the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Mar 2026
Estimation of sea ice air-bubble and brine pocket distribution for scattering and emission model parametrization
Abstract. Scattering and absorption from air bubbles, voids, and brine pockets significantly affect radar and microwave radiometer measurements of sea ice and light propagation through sea ice. However, there are only a limited number of in situ measurements of the size of natural sea ice inclusion and its distribution. Here, we used a high-resolution data set of 90-mm wide and 1-mm thin ice slices of various types of Arctic sea ice to estimate the autocorrelation length and density of the inclusions. The data set was collected during the MOSAiC International Arctic Drift Expedition 2019–20 during the winter months of January and February 2020. Thin ice slices from new ice, first-year ice, level second-year ice, second-year hummocks, and a refrozen melt pond were collected and analyzed. The 50-percentile autocorrelation lengths derived (Lobs), a measure of the size and distribution of inclusions, for new ice and brine ice brine pockets of the first-year have mean values between 0.11 and 0.30 mm and a vertical anisotropy ratio (Lz) and horizontal (Lx) of 1.7–3.0 with respect to the ice surface. The exponential model was fitted to the observed autocorrelation function with a delay between 0–2 Lobs. The exponential correlation lengths derived (Lexp) correspond to the 50 percentile Lobs for the ordinary (horizontal) image samples (Lexpx) and the transposed (vertical) images (Lexpz). For new and first-year ice with varying salinity and brine pocket image density, the autocorrelation length is a very robust measure of the size and distribution of brine pockets. For new ice, we find a Lobsx or Lexpx of 0.18 mm and with a Lz / Lx anisotropy of 2 and for first-year ice, we find a Lobs or Lexp of 0.16 mm with a Lz / Lx anisotropy of 3. The samples from the hummock and the refrozen melt pond had 50 percentile Lobsx and Lobsz air bubble autocorrelation lengths varying in the range [0.22, 0.73] mm and [0.22, 0.74] mm and [0.17, 0.56] mm and [0.17, 0.79] mm, respectively. The very consistent Lobs for new and first-year ice can be used to constrain sea ice microwave emission and scattering models.
Competing interests: My co-authors John Yackel, Vishnu Nandan and Lars Kaleschke are members of “The Cryosphere” editorial board.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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RC1: 'Comment on egusphere-2026-1440', Anonymous Referee #1, 28 Apr 2026
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AC1: 'Reply on RC1', Rasmus Tage Tonboe, 15 Jun 2026
Dear Reviewer, thanks for the comprehensive review of the MS. The following is a point to point response to the comments. We have made a major revision of the MS, tuned image inclusion density to the brine and gas volume derived from the salinity, temperature and density as recommended. We have done a complete reprocessing of the data while the major conclusion remains intact.
When simulating sea ice microwave emission or backscatter using theoretical formulations for scattering e.g. the Born or the improved Born approximation, we need to be able to characterize the scattering inclusion (brine pockets or voids) distribution and size and shape in the ice. This is characterized by the auto-correlation length together with a specific distribution (e.g. exponential) and shape. Going through the literature on auto-correlation lengths it is clear that there are only very few data points and very few estimates of the auto-correlation length and inclusion distribution. We are following a methodology used earlier in deriving the autocorrelation length from thin-sections of ice e.g. F. Vallese and J. A. Kong, 1981. Correlation function studies for snow and ice. Journal of Applied Physics 52, 4921-4925, http://doi.org/10.1063/1.329453. Vallese and Kong analysed just a single section of lake ice near the ice-water interface. Therefore, we found it important to publish the dataset that we have collected consisting of 69 samples from different sea ice types. Those earlier important studies with estimates of the auto-correlation length are compared with our results. Other, more recent, studies are using micro-CT scans of ice samples which gives a 3D scan of the inclusions e.g. S. Maus, M. Schneebeli, and A. Wiegmann, A. 2021. An X-ray micro-tomographic study of the pore space, permeability and percolation threshold of young sea ice, The Cryosphere, 15, 4047–4072, https://doi.org/10.5194/tc-15-4047-2021. These studies provide a 3D-mapping at very high resolution of the sea ice inclusions for characterizing the anisotropic and complex-shape nature of inclusions. However, the samples used for CT-scans are in general too short (3.5 cm) for properly characterizing the auto-correlation length and distribution. The discussion of that constraint has been elaborated in the revised MS.
