at these papers and agree that they are not relevant to this work, but please correct us if we are wrong. Lines 37-38 cite 16 references (!), and I am not sure how some of these are relevant to the sentence they are attached to.
DATA and METHODS
I am not an expert in double differences to examine grounding zone width, but this section leaves me wondering how you can estimate the minimum and maximum grounding zone extension within a tidal cycle if you have only one day of repetitive acquisitions. If you have 24hours of difference between acquisition, wouldn’t the tide level being approximately the same. I may have completely misunderstood this section, and if so, I sincerely apologize. However, I still think that even someone without a background in differential interferometry (like me) should be able to quickly understand the physical processes by reading the methodology of this paper. I am aware that substantial past work has used 1-day repetitive acquisitions to study grounding zone migration, and I know that access to sub-daily SAR images is challenging. I am not doubting the quality of this approach; I would simply appreciate a bit more background on this.
VISCOUS AND VISCOELASTIC MODELS
I appreciate the background information in the modeling perspective, but I am unsure what Equations 1-5 and 9 really contribute to this paper. These are mostly large simplifications of any dynamic system subjected to boundary conditions, and Equation 9 represents a simple tolerance criterion. While I understand that this may be a matter of personal preference, I would consider removing them or perhaps substituting them with the actual PDEs that are resolved (viscous vs. viscoelastic, i.e., Appendix A, eq A1-A3 and A6), which would enrich the reading experience with theoretical background. Equations 1-5 and 9 could go in Appendix A.2.3, where the authors describe boundary conditions. On the other hand, Equations 6-8 are important and useful to the reader. Again, I want to stress that this may be a personal preference, but I do think that Equations 1-5 and 9 can be easily summarized in the text.
RESULTS
This section is really hard to read. There are a lot of numbers, which makes it confusing. I also find hard to distinguish whether model results, model set-up and observational data are discussed. Would dividing this section (data, model) into two subsections help? Finally, authors discuss the simulation set-up in this section, although it should rather go in the methodology section. Results section should only present the outcome of the simulations and not details about simulations themselves.
DISCUSSION
This section is also quite challenging to follow. In my opinion, this looks more of a results section rather than discussion. I am completely lost in paragraph 272-286, and it took a while to actually understand the series of inequalities that are reported here. These are much more easily visualized in figure 3, and I am not sure if verbatim reporting them is any beneficial. I think that figure 3 is perhaps the most important, but it is also hard to read, since the y-axis changes for each sub-plot. The reader cannot compare results from viscous and visco-elastic model if the y axis is different. Would a normalized GZ width (0-1) improve things? After doing so, it should be easier to merge panels a-l with panels m-x and improve the figure.
CONCLUSIONS
There is a lot of information presented here for the first time rather than in the previous sections. The conclusion section should only wrap up the work and draw final arguments. As far as I can see, paragraphs 414-421 and 451-460 provide the only physical explanation of what is presented in the paper. I think this work needs a bit more discussion about the physics behind the modeled processes. Why is elasticity so important? It improves model-data agreement, but why? What is the physical reason? I may have missed something, and I apologize if I did, but the only explanation I could find in the text is: “Therefore, an element responsible for rapid deformations, or an elastic component, becomes necessary.” To strengthen this paper, I would recommend a thorough discussion regarding the physics of elasticity applied to grounding zone migration. It looks like the model used is based on a previous publication (Stubblefield et al., 2021), so technically, this is not a presentation of a new model. If this is the case, I would appreciate more background on the physical explanation of why this modeling effort is conducted. Furthermore, these considerations should go into a discussion section rather than the conclusion itself.
SPECIFIC COMMENTS:
Line 26: Davis et al 2023, how is this recent paper related to the sentence? Davis et al 2023 does not investigate glacier stability. Also, what does ‘salient’ mean here? This sentence and pretty much all of the following cite a lot of papers (line 31, 35, 38), which makes the reading experience very slow and confusing at times.
Line 48: Gadi et al 2023. This paper investigates ice shelf melting using a numerical model. How is this paper related to “quantification of grounding zone width”?
Line 52, Chen 2023, Chen 2023a and Chen 2023b are the same paper. Please consolidate.
Line 63: Please remove parenthesis when you are using a reference as a noun.
Line 162: Really nice figure.
Line 228, 236: This information is not a result but rather an explanation of the simulation setup.
Line 260: These are results. I think the logical structure of this paper needs to be revised.
Line 275: This and the following lists of inequalities are hard to follow, but easily visualized in figure 3. Is it really necessary to write them down here?
