Aerosol complex refractive index (ACRI) is an important microphysical
parameter used for the studies of modeling their radiative effects. With
considerable uncertainties related to retrieval based on observations, a
numerical study is a powerful method, if not the only one, to provide a
better and more accurate understanding of retrieved optically effective ACRIs
of aged black carbon (BC) particles. Numerical investigations of the
optically effective ACRIs of polydisperse coated BC aggregates retrieved from
their accurate scattering and absorption properties, which are calculated by
the multiple-sphere T-matrix method (MSTM), without overall particle shape
variations during retrieval, are carried out. The aim of this study is to
evaluate the effects of aerosol microphysics, including shell/core
ratio Dp/Dc, BC geometry, BC position inside coating,
and size distribution, on retrieved optically effective ACRIs of coated BC
particles. At odds with expectations, retrieved optically effective ACRIs of
coated BC particles in coarse mode are not merely impacted by their chemical
compositions and shell/core ratio, being highly complicated functions
of particle microphysics. However, in accumulation mode, the coated BC
optically effective ACRI is dominantly influenced by particle chemical
compositions and the shell/core ratio. The popular volume-weighted
average (VWA) method and effective medium theory (EMT) provide acceptable
ACRI results for coated BC in accumulation mode, and the resulting
uncertainties in particle scattering and absorption are both less than
approximately 10 %. For coarse coated BC, the VWA and EMT, nevertheless,
produce dramatically higher imaginary parts than those of optically effective
ACRIs, significantly overestimating particle absorption by a factor of nearly
2 for heavily coated BC with a large BC fractal dimension or BC close to the
coating boundary. Using the VWA could introduce significant overestimation in
aged BC absorption analysis studies, and this may be one of the reasons why
modeled aerosol optical depth is 20 % larger than observed, since it is
widely employed in the state-of-the-art aerosol–climate models. We propose a
simple new ACRI parameterization for fully coated BC with
Dp/Dc≥2.0 in coarse mode, which can serve as a
guide for the improvement of ACRIs of heavily coated BC, and its scattering
and absorption errors are reduced by a factor of nearly 2 compared to the
VWA. Our study indicates that a reliable estimate of the radiative effects of
aged BC particles in coarse mode would require accounting for the optically
effective ACRI, rather than the ACRI given by the VWA, in aerosol–climate
models.
Introduction
The largest uncertainty in estimates of the effects of atmospheric aerosols
on climate stems from uncertainties in the determination of their
microphysical properties, which in turn determines their optical properties.
As one of the most significant microphysical properties, aerosol complex
refractive index (ACRI) should be known for modeling their radiative effects,
and the magnitude of radiative forcing is very sensitive to the ACRI,
especially the imaginary part (Raut and Chazette, 2008a). The ACRI is
determined by particle chemical composition governing its inherent scattering
and absorption properties.
Black carbon (BC), emitted from incomplete fossil fuel combustion and biomass
burning, can be coated with secondary aerosol species (e.g., organics and
sulfate) through the aging process, being one of the largest uncertainties in
estimating aerosol radiative forcing due to their complicated geometry and
mixing state (Ramanathan and Carmichael, 2008; Myhre, 2009; Bond et al.,
2013; Zhang et al., 2015). As a strong absorptive aerosol, pure BC particles
have a large ACRI, whereas our understanding of the ACRI of aged BC is still
limited because of its internal mixing with weakly absorptive coatings
(Shiraiwa et al., 2010; Cui et al., 2016; Peng et al., 2016). The ACRIs of BC internal mixtures, named
effective ACRIs, are normally obtained based on the volume-weighted average
(VWA) method and effective medium theory (EMT), and the choice of both
approaches is driven by high dependency of ACRIs on particle chemical
compositions (e.g., Kandler et al., 2009). The state-of-the-art
aerosol–climate models employ the VWA method extensively, approximating the
effective ACRIs of internally and externally mixed aerosol ensembles at each
mode for calculating their optical and radiative properties (e.g., Stier et
al., 2005; Kim at al., 2008; Zhang et al., 2012). Nonetheless, the
performances of the VWA and EMT are open questions, as several studies have
questioned the validity of both approximations in some questions (e.g.,
Voshchinnikov et al., 2007).
