Impact of brown and clear carbon on light absorption enhancement , single scatter albedo and absorption wavelength dependence of black carbon

The presence of clear coatings on atmospheric black carbon ( BC) particles is known to enhance the magnitude of light absorption by the BCcores. Based on calculations using core/shell Mie theory, we demonstrate that the enhancement of light absorption ( EAbs) by atmospheric black carbon ( BC) when it is coated in mildly absorbing material (CBrown) is reduced relative to the enhancement induced by non-absorbing coatings ( CClear). This reduction, sensitive to both theCBrown coating thickness and imaginary refractive index (RI), can be up to 50% for 400 nm radiation and 25% averaged across the visible radiation spectrum for reasonable core/shell diameters. The enhanced direct radiative forcing possible due to the enhancement effect of CClear is therefore reduced if the coating is absorbing. Additionally, the need to explicitly treat BC as an internal, as opposed to external, mixture withCBrown is shown to be important to the calculated single scatter albedo only when models treat BC as large spherical cores ( > 50 nm). For smallerBC cores (or fractal agglomerates) consideration of the BCandCBrown as an external mixture leads to relatively small errors in the particle single scatter albedo of <0.03. It has often been assumed that observation of an absorption Angstr öm exponent (AAE)>1 indicates absorption by a nonBC aerosol. Here, it is shown thatBC cores coated inCClear can reasonably have anAAEof up to 1.6, a result that complicates the attribution of observed light absorption to CBrown within ambient particles. However, anAAE<1.6 does not exclude the possibility of CBrown; ratherCBrown cannot be confidently assigned unCorrespondence to: D. A. Lack (daniel.lack@noaa.gov) lessAAE>1.6. Comparison of these model results to various ambientAAEmeasurements demonstrates that large-scale attribution ofCBrown is a challenging task using current in-situ measurement methods. We suggest that coincident measurements of particle core and shell sizes along with the AAEmay be necessary to distinguish absorbing and non-absorbing OC.

Abstract.The presence of clear coatings on atmospheric black carbon (BC) particles is known to enhance the magnitude of light absorption by the BC cores.Based on calculations using core/shell Mie theory, we demonstrate that the enhancement of light absorption (E Abs ) by atmospheric black carbon (BC) when it is coated in mildly absorbing material (C Brown ) is reduced relative to the enhancement induced by non-absorbing coatings (C Clear ).This reduction, sensitive to both the C Brown coating thickness and imaginary refractive index (RI), can be up to 50% for 400 nm radiation and 25% averaged across the visible radiation spectrum for reasonable core/shell diameters.The enhanced direct radiative forcing possible due to the enhancement effect of C Clear is therefore reduced if the coating is absorbing.Additionally, the need to explicitly treat BC as an internal, as opposed to external, mixture with C Brown is shown to be important to the calculated single scatter albedo only when models treat BC as large spherical cores (> 50 nm).For smaller BC cores (or fractal agglomerates) consideration of the BC and C Brown as an external mixture leads to relatively small errors in the particle single scatter albedo of <0.03.It has often been assumed that observation of an absorption Angström exponent (AAE)>1 indicates absorption by a non-BC aerosol.Here, it is shown that BC cores coated in C Clear can reasonably have an AAE of up to 1.6, a result that complicates the attribution of observed light absorption to C Brown within ambient particles.However, an AAE<1.6 does not exclude the possibility of C Brown ; rather C Brown cannot be confidently assigned un-1 Introduction

Black carbon and clear coatings
The absorption of solar radiation by atmospheric black carbon (BC) is thought to lead to positive top-of-atmosphere radiative forcing (i.e.atmospheric warming) about 1 / 4 of the magnitude of anthropogenic CO 2 (IPCC, 2007).Accordingly, the sources, emission strengths and climate impact of BC are a topic of significant research.
The impact of other atmospheric particulate components on BC absorption, in the form of internal mixtures of BC with primary and secondary organic aerosol (POA, SOA) and inorganic salts such at sulfate, has also drawn significant attention (e.g.Bond et al., 2006;Jacobson, 2001;Zhang et al., 2008).This is because the light absorption by an absorbing core can be enhanced when coated with a purely scattering shell (Fuller et al., 1999).The shell acts as a lens and focuses more photons onto the core than would reach it otherwise.This lensing effect has been shown theoretically to increase the absorption by an individual BC particle by 50-100% for core and shell sizes typical of the atmosphere (Bond et al., 2006) and is thought to have an important influence on the radiative forcing by BC (Jacobson, Published by Copernicus Publications on behalf of the European Geosciences Union.D. A. Lack and C. D. Cappa: Black, brown and clear carbon 2001).Absorption enhancement due to lensing has been observed for BC particles coated with SOA (Schnaiter et al., 2005) or sulfuric acid (Zhang et al., 2008), for absorbing polystyrene spheres coated with organic material (Lack et al., 2009a), graphite coated with oleic acid or glycerol (Shiraiwa et al., 2009) and for absorbing mineral dust coated in aqueous inorganic material (Lack et al., 2009b).The absorption enhancement, E Abs , is defined as the ratio of the absorption cross section, σ Abs , of a coated absorbing particle (usually BC) to an equivalent uncoated particle (see Eq. 1 below).
Evaluation of recent field data of particulate organic matter (OM, including both primary and secondary aerosol) concentrations show that particulate OM is often present with abundances similar to or larger than that of inorganic particulate matter, such as sulfate and nitrate salts (e.g.Zhang et al., 2007).In particular, a large amount of directly emitted OM is internally mixed with BC from sources such as biomass and biofuel combustion (Alexander et al., 2008;Gustafsson et al., 2009;Roden et al., 2006), and BC from internal combustion engines can become thickly coated in condensable material within hours to days of emission (e.g.Quinn et al., 2004).It is therefore reasonable to expect that a significant amount of atmospheric BC is internally mixed with OM, which therefore provides a significant opportunity for absorption enhancement and is thus the focus of current research on the evolution of mixing state of BC (e.g.Moteki et al., 2007;Schwarz et al., 2008).