Line 288: Figure 3. I think this is an important plot, but the different limits on the y-axis make it hard to compare between simulations. Would using a normalized grounding zone scale help? Additionally, consider adding this plot in the supplement. Also, please use a color scheme that is colorblind-friendly or, alternatively, different marker shapes.
Line 313: I have a philosophical issue with the term ‘validation.’ I do not think that you can validate a numerical model; you can at best evaluate how well it agrees with observations. If this model works well in the area of interest, how can you be sure that it is ‘valid’ for other regions as well?
Line 397: this reads more as a discussion rather than a conclusion.
Line 451: This paragraph is the only part of the paper that is an actual physical discussion on the importance of elasticity. I assume that the model used here was already presented in another paper. This work is therefore an extension and an important application of an existing model. In the discussion section, I was expecting a thorough discussion on the theoretical meaning and implications of including elasticity in modeling of grounding zone dynamics, which, alas, is missing. I do not think that the discussion needs to be completely re-written, but some further physical explanation of what is novel here and the overall importance of these findings would really strengthen this manuscript.
Citation: https://doi.org/10.5194/egusphere-2024-875-RC1 - AC2: 'Reply on RC1', Natalya Maslennikova, 21 Oct 2024
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RC2: 'Comment on egusphere-2024-875', Anonymous Referee #2, 24 Jul 2024
Review of "Importance of ice elasticity in simulating tide-induced grounding line variations along prograde bed slopes" by Maslennikova, et al.
This manuscript compares tidally induced grounding zone width observations to viscous and viscoelastic models to show the viscoelastic model better aligns with observed grounding zone widths. The authors calculated grounding zone widths at Totten, Moscow University, and Rennick glaciers using differential interferometric synthetic aperture radar (DInSAR) by finding the along-flow difference in grounding line location between image pairs taken at two different tide heights and implemented a 2D model of ice response to tides for parameters representative of these three glaciers. The model showed wider grounding zones for shallower bed slopes and wider grounding zones for thicker glaciers, consistent with observations. Furthermore, the model predicted that slow glaciers on steep slopes and fast glaciers on shallow slopes cause the grounding zone to respond most to ice thickness changes.
This paper represents a significant contribution toward modeling tidally induced grounding line variation by providing key comparisons to observed grounding zone widths and recommending a viscoelastic rheology be used in future modeling efforts. The formation of wide grounding zones from tides is an important process impacting basal conditions and ice dynamics, but is often neglected in larger-scale ice flow models. A better understanding of this process, such as from modeling-observation studies like this paper, is essential for more realistic modeling at this critical transition zone. However, the current structure of and analysis in the manuscript obscures this important conclusion, resulting in a difficult to read and difficult to digest manuscript. Below, we highlight four main issues, including that: the main results are hidden across multiple sections (including the appendix), making it harder for readers to understand the key messages; the revised model is not fully described; the InSAR processing does not provide enough details to reproduce or interpret the mapped grounding lines; and the presented figures and tables are often hard to interpret, decreasing their effectiveness. Because addressing these issues will require substantial reworking of the manuscript, we have opted to not list line-by-line minor comments.
- The structure of the paper hides the key contributions of this manuscript. For example, methods used in the manuscript appear in Section 2 (“Data and Methods”), Section 3 (“Viscous and viscoelastic models”), Section 4 (“Results”; e.g., lines 211-227 cover how model parameter space and mesh size were determined; lines 238-247 contains more methodological description of the modeling effort), Section 5 (“Discussion; e.g., lines 328-336 describe filtering methods), and Appendix A (“Glacier modeling”). In fact, the substantial contribution of the manuscript—a new viscoelastic model that can capture a tidally variable grounding zone—is largely relegated to the appendix rather than the methods section of the main text. Results from the methods described in the manuscript appear throughout sections 4 (“Results”), 5 (“Discussion”; e.g., lines 261-271), and 6 (“Conclusion”; e.g., lines 408-413). In addition, the conclusions (Section 6) take the manuscript in a largely unrelated direction, ending with grounding line retreat estimates over multiple decades—a topic that is explicitly not the focus of the manuscript.
