Introduction
Recent modeling and field studies have indicated that aerosol
light absorption is an important contributor to climate forcing
. Black carbon (BC), which is a product of
incomplete combustion, is the strongest solar-absorbing aerosol in the
atmosphere . BC radiative forcing from fossil fuels and
biomass burning has been estimated to be approximately
0.4 W m-2, as the second anthropogenic
contributor (after CO2) to climate forcing due to its strong
absorption of solar radiation . Sensitivity
tests suggest that the mixing state and morphology of BC aerosols can largely
affect the absorption of BC . Due to the large
uncertainties of BC morphologies and mixing states, the understanding of BC
absorption is still limited. Even when coated with non-absorbing materials,
the BC absorption can be enhanced . Many studies mainly
attribute the absorption enhancements (Eabs) to the lensing
effect .
For the estimation of BC absorption enhancements, many field measurements
have been conducted. presented factors of 1.1–1.4 for BC
absorption enhancement at a suburban site in Japan, while
indicated that the absorption enhancement factors increase from 1.4±0.3
during fresh combustions to ∼3 for aged BC at a rural site over the
North China Plain (NCP). found that BC absorption enhancement is
significantly influenced by the particle mixing state. The measured range of
Eabs is approximately 1–1.5. observed the
wavelength-dependent absorption enhancement of coated BC. In their
measurements, Eabs increased up to 3 at the shortest measured
wavelengths, while it was approximately 1.6 in the near-IR wavelength. A
negligible absorption enhancement of only 6 % for ambient BC particles was
reported by based on direct measurements over California (USA).
reported an average Eabs of 2.07±0.72 for the urban
haze in winter in northern China. However, this result was time dependent.
The absorption enhancement of BC during the urban PM2.5 pollution was 1.31±0.29 in the morning, while in the afternoon, it increased to
approximately 2.23±1.05; then, it decreased to 1.52±0.75 in the
evening. Recently, a larger Eabs value of 2.6–4.0 at Beijing, China, was
reported by . In summary, the reported Eabs values are not
consistent in different studies due to the complex aging statuses.
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 . By the numerically exact multiple
sphere T-matrix (MSTM) method, presented the absorption
enhancements of non-absorbing coatings for aged BC ranging from 1.1 to 2.4, and
they were significantly influenced by the morphology and aging statuses but
insensitive to the BC refractive index. However, previous studies have failed
to uncover the effects of coating absorption. In their studies, coatings were
considered to be non-absorptive, and BC absorption enhancements were completely
caused by lensing effects. Nevertheless, in the atmosphere, there is a type
of organic carbon (OC) that absorbs the radiation in the range of the
ultraviolet and visible spectra, which is known well as brown carbon (BrC);
BC can also be mixed with BrC. Compared with non-absorbing materials, the
absorption of BrC is significantly wavelength dependent and the imaginary
part of the refractive index for BrC has a wide range , which
results in large uncertainties for the estimation of aerosol absorption.
Therefore, the absorption of BrC has gained increasing interest
.
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 . This method can be used to
determine the imaginary part of the BrC refractive index. However, it is
difficult to understand the effects of BrC on the total aerosol absorption,
as BrC is commonly mixed with other chemical compositions. The assumption of
externally mixing can be used to evaluate the absorption of BrC and BC
separately. Nevertheless, in many cases, BC is internally mixed with other
materials. It is widely accepted that the absorption is underestimated by the
external mixing assumption when BC is coated with non-absorbing materials due
to lensing effects. However, whether this is true for BC with BrC coatings is
not clear. To understand the effects of BrC coatings, the contributions of
“lensing effects” and the total absorption enhancement of BC with BrC
coatings should be analyzed individually.
has conducted a numerical investigation on BC absorption
enhancement, BrC absorption enhancement, and lensing effects on BC mixed with BrC
by assuming a core–shell structure. While the internal mixing of BC is widely
accepted, the core–shell structure is debated
. developed a theoretical BC
aging model and concluded that the evolution of coating thickness,
morphology, and composition during the aging process could have significant
impacts on BC absorption. Freshly emitted BC commonly presents fractal
structures. As the BC ages in the atmosphere, BC becomes more compact and OC
materials can condense onto the particles. Therefore, BC can be embedded in
an OC shell . When the non-BC fraction is low, BC can still
present a near-fractal structure (referred to as thinly coated BC in this study)
. As BC is further coated, BC aggregates are collapsed into more
compact and spherical clusters when fully engulfed in coating material
(referred to as thickly coated BC in this study) .
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.
Methodology
Geometric properties of BC aerosols
In climate modeling, a spherical shape is commonly assumed for aerosols and
can be calculated with high efficiency using the Mie theory .
However, in many cases, this shape can introduce large errors compared with
the measurements due to the oversimplification of the shape. Recently, the
nonsphericity of aerosols has gained increasing interest
. Specifically, observations have indicated that uncoated
BC particles are commonly composed of numerous small spherical particles.
Fractal aggregates can be greatly used to describe their geometric
properties. Mathematically, the structure satisfies the well-known fractal
law :
ns=k0RgRDf,Rg2=1ns∑i=1nsli2,
where ns represents the number of the monomers in the cluster, R
represents the mean radius of the monomers, k0 represents the fractal
prefactor, Df represents the fractal dimension, Rg represents the
radius of gyration, and li represents the distance from the ith monomer
to the center of the cluster.
The fractal dimension is a key parameter that describes the compactness of BC
aggregates . Generally, aggregates tend to be
more compact with the increase in Df. A Df of 1 can describe an
open-chain-type shape, while the aggregates tend to be spherical as Df
approaches 3. Numerous experimental studies have been carried out to evaluate
the Df of BC aggregates. Immediately after they are emitted, BC aggregates
generally exhibit fluffy structures with a small fractal dimension (Df),
that is normally less than 2, such as the Df of BC aggregates from biomass
burnings (1.67–1.83) , the Df of BC from vehicle emissions
(1.52–1.94) , and the Df of BC from diesel combustion
(1.6–1.9) .
