General comments:

The current work evaluated the several mixing state indices (χs) derived from a global modal model (CESM2/MAM4) by a global distribution of χs derived from the machine learning (ML) model based on the results of the mixing state resolving model PartMC/MOSAIC. The authors also compared their χs against those obtained from the field observation data. This is the first study to evaluate the spatial distribution of χs in models, which are currently used for the climate predictions. Let me congratulate the authors to achieve this. The manuscript will be acceptable after the authors address the following couple of minor comments, general and specific ones.

1. The differences of χs between CESM2/MAM4 and PartMC/MOSAIC-ML should originate from different aerosol representations and different rates in aerosol dynamical processes such as rates of secondary aerosol formations, condensation/evaporation, and coagulation. However, the authors only addressed the former, the difference in aerosol representations. Is it because the latter (difference in aerosol dynamics processes) is negligibly small with compared to the former (difference in aerosol representations)? If so, please describe how the authors quantified or estimated them. Are the condensation/coagulation rates or size distributions of aerosols of the two models similar with each other?
2. How the existence of coarse mode particles in CESM2/MAM4 can make the global χs distributions different from those of PartMC/MOSAIC-ML which does not consider the existence of coarse mode particles? A part of secondary gases condenses to coarse mode particles such as mineral/anthropogenic dust and sea salt, and thus neglection of coarse mode particles can cause overestimation of condensational growth of fine mode particles. Is this effect negligibly small in the current assessment?

Specific comments:

3. Uppercase letters are used for the abbreviations of aerosol species in Sects. 2 and 3, such as SOA, POM, and BC, while lowercase letters (pom, dst, ncl, soa, and so4) are used in the panels. Any reasons? “soa” in panels and tables are different in definitions from SOA in the main text?
4. Figure 1 is not referred in the main text.

The authors verified the global distribution of aerosol mixing state represented by modal models, focusing on comparing the calculations from ML model with MAM4. The author concluded the current model simulations on aerosol mixing state had large and zonally structured errors, and ML model trained on high-detail particle resolved simulations were more representative for realistic aerosols. The technical analysis is of reasonably high quality. The interpretation and discussion could benefit from some stronger quantitative analysis. The content is suitable for publication within the scope of ACP, while some revisions are required. Please see detailed comments below.

General Comments:

Although ML model trained on high-detail particle resolved simulations is better than MAM4 for simulating aerosol mixing state, it still has some uncertainties which have not mentioned in this work. Taking the mixing of optically absorbing and non-absorbing species (χ_o) for example, the ML simulations in this work are in the range of 50-90%, significantly higher than the realistic aerosols due to greatly underestimate of BC-free particles in some regions. Earlier work (Figure 8 in Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2017-222, 2017) reported that 85%-90% of particles in the accumulation mode were BC-free particles, and internally mixed BC only accounted for 5-10% during summertime in North China Plain. The significantly underestimate of BC-free particles in ML simulations in this work is most likely attributed to irrespective of the processes of new particle formation and growth from Aitken mode to accumulation mode, which are hardly associated with particles (i.e., BC and POM) from primary emission. In term of the mixing of primary carbonaceous and non-primary carbonaceous species (χ_c), the processes of new particle formation and growth will cause a similar uncertainty like the χ_o. Therefore, in the regions where particles are dominated by new particle formation and growth processes, the methods used in the ML simulations in this work should be improved. The author should clarify this uncertainty as discussed above and give some suggests how to improve their ML simulations.

Specific comments:

Page 1/Line 7: The abbreviation can not be used here. Please give the full name of MAM 4.

Page 4/Line 88: Why the authors ran the model for the year 2011 rather than more recent years?

Page 5/Figure 1: In terms of the size distribution of the four modes (i.e., left panel), please show the diameter values of x-axis. If so, the readers can clear know the size ranges of the Aitken, accumulation, primary carbon and coarse modes.

Page 6/Line 133: not “rather then”, here should be “rather than”.

Page 6/Line 140: using a terminology as “mass absorption cross section” rather than “a mass absorption coefficient”.

Page 7/Line 164 and Line 176: For the input parameters of primary emissions of gas phase, the authors consider the NO₂. Why not considering the nitrate in the aerosol species?

Page 7/Line 182: Please claim how to calculate the errors, namely 5% for χ_o and 8% for ­χ_c and ­χ_h. What are the sources of the error? Why so small errors for model simulations?