With information scattered throughout the manuscript, it takes multiple reads to piece together the full scope of the work. Perhaps more importantly, with so much jumping between topics and concepts, there is no deeper discussion of the physical implications of the data/model comparison. For example, if the viscoelastic model is better than the viscous model because of the short time-periods involved, how does a fully elastic model compare (i.e., why not save the computation time and just implement an elastic model for realistic grounding zone width estimates as suggested by Warburton et al., 2020)? Does cross-flow heterogeneity matter for the data/model comparison (in other words, does Rennick match the best because it is the simplest geometry or another physical reason)? What are the physical reasons for the trends in Figure 5c? (note: Figure 5 is also only first introduced in the Conclusion section, which highlights this structural issue since this section should not contain new analysis). What is the physical reasoning (or even a hypothesis) for why slow glaciers on steep slopes and fast glaciers on shallow slopes cause the grounding zone to respond most to ice thickness changes (lines 284-286)? How do DInSAR measurements at these glaciers validate the model for other glaciers (suggested in the Abstract in line 20), especially with the high variability observed at just these three glaciers? We also note that the lack of “flow” in the writing of the manuscript sometimes inhibited our ability to make connections throughout the paper. For example, the model run-time discussion (lines 253-258) interrupted a clean transition from results to discussion (and likely could be included in supplementary material rather than the main text) and the “discussion” of slope coefficients (line 275-285) was quite difficult to comprehend even after multiple tries.
Overall, the entire manuscript should be revised with a close eye to structure at all scales—from making sure individual sentences are structured appropriately (e.g., lines 34-35 after the semicolon are a sentence fragment) to ensuring that information in an individual paragraph flows from the topic sentence to making sure all of the introduction is in the introduction, methods are in the methods, and so on. - There are multiple conceptual problems with the model that are un-/under-described. As suggested above, the main message of the manuscript is the appropriateness and usefulness of the viscoelastic model (compared to a viscous model), but the changes from Stubblefield et al., (2021) to make the model viscoelastic are relegated to Appendix A. Any changes from the Stubblefield et al., (2021) model are key contributions and therefore should be placed in the main text (e.g., Equations A6-A10), which can be guided by Table 1 (a table that likely can be removed if the modeling methods are appropriately described in the main text).
Beyond the lack of description of key modeling efforts in the main text, there are additional conceptual concerns with the model that are not resolved. Below is a subset of the details missing from the model description that fundamentally impact the fidelity and impact of the results. The modeling efforts undertaken in the manuscript need to both appear in the main text and be more fully described before the full impact of the manuscript can be assessed.- Model spin up occurs over a two-month period with water-level set to low tide (lines 243-246, which we note appears in the Results section): why did you choose low tide? Is that the “neutral” stress state? Does choosing a zero-tide or high-tide condition for spin up change the results of the modeled grounding zone width?
- This section describing model spin up and experiment duration uses phrases like “enhances results accuracy” and that “models adapt and stabilizes [sic]” after 3-5 days of variable tides, so that the grounding zone width during days 5–7 can be used as the modeling deliverable—how is accuracy and model stabilization defined here since these form the key deliverable of the manuscript?
- The inflow velocity of the model is prescribed as a constant, but results from across Antarctica show tidally variable ice velocity on time periods from diurnal to fortnightly and semiannual. Is this inflow boundary condition realistic and/or does variable inflow velocity matter to grounding zone width?
- How was data from BedMachine integrated into this modeling framework? For example, how was bedrock slope calculated? Figure 1 makes it clear that there is not a “single” slope value, but rather it is highly variable. Is the reported value per flowline just the slope between end points? A linear fit to all the topographic data on a flow line? A mean slope after differentiating bed topography along a flowline? Is it a slope over a certain characteristic length scale that impacts ice flow? Why even reduce the bedrock slope to a single number when the true bedrock topography along each flowline could be incorporated into the finite-element model? Does the true topography vs. a simplified version impact the results?
- The definition of H from Equation 8 is unclear. Is it only the starting glacier thickness at the position of the starting grounding line? Would you want to compare ending thicknesses at the position of the ending grounding line?
- The DInSAR processing and analysis is not fully described, which impacts the quality of the model/data comparison. Perhaps most importantly, the differential tide-heights of the interferograms are never mentioned in the manuscript, yet the results from these observations are compared to “tides with a 1 m amplitude” in the model (line 177). Since the grounding zone width depends on the tidal amplitude, are the DInSAR results showing a 1 m tidal amplitude (note: it is not clear whether this means ±0.5 m tides or ±1 m tides for the modeling effort)? If they are not, this is not an apples-to-apples comparison between the observed widths and modeled widths (i.e., the overlap between modeling results and DInSAR analysis in Figure 4c may in fact indicate that the model has substantial bias). There are some good examples showing clear DInSAR differential tide estimates in the literature (e.g., Table 1 in Milillo et al., 2017 or Table S1 in Milillo et al., 2022).
