the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 May 2024
Glacier geometry limits the propagation of thinning in Patagonian Icefields
Abstract. Climate change is causing a decline in glaciers globally, with the possibility that some may disappear during this century. Recent findings postulate that the geometric glacier-topography configuration has the capacity to limit glacier thinning upstream. The Patagonian Icefields (PI), with 15,900 km² of glaciers, are the world's largest glacial freshwater reservoir after Antarctica and Greenland. In recent decades, it has been one of the areas with the greatest mass loss worldwide due to climate change. Our research explores the relationship between glacier geometry and changes in PI glaciers to determine regions vulnerable to thinning. We studied 45 major marine- and lake-terminating glaciers in PI using the Péclet number (Pe) based on the diffusive kinematic wave model to determine the geometric state of glaciers and as a metric of vulnerability to diffusive thinning. Locations with Pe ≤ 8 experienced greater thinning and retreat, suggesting an empirical limit that encompasses more than 90 % of ice thinning. The empirical limit is related to a significant change in the slope gradient and roughness of the subglacial topography at PI due to a knickpoint in the subglacial bed. On average, ~53 % of the total ice flow of PI glaciers is below the thinning limit. Therefore, due to the current geometric state and evolution, lake-terminating glaciers may propagate frontal thinning deep inland. The empirical thinning limit provides signals of priority glaciers to investigate considering current climate change projections.
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RC1: 'Comment on egusphere-2024-1053', Whyjay Zheng, 17 Jun 2024
Dear editors and authors,
Thank you for presenting and handling the work about the (in)stability of glaciers in the Patagonian Icefields (PI) (https://doi.org/10.5194/egusphere-2024-1053). I am very excited to see the analysis of Peclet numbers applied for the first time in a region other than the Arctic and the Greenland Ice Sheet. The workflow presented here builds on previously published models with interesting analysis strategies (see my comments below). The results are not easy to comprehend at first sight (for some reasons below), but they reveal patterns that can help decide future plans for monitoring PI glacier changes.
The work is worth publishing in TC to be shared with the glaciology community, especially for those working with PI glaciers or considering using the Peclet number and its model framework on different glacier regions. There are some technical components, however, that I would like to check with the authors and discuss for potential improvement:
- I might have missed this, but what is the value of l (length of perturbation) as in equation 1?
- The idea of cumulative thinning (equations 11-12) is okay, but wouldn't it be more physically meaningful if we could link or rename this quantity to the cumulative volume loss since the terminus?
- I don't quite understand equations 13-14. The x in CT(x) is the distance from the terminus, but in equation 13, you seem to put a Peclet number in replace of x. In addition, CT(x) itself should be a percentage number by definition, but equation 14 sets it equal to Pe_{limit}, which is not a percentage, to my understanding.
- The most necessary improvement in this work is probably the percentage of ice flow (equation 15). Unlike the percentage thinning, equation 15 is not physically meaningful to me because ice flow does not add up this way. I was confused multiple times when I read the manuscript; for example, in L552: "glaciers with Pe < 4.85 have 59% of their flow below the empirical limit." (How do you have 59%, not 100%, of the ice flux in a glacier's main trunk? Is the glacier diverging to many branches?) Can you justify the use of this quantity? Alternatively, I can see this quantity might relate to the mapping of high-speed zones of a glacier, and it can physically make sense this way. However, we need a better statement in the manuscript so readers know what we are physically comparing Pe to.
- Figure 2: If this is cumulative thinning (volume loss), why does Pe = 2 have a lower value than Pe <= 1?
- For all figures with Pe as the x-axis, we should probably change the tick labels from 1 and 10 to <=1 and >=10, respectively.
- Since you put p-value in many figures -- Is "R" correlation coefficient or the coefficient of determination? Is it "R" or "R^2"? What model does the p-value test? It looks like it's testing a linear model, but this should be explicitly specified. And if it's testing a linear model, for trends that are not linear (e.g., Figure 4c and Figure 6b), R(^2) and p-value are not good indicators.
- Some information appears multiple times, such as using QGIS and some Python libraries. Since this is not a short article, I wonder if there's a way to present this once and for all and save the length.
- L600-601: The force balance model already assumes that tau_d is the sum of the three resistive forces (cf. L244-245). So what do you mean by "compensate" here?
