the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Aug 2024
Variations in the microstructure of saline ice during its growth and decay: Evidences from an experimental study
Abstract. Ice physics are highly sensitive to the ice temperature and are primarily determined by the distribution of inclusions such as gas bubbles and brine pockets within ice. However, a detailed understanding of their distributions and evolution patterns during ice freezing and melting is lacking. To address this issue, in situ experiments were conducted to collect detailed information on the variations in the microstructure of ice using continuous sampling and a high-resolution imaging system. The results revealed a 5- to 10-fold increase in the volume fraction and a 2-fold increase in the size of gas bubbles during the melting phase of ice. Moreover, the size of brine pockets in the ice surface, middle, and bottom layers clearly increased for different reasons. The nearly 30 % increase in gas bubbles observed in the middle layer was thermally driven, while the increase in the surface layer was influenced by the net shortwave radiation. Additionally, the variation in the inclusion size distribution was attributed to the merging process, most of which occurred among smaller inclusions rather than among larger inclusions. The changing ice temperature is a significant factor in the merging process of the middle layer but not for the surface or bottom layers. This study could enhance the understanding of the effect of the transfer of energy between the atmosphere and water beneath ice on the ice microstructure.
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RC1: 'Comment on egusphere-2024-2155', Anonymous Referee #1, 23 Sep 2024
This manuscript describes a study that was carried out to assess the variability of brine and gas inclusions within saline ice.
The methods and results of the study are described thoroughly.
The study sampled an ample number of brine, gas inclusions to get satisfying statistics on the population of individual inclusions. There was not however ample sampling carried out to achieve significant statistics on the spatial variability of the microstructure itself, specifically this study provides no information on the cm – m - decimeter scale variability in an ice cover.
The text is not very concise, but rather verbose, with low information content. Particularly in Section 4.
There really are no substantial conclusions. There may be a few new insights, but I am not seeing any well composed conclusions or key points that describe new insights into microstructural changes occurring during ice growth and/or decay.
Minor:
21: “ice” is frozen water, it becomes a multiphase material consisting of ice crystals, gas bubbles, and impurities when discussed in the context of (in this case) the frozen surface of a water body
27: “subglacial”, use of this word implies the authors are addressing ice as found in a glacier?
30-31: “The content of newly formed brine pockets in ice can be quantified by an effective segregation coefficient and the salinity of the underlying water.” As I read this statement, it implies there is a relationship between the content of newly formed brine pockets (i.e., the brine salinity) and the salinity of the ocean. In fact, the relationship cited by Cox and Weeks (1988) defines a relationship between the salinity of newly formed sea ice and the salinity of the ocean. Those are not the same things.
35-36: “For example, voids form due to the partial evaporation of ice or brine during internal melting.” Are the authors describing the formation of Tyndall figures in this statement? It’s not clear what this is referring to. I believe the bubbles referred to as active bubbles are gas bubbles that form within brine inclusions when the ice temperature is increased.
38: It would be more accurate to say “freezing equilibrium relationships in the water-salt system” than “ice phase diagrams”. An ice phase diagram would refer to the different phases of ice as a function of temperature and pressure.
41: Define Vb
57-58: “This inevitability introduces inaccuracies into ice models in response to varying circumstances.” This overstates the problem, as I am aware of no models that even attempt to treat the details of sea ice microstructure at a level where seasonal variations in microstructure would even be considered.
64: If this study was carried out for a water body with salinity 5 – 7 ppt, it would be important to describe how this differs from sea ice grown from water with salinity generally 30 – 32 ppt. This is especially in light of the critical threshold of 24.7 ppt, below which the temperature of maximum density exceeds the freezing temperature. The formation of sea ice in the open ocean generally occurs under conditions where the temperature of maximum density is equivalent to the freezing temperature.
364: “However, estimating the variation in Va remains challenging due to a lack of information on its influencing factors.” I am not clear what this means, or why it is written.
Figure 10 (and associated text): Is the point of this figure to show that inclusion (presumably brine inclusion?) sizes did not change in response to changes in temperature? If so, then I assert that the inclusions that were measured where not isolated and in freezing equilibrium, or it is possible that only the long dimension of inclusions was measured, and that dimension showed little sensitivity. The total volume of isolated (not connected, not drained, surrounded by ice) brine inclusions should show obvious size change as a result of change in ambient temperature (between -10, -15, 20 C), even in the lab. This fact appears to not be consistent with the statement made in lines 445-446.