Black carbon and brown coatings
Emerging research suggests that a variety of particulate OM can absorb radiation, particularly at the shorter visible and UV wavelengths (Adler et al., 2009;Barnard et al., 2008;Dinar et al., 2008;Hoffer et al., 2006;Kirchstetter et al., 2004;Rincon et al., 2009;Roden et al., 2006;Schnaiter et al., 2006;Schwier et al., 2009;Shapiro et al., 2009;Sun et al., 2007;Yang et al., 2009).In fact the mass absorption cross-section (MAC) of this so-called "brown carbon" (C Brown ) (Andreae and Gelencser, 2006) has been estimated to be of the same order as BC at 400 nm (Barnard et al., 2008;Clarke et al., 2007).Given the large abundance of particulate OM relative to BC in the atmosphere, this suggests that absorption by C Brown may be a significant fraction of total atmospheric light absorption (Clarke et al., 2007).Despite the potential contributions of C Brown to absorption of solar radiation, all theoretical studies to date of the lensing-induced E Abs have focused solely on the role of non-absorbing coatings.In the present study, we directly address how the presence of C Brown coatings (i.e.coatings that are not purely scattering) on BC cores influence the magnitude of E Abs .
A wide range of MAC and imaginary RI values for C Brown (k Brown ) have been reported in the literature.Reported k Brown values (at ∼550nm) range from 0.002 to 0.27 (Alexander et al., 2008;Hoffer et al., 2006), which compare to a value of ca.0.71 for pure BC (Bond and Bergstrom, 2006).MACs vary from 0.02 to 2 m 2 g −1 at mid visible wavelengths and from 1-10 m 2 g −1 at 350 nm.These values were derived from field measurements of particulate OM observed from Asian pollution outflow (Yang et al., 2009), African biomass combustion (Kirchstetter et al., 2004), Mexico City pollution (Barnard et al., 2008) and humic-like substances (HULIS) extracted from Amazonian biomass combustion particles (Hoffer et al., 2006).These C Brown MACs compare to a BC MAC of ca.7.5 m 2 g −1 at 550 nm or ca.12-13 m 2 g −1 at ∼350 nm (from Adler et al., 2009) and calculated assuming an absorption Angstrom exponent = 1 and extrapolating from Bond and Bergstrom (2006); see Eq. 2).The large variability in MAC for particulate OM is likely related to the variability in the composition of the OM fraction, which can include HULIS, lignin and polycyclic aromatic compounds (Andreae and Gelencser, 2006).
Attribution of observed atmospheric light absorption to C Brown is an important step in understanding the overall climate effects of aerosol.Some studies have attempted this attribution based on assumptions as to the wavelength dependence of absorption (e.g.Favez et al., 2009;Yang et al., 2009).It is often assumed that the imaginary RI for BC is wavelength (λ) independent and that the absorption crosssection for BC varies as λ −1 (Bond and Bergstrom, 2006) (discussed further below).The variation of absorption with wavelength is characterized by the absorption Angstrom exponent (AAE), defined as where σ Abs is the absorption cross-section (or observed absorption).An AAE = 1 corresponds to a λ −1 dependence of absorption.It is thought that C Brown shows strong deviations from the λ −1 relationship and it has therefore been assumed that the observation of an AAE larger than 1 is an indication of absorption by C Brown (or dust if present).However, as mentioned by Gyawali et al. (2009), the AAE of BC cores with >10nm diameter and of BC cores that are coated in scattering shells may deviate from the typically assumed AAE = 1 relationship.For example, the AAE for BC alone can be greater or less than 1, depending on the modeled core size.This must be explicitly kept in mind when assigning contributions to light absorption to C Brown .
As research into the absorption properties and ubiquity of C Brown progresses, it is prudent to consider what the impact of C Brown is on the lensing-induced absorption enhancement for BC.Consider that whereas absorption by a BC core with a purely scattering shell will have contributions to absorption by the core and E Abs by the lensing effect, a BC core coated in C Brown will have absorption contributions from the core, the absorbing shell and the E Abs from the lensing effect Atmos.Chem. Phys., 10, 4207-4220, 2010 www.atmos-chem-phys.net/10/4207/2010/(see Fig. 1 for a schematic of this effect).Given the different optical properties of C Brown compared to a purely scattering shell, the E Abs is very likely to be dependent on the wavelength of light, the absorption properties of the C Brown and shell thickness.In an effort to address the above issue, we present here a series of calculations performed using coreshell Mie theory (Bohren and Huffman, 1983) wherein we investigate the impact of a slightly absorbing, rather than purely scattering, shell on the absorption enhancement factor, E Abs and aerosol single scatter albedo (SSA).This modeling study builds on the work of Bond et al. (2006) and we remain consistent with that study by using many of the same terms, modeling parameters and discussion points.We also investigate the impact of BC cores coated in purely scattering shells on the AAE to provide further insight and recommendations for future studies attempting to elucidate the contribution of BC, C Brown and purely scattering shells.

