I think this manuscript is within the scope of GMD and does constitute a contribution to the field. The authors showcase (briefly) some recent improvements in an atmosphere model. They then proceed to applying some statistical analysis on the improved model.

The manuscript is decently written, but can be challenging to read. Most figures can be improved. The manuscript covers two distinct topics that at times come across as unrelated. Perhaps this could be two separate manuscripts focused on two separate topics? The model evaluation part is brief and incomplete; likewise, the maximum covariance part only touches the surface of the topic it is tackling. 

I have written down some reactions, comments, and questions. I hope the authors find them helpful in revising their manuscript (if they choose to do so). I don't see any major issue in this manuscript and so I will be happy if it is published in the near future :) 

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Lines 63--69: Not sure what this paragraph adds to the conversation here. Consider adding more context why this is needed or simply deleting.

Lines 76--77: This may warrant further explanation. As a somewhat informed reader, this left me wondering: What's the effective resolution of this model in sum? At what resolution are things like macrophysics and microphysics schemes are done? It is fine to refer to citations; segueing into this with a "however" left me wondering about several questions. So, I would either consider expanding slightly here (e.g., why you felt the need to point out this specific piece of information) or simply delete to avoid reading getting stuck like I was.

Line 84: Why brief? Isn't this manuscript supposed to detail these updates?

Lines 85--94: Since the Patridge et al. manuscript is in preparation, I worry this entire paragraph (section) lacks substantiation. On the one hand, someone like me having read the studies cited a few times in the past can nod in agreement about the assertion that the 2014 scheme is likely better. On the other hand, how can you convince others that your assertions are sound besides taking your words for it? A potential avenue is weakening the assertions and citing counterarguments (e.g., the meta-modeling study in doi:10.1175/JAS-D-15-0223.1 can be interpreted as saying these models perform similarly an older comparison study doi:10.1029/2011MS000074 show differences between schemes). 

Lines 95--109: This section may benefit from rewriting and clarifying. As an example, the second sentence seems incomplete, a sentence has a misplaced comma interrupting the flow and meaning of it, and finally the citation style is inconsistent (years sometimes are surrounded by parentheses; other times they are not). More substantially, this section left me wondering about dust aerosol. How is it represented and emitted? How do these changes impact it?

Line 122: Perhaps use a more conventional notation for the "approximately bigger than" unless you mean something different.

Lines 134--136: Any reasoning for this choice to parameterize this process?

Lines 145--148: These tunings may require some more detail and clarification. For example, I have no idea what RPRCON is. And second, the last sentence comes out of nowhere. Third, I have no idea what you meant by cloud forcing --- you mean cloud radiative effects like you refer to them later or something different? Altogether, the section left me wondering: What did the other preceding changes do to the forcing? Is the ~1 W/m2 solely from these three tunings or from everything together?

Line 181: What is meant by rotated here?

Line 189: What is meant by an invariant quantity here?

Lines 190--214: I do not necessarily see this as needed in the main manuscript, but if the authors deem it necessary, I would advise to reorganize the section. I would start with the raw data X, Y (as an aside, what do a x n and b x n actually mean?) and then develop Ax and Ay using the SVD before defining the correlations. I would also add --- in equation form --- what "Corr" means. Finally, I would not have hom, het, Corr, and SCF be italicized.

Lines 216--220: Is this AMIP run completely compliant with published protocols? If not, state deviations. It would be good to simply state the full description of forcers and settings. Also, 1980--2020 AMIP vs 1980--2018 CMIP6?

Figure 1 and associated text: In the bottom panel in the figure, please consider having the color bar go from -0.25 to +0.25 (i.e., symmetric). Also, any guess which processes (line 240) have led to the changes you're describing?

Figure 2 and associated text: Consider having the same y-axis for all (maybe 0.0 to 1.0) and consider adding axis labels.

Figure 3 and associated text: Maybe I am more optimistic than you, the model seems to be doing okay for stratocumulus regions. Maybe show the spatial distribution of the difference if you want to highlight the difference?

