Atmospheric black carbon (BC) is the strongest solar radiative
absorber in the atmosphere, exerting significant influences on the earth's
radiation budget. The mass absorption cross section (MAC) is a crucial
parameter for converting the light absorption coefficient (

Black carbon (BC) is an important component of atmospheric aerosols (Ramanathan and Carmichael, 2008) because of its highly absorbing property. The environmental effect of BC is nonnegligible. The absorption of BC can significantly reduce visibility (Moosmuller et al., 2009). BC is considered a major factor for adverse health effects (Highwood and Kinnersley, 2006). The fractal aggregates morphology of BC provides substantial surface area for deposition of cancerogenic matter. The insoluble nature and fine size of BC make it deposit in the lungs for a long time. Because the significant impact of BC, extensive measurements have been made to monitor atmospheric loading of BC and provide information to policymakers for mitigation.

The BC mass concentration (

Filter-based instruments, such as an aethalometer (Hansen
et al., 1984), are commonly used for routine BC observations and dedicated
campaigns (Castagna et al., 2019; Sandradewi et al., 2008; Helin et al.,
2018) because they are convenient and easy to maintain. An aethalometer does
not directly measure

The mixing state of BC is one of the crucial reasons leading to a large variation in the MAC. Field measurements have indicated that fresh BC particles are generally subject to several coating processes while being transported in the atmosphere and tend to be covered in layers of other organic or inorganic components (Shiraiwa et al., 2007; Cappa et al., 2019; Bond et al., 2006). The gathered shell that builds up on the BC core, acting as a lens to focus additional incident light on the enclosed BC core, can enhance BC light absorption (Fuller et al., 1999). As a result, a coated BC particle will have a bigger MAC than the original pure BC particle. This light absorption enhancement is termed a “lensing effect” of the BC-containing particles. For typical core-coating mixed BC-containing particles, this lensing effect was found to enhance BC absorption by 50 %–100 % (Bond et al., 2006). Schwarz et al. (2008) found that fresh soot particles internally mixed with sulfates and organics during transportation, and the lensing effect enhanced the light absorption by a factor of 1.3–1.5.

At a given wavelength, such as 880 nm, the value of the MAC relies on the size and location of the BC core, coating thickness as well as the refractive index (RI) (Fuller et al., 1999; Lack and Cappa, 2010). A simplified core-shell configuration has been introduced to illustrate the structure of BC-containing particles and calculate the relevant optical properties. Several studies have demonstrated that it is appropriate to use the core-shell configuration for aged aerosols (Majdi et al., 2020; Liu et al., 2019; Li et al., 2019).

In previous studies (Zhao et al., 2019b; Ran et al., 2016a, b; Castagna et al., 2019), the variation of the MAC due to mixing state was
not considered when deriving the EBC from

The EBC particle mass size distribution (BCPMSD) was obtained at the
Zhangqiu Meteorology Station (36

The number fraction of BC-containing aerosols (

Besides Taizhou, the comparison between AE33 and PASS-3 was also conducted
from 20 March 2018 to 30 April 2018 and from 10–19 October 2018 at Peking University (39

All measurements at the three sites were conducted in temperature-controlled (24

During the field campaign at the Zhangqiu site, the particle number size distribution (PNSD) as well as the BCPMSD were simultaneously determined using the measurement system developed by Ning et al. (2013) and improved by Zhao et al. (2019b). The polydisperse aerosol sample flow was first drawn into DMA (differential mobility analyzer) (Model 3080, TSI, USA) to select relatively monodispersed aerosol subpopulations with diameters ranging from 97 to 602 nm. Sheath and sample flows were set as 3 and 0.5 L/min, respectively. The selected monodispersed aerosol populations were further divided into two paths. One path (0.2 L/min) was drawn into AE51 for EBC measurements. The other path (0.3 L/min) was analyzed using CPC (condensation particle counter) (model 3772, TSI, USA) for number concentration measurements. As the standard sample flow for CPC 3772 is 1 L/min, a cleaned airflow of 0.7 L/min was added for compensation. A BCPMSD cycle measured here required 5 min and we averaged the data with a temporal resolution of 2 h.

The dry aerosol scattering coefficients at 525 nm were measured simultaneously to represent air pollution conditions by an integrated nephelometer (Ecotech Pty Ltd., Aurora 3000) with a flow rate of 3 L/min and temporal resolution of 1 min. Similar to the measured BCPMSD, aerosol scattering coefficients were also averaged with a temporal resolution of 2 h.

For AE51, the influence of loading effect was resolved by using

For scattering correction, a scattering correction factor

For the SP2 system, the aerosol samples were analyzed in SP2 (0.12 L/min) to
identify the BC-containing particles and in CPC (0.28 L/min) to count the
total number of particles. When a BC-containing particle travels through the
laser beam (1064 nm) inside the SP2, it emits incandescent light. The
avalanche photodetectors (APDs) around the laser beam can detect the
incandescence signal. Then the BC-containing particle is detected.

