impact of brown and clear carbon on light absorption … · 2016-01-11 · chemistry and physics...

Atmos. Chem. Phys., 10, 4207–4220, 2010www.atmos-chem-phys.net/10/4207/2010/doi:10.5194/acp-10-4207-2010© Author(s) 2010. CC Attribution 3.0 License.

AtmosphericChemistry

and Physics

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

D. A. Lack1,2 and C. D. Cappa3

1NOAA Earth System Research Laboratory, Chemical Sciences Division, 325 Broadway, Boulder, CO 80304, USA2Cooperative Institute for Research in Environmental Sciences, University of Colorado, 216 UCB, Boulder, CO 80309, USA3Department of Civil and Environmental Engineering, University of California, Davis, California 95616, USA

Received: 21 November 2009 – Published in Atmos. Chem. Phys. Discuss.: 15 January 2010Revised: 17 April 2010 – Accepted: 1 May 2010 – Published: 6 May 2010

Abstract. The presence of clear coatings on atmosphericblack carbon (BC) particles is known to enhance the mag-nitude of light absorption by theBCcores. Based on calcula-tions using core/shell Mie theory, we demonstrate that the en-hancement of light absorption (EAbs) by atmospheric blackcarbon (BC) when it is coated in mildly absorbing material(CBrown) is reduced relative to the enhancement induced bynon-absorbing coatings (CClear). This reduction, sensitive toboth theCBrown coating thickness and imaginary refractiveindex (RI), can be up to 50% for 400 nm radiation and 25%averaged across the visible radiation spectrum for reasonablecore/shell diameters. The enhanced direct radiative forcingpossible due to the enhancement effect ofCClear is there-fore reduced if the coating is absorbing. Additionally, theneed to explicitly treatBC as an internal, as opposed to ex-ternal, mixture withCBrown is shown to be important to thecalculated single scatter albedo only when models treatBCas large spherical cores (> 50 nm). For smallerBC cores(or fractal agglomerates) consideration of theBCandCBrownas an external mixture leads to relatively small errors in theparticle single scatter albedo of<0.03. It has often been as-sumed that observation of an absorption Angstrom exponent(AAE)>1 indicates absorption by a non-BC aerosol. Here, itis shown thatBC cores coated inCClear can reasonably haveanAAEof up to 1.6, a result that complicates the attributionof observed light absorption toCBrown within ambient parti-cles. However, anAAE<1.6 does not exclude the possibilityof CBrown; ratherCBrown cannot be confidently assigned un-

Correspondence to:D. A. Lack([email protected])

lessAAE>1.6. Comparison of these model results to variousambientAAEmeasurements demonstrates that large-scale at-tribution ofCBrown is a challenging task using current in-situmeasurement methods. We suggest that coincident measure-ments of particle core and shell sizes along with theAAEmaybe necessary to distinguish absorbing and non-absorbing OC.

1 Introduction

1.1 Black carbon and clear coatings

The absorption of solar radiation by atmospheric black car-bon (BC) is thought to lead to positive top-of-atmosphere ra-diative forcing (i.e. atmospheric warming) about1/4 of themagnitude of anthropogenic CO2 (IPCC, 2007). Accord-ingly, the sources, emission strengths and climate impact ofBC are a topic of significant research.

The impact of other atmospheric particulate componentson BC absorption, in the form of internal mixtures ofBCwith primary and secondary organic aerosol (POA, SOA) andinorganic salts such at sulfate, has also drawn significant at-tention (e.g. Bond et al., 2006; Jacobson, 2001; Zhang et al.,2008). This is because the light absorption by an absorb-ing core can be enhanced when coated with a purely scat-tering shell (Fuller et al., 1999). The shell acts as a lensand focuses more photons onto the core than would reachit otherwise. This lensing effect has been shown theoreti-cally to increase the absorption by an individualBC parti-cle by 50–100% for core and shell sizes typical of the at-mosphere (Bond et al., 2006) and is thought to have an im-portant influence on the radiative forcing byBC (Jacobson,

Published by Copernicus Publications on behalf of the European Geosciences Union.

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4208 D. A. Lack and C. D. Cappa: Black, brown and clear carbon

2001). Absorption enhancement due to lensing has been ob-served forBC particles coated with SOA (Schnaiter et al.,2005) or sulfuric acid (Zhang et al., 2008), for absorbingpolystyrene spheres coated with organic material (Lack et al.,2009a), graphite coated with oleic acid or glycerol (Shiraiwaet al., 2009) and for absorbing mineral dust coated in aque-ous inorganic material (Lack et al., 2009b). The absorptionenhancement,EAbs, is defined as the ratio of the absorptioncross section,σAbs, of a coated absorbing particle (usuallyBC) to an equivalent uncoated particle (see Eq. 1 below).

EAbs=σAbs−Core−Shell

σAbs−Core(1)

Evaluation of recent field data of particulate organic mat-ter (OM, including both primary and secondary aerosol) con-centrations show that particulate OM is often present withabundances similar to or larger than that of inorganic particu-late matter, such as sulfate and nitrate salts (e.g. Zhang et al.,2007). In particular, a large amount of directly emitted OMis internally mixed withBC from sources such as biomassand biofuel combustion (Alexander et al., 2008; Gustafs-son et al., 2009; Roden et al., 2006), andBC from internalcombustion engines can become thickly coated in condens-able material within hours to days of emission (e.g. Quinnet al., 2004). It is therefore reasonable to expect that a sig-nificant amount of atmosphericBC is internally mixed withOM, which therefore provides a significant opportunity forabsorption enhancement and is thus the focus of current re-search on the evolution of mixing state ofBC (e.g. Moteki etal., 2007; Schwarz et al., 2008).

