Introduction
Black carbon (BC) has been identified as the second most important
anthropogenic global warming agent in the atmosphere by virtue of its strong
absorption of solar radiation and its role as cloud condensation nuclei
(CCN) in cloud formation (Ramanathan and Carmichael, 2008; Bond et al.,
2013; Wang et al., 2013; Jacobson, 2014). BC climatic effects are
significantly influenced by the BC aging process in the atmosphere, which
transforms BC from an external to internal mixing state (Schwarz et al.,
2008; China et al., 2013) and increases its hygroscopicity (Zhang et al.,
2008; Popovicheva et al., 2011) and light absorption (Jacobson, 2001;
Shiraiwa et al., 2010; Qiu et al., 2012; Scarnato et al., 2013).
Freshly emitted BC particles are mostly hydrophobic and externally mixed
with other aerosol constituents (Zuberi et al., 2005; Zhang et al., 2008).
BC agglomerates shortly after emission to form irregular aggregates because
of multi-phase processes (Zhang et al., 2008; Pagels et al., 2009; Xue et
al., 2009). Early studies have found that BC particles age in the atmosphere
through condensation and coagulation processes (e.g., Heintzenberg and
Covert, 1984; Heintzenberg, 1989). Recent studies have confirmed that BC becomes
coated by water-soluble material during atmospheric aging, including
condensation of sulfate, nitrate, and organics (Moteki et al., 2007;
Shiraiwa et al., 2007), coagulation with preexisting aerosols (Johnson et
al., 2005; Kondo et al., 2011), and heterogeneous reactions with gaseous
oxidants (Zuberi et al., 2005; Khalizov et al., 2010; Zhang et al., 2012).
At the same time, BC aggregates also exhibit considerable restructuring and
compaction (Weingartner et al., 1997; Saathoff et al., 2003; Zhang et al.,
2008), which significantly alters BC morphology (Adachi and Buseck, 2013;
China et al., 2015). Aged BC particles experience hygroscopic growth and
activate efficiently as CCN (Zuberi et al., 2005; Zhang et al., 2008). The
hygroscopic growth of BC particles depends on their initial size, condensed
soluble material mass, surface chemical property, and ambient relative
humidity (RH) (Zhang et al., 2008; Khalizov et al., 2009b; Popovicheva et
al., 2011).
A number of laboratory experiments have been conducted to investigate the
effects of atmospheric aging on BC radiative properties. Gangl et al. (2008)
showed that internal BC–wax mixture amplifies the BC absorption coefficient by
10–90 %, depending on the amount of coating. Shiraiwa et al. (2010) found
that BC absorption enhancement due to organic coating varies significantly
for various BC sizes and coating thickness, with up to a factor of 2
enhancement for thick coatings. Under different experimental conditions,
relatively small increases (∼ 30 %) in BC absorption have
also been observed for BC coated by sulfuric acid (Zhang et al., 2008) and
some organics (Saathoff et al., 2003). Furthermore, Xue et al. (2009) and Qiu
et al. (2012) showed a less than 20 % increase in BC absorption for
organic coating, which depends on organic species and coating thickness.
Thus, the resulting large variation among different experimental studies
indicates that the aging effects on BC radiative properties strongly depend
on coating material and thickness as well as BC particle size. It is clear,
therefore, that experimental details are critically important in making
meaningful and appropriate comparisons among various experimental studies
involving BC absorption enhancement associated with coating.
Field measurements have also revealed substantial variation in BC optical
properties during atmospheric aging. Bond and Bergstrom (2006) showed that
observed BC mass absorption cross sections (MAC) vary by more than a factor
of 2 (mostly 5–13 m2 g-1) under different atmospheric
conditions. Based on direct measurements at a suburban site in Japan, Naoe
et al. (2009) showed that coating increases BC absorption by a factor of
1.1–1.4 with a larger increase for thicker coatings. Knox et al. (2009)
found an absorption enhancement of up to 45 % due to BC coating based on
measurements in downtown Toronto. Similar increases in absorption have also
been directly observed for the internal mixing of biomass-burning BC (Lack
et al., 2012). However, Cappa et al. (2012) reported that the observed BC
absorption increased only by 6 % due to internal mixing based on direct in
situ measurements over California. This suggests that coating effects on BC
absorption are rather complex in reality, which depends on different coating
material, mass, and structure influenced by emission sources and atmospheric
processes.
Adachi et al. (2010) found that many BC particles embedded within host
material are chainlike aggregates locating in off-center positions, based on
transmission electron microscope (TEM) observations for samples collected
from Mexico City. Using the discrete dipole approximation (DDA) method
developed by Draine and Flatau (1994), Adachi et al. showed that a more
realistic BC coating morphology results in 20–40 % less absorption at
visible wavelengths than a concentric core-shell shape. Based on
ground-based measurements during the California Research at the Nexus of Air
Quality and Climate Change (CalNex) campaign, Adachi and Buseck (2013)
further observed that many BC particles are only attached to host material
instead of being fully embedded within them, leading to only a slight increase in
BC absorption. They concluded that the complex mixing structure of BC
particles could explain a smaller absorption amplification by BC coating
determined from observations than the results computed from an idealized
core-shell model. China et al. (2013, 2015) classified the observed
irregular BC coating shapes into four types: embedded (heavily coated),
thinly coated, partly coated, and partially encapsulated. These complex
coating structures substantially affect BC optical properties (e.g., Videen
et al., 1994; Liu and Mishchenko, 2007; Kahnert et al., 2013), which is one
of the most important uncertainty sources in evaluating BC direct radiative
forcing (DRF) (Bond et al., 2013). Thus, a reliable estimate of BC DRF
requires a quantitative understanding of the evolution of BC radiative
properties under the influence of various morphology during atmospheric
aging.