RC1: 'Comment on egusphere-2026-1440', Anonymous Referee #1, 28 Apr 2026
This study uses high-resolution images collected during the MOSAiC expedition to systematically quantify the autocorrelation length and anisotropy of inclusions in various sea-ice types, providing valuable observational constraints for parameterizing microwave scattering models. The following suggestions are offered to further strengthen the manuscript:
- At lines 120–122, an adaptive thresholding method is employed. Why was a more widely used algorithm, such as Otsu’s method or the watershed algorithm, not considered? Would the resulting L values differ?
Reply: The image samples have a high contrast between background and inclusions and the reason for selecting the adaptive threshold method is that we could test the change of threshold directly on the change of the classification and derived parameters (L, inclusion density…). The threshold has been tuned in the revision to the image inclusion density and the derived brine and gas volume from the average first-year ice salinity, temperature, and density. We tested different thresholds and found that the change of threshold had an impact on the derived image inclusion density, but the auto-correlation length was robust to the threshold change. This robustness was a goal in itself so that the derived parameters would not depend on the image classification. The image analysis yields the components of the auto-correlation length (Lx, Lz) which is the focus of this study and the 3D dimensions of the brine pockets can be derived e.g. using micro CT 3D. The Otsu method was tested and yielded much higher image inclusion densities. We use the adaptive threshold because the image samples have varying illumination and local contrast, and localized segmentation is needed. This has been clarified in the revised MS.
- Lines 114–116 clearly state that brine drained from the thin sections and the inclusions are now air‑filled, yet lines 32–35 emphasize that the large dielectric contrast between liquid brine and air strongly influences microwave scattering. How can geometric statistics of air‑filled pores represent the scattering properties of brine‑filled pockets in situ? Is it possible to estimate the original brine volume by combining the pore geometry, salinity, and in situ temperature?
Reply: Thanks for pointing this out. This was not clearly formulated in the MS and it has now been rephrased in the revision. The brine pockets (filled with brine) in the ice core drain during the processing of the thin sections in the lab so that the brine pockets in the thin sections are now filled with air. This is why we can clearly see the difference between the ice and the brine pockets in the images (the refractive index of brine and ice is almost the same and the refractive index of air and ice are very different.)
We do not think it is a good idea to relate salinity of the sample directly with the inclusion density (for first-year ice). First of all, we have too few data points (figure 11) and the points that we have do not show a clear tendency. The inclusion density and salinity relationship in first year ice also depends on the classification threshold and temperature (which is -15 C in the lab). Also, there may be some other geometric difficulties in characterizing the 3D volume of inclusions using the 2D thin slice data, where axial symmetry cannot be assumed.
Table 6: shows two samples (Jan 24.) of the same ice, one cut vertically and one cut horizontally. It is clear from the image of the horizontally cut sample that the brine pockets have an anisotropic shape. Depending on the cut direction you will get different estimates of inclusion densities. This horizontal anisotropy is, at least partly, responsible for the poor fit between inclusion density and salinity (temperature is at -15C) (as seen in figure 11).
- The authors note at lines 303–305 that their measured L^obs values are much smaller than those reported by Nghiem et al. (1995b) and state that this discrepancy cannot be explained. Could differences in ice age, thickness, season, and geographic location be examined to account for the offset?
Reply: We have revised that statement.
The correlation lengths reported in Nghiem are not actually data points but inferred from a radar scattering model sensitivity analysis (he is using the Born and not the improved Born approximation in the backscatter model which could partly explain the discrepancy). Anyway, model biases and the fact that other input parameters in the sensitivity study could be biased could explain the discrepancy. This was not clear from the MS and this has been clarified now in the revised version.
The ice age, for example, new ice and first-year ice have an impact on the anisotropy Lz/Lx of the auto-correlation lengths and the depth in the ice.
- Only the first‑year ice samples are identified as columnar ice (lines 179–180); no crystal‑type information is provided for the other ice types such as new ice. Temperature strongly affects brine‑pocket morphology, yet only the sampling background is described (lines 74–84) without reporting the in situ ice temperature. Could the different crystal fabrics and thermal histories affect the analysis of anisotropy?
