Variations of the density of ambient black carbon retrieved by a new method: importance to CCN prediction
 ^{1}College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China
 ^{2}School of Civil and Environmental Engineering, Harbin Institute of Technology (Shenzhen), 518055 Shenzhen, China
 ^{1}College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China
 ^{2}School of Civil and Environmental Engineering, Harbin Institute of Technology (Shenzhen), 518055 Shenzhen, China
Abstract. The effective density of black carbon (BC) is a crucial factor relevant to its morphology and mixing state that would add uncertainty in evaluating its climate effect. Here, we develop a new method to retrieve the effective density of ambient BC combining field observations with the Köhler theory. The uncertainty of the new retrieval method was evaluated within ±30 %, which is primarily caused by assumptions of the hygroscopic parameter of organics and the fraction of primary organic aerosols in nonhygroscopic or hygroscopic mode. Using the new method, we obtain that the ambient BC density during the campaign varies widely from 0.14 to 2.1 g cm^{−3}, with a campaign mean density of 1.11±0.54 g cm^{−3} for internallymixed BC that accounts for 79±18 % of total BC particles. The retrieved values fall within the range of typical density of internallymixed BC reported in the literatures. We further examined the sensitivity of cloud condensation nuclei (CCN) number concentrations (NCCN) prediction to variations of BC density, showing an uncertainty of −28 %~11 % in calculating NCCN at supersaturations of 0.2 % and 0.4 % by varying the BC density within the retrieved ranges. We also find that the NCCN is more sensitive to the variations of BC density when it is <1.0 g cm^{−3}, illustrating a necessity of accounting for such effect closer to source regions where the BC particles are mostly freshly emitted. The CCN closure achieves when introducing the retrieved realtime BC density and mixing state. This study provides a unique way of utilizing field measurements to infer ambient BC density and highlights the importance of applying varying BC density values in models when predicting CCN and assessing its relevant climate effect.
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Jingye Ren et al.
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RC1: 'Comment on acp2022542', Anonymous Referee #1, 22 Sep 2022
The manuscript presents a method for retrieving BC density and implications for CCN prediction. Since the BC density is difficult to measure, it is worth trying to develop new methods for retrieving accurate BC density from available measured data. It is quite interesting. However, more work needs to be done with the manuscript before it can be accepted.
 It is not clear how the mixing state and the density of BC are retrieved based the description in the methodology section (2.2)?
 The definition of mixing state is especially not clear. What exactly the mixing state is referred to? Internal? External? Do the authors mean the mass size distributions for the internal and external BC?
 The density is calculated by equation 8, so in the calculations, there must be lots of assumptions for the relevant parameters. How each parameter in the equation is determined? Those need to be clearly described. It is obviously not well illustrated in the current version.
 The authors attribute the density fluctuations of the internally mixed BC and the bulk BC to the mixing state and the rapid aging from the variation of emissions (Fig. 3b&c). However, how the changes of emissions affect the parameters contributing to the density remains unexplored. For example, how the parameters in equation 8 are affected by changing the emissions? In addition, it is difficult to discriminate the inBC and exBC in Fig. 3a. It is suggested to change the color of the inBC to increase the contrast between them.
 Pertinent to comment #2, what factors determine the retrieved BC density? Are they explicit in equation 8? How the correlations between those factors and the BC density? Can the authors explore more on this?
 The calculation of critical size is based on pure water assumption for the surface tension and water density, which may cause uncertainties. The authors should discuss the uncertainties associated with the assumption.
 In Fig. 5, what is the measured Nccn. What method is this based on? Are they the same for the Nccn in Fig. 5 and Fig. 6? How are the differences between the CCN number concentration predicted based on the retrieved BC density and based on the HTDMA? Can the authors discuss more on this?
 Minor comments: there are a lot of typos, illsentences which need to be cleared in the revised version.
 Title: I am not quite sure this is a new method
 L4041, such an effect
 L44: applying varying BC density, an awkward phrase, please change it
 L50: The lightabsorbing capability
 L57: well understood
 L61 and others: While after aging, this is strange since it is just one sentence. There are some more the same issues throughout the manuscript.
 L63: The BC structure.
 L71: the average BC density
 L74: than that internal/ aged BC …, seems a broken sentence
 L76: internally doesn’t need a hyphen after the word
 L78: climate effect
 L81: particle hygroscopicity
 L85: was found caused by?
 L87: yet accounted for
 L94: reference cited, format is not consistent
 L116: change “Then” to “Subsequently”
 L120: Here, four diameters
 L126: by using, “by” should be deleted. Please check throughout the manuscript
 L128: et al., 2009. I am not sure this can be cited like this way. Please check throughout the manuscript
 L141, where Gf is …. This still belongs to the above paragraph, why it needs to be dented? Check all the occasions.
 L157158: assumed mixed with the other?
 L158: And thus to “Thus”
 L160: externally mixed
 L174: mass size distributions was modeled as?
 L182: by minus? by subtracting
 L188: is with an assumption of to assumes
 L193194: which showed an independence on particle size when the Dp >100 nm during the campaign period (Fan et al., 2020), was averaged and applied for the retrieval. It is hard to understand what this sentence means
 L209: in equation (7), no article “the”. Check all occasions
 L219220: were taken from previous studies
 L221222: assumed to be
 L222: The values of … was?
 L235: unlike inorganics, which the hygroscopicity, what is “which” referred to?
 L272: for calculating the …
 L273: with the assumption of to assuming
 L278: internally and externally mixed
 L280: the atmospheric aging process
 L287: with both those?
 L289/303/315: internally mixed
 L305: The density of the InBC during daytime was
 L309: The slight decreases
 L313: The diurnal cycles in BC density are consistent with those measured
 L322: McMurry
 L330: Mean probability distribution function (PDF) of the density of bulk and InBC retrieved by this study is
 L332: with a peak value
 L333: externally mixed and internally mixed
 L338: typical internal mixed BC
 L341: A previous study showed that the use of an inaccurate density value of …
 L345: what “it” represents here?
 L350: on predicted CCN number concentrations
 L360: in the atmosphere),
 Section 3.3, use 0.23% instead of 0.2%
 L414: would cause
 L417418: by assumption of to assuming
 L435: the current assumption