In this study, we have developed a theoretical BC aging model based on the
current understanding of the BC aging process, which accounts for three major
stages, namely, freshly emitted aggregates, BC coated by soluble material,
and BC particles undergoing further hygroscopic growth. We apply the
geometric-optics surface-wave (GOS) approach to compute light absorption and
scattering of BC particles at each aging stage. The theoretical calculations
are compared with laboratory measurements, followed by a systematic
evaluation of uncertainties associated with BC morphology and refractive
index. Finally, we discuss the implication of model results for BC radiative
effect assessment.
Methods
A theoretical BC aging model
Based on the current knowledge of BC atmospheric aging, we have developed a
theoretical model accounting for three major BC aging stages, as depicted in
Fig. 1. Stage I represents freshly emitted BC aggregates that are externally
mixed with other particles. Stage II represents BC particles coated by
water-soluble aerosol constituents through condensation, coagulation, and/or
heterogeneous oxidations. Stage III represents BC particles coated by both
soluble material and water through hygroscopic growth. In this study, six
typical BC coating structures (Fig. 1) have been considered for Stages II
and III to approximately represent observations in the real atmosphere or
laboratory, including embedded (i.e., concentric core-cell, off-center
core-shell, and closed-cell), partially encapsulated, and partly coated
(i.e., open-cell and externally attached) structures following the
classification presented in China et al. (2013, 2015). The concentric and
off-center core-shell structures (Martins et al., 1998; Sedlacek et al.,
2012) are a result of considerable collapse of BC aggregates into more
compact and spherical clusters when fully engulfed in coating material
(Zhang et al., 2008). The closed-cell structure is an example of where coating
material not only covers the outer layers of BC aggregates but also fills
the internal voids among primary spherules (Strawa et al., 1999). The
partially encapsulated structure is formed when only a part of BC aggregate
merges inside coating material (China et al., 2015). The open-cell and
externally attached structures are produced by coating material sticking to
a part of BC aggregates' surface (Stratmann et al., 2010; China et al.,
2015). We wish to note that the six coating structures used in this study,
including closed-cell and open-cell structures, are theoretical models and
as such, they may not completely capture detailed BC coating structures from
aircraft and ground-based observations. Further hygroscopic growth of BC
particles after Stage III could lead to the formation of cloud droplets, a
subject beyond the scope of the present study.
A theoretical model that accounts for three BC aging
stages and the associated BC structures, including freshly emitted
aggregates (Stage I), BC coated by soluble material (Stage II), and BC
after further hygroscopic growth (Stage III). Six typical structures for
coated BC at Stages II and III are considered based on atmospheric
observations, including embedded (i.e., concentric core-shell, off-center
core-shell, and closed-cell), partially encapsulated, and partly coated
(i.e., open-cell and externally attached) structures. See text for details.
Laboratory measurements
The physical and radiative properties of BC particles during aging after
exposure to sulfuric acid (H2SO4) under various RH conditions
(5–80 %) have been measured in the laboratory by Zhang et al. (2008) and
Khalizov et al. (2009a). BC aggregates were generated by incomplete
combustion of propane in a laminar diffusion burner (Santoro et al., 1983)
and were sampled by a pinhole diluter (Kasper et al., 1997). A tandem
differential mobility analyzer (TDMA) system was used to produce
singly charged mobility-classified BC particles, followed by a coating
chamber with controlled RH and H2SO4 vapor concentrations at room
temperatures (299 ± 1 K). The BC mass and size growth due to
H2SO4 and water vapor (H2O) condensation during aging were
measured by an aerosol particle mass (APM) analyzer and TDMA, respectively.
The effective density and fractal dimension (Df) of BC particles were
derived from the measured BC mobility diameter (DBC) and mass (see
Eqs. 1 and 2 in Zhang et al., 2008). The compaction and restructuring of BC
aggregates were captured by a TEM (see Fig. 1 in Zhang et al., 2008). BC
extinction and scattering cross sections were measured at 532 nm wavelength
by a cavity ring-down spectrometer (CRDS) and an integrating nephelometer,
respectively. The absorption cross section was determined from the resulting
difference between extinction and scattering cross sections. Khalizov
et al. (2009a) showed that uncertainty in measured optical cross sections of coated
BC particles is within 10 %, which primarily represents uncertainty in
relative humidity, particle size, number density, and instrument
calibration. This uncertainty, however, does not include the contribution
from multiply charged particles. For freshly emitted BC aggregates, measured
scattering cross sections involve relatively large uncertainties. More
details on laboratory experiments have been presented in Zhang et al. (2008)
and Khalizov et al. (2009a). Three experimental cases with initial DBC
of 155, 245, and 320 nm were used in this study (see Table 1). In each case,
BC particles exposed to H2SO4 vapor (1.4 × 1010 molecules cm-3)
at 5 and 80 % RH were used to represent coated BC
at Stages II and III (see Sect. 2.1), respectively.
