Dear authors,

the reviewers have raised several serious issues concerning your manuscript. I will ask (some of) them to have a second, critical look at your revised manuscript. Therefore, I ask you to upload an improved version of your manuscript.

Sincerely,

Lennart de Nooijer

Dear Dr Zhang,

thanks for your reply to the reviews. All in all, the suggested changes were quite substantial, so I will consult (some of) the original reviewers to have a look at the changes you made before acceptance.

sincerely,

Lennart

Dear Dr Zhang,

I am looking forward to see the updated version of your manuscript. Once you have uploaded an updated version, I will ask some of the original reviewers to assess whether their criticism is sufficiently replied to.

Sincerely,

Lennart de Nooijer

Dear Dr Zhang and co-workers,

I apologize for the time it took to re-assess your manuscript. I have been in contact with (some of) the original reviewers to come to the conclusion that your manuscript is almost ready to be accepted for publication. We came up with a few typos and with some suggestions for final improvements. Please use these to your advantage and I am looking forward to see the revised version of your manuscript.

Sincerely,

Lennart

For example, line 8 and 39: there is an extra space here. Please remove and check the rest of the text.
line 40: ‘mirco’ should be ‘micro’
line 137: ‘In about 500 ml diluted ammonia.’
line 217: remove one of the dots.
line 243 and elsewhere: should be ‘C. leptoporus’ rather than ‘Ca. leptoporus’.
line 234: perhaps add Tremblin et al. 2016 - PNAS in the papers using the micro filtering technique.

In relation to some previous comments:

Regarding equation 2-2: could you take a step towards isolating the effects of particle size, particle shape, particle material density, vessel shape, suspension density… etc? I don’t see this as essential to the present manuscript, if the intention is purely to improve the protocol.

Line 150: This currently reads as though the vessel is smaller than the particle, and thus doesn’t make sense.
“A significant wall effect will be detected when a particle is settling in a vessel which diameter is smaller than the particle size by two orders of magnitude (Barnea and Mizarchi, 1973)”

Regarding comment 9 by reviewer #2: although a Monte Carlo approach is indeed common, it is a rather opaque method of estimating uncertainty when the exact inputs are not specified. The uncertainty in a value is quite as important as it’s expected value so it is therefore important to be clear about what goes into this analysis. The author’s explanation here may be acceptable, but this does not mean that details of their approach should be omitted. A description of the above should at least go into the appendix for anyone who wants to reproduce their results.

Regarding comment 14 by reviewer #2: the ratio: “Nu(t=0) / D” is the number of coccoliths per unit thickness. dD doesn’t come into it as you’re not taking a derivative with respect to D. Please adjust.

The description in appendix D is much improved. The assumptions have been stated more clearly than in the first version. One point however is that when equation D-1 is presented, it should be made clear that either A) as written this is for a coccolith of a single size, with all coccoliths sinking at identical rates. Or B) that the variables N_u and v are actually distributions. It is not obvious a priori how these distributions will change throughout the course of settling and thus whether it’s valid to use the mean of the distribution for all calculations.

It is appreciated that the authors due diligence showing that constant velocity throughout settling is reasonable. This is useful and should at least be stated explicitly as a reasonable assumption.