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 . In some
cases, BC aggregates are thinly coated with other materials and still
exhibit a fractal structure. However, different from freshly emitted BC
aggregates, both lacy and compact structures can exist. Therefore, for
thinly coated BC, the Df was assumed to be in the range from 1.8 to 2.6. As
BC becomes increasingly coated, BC aggregates may transform from highly
agglomerated to nearly spherical particles. A Df=2.6 was assumed for
thickly coated BC. Even though a fractal prefactor can also vary under
different combustion and aging statuses, it has less significant effects on
the absorption of BC compared to the Df. When fixing Df to be 1.82,
demonstrated that the absorption cross section of BC aggregates
does not change substantially as the fractal prefactor varies from 0.9 to 2.1.
Therefore, a fixed fractal prefactor of 1.2 was assumed in this work.
Morphological parameters of BC aerosols, where fBC
represents the volume fraction of BC.
Parameters
Thinly coated BC
Thickly coated BC
ko
1.2
1.2
ns
1–1000
1–1000
Df
1.8, 2.2, 2.6
2.6
fBC
0.2, 0.4, 0.6, 0.8, 1.0
0.05, 0.06, 0.075, 0.1
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 ∼10–25 nm . In addition,
demonstrated that Cabs is insensitive to monomer radii when the monomer
radii are within ∼10–25 nm. As a result, for convenient application,
a fixed monomer radius of R=20 nm was assumed in this work. Based on
transmission electron microscopy (TEM) and scanning electron microscopy (SEM) imaging, the monomer number ns can reach approximately 800
. Values of 1≤ns≤1000 were considered in this work.
For an aggregate with ns monomers, the equivalent radius was given by the
equivalent volume sphere radius Rns3. The morphological
parameters considered in this work are shown in Table .
Generation of BC aerosols
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
. In addition, demonstrated that the
absorption of closed-cell structures and more realistic morphologies do not
have large deviations. Therefore, it is reasonable to use the closed-cell
model for calculating the absorption of thinly coated BC, while the
thickly coated BC is commonly represented by a structure in which BC aggregates
are encapsulated in a sphere . The typical morphologies
are shown in Fig. .
Typical morphologies of BC, ns=300,k0=1.2.
Diffusion-limited algorithms (DLAs), including the particle–cluster
aggregation (PCA) and the cluster–cluster aggregation (CCA)
methods , have been developed for the generation of aggregates.
However, adjustable DLA codes are commonly applied due to their quick
implementation and adjustable fractal parameters . In this work,
an adjustable DLA code developed by was used. Compared with
ordinary DLA codes, this code preserves fractal parameters during each step
of the aggregation, which avoids the generation of multifractal aggregates
. After the generation of the aggregates, the coatings were
added. More specifically, for thinly coated BC, the BrC shells were generated
by the adjustable algorithm, and then the BC cores were added; the details
are shown in previous studies . The thickly coated BC is
generated by covering the BrC spherical coatings on the BC aggregates, as
shown in the study of .
Light scattering method
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 , generalized
multiparticle Mie (GMM) method , MSTM method , the
geometric-optics surface-wave (GOS) method , and
discrete-dipole approximation (DDA) method , can
all be used. However, compared with other numerical methods, the MSTM has an
advantage for the calculation of optical properties for randomly oriented
particles analytically without numerically averaging over particle
orientations. Therefore, this method has high efficiency to calculate optical
properties of BC. In this work, the latest MSTM code, MSTM version 3.0
, was applied.
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 .
Calculating absorption enhancement of BC
The presence of non-BC-coated materials can result in the enhancement of BC
absorption, referred to as BC absorption enhancement (Eabs). Therefore,
Eabs can be defined as the amplification of BC absorption after BC being
coated:
Eabs=Cabs_coatedCabs_bare,
where Cabs_coated and Cabs_bare represent the absorption
cross sections of coated BC and bare BC, respectively.
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
Cabs_BrC_shell=Cabs_BrC(coated shape)-Cabs_BrC(bare shape),
where Cabs_BrC(coated shape) and Cabs_BrC(bare shape)
represent the absorption cross sections of BrC with morphologies that are
identical to coated BC and bare BC, respectively. The calculation of the
absorption of BrC shell is shown in Fig. S1 in the Supplement. In this process, we assume
that the absorption of BrC with the same shape as the coated BC is identical
to the external mixture of BrC that has the same shape as bare BC and BrC
shell. We must clarify that this disposal method neglects the blocking effect
and lensing effect of the outer BrC shell on the internal BrC. However, as the
BrC absorption is significantly less than the BC absorption with an identical
shape, the absorption caused by the blocking effect and lensing effect of
outer BrC on the internal BrC is relatively small compared with the BC
absorption. Therefore, it is reasonable to make some simplifications.
In this work, we defined a parameter (Eabs_internal) to represent the
ratio between the absorption of BC coated by BrC coatings and an external
mixture of BrC and BC:
Eabs_internal=Cabs_coatedCabs_BrC_shell+Cabs_bare.
Size distribution
The absorption of BC is significantly affected by the particle size
. Therefore, the effects of the size distribution on BC
absorption enhancement should be considered carefully. The shape of BC
particles is commonly irregular. To describe the size of each BC particle,
the radius of the corresponding equivalent volume sphere is typically used.
Based on numerous measurements, a lognormal size distribution is observed to
fit the realistic BC size distributions well , and
it is widely used in climate models for the estimation of BC radiative
forcing . However, the mean size and standard deviation
vary with the combustion status and aging status. In the atmosphere,
geometric mean radii (rg) between 0.05 and 0.06 µm for BC
are widely accepted . The geometric
standard deviation (σg) varies within a relatively narrow range.
Consequently, bare BC with rg between 0.03 and 0.1 µm is
considered for sensitivity analysis, an σg from 1.15 to 1.75. The
minimum and maximum equivalent volume radii are rmin=0.02 µm and
rmax=0.2 µm, respectively.