473: A power law could also describe the opposite, with numbers decreasing with decreasing size.
473-474: It’s not clear what is meant by “…the minimum number of bubbles was small”
476: infinite? No, there can be (lower and upper) limits on the size.
482: This ice is not warmer than studies from melting ice.
486-487: “Therefore, it could be concluded that the methods used for classifying small inclusions in different works do not considerably affect the overall statistical results.” It could also simply be that the cm / m / decimeter scale has significantly larger variability than what was observed here.
495: “…significant increase in Va of the surface layer during the melting phase.” Is this a reference to the well documented process of brine drainage? See Niedrauer and Martin 1979 https://doi.org/10.1029/JC084iC03p01176
506-507: “These bubbles partly accumulate in the middle layer as a result of their buoyancy, while others escape from the ice bottom.” Please supply a reference for these processes.
559 – 560: “…newly formed bubbles in the middle layer were partly thermally driven.” I am not clear what this means. Please rewrite for clarity.
561 – 562: I think this is describing a well-established brine drainage process.
564-565: “The changes in the brine pocket size during the freezing phase were not as notable as those during the
melting phase.” I suspect this is due to merging and draining processes, and those processes are well documented.
570: what “other mechanisms”?
Citation: https://doi.org/10.5194/egusphere-2024-2155-RC1 -
RC2: 'Comment on egusphere-2024-2155', Anonymous Referee #2, 04 Nov 2024
This study investigated the evolution of brine and gas inclusions of ice forming and melting in a brackish lake. The introduction could be substantially restructured to better situate this study in its appropriate context, which would help readers grasp the relevance and applicability of the findings and understand the specific scientific questions being addressed For instance, the section comparing other observations could serve as a useful background in the introduction. Additionally, the methods could be clarified, as it is currently challenging to follow. Specifically, two different methods were used to measure the volume fraction of gas bubbles (Va) and brine pocket volume fraction (Vb): one based on imaging and another using temperature functions. However, these methods were not compared in a sufficiently clear and transparent manner. There was no reference to the water temperature. The results are logical and outlined clearly and I followed the author’s evaluation but unfortunately, I don’t see any clear, novel conclusions from this work.
A few references are missing, see details below. The manuscript is well structured. There is no supplementary material.
Major
Figure 2 seems to identify a very circular object (3) as a brine pocket. The calculations are challenged by this. Could the author provide the circularity of these examples given in Figure 2? In addition, could this method be tested in a few samples by using tomography? Has this been done in the literature? In addition, the gas bubble (1) is out of focus and the focus needs adjusting to be able to get the true size of this bubble, maybe choosing another example image would be better.
The author applies this study’s introduction to sea ice but the ice studies formed in brackish water. A large section of the introduction emphasises the conditions of the water that the ice forms in determining the brine and gas inclusions. The brackish water was mentioned at being 5–7‰ (5-7 ppt) this is significantly lower than general sea ice conditions. I suggest the introduction could be adapted to a more relevant applications for this study of ice forming in certain regions with brackish water. A good example of this is the introduction of 4.3, this would be great in the introduction.
On Line 163 the author states Va derived from the images was greater than the real values. Is the author referring to the real values from the calculations in equation 4? If the Va calculated from the images isn’t used (line 164), then analysing why these two methods differ is a critical part of this paper and I recommend including this explanation and making it clearer that the Va calculated using the imaging method isn’t used in this study. If feasible two figures showing the comparison of Va calculations from the two methods, and the same with Vb. I then get confused which methods is used for the rest of the paper, e.g. does Figure 5 use equations 4 and 5 to calculate Va and Vb? Or are these the measured Va and Vb from the images? Maybe the two different calculations could have different symbols. E.g. Va_image, Va_true Vb_image, Vb_true so the reader knows which method is used.
What about the water temperature? Was this measured at the location of the study? It looks like the majority of melt was coming from under the ice, when looking at the last four sample temperature profiles of the ice in Figure 4. Additionally, the first two samples shown in Fig 4 I would argue are collected during the melting phase, the ice thickness seems to decrease and the ice temperature is very close to 0 degC. This changes a lot of the result section whenever the freezing phase is mentioned as the current analysis does not include these samples.
Minor
Abstract could include a sentence outlining the experiment approach… e.g. in situ experiments conducted on a brackish lake investigated the gas and brine volume change in the lake ice.
L21 multiphase of ice refers to solid liquid gas phases, not the impurities. This could be “Sea ice is a mulit-component system …” Then referring to brine, air and solid ice. This correction needs continuing in the following sentence as well.