- The authors plan to release the code after the paper is accepted. Do you also plan to release the derived data set, such as the Peclet numbers along the selected flowlines? I appreciate it if you could specify this in the Data Availability section.
There are also a few copyediting suggestions as below:
- L129: annual precipitation?
- L289: The percentage of total thinning is expressed as the thinning at position 𝑥 along the flowline as follows
- L435: the vulnerability of these
- L600: glaciers that are/have been relatively stable
- L610: I don't understand what it means to "have fewer Péclet number than the limit." Less Péclet number? What limit do you mean?
- L634: The geometry of the fjord is also a topographic condition?
- L663: The statement here has nothing to do with basal conditions. Maybe "Despite Pio XI Glacier changed its terminus state from marine to land..."?
- L815: Two Felikson et al. (2021) references.
Citation: https://doi.org/10.5194/egusphere-2024-1053-RC1 -
RC2: 'Comment on egusphere-2024-1053', Anonymous Referee #2, 23 Jun 2024
Review comments on “Glacier geometry limits the propagation of thinning in Patagonian Icefields” by Bastian Morales et al.
1. General comments:
This paper investigates the influence of glacier geometry on the recent thinning and retreat of ocean/lake terminating outlet glaciers in the Patagonia Icefields. To analyze the geometrical control on glacier changes, the authors compute the Peclet number along the flowline of 45 outlet glaciers. This approach has been proposed by a previous study (Felikson et al., 2017) and applied to glaciers in Greenland and in Svalbard (Felikson et al., 2017; 2020; Zheng, 2022).
Ocean and lake terminating glaciers in Patagonia are rapidly losing mass under the influence of increasingly negative mass balance as well as the ice-ocean/lake interaction. This is a similar situation as in Greenland, although the climate and glaciological settings in these regions are substantially different. Therefore, the application of the recently proposed analysis to Patagonia is interesting and potentially important to better understand the current and future mass loss of the glaciers. As far as I know, this is the first time that Peclet numbers are analyzed for glaciers in Patagonia.
Despite the novelty and potential importance of the study, it is difficult to understand the findings and implications of the study. The way of presentation is one reason, but I suspect fundamental problems in some of the analyses. The manuscript suffers from unclear text and equations, which get in the way of understanding. I list below my major concerns, which are followed by specific/minor comments on the manuscript.
Major concerns:
- Data analysis and presentation
The authors analyze and present the general trends and statistics obtained from 45 outlet glaciers. Except for maps showing some numbers for each glacier (Figures 5 and 6), readers are not able to see data obtained for each individual glacier. Considering the diversity of glaciers in Patagonia as well as large uncertainty in the bed elevation, showing only statistical values is not convincing and insufficient to draw conclusions. I encourage the authors to look into the details of each individual glacier as performed in previous studies (Felikson et al., 2017; 2020; Zheng, 2022). The Peclet number is a value computed from glacier geometry and ice dynamics. To use it as a measure of glacier stability, investigation of the observational data used for the computation (bed and surface elevation, ice speed, elevation change) along the flowline is necessary (e.g. Figure 2 in Felikson et al., 2017).
- Bed elevation data
In comparison with Greenland and Svalbard, observations of glacier bed elevation are sparse in Patagonia and thus subglacial geometry has a greater uncertainty. Therefore, a more careful analysis is required for the bed estimated by inversion (Farinotti et al., 2019). As suggested above, investigation of the glacier cross-section and observations along the flowline of each glacier is necessary. As indicated by the authors (Line 625), please also consider using a more recently compiled bed elevation data set (Furst et al., 2024).
- Force budget
I understand that the components of the force budget (Equations 3-5) were computed from surface strain rates obtained from ice speed maps. The authors assume full slip condition referring to a previous study (Line 261, Collao-Barrios et al., 2018), but the previous study suggested 98% sliding specifically for the fastest-flowing glacier tongue of San Rafael Glacier. It is not realistic to assume 100% slip condition for all the glaciers and regions extending upglacier.
Further, the presentation and discussion of the force balance analysis are difficult to understand. The authors argue that “glaciers retreat irreversibly when driving stress cannot be supported by the other components of the force balance” (Line 604, similar statement in Line 470). What do you mean by “cannot be supported”? The driving stress should be supported by other stress components as stated in Line 244-245. Actually, “the basal drag is calculated as the residual” (Line 267), thus I assume imbalance does not happen.
