This study uses in situ observations of droplet size distributions (DSD) and number concentrations (Nd) to investigate the relationship between DSD width (parameterized by the k parameter) and Nd. Generally, a positive k-Nd relationship is found. This relationship is parameterized and applied to Nd retrievals derived from MODIS level-2 cloud products.  

The paper is well written and the subject is definitely relevant and interesting. However, at the end of the introduction the authors state that they claim to address the issue that “the spatial scale of the data is a critical determinant of the derived k-N relationship”, which, in my view, they do not really do. Hence, I would only recommend publication if this issue is indeed addressed. I elaborate on this major comment below, after which some minor comments and suggestions are listed.

Major comment:

As said, the spatial scale on which the DSD is evaluated is critical for the k-Nd relationship. It seems that it is claimed that this issue is addressed by using high resolution (1Hz or ~100m) data. However, there is no demonstration on the scale dependency. More importantly, the resulting parameterization is then applied to correct satellite data that is on the order of 1km^2 resolution. The effective radius that is retrieved for a MODIS footprint would be the one that represents the 3^rd over the 2^nd moment of all drops near cloud top within that pixel. I would think that the k to derive Nd should the one that represents that MODIS resolution. If the mode (or effective) radii of DSDs at small scales over that footprint vary, this translates into an effectively wider total DSD for the whole footprint. So shouldn’t the in situ observations (and thus derived k-Nd relations) be evaluated over a similar scale as the MODIS observations? It could be that a similar result is then obtained, but this needs to be shown. Or maybe the authors can convince me and the readers that the k-Nd relationship derived at fine scale is correctly applied to the coarser MODIS scales, but then I would argue for a discussion in the paper making this point.

Minor comments and suggestions:

• Line 51: An interesting paper I suggest to add is the one by Sinclair et al. (GRL 2019; doi: 10.1029/2019GL085851), since they are using remote sensing rather than in situ to derive a relationship between DSD width (effective variance) and Nd. Using the conversion factor between effective variance and k from Grosvenor et al., the relationships Sinclair et al. find are somewhat comparable to the k-Nd relationship found in the current paper. Interestingly, they also find a strong relationship between LWP and k. Anyway, I leave it to the author’s choice to discuss this paper and these results.
• Line 130: The threshold radius is rather specific and demands a reasoning or reference.
• Line 146: I am quite certain that the MODIS resolution is about 1km, so then 15 pixels would translate to 15 km. The 5 km might be a typo?
• Figure 2: Interestingly, the histogram of k in panel D compares quite well with the histograms presented by Grosvenor et al (2018; their Fig 12b). Those are showing remote sensing data from the same instrument as discussed in the first minor comment. I suggest to point this out in the paper.
• Line 220, Eq 8:  Is there a reason to use this particular functional form? Are there physical/theoretical interpretation of the k_t, k_b and N* terms? I was confused at first about the subscripts B and T, which are often used for “Bottom” and “Top” of a cloud. I don’t think this is the case here, so I would suggest using other subscripts.
• Figure 6: As liquid water path can be quite well represented by 5/9 COT*Reff, figure 6 would suggest that an implication of the parameterization is that there is a dependence of k on LWP as well. That might then be in agreement with the Sinclair et al. (2019) results. Or is this not a correct interpretation?
• Figure 7: I would suggest adding a figure of parameterized k to this figure if possible.  
• Line 282: Only here the scale of a 100 m is mentioned. Please mention this when first discussing the in situ data in section 2.

Please see the PDF.