The manuscript investigates the biases in satellite retrieval of liquid water path (LWP) and cloud condensation nuclei (CDNC) using LES simulations configured to DYCOMS-II RF02. The authors compare the correlations of the two variables from three sources: direct model outputs, retrievals from equations using LES simulated values for the parameters, and retrievals from equations assuming constant parameters. The authors find that CDNC retrievals assuming constant parameters tend to increase CDNC at the cloud boundaries. They conclude that satellite-derived CDNC shows a significant positive bias, but the correlation between LWP and CDNC was very similar between the methods. The authors also find that the instrumental noise in satellite retrievals do not affect the correlation between CDNC and LWP.  The topic of this manuscript is suitable for publishing in ACP. However, the manuscript is poorly articulated, and the results are not effectively presented. The confusing variable labels in the figures further contribute to the overall lack of clarity. The current version isn't ready for publication but may be considered after some revisions. I would like the authors to respond to and address my comments. Details of my comments are as follows:

Recommendation: Major revisions

Major comments:

The current version of the manuscript lacks clarity in the following aspects:

1. I don't find the figures to provide sufficient support for the authors' arguments in the text. I suggest adding more figures to better substantiate the arguments. Please see the detailed comments below.
2. The axis variables are not clearly labeled. The authors need to clearly label the LWP and CDNC in Figs. 3-6, indicating whether they are direct model outputs or computed from equations 1-3, and whether they are pixel-level data or domain-average data. An easy way to address this is by using subscripts, e.g., LWP_true, LWP_eq3, CDNC_eq2, etc. Use overhead bars if the variables are domain average values. The titles of Figs. 3b, 4b, and 6b are confusing because the LWP in these panels is computed from equation 3, not equation 2. I suggest using a title like “Computed LWP and CDNC” or something similar.

Detailed comments:

1. 1 caption: “the calculated CDNC”. Is it calculated from eq. 1 or 2? “the retrieved LWP”. Is it calculated from eq. 3? Please also specify the sizes of the squares on the right panels.
2. Lines 35-38. The authors argue that the cloud top effective radius and liquid water path change with cloud top pressure. However, cloud top pressure is not shown in the paper or supplementary material. Please provide a figure of cloud top pressure to support this argument.
3. Line 41. Replace “liquid water content” with “liquid water path” as the former is not shown in Fig. 1.
4. Lines 41-43. I don’t see how this sentence connects to the previous one. Please revise the paragraph for better flow.
5. Lines 126-132. Since the section predominantly centers on Fig. 2, the brief reference to Fig. 3 interrupts the flow. To improve continuity, I suggest removing the discussion of Fig. 3.
6. Line 133. “The leftmost panel shows a closed cell type structure in the cloud”. It’s difficult to discern cloud structure in Fig. 2. Please include a snapshot of LWP to clarify.
7. 3 caption: “Simulations are colour coded according to CCN concentrations used in the model initialization”. Please provide a legend in the figure to reflect this.
8. Lines 136-143. I think the paper would benefit from a separate figure comparing CDNC from model output and equations 1 and 2 to support the arguments in the text. I suggest adding a scatter plot with the true CDNC from the LES on the x-axis and the computed CDNC on the y-axis. Mark the domain-average CDNCs in the plot. It would be helpful if the authors could overlay the results of aggregation so that readers do not need to refer to the Supporting Information for details. The authors might consider coloring the scatter plot with LWP values to illustrate the bias of computed CDNC in relation to cloud structure. Similar plots can be made for LWP from model output and equation 3.
9. Line 142. Please list all possible assumption biases here instead of using “e.g”.
10. Line 152. “Satellite derived CDNC values are at least two times higher than the direct LES values”. Do the authors have any idea what might be causing this?
11. Line 157. “Within individual ensemble members, the cloud internal variability contributes to the CDNC-LWP correlation and cannot be considered to be an aerosol effect on clouds”. Zhou and Feingold 2023 has reached a similar conclusion. (Zhou, X., & Feingold, G. (2023). Impacts of mesoscale cloud organization on aerosol‐induced cloud water adjustment and cloud brightness. Geophysical Research Letters, 50(13), e2023GL103417.)
12. Line 177. To improve the connection with the subsequent discussion, please make it clear that Fig. 5 represents a proxy for satellite aggregation.

Fig. 6a is identical to Fig. 4a. Replotting it is unnecessary. 

Overview

The joint relationship between LWP and cloud droplet number concentration (CDNC) is commonly used to infer the LWP adjustment to CDNC changes resulting from changes in CCN. This relationship has been assessed in satellite retrievals, but such retrievals depend on key assumptions in order to estimate CDNC and LWP. Biases associated with these assumptions are evaluated in LES simulations of the frequently analyzed DYCOMS RF02 case. Satellite retrievals of CDNC are high biased, and if constant values are used for adiabaticity and other inputs as commonly done, CDNC increases from cloud cell cores to edges, opposite of simulation output. Allowing those variables such as adiabaticity to vary based on model output produces the proper CDNC spatial pattern, though still with a high bias. The satellite retrieval LWP is unbiased overall if averaged across cells, though it tends to be overestimated in cell cores and underestimated on cell edges. For a set CCN concentration, LWP increases approximately linearly with CDNC on a log-log scale, and combining across different CCN simulations, the negative slope of the inverted “v” LWP-CDNC relationship is not produced. If adiabatic satellite retrievals of CDNC and LWP are used, inverted “v” shaped LWP-CDNC relationships are produced. Introducing 20% uncertainty to satellite retrievals of cloud optical depth and effective radius does not alter the overall LWP-CDNC relationship. The overestimate of CDNC is particularly biased at relatively low LWP. The authors thus argue that a good constraint on CCN is required because CDNC cannot be used as a proxy in such situations for representing LWP adjustments. Overall, the study presents compelling evidence that the negative slope portion of the inverted “v” LWP-CDNC relationship may not be caused by LWP adjustments to CDNC.