Modeling
To model the absorption enhancement impact of C Brown we remain consistent with the study of Bond et al. (2006) and use a RI for BC of 1.85-0.71iand a real RI of 1.55 for the non-absorbing shell (defined here as a clear coating, C Clear ).The BC core is modeled as a lognormal (LN) distribution of cores having a geometric standard deviation (GSD) of 1.1 (unless otherwise stated).The "core" and "shell" diameters, d p,core and d p,shell , refer the central sizes in the LN particle distribution.The core diameter refers to the diameter of the core alone, while the shell diameter is the diameter of the entire particle, i.e. core + shell (d p,shell = d p,particle ).The LN distribution is coated by applying the central shell-to-core diameter ratio to each core of the LN distribution (i.e. the ratio d p,shell /d p,core is conserved).
The RI of C Brown is expected to vary with wavelength and so we model across the visible radiation spectrum (380-750 nm).We have also performed some calculations at a specific wavelength of 400 nm to illustrate a single wavelength impact.Wavelengths around 400 nm are commonly used in in-situ aerosol optical property measurements.In general, the solar spectrum averaged results are more relevant for the overall climate impacts whereas the single wavelength results will assist in assessing in-situ measurements.Wavelength-dependent k Brown values have been estimated from literature observations.The SSA of particulate OM was measured by Barnard et al. (2008) to be 0.75 (at 380 nm) and is used to calculate k Brown at 380 nm.To do this we assume a particle diameter of 200 nm, a real RI of 1.55 and calculate the k Brown (using Mie theory) required to achieve an SSA of 0.75 at 380 nm; the calculated k Brown is 0.06 at 380 nm.We then apply the form of the MAC vs. wavelength curve modeled by Sun et al. (2007) (and similar to that measured by Kirchstetter et al., 2004) to produce a wavelength dependant k Brown (Fig. 2).The actual k Brown remains somewhat uncertain and may vary with location and source.To approximately account for this, we have also investigated the sensitivity of the results to the chosen k Brown by a) increasing the original k Brown by 50% and b) subtracting 0.03 from the original k Brown .These changes simulate more and less absorbing OM as measured in some studies (Adler et al., 2009;Dinar et al., 2008;Hoffer et al., 2006;Schnaiter et al., 2006) (Fig. 2).D. A. Lack and C. D. Cappa: Black, brown and clear carbon We also note here that the use of Mie theory assumes spherical particles.There is sufficient evidence that BC, usually fractal when emitted from efficient combustion, can become more compact and the overall particle spherical when coated in other inorganic and organic material (Alexander et al., 2008;Lewis et al., 2009;Zhang et al., 2008).Our modeling mostly deals with coated BC cores.In the limit of thinly coated cores, where fractal BC is more likely, the work of Liu et al. (2008) provides guidance on the differences in absorption for fractal vs. spherical BC.For smaller (15 nm) and larger (25 nm) BC spherule sizes, absorption will likely be overestimated by up to 10% and underestimated by up to 20% if represented as spherical.Recent laboratory studies of spherical particles using absorbing cores with non-absorbing coatings showed generally good agreement with predictions from Mie theory for absorption (Shiraiwa et al., 2009;Lack et al., 2009a) and extinction (Abo-Riziq et al., 2008;Lang-Yona et al., 2010).However, when non-absorbing cores with slightly absorbing coatings were considered the model/measurement agreement for extinction measurements was found to be worse (Lang-Yona et al., 2010).Given the challenges with dealing even with spherical particles, this suggests that the computational results presented here should be considered as a guide to understanding the general influence of C Brown on aerosol absorption, but that experimental verification will ultimately be needed.

