Dear authors,

I have now received two reviews for the revised version of your manuscript.

As you will see, reviewer 1 still has a number of major concerns. Their comments can be divided into two groups: one group of comments is concerned with the robustness of some results of this study. These comments need to be addressed adequately within the next submission or this paper cannot be published.

The other group of comments relate to parts of this paper which the reviewer deems unnecessary or distracting. Here I only recommend to take these comments into account to possibly improve readability of your manuscript. I will, however, obviously not make the final publication of the manuscript depend on your following the reviewers suggestions in this respect.

Please get in touch if you should require additional advice on how to proceed.

Best regards,

Dirk Notz

Dear authors,

I have now received a detailed review of the latest version of your paper. As you will see, the reviewer is still concerned about the robustness of your results because of the lack of filtering, and I share these concerns.

May I ask you to examine in a case study the potential effect of the filtering on the findings of your paper?

If you should be able to show that the effect of the filtering is small, it should suffice to say so in the manuscript.

If, however, you find that the filtering affects your results in a more substantial way, I can only accept this paper after filtering has been implemented for all your findings.

All the best,

Dirk

Dear authors,

thank you very much for submitting this revised version of your manuscript. I find that the inclusion of the filtering has significantly strengthened the robustness of your results, and that it has allowed for some very helpful discussion as now included in the new section 3.3. I am hence finally happy to accept your manuscript for publication in The Cryosphere.

I only have some minor technical issues that you might want to address for the final version.
Line number refer to the manuscript without the track changes. Please provide line numbers in the submitted manuscript for next time. Thanks.

- You could consider replacing the listing "4.5, 9 and 18 km" by "4.5 km, 9 km and 18 km" for clarity throughout the manuscript

- section 2.3, last line first paragraph: calculate -> calculated

- p.7, l.7: analyzedl -> analyzed

- p.8, l.6: "2, 3, and, 4" -> no comma after "and"

- p.9, l.5: "little" -> "few"

- p.12, l.2: "8and" -> "and"

- p.12, l.2: "MAterial" -> "Material"

- p.12, l.3: "-40 % lower" -> "40 % lower"

- Entire section 3.2.1, Figure 8: You use seven (not six) nominal length scales, must corrected a number of times (search and replace seems like the easiest option :-) )

- p.13, l.6: "and as well" -> "and"

- p.13, l.13: "taht" -> "that"

- p.13: I note that you once provide an uncertainty range for a b exponent, namely -0.09 +- 0.04. As this is a rather large uncertainty range (about 50 %), I wonder if it were helpful to include uncertainty ranges for all other numbers provided in this section. This would allow one to better judge the amount of agreement.

- p.13, l.22: "a anisotropic" -> "an anisotropic"

- p.14, l.3: "last" -> "previous"

- p.14, l.4: The bit starting with "Even a bit more..." is not a full sentence. Consider combining with previous sentence.

- p.14, l.22: "they" -> "the"

- p.14, l.22: "shallow" -> "shallower"
- p.15, l.23: Is the "-36 %" relative to the 9 km value (as implied by the preceding words" or relative to the 4.5 km value? (i.e., I can calculate that they are relative to the 9 km value, but I had expected them to be relative to the 4.5 km for consistency with the previous bracket). You could consider to name your D as D_{4.5 km} etc., which then allows you to explicitly state what this % refers to. Using the length scale as index allows you to write the following equation possibly more intuitively, as the "i" is no longer needed.

-p.16, l.8: ">" -> "more than"

-p.17, l.5 from bottom: "regional" -> "regionally"

-p.18, l.11: "stay the similar" -> "stay similar"

-p.19, l.23, "to compare" -> "to meaningfully compare" (because one can always compare, it just doesn't make sense :-) )

-p.19, l.27: "will be" -> "are"

Thanks again for submitting this manuscript to The Cryosphere.

All the best,

Dirk