It is possible that the thermal history from in ice temperature, to ambient temperature 5 - 25 degrees celsius below lab temperature and then the lab temperature at -15 C could have an impact on the auto-correlation length anisotropy. We processed the cores on the same day or on the next day after sampling to minimize recrystallization. Since these data were sampled in the field we could not control the temperature. We have now added a description of the thermal history in the procedure in the revised MS (Table 1).
- The image‑derived inclusion density is an areal fraction from two‑dimensional sections, whereas scattering models require a volumetric fraction. The manuscript does not discuss the stereological relationship between the 2D areal fraction and the 3D volume fraction. This issue should be addressed to enhance the dataset’s applicability for modeling.
Reply: We agree that this discussion was missing and we also believe that this is part of the reason that we do not find a close relationship between salinity and inclusion density (We do not have enough datapoints to establish a tendency).
However, after tuning the classification of the image inclusion density to the brine and gas volume derived from the salinity, density and temperature of first-year ice we have established a relationship between the large scale parameters (temperature, salinity and density) with the auto-correlation length of different ice types.
What we found during our analysis was that the auto-correlation lengths (and distribution) were quite similar for each type of sea ice (especially new-ice, first-year ice).
Citation: https://doi.org/10.5194/egusphere-2026-1440-AC1
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AC1: 'Reply on RC1', Rasmus Tage Tonboe, 15 Jun 2026
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RC2: 'Comment on egusphere-2026-1440', Sönke Maus, 30 Apr 2026
The authors present an analysis of the composition and microstructure of pores in sea ice from the MOSAiC expedition, based on vertical and horizontal thin section analysis of sea ice cores. Results are presented data for various ice types (new ice, first-year ice, level second-year ice, second-year hummocks, and a refrozen melt pond).
First, though the relevance of microstructure for sea ice remote sensing has been pointed out more than 3 decades ago, investigations of that kind are sparse, which is a considerable knowledge gap. Hence, the effort of the authors is to be applauded considering the amount of work that this has taken. However, there are serious issues related to the data quality, image analysis, and the destructive nature of the thin sectioning process, that limit the reliability of the results and their comparability to other data sets. At present it is not fully clear to me, if the results obtained from 2D thin sections alone can be used quantitatively as input to remote sensing algorithms. As described in this review there are many aspects that should be revised and the work needs a major revision to figure this out.
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AC2: 'Reply on RC2', Rasmus Tage Tonboe, 15 Jun 2026
Dear Sönke, thanks for the comprehensive review of the MS. The following is a point to point response to the comments. We have made a major revision of the MS, tuned image inclusion density to the brine and gas volume derived from the salinity, temperature and density as recommended. We have done a complete reprocessing of the data while the major conclusion remains unchanged.
When simulating sea ice microwave emission or backscatter using theoretical formulations for scattering e.g. the Born or the improved Born approximation, we need to be able to characterize the scattering inclusion (brine pockets or voids) distribution and size and shape in the ice. This is characterized by the auto-correlation length together with a specific distribution (e.g. exponential) and shape. Going through the literature on auto-correlation lengths it is clear that there are only very few data points and very few estimates of the auto-correlation length and inclusion distribution. We are following a methodology used earlier in deriving the autocorrelation length from thin-sections of ice e.g. F. Vallese and J. A. Kong, 1981. Correlation function studies for snow and ice. Journal of Applied Physics 52, 4921-4925, http://doi.org/10.1063/1.329453. Vallese and Kong analysed just a single section of lake ice near the ice-water interface. Therefore, we found it important to publish the dataset that we have collected consisting of 69 samples from different sea ice types. Those earlier important studies with estimates of the auto-correlation length are compared with our results. Other, more recent, studies are using micro-CT scans of ice samples which gives a 3D scan of the inclusions e.g. S. Maus, M. Schneebeli, and A. Wiegmann, A. 2021. An X-ray micro-tomographic study of the pore space, permeability and percolation threshold of young sea ice, The Cryosphere, 15, 4047–4072, https://doi.org/10.5194/tc-15-4047-2021. These studies provide a 3D-mapping at very high resolution of the sea ice inclusions for characterizing the anisotropic and complex-shape nature of inclusions. However, the samples used for CT-scans are in general too short (3.5 cm) for properly characterizing the auto-correlation length and distribution. The discussion of that constraint has been elaborated in the revised MS.