Geometric-optics surface-wave (GOS) approach
We employed the GOS approach developed by Liou et al. (2011, 2014), which
explicitly treats fractal aggregates and various coating structures, to
compute absorption and scattering properties of BC particles at three aging
stages. In the GOS approach, a stochastic procedure developed by Liou et al. (2011)
is applied to simulate homogeneous aggregates and coated particles
with different shapes in a 3-D coordinate system. In this study, we have
extended the original stochastic process to generate more complex coating
morphology, including the partially encapsulated and externally attached
structures (see Figs. S1–S6 in the Supplement). Once the
particle shape and composition are determined by the stochastic procedure,
the reflection and refraction of particles are computed with the
hit-and-miss Monte Carlo photon tracing technique. The extinction and
absorption cross sections are derived following a ray-by-ray integration
approach (Yang and Liou, 1997). Diffraction by randomly oriented
nonspherical particles is computed on the basis of Babinet's principle (Born
and Wolf, 1999) and photon-number-weighted geometric cross sections. The GOS
approach accounts for the interaction of incident waves at grazing angles
near the particle edge and propagating along the particle surface into
shadow regions, referred to as the surface wave, using the formulation
developed by Nussenzveig and Wiscombe (1980) for spheres as the basis for
physical adjustments and application to nonspherical particles (Liou et al.,
2010, 2011). The concept of the GOS approach is graphically displayed in
Fig. 2 and it is designed for computations of absorption and extinction
cross sections and asymmetry factors in line with experimental results.
A graphical representation of the geometric-optics
surface-wave (GOS) approach for light scattering and absorption by coated BC
aggregates. The GOS components include the hit-and-miss Monte Carlo photon
tracing associated with internal and external refractions and reflections,
diffraction following Babinet's principle for randomly oriented irregular
particles, and surface waves traveling along the particle edges and
propagating into shadow regions. See text for details.
Liou et al. (2010, 2011) and Takano et al. (2013) demonstrated that the
single-scattering properties of aerosols with different sizes and shapes
determined from the GOS approach compare reasonably well (differences
< 20 %) with those determined from the finite-difference
time-domain (FDTD) method (Yang and Liou, 1996) and DDA (Draine and Flatau, 1994)
for column and plate ice crystals, the superposition T-matrix method
(Mackowski and Mishchenko, 1996) for fractal aggregates, and the Lorenz–Mie
model (Toon and Ackerman, 1981) for a concentric core-shell shape. Moreover,
compared with other numerical methods, the GOS approach can be applied to a
wider range of particle sizes, shapes, and coating morphology with a high
computational efficiency, including very large particles (e.g.,
∼ 100–1000 µm snowflakes) and complex multiple inclusions
of aerosols within irregular snow grains (Liou et al., 2014; He et al.,
2014), in which the FDTD, DDA, and T-matrix methods have not been able
to be applied. As stated previously, the GOS approach has been developed
specifically for optical cross sections (i.e., extinction, absorption, and
scattering) and the asymmetry factor. Also, due to the approximation in the
use of geometric photon tracing, the GOS approach has limitation and
uncertainty for application to size parameters much smaller than 1. To
supplement GOS, we have developed the Rayleigh–Gans–Debye (RGD) approximation
coupled with GOS for very small particles, which has been cross-validated
with the superposition T-matrix method (Takano et al., 2013). Takano
et al. (2013) showed that the coupled GOS–RGD and superposition T-matrix results
are both close to the observed specific absorption of BC aggregates for the
range of size parameter considered in the present study. The coupled GOS–RGD
approach can be applied to size parameters covering 0.1 to 1000. In the
present study, the coupled GOS–RGD approach is used for fresh BC aggregates
(Stage I), while the GOS approach without RGD coupling is used for coated BC
particles (Stages II and III).
BC physical properties used in theoretical calculationsa.
Aging stageb
Pure BC
Coating material
Standard calculation
Sensitivity calculation
Mobility
Mass
Species
Mass
diameter (nm)
(10-16g)
(10-16g)
155
5.13
BC aggregates with a fractal dimension of 2.1, reactive index of
(1) BC refractive index of 1.75–0.63i; (2) fractal
I
245
13.0
–
–
1.95–0.79i, and 164/416/651 primary spherules with diameters
dimension of 2.5; (3) primary spherule diameter of 20 nm;
320
20.3
of 15 nm for three experimental cases, respectively
(4) single volume-equivalent BC sphere
155
5.13
3.67
Concentric core-shell coating structures
(1) BC refractive index of 1.75–0.63i; (2) off-center core-shell structure;
II
245
13.0
Sulfuric acid (H2SO4)
11.0
with BC refractive index of 1.95–0.79i
(3) closed-cell structure; (4) open-cell structure; (5) partially encapsulated
320
20.3
17.9
structure; (6) externally attached structure
155
5.13
Sulfuric acid and water
7.59
Concentric core-shell coating structures
(1) BC refractive index of 1.75–0.63i; (2) off-center core-shell structure;
III
245
13.0
(H2SO4–H2O)
20.7
with BC refractive index of 1.95–0.79i
(3) closed-cell structure; (4) open-cell structure; (5) partially encapsulated
320
20.3
33.6
structure; (6) externally attached structure
a Particle properties are derived from measurements
in laboratory experiments (Zhang et al., 2008) with initial BC mobility
diameters of 155, 245, and 320 nm. See text for details. b See
Fig. 1 and text for details.
