General comments:

The study of Calonne et al. provides new estimates of effective coefficients of diffusion and permeability of polar firn from two low accumulation sites in Antarctica (DomeC and LockIn) and from various snow types based on pore-scale computations on X-CT-images of cm-sized samples. New regressions are proposed based on a rescaled porosity. The rescaled porosity is an easy-to-measure parameter and substitutes open porosity in former regressions with the implication that the new formula becomes applicable without assumptions/measurements of open porosity.

The study addresses a relevant scientific question within the scope of TC. It contributes to an improved modelling approach of air-transport in firn and relates directly to the interpretation and dating of ice core records. In my opinion the scientific methods are valid but not well outlined: for the modelling part I miss a comprehensible introduction how diffusion and permeability are actually solved on the three-dimensional lattice. For the CT-data part I could not find any discussion about the limited sample size (7x7x7mm3) and its implications on the estimates of diffusivity / permeability. In the text it was mentioned that the CP-estimates are affected by the limited size, the CI-estimates maybe not. Interestingly, the open porosity profile (Schwander 1989) shows a different behaviour than both, CP and CI estimates as well (figure 5). It would be worth to know the portion of pores cutted at the surfaces. I would suspect that the high (100-CP) values for high densities result from the large amount of cutted pores that are not counted as isolated pores but count for the total pore volume. On the other hand the CI (largest pore/total pore volume) tends to be underestimated at the percolation threshold in small samples because large pores become less frequent and might be not adequate presented in the sample. This would underestimate the transport properties at the percolation threshold (= closeoff area) as well. I would really appreciate a discussion of the pore-cut effect as it is not even mentioned at all. In respect to the conclusions I am wondering if the implications that both investigated sites show no significant differences in the transport property-density relationships can give further insides into the general properties of polar firn. However due to missing information (how much is the difference in accumulation between DomeC and LockIn?, what is the reason for the huge difference in Closeoff-depth of 10m although the sites are less than 150km apart?) /adequate figures I was not able to really assess if the similarity in transport properties between the sites are expected or not.

The abstract provides a concise summary, the presentation is well structured, the language fluent and precise. Number and quality of references are appropriate. A few minor points are listed below.

Minor points/suggestions:

line0:     I would prefer a different title like “Effective coefficient of diffusion and permeability of firn at DomeC and LockIn, Antarctica and various snow types– estimates over the 100-850kgm-3 density range

The present title is a little bit misleading because at DomeC and LockIn there is no 100 kgm-3 snow, even at surface the snow is already of the order of 300 kgm-3. The authors compiled measurements of DomeC/LockIn firn (550kgm-3 and denser, 23m-133m depth) and alpine/artifical snow (100kgm-3 to 550 kgm-3).

Line 1:   ..,the entire ice sheet column… -> (change to) ...the entire firn column of polar ice sheets…

Line 10: …with density over the firn density range…snow data.  -> ..with density by extending the data set with data from alpine and artificial snow.

Line 23: …to thousand of years…               -> …to hundreds of years… (the air in the open pores is not too old, it is the age-difference between air and ice that can be reach thousand of years…)

Lines 72,73: please provide some additional information about the DomeC, LockIn and Vostok site such as mean annual temperature and accumulation rate to better assess the differences in microstructure and transport properties between the cores.

Line 79  : explain the term: “representative elementary volume”. In what respect is the volume “representative”?

Lines 84,85,86: a few more sentences about how the diffusion coefficients and permeabilities are estimated would be helpful to understand the approach solved by software Geodict.

Line 105: …CI is 100% when the porosity is fully open and 0% when pores are closed… Comment: CI defined as the ratio between the largest pore and the total pore volume can not be 0% per definition. It tends to 1/bubble-number if all pores are closed and approximately of equal volume.

Line 133:  maybe you can add an additional sentence about the CI and CP behaviour at 85m depth: here CI is 75% whereas CP is close to 0%. -> possible interpretation: pore-cut effect(?): pores cutted at the surface loose (artificially) the connection to the open pore space within the volume.

Lines 146,147: …,indicating than even after the close-off, open pores are still present, even down to 133 m depth, which … This is a misleading sentence: I would rather think that the <100% of CP below the close-off depths are caused by the amount of cutting pores that are not counted as isolated pores – again a pore-cut effect.

Figures 2, 3: What is the size of the “T” symbols in Figures 2,3 telling us? Is it the std of a set of measurements? How many measurements/ or estimates are averaged?

Lines 278,283: …For firn (550-917kgm-3)… -> For firn (550-850kgm-3)…Samples with density in the range between 850 kgm-3 and 917kgm-3 are referred to as bubbly ice (with isolated bubbles).

The manuscript presents an improved method for defining transport properties in snow and firn through the examination of microstructural parameters derived from micro CT results and numerically derived values of permeability and diffusivity. The authors propose a simple yet elegant concept of rescaled porosity which accounts for the effects of pore closure on transport values in denser/deeper firn. This approach has promise to improve prediction in firn over previous methods using open porosity of the firn. The fact that the approach improves regression models over a wide range of density values at different polar locations with different conditions also suggests the method is a promising step in developing a generalized snow permeability and diffusivity model. 

There are some mostly minor technical edits that should be addressed that are listed by line number below. In addition, I have included suggestions to clarify some of the labeling and description of the figures,  

Abstract: As written, it is not clear what was done as part of this research and what was past work (need to make the tense of the sentences consistent throughout).