1.2 Black carbon and brown coatings

Emerging research suggests that a variety of particulate OMcan absorb radiation, particularly at the shorter visible andUV wavelengths (Adler et al., 2009; Barnard et al., 2008; Di-nar 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” (CBrown) (Andreaeand Gelencser, 2006) has been estimated to be of the sameorder asBC at 400 nm (Barnard et al., 2008; Clarke et al.,2007). Given the large abundance of particulate OM rela-tive to BC in the atmosphere, this suggests that absorptionby CBrown may be a significant fraction of total atmosphericlight absorption (Clarke et al., 2007). Despite the potentialcontributions ofCBrown to absorption of solar radiation, alltheoretical studies to date of the lensing-inducedEAbs havefocused solely on the role of non-absorbing coatings. Inthe present study, we directly address how the presence ofCBrown coatings (i.e. coatings that are not purely scattering)onBC cores influence the magnitude ofEAbs.

A wide range of MAC and imaginary RI values forCBrown(kBrown) have been reported in the literature. ReportedkBrown

values (at∼550nm) range from 0.002 to 0.27 (Alexander etal., 2008; Hoffer et al., 2006), which compare to a value ofca. 0.71 for pureBC (Bond and Bergstrom, 2006).MACsvary from 0.02 to 2 m2 g−1 at mid visible wavelengths andfrom 1–10 m2 g−1 at 350 nm. These values were derivedfrom field measurements of particulate OM observed fromAsian pollution outflow (Yang et al., 2009), African biomasscombustion (Kirchstetter et al., 2004), Mexico City pollution(Barnard et al., 2008) and humic-like substances (HULIS) ex-tracted from Amazonian biomass combustion particles (Hof-fer et al., 2006). TheseCBrown MACs compare to aBC MACof ca. 7.5 m2 g−1 at 550 nm or ca. 12–13 m2 g−1 at∼350 nm(from Adler et al., 2009) and calculated assuming an absorp-tion Angstrom exponent = 1 and extrapolating from Bondand Bergstrom (2006); see Eq. 2). The large variability inMAC for particulateOM is likely related to the variabilityin the composition of theOM fraction, which can includeHULIS, lignin and polycyclic aromatic compounds (Andreaeand Gelencser, 2006).

Attribution of observed atmospheric light absorption toCBrown is an important step in understanding the overall cli-mate effects of aerosol. Some studies have attempted thisattribution based on assumptions as to the wavelength de-pendence of absorption (e.g. Favez et al., 2009; Yang et al.,2009). It is often assumed that the imaginaryRI for BC iswavelength (λ) independent and that the absorption cross-section forBC varies asλ−1 (Bond and Bergstrom, 2006)(discussed further below). The variation of absorption withwavelength is characterized by the absorption Angstrom ex-ponent (AAE), defined as

AAE = −

(ln(σAbs−λ1 / σAbs−λ2

)ln(λ1/ λ2)

)(2)

whereσAbs is the absorption cross-section (or observed ab-sorption). AnAAE= 1 corresponds to aλ−1 dependence ofabsorption. It is thought thatCBrown shows strong deviationsfrom theλ−1 relationship and it has therefore been assumedthat the observation of anAAE larger than 1 is an indica-tion of absorption byCBrown (or dust if present). However,as mentioned by Gyawali et al. (2009), theAAEof BC coreswith >10nm diameter and ofBCcores that are coated in scat-tering shells may deviate from the typically assumedAAE= 1relationship. For example, theAAE for BC alone can begreater or less than 1, depending on the modeled core size.This must be explicitly kept in mind when assigning contri-butions to light absorption toCBrown.

As research into the absorption properties and ubiquity ofCBrown progresses, it is prudent to consider what the impactof CBrown is on the lensing-induced absorption enhancementfor BC. Consider that whereas absorption by aBC core witha purely scattering shell will have contributions to absorp-tion by the core andEAbs by the lensing effect, aBC corecoated inCBrown will have absorption contributions from thecore, the absorbing shell and theEAbs from the lensing effect

Atmos. Chem. Phys., 10, 4207–4220, 2010 www.atmos-chem-phys.net/10/4207/2010/

D. A. Lack and C. D. Cappa: Black, brown and clear carbon 4209

Abs by BC Core

EAbs by Lens EAbs by Lens

Sca1ered Light Abs by CBrown

CBrown Shell CClear Shell

Sca1ered Light

Fig. 1. Schematic of the effect ofCClear andCBrown shells onBCabsorption.

(see Fig. 1 for a schematic of this effect). Given the differentoptical properties ofCBrown compared to a purely scatteringshell, theEAbs is very likely to be dependent on the wave-length of light, the absorption properties of theCBrown andshell thickness. In an effort to address the above issue, wepresent here a series of calculations performed using core-shell Mie theory (Bohren and Huffman, 1983) wherein weinvestigate the impact of a slightly absorbing, rather thanpurely scattering, shell on the absorption enhancement factor,EAbs and aerosol single scatter albedo (SSA). This modelingstudy builds on the work of Bond et al. (2006) and we remainconsistent with that study by using many of the same terms,modeling parameters and discussion points. We also investi-gate the impact ofBCcores coated in purely scattering shellson theAAE to provide further insight and recommendationsfor future studies attempting to elucidate the contribution ofBC, CBrown and purely scattering shells.