The estimates of the ACRI of coated BC can also be made from observed optical
properties, and the ACRI is inferred by obtaining a best fit to numerical
simulations with Mie theory assuming a spherical particle shape, which is
called optically effective ACRI. For instance, the optically effective ACRIs
are retrieved based on simultaneous measurements of surface aerosol
scattering and absorption coefficients, as well as size distributions (Abo
Riziq et al., 2007; Schkolnik et al., 2007; Mack et al., 2010; Stock et al.,
2011). Meanwhile, the airborne in situ measurements of particle optical
properties from a particle soot absorption photometer (PSAP), spectral
optical absorption photometer (SOAP), sunphotometer, or lidar, combined with
a Mie theory-based data analysis scheme, are also applied for the retrieval
of optically effective ACRIs (Raut and Chazette, 2008a, b; Petzold et al.,
2009; Muller et al., 2009). Muller et al. (2010) even compare retrieved
optically effective ACRIs from different techniques and reveal only partly a
reasonable agreement with significant differences for the spectra of
imaginary part remaining, indicating uncertainties during retrieval. The
uncertainties may be that those retrieval methods are based on unrealistic
spherical shape assumption, inaccurate numerical modeling, or without
considering the errors in aerosol optical measurements, and then sizeable
errors in retrieved optically effective ACRIs are posed. Moreover, these
uncertainties significantly limit our ability to understand the relationships
between the optically effective ACRI and aerosol other microphysical
properties, and furthermore to improve radiation simulations in
aerosol–climate models. Therefore, a systematic theoretical investigation on
optically effective ACRIs of internally mixed particles retrieved from
exactly calculated optical properties without particle shapes changed is a
must, which is generally missing, and will benefit our understanding of these
relationships. For coated BC particles with several chemical compositions,
their optically effective ACRIs are not only affected by their compositions,
but are also possibly impacted by their other microphysics. However, the
effects of coated BC microphysics on their optically effective ACRIs are
still under discussion and need more investigation.
Here, numerical investigations of the optically effective ACRIs of
polydisperse coated BC aggregates as examples are systematically presented
based on our current understanding, and the optically effective ACRI
influences are decomposed into that due to particle microphysical
properties, including shell/core ratio, BC fractal dimension, BC position
inside coating, and size distribution. An exact multiple-sphere T-matrix
method (MSTM) is employed to numerically calculate the absorption properties
of coated BC aggregates while the Mie method is applied for the retrieval of
optically effective ACRI. The objective is to evaluate the effects of
coating microphysics on the optically effective ACRIs of aged BC particles,
which hopefully benefits our understanding of the mechanism responsible for
the model–observation discrepancies and refining estimates of aerosol
radiative forcing. The performances of the VWA and EMT approximations are
also studied for comparison.
MethodologyCoated BC model
Freshly emitted BC particles often exist as loose cluster-like aggregates
with hundreds or even thousands of small spherical monomers (e.g., Li et
al., 2016), and the concept of fractal aggregate has shown great success and
wide applications in representing realistic BC geometries (e.g., Sorensen,
2001). The fractal aggregate can be mathematically described by the
well-known statistic scaling rule following
N=k0RgaDf,Rg=1N∑i=1Nri2,
where N is the monomer number in an aggregate, a the mean monomer
radius, k0 the fractal prefactor, Df the fractal
dimension, and Rg the gyration radius.
After being emitted into the atmosphere, BC aggregates tend be coated by
other materials, such as sulfate and organics (e.g., Schwarz et al.,
2008a; Tritscher et al., 2011), through the aging
process, and their chain-like structures tend to collapse into more compact
clusters (Zhang et al., 2008; Coz and Leck, 2011). The aged BC particles can
have BC Df of almost 3, while the fresh BC aggregates generally
show lacy structures with Df less than 2 (Liu et al., 2008).
While the fractal aggregates have been successfully employed to model the
geometries of BC particles (e.g., Dlugach and Mishchenko, 2015; Mishchenko et
al., 2016), their coating geometries are generally complicated in ambient
air. Some observations of individually aged BC particles actually show
spherical coating geometry (e.g., Schnaiter et al., 2005; Alexander et al., 2008; Zhang et al., 2008; Wu et al., 2016),
while others depict complex irregular geometries. Meanwhile, it is found that
the simple spherical coatings on BC particles have similar effects on
scattering and absorption properties to those with more complicated coating
structures (e.g., Dong et al., 2015; F. Liu et al., 2015; C. Liu et al.,
2017). To avoid the influence of overall particle shape variations on
retrieval results of optically effective ACRIs and to use the fast Mie theory
for retrieval, this study therefore considers an aggregate as the BC core,
and a spherical coating is added as the coating material, which is assumed to
be the weakly absorbing sulfate, following the numerical model developed by
Zhang et al. (2017). The sketch map of the BC aggregates coated by sulfate
with an overall spherical shape is shown in Fig. 1.
Sketch map of the geometry of coated black carbon. An example of
fractal black carbon aggregates, containing 200 monomers, is coated by
sulfate.
For this inhomogeneous internally mixed particle, the BC aggregates are
generated based on a tunable particle-cluster aggregation algorithm from
Skorupski et al. (2014). The kf of BC is assumed to be 1.2
based on Sorensen (2001). The Df can characterize the shape of
BC aggregates reasonably well, and its variation reflects BC aging processes
(Wang et al., 2017). The radius a of BC aggregate monomers is observed to
vary over a range of about 10–25 nm (Bond and Bergstrom, 2006), while the
monomer number N can alter up to approximately 800 (Adachi and Buseck,
2008). Since the monomer size has a rather weak effect on BC scattering and
absorption as Df is fixed (Liu and Mishchenko, 2007; He et al.,
2015), we consider two N values of 200 and 800 as examples of accumulation
and coarse particles, respectively, and compare three Df values
of 2.6, 2.8, and 2.98 for aged BC aggregates. After BC geometry is defined,
the shell/core ratio Dp/Dc of coated BC is
assumed to be in the range of 1.1–2.7 on the basis of the SP2 measurements
in London (D. Liu et al., 2015) and Beijing (Zhang et al., 2016). It should
be noted that some small Dp/Dc values might not be
used, because we only study the cases for BC aggregates fully coated by
sulfate. An incident wavelength of 550 nm is considered in this study, and
related refractive indices of BC and sulfate are assumed to be 1.85-0.71i
(Bond and Bergstrom, 2006) and 1.52-5.0×10-4i (Aouizerats et al.,
2010), respectively. With the internally mixed coated BC model defined, which
depicts quite realistic geometries, its random-orientation scattering and
absorption properties are exactly calculated with the robust multiple-sphere
T-matrix method (Mackowski, 2014).