Defining absorption enhancement-E abs
The E Abs of a core-shell system is defined as the ratio of absorption cross-sections (σ Abs ) of the coated and uncoated particles (Eq. 1) and here is calculated for all visible wavelengths.The physical interpretation of E Abs for a BC core with a C Clear shell is relatively straight forward compared to systems with absorbing shells because the addition of a C Clear shell leads to an increase in absorption by lensing only.However, when the shell also has an absorbing component, absorption from both the shell material and the lensing effect created by the shell contribute and must be accounted for.Here we distinguish between the contributions from the two C Brown absorption effects.First, the σ Abs of a homogenous particle (with diameter d p,shell ) of C Brown (e.g. using k Brown from Fig. 2) system is calculated across all visible wavelengths.This is repeated for a C Brown particle with diameter d p,core .The difference between these two σ Abs provides a measure of the absorption by the C Brown coating after accounting for the size dependence of absorption and scattering.This absorption by C Brown is then subtracted from σ Abs calculated as for step 1 except using a BC core with the same C Brown coating (and where the core diameter = nonabsorbing core diameter as above, see Table 1).The resultant quantity is the absorption by the BC core including lensing (but not absorption) by C Brown , and the calculated E Abs provides an estimate of the lensing effect of the C Brown .Figure 3 This is for a system having a 300nm diameter core and a 500 nm shell diameter.
shows the calculated E Abs (across all visible wavelengths) for 3 systems; 1) E Abs−CL : the "standard" E Abs for a C Brown core and C Clear shell 2) E Abs−BR : the E Abs for a BC core and C Brown shell including both the absorption and lensing components of the C Brown and 3) E Abs−BR−X : the E Abs for a BC core and shell with the absorption contribution of the C Brown removed as described above.
Based on these definitions (given explicitly in Table 1), E Abs−BR−X provides information on the magnitude of the lensing effect of C Brown only.E Abs−BR−X may differ from E Abs−CL due to either (i) modification of the photon path through the particle due to the absorbing coating, thus causing fewer (or more) photons to be focused towards the core, or (ii) absorption of photons by the coating material, thus causing fewer photons to reach the core.In this second case, the total absorption by the coated particle will be conserved (i.e. it does not matter whether a photon is absorbed within the shell or the core), but the magnitude of E Abs has been decreased.When E Abs−BR−X >1, this indicates that photons at that wavelength are still being focused onto the core due to the lensing effect.However, when E Abs−BR−X <1, this is an indication that the enhancement due to the lensing effect is overwhelmed by absorption by the coating material.In the limit of a strongly absorbing, thick coating no photons will make it to the core and E Abs−BR−X →0.
As an illustrative example, we consider a system with a BC core diameter of 300 nm and a shell diameter of 500 nm.For these conditions, it is found that E Abs−CL is essentially wavelength independent with a value of ca.1.8 (Fig. 3).In contrast, the E Abs−BR varies between 1.7 and 2.4 across  1.

Results
In this section we use the definitions of the five core/shell diameter regimes given by Bond et al. (2006) to provide insights into the 'E Abs lost' (presented as E Abs−Remaining ) that results from the coating being C Brown rather than C Clear .Of these Bond regimes the most common expected in the atmosphere are regimes 3 and 4 (see Fig. 4).Regime 3 corresponds to particles with core diameters <175 nm and thick shells (relative to the core size, with d core /d shell >0.55 but d shell >500 nm) while regime 4 corresponds to thin shells  4 and the central core and shell diameters used elsewhere in the text (e.g.Table 1) are indicated by the position of the numbers of each regime in Fig. 4a.

Impact of C Brown shell thickness and BC core size
For a given wavelength and k Brown , as the thickness of the C Brown shell increases E Abs decreases.For example, for 400 nm wavelength radiation in regimes 3 and 4 (Fig. 4a), E Abs loss can be up to 50%.For very thin shells (regime 4) the E Abs loss can be up to 10% and as shell thickness decreases, the C Brown coating behaves more like C Clear .For much thicker shells E Abs can be reduced by 80% or more (i.e. in regimes 1, 2 or 5).When averaged across all visible wavelengths (from 380-750 nm, Fig. 4b) the E Abs loss is 15-20% in regimes 3 and 4 and ∼30-50% in regimes 1, 2 and 5.The difference between 400nm E Abs and the wave-length averaged E Abs results from the assumed wavelength dependence of absorption by C Brown .The E Abs loss depends only weakly on BC core size (Fig. 4), indicating that for a given wavelength (i.e.k Brown ), the E Abs loss is predominantly a function of the amount of C Brown .

Core shell regimes from Bond et al. (2006)
Here we use core and shell diameters that form the central value of each of the five Bond et al. (2006) regimes (Fig. 4a and Table 1) and the central values for k Brown from Fig. 2  shells also prevent photons from reaching the BC core.This is evidenced by E Abs−BR−X reaching below 1 and progressing towards zero at short wavelengths where absorption by C Brown is assumed to become large (this would indicate no photons reaching the core).However, E Abs−BR−X only goes to zero for regimes 1, 2 and 5, which were described as generally unrealistic in the atmosphere.Within the more realistic regimes (regimes 3 and 4, Fig. 5c, d) E Abs is reduced from the clear coating case by 30-50% at 400 nm wavelength but E Abs−BR−X remains >1 indicating that the lensing effect is still occurring despite the attenuation of photons by the C Brown material.

Impact of Imaginary RI of C Brown
The results presented so far are calculated with an assumed k Brown , based on experimental and theoretical results (Kirchstetter et al., 2004;Barnard et al., 2008;Sun et al., 2007).A wide range of both imaginary RI and MAC for C Brown have been found and so here we investigate the sensitivity of E Abs loss to the assumed k Brown .Using the ranges of k Brown from Fig. 2 we model the E Abs−Remaining for a 60 nm diameter BC core (central core diameter of regime 3) coated in C Brown at 400 nm and 532 nm wavelength.Figure 6 shows E Abs−Remaining as a function of particle diameter and k Brown .
In these simulations, increasing the 400 nm k Brown from the lower bound k Brown (0.02) (similar to the k Brown reported by Dinar et al. 2008) to the base case k Brown (0.05) increases the E Abs loss by 20-30%.Increasing the k Brown from the base case by 50% (from 0.05 to 0.075; again, near that measured by Dinar et al., 2008) increases the E Abs loss by a further 10-15%.At 532 nm, an increase in k Brown leads to an increase in the E Abs loss of only a few percent for reasonable coating thicknesses (<500 nm) but leads to larger increases when very thick coatings are present.Further calculations (not shown) indicate that this conclusion is generally independent of the BC core diameter used.

Consideration of mixing state
Even though E Abs−BR can be large under some conditions (e.g. when C Brown coatings are thick), our focus has been on the influence of C Brown on the lensing effect.It has tacitly been assumed that absorption by C Brown , whether considered as an internal or external mixture with BC, would be accounted for and quantified (for example in models) by the mass and MAC of the C Brown .We now consider how a reduction in the lensing effect (due to C Brown ) for an internal mixture will influence the SSA and how this compares to an external mixture of BC and C Brown .A reduction in lensing means that the fraction of absorption due to the BC core will be reduced and, depending on how the contribution from C Brown is considered in a model, this may lead to uncertainty in the calculated SSA, which is the primary parameter that determines the sign of the radiative forcing by particles.For example, Jacobson (2000Jacobson ( , 2001) ) showed that failure to consider the lensing effect due to clear coatings (i.e.treatment of the aerosol population as an external rather than an internal mixture) may lead to an underestimation of the radiative forcing of BC by a factor of 2-3.However, if the lensing effect is reduced due to absorption by C Brown then this underestimation of radiative forcing will be similarly reduced, with the actual reduction dependent on the assumed wavelength dependence of the C Brown .

Mixing state assumptions and Single Scatter Albedo (SSA)
One way to interpret the lensing effect is to recognize that it corresponds to a decrease in the SSA when compared to an equivalent mass external mixture.We have calculated the difference in SSA values between an external and an internal mixture of BC and C Brown (at 400 nm assuming a k Brown of 0.05 and GSD = 1.1) and similarly for BC and C Clear ( SSA ext−int = SSA ext -SSA int , where the ext and int indicate external and internal mixtures, respectively; Fig. 7).
For the C Brown case (Fig. 7a), at small core sizes (<50 nm) the difference between the internal and external mixture SSA values is small (<0.03).For the C Clear case, for small core sizes certain coating thicknesses will give somewhat larger SSA (see Fig. 7b), but for most core/shell combinations SSA ext−int is small.Additionally, SSA ext−int is small when the coating is very thick (i.e.within regimes 1 and 2).However, for larger assumed BC core sizes the difference can become large, especially for intermediate coating thicknesses.This indicates that even though the E Abs is generally largest for small BC cores and/or very thick coatings (c.f.Fig. 5 in Bond et al., 2006), in these regimes accurate specification of the mixing state will not strongly influence the radiative properties of BC and C Brown .We have also repeated these calculations at longer wavelengths (532 nm and 700 nm) and find that the general discussion given above remains valid even though the imaginary refractive index for C Brown is smaller than at 400 nm.The main influence of mixing state in these regimes is to increase the overall particle size (i.e.cross section), which will tend to increase the total light extinction, but this will have minimal influence on the balance between absorption and scattering.However, when larger BC core sizes are used within a model, mixing state is seen to be an important factor.This is generally true whether C Brown or C Clear coatings are considered, although for C Brown coatings the importance of mixing state is lessened (consistent with the reduction in the lensing effect identified above).

Mixing state and micro-physical model assumptions
To our knowledge, no atmospheric models explicitly account the fact that BC is actually a fractal agglomerate composed of many small (10's of nm in diameter) spherules (van Poppel et al., 2005).BC is instead represented as spherical particles of some size (or with some size distribution), and the optical properties are calculated based on the spherical particle size.Rayleigh-Debye-Gans (RDG) theory posits that for a fractal particle such as BC the absorption behavior is instead dictated by the size of the individual (small) spherules, and not by the agglomerated particle as a whole, i.e. that absorption is additive (Sorensen, 2000).If coated BC particles should be treated in accordance with RDG theory (i.e. as aggregates of 20-30 nm spheres), rather than as larger spherical particles, then the above discussion suggests that the importance of treating BC as an internal mixture may be limited in terms of the direct radiative effects even though E Abs may be relatively large.However, the fact that models tend to use BC particles with relatively large diameters (i.e.>80 nm) (e.g.Kinne et al., 2003) means that the calculated radiative properties may be particularly sensitive to the choice and representation of BC mixing state.
In part, it is for the above reasons that we believe it remains a useful exercise to consider core-shell Mie theory results using BC core diameters that go beyond the typical spherule size range when calculating E Abs , SSA and AAE values for coated BC particles.Furthermore, what few experimental measurements that exist of E Abs for coated soot appear more consistent with the soot particles being single large spheres rather than small spherules (Schnaiter et al., 2003;Zhang et al., 2008).Additionally, AAE values<1 are routinely observed in ambient measurements (Bergstrom et al., 2007;Lack et al., 2008), a result that is theoretically predicted for BC spheres that are larger than ∼150 nm.Certainly more work is necessary to establish what the appropriate core size is for use in E Abs and AAE calculations in order to facilitate both interpretation of ambient measurements and accurate calculation of the radiative effects of BC (and C Brown ) in models.

Absorption wavelength dependence
The wavelength dependence of absorption is typically characterized by the absorption Angstrom exponent (AAE, Eq. 2).For "pure" BC in the atmosphere the AAE is assumed to be 1 (Bond and Bergstrom, 2006) and observations of AAE>1 are often taken as evidence of C Brown (or dust).In actuality, for AAE = 1 the BC must be of sufficiently small diameter (e.g. 10 nm) or, following from RDG theory, a BC core must be a fractal agglomerate composed of many sufficiently small individual spherules.As discussed above, some ambient data provides evidence of large BC cores (i.e. with AAE of <1).In addition, AAE values>1 are theoretically possible for BC coated in C Clear (not C Brown ) as discussed in Gyawali et al. (2009).Therefore, an assumed AAE = 1 to anchor BC absorption, and attribute C Brown absorption contains significant potential errors.

AAE variability of BC with C Clear
Here we extend the calculations of Gyawali et al. (2009) in order to make clearer the need for caution in the use of the AAE when attributing light absorption to C Brown .Figure 8a shows the AAE 380nm−750nm calculated for spherical BC cores coated in various thicknesses of C Clear .The RI used are the same as presented in the sections above, while a larger GSD of 1.7 is assumed for the LN distribution, which represents a particle size distribution from biofuel or biomass combustion (Bond et al., 2006).Figure 8a shows that the AAE 380nm−750nm for BC cores coated in C Clear is reasonably constant within 4 of the 5 core-shell regimes (regimes 1-3 and 5).Regime 4 (thin coatings on all core sizes) shows a large variability in AAE 380nm−750nm , ranging from −0.2 to 1.7, similar to the AAE behavior of uncoated BC.For the other "realistic" regime (regime 3), the AAE 380nm−750nm is generally in the range 1.4-1.6.Therefore one can only attribute absorption to C Brown with confidence if the AAE 380nm−750nm is greater than 1.4-1.6;consistent with the findings of Gyawali et al. (2009).

AAE Variability of BC with C Brown
If AAE 380nm−750nm is measured to be less than ∼1.6 this does not necessarily rule out C Brown as a significant contributor to the observed absorption.For certain core/shell size pairings, the AAE 380nm−750nm for BC cores with C Brown coatings can actually be close to (or even less than) unity, dependent upon the assumed k Brown .We consider this in more detail by determining how the AAE 380nm−750nm depends on the assumed k Brown for C Brown coatings on BC cores.This is important to consider because, even if k Brown is large, only in certain regions (e.g.downwind of a forest fire) will the ambient aerosol be predominately composed of BC and OC.More common will be situations where inorganic ions (or non-absorbing OC) also contribute to the aerosol bur- den, thus decreasing the effective imaginary RI of the coating.As expected, the relationship between AAE 380nm−750nm and k Brown depends explicitly on the core and shell diameters (Fig. 9).We have investigated three specific cases where the shell/core ratio has been varied; case 1: d p,particle /d p,core = 2; case 2: d p,particle /d p,core = 3; case 3: d p,particle /d p,core = 4.This equates to shell/core volume ratios of 7, 26 and 63, respectively.For comparison, BC has often been found in ambient samples to be ca.5-10% of the total particle mass (Quinn et al., 2002;Quinn et al., 2004), corresponding approximately to cases 1 and 2, although BC mass fraction can vary greatly depending on proximity to sources.
Considering Case 1 (Fig. 9a), it is apparent that for many core sizes the AAE 380nm−750nm does not rise above 1.6 until the k Brown is at least > 0.03 and for d p,core ≥125 nm the AAE 380nm−750nm is not >1.6 even when k Brown = 0.06.However, for particles with 50 nm ≤ d p,core ≤100 nm the AAE is noticeably greater than 1.6 after k Brown >0.02.Thus, in a region where the coatings on BC particles are relatively thin it is necessary to have relatively large k Brown in order to confidently distinguish contributions of C Brown from the generic influence of C Clear coatings on the AAE.As the shell/core volume ratio is increased the minimum k Brown needed to give AAE 380nm−750nm >1.6 is reduced.For example, for Case 3 the minimum k Brown is ∼0.01 for all core diameter sizes considered.This is because as the coating amount is increased the absorption due to the coating (as opposed to the core) is increased in proportion.Thus, for regions where the coatings on BC particles are thick it may be possible to readily identify C Brown through the AAE.
The above discussion focuses on what conditions will allow for attribution of C Brown to observed absorption.However, Fig. 9 also indicates that observation of AAE values around 1 does not definitively indicate that absorption is due to BC only.Instead, it is found that relatively significant absorption by C Brown can still result in AAE values around 1. (Note that "significant" does not have a precise definition.Here we arbitrarily interpret significant to mean the minimum k Brown needed to give a calculated SSA 380nm >0.95 for a 200 nm d p C Brown particle.Thus, with this definition we see that significant absorption by C Brown occurs when k Brown ≥0.01.This value can be compared to the k Brown that would give a "noticeable" deviation in the SSA from unity (i.e.SSA<0.98), which occurs for k Brown >0.003.For reference, the SSA values corresponding to a particular k Brown for these 200 nm particles are shown in Fig. 9.) Consistent with the above discussion, significant contributions of C Brown to absorption that still result in AAE 380nm−750nm ∼1 are most common for thinner coatings but still have a reasonable probability of occurring for thicker coatings.And in the absence of specific knowledge about the actual BC size distribution and coating thickness from measurements it is really more appropriate to consider the AAE 380nm−750nm limit of 1.6 (instead of 1), in which case it is difficult to rule out contributions of C Brown to observed absorption for nearly any reasonable core/shell combination.However, if simultaneous measurements of the total particle size distribution, BC size distribution and/or the BC mass fraction are made the aboveidentified limitations on C Brown identification may be relaxed somewhat.This is because then one would know where on the d p,coat vs. d p,core AAE contour the measurements should be compared.