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 (rg and σg) mentioned in this work
are applied for the bare BC, and the overall effective volume radius of
coated BC is equal to the sum of coating thickness and radius of bare BC.
Calculation of bulk radiative properties of BC
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 (r) of BC are commonly assumed to follow a lognormal size
distribution:
n(r)=12πrln(σg)exp-ln(r)-ln(rg)2ln(σg)2,
where rg and σg represent the geometric mean radius and geometric
standard deviation, respectively. Given the size distribution, the bulk
Cabs can be obtained using the following equation:
<Cabs>=∫rminrmaxCabs(r)n(r)dr.
The bulk Eabs and Eabs_internal are calculated as those in
Eqs. (3)–(5). The only difference is that the absorption cross section is
now the bulk absorption cross section.
Results
Effects of the imaginary part of the BrC refractive index: lensing effect and sunglasses effect
The refractive index of BC is commonly assumed to be wavelength independent
over the visible and near-visible spectral regions, and the imaginary part
kBC≈0.79 . In addition,
have
demonstrated that the uncertainties of the BC refractive index have little
impact on the absorption enhancement of coated BC aggregates. Therefore, a
typical refractive index m=1.95+0.79i of BC was adopted in this study.
The real parts of the BrC refractive indices were assumed to have a constant
value of 1.5 , while the imaginary part of the refractive index
(kBrC) was significantly dependent on wavelength at shorter visible and
ultraviolet (UV) wavelengths . Figure
shows the effects of kBrC on Eabs and Eabs_internal, where
fBC represents the BC volume fraction. Large deviations in Eabs and
Eabs_internal can be observed given different values of kBrC.
Generally, Eabs increases with kBrC, while Eabs_internal
decreases with increasing kBrC. Therefore, it is desirable to evaluate
the effects of absorbing coatings on BC absorption enhancement. Given
identical kBrC values, the absorption enhancements of thickly coated BC
increase with wavelength. However, for BC that is internally mixed with BrC,
wavelength-dependent absorption enhancements are measured to decrease with
λ . This may be due to the wavelength-dependent
kBrC. For thickly coated BC, Eabs_internal and Eabs decrease
with wavelength, but they are not a strong function of λ for
thinly coated BC. In addition, compared with BC with non-absorbing coatings,
Eabs for thinly coated BC with absorbing coatings seems to be less
wavelength dependent, while Eabs for thickly coated BC with absorbing
materials is more sensitive to wavelength.
Effects of kBrC on specific enhancement (ns=200). For
thinly coated BC, Df=2.2 and fBC=40 %; for
thickly coated BC, Df=2.6 and fBC=5 %. The blue
shading represents the Eabs_internal of larger than 1, while the
green shading describes the range of Eabs_internal of less than 1.
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. , as kBrC increases, the
value of Eabs_internal of thickly coated BC can be below 1. This
indicates that the absorption of BC internally mixed with BrC coatings may be
less than the sum of the absorption of an external mixture of BrC coatings
and BC when kBrC is large. This phenomenon can be explained from
physical insights. When the absorption of the coatings is weak, the light can
penetrate the coatings of the BC materials, and the absorption of BC is
significantly enhanced by the lensing effect. However, as the coating
absorption increases, the light is blocked by the outer coatings. Therefore,
the light cannot fully and deeply penetrate the absorbing coatings on BC. As
a result, the total absorption is less than the sum of the absorption of
coatings and BC that are calculated separately. Therefore, there is a need to
classify the BrC coating effect into lensing effect (Eabs_lensing) and
sunglasses effect (ESunglass), which represents the absorption
enhancements and blocking effects of coatings, respectively.
defined the lensing effect as the absorption enhanced by the
addition of non-black carbon. However, from a physical point, for BC with BrC
coatings, the definition may not be clear as BrC also absorbs solar
radiation, and it can be confused with Eabs. Therefore, here we redefine
the lensing effect as the absorption enhanced by addition of non-absorbing
materials. In addition, we assume that the lensing effect of BC with
absorbing coatings is the same as those with non-absorbing coatings.
Accordingly, Eabs_lensing can be calculated using
Eabs_lensing=Cabs_non-absorbingCabs_bare,
where Cabs_non-absorbing represents the absorption cross section of BC
with non-absorbing coatings. The total Eabs should be contributed to the
lensing effect, absorption of BrC shell, and the sunglasses effect. Therefore,
Eabs can be expressed by
ESunglass=-Cabs_coated-Cabs_BrC_shell-Cabs_non-absorbingCabs_bare.
Combining Eqs. (3)–(9), we can obtain ESunglass, and the negative sign
represents the fact that the sunglasses effect can cause a decrease in total
absorption. According to the definition of ESunglass, we can easily obtain
the relation that the absorption of BC coated with BrC is less than that of
an external mixture of BrC and BC when ESunglass>Eabs_lensing-1.
The sensitivity of ESunglass to kBrC is shown in Fig. .
For both thinly and thickly coated BC, ESunglass increases with
kBrC. Fixing kBrC, ESunglass of thinly coated BC decreases
with wavelength. However, for thickly coated BC, ESunglass can increase
with wavelength at large kBrC values (such as kBrC=0.16). For the
thinly coated BC, the blocking of ESunglass is less than the enhancement
of Eabs_lensing (see Figs. and ); therefore,
Eabs_internal of thinly coated BC is larger than 1. For thickly coated
BC, the blocking of ESunglass can be larger than the enhancement of
Eabs_lensing as kBrC is larger, which leads to Eabs_internal
of less than 1. The threshold value of kBrC is dependent on particle
size and mixing states. Generally, the threshold kBrC value decreases
with particle size and coating thickness, as Eabs_internal of BC
thickly coated with BrC coatings decreases with particle size and coating
thickness in the ultraviolet region (see Figs. and ).