For current filter-based instruments, the EBCs are generally derived from

To evaluate the theoretical discrepancies in the MAC values caused by the corresponding impact factors, a proper model is required to simulate the optical properties of BC-containing particles to a good approximation. Three widely employed mixing states are used to represent the structure of BC-containing aerosols: internal, external and core-shell models (Ma et al., 2011; China et al., 2015). Generally, freshly emitted BC particles are chain-like aggregates of small spheres. During the coating process, the chain-like BC aggregates become more compact as they collapse and are coated as a core by organic and inorganic materials (Bond and Bergstrom, 2006). Therefore, a core-shell configuration is more plausible (Jacobson, 2000). Ma et al. (2012) also indicated that the core-shell assumption can provide a better performance in optical closure than the internal or external models. Furthermore, Moffet et al. (2016) studied particle mixing state and morphology using scanning transmission X-ray microscopy and highlighted that core-shell structure dominated the mixing state of ambient aerosol particles. Aerosols are assumed to be core-shell mixed with a spherical BC core in the center of the coating sphere. Therefore, the Mie model was used to simulate the optical properties of BC particles with a core-shell mixing state. The consistency in observed and theoretical values obtained using Mie and core-shell morphology support the suitability of this method (Cappa et al., 2012).

Many optical simulations for BC particles with concentric sphere geometry have been reported and the corresponding results show that the absorption of a pure BC particle will be enhanced when a shell composed of nonabsorbing material deposits on this pure BC particle. Since the optical properties were focused on rather than chemical compositions of the mixed aerosols, a simplified hypothesis of BC/sulfate mixtures, which is common in the atmosphere (Khalizov et al., 2009), was introduced in the algorithm for calculating the EBC.

The reason AE33 uses 880 nm to determine the EBC is that aerosol absorption
at 880 nm is mainly from BC (Ramachandran and Rajesh, 2007). At shorter
wavelength, absorption of organic carbon is no longer negligible, leading
to difficulty extracting BC absorption from total aerosol absorption.
Therefore, the MAC at 880 nm is discussed in this study and the MAC distribution
for a wide range of core and coating sizes at the wavelength of 880 nm is
simulated with Mie scattering theory. The RI, dependent
on light wavelength, is an important parameter to determine aerosol optical
properties. However, due to different sources of BC, both the real and
imaginary part of the RI varies over a significantly wide range. Liu et al. (2018) summarized RI values for specific wavelengths and showed that the
real part is generally in the range of 1.5 to 2.0 while the imaginary part
usually varies from 0.5 to 1.1 (Sorensen, 2001; Bond and Bergstrom, 2006).
Therefore, the real part and imaginary part of the RI were set to change from
1.5 to 2.0 and from 0.5 to 1.1, respectively, with a step increase of 0.01.
Meanwhile, the RI of sulfate was set as 1.55–10

Variations in the MAC as a function of

Figure 1 presents several features of the variation pattern of the MAC at 880 nm. The MAC values varied significantly with

In this subsection, a new method is introduced to determine the EBC from the
measured

As the absorption properties of BC particles in different coating states
have been evaluated with the Mie model, as shown in Fig. 1, a simplified
algorithm was proposed for deriving the BCPMSD through a pre-calculated look-up
table. For each

Schematic diagram of the iterative algorithm for retrieving the
EBC at a fixed particle diameter based on the look-up table of the MAC, particle
size and core size.

It should be pointed out that the retrieval algorithm of the BCPMSD is based on
the assumption that BC-containing particles of a fixed diameter are all
core-shell mixed and the corresponding

Figure 3 provides a comprehensive overview of the variations in measured and
retrieved size-resolved parameters during the campaign. As evident from Fig. 3a, for the BCPMSD derived by the new method, two modes were found. Figure 4a shows the averaged BCPMSD derived from the new method and AE33 during
the campaign. The fine mode was located between 97–240 nm while the
coarse mode was located between 240–602 nm. Figure 3b represents the
relative deviations between the BCPMSD derived from the newly proposed
method and those derived from a constant MAC value of 7.77 m

Time series of

Figure 3e shows the time series of the EBC in fine and coarse modes. The EBCs were more concentrated in the fine mode than in the coarse mode. The EBCs in fine mode were found to be higher than those in the coarse mode for 73 % of the campaign duration. The variation trends of the bulk EBCs calculated by considering the variations of the MAC and a constant MAC were similar (Fig. 3f). The bulk EBCs calculated by the new method were higher than those derived by the constant MAC in 83 % of the campaign duration.

