This manuscript by Yuan et al. reports a new algorithm to quantifying the heterogeneity in aerosol hygroscopicity, by using the data from H-TDMA. Average per-particle species diversity Dα, the bulk population species diversity Dγ, and their affine ratio χ was calculated as three indices to describe aerosol heterogeneity. These data are valuable and the figures presented in the paper are good description of the research. Therefore, I would suggest publication after the following comments have been addressed.

Specific comments:

Line 28-29: “Considering that ambient aerosol particles in an aerosol population differ dramatically in chemical composition due to the complex sources and aging processes.” The authors might find the following paper relevant findings from individual particle analysis by electron microscope and models. For example, recent studies focused on different kinds of mixing states such as Journal of Geophysical Research: Atmospheres 2022, 127, (5), e2021JD036055; Atmos. Chem. Phys. 2021, 21, (23), 17727-17741; Environmental Science & Technology 2021, 55, (24), 16339-16346."

Line 43: may change from “black carbon (BC)-containing” to “black carbon-containing (BC-containing)”

Line 48: “most literature is” should use plural form

Line 50: “we propose” -> “we proposed”

Line 59: “propose” should be “proposed”

Line 52: “will describe” should be described

Line 53: “will be” should be “was”

Line 54: “are discussed” should be “were discussed”

Line 55: “comes” should be “came”

Line 81: why the font of “TDMA_fit” is different?

Line 139: “ageing” is different with other “aging” in your article, here should be unified

Line 154: “ranges 1 to 2” should be added “from”

Line 155-156: “it is 1 when … while 2 when …”, the grammar here is strange. May add “the” or “be” behind “while”

Figure 2: Does blue represent the LH or grey represent the LH? Need explanations here.

Line 186: why chose 110 nm aerosol? Need reasons here.

Line 190: why is χ high at night? Here needs more explanations.

Line 217: remove “will”

Figure 6 (a) and (d) need a legend

Line 230: “Aitken mode” Why capitalize here?

This paper presents a method of how to derive metrics of diversity of a particle population with respect to hygroscopicity using H-TDMA measurements. The authors also demonstrate the use of their method by applying it to a dataset from the ambient atmosphere. This work fulfills an important need in our community, and I commend the authors on their contribution. So far, it has been very challenging to quantitatively derive these metrics from measurements since they rely on the quantitative knowledge of per-particle composition which have been challenging to obtain. Given that H-TDMA datasets have been collected in many different environments and could all be analyzed using the method described in this paper, this work has a great potential for deepening our understanding of aerosol mixing state in the ambient atmosphere and for providing much needed data to validate mixing-state-aware models.

The paper is concise and well-structured. It fits within the scope of ACP and I recommend publication after a few minor comments are taken into account.

1. line 21: The statement that heterogeneity in hygroscopicity is not considered in models is a little strong. Sectional models do capture the dependence in (average) hygroscopicity with size and modal model capture the variation in hygroscopicity for different sub-population. I suggest saying “not fully considered” or “not adequately considered”. In fact, it is the case that many modeling approaches do provide some information about how hygroscopic and non-hygroscopic species are mixed (e.g., MAM4 in CESM) but so far, suitable measurement data has been lacking to validate these predictions. Developing a method to provide this kind of data is the contribution of this study.
2. Nitpicky terminology comment: The term “aerosol” already refers to a population, so there is no need to say “aerosol population”.
3. Line 32: Where the kappa-pdf is introduced would be a good place to cite Su et al., 2010, Atmos. Chem. Phys., 10, 7489–7503, 2010, where a general concept and mathematical framework of particle hygroscopicity distribution for the analysis and modeling of aerosol hygroscopic growth and CCN activity is presented.
4. Explanation starting at line 104: This applies for one particular particle size, I suggest making this clear at the start of this section.
5. Equations 2 and 4: add limits to the integral.
6. Equations 8 and 9: suggest to not use ii as the counter variable. Use k or \ell, for example.
7. Line 141: Can you explain a bit more why kappa for the coarse mode is assumed to be 0? Couldn’t you have non-hygroscopic primary particles in the coarse mode that have aged and acquired some coating materials that make the more hygroscopic (or at least increase their kappa to > 0)?
8. Line 170-173: These sentences are unclear, can you please rephrase?
9. In the introduction/conclusion, you could stress more explicitly that existing H-TDMA datasets could be analyzed using this algorithm. This could have a large impact on how we use and think about these datasets and will help providing data for constraining models.