This paper constructed a global aerosol fine mode fraction (FMF) dataset using combined physical and statistical methods. The dataset showed overall superior performance over existing satellite products. This is a good paper, providing a useful set of information to study the distribution and potentially climate impact of anthropogenic aerosols. I recommend publication of the paper after addressing a few questions. Although my recommendation is a major revision, the comments should not be difficulty to fix, but I think will increase of the credibility of the method and data.

Specific comments:

1. A 10 fold cross validation seems too simple. It would be interesting to see how the method perform on different sites or different years. Therefore, an out of site validation (e.g., predicting FMF at AERONET sites whose data are not used for training) or out of period validation (i.e., using part of the time series as training and the rest as validation) is highly recommended to increase the robustness of the results.
2. How are the input variables selected? Are they all necessary or there might be some redundant inputs? Since MODIS AE is used as input, I don’t see how some meteorology variables, such as boundary layer height, winds, RH are physically related to FMF.
3. Although the proposed model produces the best FMF among different satellite products, there is still an obvious bias compared with AERONET. Also at some sites the agreement is low, such as Australia, North Africa, Mid East, etc. These all seem to be desert regions, could this be related to surface, or optical property assumption for non-spherical particles? Some more in-depth error analysis would be helpful to fully evaluate the performance of the technique.

The authors need to address the following major points.

The motivation of this manuscript is to address the following issues raised by the authors, the first issue is the Chen et al (2020) method is not applied on a global scale, the second issue is that ‘Zhang et al (2016) noted that satellite –measured multi-spectral reflectance of ground-based data alone was not sufficient to retrieve FMFs with high accuracy’ (the meaning of this sentence is not quite clear to me), my interpretation is that the use of (only) spectral information from satellite measurements is not enough for the retrieval of FMF, this two reasons are not really solid enough to continue the work proposed in this manuscript. Both manuscripts mentioned above focus on the original level 2 spatial scale (with a very quick look at these two papers), while this work focuses on the level 3 data, the average of spatial resolution from kilometre to degree can make all problems significantly easier, both technically and scientifically. Even later, the authors point to their own previous publication (Yan et al., 2021b) and claimed ‘As shown by Yan et al. (2021b), the global land Phy-based FMF is still unreliable.’, in which the authors even started ‘seasonal FMF characteristics and trends’ analysis using the ‘unreliable’ dataset. This is quite misleading for the understanding of the motivation for the developments in this manuscript, even from the very first step. I think the work should start from level 2 dataset rather than level 3.

The second major point the authors highlighted is that the method is a combination of physical and deep learning approach, this is also quite confusion. As presented in section 2.4, this dataset is created by the new algorithm described in this manuscript for the first time, however, my feeling is that it is a mixture of previous publications without a clear description of the method itself.  Meanwhile, the authors mark this paper as a 'Data description paper' in the submission. I never saw a 'Data description paper' without a clear and solid 'Method description paper' before. The key physical part is the LUT-SDA, described in equation (1). Firstly, I am confused why we have two af here? Second, I can not understand how the combination between the physical method and deep learning is achieved. To my personal view, it is still a deep learning method with certain parameters from some physical derivation, however, your major input, aerosol optical thickness, is derived from a physical model (MODIS retrieval algorithm) as well, you cannot claim it is a combination of physical and deep learning method becuase some inputs for the deep learning is from a product derived from a physical method.

The third major point is the comparison between different satellite products, the authors need to be aware that it is really the same parameter in the comparison or not, ‘bad’ agreements between satellite FMF products and the AERONET FMF product do not reveal anything because these FMF are not the same FMF due to different assumptions in particle size distribution and the ‘cutting criteria’ in the level 2 retrieval process, the FMF derived from this paper is somehow with knowledge (maybe certain inputs as well, not sure about it) from AERONET, it is not surprise at all to have a better agreement with AERONET measurements later. It really makes no sense to include the MODIS comparison since it is already removed  in the new version of dataset. The remove of FMF product in MODIS dataset also indicates how uncertain such a parameter can be.

The fourth major point is the application of this dataset, my personal view is that it is too early to sell it as a dataset which is mutual enough for a trend analysis, especially since the application of (both fine and coarse as total) aerosol optical thickness is still quite questionable. Even at the last part of the manuscript, the authors claim some significant trends from the new satellite product are not revealed by AERONET measurements due to the scale issue, this simply reveals the limited representative of these AERONET sites in your regions, rather than anything with respect to the satellite data quality.

In this manuscript, the authors developed and presented the new dataset of fine-mode fraction over global land during 2001-2020. The method they proposed is a hybrid physical and deep learning method, which is the physical model output calibration with DL. Generally, this FMF dataset can be useful for studies of anthropogenic aerosol and also the PM2.5 estimation. The paper is written in a consistent workflow and the inter-comparisons in terms of different methods and official products are very comprehensive. However, I think some concerns and issues need to be addressed.

Major comments:

1. We know that in deep learning modeling, the test dataset should be independent of the training dataset to avoid the data leakage, therefore my first concern is that the validation for FMF is independent. In Figure 3a, the authors use the AERONET data for training and testing. A more rigorous validation should be added. My suggestion is to conduct independent validation by FMF from other sources of FMF observations, or the Phy-DL FMF is only reliable over the pixels with AERONET sites.
2. My second concern is the use of meteorological data, which are very different inputs compared to previous studies. I can see the meteorological data are widely used in fine particulate (PM2.5) retrievals because meteorology has statistical correlation and physical interaction with the PM2.5. While in this study, the author simply explained their reason as “the impact of meteorological factors”, and what is this “impact” to make them use the meteorological data is not mentioned. For example, the temperature is introduced as input, I don’t see the influence of temperature on FMF or how it can improve the retrieval accuracy.
3. For the physical model, although LUT-SDA has been used in other studies before, it is better for authors to emphasize its disadvantage with more details, rather than just listing its applications.
4. Last I think the uncertainty of this Phy-DL FMF should have a more in-depth discussion. The major content in Results is the inter-comparisons of different results in terms of different methods and FMF products, which are good, but there should be more discussion on the sources of uncertainty of this Phy-DL FMF. For example, the Figure 6 compared performance over different land types and barren land has the worst performance for all three FMFs, so the authors could discuss how the physical characteristics of barren land affected the retrieval performance.

Minor comments:

1. in Line 44. The “performed previously,; currently” should be “performed previously; currently”
2. Figure 1. AATSR and VIIRS also provide FMF products but they were not discussed in this paper. The reason for using MODIS rather than AATSR and VIIRS should also be mentioned.
3. in Line 56. The Yonsei Aerosol Retrieval algorithm (Choi et al., 2016) is not for MODIS land-based FMF retrievals, it is for GOCI.
4. in Line 103. There is no direct relative humidity data ERA5. Usually it is calculated from dew point temperature.
5. in Line 104. The “ERA5” mentioned for the first time without given the full name.
6. in Line 210. The “yr” mentioned for the first time without given the full name.
7. in 3.2. Both past and present tense showed in this part when describing the same thing. For example, “in India, FMFs are noticeably higher in autumn and winter, especially in Northern India (i.e., the Indo-Gangetic Plain), where the FMF was greater than 0.87”, and they should be either past or present tense.
8. in Figure 6a. Why do you choose to compare the result in bins of FMF?
9. in Line 318 and 320. “eastern China” or “Eastern China”?
10. I noticed the plurals appeared randomly, for example, it is “AERONET FMF” or “AERONET FMFs”. Make sure the plurals are consistent in the paper.