the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Thermal Conductivity of Snow on Arctic Sea Ice
Henning Löwe
Lucille Gimenes
David N. Wagner
Ruzica Dadic
Rafael Ottersberg
Stefan Hämmerle
Martin Schneebeli
Abstract. Snow significantly impacts the seasonal growth of Arctic sea ice due to its thermally insulating properties. Various measurements and parametrizations of thermal properties exist, but an assessment of the entire seasonal evolution of thermal conductivity and snow resistance is hitherto lacking. Using the comprehensive snow data set from the MOSAiC expedition, we have evaluated for the first time the seasonal evolution of the snow's thermal conductivity and thermal resistance on different ice ages (leads, first and second-year ice) and topographic features (ridges). Combining different measurement parametrizations and assessing the robustness against spatial variability, we infer and quantify a hitherto undocumented feature in the seasonal dynamics of snow on sea ice. We observe an increase in thermal conductivity up to March and a decrease thereafter, both on first-year and second-year ice before the melt period started. Since a similar non-monotonic behaviour is extracted for the snow depth, the thermal resistance of snow on level sea ice remains approximately constant with a value of 515 ± 404 m2 K W−1 on first-year ice and 660 ± 475m2 K W−1 on second-year ice. We found approximately three times higher thermal resistance on ridges (1411 ± 910 m2 K W−1). Our findings are that the micropenetrometer-derived thermal conductivities give accurate values, and confirm that spatial variability of the snow cover is vertically and horizontally large. The implications of our findings for Arctic sea ice are discussed.
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Amy R. Macfarlane et al.
Status: final response (author comments only)
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RC1: 'Comment on egusphere-2023-83', Anonymous Referee #1, 16 Feb 2023
General comments
The paper provides a dataset of effective thermal conductivity of snow on sea ice from tomographic images as well as from SnowMicroPen measurements. Data from the tomographic images are used to study the anisotropy of the thermal conductivity and assess existing parameterizations based on density. A new fitted regression is suggested. Data from the SMP measurements are used to study how thermal conductivity evolves with time and how it varies for 4 situations: snow lying on first year ice, on second year ice, on leads and snow on ridges. Associated variability in snow height and snow density are also presented and used to provide possible explanations for thermal conductivity variations.
The presented study will be largely beneficial for the snow and ice community as it provides a key dataset for the energy balance of sea ice. The dataset, involving in situ microCT, is unique. An impressive amount of field work and data analysis was provided and should be acknowledge. The idea to use SMP measurements to access more data and investigate spatial and temporal variations is new and seems well-suited.
However, the paper does not meet scientific standards in terms of data description and analysis. Some data lack thorough description or seem to be interpreted only half-way. Some statements are unclear or lack quantitative support. Additional work will be required to rigorously address the topic and provide a comprehensive presentation. I strongly encourage the authors to improve the paper as the topic can make for an important publication.
The major issues regard
- FEM computations of effective thermal conductivity
- It is unclear how the effective thermal conductivity was computed from the 3D images (see specific comment below) and which value of thermal conductivity is plotted in the different figures. Especially, in Figure 2, I believe it is the z-component of the thermal conductivity that is plotted, unlike what is mentioned. This point impacts the interpretation of the figure.
- Little information is provided on the relationship between thermal conductivity and microstructure. It is restricted to density although the authors have data of correlation length and geometrical anisotropy but they are not presented.
- The new dataset needs to be compared to existing datasets for snow on sea ice. The comparisons done with the Yen, Sturm and Calonne parameterizations are relevant, but in a first step it is indispensable to compare with the available data of thermal conductivity of snow on sea ice.
- parameterizations of thermal conductivity
- The equations of the tested parameterizations, their domain of validity (density range) and information about how they were obtained (measurements, simulations) are lacking.
- The evaluation of the parameterizations lacks scientific rigor and is only qualitative (e.g. performances described only by “work well” (line 232)). The comparisons should be supported by statistical scores. Performance scores for low/high density and low/high anisotropy should be provided if discussed. The authors recommend using Equation (3) for snow on sea ice but arguments are elusive. The authors should review their statistical measure they use. R2values are insufficient for the conclusion they make.
- The description of the proposed parameterization with anisotropy is incomplete and its purpose is unclear. First, the complete set of equations should be provided including the term k(L) from Löwe et al. 2013 as well as the values for the involved parameters Ω, β, k0. There are two components kz and kx described in Equation (2) of Löwe et al. 2013 and it is not mentioned which one is used. With this complete description, it is still unclear how this parameterization with anisotropy can be applied to other density datasets to derive the thermal conductivity. The benefit for the paper and the general profit are unclear.