Review of egusphere-2026-1440
Reply: Thanks for the thorough review of the MS. Just to be clear, our reply responds to this review and not to the mails that you sent me after submitting the review.
I Summary and assessment
This is a review of the manuscript Estimation of sea ice air-bubble and brine pocket distribution for scattering and emission model parametrization by Rasmus T. Tonboe et al.
The authors present an analysis of the composition and microstructure of pores in sea
ice from the MOSAiC expedition, based on vertical and horizontal thin section analysis
of sea ice cores. Results are presented data for various ice types (new ice, first-year ice,
level second-year ice, second-year hummocks, and a refrozen melt pond).
First, though the relevance of microstructure for sea ice remote sensing has been
pointed out more than 3 decades ago, investigations of that kind are sparse, which is a
considerable knowledge gap. Hence, the effort of the authors is to be applauded considering
the amount of work that this has taken. However, there are serious issues related
to the data quality, image analysis, and the destructive nature of the thin sectioning process,
that limit the reliability of the results and their comparability to other data sets. At
present it is not fully clear to me, if the results obtained from 2D thin sections alone can
be used quantitatively as input to remote sensing algorithms. As described in this review
there are many aspects that should be revised and the work needs a major revision to
figure this out.
II Specific comments
General topics
- The introduction gives a good overview of the relevance of microstructure for remote
sensing of sea ice. However, the general reader would profit a lot from a table or heat
map that summarises the microstructural (inclusions lengths, number and aspect ratios)
and bulk properties (brine and air volume fractions, brine temperatures) and ranks them
in terms of their relevance for active and passive remote sensing (e.g. by +, ++, +++
etc.).
Our analysis, testing different image classification thresholds and image contrasts, found that the autocorrelation length was the most robust structural parameter and that the inclusion density was sensitive to classification threshold and when relating it to salinity, there were not enough data points for deriving tendencies. Furthermore, the analysis of the 2D slices did not characterize the volume of brine channels. These concerns about the inclusion density were expressed in the initial submission, but in the revised version this is clearly stated and we have chosen to focus on estimating the autocorrelation length. The conclusions where the autocorrelation length magnitude and aspect ratio can be categorized for different ice types is unchanged and this is in addition our recommendation for modellers to use specific autocorrelation lengths for different types of sea ice, following the logic in Nghiem et al. 1995b.
- On average, inclusion densities obtained by the authors in 2D thin sections should
correspond to the sum of 3D brine and air volume fractions.
While this may be true for first-year ice on average we do not have very few points to evaluate this. We have anyway made a tuning of the classification to match the average brine and gas volume derived from first-year ice salinity, temperature and density.
The authors find inclusion densities that, depending on ice type and location, range between 0.05 and 0.45. However, when checking the brine volume fractions for new ice and first year ice, where it can be computed from the ice salinity (and the temperature in the cold room), one obtains brine volume fractions that are much smaller. E.g., for young ice (Table 2) the inclusion densities (0.09-0.18) obtained by the authors are a factor of 2-3 larger than the nominal brine volume fractions (0.05-0.07 based on given ice salinities). In many samples this would imply air volume fractions of 0.1 or higher. Such air volume fractions of 0.1 are unlikely for young and first-year ice, for which 3D observations mostly show values in the range 0.005-0.02 and maximum of 0.04 (Crabeck et al., 2016; Maus et al., 2021; Salomon et al., 2021) and also high accuracy density data seldom show air volumes exceeding these ranges (Pustogvar and Kulyakhtin, 2016). Hence, considering other studies, the determined inclusion fractions appear to be a factor of two too large. While the authors try to explain this with brine drainage during sampling and processing - this should also have affected other studies, and due to the cold conditions under which many MOSAiC cores were taken, I would not expect that these samples should be outstanding in this respect. Also the density values tabulated by the authors (from FY ice and young ice) are not supporting such high air volume fractions.
Reply: First of all we are not trying to explain the mismatch between the salinity derived brine volume and the inclusion density with brine drainage during sampling and processing. We have clarified our argumentation in the revised MS to avoid that misunderstanding.