For ambient atmospheric applications, it is meaningful to consider bulk
particle optical properties averaged over a certain size distribution. This
study explores an ensemble of BC aggregates with different sizes but the same
sulfate coating fraction (i.e., same Dp/Dc), and a
lognormal size distribution is assumed with the form of
n(r)=12πrln(σg)exp-ln(r)-ln(rg)2ln(σg)2,
where σg is the geometric standard deviation and
rg is the geometric mean radius (e.g., Yurkin and Hoekstra,
2007; Schwarz et al., 2008b). As particles in
accumulation and coarse modes contribute dominated light scattering and
absorption, we only consider coated BC in both modes. For the accumulation
mode, the radius range is set as 0.05–0.5 µm in steps of
0.005 µm, while the coarse radius range is assumed to be
0.5–2.5 µm in steps of 0.05 µm as ambient aerosols with
sizes larger than 5 µm are few (Zhang et al., 2014, 2018; Zhang and
Mao, 2015). Note that the exact sizes of BC aggregates are known based on
these coated BC sizes and shell/core ratios. To better understand the
behavior at different particle size modes, size distributions in accumulation
and coarse modes are utilized separately, which are similar to those applied
in the aerosol–climate models (Zhang et al., 2012). In this study, we
consider the size distributions of coated BC aggregates (i.e., BC–sulfate
internal mixtures) with rg of 0.075 and 0.75 µm, and
σg of 1.59 and 2.0 in accumulation and coarse modes,
respectively (Zhang et al., 2012). With given particle size distributions,
the bulk scattering cross section (Csca) and absorption cross
section (Cabs) of coated BC follow the equations of
Csca=∫rminrmaxCsca(r)n(r)d(r),Cabs=∫rminrmaxCabs(r)n(r)d(r).
With the inhomogeneous coated BC model defined and its exact scattering and
absorption properties obtained, it is possible to retrieve its optically
effective ACRI with more details.
Retrieval approach
The retrieval approach is similar to the methods described in previous
studies (e.g., Mack et al., 2010; Stock et al., 2011; Zhang et al., 2013),
with the only differences being that the inherent aerosol optical properties
are exactly calculated rather than measured and particle overall shapes are
not changed during retrieval. Among all particle optical properties, the
scattering and absorption are selected for retrieval, since both are
basically governed by the real and imaginary parts of the ACRI, respectively.
As coated BC models are overall spherical, the optically effective ACRI is
determined by an iterative algorithm based on Mie theory, utilizing particle
size distributions and calculated scattering and absorption cross sections.
Exploiting all calculations, the designed inversion scheme to retrieve the
optically effective ACRI follows.
Based on a guess for a real part, n, and an imaginary part, k, of the
ACRI at a given wavelength, two look-up tables are built from the database
with known size distribution. One look-up table encompasses the scattering
cross sections and the other contains the absorption cross sections. For
physically based sense, guessed real and imaginary parts of the optically
effective ACRI are within refractive index ranges of known compositions of
simulated internally mixed particles. Thus in our retrieval, the guessed real
part of a refractive index varies from 1.52 to 1.85 with an equidistant space
of 0.001 and the imaginary part changes from 5.0×10-4 to 0.71 with
a logarithmic interval of 0.005. Then the retrieval algorithm simultaneously
varies n and k and scans through all physically possible ACRI values
within a selected resolution until it minimizes χ2:
χ2(n,k)=1N∑i=1NCsca,calculated(n,k)-Csca,inherentCsca,inherenti26+Cabs,calculated(n,k)-Cabs,inherentCabs,inherenti2,
where Csca,inherent and Cabs,inherent are inherent
scattering and absorption cross sections of simulated internally mixed
particles, χ2(n,k) generates the fractional difference of the
calculated scattering and absorption cross sections relative to the inherent
properties, and N is the number of calculations during the retrieval. The
χ2(n,k) values for particle scattering and absorption are minimized
by optimizing initial guess ACRI values, yielding an optically effective ACRI
at this wavelength. Since particle scattering is mainly determined by the
magnitude of n, while its absorption is
primarily governed by the magnitude of k, the
minimization of χ2(n,k) should retrieve a unique result of optically
effective ACRIs.