The EBCs calculated from the new method and AE33 for different aerosol size
ranges were statistically analyzed. As shown in Fig. 4, for all EBCs of
aerosols ranging between 97–602 and 97–280 nm derived from the new
method and AE33, strong linear relationships were observed with correlation
coefficients of 0.99 and 1.00, respectively. The ratios between the EBCs
derived from AE33 and the new method for aerosol diameter ranges of 97–602 and 97–280 nm were 0.84 and 0.69, respectively, indicating that
the EBC obtained from AE33 was 16 % lower for bulk aerosol particles and
31 % lower for aerosols smaller than 280 nm. For the diameter range of 280–602 nm, the MAC values varied significantly and the deviations in the EBC derived
from the new method and AE33 were divided into two types with a boundary of
0.7

Comparison between the EBC derived from the new method and from
a constant MAC of 7.77 m

An idealized concentric core-shell model with a spherical BC core fully coated by sulfate was configured to study the MAC of BC aerosols and derive the EBC in this study. However, freshly emitted BC particles were found to normally exist in the form of loose cluster-like aggregates with numerous spherical primary monomers (Liu et al., 2015). Soon after, these aggregates become coated with other components and collapse to a more compact form during the coating process (Zhang et al., 2008; Peng et al., 2016). Therefore, the uncertainty in the idealized core-shell configuration is discussed in this subsection.

The fractal aggregates of BC have been well described by fractal geometries
through the well-known statistical scaling law (Sorensen,
2001):

In order to generate fractal-like aggregates with given

The fractal dimensions for aged BC aggregates are generally close to 3
(Kahnert et al., 2012). The aim of this study is to evaluate the effects
of aerosol microphysics on the absorption enhancement of fully coated BC
particles, which can be regarded as the aged BC aerosols. Therefore, the
fractal dimension

As the traditional Mie model is not available for the fractal aggregates,
the widely used multiple sphere T-matrix (MSTM) method is employed here to quantify the absorption
properties of BC clusters (Mackowski and Mishchenko, 1996; Mackowski,
2014). The addition theorem of vector spherical wave functions is used in the
MSTM method to describe the mutual interactions among the system. The

The deviations shown in Fig. 5 are derived by subtracting the MAC values
calculated by the MSTM model from those calculated by the Mie model. The results show
that most of the MAC values calculated by assuming BC particles in the form
of cluster-like aggregates are smaller when the size of BC core is smaller
than 150 nm and the overall deviation is within 4 %, which indicates that
Mie theory is a good approximation to the BC aggregates even when

Relative deviations of the MAC values calculated by the idealized
concentric core-shell model and letting BC particles be in the form of
cluster-like aggregates. The solid line is the

Figure 6 shows the deviation of the BCPMSD calculated from different

The derived BCPMSD by using different constant BC-containing particle fractions. The solid black line represents the result derived from a fraction of 17 %. The dashed black line and blue line show the results derived from fractions of 8.5 % and 34 % , respectively.

As the RI of BC is still reported to vary over a wide range and the MAC used
in this study was a mean value, it is critical to assess the impact caused
by variation in the real and imaginary parts of the RI on the calculated MAC and
the derived EBC. For aerosol particles with given

Figure 7a shows the uncertainties in the MAC along different values of

Uncertainty in the MAC of BC when

The variation of the EBC caused by the uncertainties in the RI was further
evaluated. As stated in Sect. 3.2, for a MAC (880 nm) point at
(

There was significant variability in the MAC values of BC with the size of the BC core and the thickness of the coating, which exerted a significant influence on the optical method for deriving the EBC. In this study, a new method was proposed to derive the EBC considering the lensing effect of the core-shell structure and the consequent MAC variations.

A look-up table describing the variations of the MAC at 880 nm attributed to the
coating state and size of the BC core was established theoretically using the Mie
simulation and assuming a core-shell configuration for BC-containing
aerosols. The MAC at 880 nm varied significantly with different sizes of
core and shell from less than 2 m

This newly proposed method was applied to a campaign measurement on the NCP.
There were two modes for the BCPMSD at the accumulation mode separated by 240 nm. For 73 % of the cases, the EBCs of the fine mode were larger than those
of the coarse mode during the measurement. The EBCs derived by the new method
were mostly lower than those derived by a constant MAC of 7.77 m

Uncertainty analysis was carried out with respect to assumptions used in this study. The uncertainty caused by the idealized core-shell model was analyzed by substituting the core with cluster-like aggregates using the MSTM method, and the resulting relative uncertainties were within 15 %. The uncertainties caused by using a constant number fraction of BC-containing particles were analyzed by halving and doubling its value, and the results showed that particles larger than 200 nm were insensitive to the number fraction of BC-containing particles, whereas for particles smaller than 200 nm, the EBCs would be underestimated if the BC-containing particle fraction was underestimated. The uncertainty in the derived EBC that was caused due to the wide range of RI of the BC core was also studied. The results indicated that the uncertainty of the imaginary part results in larger uncertainties to the MAC compared with the real part. The relative uncertainty of the derived EBC was within 35 %.

This study provides a new way to derive the EBC from

The code used in this study are available upon request from the authors.

The measurement data involved in this study are available from the authors upon request.

The supplement related to this article is available online at:

CZ determined the main goal of this study. WZ and WT designed the methods. WZ carried them out and prepared the paper with contributions from all coauthors.

The authors declare that they have no conflict of interest.

This research was supported by the National Natural Science Foundation of China (grant no. 41590872).

This paper was edited by Alexander Kokhanovsky and reviewed by three anonymous referees.