Anyway, thanks for the comment, the mismatch between the salinity derived brine volume and the inclusion density is a valid point. As pointed out to Reviewer 1, our 2D analysis seems to have limitations for characterising the volume. The brine channels are not geometric cylinders, and further, the brine channels are not always aligned perfectly along the vertical image axis. Brine channels have a complex “tree” structure which means that the channels cross the slices cut perfectly in the horizontal and vertical direction and it is therefore difficult to characterize the true extent of the channels. We expressed our skepticism to the inclusion density / brine volume relationship in our initial submission and we have further emphasised that in the revision.However, as stated in the previous comment we have now tuned the classification threshold for the image inclusion density to match the average brine and gas volume derived from its properties.
- The air volume based on the inclusion densities derived from thin sections should
be quantified in the table. This can be done by subtracting the brine volume based on
salinity (that also should be listed, when possible) from the inclusions density.
Also two explanations of these too high apparent air volumes should be better discussed:
- May non-destructive thin-sectioning lead to much higher inclusion density due to some
surface and melting effects?. I am not aware of studies that have clearly shown this.
Reply: We are not inferring that “non-destructive thin-sectioning” could lead to higher inclusion density due to surface and melting effects.
- In the freeboard one can expect larger air volume fractions, and the tabulated data appear
to show largest inclusion densities there. This difference between results for the ice
above and below freeboard should be outlined and quantified - highlighting the freeboard
data in images.
Reply: New- and first-year ice inclusions are filled with brine and gas and in second year ice the inclusions are filled with air. In the refrozen melt-pond the upper part of the core < 31 cm is dominated by air filled inclusions and the core > 31 cm is dominated by brine pockets. Those few samples where there are both air and brine inclusions (visual inspection) have been flagged (with *).
- I recommend a supervised segmentation to circumvent the problem of too large
inclusion density. As known from earlier work (Perovich and Gow, 1991, 1996, e.g.,) the
method of thin section analysis can hardly distinguish between air and brine inclusions.
Perovich and Gow (Perovich and Gow, 1991, 1996) thus approached the segmentation
problem as follows. For young and first-year ice they neglected the air volume and set
the segmentation threshold to that grey level at which the inclusion density matches the
theoretical brine volume based on salinity and temperature. When density measurements
are available, as for some MOSAiC data, one may set the threshold porosity to the brine
volume plus the air volume based on density.
Reply: Judging from visual inspections there are only a few cases where there are both air and brine inclusions in the samples. As explained above, these two types of inclusions are normally separated into different samples. We agree with you that making a classification where air and brine inclusions are separated can be difficult, most likely also very uncertain, and since it is only a few cases and it does not affect our conclusions since we have chosen just to flag those affected samples.
- Such a supervised segmentation, previous point 4., should give more reliable length
scales. The authors have argued that changes in the segmentation threshold in the ranges
tested have little effect on inclusion lengths, but they only describe a threshold change
that increases the inclusion density (Section 5.1 and Fig. 16). However, as the applied
segmentation seems to give too high inclusion density, this should be changed and the
effect on length scales determined.
Reply: We are estimating the vertical and horizontal components of the auto-correlation length (not inclusion lengths) which are relatively insensitive to the classification threshold. We think that the dataset that we have for tuning a classification is small but we have anyway made a tuning of the classification to match the image inclusion density of first-year ice with the brine and gas volume from its properties (see previous reply).
- The authors use the autocorrelation function to determine the pore length scales
in vertical and horizontal cross sections. This method is known to be robust to noise.
However, the autocorrelation method could also be applied to unsegmented grey level
images. If one invests the effort to segment images it is more suitable to employ other
pore size metrics of which several have been employed in earlier studies (Lieb-Lappen
et al., 2017; Maus et al., 2021; Salomon et al., 2021; Oggier and Eicken, 2022, e.g.,). I
rate it as unlikely that the pore anisotropy is properly retrieved via the autocorrelation
function when the grain orientation (c-axis, direction sub-grains or plates) changes within
the area for the autocorrelation (in that the latter contains several grains). There are
little studies of such details for sea ice, but the master thesis by Buettner (2011) does
clearly show this.
Reply: Thanks for the comment. I think that this is perhaps a topic for further studies, using 3D CT-scans. The objective here is to estimate the vertical and horizontal components of the auto-correlation length and distribution.
Specific comments
L 48-53. As under general topics, consider a table that states the different properties and
ranks them in terms of importance for microwave remote sensing.