As the optically effective ACRIs of coated BC with fixed microphysical
parameters (such as shell/core ratio, BC fractal dimension, size
distribution) are retrieved, it is possible to study the impacts of these
microphysical parameters on retrieved optically effective ACRI with more
details. The optically effective ACRI of internally mixed particles here is
defined as an ACRI that provides almost the same scattering and absorption
properties as their inherent properties, based on known size distribution and
overall particle shapes for homogeneous particles. Please note that aged BC
particles have complicated shapes in ambient air (D. Liu et al., 2017), and
coated BC considered in this study represents a case study, resembling the
findings presented by Schnaiter et al. (2005), to give
insights into the effects of particle microphysics on its optically
effective ACRI.
Results and discussionEffect of coated BC morphologies on its optically effective ACRI
This study focuses on the influence of the microphysics of coated BC
aggregates on their optically effective ACRIs, and, therefore, the properties
of the microphysics are our interest. The coated BC optically effective ACRI
depends not only on the particle shell/core ratio (i.e.,
Dp/Dc), but also on particle morphology (i.e., the
physical arrangement of BC with respect to other components within a given
particle). With sulfate coating geometry fixed and BC fully coated, we will
consider two other morphological factors: BC geometry and BC position inside
sulfate coating.
To show the effect of BC geometry on coated BC optically effective ACRIs, the
concentric core-shell structures (i.e., mass centers located at the coating
center) with inside BC aggregates exhibiting fractal dimensions of 2.6, 2.8
and 2.98 are considered. Figure 2 compares retrieved optically effective
ACRIs of these coated BC aggregates with different BC geometries at different
shell/core ratios, while the introduced differences of scattering and
absorption cross sections are illustrated in Fig. 3. The differences are
relative errors of scattering and absorption cross sections induced by
retrieved effective ACRIs compared with initial inherent optical properties.
The retrieved ACRIs of internally mixed coated BC particles are optically
effective, since the relative errors for both scattering and absorption cross
sections are within 1 % (see Fig. 3a and b). For comparison, the ACRIs of
coated BC aggregates derived from the popular volume-weighted average method
and Bruggeman effective medium theory, as well as their induced differences
of scattering and absorption, are also shown in Figs. 2 and 3. The properties
are averaged over an ensemble of BC–sulfate internally mixed particles with
the aforementioned size distributions for accumulation and coarse modes
separately.
The real (a and b) and imaginary (c and
d) parts of retrieved optically effective aerosol complex refractive
indices (ACRIs) of black carbon aggregates coated by sulfate as a function of
shell/core ratio (Dp/Dc, spherical
volume-equivalent particle diameter/BC core diameter), in accumulation
(a and c) and coarse (b and d) modes,
respectively. Black squares, red circles and blue up-triangles indicate BC
fractal dimensions of 2.98, 2.8 and 2.6, respectively. The ACRIs given by the
popular volume-weighted average method (magenta down-triangles) and Bruggeman
effective medium theory (olive diamonds) are also considered for comparison.
As shown in Fig. 2, in accumulation mode, it is expected that, as
Dp/Dc increases (i.e., BC content decreases),
both n and k of retrieved
optically effective ACRI of concentric coated BC aggregates will decrease. With
Dp/Dc varying from 2.7 to 1.5, the real part of the optically
effective ACRI of accumulation coated BC increases from ∼1.53 to
∼1.60, whilst its imaginary part becomes almost 6 times larger from ∼0.038
to ∼0.216 (see Fig. 2a and c). As BC fractal dimension increases (i.e., BC
becomes more compact), the real part of the optically effective ACRI shows a
slight decrease in accumulation mode, whereas the reverse is true for
the retrieved imaginary part. For mass-center positions of different BC
geometries fixed within sulfate coating, retrieved optically effective ACRIs
of accumulation particles are slightly sensitive to their inside BC
geometries, with differences of less than 1 % and 5 % for n and k,
respectively. Compared to the optically effective ACRIs of concentric coated
BC aggregates in accumulation mode, the imaginary parts of ACRIs estimated
from the VWA and EMT are lower by 2 %–7 % and 9 %–15 %, respectively,
depending on Dp/Dc and BC fractal dimension, while their real
parts are slightly higher, with differences within 2 %. As a result, the
VWA and EMT overestimate coated BC scattering cross sections by 2 %–7 % and
4 %–11 % and underestimate absorption cross sections by 1 %–4 % and
5 %–11 %, respectively (see Fig. 3c and e). Meanwhile, the VWA performs
slightly better than the EMT for coated BC in accumulation mode.
The relative differences of scattering and absorption cross sections
of black carbon aggregates coated by sulfate induced by their optically
effective complex refractive indices (a and b), and
refractive indices based on the volume-weighted average method (c
and d) and Bruggeman effective medium theory (e and
f) as a function of shell/core ratio
(Dp/Dc), in accumulation (a, c and
e) and coarse (b, d and f) modes,
respectively. Black squares, red circles and blue triangles indicate BC
fractal dimensions of 2.98, 2.8 and 2.6, respectively. Solid symbols denote
scattering coefficients, while open interiors indicate absorption
coefficients.