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,
found that the absorption of BC with fluffy structures is significantly
enhanced by a core–shell structure at λ=0.55 µm. However, for
thickly coated BC, BC absorption is underestimated at the UV, visible, and IR
wavelengths . have also demonstrated that the
Cabs of thickly coated BC with non-absorbing coatings is significantly
underestimated by a core–shell sphere and investigated the effects of
off-center BC. Their results indicated that the Cabs values of aged BC
covered with thick non-absorbing coatings are approximately 1.44 times higher
than those calculated with a core–shell sphere model. Nevertheless, the
effects of coating absorption on the applicability of the core–shell sphere
model have not been evaluated. As shown in Fig. , Cabs for
thinly coated BC is enhanced by a core–shell sphere structure in the visible
spectral region, which agrees with the study of ,
while it is underestimated in the ultraviolet region. In addition, the ratio
of Cabs of thinly coated BC to the core–shell sphere model increases with
kBrC. However, the applicability of the core–shell sphere model to
thickly coated BC is diverse. Consistent with , thickly coated BC
absorption is underestimated by the core–shell sphere model when coated with
non-absorbing materials. Nevertheless, as kBrC increases, the
underestimation becomes insignificant. The reason may be that less light can
penetrate deeply into the BC as the kBrC increases, which leads to less
variation in absorption. Therefore, the morphological effects of BC are
relatively small.
Effects of kBrC on the applicability of core–shell sphere (ns=200).
The Eabs, compared with that for the core–shell sphere model, is also
calculated. For thinly coated BC, the Eabs is significantly
overestimated by the core–shell sphere model. However, this overestimation is
alleviated by an increasing kBrC. For BC that is thickly coated with
non-absorbing materials, the Eabs is underestimated by the core–shell sphere
model at all wavelengths, while it decreases as kBrC becomes larger. The
Eabs can be overestimated by the core–shell sphere model in the ultraviolet
spectral region when kBrC is large. Therefore, the absorption
characteristics of BC are significantly affected by the absorption of
coatings. To agree with the measurements, typical kBrC values are
assumed according to , as shown in Fig. S2. In this work,
kBrC values of 0.168, 0.114, 0.0354 and 0.001 were assumed for 4 typical
wavelengths (λ=350, 404, 532 and 700 nm,
respectively) via interpolation.
Eabs and Eabs_internal of thinly coated BC
with BrC coatings at different size distributions (Df=2.2, fBC=40%).
Bulk radiative properties: effects of the size distribution
The sensitivity study conducted by showed that the Eabs for
aged BC was significantly affected by the size distribution. They reported
different Eabs values of ∼1.7–2.4 and ∼2.0–2.7 for
accumulated and coarse modes, respectively. By setting the fractal dimension
to be 2.2 and fBC to be 40 %, the variations in BC absorption
enhancements for different particle size distributions are shown in Fig. . Generally, weaker absorption enhancement can be observed by
increasing λ from the ultraviolet region to the visible region, which is in
agreement with the study of . By defining the monomers' radii,
demonstrated that the absorption cross section is significantly
affected by the particle size, and the cubic fit can greatly describe the
relations among equivalent volume radii for freshly emitted BC. However, for
the absorption enhancement of thinly coated BC, the effects of size
distribution are not obvious. With variations in rg and σg, the
absorption enhancement changes at ranges of ∼1.563–1.603, ∼1.427–1.465,
∼1.2440–1.275, and ∼1.146–1.169 at λ=0.35,
0.404, 0.532, and 0.7 µm, respectively. The relative
uncertainty in the absorption enhancements caused by the size distribution
are 2.56 %, 2.66 %, 2.81 %, and 2.01 %, respectively. The effects of the size
distribution on the absorption enhancement of thinly coated BC are similar at
different wavelengths. Generally, Eabs has the largest value when both
rg and σg are extremely small or extremely large.
Similar to Fig. , but for Eabs_lensing and ESunglass.
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),
Eabs_internal is also calculated. Eabs_internal of thinly coated
BC is greater in the visible region due to the insignificant sunglasses
effects. The sensitivity of Eabs_internal is also not obvious to the
size distribution. With the size distribution varying, Eabs_internal
changes in the range of ∼1.055–1.099, ∼1.081–1.112, ∼1.132–1.147, and ∼1.140–1.165 for λ=0.35, 0.404,
0.532, and 0.7 µm, respectively, and the relative uncertainties are all
below 2 %. In addition, Eabs_lengsing shares a dependence
on size distribution similar to Eabs in the visible wavelengths. The reason is
that the Eabs mainly derives from lensing effects due to the weak
absorption of coatings. However, for ultraviolet wavelengths, there is a
completely different pattern due to the sunglasses effect.
Eabs and Eabs_internal of BC thickly coated
with BrC at different size distributions (Df=2.6,
fBC=6%).
Similar to Fig. , but for Eabs_lensing and ESunglass.
As both the lensing effect and sunglasses effect may affect the
Eabs_internal, Eabs_lensing and ESunglass are also
investigated, and the results are shown in Fig. . Here
Eabs_lensing-1 represents the Eabs enhancement caused by the
lensing effect, and ESunglass is the Eabs decrease caused by the
sunglasses effect. For thinly coated BC, although both Eabs_lensing and
ESunglass decrease with increasing λ, compared with
ESunglass, Eabs_lensing has less spectral dependence.
Eabs_lensing-1 is in the range of ∼0.205–0.283, ∼0.186–0.251, ∼0.163–0.2, and ∼0.147–0.171 for
λ=0.35, 0.404, 0.532, and 0.7 µm, respectively. However,
ESunglass can reach approximately 0.2 at λ=0.35 µm, but is
about 0 at λ=0.7 µm. In addition, for thinly coated BC, the
enhancements of the lensing effect are stronger than the blocking of the
sunglasses effect. Therefore, Eabs_internal is above 1 for thinly coated
BC (as shown in Figs. and ).