Page 11/Line 248-250: The authors claim that their simulations of ML model can not well represent the mixing state of sea salt. This will cause how much errors in the ocean regions?

Page 13/Line 279-284: The authors state that the threshold is set to a relatively large value in MAM4 and their results are a reflection of this fact. Could the authors provide a reasonable value or range of the threshold based on their results?

Page 15/Line 326-327: Here do not need the full name of χ_o, ­χ_c and ­χ_h.

Page 17-18/Figure A1 and Figure A2: The authors use a1, a2 and a4 represent different modes? Why is there no a3?

General Comments:

Zheng and coauthors have undertaken a novel comparison of predicted aerosol mixing state between their highly-detailed particle-resolved model and an existing Earth system model (CESM2). The authors are able to leverage the impressive numerical formulation of PartMC-MOSAIC and the machine learning approaches they have developed to provide some context as to how well the widely used modal method is able to capture aerosol mixing state. The paper is especially well-written, the content is well-organized, figures are well-constructed. In short, the manuscript was a pleasure to read. I encourage ACP to publish this paper, considering it is one of many steps toward a more sophisticated future landscape of aerosol modeling approaches. However, I do have a couple of topics I would appreciate the authors commenting on in the manuscript to make sure they are resolved or documented before moving on from this study.

Major Concerns:

1. The relevance of the selected ML input parameters for predicting aerosol mixing state is clear, especially for an exercise where one is feeding the inputs from actual measurements to model. However, in this study, it is the CESM2 fields that are being used to specify the parameters, including the concentrations of each aerosol species. Since the aerosol formulation in the CESM2 has an impact on the speciated aerosol concentrations (e.g. the authors mention the example of BC transferring to the mixed mode and depositing faster), how can the authors be confident that the ML fields in Fig. 3 are actually realistic if they are based on CESM2 model data that they are arguing is at least partially corrupted? Forgive the unproven hypothetical here, but in the extreme, couldn't it be possible that the MAM4 model gives erroneous PM species concentrations that compensate with an erroneous framework to yield an accurate mixing ratio field? The authors provide helpful discussion in section 5.3 to address this, so that extreme example is unlikely. But would they consider adding some results that show the variability in their ML fields with reasonable variation in the underlying inputs, perhaps based for input ranges informed by the biases of the CESM2 speciated PM predictions?
2. Additionally, would the authors please explain why other parameters relevant for sources are not appropriate for the ML input? I'm thinking of data like land use, human population, and wind speed that could help inform dust, carbon, and sea spray mixing state. If it's been documented, as the authors say, that the mixing state parameter goes down close to sources, why not use that information in this exercise? Maybe this would require running the ML training cases for longer than 24 hrs to get a signal for aging (i.e. distance from sources) on mixing state?
3. My main concern with this study is that the authors have chosen to focus on surface data from the global model, and yet are interested in impacts on radiative forcing and cloud-aerosol interactions. Certainly, to know the true scope of the potential problem in misrepresentation of aerosol mixing state, the full atmospheric column needs to be taken into account.
4. Do the authors have any idea how PartMC-MOSAIC ML performs with scavenging in place? The ML input parameters don't include hydrometeors or cloud cover as a marker for aerosol removal. It seems like the impact of a major process like cloud scavenging will be extremely important to understand from at least a few points of view: 1) impact on ML representation of PartMC-MOSAIC and 2) divergence between ML and MAM4 in the context of clouds/fog.

Minor Suggestions/ Typos:

1. Abstract: I recommend adding a few words or a sentence to the end of the abstract that explicitly connects back to the main motivation, which I assume to be a better quantification of radiative forcing and aerosol-cloud interactions. How significant is the 70% modal model bias for those aims?
2. Page 2, lines 38-43: A related issue is the transfer of particles from smaller modes to larger ones during growth, even if this is among "pure" modes. Also, removal of particles due to scavenging by cloud activation is difficult to reconcile.
3. Page 4, line 88: Please add an explicit reference for the MAM4 long-range transport bias.
4. Fig. 1: Legend obscures data in right panel.
5. Section 3.3: I'm sure there are many applications for grouping surrogate species in different ways, but I think an important one worth mentioning is heterogeneous reactions on surfaces of (e.g.) primary dust or sea spray particles. There is probably much overlap with the hygroscopicity mixing state index. If the authors agree, perhaps a comment could be added to that effect.