Unlike accumulation mode, the retrieved optically effective ACRI of
concentric coated BC in coarse mode depicts distinctive patterns, which is
illustrated in Fig. 2b and d. The impact of particle microphysics on the
optically effective ACRIs of coarse concentric coated BC is complicated,
especially for their real parts, which show strong oscillations as a function
of the shell/core ratio. The imaginary parts of retrieved optically
effective ACRIs of coated BC aggregates in coarse mode generally decrease
with the increase in Dp/Dc or BC fractal dimension.
The imaginary parts of derived ACRIs based on the VWA and EMT can be higher
than those of retrieved optically effective ACRIs by a factor of ∼3,
and the resulting overestimation of absorption cross sections of coarse
concentric coated BC can be as high as ∼75 %. The optically
effective ACRI, producing coated BC scattering and absorption with
differences less than 1 %, performs predominantly better than the VWA and
EMT in coarse mode, and the VWA and EMT result in more uncertainties in
particle absorption than scattering. Furthermore, the VWA and EMT
overestimate more absorption and underestimate more scattering for coarse
coated BC with a larger BC fractal dimension or Dp/Dc.
The simulations discussed above assume coated BC with a concentric core-shell
structure, which does not always represent realistic aerosols, whereas coated
BC with an off-center core-shell structure may be certainly true for some
ambient particles. Figure 4 portrays retrieved optically effective ACRIs of
coated BC aggregates (BC fractal dimension of 2.8) with the aforementioned
size distributions for two different off-center structures compared to the
concentric core-shell structure. For two off-center core-shell structures
assumed, one is BC aggregates located in the middle of a radius of the
coating sphere and the other is BC in an outer position as close as possible
to the coating boundary. It is evident that coated BC optically effective
ACRIs in accumulation mode decrease with increasing
Dp/Dc for various BC inside positions (see Fig. 4a
and c). The optically effective ACRIs of accumulation coated BC aggregates
are generally sensitive to the BC position inside sulfate coating, with
variations of 1 % and 20 % for n and k, respectively. When BC
aggregates move from the coating center to the boundary, the real parts of
retrieved optically effective ACRIs in accumulation mode are found to
increase slightly, as opposed to the decrease in their imaginary parts. For
accumulation BC aggregates with different core-shell structures, the VWA and
EMT give relatively close ACRIs to their optically effective ACRIs, with n
differences both within 1 % and k differences less than 11 % and
14 %, respectively. In coarse mode, the real parts of retrieved optically
ACRIs show intricately strong variations in the shell/core ratio and
BC inside position, and their imaginary parts are generally decreasing, with
BC becoming closer to the coating boundary (see Fig. 4b and d). The imaginary
parts of retrieved optically effective ACRIs of coarse coated BC with
different BC inside positions are significantly lower than those given by the
VWA and EMT, indicating severe overestimation of coarse particle absorption
by the VWA and EMT.
The real (a and b) and imaginary (c and
d) parts of retrieved optically effective aerosol complex refractive
indices (ACRIs) of black carbon aggregates coated by sulfate (BC fractal
dimension of 2.8) as a function of shell/core ratio
(Dp/Dc), in accumulation (a and c)
and coarse (b and d) modes, respectively. Three BC coating
morphologies are considered, i.e., a core shell with BC mass center located
at the particle geometric center (black squares) and two off-center
core-shell structures including BC aggregates lying in the middle position of
a particle radius (red circles) and the outer position close to the spherical
boundary (blue up-triangles). The ACRIs based on the popular volume-weighted
average method (magenta down-triangles) and Bruggeman effective medium theory
(olive diamonds) are compared.
Figure 5 illustrates the differences of scattering and absorption cross
sections of coated BC aggregates with different BC inside positions induced
by the VWA, EMT and optically effective ACRIs. The optically effective ACRIs
cause differences of coated BC scattering and absorption within 1 %
compared to its inherent properties in both accumulation and coarse modes,
whereas the VWA and EMT induce large particle scattering and absorption
differences, especially in coarse mode. One can see that, in coarse mode,
the VWA and EMT can overestimate coated BC absorption as high as ∼90 % at
some coating states, and they overestimate more for BC closer to coating
boundary.
The relative differences of scattering and absorption cross sections
of black carbon aggregates coated by sulfate (BC fractal dimension of 2.8)
induced by their optically effective complex refractive indices (a
and b), and refractive indices based on the volume-weighted average
method (c and d) and Bruggeman effective medium theory
(e and f) as a function of shell/core ratio
(Dp/Dc), in accumulation (a, c and
e) and coarse (b, d and f) modes,
respectively. Three BC coating morphologies are considered, i.e., a core
shell with the BC mass center located at the particle geometric center (black
squares) and two off-center core-shell structures including BC aggregates
lying in the middle position of a particle radius (red circles) and the outer
position close to the spherical boundary (blue triangles). Solid symbols
denote scattering coefficients, while open interiors indicate absorption
coefficients.
