the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Mar 2025
Calorimetric in-situ determination of ice water content in two Alpine glaciers
Abstract. Temperate glacier ice contains liquid water at different concentrations. How much exactly depends on the history of ice formation, the heat supply from dissipative deformation, and on the drainage pathways between ice crystals. The interstitial liquid water content strongly influences the ice viscosity and therefore glacier flow speed. The hydrological system of glaciers is strongly affected by the porosity of the ice matrix. Also, material properties, such as seismic velocities, electromagnetic susceptibility and dielectricity are strongly affected. This renders seismics and radar suitable to measure water content in a glacier. An independent in-situ method is a calorimetric determination by tracking an artificially induced freezing front within the material. Here, we report on two experiments from an artificial cave within a glacier and form a tunnel at the base of a glacier. In both experiments, a liquid water content of 1–2 % was found by analyzing the measured cooling rates with a detailed numerical model of the experimental setup.
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Status: closed (peer review stopped)
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RC1: 'Comment on egusphere-2025-832', Thomas Chauve, 14 Apr 2025
- AC1: 'Reply on RC1', Martin Lüthi, 07 Jul 2025
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RC2: 'review on egusphere-2025-832', Anonymous Referee #2, 20 May 2025
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AC2: 'Reply on RC2', Martin Lüthi, 07 Jul 2025
see attachment
Citation: https://doi.org/10.5194/egusphere-2025-832-AC2 - AC3: 'Reply on RC2', Martin Lüthi, 07 Jul 2025
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AC2: 'Reply on RC2', Martin Lüthi, 07 Jul 2025
Status: closed (peer review stopped)
-
RC1: 'Comment on egusphere-2025-832', Thomas Chauve, 14 Apr 2025
The article "Calorimetric in-situ determination of ice water content in two Alpine glaciers" by Lüthi et al. presents an innovative experimental setup aimed at measuring the water content within temperate glaciers in situ—a task that remains particularly challenging, especially near the bedrock interface, where deformation has the greatest influence on ice column flow. Accurately determining this ice property is essential for modeling glacier dynamics, as the presence of interstitial water significantly affects ice rheology. In particular, it can alter the stress exponent in Glen’s flow law (e.g., n ≈ 1 in the presence of water, compared to n ≈ 3 in its absence [1]). As such, the topic is highly relevant to the glaciological community targeted by The Cryosphere. However, in its current form, I consider that the manuscript requires major revisions before it can be considered for publication.
Major comments :
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Concerning the implementation of the heat transfer model I have a significant concern about the numerical modeling of heat transfer presented in the manuscript. Given the numerical setup, which is radially symmetric around the heating element, I would expect the numerical simulation to reflect this symmetry—that is, the temperature evolution at points equidistant from the heater (i.e., at ±d) should be identical. However, this is clearly not the case in Figures 4, 5, B1, and C1, where the dashed lines show differing temperature evolutions for sensors located symmetrically around the heating source. This raises questions about the numerical implementation: Why does the model exhibit this asymmetry? Is it a result of mesh discretization, boundary condition settings, or another factor? Clarification is needed, as this issue could have implications for the interpretation of the temperature signal and, by extension, the derived water content.
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Line 130 : The authors state that « The temperature evolution at sensors with at the same nominal distance from the cooling head differ considerably in our experiments, especially for small distances. Obviously, inhomogeneities in the polycrystalline ice can largely influence the spreading of the cooling wave. » Therefore, if the small distances sensors are more impacted by the material heterogeneities, why do you use those in order to fit the temperature evolution and therefore water content. Will it be more representative to use the sensor that are the furter of the cooling head as it will reduce the impact of the heterogeneity and lead to better water content estimation. For instance, in figure 5 the sensor at ± 10 cm present les variabilities that the one at ± 5 cm but the agreement with the model is worst.
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Following up on the concern regarding the numerical modeling (comment 2), I also find that the comparison between measurements and model output lacks sufficient statistical analysis to convincingly support the conclusions. Although the authors performed five measurements at each of the two sites, only a single representative result is used for comparison in each case. It is unclear why the remaining measurements are not utilized to provide a more statistically robust assessment of the water content. Could the authors include all datasets and present metrics such as the mean, standard deviation, or confidence intervals to better quantify the model–data agreement? Doing so would strengthen the validity of the inferred water content and improve the overall credibility of the method.
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In the paragraph spanning lines 21–26, the authors compare their calorimetric measurements of water content with radar-derived estimates. However, I would ask the authors to critically consider whether these two methods are probing the same type or scale of water content. Given the spatial resolution and physical principles involved, the calorimetric method likely captures interstitial water localized at grain boundaries (as discussed, for example, in De La Chapelle et al., 1997 [2]), while radar methods may be more sensitive to macroscopic features such as water-filled crevasses or pockets, depending on frequency and resolution. These two types of water may differ not only in their physical distribution but also in their respective impacts on ice rheology and, thus, glacier dynamics. I recommend that the authors elaborate on this point to clarify the physical interpretation of their comparison and to avoid overstating the agreement between the two methods.
