Dear authors,

Thank you for submitting your revised manuscript. I have received one review of this revision, and from that review and my own reading of the paper and Response to Reviewers, find that your paper may be acceptable for publication in AMT after a few minor revisions. These are largely textual and I don’t anticipate they should be too much trouble.

I broadly agree with the reviewer’s comments – please find attached their review with annotated pdf of your paper. There are a few general comments and then some annotations on the text itself. Please let me know if you have any questions about these. I agree that the quality of the AOD retrievals is not as high as some other instruments, but this is of course partially a factor of the information content of the sensors it has been applied to and the fact it is a fairly new approach. So I would encourage the reviewer’s suggestion to add a few more sentences about next steps for refinement or potential application to other sensors (I imagine MISR could conceptually work due to the 9 cameras on the instrument).

On your equation 2 the review suggests adding a ^2 at the end, but I think the way you have it written is correct, as there is already a sigma^2 inside the curved brackets (in contrast to equation 1). However I do think the curved brackets can consequently be removed from the equation. Either that or retain them and move the squared symbol from inside to outside.

On the topic of CHRIS PROBA aerosol retrievals (you and the reviewer both remarked that this instrument has not been used much for aerosol retrieval): there is one other effort I am aware of, led by Peter North’s group in Swansea. See e.g. this paper (Davies et al., IEEE 2010), which is worth reading and citing: https://ieeexplore.ieee.org/document/5256163/ I am not sure of the current status of that algorithm, however; the lead author (Will Davies) is now at Reading. It is a different concept to your algorithm, building on the approach that the Swansea group had developed for the ATSRs.

The algorithmic approach you outlined in Part I is quite novel and it’s interesting to see the practical application to satellite data here. I look forward to its further development and results.

Best wishes,

Andrew

Dear authors,

Thank you for submitting your revised manuscript. I feel you have covered the reviewer comments sufficiently in this version, but there are a few small technical points I’d appreciate if you could check before the paper is accepted for publication AMT.

I see in equation 2 you added the extra squared symbol at the end as the referee suggested. However from my reading (see my comments with the last decision letter) I noted that I think the referee's suggestion to add the squared term there was an error. Can you double-check this?

The reason is that this way you have sigma^2 inside the brackets, and now another ^2 outside. Compare with for example the notation in equations 1 or 4. So I think you can either delete the one inside, or delete the ( ) and the ^2 outside. Does that make sense? I have emailed you a screenshot which outlines the two ^2. If you could please check this and correct if necessary/explain why not necessary, I would appreciate it.

A few other small things (lines refer to the 'track changes' version):

- line 245 says "tthat" instead of "that"
- line 303, "on" should be deleted
- Fig 12: Your most recent response to reviewers notes that QI is rounded to the nearest 0.1, but I think it would be good to add a sentence to the caption here as well, as this is not listed in the body text.

Please let me know if you have any questions.

Best wishes,

Andrew

Dear authors,

Thank you for double-checking and correcting the equation, after your previous revision. I am now pleased to accept this paper for publication in AMT.

Best wishes,

Andrew