The InSAR processor used is not mentioned in the manuscript (and thus the results are not reproducible). The text says uncertainty of manual grounding-line mapping was “empirically determined” to be 200 m (line 228) with no additional explanation. What were the methods for assessing the uncertainty in grounding line delineation? The DInSAR grounding lines at high and low tide are (unsurprisingly) wiggly in Figure 1 and appear to intersect for Moscow University and Totten—how do you proceed when the low-tide grounding line is upstream of the high-tide grounding line (negative grounding zone width)? Do the tidal flexure patterns deviate from those observed on the glaciers studied in Rignot et al., (2014) and would that impact your results?
Finally, how were the flow lines for determining grounding zone width chosen? They look quite straight; are they the true path of an ice parcel or an estimate? Would choosing different flowlines substantially impact your results? We quickly show that estimated flowlines on Totten Glacier (below, left panel, black lines) do not match the lines in Figure 1 (below, right panel) with substantial differences in flow direction, suggesting grounding zone widths reported in the manuscript may contain substantial unaccounted for error:
- Figures and tables are not of publishable quality. For example, Figure 1 does an excellent job at conveying a lot of information, but there are several aspects that make it hard to interpret. There are no figure limits for this journal, so it is not clear why so much information is compressed into one figure. Unpacking the panels into multiple figures will help strengthen your argument as will considering the following issues:
- Having the same color scale with different ranges makes comparison between glaciers unintuitive. Color scales should be sequential and perceptually uniform covering the same range for all three glaciers where reasonable and explicitly stating if you diverge from this standard to make sure the reader does not misinterpret a panel (as we did initially).
- Several labels are far too small and hard to read. For example, the numbering of the flowlines is near impossible at 100%.
- Several color choices are difficult to distinguish. For example, the blue dashed line indicating the high (low) tide grounding line is nearly invisible in panel l (o).
- Please label which glacier corresponds to which column.
- Colorbars in the bottom two rows should not be labeled dz as the colors show a wrapped interferogram. It is not even clear that this is phase projected into the vertical z component, so clarity on this label is important.
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Figure 3 does not provide a clear message and left us confused. Is there a specific trend that we are supposed to observe? If so, it might be beneficial to extract the panels that show this trend and move the rest to the supplement. If all the panels are important, we suggest adding additional labels showcasing what comparisons are relevant. Additionally, please make the axes limits consistent between plots so the reader can effectively compare between panels.
The horizontal bars in Figure 4 are not “error bars” as described, but rather are a range of modeling results (at least in our interpretation; the description of these bars in the text and caption was confusing). How are the pink and green outlines calculated in Figure 4 and 5? Why do different glaciers have different bin sizes in the histograms for Figure S3? Table 2 does not explain what these numbers represent (e.g., are these means of the minimum, mean, and maximum of each flowline? What is represented by the ± value?). Also “MeASURESs2” is not a data product— MEaSUREs is an acronym for a NASA funding program (Making Earth System Data Records for Use in Research Environments). The organization of Table A1 is confusing—some of the geometric quantities are scalars, but there is a separate table heading for scalar quantities? H likely should be H(t), l should be l(t), there are no units provided (which would be quite helpful for the reader), and the scalars are bolded, which may be interpreted as a vector quantity. The figures and tables all require dedicated consideration to make best use of journal space to support the text.
Citation: https://doi.org/10.5194/egusphere-2024-875-RC2 - AC3: 'Reply on RC2', Natalya Maslennikova, 21 Oct 2024
- The structure of the paper hides the key contributions of this manuscript. For example, methods used in the manuscript appear in Section 2 (“Data and Methods”), Section 3 (“Viscous and viscoelastic models”), Section 4 (“Results”; e.g., lines 211-227 cover how model parameter space and mesh size were determined; lines 238-247 contains more methodological description of the modeling effort), Section 5 (“Discussion; e.g., lines 328-336 describe filtering methods), and Appendix A (“Glacier modeling”). In fact, the substantial contribution of the manuscript—a new viscoelastic model that can capture a tidally variable grounding zone—is largely relegated to the appendix rather than the methods section of the main text. Results from the methods described in the manuscript appear throughout sections 4 (“Results”), 5 (“Discussion”; e.g., lines 261-271), and 6 (“Conclusion”; e.g., lines 408-413). In addition, the conclusions (Section 6) take the manuscript in a largely unrelated direction, ending with grounding line retreat estimates over multiple decades—a topic that is explicitly not the focus of the manuscript.
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