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Although many of the issues listed below might typically be considered minor, their frequency and impact on readability warrant more serious attention. The manuscript appears to lack a thorough final proofreading, and numerous typographical errors and formatting problems detract from the clarity of the work. Examples include:
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Line 63: Reference to “Fig. ??”.
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Figure 3: The caption refers to subfigures (a) and (b), but these labels are not present in the actual figure. Additionally, the color scale ticks are too small to be legible.
-
Line 104: The expression “(re4)” is unclear and appears to be either a typo or an undefined term.
-
Figures in general: Font sizes are consistently too small across all figures, and in some cases, text overlaps with graphical elements—for example, in Figure 5, the labels "-10" and "10" overlap with the plotted curves.
-
Figure 4: green dash lines look continous (left figure) and is not visible (right figure)
These issues significantly hinder comprehension and need to be addressed comprehensively in a revised version.
Minor comment :
-
The authors state that “Soluble and insoluble impurities might complicate the picture (Harrison and Raymond, 1976), but will be ignored in this study.” However, based on the visual appearance of the ice in Argentière Glacier (e.g., Figure 2), this assumption seems rather strong. Could the authors elaborate briefly on the expected effects of such impurities and justify their exclusion more clearly?
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I recommend citing Schohn et al., 2025 [1] to strengthen the argument on the influence of water content on ice rheology. This would help contextualize the results within the most recent developments in the field.
-
The manuscript would benefit from a clearer presentation of the physical parameters used in the simulations—specifically, the thermal diffusivity of ice (κ), its heat capacity (C), and the latent heat of freezing (L), mesh size. Including these in a dedicated table would enhance transparency and reproducibility.
-
For clarity and completeness, I would also suggest adding a summary table listing all experimental measurements, including imposed temperature values, the positions of the sensors, and duration.
-
Line 125: “which would agree” — Why do you think that the values you measure in Argentière Glacier should “agree” with those from other glaciers, given that you previously state that water content “depends on the history of ice formation, the heat supply from dissipative deformation, and on the drainage pathways between ice crystals”? Do you expect these factors to be similar across all glaciers?
[1] Schohn, Collin M. / Iverson, Neal R. / Zoet, Lucas K. / Fowler, Jacob R. / Morgan-Witts, Natasha Linear-viscous flow of temperate ice 2025-01 Science , Vol. 387, No. 6730 American Association for the Advancement of Science (AAAS) p. 182-185
[2] De La Chapelle , S. / Milsch, H. / Castelnau, O. / Duval, P. Compressive creep of ice containing a liquid intergranur phase: Rate‐controlling processes in the dislocation creep regime 1999-01 Geophysical Research Letters , Vol. 26, No. 2 American Geophysical Union (AGU) p. 251-254
Citation: https://doi.org/10.5194/egusphere-2025-832-RC1 - AC1: 'Reply on RC1', Martin Lüthi, 07 Jul 2025
-
-
RC2: 'review on egusphere-2025-832', Anonymous Referee #2, 20 May 2025
-
AC2: 'Reply on RC2', Martin Lüthi, 07 Jul 2025
see attachment
Citation: https://doi.org/10.5194/egusphere-2025-832-AC2 - AC3: 'Reply on RC2', Martin Lüthi, 07 Jul 2025
-
AC2: 'Reply on RC2', Martin Lüthi, 07 Jul 2025
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- 1
The article "Calorimetric in-situ determination of ice water content in two Alpine glaciers" by Lüthi et al. presents an innovative experimental setup aimed at measuring the water content within temperate glaciers in situ—a task that remains particularly challenging, especially near the bedrock interface, where deformation has the greatest influence on ice column flow. Accurately determining this ice property is essential for modeling glacier dynamics, as the presence of interstitial water significantly affects ice rheology. In particular, it can alter the stress exponent in Glen’s flow law (e.g., n ≈ 1 in the presence of water, compared to n ≈ 3 in its absence [1]). As such, the topic is highly relevant to the glaciological community targeted by The Cryosphere. However, in its current form, I consider that the manuscript requires major revisions before it can be considered for publication.
Major comments :
Concerning the implementation of the heat transfer model I have a significant concern about the numerical modeling of heat transfer presented in the manuscript. Given the numerical setup, which is radially symmetric around the heating element, I would expect the numerical simulation to reflect this symmetry—that is, the temperature evolution at points equidistant from the heater (i.e., at ±d) should be identical. However, this is clearly not the case in Figures 4, 5, B1, and C1, where the dashed lines show differing temperature evolutions for sensors located symmetrically around the heating source. This raises questions about the numerical implementation: Why does the model exhibit this asymmetry? Is it a result of mesh discretization, boundary condition settings, or another factor? Clarification is needed, as this issue could have implications for the interpretation of the temperature signal and, by extension, the derived water content.