Generally, retrieved optically effective ACRIs of coated BC aggregates show
significantly distinctive patterns in accumulation and coarse modes. In
accumulation mode, besides the shell/core ratio, the optically
effective ACRIs are slightly sensitive to BC geometry and BC position inside
sulfate coating. Their retrieved real parts increase slightly as BC becomes
loose or BC is located closer to the coating boundary, whereas the reverse is
true for their imaginary parts. Nevertheless, in coarse mode, the real parts
of optically effective ACRIs are highly complex functions of the
shell/core ratio, BC fractal dimension and BC inside position, while
their imaginary parts generally increase with BC fractal dimension decreasing
or BC close to the coating center. Meanwhile, the VWA and EMT show acceptable
performance for estimating ACRIs of coated BC in accumulation mode, resulting
in uncertainties in scattering and absorption, both within approximately
10 %, whereas in coarse mode, the VWA and EMT, generating dramatically
higher imaginary parts than those of optically effective ACRIs, can
significantly overestimate coated BC absorption by a factor of nearly 2,
particularly for heavily coated BC with a large BC fractal dimension or BC
close to the coating boundary.
Effect of coated BC size distribution on its optically effective
ACRI
As demonstrated in Bond et al. (2006), particle size distribution affects
coated BC absorption properties and its BC absorption amplification due to
weakly absorbing coatings. Figure 6 illustrates the variations of retrieved
ACRIs of concentric coated BC aggregates (BC fractal dimension of 2.8) with
different particle size distributions at different shell/core ratios.
The real parts (panels a–d) and imaginary parts (panels e–h) of retrieved
ACRIs are depicted in Fig. 6, respectively, and the panels from left to right
correspond to the optically effective ACRIs in accumulation and coarse modes,
and the ACRIs given by the VWA and EMT. The lognormal size distributions are
assumed for the coated BC particles with rg (x axis) ranging
from 0.025 to 0.15 µm and from 0.5 to 1.0 µm in
accumulation and coarse modes, respectively, and σg fixed as
the aforementioned values. Figure 6 clearly shows that the optically
effective ACRIs of coated BC aggregates are sensitive to particle size
distribution and shell/core ratio. For accumulation coated BC, the
retrieved optically effective ACRI shows weak variation in particle size
distribution, and with rg increasing, its imaginary part
increases mildly for thin coating (i.e., small Dp/Dc),
whereas the real part decreases. Nevertheless, in coarse mode, the variation
of retrieved optically effective ACRI becomes strong, and its imaginary part
generally shows a decreasing trend as rg increases. Compared to
the results in accumulation mode, retrieved optically effective ACRIs of
concentric coated BC aggregates in coarse mode become more sensitive to
particle size distribution and shell/core
ratio, i.e., showing larger variation. Considering that the BC/sulfate
volume ratio is a constant as Dp/Dc is fixed, ACRI
results given by the VWA and EMT are not sensitive to particle size
distribution and are expressed by the horizontal lines in the figure. In
accumulation mode, the VWA and EMT provide acceptable ACRI results for
different size distributions with scattering and absorption uncertainties
within ∼10 % (not shown), and the VWA shows mildly better
performance than the EMT in estimating the imaginary part. However, in coarse
mode, the imaginary parts are severely overestimated by the VWA and EMT at
different size distributions when compared to retrieved optically effective
ACRIs, indicating that the VWA and EMT overrate aged BC absorption
significantly. This is consistent with the results of Bond et al. (2006),
which suggest that the VWA for the refractive index is unrealistic, leading
to unphysical results and overestimation of particle absorption.
The retrieved optically effective aerosol complex refractive indices
of BC aggregates coated by sulfate (BC fractal dimension of 2.8) with a
different shell/core ratio (Dp/Dc) and particle
size distribution for the accumulation (a, e) and coarse
(b, f) modes, respectively. The estimated refractive
indices given by the volume-weighted average method (c, g)
and Bruggeman effective medium theory (d, h) are considered
for the coarse mode. The real and imaginary parts correspond to panels
a, b, c and d, and e,
f, g and h, respectively. The geometric standard
deviations (σg) for applied lognormal distribution are 1.59
and 2.0 for accumulation and coarse aerosols, respectively.
A new assumed ACRI parameterization for heavily coated BC as a
correction for the VWA approximation
As discussed above, the VWA approximation employed in the state-of-the-art
aerosol–climate models extensively could result in significant errors in the
absorption of thickly coated BC aggregates in coarse mode (specifically,
Dp/Dc≥2.0), although it gives acceptable results
for fully coated BC in accumulation mode and thinly coated BC in coarse mode.