2 Modeling

To model the absorption enhancement impact ofCBrown weremain consistent with the study of Bond et al. (2006) anduse aRI for BC of 1.85–0.71i and a realRI of 1.55 for thenon-absorbing shell (defined here as a clear coating,CClear).TheBC core is modeled as a lognormal (LN) distribution ofcores having a geometric standard deviation (GSD) of 1.1(unless otherwise stated). The “core” and “shell” diameters,dp,core anddp,shell, refer the central sizes in theLN particle

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Fig. 2. Wavelength dependent mass absorption cross-section(MAC) of CBrown with a form as given by Sun et al. (2007) andwhere the absolute magnitude of thekBrown (solid black line) hasbeen deduced from Barnard et al. (2008). Dashed lines indicatekBrown upper and lower bounds for our modeling.

distribution. The core diameter refers to the diameter of thecore alone, while the shell diameter is the diameter of theentire particle, i.e. core + shell (dp,shell= dp,particle). The LNdistribution is coated by applying the central shell-to-core di-ameter ratio to each core of theLN distribution (i.e. the ratiodp,shell/dp,core is conserved).

The RI of CBrown is expected to vary with wavelengthand so we model across the visible radiation spectrum (380–750 nm). We have also performed some calculations at aspecific wavelength of 400 nm to illustrate a single wave-length impact. Wavelengths around 400 nm are commonlyused in in-situ aerosol optical property measurements. Ingeneral, the solar spectrum averaged results are more rele-vant for the overall climate impacts whereas the single wave-length results will assist in assessing in-situ measurements.Wavelength-dependentkBrown values have been estimatedfrom literature observations. The SSA of particulate OM wasmeasured by Barnard et al. (2008) to be 0.75 (at 380 nm)and is used to calculatekBrown at 380 nm. To do this we as-sume a particle diameter of 200 nm, a realRI of 1.55 andcalculate thekBrown (using Mie theory) required to achievean SSA of 0.75 at 380 nm; the calculatedkBrown is 0.06 at380 nm. We then apply the form of the MAC vs. wavelengthcurve modeled by Sun et al. (2007) (and similar to that mea-sured by Kirchstetter et al., 2004) to produce a wavelengthdependantkBrown (Fig. 2). The actualkBrown remains some-what uncertain and may vary with location and source. Toapproximately account for this, we have also investigated thesensitivity of the results to the chosenkBrown by a) increasingthe originalkBrown by 50% and b) subtracting 0.03 from theoriginal kBrown. These changes simulate more and less ab-sorbing OM as measured in some studies (Adler et al., 2009;Dinar et al., 2008; Hoffer et al., 2006; Schnaiter et al., 2006)(Fig. 2).

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We also note here that the use of Mie theory assumesspherical particles. There is sufficient evidence that BC, usu-ally fractal when emitted from efficient combustion, can be-come more compact and the overall particle spherical whencoated in other inorganic and organic material (Alexanderet al., 2008; Lewis et al., 2009; Zhang et al., 2008). Ourmodeling mostly deals with coatedBC cores. In the limitof thinly coated cores, where fractalBC is more likely, thework of Liu et al. (2008) provides guidance on the differ-ences in absorption for fractal vs. spherical BC. For smaller(15 nm) and larger (25 nm)BC spherule sizes, absorptionwill likely be overestimated by up to 10% and underesti-mated by up to 20% if represented as spherical. Recent lab-oratory studies of spherical particles using absorbing coreswith non-absorbing coatings showed generally good agree-ment with predictions from Mie theory for absorption (Shi-raiwa et al., 2009; Lack et al., 2009a) and extinction (Abo-Riziq et al., 2008; Lang-Yona et al., 2010). However, whennon-absorbing cores with slightly absorbing coatings wereconsidered the model/measurement agreement for extinctionmeasurements was found to be worse (Lang-Yona et al.,2010). Given the challenges with dealing even with spheri-cal particles, this suggests that the computational results pre-sented here should be considered as a guide to understandingthe general influence ofCBrown on aerosol absorption, butthat experimental verification will ultimately be needed.

3 Defining absorption enhancement-Eabs

The EAbs of a core-shell system is defined as the ratio ofabsorption cross-sections (σAbs) of the coated and uncoatedparticles (Eq. 1) and here is calculated for all visible wave-lengths. The physical interpretation ofEAbs for a BC corewith a CClear shell is relatively straight forward comparedto systems with absorbing shells because the addition of aCClearshell 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 ef-fect created by the shell contribute and must be accountedfor. Here we distinguish between the contributions from thetwo CBrown absorption effects. First, theσAbs of a homoge-nous particle (with diameter dp,shell) of CBrown (e.g. usingkBrown from Fig. 2) system is calculated across all visiblewavelengths. This is repeated for aCBrown particle with di-ameterdp,core. The difference between these twoσAbs pro-vides a measure of the absorption by theCBrown coating afteraccounting for the size dependence of absorption and scat-tering. This absorption byCBrown is then subtracted fromσAbs calculated as for step 1 except using aBC core with thesameCBrown coating (and where the core diameter = non-absorbing core diameter as above, see Table 1). The resultantquantity is the absorption by theBC core including lensing(but not absorption) byCBrown, and the calculatedEAbs pro-vides an estimate of the lensing effect of theCBrown. Figure 3

3.0

2.5

2.0

1.5

1.0

0.5

0.0

E Abs

(,

, )

750700650600550500450400Wavelength (nm)

1.0

0.8

0.6

0.4

0.2

0.0

E Abs

-Rem

aini

ng (

)

Fig. 3. Example of calculatedEAbs for a BC core andCClearshell (EAbs−CL, solid black),BCcore andCBrown shell (EAbs−BR,dashed gray) andBCcore andCBrown shell withCBrown absorptioncontribution removed (EAbs−BR−X , solid gray). The reduction inthe absorption enhancement in going from a clear to an absorbingcoating,EAbs−Remaining, is shown as the dashed black (right axis).This is for a system having a 300nm diameter core and a 500 nmshell diameter.

shows the calculatedEAbs (across all visible wavelengths)for 3 systems; 1)EAbs−CL: the “standard”EAbs for aCBrowncore andCClearshell 2)EAbs−BR: theEAbs for aBCcore andCBrown shell including both the absorption and lensing com-ponents of theCBrown and 3)EAbs−BR−X : theEAbs for aBCcore and shell with the absorption contribution of theCBrownremoved as described above.