Theoretical calculations
We used BC physical properties measured from laboratory experiments (see
Sect. 2.2) as input to theoretical calculations (see Table 1). In standard
calculations, the freshly emitted BC aggregates (Stage I) were assumed to be
comprised of primary spherules with a diameter (Dp) of 15 nm measured from the
experiments and were constructed by the GOS stochastic procedure to
reproduce the measured mass and fractal dimension (i.e., 2.1) of BC
aggregates. The BC mass was the product of measured BC effective densities
and mobility volumes. The mass of H2SO4 coating on BC at Stage II
was derived from the observed relationship between condensed
H2SO4 mass and particle diameter at 5 % RH. The mass of H2O
condensed on H2SO4-coated BC at Stage III was derived from the
measured hygroscopic mass growth ratio of H2SO4-coated BC at
80 % RH. In standard calculations, we used a concentric core-shell
structure for coated BC particles at Stages II and III because of the strong
particle compaction during aging based on laboratory observations (Zhang et
al., 2008). Thus, BC core size and coating thickness were computed from the
mass of BC and H2SO4/H2O coating. The refractive index (RI)
of H2SO4–H2O coating at Stage III was derived as the
volume-weighted RI of H2SO4 and H2O. We used a BC RI of 1.95–0.79i (upper bound) recommended by Bond and Bergstrom (2006) and a BC
density of 1.77 g cm-3 suggested by Zhang et al. (2008). Under the
preceding conditions, computations of BC optical properties at 532 nm
wavelength were carried out for comparison with laboratory measurements. The
comparison between GOS and experimental results in this study provides an
additional dimension of validation/cross-check of the GOS approach.
In addition, we conducted four sensitivity calculations for Stage I and six
sensitivity calculations for Stages II and III to quantify uncertainties
associated with BC RI and morphology (see Table 1). In the first sensitivity
calculation for each aging stage, a lower bound of BC RI of 1.75–0.63i
recommended by Bond and Bergstrom (2006) was used. For the other three
sensitivity tests on morphology effects at Stage I, we increased BC fractal
dimension from 2.1 to 2.5 and primary spherules diameter from 15 to 20 nm
without changing BC mass, and replaced BC aggregates with a single
volume-equivalent sphere. We then applied five types of BC
coating structures, including off-center core-shell, closed-cell, open-cell,
partially encapsulated, and externally attached structures (see Fig. 1 and
Sect. 2.1), and conducted five additional sensitivity calculations for both
Stages II and III. Specifically, the off-center core-shell structure assumes
a spherical BC core internally tangent to the particle surface with the same
size as the concentric core-shell structure used in standard calculations.
The closed-cell structure assumes that all primary spherules have the same
concentric core-shell shape with a BC core diameter of 15 nm. The open-cell
structure also assumes a diameter of 15 nm for all primary spherules, which
are either pure BC or pure coating material. Both closed- and open-cell
structures were constructed to have the same fractal dimension as measured
in the experiments. The partially encapsulated structure assumes that a
random part of BC aggregates is inside a spherical coating particle (Figs. S1–S6),
while the externally attached structure assumes that a single
spherical coating particle is randomly sticking to a part of the BC aggregate's
surface (Figs. S1–S6). BC primary spherules in both structures have
diameters of 15 nm. We note that assuming a cluster of spheres for the
above-mentioned coating structures may not be sufficiently realistic and
that nonspherical morphology models without restrictions to composite of
spheres appear to be more plausible (Adachi et al., 2010), a challenging
subject to be investigated in future work.
Results and discussions
Fresh BC aggregates (Stage I)
Figure 3 shows the extinction, absorption, and scattering cross sections (at
532 nm) of fresh BC aggregates at Stage I based on laboratory measurements
and theoretical calculations using different BC RI and morphology. For
comparison with experimental measurements, theoretical results with BC RI of
1.95–0.79i (i.e., standard calculations) are used unless stated otherwise.
The calculated extinction cross sections are consistent (differences ≤ 20 %)
with measurements for fresh BC aggregates at Stage I with different
sizes (i.e., DBC= 155, 245, and 320 nm). However, theoretical
calculations tend to overestimate and underestimate extinction for the
smallest and largest BC aggregates, respectively. The discrepancies between
theoretical and measured BC absorption cross sections at Stage I increase
from 7 % (overestimate) to -15 % (underestimate) as BC size becomes
larger (Fig. 3). Although the calculated scattering cross sections at Stage
I are consistently overestimated for different BC sizes compared with
measurements, the absolute discrepancies are small. This overestimate is
partly because of the uncertainty associated with extinction and absorption
calculations for small particles, where theoretical results overestimate
(underestimate) extinction cross sections more (less) than absorption cross
sections for DBC of 155 nm (DBC of 245 and 320 nm). The scattering
measurements also contribute to the discrepancy in view of the fact that the
integrating nephelometer misses light scattering signals at near-forward
directions (Anderson and Ogren, 1998). We note that the calculated single
scattering albedo (SSA; ∼ 0.16) of BC aggregates at Stage I is within the range of
0.15–0.3 measured for BC from different combustion sources (Bond and
Bergstrom, 2006), while the experimentally measured SSA is smaller than 0.10
due to the relatively open and loosely connected BC aggregate structures
(Khalizov et al., 2009a).