This is a very informative study that is thorough in its methods. Its conclusions should aid improved interpretation of satellite retrieved cloud microphysical properties that are used to infer aerosol-cloud interactions. More studies like this are needed to sufficiently understand and design proper model-observation comparisons. I don’t have any major concerns with the study but have some minor comments, mostly related to clarification, that I think could improve the study if addressed.

Comments

1. Lines 22-24: This sentence would be more informative if it explicitly stated what the counteracting physical processes and satellite retrieval challenges were with respect to the studies cited.
2. Line 38: I believe “higher boundary layer” should be “boundary layer depth change”.
3. Line 42: State what the increased CDNC at the cell boundaries is relative too, presumably real CDNC values?
4. Line 45: Is the estimate of the aerosol effect on LWP referenced here based on joint distributions of LWP and CDNC or how is the true effect quantified from which the bias is determined? Beyond the question of whether the LWP-CDNC joint distribution is accurately retrieved, there is the question of whether it can even be used to estimate LWP adjustment when derived from Eulerian statistics, e.g., considering that a process such as the entrainment-evaporation feedback can take several hours to days to alter the LWP in response to a change in CDNC along Lagrangian trajectories (e.g., Christensen et al. 2023, 2024).
5. Line 108: Clarify that these parameters are not necessarily constant even though they can be and often are assumed to be constant.
6. Line 143: I see low biases in LWP at the cloud cell boundaries and high LWP biases in the cell centers.
7. Figure 3 and discussion about it: The positive slope of LWP with respect to CDNC is often assumed to be caused by precipitation suppression. That could be the case when combining multiple different CCN simulations, but for a single simulation, the positive slope is simply representing the horizontal structure of the cell where air moves from the high LWP, high CDNC core outward toward low LWP, low CDNC cell edges, correct? Is it worth clearly distinguishing between these 2 causes and interpretations?
8. Line 161-162: Making adiabaticity the same in a model and satellite analyses also brings CDNC-LWP relationships into better alignment (e.g., Fig. 21 in Varble et al., 2023).
9. Lines 193-194: I don’t completely follow the argument here regarding subadiabatic points not contributing to the LWP-CDNC inverted “v” shape since it is referencing the relationship of LWP with CCN rather than CDNC in Figure 5. Adiabaticity will impact the CDNC calculation, but CCN is not impacted, so what allows for the connection of Figure 5 to the LWP-CDNC correlation?
10. Lines 203-204: This is true but if you combine Figures S12-14 like was done for Figures 4-5, could an inverted “v” LWP-CDNC correlation be produced?
11. In the supplemental material, it mentions that a negative LWP-CDNC slope is produced when combining different times (cloud types) and CCN concentrations, which seems important, but I didn’t see it highlighted in the main manuscript (although maybe I missed it or misinterpreted the supplemental text).
12. Supplemental text line 80: what is the correction factor introduced?
13. Figure S5: The CER plot is saturated from the maximum value of 10 um. Perhaps extend the CER range to show more structure. Also, the LWP Equation (3) panel uses a color scale that is not ideal for anomalies because it isn’t clear where the zero crossover is. I suggest a diverging color scale or a contour of the 0 line (if not too noisy).
14. Supplemental text lines 92-93: Larger biases are seen at cloud edges, but are the cores biased in the opposite direction too?
15. Figure S10: Why does the color bar have such a large range? It’s difficult to see structure in the plots because of this.
16. Supplemental text lines 140-141: If using words like “extreme” and “very” here, I suggest adding numerical values to reference since interpretations of these words varies. Further, I suggest softening this sentence a bit to say that the satellite-retrieved inverted “v” can be caused by these biases rather than it is caused by them since this is based off of a single LES case.

References

Christensen, M. W., Ma, P.-L., Wu, P., Varble, A. C., Mülmenstädt, J., and Fast, J. D.: Evaluation of aerosol–cloud interactions in E3SM using a Lagrangian framework, Atmos. Chem. Phys., 23, 2789–2812, https://doi.org/10.5194/acp-23-2789-2023, 2023.

Christensen, M. W., Wu, P., Varble, A. C., Xiao, H., and Fast, J. D.: Aerosol-induced closure of marine cloud cells: enhanced effects in the presence of precipitation, Atmos. Chem. Phys., 24, 6455–6476, https://doi.org/10.5194/acp-24-6455-2024, 2024.

Varble, A. C., Ma, P.-L., Christensen, M. W., Mülmenstädt, J., Tang, S., and Fast, J.: Evaluation of liquid cloud albedo susceptibility in E3SM using coupled eastern North Atlantic surface and satellite retrievals, Atmos. Chem. Phys., 23, 13523–13553, https://doi.org/10.5194/acp-23-13523-2023, 2023.