The authors evaluate the semi-direct effect of dust aerosol over low-levels clouds in the North Atlantic Ocean with CloudSat radar and CALIOP lidar observations. They show that the summer free-tropospheric dust layer overlying low clouds induces a shortwave heating response which strengths the boundary layer inversion, consistent with previous studies of biomass burning aerosols (positive semi-direct effect). But also, due to the large dust particle sizes, a significant longwave warming response. The dust-induced longwave warming dominates the heat budget and leads to overall less cloud-top cooling (~10%) which reduces cloud cover (novel negative semi-direct effect).

The paper presents an interesting new finding about the longwave semi-direct effect of aerosols on low-level clouds. The authors discuss first the response of cloud cover, and then the response of heating rates, to dust optical depth, dust layer geometric thickness, and dust-layer base altitude. They use a radiative transfer model (SBDART) to quantify the cloud sensitivity to perturbations in each of these aspects, as well as meteorological quantities.

Overall, the results are interesting. However, I have some confusion about the methods used for the analysis, particularly the approach taken to remove confounding effects of meteorology and how to separate the impact of each metric of the dust layer.

Mainly, why have you chosen to split up the data into so many “categories” and compute the partial derivatives of interest as differences between categories instead of computing them with a multiple linear regression?

• For the meteorology, why do you choose to analyze each 5x5° box separately rather than e.g. extending a cloud controlling factor analysis to include the dust properties of interest? Wouldn’t this better remove any confounding meteorological factors, rather than just looking at some “small area”? Because surely there will be some variability still within 5x5° boxes.
• For section 2.2.2 why do you split just into “low” and “high” dust optical depth? Why not have a continuous variable for the DOD?
• If instead of making these artificial categories and thresholds you used the continuous variables, you probably would be able to retain more data and have more statistical significance (instead of throwing out so many profiles that don’t meet the minimum 180 per category).
• If you are concerned that some of these relationships may be quite nonlinear, so a linear regression wouldn’t be suitable, maybe you could consider something like ln(DOD) instead of DOD directly.

Minor comments:

• L101/102: I think you have swapped reference to Fig 1c and 1d. The figure caption says that 1c is showing change in cloud cover when all aerosols are present and 1d is for when only dust is present.
• L170: How can the dust “coexist with” but also be “typically above” the cloud layer?
• L548: Is this a good estimate? What if the clouds are not stratiform and pushing through the inversion layer?
• L1059/1065/1066: “LST” should be “LTS” for lower-tropospheric stability

In my opinion, this is a long, but good paper that presents a thorough study examining several aspects of dust influences on underlying low-level clouds. My overall sense is that the topic is of interest to the community, the methodology is sound, and the presentation is of high quality. Nonetheless, I feel that the manuscript needs some refinement before publication. The necessary improvements seem fairly minor and include mainly some clarifications, elaborations on a few points, and wording changes. Please find my specific comments below.

Minor issues about content

1. Line 222: It could help some readers if the manuscript briefly explained the relationship between depolarization and particle sphericity and briefly discussed the reason why the depolarization ratio differs for different aerosol populations (e.g., non-sphericity).
2. Lines 330-334: It could help to explain somewhere why there is no sensitivity to humidity: Does this indicate that dust is not too hygroscopic?
3. Line 378: It would help to clarify the text “meteorological variability is roughly invariant”: What is meant by variability being invariant? The same applies to Lines 535-536.
4. Section 2.2.4: This section should specify somewhere the solar zenith angle(s) used in the SBDART simulations. Are the calculated radiative fluxes for the local times of CALIPSO-CloudSat overpasses or are they daily average values? This is quite important for the shortwave simulations mentioned in Line 480 and elsewhere in the manuscript.
5. Section 2.2 or 3.1: I wonder if the impact of dust layer base altitude partly comes from the fact that if dust base altitude is low, only clouds at very low altitudes can be considered (given the required 200 m separation between clouds and dust), whereas if the dust base is higher, even clouds at higher altitudes may be included. This could perhaps be significant if very low and slightly higher clouds responded differently to the effects of dust above.
6. Line 772: I wonder if “shortwave cooling” should be changed to “shortwave warming”. If this was not the case, a clarification could help explain whether this refers to the shortwave impact of the dust layer, which is indeed cooling, or to the overall shortwave effect of sunlight, which is warming. (I think the latter, as sentence begins with “In contrast to the dust layer”.) 
7. Lines 829-831: The finding that longwave warming increases with dust geometrical thickness seems puzzling to me, as a thicker dust layer means that some of the dust is at higher altitudes and is therefore cooler, emitting less longwave radiation towards the clouds below. It would help to include an explanation or at least a hypothesis about this. Could perhaps a relationship between dust geometric thickness and dust optical depth play a role? The same applies to Lines 837-838 and Lines 1100-1102.
8. Line 1030: The text says that “these factors have little impact on the cloud response to dust-layer characteristics”, whereas Figure 14 only shows that these factors have little impact on dust characteristics but does not directly show the effect of dust on the clouds below. I guess the argument is that if these factors don’t have a strong relationship with dust properties, they cannot affect dust influences on clouds either—but it would help to clarify this in the text.

Minor wording issues

1. Manuscript title: I think there should be no period at the end of the title. Also, as it is more typical to have titles that are not full sentences (with subject, verb, object, etc.) but are descriptors of the topic, I’d suggest rephrasing the title to something along the lines of “Dust semi-direct effects: The influence of dust-induced longwave radiation on low-level cloud response to free-tropospheric dust over the North Atlantic Ocean”. This could help because the verb in the current wording, “influences”, is a word that is sometimes a noun—and I needed to read the title several times to realize that here it is a verb.
2. Manuscript text and figures: The manuscript often uses three acronyms for dust characteristics: DB, GT, DOD for the base height, geometric thickness and optical depth of dust layers, respectively. For consistency, I recommend changing the notation to include the letter D even for dust geometric thickness (making it DGT), and to include the letter H representing “height” for dust base height (making it DBH). This would treat all three quantities consistently, with three-letter acronyms representing three-word quantities (DBH, DGT, DOD). Even when full words are used, I recommend adding, for consistency, “dust” in front of “geometric thickness” (just as dust is mentioned for “dust base height” and “dust optical depth”).
3. Lines 35, 38, and 40: I suggest deleting the words “the”.
4. Line 42: I suggest adding a comma after “interactions”.
5. Line 58: I recommend deleting the letter “s” from the end of “types”.
6. Line 61: I recommend changing “In addition” to something like “On the other hand”.
7. Lines 65-66: The wording should be refined to clarify “far more substantial”: More substantial than for what clouds? Perhaps changing “their influences on marine low-level clouds are far more substantial” to “their influences are by far the most substantial on marine low-level clouds”.
8. Figure 1: For Figure 1c, it would help to clarify whether assuming that all aerosols are above the cloud layer implies that there is no aerosol inside or below the cloud layer. It should also be clarified whether the color bar for Figure 1d also applies to Figure 1c. The color bar should also have a label indicating what the colors represent. (The caption explains this a bit, but it should still be shown in the figure as well.)
9. Line 77: It should be clarified what the word “Method” refers to—perhaps Section 2.2?
10. Line 102: I suggest changing “like” to “similarly to studies of”.
11. Line 130: I suggest deleting “the” after “of”.
12. Line 133: Because of the presence of “While” at the beginning of the sentence, the text “, however,” should be deleted.
13. Line 140: I recommend deleting the letter “s” from “aerosols”.
14. Line 171: I recommend adding “in” or “during” after “than”.
15. Figure 2: In the legend of Panel a, a letter “s” should be added at the end of “month”.
16. Line 168: I suggest changing “retrievals” to “operational data products”.
17. Line 170: The word “is” should be added before or after “typically”.
18. Line 183: I recommend changing “aerosols, clouds, and radiative fluxes” to “aerosol, cloud, and radiative flux”. I also recommend adding a comma after “observations”.
19. Line 186: I recommend either adding “the” in front of CALIPSO, or removing “satellite”.
20. Line 189: The letter “s” should be deleted from the end of “Aerosols”.
21. Line 191: I recommend deleting the hyphen between “remote” and “sensing”.
22. Line 193: I recommend changing the symbol “~”to “≈” all three times (and throughout the manuscript).
23. Lines 196, 230, 241, and throughout the manuscript: There should be a space in “532nm”.
24. Line 202” I recommend adding a letter “s” at the end of “measurement”.
25. Line 206: I recommend adding “the” or “this” after “improved”.
26. Lines 259-260: Either a “the” should be added after “on”, or “satellites” should be deleted.
27. Line 263: I recommend adding “the” after “from”.
28. Line 374: I recommend replacing “confound” by “be confounded” or by “complicated”.
29. Line 380: The word “degree” could be replaced by the degree sign, as in Line 384 and elsewhere.
30. Lines 407-408: As is, f_cat is singular and f_lowcld is plural; consistency should be achieved by changing one or the other.
31. Line 419: I recommend changing the word “study” to “paper” or “manuscript”.
32. Line 481 and elsewhere as needed: I recommend changing “net” to “total”, as net would imply the difference (and not the sum) of two quantities. If it is the difference, though, that should be explained.
33. Line 526: A comma should be added after “Subsidence”.
34. Line 554 and elsewhere in the manuscript: The letter “s” in “section” should be capitalized whenever it is for a specific section identified by its number (e.g., Section 3.1).
35. Line 708: For clarity, the word “the” should be changed to “increases in all three considered”.
36. Lines 720 and 721: The hyphens could be deleted from “dust-layer” and “dust-base”, for consistency with the rest of the manuscript.
37. Line 746: The last digit (“3”) should be deleted from “approximately 0.723 km”.
38. Lines 773 and 774: The “s” should be deleted from the end of “rates”.
39. Lines 819-820: For clarity, I recommend changing “change” to “increase”, and adding “increased” after “pattern of” (if this is correct). A similar clarification is also needed in Line 1104.
40. Line 825: I recommend deleting the word “the”.
41. Line 857: I recommend changing “on” to “to”.
42. Lines 858 and 859: I recommend adding “larger” after “times”, if this is correct.
43. Line 865: I recommend adding “the contribution of” after “than”. I also recommend changing “sensitively” to “sensitivity”.
44. Line 883: I recommend changing “proportion” to “fraction”.
45. Line 958: I recommend inserting the words “influence of” after “from the”.
46. Line 980: The caption should clarify what kind of altitude is along the right side y axis: Is this perhaps cloud top height or dust layer top or thickness?
47. Lines 1059, 1065, and 1066: I guess “LST” should be changed to “LTS”.
48. Line 1069: The word “sensitively” should be deleted, or the word “depends sensitively on” should be replaced by “is sensitive to”.
49. Line 1074: I recommend inserting “simulations for the period” at the beginning of the line.
50. Line 1089: My sense is that the word “relative” should be deleted, as the paper examines the absolute altitude of dust layer base above sea level, but does not examine the separation between cloud and aerosol layers (which would be a “relative altitude”).
51. Line 1234: There should be a space after “clouds”.
52. Line 1257: I recommend replacing “, especially studies found the” by “. Most importantly, studies found an”.