L23- proportions of these components vary depending on the conditions of the ice, I recommend replacing formations, freezing, melting phase with “ice age, atmospheric and ocean conditions when forming, dynamic history, thermodynamic conditions”
L26 I thought because of the brine the author was talking about sea ice but this reference to subglacial water is confusing. I would also rather refer to the snowcover rather than the atmosphere because sea ice without snow above is quite uncommon.
L29- Does “Natural ice” still refer to sea ice? Please specify if so why the author is now comparing to non-natural ice.
L31 Add an explanation of “effective segregation coefficient”
L32- “related to many factors” can the author provide some examples?
L33 What does it mean when the author refers to the “solution” is this referring to ocean water here or brine? Please clarify
L33 Here “ice temperature changes” could be warming or cooling. This quickly jumps to melting conditions before these two are addressed.
L34 should this be gas-“pressure” equilibrium and brine-“phase” equilibrium?
L35 Please provide reference for the sentence “voids form due to the partial evaporation of ice or brine during internal melting.”
L40 Please give details on the “latest mushy layer theory”
L41 Define Vb here
L43-45 How is the seasonal variability of surface scattering layer relevant to this study? This seems to jump a lot.
L46 Wasn’t the morphology of ice inclusions already discussed? Why “another. The introduction seems to be a bit dis-ordered.
L49 What does “their” refer to? Gas or brine? This paragraph jumps between talking about gas and brine. To make it easier for the reader maybe this could be clearly divided into two paragraphs
Paragraph 53, same here, is the author talking about gas or brine when referring to “inclusions?”
L56 “Due to the lack of seasonal variations in ice inclusions, it remains challenging to precisely obtain variations in ice physical properties.” Lack of what? Measurements? Data? Observations? There are a lot of variations in ice properties!
L58 “response to varying circumstances” what does this mean? Varying conditions of the ice e.g. temperature or something else?
L58 “for the first time.” Tomography is a form of imaging so I wouldn’t say this is true. See :
- Lieb-Lappen, R.M., Golden, E.J. and Obbard, R.W., 2017. Metrics for interpreting the microstructure of sea ice using X-ray micro-computed tomography. Cold Regions Science and Technology, 138, pp.24-35.
- Maus, S., Schneebeli, M. and Wiegmann, A., 2021. An X-ray micro-tomographic study of the pore space, permeability and percolation threshold of young sea ice. The Cryosphere, 15(8), pp.4047-4072.
L93 What is the cold antifreeze liquid? Can the author reference other studies using the same liquid?
L121 Va and Vb are not defined
L125 what are the functions F1 and F2?
Section 2.3.2: Can the author create a multi-image figure showing the image processing steps of applying a gaussian filter, segmentation and categorisation etc.
L151 why were the batch-segmented inclusions larger than the manually segmented inclusions?
L169, why not use area of the bubble/inclusion rather than the diameter or length?
L230 move the definitions of Va and Vb to when then are initially mentioned (L121)
L 243 “becomes brine.” Could be re-worded to increases brine volume. The water is reducing the brine concentration, and reducing the brine density. The gas bubbles expanding is also an effect of the increase in temperature. If the brine is removed from the system, the gas bubbles would still expand.Can you explain a bit more why these are linked? This also shows in your Va and Vb plots, they don’t seem to be correlated.
L307 In figure 7 as the ice melts, the bottom brine pocket size aligns with the middle layer a lot more. Is this because the measured bottom layer has melted away and you are now measuring the middle layer from the pervious core? Could this influence the discussion?
L308 what is speeds referring to here?
L385 speed is also referred to here, maybe a typo of size?
Section 4.2 I generally enjoyed this section, could you add details on the salinities of the difference studies? This might help with explaining the influence of a study in brackish water compared to sea water.
L533 and the temperature was a lot higher
Missing references:
Carte, A. E. (1961), Air bubbles in ice, Proc. Phys. Soc., 77, 757–768.
Dadic, R., Light, B. and Warren, S.G., 2010. Migration of air bubbles in ice under a temperature gradient, with application to “Snowball Earth”. Journal of Geophysical Research: Atmospheres, 115(D18).
Jones, S. J., and G. P. Johari (1977), Effect of hydrostatic pressure on air bubbles in ice, in Isotopes and Impurities in Snow and Ice, IAHS Redbooks, vol. 118, pp. 23–28, IAHS, Gentbrugge, Belgium.