For thickly coated BC in coarse mode, with all previous microphysical factors
considered, it seemingly becomes possible to decompose the influences of
coated BC microphysics on their optically effective ACRIs and to do the
parameterization. Nonetheless, the optically effective ACRIs of coarse coated
BC are highly intricate functions of their microphysical properties
parameterized by multiple parameters (e.g., BC fractal parameters, coating
parameters and shell/core ratio), and cannot simply be represented by
these microphysical parameters adequately. Because the ACRIs of internally mixed particles are dependent on their chemical compositions, the traditional VWA approach to their determination is to calculate them from their bulk chemical compositions and known values of the refractive indices of the pure components. This may be a reasonable approach for approximation
of the real part of ACRIs, whereas the corresponding values for calculation
of the imaginary part are not as good as their real counterparts (e.g.,
Marley et al., 2001). Meanwhile, for
heavily coated BC in coarse mode with various microphysics, the VWA generates
dramatically higher imaginary parts than those of optically effective ACRIs
to varying degrees. Thus, the imaginary part of heavily coated BC in coarse
mode is considered to be that given by the VWA divided by a factor, which may
show better results, whilst its real part is the same as that approximated by
the VWA. To be simple and specific, the factor for dividing the imaginary
part given by the VWA is assumed to be 2, and a new assumed parameterization
of ACRIs of BC heavily coated by sulfate in coarse mode is expressed by
neffective(λ)=(nBC(λ)×VBCVBC+Vsulfate+nsulfate(λ)7×VsulfateVBC+Vsulfate)/2,keffective(λ)=12×(kBC(λ)×VBCVBC+Vsulfate+ksulfate(λ)8×VsulfateVBC+Vsulfate)/2,
where neffective and keffective denote the real part and
imaginary part of parameterized ACRI, λ the wavelength of light,
nBC and nsulfate the real parts of pure BC and sulfate, kBC and ksulfate the imaginary parts of BC and sulfate, and VBC
and Vsulfate the volumes of BC and sulfate, respectively.
To demonstrate the performance of the simple expressions in approximating ACRIs of fully coated BC
aggregates in coarse mode with Dp/Dc≥2.0, Fig. 7
compares induced relative errors of scattering and absorption coefficients of
coarse coated BC with the aforementioned fixed size distributions based on
ACRIs from the popular VWA and Eqs. (7)–(8). The cases of coarse coated BC
with BC fractal dimensions of 2.8 and 2.98 are illustrated in panels (a),
(b), (e) and (f) and panels (c), (d), (g) and
(h) of the figure. It is clear that the assumed
new ACRI parameterization method shows a better performance than the VWA in
the estimation of scattering and absorption of heavily coated BC with various
coating microphysics in coarse mode. Compared to the VWA, the new
parameterization method reduces the relative errors in estimating absorption
cross sections of coarse coated BC by a factor of nearly 2. Surprisingly, the
errors of scattering cross sections of coated BC are also lessened, although
the real part of the ACRI in the assumed parameterization method is
considered to the same as that in the VWA. As the effects of particle
microphysics on optically effective ACRIs of coarse coated BC are rather
complicated, it is difficult to find a “best” parameterization for the
optically effective ACRI based on its microphysics. However, Fig. 7 indicates
that the simple ACRI approximation we assume gives a better estimation than
the VWA, which are widely used in aerosol–climate models, on the optical
properties of heavily coated BC in coarse mode.
Comparisons between the relative differences of scattering and
absorption coefficients of coarse coated black carbon aggregates induced by
the refractive indices based on the volume-weighted average method
(a, c, e, g) and those given by the
parameterized method described by Eqs. (7) and (8) in the main text
(b, d, f, h). Two BC fractal dimensions
of 2.8 (a, b, e and f) and 2.98 (c, d, g and h) are considered, and the
induced differences for absorption and scattering cross sections are shown in
(a)–(d) and (e)–(h), respectively. The solid lines indicate the cases of
core-shell structures with the BC mass center located in the particle
geometric center, while the gray areas denote the cases of all possible
core-shell structures with BC aggregates inside the sulfate coating.
Atmospheric implications
Our theoretical analysis depicts retrieved optically effective ACRI of coated
BC sensitive to its shell/core ratio, BC geometry, BC position inside
coating, and size distribution. Due to aged BC particles having complicated
coating morphologies in ambient air, which can be provided by individual
particle analysis (Adachi and Buseck, 2008; Li et al., 2016; Wang et al.,
2017), coated BC considered in this study represents case studies, such as
those BC particles observed under polluted urban environments (Peng et al.,
2016; Chen et al., 2017), to give insights into the effects of particle
microphysics, resembling the findings presented by
Schnaiter et al. (2005). The study indicates that
retrieved optically effective ACRIs of coated BC aggregates show distinctive
patterns in accumulation and coarse modes. In accumulation mode, retrieved
optically effective ACRIs of coated BC are more impacted by their chemical
compositions and composition ratio, which look like the real ACRI, and the
influences by their other microphysics are generally limited. However, in
coarse mode, the results challenge conventional beliefs, and retrieved
optically effective ACRIs of coated BC are highly complicated functions of
particle microphysics. That is to say, the optically effective ACRIs of
coarse coated BC are not only affected by their chemical compositions and
composition ratio, but are also impacted by their other microphysics (such as
size distribution and BC geometry). This makes the notion of refractive index
become somewhat ill-defined for internally mixed particles, since it is not
the real particle refractive index, but an optically effective refractive
index. This study also indicates that the VWA and EMT, giving acceptable
ACRIs for internally mixed particles in accumulation mode, produce a higher
imaginary part of ACRI than that of optically effective ACRI, and could
overestimate heavily coated BC absorption significantly in coarse mode. This
may be one of the reasons why modeled aerosol optical depth is 20 %
larger than observed (Roelofs et al., 2010), since the VWA approximation is
widely employed in the state-of-the-art aerosol–climate models. To reduce
the uncertainties, we propose a simple ACRI parameterization method for
heavily coated BC in coarse mode (specifically, Dp/Dc≥2.0), which reduces the scattering and absorption errors of coated BC by
a factor of nearly 2 in comparison with the VWA, although absorption errors
of coated BC with some microphysics are still relatively high. As such, in
order to produce reliable estimates of BC radiative forcing in
aerosol–climate models, the optically effective ACRI, rather than the ACRI
given by the VWA, appears to be essential, especially for aged BC in
coarse mode.
