Using the numerically exact multiple sphere

Recent modeling and field studies have indicated that aerosol
light absorption is an important contributor to climate forcing

For the estimation of BC absorption enhancements, many field measurements
have been conducted.

Although the field measurements can provide referential absorption
enhancement values for different aging statuses and regions, causes of these
enhancements are not clear. For example, what is the main factor that causes complex absorption enhancements: morphology, the mixing states or the
types of coatings? To our best knowledge, field measurements currently have difficulty
answering these questions. Numerical simulation is a strong tool
that reveals the mechanism responsible for the complex absorption
enhancements. To improve the understanding of the complex absorption
enhancements of BC, numerical studies have also been conducted. For instance,
based on the core–shell Mie theory, the absorption enhancement factors have
been estimated up to 3

Many studies have been conducted to evaluate the absorption of BrC. One
typical method for the determination of BrC absorption is isolating BrC by
extracting filtered samples

In this study, a numerical investigation was conducted to explore the factors that contribute to the complex absorption enhancement of BC with BrC coatings for different mixing states. Two types of mixing states were considered: thinly coated BC and thickly coated BC. Thinly coated BC is assumed to be those with a BC volume fraction over 20 %, and the other BC is considered to be thickly coated. The results would give further understanding for the causes of BC absorption enhancements and suggestions for the inferred BC mixing states.

In climate modeling, a spherical shape is commonly assumed for aerosols and
can be calculated with high efficiency using the Mie theory

The fractal dimension is a key parameter that describes the compactness of BC
aggregates

However, under the effects of atmospheric aging, the structures and chemical
compositions of BC may change. Aged BC tends to be mixed with other chemical
components, and the shape becomes more compact. Therefore, in the atmosphere,
aggregates can have fractal dimensions of up to 2.6

Morphological parameters of BC aerosols, where

The monomer radius and monomer number are two key parameters that determine
the particle size. Even though the monomers' radii are polydispersed in the
atmosphere, they vary within a narrow range. Monomer radii are commonly
observed within

The morphologies of coated BC considered in this work are classified into two
categories: thinly coated BC and thickly coated BC. The closed-cell
structure, which is an example of where coating material that not only covers
the outer layers of BC aggregates but also fills the internal voids among
primary spherules, can be used to represent the thinly coated BC

Typical morphologies of BC,

Diffusion-limited algorithms (DLAs), including the particle–cluster
aggregation (PCA)

To calculate the radiative properties of BC in this work, numerical solution
methods from Maxwell's equations, including the finite-difference time-domain
(FDTD) method

In this study, all the radiative properties of BC were calculated based on
the assumption that BC particles and their mirror counterparts are present in
equal numbers in the ensemble of randomly oriented particles. In the atmosphere,
it is reasonable to assume that the possibility of each particle direction is
identical, which mathematically satisfies the definition of random
orientation

The presence of non-BC-coated materials can result in the enhancement of BC
absorption, referred to as BC absorption enhancement (

As BrC also absorbs solar radiation, it is also desirable to compare the
absorption of BC coated by BrC coatings with BC and an external mixture of
BrC and BC. The absorption of the BrC shell is calculated as

In this work, we defined a parameter (

The absorption of BC is significantly affected by the particle size

To estimate the effects of coating thickness on the absorption properties of
BC, we assumed that BrC coating ratios are independent of BC size. The
difference between the size distributions of bare BC and coated BC is
attributed to the coating thickness. The size distribution of bare and
coated BC is shown in Fig. S2. Even though the assumption does not
completely agree with the real cases, it is reasonable to make some
simplifications for the sensitivity analysis. Here, we must clarify that the
size distribution parameters (

To make our work more consistent with real circumstance, bulk optical
properties are considered. These properties are calculated by averaging over
a certain particle size distribution. In application, the equivalent volume
radii (

The refractive index of BC is commonly assumed to be wavelength independent
over the visible and near-visible spectral regions, and the imaginary part

The real parts of the BrC refractive indices were assumed to have a constant
value of 1.5

Effects of

Many studies have noticed that the lensing effect can greatly enhance the
absorption of BC. However, there is also an opposite effect, which is
commonly neglected. As shown in Fig.

Combining Eqs. (3)–(9), we can obtain

The sensitivity of

Although the core–shell sphere model has been debated for a long time, it is
still widely used in climate models. By combining the electron tomography
(ET) and DDA method,

Effects of

The

The sensitivity study conducted by

Similar to Fig.

The absorption of BrC and BC is considered separately in most cases. To
investigate the difference between the absorption of internally mixed BC and
the total absorption of BrC and BC (calculated separately),

Similar to Fig.

As both the lensing effect and sunglasses effect may affect the

Figure

The effects of the size distribution on the lensing effect and sunglasses
effect of thickly coated BC are shown in Fig.

To make our calculation meaningful, we compare the calculated

MAC (m

Figure

The relative deviations of absorption properties between

At different wavelengths, the effects of

Similar to Fig.

To reveal the factors that contribute to the complex

Figure

At visible wavelengths, the

There is a different dependence on

Comparison of BC coated with non-absorbing materials and that coated
with BrC (

In addition, the

Using the MSTM method, the

Generally,

To make our calculation more consistent with real circumstance, the bulk
absorption was calculated and the

The sunglasses effect and lensing effect are compared at different wavelengths.

In this work, complex morphologies and mixing states are considered. Although current climate models do not simulate any morphological information of aerosols, many laboratory studies have been conducted to investigate the BC morphologies in different mixing states and in different regions. Therefore, our calculations can be applied according to specific mixing states (such as composition ratios) and regions. However, we acknowledge that the understanding of the relation between BC morphology and the composition ratio is still limited. Therefore, further laboratory investigations for the coated BC morphologies should be conducted in the future.

Our data are all exhibited in the figures.
We have only a supplementary pdf file, which is available on the

The supplement related to this article is available online at:

JL and QZ conceived the presented idea. JL developed the models, performed the computations, and wrote the paper. YZ and FW verified the simulation methods and results. QZ revised the paper and supervised the findings of this work. All authors discussed the results and contributed to the final paper.

The authors declare that they have no conflict of interest.

This work was financially supported by the National Key Research and Development Plan (grant nos. 2016YFC0800100 and 2017YFC0805100), National Natural Science Foundation of China (grant nos. 41675024 and U1733126), and Fundamental Research Funds for the Central Universities (grant no. WK2320000035). We particularly thank Daniel W. Mackowski and Michael I. Mishchenko for the MSTM code. We also acknowledge the support of the supercomputing center of USTC. We particularly thank the three anonymous reviewers for their constructive suggestions. Edited by: James Allan Reviewed by: three anonymous referees