Maeno, N. (1967), Air bubble formation in ice crystals, in Physics of Snow and Ice, Proceedings of the International Conference on Low Temperature Science, Hokkaido Univ., Sapporo, edited by H. Oura, pp. 207–218, Bunyeido, Sapporo, Japan.
Shreve, R. L. (1967), Migration of bubbles, vapor figures, and brine pockets in ice under a temperature gradient, J. Geophys. Res., 72(16), 4093–4100, doi:10.1029/JZ072i016p04093.
Citation: https://doi.org/10.5194/egusphere-2024-2155-RC2
Status: closed
-
RC1: 'Comment on egusphere-2024-2155', Anonymous Referee #1, 23 Sep 2024
This manuscript describes a study that was carried out to assess the variability of brine and gas inclusions within saline ice.
The methods and results of the study are described thoroughly.
The study sampled an ample number of brine, gas inclusions to get satisfying statistics on the population of individual inclusions. There was not however ample sampling carried out to achieve significant statistics on the spatial variability of the microstructure itself, specifically this study provides no information on the cm – m - decimeter scale variability in an ice cover.
The text is not very concise, but rather verbose, with low information content. Particularly in Section 4.
There really are no substantial conclusions. There may be a few new insights, but I am not seeing any well composed conclusions or key points that describe new insights into microstructural changes occurring during ice growth and/or decay.
Minor:
21: “ice” is frozen water, it becomes a multiphase material consisting of ice crystals, gas bubbles, and impurities when discussed in the context of (in this case) the frozen surface of a water body
27: “subglacial”, use of this word implies the authors are addressing ice as found in a glacier?
30-31: “The content of newly formed brine pockets in ice can be quantified by an effective segregation coefficient and the salinity of the underlying water.” As I read this statement, it implies there is a relationship between the content of newly formed brine pockets (i.e., the brine salinity) and the salinity of the ocean. In fact, the relationship cited by Cox and Weeks (1988) defines a relationship between the salinity of newly formed sea ice and the salinity of the ocean. Those are not the same things.
35-36: “For example, voids form due to the partial evaporation of ice or brine during internal melting.” Are the authors describing the formation of Tyndall figures in this statement? It’s not clear what this is referring to. I believe the bubbles referred to as active bubbles are gas bubbles that form within brine inclusions when the ice temperature is increased.
38: It would be more accurate to say “freezing equilibrium relationships in the water-salt system” than “ice phase diagrams”. An ice phase diagram would refer to the different phases of ice as a function of temperature and pressure.
41: Define Vb
57-58: “This inevitability introduces inaccuracies into ice models in response to varying circumstances.” This overstates the problem, as I am aware of no models that even attempt to treat the details of sea ice microstructure at a level where seasonal variations in microstructure would even be considered.
64: If this study was carried out for a water body with salinity 5 – 7 ppt, it would be important to describe how this differs from sea ice grown from water with salinity generally 30 – 32 ppt. This is especially in light of the critical threshold of 24.7 ppt, below which the temperature of maximum density exceeds the freezing temperature. The formation of sea ice in the open ocean generally occurs under conditions where the temperature of maximum density is equivalent to the freezing temperature.
364: “However, estimating the variation in Va remains challenging due to a lack of information on its influencing factors.” I am not clear what this means, or why it is written.
Figure 10 (and associated text): Is the point of this figure to show that inclusion (presumably brine inclusion?) sizes did not change in response to changes in temperature? If so, then I assert that the inclusions that were measured where not isolated and in freezing equilibrium, or it is possible that only the long dimension of inclusions was measured, and that dimension showed little sensitivity. The total volume of isolated (not connected, not drained, surrounded by ice) brine inclusions should show obvious size change as a result of change in ambient temperature (between -10, -15, 20 C), even in the lab. This fact appears to not be consistent with the statement made in lines 445-446.
473: A power law could also describe the opposite, with numbers decreasing with decreasing size.
473-474: It’s not clear what is meant by “…the minimum number of bubbles was small”
476: infinite? No, there can be (lower and upper) limits on the size.
482: This ice is not warmer than studies from melting ice.
486-487: “Therefore, it could be concluded that the methods used for classifying small inclusions in different works do not considerably affect the overall statistical results.” It could also simply be that the cm / m / decimeter scale has significantly larger variability than what was observed here.