Based on these definitions (given explicitly in Table 1),EAbs−BR−X provides information on the magnitude of thelensing effect ofCBrown only. EAbs−BR−X may differ fromEAbs−CL due to either (i) modification of the photon paththrough the particle due to the absorbing coating, thus caus-ing fewer (or more) photons to be focused towards the core,or (ii) absorption of photons by the coating material, thuscausing 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 withinthe shell or the core), but the magnitude ofEAbs has beendecreased. WhenEAbs−BR−X>1, this indicates that photonsat that wavelength are still being focused onto the core dueto the lensing effect. However, whenEAbs−BR−X<1, this isan indication that the enhancement due to the lensing effectis overwhelmed by absorption by the coating material. In thelimit of a strongly absorbing, thick coating no photons willmake it to the core andEAbs−BR−X →0.

As an illustrative example, we consider a system with aBC core diameter of 300 nm and a shell diameter of 500 nm.For these conditions, it is found thatEAbs−CL is essentiallywavelength independent with a value of ca. 1.8 (Fig. 3).In contrast, theEAbs−BR varies between 1.7 and 2.4 across



Table 1. Parameter descriptions.

Parameter Description Symbol Calculation Method/Equation

AbsorptionCross Section

BC Core σAbsCore Mie Theory (RIcore= 1.85 + 0.71i)

BC Core & CClearShell σAbsCoreClear Core Shell Mie Theory (RIcore= 1.85 + 0.71i, RIcoat= 1.55 +0.0i)

BC Core & CBrown Shell σAbsCoreBrown Core Shell Mie Theory + Brown Carbon Imaginary RI(kBrown) from Fig. 2. (RIcore= 1.85 + 0.71i, RIcoat= 1.55 +kBrown)

CBrown Particle of dp,shell – CBrown Particle of dp,core σAbsBrown Core Shell Mie Theory + Brown Carbon Imaginary RI(kBrown) from Fig. 2. (RI = 1.55 + kBrown)

AbsorptionEnhancement

BC Core & CClearShell EAbs−CL EAbs−CL =σAbsCoreClear

σAbsCore

BC Core & CBrown Shell EAbs−BR EAbs−BR =σAbsCoreBrown

σAbsCore

BC Core & CBrown Shell – CBrown Absorption EAbs−BR−X EAbs−BR−X =σAbsCoreBrown−σAbsBrown

σAbsCore

AbsorptionEnhancementLoss

Difference between enhancement with CClear and CBrownshell.

EAbs−Remaining EAbs−Remaining=σAbsCoreBrown−σAbsBrown

σAbsCoreClear

Table 2. Central core and shell diameters from the fiveEAbsregimes of Bond et al. (2006)

Bond et al. (2006)Regime #

Central CoreDiameter(nm)

Central ShellDiameter(nm)

1 25 15002 100 15003 60 3304 300 4005 300 1500

the visible spectrum. This largerEAbs−BR results from ab-sorption byCBrown. When the absorption of theCBrownshell is accounted for we see that the adjusted enhance-ment,EAbs−BR−X , is reduced below theEAbs−CL at all wave-lengths. The wavelength dependence ofEAbs−BR derivesfrom the wavelength dependence of theCBrown absorption,described above. The reduction inEAbs for any conditionsis characterized by calculating the remaining enhancement,EAbsRemaining, as defined in Table 1.

4 Results

In this section we use the definitions of the five core/shelldiameter regimes given by Bond et al. (2006) to provide in-sights into the ‘EAbs lost’ (presented asEAbs−Remaining) thatresults from the coating beingCBrown rather thanCClear. Ofthese Bond regimes the most common expected in the atmo-sphere are regimes 3 and 4 (see Fig. 4). Regime 3 corre-sponds to particles with core diameters<175 nm and thickshells (relative to the core size, withdcore/dshell >0.55 butdshell >500 nm) while regime 4 corresponds to thin shells

a)

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Core Diameter (nm)1.00.80.60.40.20.0

EAbs-Remaining

1 52

3 4

400 nm Wavelength

Fig. 4. (a) CalculatedEAbs−Remaining for different BC core andCBrown shell diameters at 400 nm wavelength. Regime numbersfrom Bond et al. (2006) and position of central values used forthese regimes also shown.(b) Same as (a) but integrated over allvisible light wavelengths.



a) b)

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e)

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5)

Fig. 5. CalculatedEAbs for BC cores havingCClearshells (EAbs−CL, solid black) andCBrown shells (EAbs−BR−X , solid gray). Eachnumbered panel corresponds to the central conditions of the numbered regimes in Bond et al. (2006). The dashed line showsEAbs−Remaining

(dcore/dshell >0.55) on cores of all sizes. Regime numbersare labeled in Fig. 4 and the central core and shell diametersused elsewhere in the text (e.g. Table 1) are indicated by theposition of the numbers of each regime in Fig. 4a.