Comparing modeled AAE with ambient measurements
Although an AAE of 1.6 is not an absolute reference point, especially given the results from 4.5.2, at the wavelengths considered here it does serve as a general first approximation and lower limit to AAE for absolute attribution of C Brown .With this in mind, it is interesting to consider that almost 90% of AAE measurements over 2 months of ambient sampling during the GoMACCS field campaign (SE USA, Bates et al., 2008) were less than 1.6 (Bergstrom et al., 2007 (2009) found that the AAE 405nm−870nm during a month very strongly impacted by biomass burning fires was above the 1.6 limit ∼75% of the time (60% after accounting for the uncertainty in the measurements).Although differences in particle morphology may contribute to the observed variability in these ambient AAE observations, taken all together this indicates that very few ambient AAE measurements (in the diverse regions studied) are above the 1.6 limit and therefore cannot provide certain C Brown attribution (at least in the absence of more specific knowledge of the core and shell sizes during the measurement periods).However, at the same time none of these observations can rule out the possibility that C Brown is a pervasive contributor to sub-micron aerosol light absorption.Therefore, when attempting to investigate the impact of C Brown on AAE it is important to consider to some degree the underlying core shape, spherule density, shell diameter, mixing state and SSA before any reliable quantification can be undertaken.The difficulty in simultaneously quantifying these parameters in ambient experiments, particularly core shapes, spherule densities and coating thickness will be a challenging task.Related to this is whether in-situ filterbased methods of measuring absorption appropriately represent AAE.Given that AAE is sensitive to both C Clear and C Brown coating thickness and that there is some evidence that filter based methods suffer from biases under elevated OC content (Cappa et al., 2008;Kondo et al., 2009;Lack et al., 2008), caution must be applied to these measurement methods and the derived parameters such as AAE.It must also be noted here that that the AAE is dependent on the choice of wavelengths (as shown in Fig. 8b).Our discussion above is based on 380 nm and 750 nm radiation, the extreme wavelengths of the visible light spectrum.

Measurement and analysis of ambient AAE
As a final consideration, we mention that care must be taken in extracting AAE values from measurements when absorption is measured at more than two wavelengths.In addition to Eq. ( 2), AAE values have been determined from the linearfit slope of a log-log plot of absorption vs. wavelength (e.g.Bergstrom et al., 2007).When there are many wavelengths considered (such as from sun photometer measurements), it is likely that the fitting method will give "good" results.However, if absorption is measured at only three wavelengths (as is commonly done from in-situ measurements) the fit re-sults can give both qualitative and quantitatively different results than if wavelength pairs are used (Eq.2).Take as an example the laboratory measurements of Schnaiter et al. (2005) where the influence of coatings of α-pinene + ozone SOA on BC absorption was investigated.Based on the fitting method, they reported that the addition of the SOA coatings led to a decrease in the AAE, from 1.13 for uncoated BC to 0.8 for thickly coated BC.In contrast, we estimate (from their Fig. 9) that if the AAE had instead been determined using Eq. ( 2), it would have been found to increase with the addition of SOA coatings, from ∼0.8 to 1.5 (for 450 nm-550 nm) and from ∼0.9 to 1.2 (for 450 nm -700 nm).Thus, any discussion of AAE's deduced from measurement must always be considered in the context of the analysis methodology.

Summary, conclusions and recommendations
Purely scattering shells on black carbon (BC) cores can significantly enhance the absorption by that core as a result of focusing of light towards the BC core by the shell material (Bond et al., 2006).However, if those shells are mildly absorbing (C Brown ) this enhancement (E Abs ) can be reduced, with the specific extent of reduction dependent upon the radiation wavelength, imaginary RI (k Brown ) and thickness of the shell.Estimates of the absorption strength of C Brown from the literature are highly variable, likely depending on the C Brown source and composition; certainly further research is required to fully understand this variability as the overall climate impacts of C Brown will depend importantly on the exact wavelength dependence of the absorption (e.g.Flores et al., 2009).Nonetheless, using a mid-range estimate for k Brown we have shown, using core/shell Mie theory calculations, that E Abs can be reasonably reduced from the clear coating case by up to 50% at 400nm radiation and up to 25-30% averaged across the visible radiation spectrum.This could be a significant reduction of predicted E Abs depending on the ubiquity of C Brown .The E Abs reduction is sensitive to both the thickness of the C Brown shell and the k Brown but is relatively insensitive to BC core size for a given coating thickness.At the extreme limit of thick C Brown shells and shorter visible wavelengths, the C Brown can eliminate E Abs entirely by completely shielding the BC core from photons.
We have also assessed the importance of considering C Brown as an internal mixture with BC, as opposed to an external mixture, in terms of the effect on the particle single scatter albedo (SSA), and ultimately the direct radiative forcing.Large differences in the calculated SSA between the internal and external mixtures are only found when large BC cores are used.When small BC cores are used (or if it is assumed that the larger particles are actually aggregates of small individual spherules) the SSA differences are found to be minor ( SSA<0.03).However, compared to the clear coating case, the potential mis-representation of the radiative forcing by not including the absorption enhancement effect D. A. Lack and C. D. Cappa: Black, brown and clear carbon (i.e. external mixtures) is lessened due to the reduced lensing impact of C Brown .
The absorption Angstrom exponent (AAE) is often used to identify atmospheric contributions of C Brown to visible light absorption from ambient particle optical property measurements.Generally, this is done by assuming that only C Brown and dust have AAE >1 and thus that any observation of AAE>1 indicates the presence of C Brown and/or dust.However, the AAE for BC cores can vary around 1 (−0.2, +1.3) with significant deviations from 1 occurring for assumed larger diameters, where it is uncertain if the BC exists as a dense spherical particle.For BC particles coated in purely scattering material it is possible to obtain AAE values significantly greater than 1, with values as large as 1.6 common (for the specific wavelength pairs considered here).Thus, attribution of C Brown to the observed absorption can only be made with confidence if the AAE is measured to be>1.6.Conversely, we have shown that the measurement of AAE values close to 1 does not rule out significant contributions from C Brown to absorption.Our calculations suggest that attempts to quantitatively (or even qualitatively) attribute light absorption to C Brown from measurement of the wavelength dependence of absorption will be most successful if conducted concurrent with measurements of BC and total particle size distributions.