Reply: The objective here is to estimate the vertical and horizontal components of the auto-correlation length and distribution. These parameters are affecting the microwave scattering and dielectrics together with temperature together with electromagnetic wavelength, incidence angle and if it is thermal microwave emission or backscatter. When looking at natural sea ice, snow cover may affect the importance of sea ice microstructure. It will have different importance for different applications e.g. sea ice concentration and snow depth mapping. We think that a simplified table will end up being misleading instead.
L 51-62. Consider to show a figure sketch where the different length scales are defined.
Reply: The length scales are shown in Figure 2.
L 54-57. Can you discuss the question: What is better to have for microwave modelling
- the autocorrelation lengths or the exact inclusion size and aspect ratios?
Reply: The auto-correlation lengths are input to microwave scattering models together with the shape of the inclusions. This has been further clarified in the revised manuscript.
L 57-62. I would not give so many specific numbers here, but be more general, and
keep the numbers for the discussion.
Reply: Thanks, we have moved this to the discussion.
Fig. 3. More examples for the different ice types, and vertical versus horizontal cuts,
would be good to show here, that the reader gets a qualitative impression.
Reply: The truth is that there are not so many cases where there are both horizontal and vertical cuts of the same ice, we have provided two examples (new ice and first-year ice) but perhaps not enough for a quantitative understanding.
L115-116. we believe that the brine has drained during the processing of the FYI samples
and that the dark patches/ inclusions in the sample are now filled with air. –> This
has not been documented by e.g. Perovich and Gow (1996) and I rate it unlikely for
FY ice. To support this statement, at least to get an indication, one needs to melt the
thin section ice, measured its salinity, and correct for the distilled water amount for gluing.
Reply: Thanks for pointing this out. This statement was not clearly formulated. We have now reformulated this statement in the revised MS.” The loss of brine during the extraction and transport of the ice core is probably small. However, during processing of the thin sections with the diatome slicer the brine drains from the brine pockets.”
L124-L132. The ordinary and transposed directions are clearly defined, and have a
physical meaning for vertical thin sections. But how do you treat the horizontal ones? In
that case one should choose the ordinary direction normal to the plates (in direction of
the c-axis). If not the analysis will not give the minor and major axis lengths properly.
The analysis gives the two orthogonal components of the auto-correlation length. This is clarified in Section 3 of the revised MS. The vertical and horizontal samples in table 6 shows that even for the vertical sample the minor and major axis are not perfectly horizontally and vertically oriented (this also changes across the sample). The brine pockets are not perfect rectangles, they are even bent making it very difficult to align with the major and minor axes.
L131. While ACF has been defined in the introduction I would repeat this here (or
move definition here).
Reply: The ACF is defined in Eq. 1, line 137.
L135-L147. Two points are noteworthy: (i) This discussion about the uncertainty in
the autocorrelation length may not be applicable, as there are other length scales than the
sample diameter that are involved (grain size, spacing of wide secondary brine channels).
E.g., when the grain orientation changes. (ii) The advantage of using an autocorrelation
function is that it is robust to noise and can be applied to non-segmented images. This
probably explains why the authors find little change in length scales when changing the
segmentation, see section 5.1. However, the approach of using an autocorrelation length
likely has limitations for microstructures with different modes of inclusion sizes and orientation.
Other methods to obtain length scales (e.g. mean intercept length or ellipse
fitting algorithms) may be superior.
Reply: We do not think that our dataset is ideal for deriving these parameters. We follow a methodology used in earlier studies for deriving the sea ice autocorrelation length for input to scattering models (Valese and Kong, 1981).
L195. Is there any reason for chosen 2.5 and 97.5 percentiles. Choosing 10 and 90
would allow comparison with other work, for example Eicken et al. (2000).
Reply: Because microwave scattering is highly non-linear, the extremes of the distribution are important and that is the reason for selecting 2.5, (50) and 97.5.
Fig. 11. With these axis scales it is difficult to see the data trends and the difference
between horizontal and vertical sections. I would plot the data without confidence - just
the median values, and perhaps use an extra Figure for the largest and smallest pores
(2.5 and 97.5 percentile, or other choices).
Reply: For the reasons mentioned above we have chosen to retain the 2.5 and 97.5 confidence intervals.