Conclusions
This study numerically explores the impacts of coating microphysics on the
optically effective ACRIs of polydisperse coated BC particles, which are
retrieved from exactly calculated scattering and absorption properties
without variations in overall particle shapes during retrieval. The numerical
simulations conducted here have multiple controllable microphysical
variables, i.e., shell/core ratio, BC geometry, BC position inside
sulfate coating and size distribution, and we attempt to constrain these
variables within realistic ranges as determined by observation-based studies.
The fractal aggregate is employed to model the realistic BC geometry, and
optical properties of spherical coated BC aggregates are calculated by
utilizing the numerically exact multiple-sphere T-matrix method. The fast-Mie-theory-based data analysis scheme is applied for retrieving the optically
effective ACRIs of coated BC, and the numerical results are analyzed to
better understand retrieved optically effective ACRIs in relation to the
controllable microphysical variables.
Our results reveal that retrieved optically effective ACRIs of coated BC
aggregates depict significantly different patterns in accumulation and coarse
modes. With BC becoming loose or close to coating the boundary, the real
parts of retrieved optically effective ACRIs of accumulation-coated BC
increase slightly, as opposed to the decrease for the imaginary parts. The
retrieved optically effective ACRIs of coated BC in accumulation mode are
predominantly influenced by their chemical compositions and composition
ratio, which makes it reasonable and looks like the real ACRIs, although it
is slightly sensitive to BC geometry, BC position inside the coating and
particle size distribution. Nonetheless, retrieved optically effective ACRIs
of coarse coated BC are highly complicated functions of particle
microphysics, and this challenges conventional beliefs given by the VWA and
EMT. The VWA and EMT exhibit acceptable performances for estimating ACRIs of
coated BC in accumulation mode, and resulting uncertainties in scattering and
absorption are both within approximately 10 %. In coarse mode, the VWA
and EMT, nevertheless, produce dramatically higher imaginary parts than those
of optically effective ACRIs, and can significantly overestimate coated BC
absorption by a factor of nearly 2, especially for heavily coated BC with a
large BC fractal dimension or BC close to the coating boundary. This is
probably one of the reasons why modeled aerosol optical depth is 20 %
larger than observed (Roelofs et al., 2010), as the VWA approximation is
widely employed in the state-of-the-art aerosol–climate models.
Although the parameterization of the optically effective ACRI of coarse
coated BC is difficult and challenging, we propose a simple ACRI
parameterization method for heavily coated BC with Dp/Dc≥2.0 in coarse mode, and its scattering and absorption errors are
decreased by a factor of nearly 2 compared to the VWA. Overall, this work
clearly highlights the importance of accounting for the optically effective
ACRI, rather than the ACRI given by the VWA, for producing reliable estimates
of radiative forcing of coated BC, especially in coarse mode, in
aerosol–climate models. However, caution may be taken in interpreting our
results as a comprehensive guide, as the closure studies between observation
and numerical models on aged BC properties still show poor agreement (Radney
et al., 2014).
Data availability
The data obtained from this study are available upon
request from Mao Mao (mmao@nuist.edu.cn) or Xiaolin Zhang
(xlnzhang@nuist.edu.cn) and are also available at
https://github.com/xiaolinzhang/Data_FOR_ACP-2018-1279 (last access:
19 May, 2019; Zhang, 2019).
The supplement related to this article is available online at: https://doi.org/10.5194/acp-19-7507-2019-supplement.
Author contributions
XZ and MM designed the research plan. YY gave some
suggestions for the revision. XZ carried it out, performed the simulations,
and prepared the manuscript with contributions from all the co-authors.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We particularly acknowledge the source codes of MSTM 3.0 from Daniel W. Mackowski and
Michael I. Mishchenko. We also gratefully appreciate the supports
from the Special Program for Applied Research on Super Computation of the
NSFC-Guangdong Joint Fund (the second phase) under grant no. U1501501.
Financial support
This work is financially supported by the National Natural Science Foundation of China (NSFC) (nos. 91644224 41505127, and 21406189), the Natural Science Foundation of Jiangsu Province (no. BK20150901), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (no. 15KJB170009), and the Key Laboratory of Meteorological Disaster, Ministry of Education (no. KLME201810). This work is also supported by the Startup Foundation for introducing Talent of NUIST (nos. 2015r002 and 2014r011), a China Postdoctoral Science Foundation Funded Project (no. 2016M591883), and Jiangsu Planned Projects for Postdoctoral Research Funds (no. 1601262C).
Review statement
This paper was edited by Yves Balkanski and reviewed by two anonymous referees.
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