AC1: 'Reply on RC1', Fang Zhang, 09 Nov 2022
The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp2022542/acp2022542AC1supplement.pdf

RC2: 'Comment on acp2022542', Anonymous Referee #2, 26 Sep 2022
This study attempts to derive the “density” of BC from the hygroscopic growth factor measured by the HTDMA and total BC mass by the aethalometer. I appreciate the authors’ effect to derive the density of BC from measurements not directly linking with BC. This is indeed challenging from a bulk HTDMA measurement to derive BC information, as the BC only constitutes of a small fraction of ambient atmospheric particles. However, the current method is still not convincing. The crucial points are:
1)The total hydrophobic particle number was measured, and a fixed fraction of 70% of hydrophobic OA is used to obtain the hydrophobic BC from the total. This fixed “70%” is obviously not correct. Additionally, how have you got the number concentration of OA.
2) A fixed effective density of 0.4 g cm3 is assumed for hydrophobic BC to derive its mass, which is not correct. The effective density of BC obviously depends on the particle shape and it can’t be fixed.
3) By the following very complicated calculations, are you attempting to derive the BC density only for the hydrophilic mode? It is very confusing here as you have just used a fixed density of 0.4 but now why performing such calculation again.
The effective density of BC can be obtained through combing the SMPS and mass measurement as many people did (as the authors are aware), I can’t really understand why the authors have spent such efforts using an HTDMA measurement to perform such analysis (but this instrument is not intrinsically designed for such application).

AC2: 'Reply on RC2', Fang Zhang, 09 Nov 2022
The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp2022542/acp2022542AC2supplement.pdf

AC2: 'Reply on RC2', Fang Zhang, 09 Nov 2022
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