L207. transposed –> similar to the note on L124-132 and the discussion of the autocorrelation
approach: The Lx/Ly anisotropy for horizontal sections can only be derived
properly in the following way: 1. Selecting single grains 2. Align the ordinary direction
with the plates in the grains.
Reply: You are asking for something that we cannot do with our data. Here Lx is the horizontal component of the autocorrelation length and Lz is the vertical component, this is specified in the MS. Their ratio is a measure of the vertical and horizontal anisotropy. Looking at single grains will not give the distribution which is what is needed in scattering models.
L203-243. The results paragraph with many numerical values is only illustrated by
one Figure (11), which could be improved.
Reply: OK, good point, now we have reorganized the text so that the results figures 10, 11, 12, 13 are presented in the results section. In addition to the figures we have 9 tables where most of the numbers in the results section are coming from.
L247-248. On average, there is a relationship between salinity and inclusion density,
but we do not have enough data points to properly characterize this relationship shown
in Figure 12. –> As pointed out above (general comment 2) this relationship should be
essential for the segmentation process and interpretation of the results. In the Figure you
should plot the line for the theoretical brine volume that falls below all data points. You
may also use a second scale on the abscissa for the brine volume (as salinity and brine
volume are very close to linearly related at fixed temperature). The difference between
the line and ypur data points will then correspond to the air volume fraction that your
analysis corresponds to.
Reply: We have followed your recommendation to tune the image inclusion density to the derived brine and gas volume (see earlier response). After the revision we have modified figure 12 and removed figure 13 because it was not relevant anymore.
L305-307. We were unable to characterize the relationship Lobs with the new- and
first-year ice salinity and we were unable to confirm the systematic horizontal anisotropy
ratio of 7 as reported by Nghiem et al. (1995b) due to an insufficient number of samples.
However, the lead / new-ice sample from 24 January 2020 showed a horizontal anisotropy
(Ly/Lx) of 1.4. – > see general point 6 above, that the method here is not suited to
derive anisotropy. In addition lower temperature may facilitate splitting of pores - see
note on L303-304. Note also that Nghiem et al. (1995b) did not make own observations
but only assumed such ratio based on limited observations.
Reply: Thanks for pointing this out. This was not clearly formulated and it has been reformulated in the revised MS.
L303-304. Smaller inclusions could be related to imaging at a temperature as low
as -15 ℃. At such low temperature the pores break up into strings of less anisotropic
inclusions see (Assur, 1958; Anderson and Weeks, 1958; Weeks and Ackley, 1986) for earlier
conceptual work and Mausetal2021,Maus2025 for a more recent analysis of micro-CT
data. Spatial resolution may also be an issue that limits the determination of thin pore
featues. The voxel size is only 30 μm in this study and gives a nominal spatial resolution
(Nyquist Theorem) of 2 x 30 = 60 μm. In view of typical similar median pores sizes at low
temperatures discussed by Maus et al. (2021) this is likely too small to retrieve connected
pore distributions properly.
Reply: Thanks for pointing this out. We have included a note on this in the revised MS.
L305-307. As noted above, under general points, the autocorrelation function is, for
variable grain size directions, not suitable to derive the anisotropy properly. The data on
pore aspects rations based on which Nghiem et al. (1995b) had based their model were
obtained from pore analysis and may represent a more realistic anisotropy (though these
values must be viewed as tentative as they were based on qualitative inespection of 2D
thin sections rather vrthan statistics). However, as noted in the last paragraph, small
aspect ratios may also be the the consequence of temperature-dependent splitting of long
pores into strings of inclusions.
Reply: Thanks for pointing this out. We have discussed the sensitivity study in Nghiem et al 1995b in the revised MS.
References
Anderson, D.L., Weeks, W.F., 1958. A theoretical study of sea ice strength. Trans. Amer.
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Citation: https://doi.org/10.5194/egusphere-2026-1440-AC2
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AC2: 'Reply on RC2', Rasmus Tage Tonboe, 15 Jun 2026
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This study uses high-resolution images collected during the MOSAiC expedition to systematically quantify the autocorrelation length and anisotropy of inclusions in various sea-ice types, providing valuable observational constraints for parameterizing microwave scattering models. The following suggestions are offered to further strengthen the manuscript: