Overall comment

This study explores roles of spatial and temporal aggregation on quantifying albedo susceptibility (S_o) biases by analyzing the outputs of an ensemble of 127 large eddy simulations of marine stratocumulus. The authors designed three methodologies (L2, L3, and L2_N), which mimic common satellite-based analyses in different ways, to identify the influences of the adiabatic drop concentration Nd retrieval, the correlation between aerosol and cloud fields, and the extent of reduced variance in cloud albedo and Nd. The LES simulations also provide an opportunity to obtain the ‘true’ Nd, by which the effectiveness of adiabatic assumption used in satellite retrievals can be assessed. As a consequence of such an analysis, the authors obtained a series of interesting results regarding the influencing factors on albedo susceptibility biases. I think this is a very nice study, and the results presented also have significant implications for reconciling currently diverse observation-based estimates of aerosol indirect effects.

I would recommend this paper be published in Atmospheric Chemistry and Physics after my specific questions/concerns listed below are addressed appropriately.

Specific comments

Line 106-111: If I understand correctly, B (in Eq. 9) is only relevant to the sensitivity of L to Nd, i.e., dln(L)/dln(Nd), not to the whole albedo sensitivity. It’s a bit confusing for me how authors translate B to the theoretical calculation of the S_o biases?

Line 128: As for the LES, why did the authors only choose “nocturnal” instead of “diurnal” simulations or both?

Line 139: How did the authors determine γ value in the calculation of Ac from simulated cloud optical depth?

Line 184: At what spatial resolution is cloud fraction defined here? Is it at 48km x 48km, or defined at 800m and 6 km respectively and then averaged up for whole domain?

Line 186: It is expected that high fc (homogeneous clouds) would be associated with low bias in S. Why is the opposite here?

Line 184-192: The comparison between L2 and L3 methods here is to illustrate the aggregation biases associated with Jensen’s inequality. Actually, there is already another practical method accounting for this issue based on satellite observations. For example, the MODIS L3 product includes a cloud optical depth-effective radius joint histogram which was suggested to consider the non-linearity in the calculation of Nd (e.g. Quaas et al., 2008; Grandey and Stier, 2010). Thus, it might be interesting to evaluate the effectiveness of this method from the LES data in this study.

Line 274: How did the authors select these 58 simulations? Is there an objective criterion? Will it introduce artificial selection on cloud regimes? To show the robustness, it is useful to present the results from all 127 simulations, at least in the supplement information.

Line 280: It’s interesting that the separation of these branches for L2_N is not as evident as L2 and L3. What is the underlying reason? The authors should explain in more detail.

Line 300: Generally, a negative bias in retrieved Nd is expected duo to a positive bias in CER and a negative bias in COT for spatially inhomogeneous scenes according to the Eq.2 (Grosvenor et al., 2018). Thus, it is kind of surprising that the retrieved Nd for open-cellular clouds is larger than the true Nd.

Line 317: It is not quite clear that how the authors conducted the regression fits. As for ∑S_o, does the ‘individual scenes’ here mean the whole domain? In this case, the regression fit was conducted over all 4x4- (or 30x30-) resolved grids in each scene, and then ∑S_o was calculated by averaging up the individual S over all scenes (including the variations along both time and different simulations). Please clarify more detail on how the authors conducted the analysis.

Grandey, B. S., and P. Stier (2010), A critical look at spatial scale choices in satellite-based aerosol indirect effect studies, Atmos. Chem. Phys., 10(23), 11459–11470, doi:10.5194/acp-10-11459-2010.

Grosvenor, D. P. et al. Remote sensing of cloud droplet number concentration in warm clouds: a review of the current state of knowledge and perspectives. Rev. Geophys. 56, 409–453 (2018)

Quaas, J., O. Boucher, N. Bellouin, and S. Kinne (2008), Satellite-based estimate of the direct and indirect aerosol climate forcing, J. Geophys. Res., 113, 05204, doi:10.1029/2007JD008962.

General comment:

This study analyzes output of LES simulations for marine stratocumulus clouds to investigate how small-scale cloud variables and their relationships to aerosols are aggregated to manifest the albedo susceptibility bias occurring at larger scales typical of satellite-based analysis with L2 and L3 datasets. For this purpose, theoretical relationships between key statistical properties are reviewed and applied to the LES output to quantify the albedo susceptibility bias as a function of several statistical properties and cloud water susceptibility for different aggregation scales. This study offers a nice demonstration of how spatial cloud inhomogeneity and non-linear aerosol-cloud relationships are a source of uncertainty in quantifying the albedo susceptibility, directly relevant to radiative forcing due to aerosol-cloud interaction. I have some minor comments mostly regarding the presentation and/or clarification as listed below and I would recommend the manuscript to be considered for publication in ACP after the authors properly address the comments.

Specific comment:

Section 3.1: It is hard (at least for me) to understand in detail how the LES output variables (at the native model grid resolution) are averaged and/or aggregated into different spatial scales. In particular, I am confused with the term “aggregated” which seems to mean “averaged” for some parts and to mean “accumulated” for other parts. I would appreciate the authors to clarify if each “aggregated” means “averaged” or “accumulated”. Please look at the Minor Points listed below for specific locations in the text for this clarification.

Line 188-190: “This is because L3 averaging has a stronger smoothing effect on broken cloud fields, and therefore somewhat unexpectedly reduces the averaging bias for broken cloud fields compared to solid cloud fields”: Does this explain the negative values of the albedo susceptibility in Fig. 3b?

Section 4.1.3: The argument here associated with Fig. 10 is of particular importance in the context of cloud water adjustment and its impact on albedo. It is interesting to see that the tight correlation between S0 and L adjustment biases relates inversely with cloud fraction between L2 and L3. How can this reversed relation be understood? Please add some more discussion.

Minor point:

Equation 6: Is this B_x inverse of the bias?

Fig. 1: Are the numbers labelled for contours in percent?

Line 135: Insert ‘of’ between ‘fields’ and ‘drop’

Line 138: “Both cloud water and rain water contribute to tau and re”: Does this mean that re is computed as the ratio of third to second moments of the whole range of the bimodal size distribution? If so, is it consistent with what satellite measurement looks at given satellite measurement is sensitive primarily to the cloud mode alone?

Line 146: “aggregated”: Does this mean “averaged”?

Line 151: “at the pixel level”: Does this mean the model native resolution (200m)?

Line 162: “aggregated”: Does this mean “averaged”? Namely, are tau and re first averaged to n=4 and n=30, and then Equations (2) and (3) are applied to them to derive Nc and L?

Line 201: Fig. 3 -> Fig. 4 (?)

Line 206: Does this “aggregate” mean “average”?

Line 214: Please state that b(6km) and b(800m) are denoted as b_hat_overbar and b_hat, respectively.

Fig. 3 etc.: Please put the panel titles as “L2”, “L3” and “L2N”.

General

Based on large-eddy simulations of marine cloud fields off California, this study explores the effects that spatial and temporal averaging as explicitly and implicitly done in satellite data analysis can have on the study of aerosol--cloud--climate interactions. The authors present a careful and well-documented analysis that puts existing satellite-based studies into perspective. I think this is a strong paper already, but have a few remarks mostly concerning methodology.

Details

• line 10: which biases? Bias of aggregation vs. inndividual models, or the other way around?
• line 11: Explain L
• line 49: 'known'
• line 89: 'interest'
• line 93: 'well-known'
• line 96: 'the' standard deviation
• line 138: For 'cloud top', do you use the top-most layer of the model, or do you allow for some radiation penetration into the cloud, as found in satellite retrievals at smaller MIR wavelengths?
• line 146: In the aggregation, did you consider partial cloudiness in your cells as a weighting factor, i.e. via horizontal cloud fraction?
• line 148: Why did you choose 800mx800m to get 'close to the typical 1 km ...' of MODIS instead of using n=5 directly?
• Figures 11 and 12: Harmonizing the color bars on a and b would make it easier to compare both - assuming that any spatial detail was retained in so doing
• line 289: (sub)adiabatically
• lines 376--380: This is quite substantial, and the result that most surprised me. Based on this insight, do you have suggestions on how to improve Nd retrievals?