Laboratory measurements and theoretical calculations of
BC extinction (left column), absorption (middle column), and scattering
(right column) cross sections (at 532 nm) at three aging stages for BC with
initial mobility diameters (DBC) of 155 nm (top row), 245 nm (middle
row), and 320 nm (bottom row). Black circles represent mean values from
measurements and black error bars indicate experimental uncertainties
reported by Zhang et al. (2008) and Khalizov et al. (2009a). Green squares
indicate results from the standard theoretical calculations (see Table 1 for
details). Red error bars indicate the range of theoretical calculations
using a BC refractive index of 1.95–0.79i (upper bound) and 1.75–0.63i
(lower bound). Blue error bars represent the upper and lower bounds of
sensitivity calculations using different BC morphology with a refractive index
of 1.95–0.79i (see also Fig. 1 and Table 1).
Sensitivity calculations show that using a BC RI of 1.75–0.63i narrows the
gap between calculated and measured scattering cross sections of fresh BC
aggregates by up to a factor of 2 (Fig. 3). Because of using the BC RIs of
1.95–0.79i (upper bound) and 1.75–0.63i (lower bound), the extinction and
absorption cross sections of fresh BC aggregates can vary by 25–40 % and
20–30 %, respectively, while the scattering cross section ranges from
50 to 65 % with a higher sensitivity for larger BC sizes. Based on the
T-matrix calculations using a BC RI of 2–1i and 1.75–0.5i, Liu et al. (2008)
showed variation of 50–70 % in BC absorption and scattering cross sections
depending on aggregate structures, which is comparable to the results
derived in this study. Scarnato et al. (2015) also found a strong dependence
of BC absorption on BC RI for uncoated aggregates using the DDA method.
Figure 4 shows the extinction, absorption, and scattering cross sections for
different aggregate morphology normalized by BC aggregate cross sections
determined from standard calculations (i.e., fractal aggregates with a
Df of 2.1 and Dp of 15 nm; see Sect. 2.4) at Stage I. We found
that a 20 % increase in Df (i.e., more compact structure) decreases
BC absorption and scattering cross sections by 20–50 %, with greater
reductions for larger BC sizes. Using the DDA method, Scarnato et al. (2013)
also found a smaller BC absorption of more compact structures. Liu et
al. (2008) applied a T-matrix calculation to show that as Df increases from
1.5 to 3, the absorption of BC aggregates either decreases monotonically or
decreases until Df reaches a certain value and then increases,
depending on BC RI, size and the number of primary spherules. This is
because the amount of BC directly exposed to the incident light becomes
smaller as Df increases, while the growing interaction among primary
spherules could increase light absorption (Liu et al., 2008). The present
calculations illustrated that BC absorption and scattering are weakly
dependent on the size of primary BC spherules. An increase in the spherule
diameter from 15 to 20 nm results in less than 10 % variation in BC
extinction, absorption, and scattering cross sections (Fig. 4), which is
consistent with the T-matrix results presented by Liu and Mishchenko (2007)
who concluded that the monomer size has a rather weak effect on BC
scattering and absorption, if fractal dimension is fixed. Nevertheless, the
effect of monomer size on BC optical properties could vary significantly
depending on BC aggregate shape, size, the number of primary spherules, and
BC RI (Liu et al., 2008; Kahnert et al., 2014). Assuming a volume-equivalent
BC sphere instead of fractal aggregates results in 5–25 % weaker
absorption and extinction and up to 65 % smaller scattering cross sections
for different BC sizes, compared with BC aggregates in standard
calculations. The stronger absorption and scattering from aggregate
structures is due primarily to the interaction between neighboring primary
spherules of BC aggregates (Fuller, 1995). The present calculated increase
(5–20 %) in absorption from sphere to aggregate structures is slightly
smaller than the value (∼ 30 %) reported by Bond and
Bergstrom (2006), because of different numbers and sizes of primary
spherules, aggregate shapes, and fractal dimensions employed in calculations
(Iskander et al., 1991; Liu et al., 2008; Kahnert et al., 2014). Using the
T-matrix method, Kahnert and Devasthale (2011) showed a
radiative forcing of BC aggregates that was 2 times higher than the volume-equivalent sphere
counterparts.
Extinction (red), absorption (blue), and scattering
(orange) cross sections (at 532 nm) for different BC morphology normalized
by BC aggregate cross sections determined from standard calculations at
aging Stage I for initial BC mobility diameters (DBC) of 155 nm (a),
245 nm (b), and 320 nm (c). Results for four BC structures are
shown, including BC aggregates in standard calculations (circles) with a
fractal dimension (Df) of 2.1 and a primary spherule diameter (Dp)
of 15 nm, BC aggregates with Df of 2.5 (triangles; versus 2.1 in
standard calculations), BC aggregates with a Dp of 20 nm (squares;
versus 15 nm in standard calculations), and a single mass-equivalent BC
sphere (crosses; versus fractal aggregate in standard calculations). Dashed
horizontal lines indicate a value of 1.