4.1 Impact of CBrown shell thickness andBC core size

For a given wavelength andkBrown, as the thickness of theCBrown shell increasesEAbs decreases. For example, for400 nm wavelength radiation in regimes 3 and 4 (Fig. 4a),EAbs loss can be up to 50%. For very thin shells (regime 4)the EAbs loss can be up to 10% and as shell thickness de-creases, theCBrown coating behaves more likeCClear. Formuch thicker shellsEAbs can be reduced by 80% or more(i.e. in regimes 1, 2 or 5). When averaged across all visi-ble wavelengths (from 380–750 nm, Fig. 4b) theEAbs loss is15–20% in regimes 3 and 4 and∼30–50% in regimes 1, 2and 5. The difference between 400nmEAbs and the wave-

length averagedEAbs results from the assumed wavelengthdependence of absorption byCBrown. TheEAbs loss dependsonly weakly onBC core size (Fig. 4), indicating that for agiven wavelength (i.e.kBrown), theEAbsloss is predominantlya function of the amount ofCBrown.

4.2 Core shell regimes from Bond et al. (2006)

Here we use core and shell diameters that form the centralvalue of each of the five Bond et al. (2006) regimes (Fig. 4aand Table 1) and the central values forkBrown from Fig. 2 togain further insight into the effect ofCBrown on EAbs. Fig-ure 5 presents these results with regime numbers given inthe top left of each plot. As discussed above it is clear thatEAbs is reduced for very thickCBrown shells (Fig. 5a, b ande). It is also evident that not only does theCBrown shell re-duce the number of additional photons being directed to thecore (i.e. reduction in lensing), but sufficiently thickCBrown



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6 7 8 9100

2 3 4 5 6 7 8 91000

2

Shell Diameter (nm)

Regimes 3 and 4 Regime 2

400nm 532nm

Fig. 6. CalculatedEAbs−Remainingfor a 60 nm diameterBC coreand varyingCBrown shell diameters at 400 nm and 532 nm wave-length for high (thick dashed line), mid (solid black line) and low(thin dashed line)kBrown values corresponding to Fig. 2.

shells also prevent photons from reaching theBC core. Thisis evidenced byEAbs−BR−X reaching below 1 and progress-ing towards zero at short wavelengths where absorption byCBrown is assumed to become large (this would indicate nophotons reaching the core). However,EAbs−BR−X only goesto zero for regimes 1, 2 and 5, which were described as gen-erally unrealistic in the atmosphere. Within the more real-istic regimes (regimes 3 and 4, Fig. 5c, d)EAbs is reducedfrom the clear coating case by 30–50% at 400 nm wavelengthbutEAbs−BR−X remains>1 indicating that the lensing effectis still occurring despite the attenuation of photons by theCBrown material.

4.3 Impact of Imaginary RI of CBrown

The results presented so far are calculated with an assumedkBrown, based on experimental and theoretical results (Kirch-stetter et al., 2004; Barnard et al., 2008; Sun et al., 2007).A wide range of both imaginaryRI and MAC for CBrownhave been found and so here we investigate the sensitivity ofEAbs loss to the assumedkBrown. Using the ranges ofkBrownfrom Fig. 2 we model theEAbs−Remainingfor a 60 nm diam-eterBC core (central core diameter of regime 3) coated inCBrown at 400 nm and 532 nm wavelength. Figure 6 showsEAbs−Remainingas a function of particle diameter andkBrown.In these simulations, increasing the 400 nmkBrown from thelower boundkBrown (0.02) (similar to thekBrown reported byDinar et al. 2008) to the base casekBrown (0.05) increases theEAbs loss by 20–30%. Increasing thekBrown from the basecase by 50% (from 0.05 to 0.075; again, near that measuredby Dinar et al., 2008) increases theEAbs loss by a further10–15%. At 532 nm, an increase inkBrown leads to an in-crease in theEAbs loss of only a few percent for reasonablecoating thicknesses (<500 nm) but leads to larger increaseswhen very thick coatings are present. Further calculations

(not shown) indicate that this conclusion is generally inde-pendent of theBC core diameter used.

4.4 Consideration of mixing state

Even thoughEAbs−BR can be large under some conditions(e.g. whenCBrown coatings are thick), our focus has beenon the influence ofCBrown on the lensing effect. It has tac-itly been assumed that absorption byCBrown, whether con-sidered as an internal or external mixture withBC, wouldbe accounted for and quantified (for example in models) bythe mass andMAC of the CBrown. We now consider how areduction in the lensing effect (due toCBrown) for an inter-nal mixture will influence theSSAand how this compares toan external mixture ofBC andCBrown. A reduction in lens-ing means that the fraction of absorption due to theBC corewill be reduced and, depending on how the contribution fromCBrown is considered in a model, this may lead to uncertaintyin the calculatedSSA, which is the primary parameter thatdetermines the sign of the radiative forcing by particles. Forexample, Jacobson (2000, 2001) showed that failure to con-sider the lensing effect due to clear coatings (i.e. treatmentof the aerosol population as an external rather than an inter-nal mixture) may lead to an underestimation of the radiativeforcing of BC by a factor of 2–3. However, if the lensingeffect is reduced due to absorption byCBrown then this un-derestimation of radiative forcing will be similarly reduced,with the actual reduction dependent on the assumed wave-length dependence of theCBrown.