495: “…significant increase in Va of the surface layer during the melting phase.” Is this a reference to the well documented process of brine drainage? See Niedrauer and Martin 1979 https://doi.org/10.1029/JC084iC03p01176
506-507: “These bubbles partly accumulate in the middle layer as a result of their buoyancy, while others escape from the ice bottom.” Please supply a reference for these processes.
559 – 560: “…newly formed bubbles in the middle layer were partly thermally driven.” I am not clear what this means. Please rewrite for clarity.
561 – 562: I think this is describing a well-established brine drainage process.
564-565: “The changes in the brine pocket size during the freezing phase were not as notable as those during the
melting phase.” I suspect this is due to merging and draining processes, and those processes are well documented.
570: what “other mechanisms”?
Citation: https://doi.org/10.5194/egusphere-2024-2155-RC1 -
RC2: 'Comment on egusphere-2024-2155', Anonymous Referee #2, 04 Nov 2024
This study investigated the evolution of brine and gas inclusions of ice forming and melting in a brackish lake. The introduction could be substantially restructured to better situate this study in its appropriate context, which would help readers grasp the relevance and applicability of the findings and understand the specific scientific questions being addressed For instance, the section comparing other observations could serve as a useful background in the introduction. Additionally, the methods could be clarified, as it is currently challenging to follow. Specifically, two different methods were used to measure the volume fraction of gas bubbles (Va) and brine pocket volume fraction (Vb): one based on imaging and another using temperature functions. However, these methods were not compared in a sufficiently clear and transparent manner. There was no reference to the water temperature. The results are logical and outlined clearly and I followed the author’s evaluation but unfortunately, I don’t see any clear, novel conclusions from this work.
A few references are missing, see details below. The manuscript is well structured. There is no supplementary material.
Major
Figure 2 seems to identify a very circular object (3) as a brine pocket. The calculations are challenged by this. Could the author provide the circularity of these examples given in Figure 2? In addition, could this method be tested in a few samples by using tomography? Has this been done in the literature? In addition, the gas bubble (1) is out of focus and the focus needs adjusting to be able to get the true size of this bubble, maybe choosing another example image would be better.
The author applies this study’s introduction to sea ice but the ice studies formed in brackish water. A large section of the introduction emphasises the conditions of the water that the ice forms in determining the brine and gas inclusions. The brackish water was mentioned at being 5–7‰ (5-7 ppt) this is significantly lower than general sea ice conditions. I suggest the introduction could be adapted to a more relevant applications for this study of ice forming in certain regions with brackish water. A good example of this is the introduction of 4.3, this would be great in the introduction.
On Line 163 the author states Va derived from the images was greater than the real values. Is the author referring to the real values from the calculations in equation 4? If the Va calculated from the images isn’t used (line 164), then analysing why these two methods differ is a critical part of this paper and I recommend including this explanation and making it clearer that the Va calculated using the imaging method isn’t used in this study. If feasible two figures showing the comparison of Va calculations from the two methods, and the same with Vb. I then get confused which methods is used for the rest of the paper, e.g. does Figure 5 use equations 4 and 5 to calculate Va and Vb? Or are these the measured Va and Vb from the images? Maybe the two different calculations could have different symbols. E.g. Va_image, Va_true Vb_image, Vb_true so the reader knows which method is used.
What about the water temperature? Was this measured at the location of the study? It looks like the majority of melt was coming from under the ice, when looking at the last four sample temperature profiles of the ice in Figure 4. Additionally, the first two samples shown in Fig 4 I would argue are collected during the melting phase, the ice thickness seems to decrease and the ice temperature is very close to 0 degC. This changes a lot of the result section whenever the freezing phase is mentioned as the current analysis does not include these samples.
Minor
Abstract could include a sentence outlining the experiment approach… e.g. in situ experiments conducted on a brackish lake investigated the gas and brine volume change in the lake ice.
L21 multiphase of ice refers to solid liquid gas phases, not the impurities. This could be “Sea ice is a mulit-component system …” Then referring to brine, air and solid ice. This correction needs continuing in the following sentence as well.
L23- proportions of these components vary depending on the conditions of the ice, I recommend replacing formations, freezing, melting phase with “ice age, atmospheric and ocean conditions when forming, dynamic history, thermodynamic conditions”
L26 I thought because of the brine the author was talking about sea ice but this reference to subglacial water is confusing. I would also rather refer to the snowcover rather than the atmosphere because sea ice without snow above is quite uncommon.
L29- Does “Natural ice” still refer to sea ice? Please specify if so why the author is now comparing to non-natural ice.