Coated BC particles (Stages II and III)
The extinction, absorption, and scattering cross sections (at 532 nm) of
coated BC particles at aging Stages II and III determined from laboratory
measurements and theoretical calculations are depicted in Fig. 3.
Theoretical results with the BC RI of 1.95–0.79i are used for comparison
with experimental measurements unless stated otherwise. The calculated
optical cross sections (i.e., extinction, absorption, and scattering) of
coated BC at Stages II and III are in general agreement (differences ≤ 30 %)
with laboratory measurements, because of the observed efficient
structure compaction during aging in laboratory experiments (Zhang et al.,
2008). However, theoretical calculations tend to overestimate extinction and
absorption for DBC of 155 and 245 nm at both Stages II and III, while
the extinction and absorption for the largest particle (DBC of 320 nm)
is underestimated at Stage II. The calculated scattering cross sections are
overestimated for the smallest BC size (DBC of 155 nm) at Stage II, but
tend to be underestimated for larger BC sizes at Stage III, particularly for
DBC of 320 nm. The present sensitivity calculations show that the
discrepancy in scattering for DBC of 320 nm at Stage III cannot be
explained by uncertainties associated with BC RI or coating morphology (Fig. 3),
which, however, could be attributed to uncertainty associated with the
coating mass of H2SO4 and H2O. We assumed only H2O
condensation during BC hygroscopic growth from Stage II to III in the
calculation of coating mass, which may not be accurate considering that
H2SO4 condenses on BC surface simultaneously along with H2O.
A sensitivity calculation shows that replacing H2O by H2SO4
in the coating material reduces scattering discrepancy to 10 % for
DBC of 320 nm at Stage III, since H2SO4 is more reflective
than H2O, but increases the overestimate in BC absorption from 17 to
25 %.
Theoretical calculations show that using a BC RI of 1.75–0.63i decreases
extinction and absorption cross sections of coated BC particles by 10–17 %
at Stage II and by 5–15 % at Stage III for different BC sizes, which,
however, is smaller compared with the decrease for fresh BC aggregates
(20–40 %). The scattering cross sections of coated BC particles decrease
by up to 50 % due to the use of smaller BC RI for different BC sizes and
aging stages.
Figures 5 and 6 show the extinction, absorption, and scattering cross sections
for different coated BC structures normalized by cross sections of the
concentric core-shell structure determined from standard calculations. The
off-center core-shell structure has little impact on BC optical properties
at Stage II (Fig. 5) with differences of less than 10 % compared with the
concentric core-shell structure, primarily because of the thin coating
layer. As the coating thickness increases after hygroscopic growth, the
off-center core-shell structure results in a 5–30 % decrease in
extinction, absorption, and scattering cross sections at Stage III (Fig. 6).
This finding is consistent with the result presented by Adachi et al. (2010)
using the DDA method, where they found up to 30 % reductions in BC
absorption depending on the position of BC core inside coating material. A
recent T-matrix study (Mishchenko et al., 2014) also showed that the
absorption of BC–water mixture tends to decrease as a BC particle moves from
the droplet center to the boundary.
Extinction (red), absorption (blue), and scattering
(orange) cross sections (at 532 nm) for different coating morphology
normalized by cross sections of concentric core-shell structures determined
from standard calculations at aging Stage II (BC coated by sulfuric acid
(H2SO4)) for initial BC mobility diameters (DBC) of 155 nm
(a), 245 nm (b), and 320 nm (c). Six BC coating structures are
considered, including concentric core-shell (circles), off-center core-shell
(triangles), closed-cell (squares), open-cell (crosses), partly encapsulated
(diamonds), and externally attached (asterisks) structures (see also Fig. 1).
Dashed horizontal lines indicate a value of 1.
Same as Fig. 5, but for aging stage III where BC
particles are coated by both sulfuric acid and water
(H2SO4–H2O).
Compared with the concentric core-shell structure, the closed-cell structure
tends to have stronger absorption and weaker scattering for DBC of 245
and 320 nm at Stages II and III, while the reverse is true for the open-cell
structure (Figs. 5 and 6). This is in line with the conclusion presented in
Liou et al. (2011) that closed-cell aggregates have larger absorption and
smaller SSA than their open-cell counterparts. The closed-cell structure has
a larger surface area for the interaction of the incident light with each
primary spherule that acts as a coated core-shell unit, leading to a
stronger lensing effect and thus stronger absorption compared with the
concentric core-shell structure. However, the open-cell structure lacks a
closed coating structure to produce efficient lensing effects. The coating
spherules sticking to pure BC spherules in the open-cell structure increase
the interaction between the incident light and nonabsorbing coating
material, resulting in a stronger scattering.