- the introduction, which lacks a comprehensive description of the state of the art. Some relevant studies are provided in the introduction but it needs reorganization and completion, so the picture of the state of the art and the current limitations become clear. The reader should know which measurements were done on the thermal conductivity for snow on sea ice, which tools were used, and what range of values was found. To give an example, Sturm et al. 2002 “Thermal conductivity and heat transfer through the snow on the ice of the Beaufort Sea” appears but there is no description. This comment also refers to the parameterizations and the modeling – how is currently model snow on sea ice heat transfer? In the current state, the introduction mixes studies for ice, snow and snow on ice, which is confusing.
Specific comments
27: It could be helpful to include one sentence of the main characteristics of snow on sea ice. This way the reader can follow when the importance of the different heat transport processes are discussed.
28 “3/ vapour diffusion between the snow grains” → do you refer to phase change?
34 ”X-ray micro-computed tomography (microCT) has enabled snow research to advance by measuring the exact ice skeleton without damaging it (Riche and Schneebeli, 2010)” → this reference is not the paper introducing CT on snow.
39: “Density is currently used to parametrize thermal conductivity because it is a simple, low cost and quick measurement in the field” → no; first of all, it is because of the first order dependency between thermal conductivity and density.
51 “Spatial heterogeneity of the snow on sea ice requires a very high number of measurements, which can not only be realized by microCT.” → replace with “The study of spatial heterogeneity of the snow on sea ice requires a very high number of measurements, which can not only be realized by microCT.” Also, choose your wording between heterogeneity or variability, throughout the paper.
62: “We up-scaled individual microCT” and throughout the paper → it is unclear what up-scaling refers to.
91: the cylindrical drill was operated by hand or was an electric drill used?
151: The interest of computing thermal resistance R, compared to solely thermal conductivty, should be mentioned here.
Figure 2: It is unclear why snow samples with vertical anisotropy show higher values of keffFEM and inversely for horizontal anisotropy. Is keffFEM the average of keff(x), keff(y) and keff(z), with keff(x) the effective thermal conductivity computed under a heat flux in the x-direction and so on for y and z? This needs to be clearly defined in Section 2.2.1.
Figure 2: a zoom for the 0 – 300 density range would be helpful to read the data.
107 : « The thermal conductivity of the micro-CT sub-samples … were compared ... as seen in Fig2.. » Figure 2 should be placed in Section 3.1 where it is actually described.
159 SWE is not defined
161 « Due to a reduction of density... » → rewrite the sentence
175 : It would be informative to describe which type of snow has low Ak values and high values (depth hoar?), if possible. To my knowledge, there has been little report of Ak values as low as 0.25 in the past, so it would be interesting to know what kind of snow it is.
In addition, the range of values of the geometrical anisotropy should be provided here, so the link between both anisotropy ratios can be done.
Legend of Figure 3 : description of the bar plots of color yellow and green is missing.
Section 3.1. Overall, the link between the thermal conductivity and snow microstructure could be better addressed. An idea could be to provide a CT image of a typical stratigraphy of snow on sea ice together with vertical profiles of density, correlation length, Ag, thermal conductivity, and Ak.
185: remove parenthesis
Legend Figure 4. Check the structure of the sentence.
187: “Without including anisotropy in the parameterization, kMac(I) eff is the best representation of keff, as it has the highest r2 value compared to this dataset”. Only commenting on the performance of the regression that was fitted to the dataset is weak in terms of finding – it was not necessary to compare with other (independent) parameterizations to come to this conclusion. To allow for fair comparisons, the validity range for the regression of Yen and Sturm, which have an upper density limit, should be provided.
Section 3.3: provide a general description of Figure 5 before giving detailed comments.
188: “We use this parametrization and introduce the SMP to upscale our measurements of keff , of which we do not have corresponding Ak or Ag measurements”. Is the second part of the sentence necessary? I don’t understand the link with Ak and Ag here.
190 to 194: This paragraph could be placed in Section 3.3, as it is about using SMP and harmonic means to explore spatial and temporal variability and not about comparing parameterizations.
Figure 5: The legend needs to be reviewed (repetitions, incorrect wording). The meaning of the grey box and of the grey stars are missing.
197: As a general comment, the paper is lacking descriptions of figures or tables. For example, it is too not sufficient to write “Table 1 gives the median and standard deviation of each.” without any supporting comment. A short sentence as “On average more snow is found on Ridges with HS = 335 mm and less on Leads with 84 mm” is very helpful for the reader.
