the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
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 glaciertopography 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 laketerminating 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, laketerminating 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 egusphere20241053', Whyjay Zheng, 17 Jun 2024
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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/egusphere20241053). 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 1112) 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 1314. 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 highspeed 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 xaxis, we should probably change the tick labels from 1 and 10 to <=1 and >=10, respectively.
 Since you put pvalue in many figures  Is "R" correlation coefficient or the coefficient of determination? Is it "R" or "R^2"? What model does the pvalue 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 pvalue 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.
 L600601: The force balance model already assumes that tau_d is the sum of the three resistive forces (cf. L244245). 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/egusphere20241053RC1 
RC2: 'Comment on egusphere20241053', Anonymous Referee #2, 23 Jun 2024
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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 iceocean/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 crosssection 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 35) were computed from surface strain rates obtained from ice speed maps. The authors assume full slip condition referring to a previous study (Line 261, CollaoBarrios et al., 2018), but the previous study suggested 98% sliding specifically for the fastestflowing 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 244245. 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 2324. 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 657669). 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 549575). 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 wellperformed and fails to draw conclusions.
Specific/minor comments:
Line 21: “Gt year1 annually” is redundant.
Line 33: complex “changes in” stresses...?
Line 45: “melting caused by water bodyglacier 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 9596: 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 106121: I wonder if reviewing such details and numbers is necessary for this paper.
Line 135146: 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 225226: “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(x_{i})=−dh(x_{i})/{∑_{j=1}^{N }−dh(x_{j})}
Equation 14: The Lefthand side is cumulative thinning, whereas the righthand side is the Peclet number. I am confused.
Line 317: “slope gradient” >> Do you mean “slope”?
Line 323324: What do you mean by “slope difference”?
Line 331: “we classified ...” >> This is already described before (Line 274 and 298).
Line 342343: 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 397405: 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 8AI 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 673674: 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 788793: What is the difference between 2018a and 2018b?
Line 812817: Duplicated?
Citation: https://doi.org/10.5194/egusphere20241053RC2
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