4.4.1 Mixing state assumptions and Single ScatterAlbedo (SSA)

One way to interpret the lensing effect is to recognize thatit corresponds to a decrease in theSSAwhen compared toan equivalent mass external mixture. We have calculatedthe difference in SSA values between an external and aninternal mixture ofBC and CBrown (at 400 nm assuming akBrown of 0.05 and GSD = 1.1) and similarly forBC andCClear(1SSAext−int = SSAext – SSAint, where the ext and intindicate external and internal mixtures, respectively; Fig. 7).For theCBrown case (Fig. 7a), at small core sizes (<50 nm)the difference between the internal and external mixtureSSAvalues is small (<0.03). For theCClear case, for small coresizes certain coating thicknesses will give somewhat larger1SSA(see Fig. 7b), but for most core/shell combinations1SSAext−int is small. Additionally, 1SSAext−int is smallwhen the coating is very thick (i.e. within regimes 1 and2). However, for larger assumedBC core sizes the differ-ence can become large, especially for intermediate coatingthicknesses. This indicates that even though theEAbs is gen-erally largest for smallBC cores and/or very thick coatings(c.f. Fig. 5 in Bond et al., 2006), in these regimes accuratespecification of the mixing state will not strongly influencethe radiative properties ofBC and CBrown. We have also



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repeated these calculations at longer wavelengths (532 nmand 700 nm) and find that the general discussion given aboveremains valid even though the imaginary refractive index forCBrown is smaller than at 400 nm. The main influence of mix-ing state in these regimes is to increase the overall particlesize (i.e. cross section), which will tend to increase the totallight extinction, but this will have minimal influence on thebalance between absorption and scattering. However, whenlargerBC core sizes are used within a model, mixing state isseen to be an important factor. This is generally true whetherCBrown orCClearcoatings are considered, although forCBrowncoatings the importance of mixing state is lessened (consis-tent with the reduction in the lensing effect identified above).

4.4.2 Mixing state and micro-physical modelassumptions

To our knowledge, no atmospheric models explicitly accountthe fact thatBC is actually a fractal agglomerate composedof many small (10’s of nm in diameter) spherules (van Pop-pel et al., 2005).BC is instead represented as spherical par-ticles of some size (or with some size distribution), and theoptical properties are calculated based on the spherical parti-cle size. Rayleigh-Debye-Gans (RDG) theory posits that fora fractal particle such asBC the absorption behavior is in-stead dictated by the size of the individual (small) spherules,and not by the agglomerated particle as a whole, i.e. that ab-sorption is additive (Sorensen, 2000). If coatedBC particles

should be treated in accordance withRDG theory (i.e. as ag-gregates of 20–30 nm spheres), rather than as larger sphericalparticles, then the above discussion suggests that the impor-tance of treatingBC as an internal mixture may be limitedin terms of the direct radiative effects even thoughEAbs maybe relatively large. However, the fact that models tend touseBC particles with relatively large diameters (i.e.>80 nm)(e.g. Kinne et al., 2003) means that the calculated radiativeproperties may be particularly sensitive to the choice and rep-resentation ofBC mixing state.

In part, it is for the above reasons that we believe it re-mains a useful exercise to consider core-shell Mie theoryresults usingBC core diameters that go beyond the typicalspherule size range when calculatingEAbs, SSAand AAEvalues for coatedBC particles. Furthermore, what few ex-perimental measurements that exist ofEAbs for coated sootappear more consistent with the soot particles being singlelarge spheres rather than small spherules (Schnaiter et al.,2003; Zhang et al., 2008). Additionally,AAE values<1 areroutinely observed in ambient measurements (Bergstrom etal., 2007; Lack et al., 2008), a result that is theoretically pre-dicted forBCspheres that are larger than∼150 nm. Certainlymore work is necessary to establish what the appropriate coresize is for use inEAbs andAAEcalculations in order to facil-itate both interpretation of ambient measurements and accu-rate calculation of the radiative effects ofBC (andCBrown) inmodels.



4.5 Absorption wavelength dependence

The wavelength dependence of absorption is typically char-acterized by the absorption Angstrom exponent (AAE, Eq. 2).For “pure”BC in the atmosphere theAAE is assumed to be 1(Bond and Bergstrom, 2006) and observations ofAAE>1 areoften taken as evidence ofCBrown (or dust). In actuality, forAAE= 1 theBC must be of sufficiently small diameter (e.g.10 nm) or, following fromRDG theory, aBC core must be afractal agglomerate composed of many sufficiently small in-dividual spherules. As discussed above, some ambient dataprovides evidence of largeBC cores (i.e. withAAE of <1).In addition,AAEvalues>1 are theoretically possible forBCcoated inCClear (not CBrown) as discussed in Gyawali et al.(2009). Therefore, an assumedAAE= 1 to anchorBC ab-sorption, and attributeCBrown absorption contains significantpotential errors.

4.5.1 AAE variability of BC with CClear

Here we extend the calculations of Gyawali et al. (2009)in order to make clearer the need for caution in the use ofthe AAE when attributing light absorption toCBrown. Fig-ure 8a shows theAAE380nm−750nm calculated for sphericalBC cores coated in various thicknesses ofCClear. The RIused are the same as presented in the sections above, whilea larger GSD of 1.7 is assumed for theLN distribution,which represents a particle size distribution from biofuel orbiomass combustion (Bond et al., 2006). Figure 8a showsthat theAAE380nm−750nm for BC cores coated inCClear isreasonably constant within 4 of the 5 core-shell regimes(regimes 1–3 and 5). Regime 4 (thin coatings on all coresizes) shows a large variability inAAE380nm−750nm, rang-ing from −0.2 to 1.7, similar to theAAE behavior of un-coatedBC. For the other “realistic” regime (regime 3), theAAE380nm−750nmis generally in the range 1.4–1.6. Thereforeone can only attribute absorption toCBrown with confidence iftheAAE380nm−750nm is greater than 1.4–1.6; consistent withthe findings of Gyawali et al. (2009).