Changes in the force balance components near the glacier fronts between 2000 and 2018 are presented in page 23-24. Some numbers show very large changes, represented by >1000% increase in lateral and longitudinal stresses at Penguin Glacier (Line 481). Without detailed analysis, such a rapid change is difficult to accept and cannot be simply connected to the argument “the increase in stress appears to support the Penguin Glacier's relative stability” (Line 482).
- Percent ice flow
It is hard to understand the concept of “the percent ice flow” defined by Equation 15. CT is “the cumulative thinning from the glacier front in percent” (Line 295), thus Equation 15 gives a mean of CT between the front and the empirical thinning limit. Why do you call this value the percent ice flow? I am not able to follow the analysis and discussion of this value.
- Discussion of the data and results
It is a pity that the conclusion of the paper tells not much more than “90% of the ice thinning is occurring below the locations with Pe<8” (Line 657-669). This is because the complex data sets presented in the “3 Results” section are not properly discussed in the “4 Discussion” section. In “4.1 Empirical limit ...”, no clear interpretation is given to the relatively large Peclet number found for the upper limit of the thinning. “4.2 Evolution Controlled by Upstream Geometry” discusses the advancing Pio XI Glacier, but difficult to find the point of the argument from previous studies in other regions (Line 549-575). The rest of the section describes previous studies and the discussion is not based on the results obtained in this study. Except for the section “4.3 Limitations of our analysis and future work”, the discussion is not well-performed and fails to draw conclusions.
Specific/minor comments:
Line 21: “Gt year-1 annually” is redundant.
Line 33: complex “changes in” stresses...?
Line 45: “melting caused by water body-glacier contact” >> “melting due to upwelling plume”?
Line 65: The statement “3 mm increase...” is after Zemp et al. (2019).
Line 82: “terrain elevation values” >> Do you mean “surface elevation”?
Line 84: What do you mean by “characteristic terrain elevation values”? Definition?
Line 95-96: Please consider significant digits of these numbers in %.
Line 101: “quickest” >> fastest flowing?
Line 102: “second largest” >> San Quintin is the largest in the Northern Patagonia Icefield. Do you mean “second fastest”?
Line 106-121: I wonder if reviewing such details and numbers is necessary for this paper.
Line 135-146: Please also consider more recent studies, e.g. Sauter et al., 2020 (Hydrol. Earth Syst. Sci.), Wiedemann et al., 2018 (Front. Earth Sci.) and Salazar et al., 2024 (Climate Dynamics).
Line 190: “q is the ice flow” >> ice flux?
Line 190: the “surface” slope of?
Line 199: “upper current” >> upglacier?
Line 225-226: “We used the NumPy, Pandas, and SciPy libraries .....” >> This or similar statements are repeated many times.
Line 236: “... between 2000 and 2018 in PI glaciers ...” >> Not only here, but “PI glaciers” is not necessary.
Equations 11 and 12: The notations are odd. Do you mean something like this? dH(xi)=−dh(xi)/{∑j=1N −dh(xj)}
Equation 14: The Left-hand side is cumulative thinning, whereas the right-hand side is the Peclet number. I am confused.
Line 317: “slope gradient” >> Do you mean “slope”?
Line 323-324: What do you mean by “slope difference”?
Line 331: “we classified ...” >> This is already described before (Line 274 and 298).
Line 342-343: The first two sentences are not necessary.
Figure 2: Please use the same scale for the vertical axes of the two plots. I wonder why accumulated thinning (%) decreases upglacier from Pe=1 to 2 (Figures 2a and b) and Pe=8 to 9 (Figure 2a).
Line 343: The first sentence in the figure caption is not necessary. Should be in the main text.
Line 371: What do you mean by “force balance increases”? It’s not a quantity.
Line 386: “thinning limit” >> Is this the same as “empirical limit”? Please be consistent.
Line 394: What do you mean by “geometric limit”?
Line 397-405: Please consider the significant digits for the numbers.
Figure 5E: I am confused by the different scales given to the three maps.
Line 418: “Fig. 8” >> Which plot in Figures 8A-I supports this statement?
Line 427: “Fig. 8” >> Isn’t it Figure 6? I am confused.