Figure illustrates the effects of size distribution on Eabs
and Eabs_internal of thickly coated BC. Compared with thinly coated BC,
there is a different effect pattern for thickly coated BC. For ultraviolet
wavelengths (e.g., λ=0.35 and 0.404 µm), absorption
enhancements decrease as rg or σg increases. This indicates that
as the particle becomes larger or the size distribution becomes wider, the
absorption enhancements become weaker. However, for the visible wavelengths,
the effects of the size distribution are quite complicated. The absorption
enhancements are relatively small when both rg and σg are
extremely large or small. The peak value commonly occurs when σg is
extremely small. concluded that the Eabs of aged BC is more
sensitive to the size distribution in the accumulation mode (in which
σg is relatively small), while the Eabs of coarsely coated BC
aggregates (i.e., with large σg) show little variation with rg.
This is precisely true for BC with weak absorbing coatings, as shown in the
results for λ=0.7 µm. However, for BC with absorbing coatings,
Eabs is sensitive to the size distribution for both modes. When fixing
the fBC to be 6 %, as rg and σg vary, the absorption
enhancements change in the ranges of ∼3.7–7.1, ∼3.85–5.80,
∼3.06–3.74, and ∼1.63–2.59 for λ=0.35, 0.404, 0.532, and 0.7 µm, respectively, and the uncertainties
in Eabs can reach up to 91.9 %, 50.7 %, 22.2 %, and 60.7 %, respectively.
Eabs_internal of thickly coated BC is also significantly affected by
the size distribution. With the rg varying in the range of 0.03–0.1 µm
and σg varying in the range of 1.15–1.75, Eabs_internal
varies in the range of 0.871–1.053, 0.891–1.121, 1.115–1.383, and 1.615–2.442 for
λ=0.35, 0.404, 0.532, and 0.7 µm,
respectively. In addition, effects of the size distribution on
Eabs_internal and Eabs are related to wavelength.
Eabs_internal decreases with particle size (i.e, increasing rg) at
ultraviolet wavelengths, while it increases as the particles become larger at
visible wavelengths (also see Fig. S6). Based on physical insights, the
reason may be due to two aspects. When the wavelength is in the ultraviolet
region, the absorption of the coatings is large; therefore, the blocking
effects of the coatings are obvious. Given identical fBC values, the
superficial area of the outer coating becomes lager as the particle size
increases. As a result, the blocking effects of the outer coatings increase.
Therefore, the Eabs_internal decreases. At visible wavelengths, the
absorption of the coatings is negligible, and the light can penetrate deeply
into BC. At that point, the main factor is the enhancement of the lensing
effect, and the larger particles may cause a larger superficial area, which
leads to the enhanced Eabs_internal. Eabs shares similar
dependences on the size distribution for different wavelengths. In addition,
Eabs_internal can be less than 1. This means that the enhancement of
the lensing effect is less than the blocking of the sunglasses effect. In
climate models, the σg is commonly assumed to be a fixed value, and
the BC size distribution is commonly assumed to be in accumulation mode
. The effects of the size distribution at fixed σg=1.5
are supplemented in Figs. S4–S7.
The effects of the size distribution on the lensing effect and sunglasses
effect of thickly coated BC are shown in Fig. . Eabs_lensing
is in the range of 2.197–2.514, 2.045–2.486, 1.844–2.526, and 1.6147–2.568 at
λ=0.35, 0.404, 0.532, and 0.7 µm,
respectively. It seems that Eabs_lensing is more sensitive to the size
distribution in the visible region compared with the ultraviolet region. However,
Eabs_lensing at different wavelengths does not deviate largely, and the
uncertainty is within 25 %. However, effects of the size distribution on
ESunglass largely depend on the wavelength. Fixing fBC=6%,
ESunglass is in the range between 1.586 and 2.062 at λ=0.35 µm and in the range between 0.001 and 0.027 at λ=0.7 µm. In addition,
from Fig. , we can also see that the enhancement of the lensing
effect (represented by Eabs_lensing-1) is less than the blocking
of the
sunglasses effect in the ultraviolet region for thickly coated BC, while the
opposite phenomenon is observed in the visible region.
Bulk radiative properties: effects of the composition ratio
To make our calculation meaningful, we compare the calculated Eabs and
mass absorption cross section (MAC) with the measurements of .
The measurement results for Eabs and MAC are estimated from Fig. 1 and
supplementary Fig. 2 of . MAC is calculated using
MAC=Cabs_coated/mBC,mBC=∫rminrmaxρBC43πr3n(r)dr,
where mBC and ρBC represent the mass and mass density of BC,
respectively. To agree with measurements, the coating thickness is determined
by the mass ratio of BrC and BC components MR. In this study, MR is
calculated by:
MR=ρBrC⋅(1-fBC)/(ρBC⋅fBC),
where ρBrC represents the mass density of BrC. In this work, we
assume ambient BC mainly composed of primary organic matter with a low degree
of oxidation. Based on the study of , an OC mass density range
of 1–1.2 g cm-3 has been used by . ρBrC=1.1 g cm-3 is
assumed in this work. For the BC mass density, the study of
gives values of ρBC=0.625 g cm-3
and ρBC=1.125 g cm-3. However, pointed out that the values may not be
representative for BC in the atmosphere. and
suggested ρBC in the range of 1.8–1.9 g cm-3, while
found the ρBC value of 1.9–2.1 g cm-3.
suggested using a value of 1.8 g cm-3. Figure S8 compares the
computations with measurements by assuming ρBC=1.8 g cm-3. We
assume that Eabs and MAC at λ=0.7 µm do not deviate largely
with those at λ=0.781 µm. Modeled Eabs at λ=0.7 µm agrees
well with the measurements. Although Eabs at
λ=0.404 µm seems to be relatively higher than the measurements,
it does not deviate largely from the measurements. However, modeled MAC is a
little smaller than the measured MAC. Similar results were obtained for bare
BC (; ). Therefore, ρBC=1.8 g cm-3 may
be a little high for estimation of MAC.