Section 3.3 (related to the previous comment). The writing of this section should be improved. The description of the figures should include more quantitative descriptions. No value is provided in the entire section. For example, line 196 – 199: snow height trends are described using “increase” / “decrease” / “highly variable” / “high spatial heterogeneity” without providing supporting values.
199 “Leads and ridges show consistently high spatial heterogeneity” → Is it shown on Figure 5?
Figure 6. Provide a comprehensive description of the figure. Increase the figure resolution as the text (n=, M =) is difficult to read on a printed copy of the paper. Some sentences of the legend are actually figure analysis and should be placed in the text.
208 “keff has a slightly lower median on FYI and SYI, compared to leads and ridges with a higher keff”. The first comment should rather be that values of harmonical mean of keff for each site are very close to each other. The grouping FYI-SYI and leads-ridges is not clear.
The temporal increase in density and keff is rather until between February and March depending on the site (Fig 5).
217 “When using these parametrizations to investigate the heterogeneity of the snow cover, the microCT was not an ideal method for obtaining a representative sampling of the snow cover due to the time required for one measurement” → suggestion: To investigate the spatial variability of the snow cover, the microCT is not an ideal method due to the time required for one measurement
229 “A snow sub-sample with a density of 400 kg m−3 can have a thermal conductivity value ranging from 0.2 W K−1m−1 to 0.6 W K−1m−1 if the snow is isotropic or anisotropic, respectively.” → This should read as “if the snow is isotropic or anisotropic in the vertical direction, respectively”. Anisotropy in the horizontal direction leads to even lower values, if the interpretation of this figure is correct.
Section 4.2: It could be interesting to discuss the possible impacts of the ice type and the topography on snow and so on the thermal conductivity. What was the initial motivation to study snow on different ice types, did you expect differences? (this could be included in the introduction).
Line 259 – 266: this paragraph is not about spatial variability as it is about comparing measured values with values used in models, so it appears out of subject here.
265: It is an open question what the influence of convection is, but we need to answer the question…” → in the introduction, it is mentioned that convection is reduced in wind slabs on sea ice. More context is required to understand why we refer to convection here.
292 “As snow undergoes metamorphism, we expect its thermal conductivity to increase as the density increases.” → Not all types of metamorphism involve a density increase; temperature gradient metamorphism can keep snow at about constant density. Explanation needs improvement.
293 “We now work to understand the process causing a reduction in density after March.” → provide order of magnitude of the reduction in density. Are we trying to understand a gap of 5 or 100 kg/m3?
298 “Fresh snowfall as input would lower the average density. A layer with low thermal conductivity kMac(I)eff leads to a drastic decrease in the average thermal conductivity. We can see in Wagner et al. (2022) that we had fresh snowfall during this period.” → Be more specific that “we had snowfall”. It could be mentioned that this is not seen in the snow height data in Figure 5, as there is no increase. Also, snowfalls are always fresh.
312 “Penetration of the hard density layers at the snow-ice interface became thinner due to sublimation” →not understandable.
318 “Crocus and SNOWPACK simulate lower layers with high density and high thermal conductivity, and surface layers with low values for both variables (Domine et al., 2019), whereas we have presented the opposite.” → It is not shown in the paper that you have opposite results. There is no clear trend in the vertical profile of thermal conductivity, as seen in Figure 1, and it is not described in the text. No density profiles are shown. So additional data / figure should be provided to support this comment or this paragraph should be deleted. Also, SNOWPACK and Crocus are not defined.
321 “Due to the combination of this seasonal trend in density and kMac(I)eff snow depths, we see no change of R” → wording
340 “It was found that a combination of fresh snowfall, high wind speeds causing erosion and re-deposition (initiating a SWE reduction during a storm event, as shown in Wagner et al. (2022)), vapour diffusion within the snow and changes at the snow-ice interface (further analysis of this interface is needed to draw concrete conclusions. However, this is not in the scope of this study), could all result in the density reduction across the snow profile.” → this sentence should be shortened.
Conclusion: The conclusion could be improved to provide a clearer picture of the main contributions / findings of the paper.
Citation: https://doi.org/10.5194/egusphere-2023-83-RC1 -
AC1: 'Reply on RC1', Amy Macfarlane, 24 Jun 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-83/egusphere-2023-83-AC1-supplement.pdf
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RC2: 'Comment on egusphere-2023-83', Anonymous Referee #2, 04 Apr 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-83/egusphere-2023-83-RC2-supplement.pdf
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AC2: 'Reply on RC2', Amy Macfarlane, 24 Jun 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-83/egusphere-2023-83-AC2-supplement.pdf
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AC2: 'Reply on RC2', Amy Macfarlane, 24 Jun 2023
Amy R. Macfarlane et al.
Amy R. Macfarlane et al.
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