Linen 529: “According to our results,” >> Which results? This is one example that I find difficulty in following the discussion. Please support your argument with data.
Line 658: “suggesting the existence of an empirical limit” >> Pe ≤ 8 was obtained by setting 90% as the threshold of so called empirical thinning limit. Why Pe ≤ 8 suggests the existence of such a limit?
Line 673-674: I understand the potential importance of the analysis, but difficult to follow this conclusion. What is “geometric state”? Which data show it is “a key indicator” and “essential”?
Line 788-793: What is the difference between 2018a and 2018b?
Line 812-817: Duplicated?
Citation: https://doi.org/10.5194/egusphere-2024-1053-RC2 -
RC3: 'Comment on egusphere-2024-1053', Timothy Bartholomaus, 14 Sep 2024
Review of “Glacier geometry limits the propagation of thinning in Patagonian Icefields”
By Morales et al.
Under consideration for publication in The Cryosphere
September 2024
The manuscript by Morales and others represents a major and impressive amount of work, with a thorough assessment of the interactions between glacier geometry and past and future change of the Patagonian Icefields. To my knowledge, the work is unique and novel, and, through coupling Peclet number analysis with force balance analysis, is innovative in its approach. The authors link the rapid decline of some glaciers within the Patagonian Icefields to their particular geometric properties.
However, despite the significance and extent of this work, several factors limit the impact of this work and prevent me from endorsing it for publication in its current form.
These general points are:
- The methods section is hard to follow, so it is difficult for me to know what exactly is being presented in the results section. I don’t believe I would be able to reproduce this work. For example, I’m not sure how the authors assign a single Pe to an entire glacier (or region of a glacier?), as in Figure 6E.
- The results presented are so extensive and thorough that it is hard to identify the specific patterns that the authors intend to draw the readers’ attentions to. The same is true for the Study Area section. Within the scatter plots of Figs 5-8, there are so many plots and most of them do not appear to be discussed at all. I recommend that the authors identify just those critical pieces of information necessary to support their discussion and conclusions sections and eliminate the remainder. Superfluous information, while potentially valuable for some purposes, distracts from the main points and “muddies the water,” reducing the impact of your paper.
- At the same time, some of the results discussed in the text, like the percentage of the modern Patagonian Icefields that are susceptible to future, diffusive thinning, do not appear supported by any figures. I’m not sure where to find this valuable information.
- Given the length of the manuscript, and the need to better highlight/focus on particularly critical scientific results, it may well be necessary to cut significant portions of the text, and perhaps even analyses, in order to keep the length reasonable and not distract the reader with non-essential detail.
- The fluency of the writing is not where it needs to be. I suggested grammatical edits for the first page or so before I stopped. The entire manuscript needs careful editing for clarity of language.
- Throughout the manuscript, “ice flow” is used where some form of ice amount seems implied, like glacier surface area. Please correct.
In light of these limitations, I do not feel like I was able to properly evaluate the present work. I could not follow the chain from methods to results to discussion. As such, I would not consider this a complete and thorough review. After revision, the manuscript will require a fresh and complete review.
I wish I could be more encouraging as to the state of the present work, and I applaud the ambition of the current study. My best wishes to the authors.
Line edits follow.
Tim Bartholomaus
University of Idaho
USA
L 10: Some ambiguity-- gradient of slope of the bed, or of the surface? If surface, I think this would be more clear if this was the “gradient of surface topography.” Unless you intend to actually refer to the topographic curvature, as in the gradient of the gradient of surface elevation (which is what you’ve written)?
L 11-12: Why 53% of “ice flow,” Do you just mean surface area? How do you quantify a percent of ice flow? What’s the baseline for that ratio?
L 17-18: “allows us to project” makes it seem like you’re taking credit for this work.
L 20: “that glaciers there have lost”
L 26: specify what types of “contributions” you’re referring to.
L 27-28: Glacier geometry plays a much broader role on ice flow than is supported just by these manuscripts. Broader lit review is necessary. Even to a textbook.
L 29: access of meltwater to what?
L 30: the “balance of forces” is nearly synonymous with ice flow dynamics. Why is this point different than the citations for ice flow dynamics?