Enhancement in BC absorption (top) and scattering
(bottom) during aging from freshly emitted aggregates at Stage I to BC
coated by sulfuric acid (H2SO4) at Stage II (circles), and by both
sulfuric acid and water (H2SO4–H2O) at Stage III (crosses)
for initial BC mobility sizes (DBC) of 155 nm (left), 245 nm (middle),
and 320 nm (right). The enhancements for different BC coating morphology are
shown, including concentric core-shell, off-center core-shell, closed-cell,
open-cell, partly encapsulated, and externally attached structures (see also
Fig. 1). The reference case for enhancement calculation is the fresh BC
aggregate measured in laboratory experiments, which is used for all six BC
coating morphology cases. Thus, the enhancement is computed as the ratio of
calculated absorption/scattering cross sections of coated BC particles to
observed values of fresh BC aggregates. Also shown is the measured
enhancement from laboratory experiments (Obs.). Horizontal dashed lines
indicate a value of 1.0.
The extinction and absorption cross sections of partially encapsulated and
externally attached structures are consistently lower than those of the
concentric core-shell structure by 30–80 % for different BC sizes (Figs. 5
and 6). This is because the relatively open coating structure leads to
inefficient lensing effect for partially encapsulated and externally
attached structures, in which a part of BC aggregates is shielded from
interaction with incident photons that are backscattered by the attached
nonabsorbing coating material. Adachi et al. (2010) showed that the
concentric core-shell structure has a 20–30 % stronger absorption than BC
aggregates that are fully embedded within host sulfate. Thus, the partially
encapsulated structure with only a part of BC aggregates embedded inside
coating material in the present study could further decrease the absorption
and lead to much smaller absorption values than a concentric core-shell
structure. Kahnert et al. (2013) found that the difference in BC absorption
between concentric core-shell and encapsulated structures strongly depends
on particle size, BC volume fraction, and wavelength, based on the DDA
calculation. Interestingly, we found that the absorption of partially
encapsulated structure is 10–40 % weaker than that of externally attached
structure with larger differences for thicker coating, while their
scattering cross sections are similar (differences ≤ 5 %). The
preceding analysis demonstrates that coating structures exert a significant
impact on BC optical properties. Thus, in order to produce reliable and
accurate estimates of BC radiative forcing in climate models, the
development of a realistic BC coating morphology parameterization appears to
be essential, which, however, could be a challenging task in view of limited
observations available at the present time.
Evolution of BC absorption and scattering
Figure 7 shows the enhancement in absorption and scattering during BC aging
from freshly emitted aggregates (Stage I) to BC coated by H2SO4
(Stage II) and by H2SO4–H2O (Stage III) for different BC
coating structures and sizes. The measured BC absorption increases by
10–45 % due to coating, while the concentric core-shell model results in a
20–65 % absorption increase depending on BC sizes and aging stages. This
implies that assuming a concentric core-shell shape could overestimate BC
radiative forcing. Adachi et al. (2010) found that using a more realistic BC
coating morphology from field measurements leads to about 20 % less BC DRF
than using a concentric core-shell shape.
Moreover, coated BC particles with closed-cell structures enhance absorption
by 50–100 % for Stage II and more than 100 % after hygroscopic growth
(Fig. 7). In contrast, the open-cell structures produce less than 10 %
increase in absorption during aging for DBC of 245 and 320 nm, while
the enhancement tends to be stronger for smaller BC size (DBC= 155 nm).
Surprisingly, we found that the partially encapsulated and externally
attached BC structures have a weaker absorption than fresh BC aggregates,
probably because that the two structures in the absence of fully embedded
shape have no efficient lensing effect and that the nonabsorbing coating
material blocks the photons coming from behind BC aggregates and produces a
shadowing effect (Liu and Mishchenko, 2007). This shadowing effect could
also explain the decreasing BC absorption for partially encapsulated,
externally attached, and open-cell structures when coating material
increases during Stages II to III. Adachi and Buseck (2013) and Scarnato
et al. (2013) found that BC particles attached to or partially immersed in host
material, instead of fully embedded within them, do not show noticeable
increases in BC absorption relative to uncoated aggregates based on DDA
calculations. Bond et al. (2006) recommended a 50 % increase in BC
absorption to account for the averaged coating effect during atmospheric
aging. However, in light of the preceding analysis, the morphology,
composition, and amount of coating play significant roles in altering the BC
optical properties during aging. It appears that a fixed enhancement factor
may not represent the realistic increase in BC absorption due to complex
coating, particularly over regions with highly heterogeneous aging
conditions.
Compared with absorption enhancement, BC coating results in a much larger
increase in scattering, with a greater enhancement for a larger amount of
coating material (Fig. 7). The measured scattering cross sections from
laboratory experiments for different BC sizes increase by a factor of 5–6
from Stage I to II and a factor of 11–13 from Stage I to III. Theoretical
calculations show that the increase in scattering from Stage I to II varies
from a factor of 3 to 8 for DBC of 245 and 320 nm depending on coating
morphology, while both the magnitude and variation of enhancement are much
larger for DBC of 155 nm ranging from a factor of 6 to 15. After
hygroscopic growth (Stage III), BC scattering further increases by
20–200 % for different coating structures relative to that at Stage II.
Cheng et al. (2009) observed that the increase in BC scattering, due to both
the increased amount of coating and the transition of uncoated to coated BC,
can reach up to a factor of 8–10 within several hours' aging at a polluted
site in northeastern China, which is comparable to laboratory measurements
and theoretical calculations presented above.