4.5.2 AAE Variability of BC with CBrown

If AAE380nm−750nmis measured to be less than∼1.6 this doesnot necessarily rule outCBrown as a significant contributorto the observed absorption. For certain core/shell size pair-ings, theAAE380nm−750nm for BC cores withCBrown coat-ings can actually be close to (or even less than) unity, de-pendent upon the assumedkBrown. We consider this in moredetail by determining how theAAE380nm−750nm depends onthe assumedkBrown for CBrown coatings onBC cores. Thisis important to consider because, even ifkBrown is large,only in certain regions (e.g. downwind of a forest fire) willthe ambient aerosol be predominately composed ofBC andOC. More common will be situations where inorganic ions(or non-absorbingOC) also contribute to the aerosol bur-

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den, thus decreasing the effective imaginaryRI of the coat-ing. As expected, the relationship betweenAAE380nm−750nmandkBrown depends explicitly on the core and shell diameters(Fig. 9). We have investigated three specific cases where theshell/core ratio has been varied; case 1:dp,particle/dp,core= 2;case 2: dp,particle/dp,core= 3; case 3:dp,particle/dp,core= 4.This equates to shell/core volume ratios of 7, 26 and 63,respectively. For comparison,BC has often been found inambient samples to be ca. 5-10% of the total particle mass(Quinn et al., 2002; Quinn et al., 2004), corresponding ap-proximately to cases 1 and 2, althoughBC mass fraction canvary greatly depending on proximity to sources.

Considering Case 1 (Fig. 9a), it is apparent that for manycore sizes theAAE380nm−750nm does not rise above 1.6 un-til the kBrown is at least> 0.03 and fordp,core≥125 nm theAAE380nm−750nm is not>1.6 even whenkBrown = 0.06. How-ever, for particles with 50 nm≤ dp,core≤100 nm theAAE isnoticeably greater than 1.6 afterkBrown>0.02. Thus, in a re-gion where the coatings onBC particles are relatively thin itis necessary to have relatively largekBrown in order to con-fidently distinguish contributions ofCBrown from the generic



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influence ofCClear coatings on theAAE. As the shell/corevolume ratio is increased the minimumkBrown needed to giveAAE380nm−750nm>1.6 is reduced. For example, for Case 3the minimumkBrown is ∼0.01 for all core diameter sizes con-sidered. This is because as the coating amount is increasedthe absorption due to the coating (as opposed to the core) isincreased in proportion. Thus, for regions where the coat-ings onBC particles are thick it may be possible to readilyidentify CBrown through theAAE.

The above discussion focuses on what conditions will al-low for attribution ofCBrown to observed absorption. How-ever, Fig. 9 also indicates that observation ofAAE valuesaround 1 does not definitively indicate that absorption is dueto BC only. Instead, it is found that relatively significantabsorption byCBrown can still result inAAE values around1. (Note that “significant” does not have a precise defini-tion. Here we arbitrarily interpret significant to mean theminimumkBrown needed to give a calculatedSSA380nm>0.95for a 200 nmdp CBrown particle. Thus, with this definitionwe see that significant absorption byCBrown occurs whenkBrown≥0.01. This value can be compared to thekBrown thatwould give a “noticeable” deviation in the SSA from unity(i.e. SSA<0.98), which occurs forkBrown >0.003. For refer-ence, theSSAvalues corresponding to a particularkBrown forthese 200 nm particles are shown in Fig. 9.) Consistent withthe above discussion, significant contributions ofCBrown toabsorption that still result inAAE380nm−750nm∼1 are mostcommon for thinner coatings but still have a reasonable prob-ability of occurring for thicker coatings. And in the absenceof specific knowledge about the actualBC size distributionand coating thickness from measurements it is really moreappropriate to consider theAAE380nm−750nm limit of 1.6 (in-stead of 1), in which case it is difficult to rule out contribu-tions of CBrown to observed absorption for nearly any rea-sonable core/shell combination. However, if simultaneousmeasurements of the total particle size distribution,BC sizedistribution and/or theBC mass fraction are made the above-identified limitations onCBrown identification may be relaxedsomewhat. This is because then one would know where onthedp,coat vs.dp,core AAEcontour the measurements shouldbe compared.

4.5.3 Comparing modeled AAE with ambientmeasurements

Although anAAE of 1.6 is not an absolute reference point,especially given the results from 4.5.2, at the wavelengthsconsidered here it does serve as a general first approximationand lower limit toAAE for absolute attribution ofCBrown.With this in mind, it is interesting to consider that almost90% ofAAE measurements over 2 months of ambient sam-pling during theGoMACCSfield campaign (SE USA, Bateset al., 2008) were less than 1.6 (Bergstrom et al., 2007). Ad-ditionally, our own analysis indicates thatAAE values dur-ing the 2002 and 2004NEAQScampaigns (NE USA, Bates



et al., 2005; Sierau et al., 2006) were less than 1.6∼75%and 100% of the time, respectively. The campaign averageAAE370nm−950nm from Yang et al. (2009) (East Asia) was1.46(±0.27) and was only 1.49(±0.08) during periods iden-tified as being influenced by biomass burning, whereCBrownis expected. Favez et al. (2009) sampled agricultural biomasscombustion and rareley sawAAE>1.5 in over a week of sam-pling. Again, these are combustion conditions where contri-butions fromCBrown are somewhat expected. Gyawali et al.(2009) found that theAAE405nm−870nm during a month verystrongly impacted by biomass burning fires was above the1.6 limit ∼75% of the time (60% after accounting for theuncertainty in the measurements). Although differences inparticle morphology may contribute to the observed variabil-ity in these ambientAAEobservations, taken all together thisindicates that very few ambientAAE measurements (in thediverse regions studied) are above the 1.6 limit and thereforecannot provide certainCBrown attribution (at least in the ab-sence of more specific knowledge of the core and shell sizesduring the measurement periods). However, at the same timenone of these observations can rule out the possibility thatCBrown is a pervasive contributor to sub-micron aerosol lightabsorption.

