A theoretical black carbon (BC) aging model is developed to account for
three typical evolution stages, namely, freshly emitted aggregates, BC coated
by soluble material, and BC particles undergoing further hygroscopic
growth. The geometric-optics surface-wave (GOS) approach is employed to
compute the BC single-scattering properties at each aging stage, which are
subsequently compared with laboratory measurements. Theoretical calculations
are consistent with measurements in extinction and absorption cross sections
for fresh BC aggregates with different BC sizes (i.e., mobility diameters of
155, 245, and 320 nm), with differences of

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 (

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 m

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.

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.

The physical and radiative properties of BC particles during aging after
exposure to sulfuric acid (H

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

BC physical properties used in 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 (

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 1.75–0.63

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
1.95–0.79

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 (

Sensitivity calculations show that using a BC RI of 1.75–0.63

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

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 (

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 1.95–0.79

Theoretical calculations show that using a BC RI of 1.75–0.63

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

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
(H

Same as Fig. 5, but for aging stage III where BC
particles are coated by both sulfuric acid and water
(H

Compared with the concentric core-shell structure, the closed-cell structure
tends to have stronger absorption and weaker scattering for

Enhancement in BC absorption (top) and scattering
(bottom) during aging from freshly emitted aggregates at Stage I to BC
coated by sulfuric acid (H

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

Figure 7 shows the enhancement in absorption and scattering during BC aging
from freshly emitted aggregates (Stage I) to BC coated by H

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

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

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

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.

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

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

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.

This research was supported by the NSF under grant AGS-0946315 and AGS-1523296, by the DOE Earth System Modeling program under grant DESC0006742, and by subcontract S100097 from the Texas A&M Research Foundation, which is sponsored by NASA under grant NNX11AK39G. Pacific Northwest National Laboratory is operated for DOE by Battelle Memorial Institute under contract DE-AC05-76RL01830. R. Zhang acknowledges the support by the Robert A. Welch Foundation (A-1417). Users can access the data in this study through the corresponding author. Edited by: M. Shiraiwa