This is my second review of the manuscript βImpact of sea ice floe size distribution on seasonal fragmentation and melt of Arctic sea ice" by Bateson et al. I appreciate the authors' careful examination of my comments from before, and am happy to see many improvements in the manuscript. I think this work is compelling, timely, at the front of the literature, but has issues at its core that need to be resolved. I will simply get to the heart of the matter.
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1) I reiterate the use of an "upper-truncated FSD" is not well-justified. The origin of the terminology "truncated power-law distribution" in the current FSD literature comes from Burroughs and Tebbens (2001) - regarding measurement truncation. Stern (2018) hypothesized that an observed tail-off of the FSD at high sizes in a well-known paper of Toyota *could* be explained by a combination of measurement truncation error and an erroneous use of a cumulative distribution. If this hypothesis is generally true, the implication is that the power law extends across all sizes - not that it is truncated. If this hypothesis is false, Toyota's suggestion of different scaling behavior at large scales is true. Regardless of which is correct, neither supports the use of a single power-law distribution between two arbitrary sizes, where the highest size is set by physics, not observational limitations.
2) Thus issues remain with the use of l_{max} as a controlling parameter in Sec.2.4. As previously noted, changing l_{max} for any reason while maintaining the constraints of Eq (8-9) alters the number/area of floes at all sizes below l_{max}. But physically, why? It is unclear in this manuscript why changes to sea ice at the highest size should be connected to changes at the lowest size, but the normalization makes this connection explicit.
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Here's another way of thinking about the l_{max} issue. l_{max} is the scale with (by definition) the least number of floes. Because the exponents of your power-law section are always above 2, the area distribution, x^2 N, also declines with increasing size - so the scale l_{max} is also that with the least floe area. Intuitively, then, how could your model be tested? It is the hardest-to-observe scale in the problem, all the scales above it are dependent on it, but a real measurement would be pressed to decide which scale matters, and how it is evolving because of the known truncation error issues. Would this require simply tracking a single, large floe? Can you justify why in your equations, a small lateral melt on the biggest floes would lead to huge changes in the numbers of small floes?
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These two features of the discussion make interpreting the (well-presented) results difficult. Even at the fairly liberal "this is for convenience" level, why multi-scale variability at all scales is so related to this scale is not justified here. The evolution terms for l_{max} are stated, not derived, in a few lines, but the entire work depends on them, and no plots of l_{max} are shown in the paper. What is the time evolution of the FSD required of these equations? Does it make sense?
My major suggestion is the authors present a justification/derivation/explanation of (10,12,13) to show that the FSD evolution terms are justified. This doesn't need to be very long, but necessary for the reader to evaluate what such equations mean and how they affect the distribution.
It would also be nice (but more work) if the authors convert the parameterization to a new, "untruncated" one characterized by l_{min} and R, where R is the effective floe size. You will (as you already do) have to impose a finite-size cutoff on the floe size to integrate sea ice area for some exponents, but this cutoff would be a fixed property of the system not a parameterized one. Then equations (10-13) are mappable to equations in R instead of l_{max}. When you do that, the equations can be evaluated in a slightly more familiar and appealing context, avoiding the confusing truncated power-law issue altogether.
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Small comment: would it be possible also to include the wave-fracture mode (changing l_{max} to lambda/2) explicitly in Fig 1? |

Thank you for your detailed response to the two reviews. I have considered these and believe your paper may be acceptable for publication after major revisions, however will need to clarify some points were adequately addressed with the reviewers. I invite you to provide a revised manuscript.

There are some points I would like to clarify in your response.

You reference Stern et al 2013a. I can not find this paper in your citations. I think you mean 2018a. Incidentally, my read of this paper was that the exponent in the power law for flow size distribution was not exactly consistent, and they had difficulties understanding why. They do argue that a single power law can fit across a wide range of floe sizes (and point out a potential issue with data showing regime shifts as a truncation error), but they do not find a consistent value for the exponent. I see that you comment on a potential seasonality of the exponent in your introduction, and you discuss the possible range of the exponent in your model design, so you might want to check page 5 of your response to reviewer 2.

You asked my editorial opinion on the figures. Regarding how you present the units, I prefer not to use a slash. Some people might interpret this as the unit being raised to the power -1. Regarding the captions, I will leave this up to you. The caption should include information needed to interpret the figure and not information that one would expect to find in the manuscript text. Though sometimes it is handy to describe the data in the figure more fully.

Please include the data availability section.

Finally, if you can make a version of the manuscript with track changes this will greatly help review. You are recommended to use latexdiff, if you are writing in latex:

https://www.the-cryosphere.net/for_authors/submit_your_manuscript.html

Looking forward to your revision,

Jenny