L31 Add an explanation of “effective segregation coefficient”
L32- “related to many factors” can the author provide some examples?
L33 What does it mean when the author refers to the “solution” is this referring to ocean water here or brine? Please clarify
L33 Here “ice temperature changes” could be warming or cooling. This quickly jumps to melting conditions before these two are addressed.
L34 should this be gas-“pressure” equilibrium and brine-“phase” equilibrium?
L35 Please provide reference for the sentence “voids form due to the partial evaporation of ice or brine during internal melting.”
L40 Please give details on the “latest mushy layer theory”
L41 Define Vb here
L43-45 How is the seasonal variability of surface scattering layer relevant to this study? This seems to jump a lot.
L46 Wasn’t the morphology of ice inclusions already discussed? Why “another. The introduction seems to be a bit dis-ordered.
L49 What does “their” refer to? Gas or brine? This paragraph jumps between talking about gas and brine. To make it easier for the reader maybe this could be clearly divided into two paragraphs
Paragraph 53, same here, is the author talking about gas or brine when referring to “inclusions?”
L56 “Due to the lack of seasonal variations in ice inclusions, it remains challenging to precisely obtain variations in ice physical properties.” Lack of what? Measurements? Data? Observations? There are a lot of variations in ice properties!
L58 “response to varying circumstances” what does this mean? Varying conditions of the ice e.g. temperature or something else?
L58 “for the first time.” Tomography is a form of imaging so I wouldn’t say this is true. See :
- Lieb-Lappen, R.M., Golden, E.J. and Obbard, R.W., 2017. Metrics for interpreting the microstructure of sea ice using X-ray micro-computed tomography. Cold Regions Science and Technology, 138, pp.24-35.
- Maus, S., Schneebeli, M. and Wiegmann, A., 2021. An X-ray micro-tomographic study of the pore space, permeability and percolation threshold of young sea ice. The Cryosphere, 15(8), pp.4047-4072.
L93 What is the cold antifreeze liquid? Can the author reference other studies using the same liquid?
L121 Va and Vb are not defined
L125 what are the functions F1 and F2?
Section 2.3.2: Can the author create a multi-image figure showing the image processing steps of applying a gaussian filter, segmentation and categorisation etc.
L151 why were the batch-segmented inclusions larger than the manually segmented inclusions?
L169, why not use area of the bubble/inclusion rather than the diameter or length?
L230 move the definitions of Va and Vb to when then are initially mentioned (L121)
L 243 “becomes brine.” Could be re-worded to increases brine volume. The water is reducing the brine concentration, and reducing the brine density. The gas bubbles expanding is also an effect of the increase in temperature. If the brine is removed from the system, the gas bubbles would still expand.Can you explain a bit more why these are linked? This also shows in your Va and Vb plots, they don’t seem to be correlated.
L307 In figure 7 as the ice melts, the bottom brine pocket size aligns with the middle layer a lot more. Is this because the measured bottom layer has melted away and you are now measuring the middle layer from the pervious core? Could this influence the discussion?
L308 what is speeds referring to here?
L385 speed is also referred to here, maybe a typo of size?
Section 4.2 I generally enjoyed this section, could you add details on the salinities of the difference studies? This might help with explaining the influence of a study in brackish water compared to sea water.
L533 and the temperature was a lot higher
Missing references:
Carte, A. E. (1961), Air bubbles in ice, Proc. Phys. Soc., 77, 757–768.
Dadic, R., Light, B. and Warren, S.G., 2010. Migration of air bubbles in ice under a temperature gradient, with application to “Snowball Earth”. Journal of Geophysical Research: Atmospheres, 115(D18).
Jones, S. J., and G. P. Johari (1977), Effect of hydrostatic pressure on air bubbles in ice, in Isotopes and Impurities in Snow and Ice, IAHS Redbooks, vol. 118, pp. 23–28, IAHS, Gentbrugge, Belgium.
Maeno, N. (1967), Air bubble formation in ice crystals, in Physics of Snow and Ice, Proceedings of the International Conference on Low Temperature Science, Hokkaido Univ., Sapporo, edited by H. Oura, pp. 207–218, Bunyeido, Sapporo, Japan.
Shreve, R. L. (1967), Migration of bubbles, vapor figures, and brine pockets in ice under a temperature gradient, J. Geophys. Res., 72(16), 4093–4100, doi:10.1029/JZ072i016p04093.
Citation: https://doi.org/10.5194/egusphere-2024-2155-RC2
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