Fig. 1 .
Fig. 1.Schematic of the effect of C Clear and C Brown shells on BC absorption.

Fig. 2 .
Fig. 2. Wavelength dependent mass absorption cross-section (MAC) of C Brown with a form as given by Sun et al. (2007) and where the absolute magnitude of the k Brown (solid black line) has been deduced fromBarnard et al. (2008).Dashed lines indicate k Brown upper and lower bounds for our modeling.

Fig. 3 .
Fig. 3. Example of calculated E Abs for a BC core and C Clear shell (E Abs−CL , solid black), BC core and C Brown shell (E Abs−BR , dashed gray) and BC core and C Brown shell with C Brown absorption contribution removed (E Abs−BR−X , solid gray).The reduction in the absorption enhancement in going from a clear to an absorbing coating, E Abs−Remaining , is shown as the dashed black (right axis).This is for a system having a 300nm diameter core and a 500 nm shell diameter.

Fig. 5 .
Fig. 4. (a) Calculated E Abs−Remaining for different BC core and C Brown shell diameters at 400 nm wavelength.Regime numbers from Bond et al. (2006) and position of central values used for these regimes also shown.(b) Same as (a) but integrated over all visible light wavelengths.

Fig. 6 .
Fig. 6.Calculated E Abs−Remaining for a 60 nm diameter BC core and varying C Brown shell diameters at 400 nm and 532 nm wavelength for high (thick dashed line), mid (solid black line) and low (thin dashed line) k Brown values corresponding to Fig. 2.

Fig. 7 .
Fig. 7. Contour plots of the calculated difference in the SSA between an external mixture and an internal mixture for a coated BC particle with a C Clear coating (a) and a C Brown coating (b) are shown as a function of core and shell diameter.Contours are shown only when | SSA ext−int | >0.03.The color scale shown applies to both graphs.The actual SSA for the BC/C Clear (c) and BC/C Brown (d) internal mixtures are shown for reference.Note that absorption by the C Brown shell narrows the size region over which large differences between the internal and external mixture are found.

Fig. 8 .
Fig. 8. (a) Modeled AAE 380nm−750nm for variable core diameter and C Clear shell thicknesses.(b) Modeled AAE as a function of wavelength choice for a 60 nm core and 330 nm diameter coating (central values of regime 3).The black square and black circle indicates wavelength combinations used in this study and Bergstrom et al. (2007) respectively.

Fig. 9 .
Fig. 9.The AAE 380nm−750nm calculated as a function of the imaginary RI for different assumed BC core diameters (indicated by the different color lines) and C Brown shell thicknesses.Calculations were done using d p,particle /d p,core equal to (a) 2, (b) 3 and (c) 4. The corresponding volume ratios are given on the figure.For reference, the SSA values associated with the given imaginary refractive indices are shown on the top axis (calculated for a d p = 200nm particle at 380nm).The gray regions in all panels indicates the area where 1<AAE 380nm−750nm >1.6 and the green region where AAE 380nm−750nm <1.

Table 2 .
Central core and shell diameters from the five E Abs regimes ofBond et al. (2006) the visible spectrum.This larger E Abs−BR results from absorption by C Brown .When the absorption of the C Brown shell is accounted for we see that the adjusted enhancement, E Abs−BR−X , is reduced below the E Abs−CL at all wavelengths.The wavelength dependence of E Abs−BR derives from the wavelength dependence of the C Brown absorption, described above.The reduction in E Abs for any conditions is characterized by calculating the remaining enhancement, E AbsRemaining , as defined in Table Favez et al. (2009)Sierau et al., 2006)tes that AAE values during the 2002 and 2004 NEAQS campaigns (NE USA,Bates et al., 2005;Sierau et al., 2006)were less than 1.6 ∼75% and 100% of the time, respectively.The campaign average AAE 370nm−950nm fromYang et al. (2009)(East Asia) was 1.46(±0.27)andwasonly1.49(±0.08)duringperiodsidentifiedas being influenced by biomass burning, where C Brown is expected.Favez et al. (2009)sampled agricultural biomass combustion and rareley saw AAE>1.5 in over a week of sampling.Again, these are combustion conditions where contributions from C Brown are somewhat expected.Gyawali et al.