concluded that the MAC value of 7.5±1.2 m2 g-1 for bare BC
can be assumed at λ=0.55 µm by reviewing 21 publications of MAC
measurements. However, our calculated MAC of 6.02–6.2 m2 g-1 (see Table )
at λ=0.532 µm lies below the range of MAC values suggested
by . Similar conclusions were drawn by and
. However, our calculated MAC agrees well with the calculated MAC
of 6.0±0.1 m2 g-1 by at λ=0.55 µm. As MAC
depends significantly on BC mass density, to agree with measurements,
used ρBC=1.0 g cm-3. However, as pointed by
, the measured MAC and modeled MAC were not at the same
wavelength, therefore leading to too low retrieved ρBC. To raise the
computed MAC values to the average observed value of MAC = (7.5±1.2) m2 g-1,
ρBC=1.3–1.4 g cm-3 was suggested by .
However, this ρBC value is rather drastically smaller than the value
suggested by . Therefore, suggested assuming
ρBC=1.5–1.7 g cm-3 to raise the computational MAC results to
the lower bound of the observations. By assuming ρBC=1.5 g cm-3,
the comparison of modeled MAC and Eabs with measurements is shown in
Fig. S9. Overall, the modeled MAC and Eabs agree relatively well with
the measurement by assuming ρBC=1.5 g cm-3. Therefore, ρBC=1.5 g cm-3 is assumed in this study. In addition, according to the
previous studies , the shell / core ratio Dp/Dc
(equivalent particle diameter divided by BC core diameter) was observed to be
commonly in the range of 1.1–2.7, and the corresponding MR is
approximately 0.24–13.9.
Therefore, MR of 0–13.9 is
considered in this work.
MAC (m2 g-1) for bare BC at different Df values (rg=0.06 µm, σg=1.5).
λ (nm)
Df=1.8
Df=2.2
Df=2.6
350
9.30
9.03
8.48
404
8.14
7.95
7.60
532
6.20
6.11
6.02
700
4.68
4.64
4.65
Eabs and Eabs_internal of thinly coated BC
with BrC coatings varying with MR for different
Df values (rg=0.06 µm, σg=1.5).
Figure compares the Eabs and Eabs_internal for
thinly coated BC with different fractal dimensions at different composition
ratios. Following , a rg of 0.06 µm and a
σ of 1.5 are assumed to reflect the real size distribution of BC. It
is expected that as the coatings increase, Eabs becomes much stronger.
With MR varying from 0 to 2.93, Eabs variations of ∼1–2.5,
∼1–2.2, ∼1–1.6, and ∼1–1.285 are obtained for
λ=0.35, 0.404, 0.532, and 0.7 µm,
respectively. The Eabs for thinly coated BC with weakly absorbing
materials (i.e., λ=0.7 µm) is significantly lower than that
for the
core–shell sphere, as reported by , where Eabs can reach
approximately 1.5 when the shell / core ratio is 1.6 (MR=2.2709) at
λ=0.55 µm. Even though the results are gained at two different
wavelengths, the Eabs for BC that is coated with weakly absorbing
coatings should not deviate substantially between λ=0.55 µm and
λ=0.7 µm (see Fig. ). Therefore, the differences from
the previous study are mainly caused by the BC shape, as demonstrated in
Fig. . When the relative contents of BC vary, substantial
variations in Eabs_internal can also be observed. As MR varies in
the range of 0–2.93, Eabs_internal increases from 1 to 1.07, 1 to 1.1,
1 to 1.22, and 1 to 1.285 for λ=0.35, 0.404, 0.532, and 0.7 µm, respectively. Eabs_internal of thinly coated
BC increases with MR in the visible spectral region, while a little
decrease in Eabs_internal can be observed in the ultraviolet region as
MR increases when MR is larger than a threshold value. This is mainly caused by
the blocking of the sunglasses effect.
The relative deviations of absorption properties between
Df=1.8 and Df=2.6 for thinly coated BC with BrC
coating (fBC=20%).
At different wavelengths, the effects of Df may vary. Eabs_internal
increases with Df in the visible wavelengths, as the more compact
structure can lead to a greater lensing interaction. While in the ultraviolet
region, as the structure becomes more compact, the interaction of absorbing
coatings also increases; therefore, the blocking effects of outer coatings
are greater. Therefore, the Eabs_internal can decrease with Df when
Df is greater than a threshold value. Even though and
showed that the effects of Df on Cabs are not obvious for
thinly coated BC, for Eabs of thinly coated BC, the sensitivity of Df
has not been investigated. To quantify the effects of Df, the relative
deviations between Df=1.8 and Df=2.6 are also calculated for
thinly coated BC. From Fig. , we found that the differences in
Eabs and Eabs_internal among different values of Df are larger
for thicker coatings. Therefore, to evaluate the maximum uncertainty, the
fBC is fixed to be 20 %. As shown in Fig. , the differences
in Eabs and Eabs_internal between Df=1.8 and Df=2.6 are all
below 5 %. Eabs of BC thinly coated with non-absorbing coatings is more
obviously affected by Df. However, the relative deviations between
Df=1.8 and Df=2.6 do not exceed 12 % (as shown in Fig. S10.).
Similar to Fig. , but for Eabs_lensing and ESunglass.
Eabs and Eabs_lensing of thickly coated BC
with BrC coatings varying with MR (rg=0.06 µm, σg=1.5).
To reveal the factors that contribute to the complex Eabs_internal,
the effects of MR on Eabs_lensing and ESunglass of
thinly coated BC are investigated at different wavelengths.
Eabs_lensing increases with MR for all wavelengths. It seems that
the sensitivity of Eabs_lensing to MR is more obvious
in the
ultraviolet region compared with the visible region. Fixing Df=2.2, with MR
varying from 0 to 2.93, Eabs_lensing increases from 1 to 1.46, 1.4,
1.32, and 1.25 for λ=0.35, 0.404, 0.532, and 0.7 µm, respectively.