L 32: Much better would be to cite some of the old Nye or Harrison papers that are first cited in Felikson 2017, for example “The response of glaciers and ice-sheets to seasonal and climatic changes” by Nye in 1960.
L 37: “glaciers in West Greenland” or “glaciers in western Greenland”
L 38: “it has been found” use active voice
L 39: revise typos
L 40: “overdeepened regions”
L 41: I think you mean retreat “extent” (as in length), not duration as in time.
Here, I’m ceasing line edits. There are too many to track and suggest edits for each one. This manuscript will need thorough and complete editing for grammar and clarity.
L 63: In referencing potential for sea level rise, cite the original papers that the IPCC cites, not the IPCC itself.
L 67: here again is ice flow, when I think you mean ice field, as in “area” (not motion).
L 120: This is starting to feel like a laundry list of various glacier facts, without a framework for identifying what are the most important points. Can you synthesize more so as to better call attention to what facts are most relevant for the paper?
L122-146: Again, this is a lot of information, and I, the reader, don’t yet have any real context as to what of this is necessary or how it would slot into the paper. This section should all be motivated by the Intro. I don’t see how it is.
Figure 1: This is a beautiful map. Nice going
L 164: Why not use the glacier thickness data from Millan 2022? In that paper, they show that it performs much better than the Farinotti dataset for icefields, and so is much more appropriate here.
L 180: I’m not clear on what it means to use the gradient of the velocity as a mask for flowlines. Also, I would call these “profiles” rather than flowlines if they’re manually delineated and not actually following flow. Why aren’t they just following flow? That would be cleaner and preferable to using manually delineated profiles. I’ve written a tool to extract flowlines from any velocity dataset and it’s here: https://github.com/tbartholomaus/project-tools
Maybe it’s useful to you?
L 190: specify “surface slope”
L 191: partial with respect to x needs no definition
L 193: “motion of the perturbation” as a whole is more than just advection.
L 197: “length”? do you mean span? Or distance from the terminus?
L 199: What is “upper current”?
L 205-206: Are these characteristic dimensions of some sort, or dimensions at a specific location?
L 206: is U_0 the average speed? Sliding speed?
L 213: How did you combine data from the full glacier lengths to arrive at an average Pe value for each glacier?
L 224: What are “distance units”?
L 229: Do you mean Meier et al., as the authors, or are you referring to yourselves?
L 261: I’m not aware of this reference, but surely there’s some caveat to this. 98% sliding can’t be true throughout the entire icefield…. Even up at high elevation, slow-flowing areas? Even on the Greenland Ice Sheet, at a spot with about 100 m/a flow, internal deformation is 30-50% of the surface speed. I don’t think this need throw off your entire analysis, but it seems important to recognize and consider the implications.
L 266: the value you give for gravity is an acceleration, not a force.
L 270: Why is this averaging approach? Also, what if the flow lines branch and either stay apart or re-converges around a nunatak? Then the different lengths of flowlines at a given locale might be offset, and the averaging would be inappropriate.
L 271: Filtering in the along-flow direction?
L 275: Are these Pe classes just rounded Pe values? If so, why introduce a different term than just the Pe values themselves? If not, how does this differ from rounded Pe values?
L 279-280: No part of this sentence makes sense to me. Please find another way to convey your intention.
L 291: These ‘d’s are typically differential operators and should not be used otherwise. For changes or differences, I recommend using capital Deltas.
L 292-293: Odd mixing of actual coordinates (“x”s) and indices in this terminology. Obscures meaning.
L 293: How is position N decided?
L 296: Again, while your code is probably written with respect to indices, finding indices in your equations is unnecessarily confusing.
L 292-301: I’m really not following these methods. Can you revise the text to clarify? Or include a figure? On further consideration, the notation in equations 11 and 12 seems more complicated than necessary. Maybe reviewing with a mathematics colleague might help you find a more straightforward way of writing this out.
L 298: How do you define these Pe classes?
L 301: There’s a little too much in this sentence to follow. Can you break into smaller pieces to make it easier to digest?
L 312: I think you mean percent of area, not percent of ice flow.
L 314: I’m finding this page quite difficult to follow. I don’t really understand how you’re running your analysis, and what the variables you’re producing and discussing later in the paper will be.
L 317: By slope gradient, do you mean the second derivative of the surface elevation? As in the terrain curvature, or the change in surface slope? Or do you just mean the surface slope?