Atmospheric implications
Our theoretical calculations have shown that BC absorption and scattering
are highly sensitive to coating morphology and the amount of coating at
different aging stages. This suggests that the change of BC coating states
(e.g., coating thickness, morphology, and composition) during the aging process
in the real atmosphere could substantially affect BC radiative properties
and thus its climatic effects. Metcalf et al. (2012) observed that the mean
BC coating thickness increases from ∼ 95 nm over urban areas
within boundary layers to ∼ 150 nm in its downwind regions and
∼ 190 nm in the free troposphere, with number fractions of thickly coated BC in the free troposphere and downwind
regions higher than near the source by a factor of 2. Such large variations in BC coating thickness
and number fraction of thickly coated BC during aging have also been
observed over the tropics from the ground to high altitudes (Schwarz et al.,
2008), implying a strong dependence of BC coating state on aging condition
and timescale that BC particles have experienced. Furthermore, atmospheric
observations also suggest large variability in the composition of coating
materials (Moteki et al., 2007; Metcalf et al., 2012) and coating morphology
(China et al., 2013, 2015) during BC aging under different atmospheric
conditions. Thus, better characterizations of BC coating mass, composition,
and morphology during aging are critically important to accurately estimate
BC radiative effects.
However, many global models tend to use fixed BC optical properties or
simplified core-shell models for the computation of BC radiative effects
(Bond et al., 2013), which may not be representative and sufficiently
accurate in view of various BC coating states in the real atmosphere. This
study suggests that a reliable estimate of BC radiative effects in climate
models would require the representation of a dynamic BC aging process with
realistic coating structures, especially for regional analysis with highly
heterogeneous atmospheric conditions.
Conclusions
We developed a theoretical model that accounts for three typical BC aging
stages, including freshly emitted aggregates, BC coated by soluble material,
and coated BC particles after further hygroscopic growth. The GOS approach
was used to compute BC absorption and scattering at each aging stage, which
was coupled with a stochastic procedure to construct different BC
structures. The theoretical calculations were compared with laboratory
measurements, followed by a systematic analysis of uncertainties associated
with BC RI and morphology. Finally, we discussed atmospheric implications of
our results in the assessment of BC radiative effects.
Theoretical calculations yielded consistent extinction (sum of absorption
and scattering) cross sections for fresh BC aggregates at Stage I, with
differences of less than 20 % compared with measurements. Theoretical
calculations underestimated BC absorption by up to 25 %, while
overestimated BC scattering for different sizes, because of uncertainties
associated with both theoretical calculations for small particles and
scattering measurements in laboratory experiments. Sensitivity calculations
showed that variation of the extinction and absorption cross sections of
fresh BC aggregates is 20–40 % due to the use of upper and lower bounds of
BC RIs, while variation of the scattering cross section ranges from 50
to 65 % with a higher sensitivity for larger BC sizes. We also found that
the optical cross sections of BC aggregates are sensitive to fractal dimension, but
insensitive to the size of primary spherules. Using volume-equivalent
spheres instead of aggregates decreased the BC absorption at Stage I.
The measured extinction, absorption, and scattering cross sections of coated
BC were generally captured (differences ≤ 30 %) by theoretical
calculations using a concentric core-shell structure for Stages II and III.
However, theoretical calculations tend to overestimate extinction and
absorption for DBC of 155 and 245 nm at Stages II and III, while the
scattering tends to be underestimated for larger BC sizes at Stage III,
particularly for DBC of 320 nm due partly to the uncertainty associated
with H2SO4–H2O coating mass. Sensitivity analyses showed that
the effects of BC RI on extinction and absorption for coated BC were much
smaller than that for fresh BC aggregates. The off-center core-shell
structure resulted in up to 30 % less absorption and scattering cross
sections than the concentric core-shell structure. The open-cell structure
tended to have weaker absorption and stronger scattering than the concentric
core-shell structure, while the reverse is true for the closed-cell
structure. Compared with the concentric core-shell structure, the partially
encapsulated and externally attached structures had substantially smaller
absorption and scattering cross sections due to the lack of efficient
lensing effects.
Theoretical calculations showed that using a concentric core-shell structure
overestimated the measured enhancement in BC absorption by up to 30 %
during aging. The closed-cell structure led to increases in BC absorption
higher than measured values by a factor of 2, while the open-cell
structure did not show a noticeable increase in absorption for DBC of
245 and 320 nm during aging. The partially encapsulated and externally
attached coating structures had a weaker absorption than fresh BC
aggregates, likely produced by the shadowing effect from nonabsorbing
coating material as well as the lack of efficient lensing effect. The
increase in BC scattering during aging was much stronger than absorption,
ranging from a factor of 3 to 24 depending on BC size, morphology, and aging
stage. Thus, the present analysis showed that BC optical properties are
highly sensitive to BC morphology and coating mass at different aging
stages.
Our theoretical calculations suggested that the evolution of BC coating
states (e.g., coating thickness, morphology, and composition) during aging
in the real atmosphere could exert significant impacts on BC radiative
properties and thus its climatic effects, particularly over regions with
high heterogeneity. Therefore, to accurately estimate BC radiative effects
requires the incorporation of a dynamic BC aging process accounting for
realistic coating structures in climate models.