Line 130 : The authors state that « The temperature evolution at sensors with at the same nominal distance from the cooling head differ considerably in our experiments, especially for small distances. Obviously, inhomogeneities in the polycrystalline ice can largely influence the spreading of the cooling wave. » Therefore, if the small distances sensors are more impacted by the material heterogeneities, why do you use those in order to fit the temperature evolution and therefore water content. Will it be more representative to use the sensor that are the furter of the cooling head as it will reduce the impact of the heterogeneity and lead to better water content estimation. For instance, in figure 5 the sensor at ± 10 cm present les variabilities that the one at ± 5 cm but the agreement with the model is worst.
Following up on the concern regarding the numerical modeling (comment 2), I also find that the comparison between measurements and model output lacks sufficient statistical analysis to convincingly support the conclusions. Although the authors performed five measurements at each of the two sites, only a single representative result is used for comparison in each case. It is unclear why the remaining measurements are not utilized to provide a more statistically robust assessment of the water content. Could the authors include all datasets and present metrics such as the mean, standard deviation, or confidence intervals to better quantify the model–data agreement? Doing so would strengthen the validity of the inferred water content and improve the overall credibility of the method.
In the paragraph spanning lines 21–26, the authors compare their calorimetric measurements of water content with radar-derived estimates. However, I would ask the authors to critically consider whether these two methods are probing the same type or scale of water content. Given the spatial resolution and physical principles involved, the calorimetric method likely captures interstitial water localized at grain boundaries (as discussed, for example, in De La Chapelle et al., 1997 [2]), while radar methods may be more sensitive to macroscopic features such as water-filled crevasses or pockets, depending on frequency and resolution. These two types of water may differ not only in their physical distribution but also in their respective impacts on ice rheology and, thus, glacier dynamics. I recommend that the authors elaborate on this point to clarify the physical interpretation of their comparison and to avoid overstating the agreement between the two methods.
Although many of the issues listed below might typically be considered minor, their frequency and impact on readability warrant more serious attention. The manuscript appears to lack a thorough final proofreading, and numerous typographical errors and formatting problems detract from the clarity of the work. Examples include:
Line 63: Reference to “Fig. ??”.
Figure 3: The caption refers to subfigures (a) and (b), but these labels are not present in the actual figure. Additionally, the color scale ticks are too small to be legible.
Line 104: The expression “(re4)” is unclear and appears to be either a typo or an undefined term.
Figures in general: Font sizes are consistently too small across all figures, and in some cases, text overlaps with graphical elements—for example, in Figure 5, the labels "-10" and "10" overlap with the plotted curves.
Figure 4: green dash lines look continous (left figure) and is not visible (right figure)
These issues significantly hinder comprehension and need to be addressed comprehensively in a revised version.
Minor comment :
The authors state that “Soluble and insoluble impurities might complicate the picture (Harrison and Raymond, 1976), but will be ignored in this study.” However, based on the visual appearance of the ice in Argentière Glacier (e.g., Figure 2), this assumption seems rather strong. Could the authors elaborate briefly on the expected effects of such impurities and justify their exclusion more clearly?
I recommend citing Schohn et al., 2025 [1] to strengthen the argument on the influence of water content on ice rheology. This would help contextualize the results within the most recent developments in the field.
The manuscript would benefit from a clearer presentation of the physical parameters used in the simulations—specifically, the thermal diffusivity of ice (κ), its heat capacity (C), and the latent heat of freezing (L), mesh size. Including these in a dedicated table would enhance transparency and reproducibility.
For clarity and completeness, I would also suggest adding a summary table listing all experimental measurements, including imposed temperature values, the positions of the sensors, and duration.
Line 125: “which would agree” — Why do you think that the values you measure in Argentière Glacier should “agree” with those from other glaciers, given that you previously state that water content “depends on the history of ice formation, the heat supply from dissipative deformation, and on the drainage pathways between ice crystals”? Do you expect these factors to be similar across all glaciers?
[1] Schohn, Collin M. / Iverson, Neal R. / Zoet, Lucas K. / Fowler, Jacob R. / Morgan-Witts, Natasha Linear-viscous flow of temperate ice 2025-01 Science , Vol. 387, No. 6730 American Association for the Advancement of Science (AAAS) p. 182-185
[2] De La Chapelle , S. / Milsch, H. / Castelnau, O. / Duval, P. Compressive creep of ice containing a liquid intergranur phase: Rate‐controlling processes in the dislocation creep regime 1999-01 Geophysical Research Letters , Vol. 26, No. 2 American Geophysical Union (AGU) p. 251-254