Dear Dr. Lieblappen and co-authors

Thank you for your response to the reviewers comments. Reviewer 1 is happy with your response, and has some minor points to correct. Your response to the comments has resulted in improvements to the methodology write up and technical descriptions in the paper. There are, however, still some additional points I need to raise.

The key results presented in this paper are detailed microphysical analysis of two cores. You are developing some new statistical metrics to describe connectivity in brine channel networks. As the paper is written it is very difficult to follow how this builds a model as claimed in the abstract. I can see how particular parameters provide limits on fluid flow through the ice, and I think this is what you are getting at in your concept of a statistical model. The manuscript could be greatly improved if you clarify the model in a summary near the end of the paper. Specifically, the sentence in your conclusion "The probability distributions shown represent a sampling of the various microstructural behaviors needed to statistically create a brine channel network parameterized by depth and temperature" is really overly general. Can you follow on from this statement to lead the reader through the structural behavior that characterizes the network? What does this structural behavior mean for physical processes controlling fluid flow in the ice. A guiding paragraph would really help lead the reader to why your rather detailed results sections are worth delving into.

There are still places in your methodology where it becomes hard to follow how you build particular metrics. My confusion is around visualizing the subsamples, and how pores are tracked between layers in the core. I would suggest that you consider if you can use terminology that is more intuitive for the reader to understand. I am happy with your mathematical description provided I can find my way through, and some readers may get confused by terminology that is not intuitive to them!

Minor comments. Line numbers refer to the manuscript with markup.

page 4, line 15.
Why does the maximal ball method best fit the microCT data? Are their trade offs in accuracy using this method compared to others?

page 4, line 16:
Missing "a" after "structure in"

page 4, line 26:
Would it be clearer to the reader to not use "our" in "the direction of our progression through the sample"? I believe you are moving downward through core slices in your analysis, which could be though of as following fluid pathways in gravity drainage. Is this correct? Perhaps rephrase to refer to the sample order more precisely.

page 7, line 21:
"is" missing from before "shown in Fig. 3".

page 8, line 23:
It is not clear what the "subsample" is. Can you refer back to the methodology section here, as I do not rememver subsample being defined.

In general it may help the reader if you can more succiently allign your description of connectivity with actual brine channels in figure 1, perhaps leading readers through an example of how a brine channel is followed through the core.

page 11, line 6:
Two "boths", one needs to be removed.

page 12, line 20:
"we could selected the 15316 paths" - strange grammar.
I would suggest you carefully proof read, there are a few places where grammar could be improved.

page 12, line 22:
Statistical repeated in this sentance, and seams redundant.

page 13, line 23-24:
Many readers will skip most of the paper and just read the conclusions. They will not know what "throat size" is. The paper would be much stronger if you can write the conclusions in plain language, pointing out what your findings actually mean for fluid flow in sea ice, for example.

Caption figure 2: "the Iceberg Site". Correct throughout.
Caption figure 4: I think you need to replace "sample" with "subsample".
Ditto for figure 5.

Your observations paint a picture of the differing structure of brine channals in columner and granular ice, and how these vary with depth and temperature in a core. While this is technically interesting, and I can see the application to building models of brine in sea ice, it is not clear from your manuscript why the reader should really care about these observations. What is the broader context? Can you provide some statements as to the impact of your findings in the conclusions? You do not describe how the metrics developed can be used to characterise sea ice properties that are relevent to processes within or associated with sea ice. This broader context is needed for this paper to be impactful and meet the standards of The Cryosphere. I echo reviewer 1's comment (which they made in regard to the discussion on Markov chains) that more physical interpretation would strengthen the paper.

I believe improvements to readability and describing the context of your results would increase the interest and impact of this paper. I am suggesting minor revisions, as all comments are related to readability of the manuscript. In general, I find the contents of the paper will be of interest to the sea ice community, with a unique data set and novel approach to modeling sea ice porosity. If you should need more time to edit the paper (I realize adding the context requested is a substantial task) please contact me.

Best regards,
Jenny