In addition, more compact structure can result in
stronger lensing interaction among monomers and thus leads to an
Eabs_lensing increase with Df. Moreover, compared with the visible
region, the effects of Df are more obvious at the ultraviolet region.
ESunglass also increases with Df, as a more compact structure may lead
to stronger blocking interaction among BC monomers. As expected,
ESunglass is stronger in the ultraviolet region, while it tends to be 0 in
the visible region. As MR reaches 2.93, ESunglass can reach
approximately 0.46 at λ=0.35 µm, while ESunglass is below
0.02 at λ=0.7 µm.
Figure demonstrates the absorption enhancements of thickly coated
BC at different wavelengths for different composition ratios. Similar to
thinly coated BC, Eabs increases with increasing MR or decreasing
λ. When setting rg=0.06 µm and σg=1.5, as MR
varies from 6.6 to 13.9, Eabs increases from 3.4 to 5.4 and 3.25 to 5.2
for λ=0.35 and λ=0.404 µm, respectively, while
Eabs varies from 2.78 to 3.96 and 2.2 to 2.4 for λ=0.532
and 0.7 µm, respectively. In addition, the Eabs seems to be more
sensitive to the composition ratios in the ultraviolet wavelengths. This may
be caused by the absorption of coatings, which can substantially enhance the
total absorption. In addition, the combined Eabs values of thinly coated
and thickly coated BC range for BC with BrC coatings is much wider
than that for BC with non-absorbing coatings (Eabs of ∼1–2.4)
.
At visible wavelengths, the Eabs_internal is greater than 1 due to the
small blocking effects of BrC. Defining rg to be 0.06 µm and
σg to be 1.5, as MR varies from 6.6 to 13.9, Eabs_lensing
ranges from ∼1.222 to 1.337 and ∼2.115 to 2.357 for λ=0.532 and 0.7 µm, respectively. This indicates that the total
absorption of BC and BrC can be substantially enhanced by the lensing
effects. However, for ultraviolet wavelengths, the Eabs_internal is
less than 1. Eabs_internal is within ∼0.913–0.924 and
∼0.956–0.974 for λ=0.35 and λ=0.404 µm,
respectively. This demonstrates the absorbing coatings can significantly
block the light into BC. Therefore, the total absorption is less than the sum
of BrC absorption and BC absorption. In recent studies, the enhancements of
lensing effects has gained increasing attention. However, few studies have
investigated the blocking effects of absorbing coatings. As a matter of fact,
the blocking effect of absorbing coatings is also a significant factor that
affects the total absorption, as the Eabs_internal can be below 1. This
indicates that the blocking effects of absorbing coatings may be greater than
the enhancements of the lensing effects. Therefore, when BC is coated with BrC,
we should not only focus on the enhancements of the lensing effects but also
carefully consider the blocking effects of the coatings.
There is a different dependence on MR for Eabs_internal at different
wavelengths. Eabs_internal increases with MR at relatively long
wavelengths (eg. λ= 0.7 µm), while decreases as the coatings
become thicker at relatively short wavelengths (0.404 and 0.532 µm).
This phenomenon can also be explained from physical insights. When the
wavelength is short, increased thickness of the coatings may lead to a
greater sunglasses effect, which weakens the total absorption of the coatings
and BC. However, at λ=0.7 µm, enhanced Eabs_internal can
be obtained by increasing the coatings due to the negligible blocking effects
of the coatings. In addition, Eabs_internal increases with wavelength
due to the decrease in coating absorption (see Fig. ).
Eabs_internal of thickly coated BC is insensitive to MR at
λ=0.35 µm due to the similar variations in Eabs_lensing
and ESunglass with MR. As MR varies from 6.6 to 13.9,
Eabs_lesnig increases from 2.204 to 2.363, 2.214 to 2.390, 2.216 to
2.473, and 2.165 to 2.509 at λ=0.35, 0.404, 0.532, and 0.7 µm, respectively. Meanwhile, ESunglass is largely affected by
wavelengths. At λ=0.35 µm, ESunglass is in the range from
1.523 to 1.807, while ESunglass approaches 0 at λ=0.7 µm.
It can also be seen from Fig. that
ESunglass>Eabs_lensing-1
at λ=0.35 and 0.404 µm. Therefore, Eabs_internal is less than 1.
Comparison of BC coated with non-absorbing materials and that coated
with BrC (rg=0.06 µm, σg=1.5).
Df=2.2 and Df=2.6 were assumed for thinly coated and
thickly coated BC, respectively.
demonstrated that there are different wavelength dependencies
for BC that is coated with absorbing and weakly absorbing materials.
Eabs for BC coated with humic acid was observed to vary from 3.0
to approximately 1.6 as λ increased from 0.554 to 0.84 µm,
while it seemed to be essentially wavelength independent for BC that is
coated with sodium chloride. Figure compares the wavelength
dependencies of BC coated with non-absorbing materials and BrC. For
thinly coated BC, there are substantial wavelength dependencies for BC coated
with BrC. By setting fBC to be 40 %, Eabs increases
from 1.15 to 1.57 with λ varying from 0.7 to 0.35 µm, which
results in an approximately 49.6 % increase. However, when coated with
non-absorbing materials, Eabs exhibits small
wavelength dependences. This leads to approximate 8.7 % increases as
λ decreases from 0.7 to 0.35 µm. Furthermore, for
thickly coated BC, Eabs is significantly wavelength dependent for
BC with BrC coatings. The decrease in λ from 0.7 to 0.35 µm
would result in an approximately 100 % increase in Eabs, while
Eabs seems to be essentially wavelength independent for BC with
non-absorbing coatings (Eabs_lensing); it is approximately 2.4
when fBC=6%, which is consistent with the value reported by
. The differences of Eabs_lensing of thickly coated
BC between λ=0.35 and 0.7 µm are below 6.2 %. Therefore,
the variation in kBrC should be mainly responsible for the
significant wavelength dependencies of Eabs for BC with BrC
coatings when the wavelength is long. For ultraviolet wavelengths (λ
from 0.35 to 0.404 µm), wavelength dependence of
Eabs is relatively small, as the Eabs may increase
with wavelength when kBrC is fixed at a large value (see
Fig. ), which can reduce the wavelength dependence. Therefore, the
contribution of kBrC to the wavelength dependence should be
further analyzed in ultraviolet wavelengths in the future.