I.e., on line 1, “To this end, different regressions were proposed to estimate the effective coefficient of diffusion and permeability of firn.” When I read this, I get the sense that this is part of the work that is being presented. I think it could be written as (just a suggestion), “To this end, different regressions have been proposed in the past to estimate the effective coefficient of diffusion and permeability of firn,”

Line 3 (and example of shifting tense): “were little evaluated as data of these properties are scarce”

could be written, “have not been evaluated very often as data of these properties are scarce”

Line 10: “by including snow data.” What snow data does this refer to? The micro-CT data? Or are you referring to surface snow vs. firn at depth?

Line 11: “Classical analytical models and regressions from literature are evaluated.” Evaluated compared to what?

Line 15 “with φoff the close-off porosity.” Should be “with φoff equal to the close-off porosity.” Or something similar since with “φoff the close-off porosity” is not a complete phrase.

Line 20: Air entrapped in the closed pores of ice preserved past atmospheric air, from couple of thousands to few millions of years old, providing invaluable data on past Earth’s environment.

Couple of suggestions: “preserved” should be “is preserved” or “preserves”

“from couple of thousands to few millions of years” should be “on the order of a few thousand years to a few million years old” or “thousands to millions of years old”

Line 23: “Among others challenges” should be “Among other challenges”

Line 29: “til” should be “until”

Line 48: “Only few parameterizations are based on measurements or modeling over the entire firn column (Adolph and Albert, 2014), limiting their range of validity (Tab. 1).” is slightly confusing, suggest rewriting as “Few parameterizations are based on measurements or modeling…”

Line 49: “Especially, it is crucial to describe well air transport properties in the lock-in zone from the beginning of the pore closure to the close-off.” should be:

It is especially crucial to describe air transport properties well in the lock-in zone

Line 59: “plus few data of Vostok” should be “in addition to a few data from Vostok” It would be helpful to explain here what those data are, since it starts to get confusing in the results section and in Figure 1 about what data from Vostok were used. I.e., it seems like it was density, SSA, diffusivity and permeability from 80 m depth. Maybe it makes sense to say that, i.e., “in addition, density, SSA and diffusivity and permeability from 80 m depth from Vostok were used.”

Line 62: “allowing to assess the anisotropy of properties and compare lateral to vertical gas transport”

Line 63: “A variety of parameter to characterize firn microstructure was also estimated from images” should be “A variety of parameters to characterize…”

Line 75: til should be until

Line 76:  ”controlled conditions in cold-laboratory” should be “controlled conditions in a cold-laboratory” or r controlled conditions in the cold-laboratory

Line 106: “This index allows to describe more accurately the pore closure in firn and bubbly ice than the classical closedto-total porosity ratio, the latter being sensitive to the sample size (Burr et al., 2018).” Should be “This index allows the pore closure in firn and bubbly ice to be more accurately described than…”

Figure 1: The circles are hard to see in the figure for diffusivity and permeability because they show up as half circles in the figures and resemble the diamonds. Is there another symbol that can be used to make it clearer? Also, the square symbols are very hard to see. Could they be black instead of grey so that they show up better? I also cannot see the black diamond indicated the Vostok values for CP and CI, but again, this is unclear if this was calculated for the Vostok core. It’s also hard, but not impossible, to see the Vostok value indicated by the black diamond on the Density graph. Not sure if there is a way to make the black diamond more visible? Can it be layered on top of the other sites’ data points?

Last thing, it would be helpful if the two dashed lines that indicate the close-off depths were either listed in the legend (i.e., if the difference between the two shades of grey were designated), or if there was a label on the figure that indicated which dashed line designated the Dome C close-off depth and which line designates the Lock In close-off depth. If that makes the figure too cluttered, perhaps that can at least be specified in the figure legend.

Line 124: evolves should be evolve

Line 129: value should be values

Line 152: “Both figures show dimensionless permeability values, i.e. permeability values K divided by the equivalent sphere radius r = 3/(SSA × ρi) to the square.” I’m not sure what “to the square” refers to. Is it that the squares in the figure denote the dimensionless permeability? That could be written as “as designated by the squares in Figure 2.”

Figure 2: What do the T symbols pointing up or down indicate? Are the in different directions just so that they show up differentiated from one another when they overlap, or is there a physical significance? Also, should the rescaled porosity be defined earlier in the paper so that the inset in the figure is better defined? As it is, the definition doesn’t come for another couple pages.

Line 173: “Those extremes values” should be “extreme values”

Line 196: “a assemblage” should be “an assemblage”

Figure 4 caption: What do the dotted lines represent in the right-hand figures?

Table 1: This table is a very nice summary of the available relationships for permeability and diffusivity.

Line 225: “To provide a satisfactory estimates of diffusion coefficient” should be “To provide satisfactory estimates of diffusion coefficient”

Line 232: “Figure 5 allows comparing the computed data” should be “Figure 5 compares the computed data”

Line 245: “Permeability predicted by the regressions of Freitag 2002 and Adolph 2014 match overall well our data.” should be “Overall, permeability predicted by the regressions of Freitag 2002 and Adolph 2014 match our data well.”

Line 279: ” although their dataset originate” should be “although their datasets originate”