the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
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
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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 -
RC1: 'Comment on egusphere-2024-875', Anonymous Referee #1, 20 Jun 2024
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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
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