L 319: How do you turn prograde and retrograde slopes into percents?
L 336: What is an “analysis of terminus”?
L 344-351: Unfortunately, I don’t quite understand the methods sufficiently to interpret this figure.
L 367: Please introduce the force balance results generally first, before diving into their changes and how changes in force balance coincide with changes in geometry.
L 374-375: How is it possible for all the resistive forces to drop, but the driving stress to not drop? Otherwise, the forces are not in balance. The fact that the basal drag is the residual requires that the forces stay balanced and I’m not sure how this statement could make sense. This same point persists in Fig. 4. How can the driving stress increase, but all of the resistive stresses drop?
L 376-377: This last sentence more appropriately belongs in the discussion section.
Figure 4: What are the R and p-values here? I wouldn’t have thought there should be a good basis for a linear relationship between these two terms. What’s the physical justification? If there isn’t a physical justification, then take these terms off.
L 385-386: Can you include a plot to show these relationships? Again, I suspect you’re using “ice flow” when you really mean “ice area”?
Figure 5: Are all the symbols individual glaciers? The last line of the caption implies it. Why are there no symbols for land-terminating glaciers?
L 387: I don’t understand this statement. Isn’t the empirical thinning limit an up-glacier location, where the Pe value exceeds some threshold (threshold of 8, in this case)? If so, how can the glacier have retreated past it? This isn’t the empirical limit for retreat, is it?
L 398: Inappropriate, or unnecessary, 4 significant figures presented. Here and all the other four significant figure numbers in this paragraph.
L 415-416: What does this sentence mean?
L 418: Is Figure 8 mentioned here before Figs 6 and 7? All figures should be numbered according to the order they appear in the text.
L 420-421: Are these the lowest Pe values of this icefield? What do you mean as “standing out?” With respect to what?
L 419-426: Maybe it would be useful to plot or just make a table of these numbers? In paragraph form, I’m not sure what of these numbers are particularly important or noteworthy. Perhaps you could put all the numbers in a table, and then just synthesize them a little more to highlight the particularly important results.
L 427: Write out “retreat and thinning,” and perhaps first identify within the results section that thinning and retreat co-occur.
Figure 7: The font sizes for the subscripts of the different stress components are too small to read.
Figure 7: I’m afraid I don’t quite understand what is meant by a “median of averages” for the Peclet numbers. But to interpret, I need to know where these Pe values are for- and what they represent for each glacier. I assume this is for some region near the terminus? But I didn’t understand the methods sufficiently to get this.
Figure 7: There is so much information in this figure but it is just barely discussed in the text. Maybe only at line 470? Cut out any information that is not discussed in the text and essential to your discussion points/conclusions, as set up by your introduction section.
L 470-471: Because glaciers are an example of Stokes flow, the stresses on a parcel of ice must always balance. If you’re finding that forces do not balance, either you’re violating Stokes flow and the principles of a force balance, or I’m missing an important piece of your analysis.
L 477: Inappropriate number of digits again.
L 483: Or, I might write that “The high Pe value of Penguin Glacier reflects geometric factors that allow Penguin to adjust its force balance through an increase in basal drag, without retreating.”
L 528-533: These are important discussion points, but the figures that demonstrate this are not clear. The important results are buried in too complete a representation of all the different results of your study. Strip down information content throughout the paper so that the important results shine, and set you up for your discussion section, like here.
L 541: Again, this is a result that I would really like to see conveyed in a convincing, elegant, clear figure. If you’ve shown it already, I’m afraid that I’ve missed its demonstration.
L 544: 42 km is almost the full width of the icefield! Worth pointing out.
L 553: I thought that Pe = 8 was the key value, but here you’re writing that it’s 4.85? With three significant digits? I’d think two was more appropriate given the precision of the analysis and the many approximations necessary.
L 578: Vulnerability is not “also” controlled by geometry. But Pe IS glacier geometry. The two points are one and the same.
L 630: I don’t quite capture the implication of this statement. Please make it more explicit.
L 667-669: Be specific about the particular ways these glaciers stand out. In their distance to Pe=8? Or some other characteristic?
L 680: Code should be available now, at the time of review.
Citation: https://doi.org/10.5194/egusphere-2024-1053-RC3
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