In addition, the Eabs_internal of BC coated with BrC is also
significantly wavelength dependent. Fixing fBC=40 % and 6 %,
respectively, with λ varying from 0.35 to 0.7 µm,
Eabs_internal increases from 1.05 to 1.18 and from approximately 0.92
to 2.3, respectively. Eabs_lensing-1 and ESunglass are also
compared in Fig. . ESunglass decreases significantly with
λ for both thinly and thickly coated BC. For thinly coated BC,
Eabs_lensing-1 is larger than ESunglass for all wavelengths.
However, ESunglass can be stronger than Eabs_lensing-1
in the
ultraviolet region for thickly coated BC. This indicates that the total
absorption of BC and BrC is weakened by internal mixing. Therefore, the
sunglasses effect should also be noticed for the estimation of aerosol
absorption.
Summary and discussion
Using the MSTM method, the Eabs
and Eabs_lensing of BC with BrC coatings were investigated at
λ=0.35, 0.404, 0.532, and 0.7 µm, respectively. The main
findings of this work are as follows.
Generally, Eabs increases with kBrC while Eabs_interanl
decreases as kBrC becomes larger. For the thinly coated BC,
Eabs_internal is greater than 1 due to the enhancements of the lensing
effects. However, for thickly coated BC, the Eabs_internal can be less
than 1. This indicates the total absorption of BrC and BC is less than the sum of
BrC and BC absorption individually, which is opposite to BC that is coated
with weakly absorbing coatings. This phenomenon may be caused by the blocking
effects of outer coatings. As the absorption of coatings increases, less
light can penetrate into BC materials. Therefore, the total absorption of BrC
and BC is weakened, resulting in Eabs_internal of less than 1. This
effect is named the “sunglasses effect” in this study.
Cabs of thinly coated BC is underestimated by the core–shell sphere model in
the ultraviolet region while it is overestimated in the visible region. In
addition, the ratio of Cabs of thinly coated BC to that of the core–shell
sphere model increases with kBrC. Eabs of thinly coated BC is
enhanced by the core–shell sphere while the enhancements are alleviated by
increasing kBrC. There are different dependencies for thickly coated BC.
Cabs of thickly coated BC is underestimated by the core–shell sphere model
for all wavelengths while the underestimation becomes negligible as kBrC
becomes very large. Eabs of thickly coated BC with non-absorbing materials
is underestimated by the core–shell assumption. However, the ratio of Eabs
of thickly coated BC to the core–shell sphere model decreases with increasing
kBrC, and Eabs is enhanced by the core–shell sphere in the visible
region, when the absorption of coatings is large.
To make our calculation more consistent with real circumstance, the bulk
absorption was calculated and the kBrC is selected by interpolation
based on the study of . For thinly coated BC, the effects of size
distribution on Eabs are not obvious. The uncertainties of size
distribution result in Eabs differences of less than 2.56 %, 2.52 %,
2.32 %, and 2.16 % for λ=0.35, 0.404, 0.532,
and 0.7 µm, respectively. However, Eabs of thickly coated BC is
quite sensitive to the size distribution. Eabs differences of
approximately 92 % can be obtained as rg and σg vary for
λ=0.35 µm. In addition, different from Eabs of
2.2–2.4 for thickly coated BC with weakly absorbing coatings, Eabs
of 3.4–5.4 is observed for BC with BrC coatings at λ=0.35 µm as MR
is in the range of ∼6.6–13.9. Specifically, as MR increases to
approximately 13.9, Eabs of larger than 3.96 can be observed at
0.532 µm, which is a little higher than the commonly measured Eabs
of 1.05–3.5 at this wavelength. For thinly coated BC, Eabs of BC
with weakly absorbing coatings is in the range of approximately ∼1–1.3
for λ=0.7 µm (i.e., BC with weakly absorbing coatings) while a
wider range of ∼1–2.5 is obtained for λ=0.35 µm. In
summary, the Eabs range of BC with BrC coatings is much wider than that of
BC with non-absorbing coatings.
The sunglasses effect and lensing effect are compared at different wavelengths.
Esunglass is less than Eabs_lensing-1 for thinly coated BC. This
indicates the blocking of the sunglasses effect is less than the enhancement of
the lensing effect, so the Einternal>1 for thinly coated BC. However,
Esunglass can be larger than Eabs_lensing-1 in the ultraviolet region
for thickly coated BC, which leads to Einternal<1. Therefore, the
absorption of BC thickly coated with BrC can be less than an external mixture of
BC and BrC. In the visible region, Esunglass is less than
Eabs_lensing-1 due to the small sunglasses effect.
Eabs of BC with BrC coatings is more wavelength dependent than
that
with non-absorbing coatings. For thinly coated BC, Eabs of BC with
non-absorbing coatings leads to an approximately 8.7 % increase as λ
decreases from 0.7 to 0.35 µm while the difference can reach
approximately 50 % for BC with BrC coatings. For thickly coated BC, the
decrease in λ from 0.7 to 0.35 µm would result in an
approximately 100 % increase in Eabs for BC with BrC coatings. However,
Eabs of BC with non-absorbing coatings seems to be to be essentially
wavelength independent. In addition, for thinly coated BC, the effects of
Df are not obvious for Eabs and Eabs_lensing. The uncertainties
of Eabs and Eabs_internal caused by Df all are less than 5 %.
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.