Large uncertainties remain when estimating the warming effects of ambient
black carbon (BC) aerosols on climate. One of the key challenges in modeling
the radiative effects is predicting the BC light absorption enhancement,
which is mainly determined by the mass ratio (MR) of non-BC coating material to
BC in the population of BC-containing aerosols. For the same MR, recent
research has found that the radiative absorption enhancements by BC are also
controlled by its particle-to-particle heterogeneity. In this study, the BC
mixing state index (

Black carbon (BC) aerosols absorb solar radiation, thus exerting warming effects on the earth's energy system (Bond et al., 2006, 2013). However, large uncertainties remain when quantifying the BC warming effects (Menon et al., 2002; Koch et al., 2009; Jacobson, 2010; Cui et al., 2016). Most of the BC particles were emitted from incomplete combustion of bio-fossil fuel (Bond et al., 2013). After being initially emitted, the BC particles experience an aging process with some other non-BC components coated on the BC particles (Peng et al., 2016, 2017). During the aging process, the light absorption of BC aerosols would increase, which is well known as the “lensing effect” (Saleh et al., 2013, 2014). One critical challenge in estimating the BC warming effects is quantifying the lensing effects of ambient BC aerosols (Liu et al., 2017).

The light absorption enhancement (

Many factors, such as the morphology of the BC core, the position of BC core
inside coating, the coating thickness, chemical properties of coating
materials, and size distribution of the BC, influence the

The measured

In this study, we developed a BC mixing state index (

The field measurements were conducted at a suburban site in Taizhou
(119

The size-resolved BC core distribution and non-BC coating thickness were
measured using a differential mobility analyzer (DMA, model 3081, TSI,
USA) in tandem with a single-particle soot photometer (SP2, Droplet
Measurement Technologies, USA). For detailed information on the DMA, the reader is referred to
Zhao et al. (2019c). SP2 can measure the BC mass concentration from the
incandescence signals emitted by the BC particle, which is heated to around
6000 K by a laser with a wavelength of 1064 nm (Zhao et al., 2020b).
Along with the measurement of size-resolved BC distributions, a nephelometer
(Aurora 300, Ecotech, Australia) (Müller et al.,
2011) was employed to measure the aerosol scattering coefficient
(

In this study, the SP2 was placed behind the DMA to measure the size-selected
distribution of BC core and non-BC coating thickness. The schematic
instrument setup is shown in Fig. S2, and the reader is referred to Sect. 2 in
the Supplement for details. The DMA was set to scan the aerosols'

A Mie scattering core–shell model (Bohren et al., 2007) was
employed to calculate the aerosol absorption coefficient (

We calculate the single-particle

Along with calculating the

In this study, the mass-weighted mixing state index for BC-containing
particles (

For each particle

A mixing state diagram as shown in Fig. 2 was employed for better understanding of the dispersion of BC mixing states. Nine different aerosol populations are given and summarized in Table 1. For each group, we include six BC-containing particles with different mass concentrations of BC core and non-BC coating material.

Mixing state diagram to illustrate the relationship between

Detailed information of the BC particles shown in Fig. 2.

For group 1, the amounts of BC are very small (near zero), and most of the
aerosols are composed of the non-BC component. The

For groups 2, 3, and 4, the mass concentration ratios of the BC component to
the non-BC component are 1 : 5, 2 : 4, and 3 : 3 respectively. All of the

For groups 4, 5, 6, and 7, the mass concentration ratios of the BC component
to the non-BC component are all 1 : 1, while the BC component is mixed to a
different extent. It is easy to conclude that the BC particles of group 7
are most well mixed among these four groups. The corresponding

As for groups 8 and 9, the mass concentration ratios of the BC component to
the non-BC component are 1 : 6.1. The

From the different groups, the average particle species diversity

Figure S6 gives the time series of our field measurement results. During the
field measurements, the

For a better understanding of the characteristics of the above parameters,
we only present the time series of these parameters during a pollution
period between 27 and 30 May in Fig. 3. As shown in Fig. 3, the MR
increased from about 2 to 4 when the

Measured time series of

Daily variation of the measured

The corresponding mean values of BC-containing number size distributions
under different

For each of the measured group of size-resolved distribution of BC core and
coating thickness, we calculated the corresponding MR,

Relationship between the BC

Overall, the BC

A schematic diagram as shown in Fig. 6 to denote the relationship between
the

Schematic diagram that denotes the relationship between

The calculated

It is worth noting that the increasing ratio is almost the same when the MR
is in the range of 0 and 3. Therefore, the

A Monte Carlo simulation was carried out for a better understanding of the
relationship between

From Fig. 7a, the calculated

As for the uncertainties of simulated

Larger uncertainties remain when estimating the warming effects of ambient BC aerosols due to the poor understanding of the ambient BC light absorption enhance ratio. Previous studies find that the light absorption of ambient aerosols was mainly determined by the morphology of the BC core, the position of the BC core inside coating, the coating thickness, and the size distribution of the BC. We find that there are more than 20 % of uncertainties for the same measured mean coating thickness, i.e. the same measured MR based on the field measurements of the size-resolved distribution of BC core and coating thickness. However, there was no study until now, to the best of our knowledge, that attempts to constrain the uncertainties.

In this study, we developed the BC mixing state index

The new finding of our study is that the mixing state index can contribute
to improvements in the accuracy of simulating the BC radiative effects. In
the particle-resolved simulation of ambient aerosols, the
particle-to-particle heterogeneity of BC-containing aerosols can be resolved
by simply introducing the BC mixing state index

The research data are available within the paper.

The supplement related to this article is available online at:

GZ wrote the manuscript. CZ, MH, TT, SG, ZW, YZ, and GZ discussed the results.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research has been supported by the China Postdoctoral Science Foundation (grant no. 2021M700192), the National Natural Science Foundation of China (grant no. 41590872), and the National Key R&D Program of China (grant no. 2016YFC020000: Task 5).

This paper was edited by Manvendra K. Dubey and reviewed by three anonymous referees.