Therefore, when attempting to investigate the impact ofCBrown on AAE it is important to consider to some degreethe underlying core shape, spherule density, shell diameter,mixing state andSSAbefore any reliable quantification canbe undertaken. The difficulty in simultaneously quantifyingthese parameters in ambient experiments, particularly coreshapes, spherule densities and coating thickness will be achallenging task. Related to this is whether in-situ filter-based methods of measuring absorption appropriately rep-resentAAE. Given thatAAE is sensitive to bothCClear andCBrown coating thickness and that there is some evidence thatfilter based methods suffer from biases under elevated OCcontent (Cappa et al., 2008; Kondo et al., 2009; Lack et al.,2008), caution must be applied to these measurement meth-ods and the derived parameters such asAAE. It must also benoted here that that theAAE is dependent on the choice ofwavelengths (as shown in Fig. 8b). Our discussion above isbased on 380 nm and 750 nm radiation, the extreme wave-lengths of the visible light spectrum.

4.5.4 Measurement and analysis of ambientAAE

As a final consideration, we mention that care must be takenin extractingAAE values from measurements when absorp-tion is measured at more than two wavelengths. In additionto Eq. (2),AAEvalues have been determined from the linear-fit slope of a log-log plot of absorption vs. wavelength (e.g.Bergstrom et al., 2007). When there are many wavelengthsconsidered (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 re-sults than if wavelength pairs are used (Eq. 2). Take as an ex-ample the laboratory measurements of Schnaiter et al. (2005)where the influence of coatings ofα-pinene + ozoneSOAonBCabsorption was investigated. Based on the fitting method,they reported that the addition of theSOAcoatings led to adecreasein the AAE, from 1.13 for uncoatedBC to 0.8 forthickly coatedBC. In contrast, we estimate (from their Fig. 9)that if theAAEhad instead been determined using Eq. (2), itwould have been found toincreasewith the addition ofSOAcoatings, 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 ofAAE’s deduced from measurement must always be consid-ered in the context of the analysis methodology.

5 Summary, conclusions and recommendations

Purely scattering shells on black carbon (BC) cores can sig-nificantly enhance the absorption by that core as a result offocusing of light towards theBC core by the shell material(Bond et al., 2006). However, if those shells are mildly ab-sorbing (CBrown) this enhancement (EAbs) can be reduced,with the specific extent of reduction dependent upon the radi-ation wavelength, imaginary RI (kBrown) and thickness of theshell. Estimates of the absorption strength ofCBrown from theliterature are highly variable, likely depending on theCBrownsource and composition; certainly further research is requiredto fully understand this variability as the overall climate im-pacts ofCBrown will depend importantly on the exact wave-length dependence of the absorption (e.g. Flores et al., 2009).Nonetheless, using a mid-range estimate forkBrown we haveshown, using core/shell Mie theory calculations, thatEAbscan be reasonably reduced from the clear coating case byup to 50% at 400nm radiation and up to 25–30% averagedacross the visible radiation spectrum. This could be a sig-nificant reduction of predictedEAbs depending on the ubiq-uity of CBrown. TheEAbs reduction is sensitive to both thethickness of theCBrown shell and thekBrown but is relativelyinsensitive toBC core size for a given coating thickness. Atthe extreme limit of thickCBrown shells and shorter visiblewavelengths, theCBrown can eliminateEAbs entirely by com-pletely shielding theBC core from photons.

We have also assessed the importance of consideringCBrown as an internal mixture withBC, as opposed to anexternal mixture, in terms of the effect on the particle sin-gle scatter albedo (SSA), and ultimately the direct radiativeforcing. Large differences in the calculated SSA betweenthe internal and external mixtures are only found when largeBC cores are used. When smallBC cores are used (or if itis assumed that the larger particles are actually aggregatesof small individual spherules) the SSA differences are foundto be minor (1SSA<0.03). However, compared to the clearcoating case, the potential mis-representation of the radiativeforcing by not including the absorption enhancement effect



(i.e. external mixtures) is lessened due to the reduced lensingimpact ofCBrown.

The absorption Angstrom exponent (AAE) is often usedto identify atmospheric contributions ofCBrown to visiblelight absorption from ambient particle optical property mea-surements. Generally, this is done by assuming that onlyCBrown and dust haveAAE >1 and thus that any observa-tion of AAE>1 indicates the presence ofCBrown and/or dust.However, theAAE for BC cores can vary around 1 (−0.2,+1.3) with significant deviations from 1 occurring for as-sumed larger diameters, where it is uncertain if theBC ex-ists as a dense spherical particle. ForBC particles coated inpurely scattering material it is possible to obtainAAE val-ues significantly greater than 1, with values as large as 1.6common (for the specific wavelength pairs considered here).Thus, attribution ofCBrown to the observed absorption canonly be made with confidence if theAAE is measured tobe>1.6. Conversely, we have shown that the measurementof AAE values close to 1 does not rule out significant con-tributions fromCBrown to absorption. Our calculations sug-gest that attempts to quantitatively (or even qualitatively) at-tribute light absorption toCBrown from measurement of thewavelength dependence of absorption will be most success-ful if conducted concurrent with measurements ofBC andtotal particle size distributions.

Acknowledgements.Funded through NOAA’s Atmospheric Com-position and Climate Program within the Climate Program Office.

Edited by: L. M. Russell

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