Figure 4 and associated text: I would have appreciated seeing the total means on these figures like you showed earlier. Again, consider having the difference plot with a symmetric color bar (-70 to +70 or so). Given the plots as well as the discussion, maybe it is worth showing the combined (SW + LW) CRE?

Figure 5 and associated text: As you say, these plots should be remade with better color bars. Also, because of the significant differences (underestimation by half), it may be worthwhile to give more reasoning and context. How worried should you be about this weakness of the model? Are there any tunings or strategies to remedy the situation? Have other modeling centers faced similar problems?

Figure 6 and associated text: What's going on with MODIS near the poles? If no values are available there, maybe it is worth denoting that with white (like in Figure 7) as opposed to 0. Also, consider extending the color bar to 0.

Figure 7 and associated text: Oh, so this comparison kind of makes no sense. Why not add cloud-top diagnostics to your model? The MODIS simulator can do that or a simple cloud-top algorithm can do the job too. I would remove this comparison if there is no better comparison. There is no need to muddy the water with badly constructed comparison here in my opinion.

Figure 9 and associated text: I think it would be better to redo the figure and ensure the color bars are the same for all AOD panels on the one hand, and all cloud fraction panels (ideally, 0 to 1) on the other hand.

Line 393 and thereabouts: You're essentially describing the aerosol effective radiative forcing, but somehow only discussing two of the well known mechanisms. An example of a missing one is precipitation suppression. How did you exclude it from your two hypothesized processes? I am glad you're citing the Gryspeerdt et al. 2019 paper, but I am not sure your text gives a proper summary of the convoluted nature of all of this... 

Figure 14: Is the figure spreading on two pages intentionally? Maybe reorganize it so that it fits on one page? 

The entirety of section 4: Please say more about the data sampling and processing. How many years were included? When the data was put in the statistical analysis framework, what was the frequency of sampling or was it just monthly/yearly means? What are the implications? From Figure 13, it appears you're using 40 years worth of data, monthly averaged? Maybe this was somewhere in the text but I missed? 

The entirety of section 4: Maybe putting lat/lon ticks (and their values) on the figures will be helpful?

The entirety of section 4: Maybe doing the same analysis on both model versions (the improved and the one before it) will be interesting?

Line 434 and thereabouts: Would you mind elaborating regarding what you mean here? For example, I think studying things at cloud top is likely better than studying them elsewhere; at the end of the day, that's where the radiation is reflected, no? Another, how do your model runs avoid the sampling issues related to simultaneous aerosol and cloud retrievals? How are you analyzing/sampling your model data?

Lines 437--438: Say more. Why could it be a good proxy? What makes you say so?

Lines 449: Based on what specifically can it be attributed? What you showed in the maximum covariance analysis? I am not sure if that's as clear cut as you're saying here, so I encourage further discussion.

Code and data: Thank you for making your analysis scripts readily available! Maybe mention that you're also including the MC code out there?

This study illustrated the importance of aerosols, clouds, and their interactions in the climate system and the potential impact of accurately modeling these processes on the uncertainty of future climate projections, and analyzed in detail the latest improvements in aerosol and cloud properties and maximum covariance analyses in the EC-Earth3-AerChem model. This study is of great significance for improving the accuracy of global Earth system models in climate prediction. It is recommended that the manuscript can be published after minor revisions.

1. In studying the covariance of AOD and CD, why was the maximum covariance analysis method used? What are the advantages over other analysis methods?

2. The spatial distribution of the difference between ECE3-FORCeS and observations can be added in Fig. 1 to reflect the comparison between simulations and observations.

3. The article mentions in section 3.1 that the ECE3-FORCeS model better reproduces the spatial distribution of the total cloud amount, but is biased higher in the polar regions and explains that it is due to low clouds. Could you explain more about the bias. What caused the bias to be much higher in the polar regions than in the equatorial and mid-latitude regions?

4. It looks to me that the changes in cloud fraction are mostly at high latitude regions. Does that mean the updates within FORCeS only work for limited regions?

5. Line 380: Please add relevant references.

6. It is recommended that the conclusion section further explicitly summarize the contribution of model improvements to climate prediction and the innovation and limitation of this study.