Estimation of a ”radiatively correct” black carbon ...

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Estimation of a ”radiatively correct” black carbonspecific absorption during the Mexico City Metropolitan

Area (MCMA) 2003 field campaignJ. C. Barnard, E. I. Kassianov, T. P. Ackerman, K. Johnson, B. Zuberi, L. T.

Molina, M. J. Molina

To cite this version:J. C. Barnard, E. I. Kassianov, T. P. Ackerman, K. Johnson, B. Zuberi, et al.. Estimation of a ”radia-tively correct” black carbon specific absorption during the Mexico City Metropolitan Area (MCMA)2003 field campaign. Atmospheric Chemistry and Physics, European Geosciences Union, 2007, 7 (6),pp.1645-1655. �hal-00296182�

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Atmos. Chem. Phys., 7, 1645–1655, 2007www.atmos-chem-phys.net/7/1645/2007/© Author(s) 2007. This work is licensedunder a Creative Commons License.

AtmosphericChemistry

and Physics

Estimation of a “radiatively correct” black carbon specificabsorption during the Mexico City Metropolitan Area (MCMA)2003 field campaign

J. C. Barnard1, E. I. Kassianov1, T. P. Ackerman1,*, K. Johnson2,** , B. Zuberi2,*** , L. T. Molina 2, and M. J. Molina2,**

1Pacific Northwest National Laboratory, Richland, WA, USA2Massachusetts Institute of Technology, Cambridge, MA, USA* now at: University of Washington, Seattle, WA, USA** now at: University of California, San Diego, CA, USA*** now at: GEO2 Technologies, Woburn, MA, USA

Received: 1 April 2005 – Published in Atmos. Chem. Phys. Discuss.: 23 June 2005Revised: 9 February 2007 – Accepted: 19 March 2007 – Published: 27 March 2007

Abstract. During the Mexico City Metropolitan Area(MCMA) field campaign of 2003, measurements of theshortwave radiation field allowed the inference of theblack carbon (BC) specific absorption,αλ, defined as themonochromatic absorption cross section per unit mass (withunits of m2/g). The averaged values ofαλ derived from themethod here are either 8.9 m2/g or 8.2 m2/g at 500 nm, de-pending upon the physical and optical parameters assumedfor BC. These results are reasonably consistent with thoseof Schuster et al. (2005), 9.5 m2/g, and Baumgartner et al.(2002), 7.0 m2/g, both measured at 550 nm. Theαλ val-ues reported in this paper should only be considered effec-tive, “radiatively correct” values because when used in ra-diative transfer calculations the calculated irradiances matchthe measured irradiances at 500 nm. The specific absorptionso defined can assume a wide range of values, dependingupon: (1) the assumptions made prior to the retrieval (e.g.,shell/core aerosol configuration), and (2) values chosen forBC density and refractive index. The range of possible val-ues is large, corresponding to a “worst case” uncertainty ofabout±70%, assuming that all errors are additive and of thesame sign so that no error cancellation occurs.

1 Introduction

Black carbon is found throughout the atmosphere, is mostlyof anthropogenic origin, and is thought to be the most im-

Correspondence to: J. C. Barnard([email protected])

portant contributor to aerosol absorption of solar radiation.A key measure of the absorption efficiency of BC is the spe-cific absorption,αλ, defined as the monochromatic absorp-tion cross section per unit mass, typically given in units ofm2/g. The specific absorption is a function of wavelength,as indicated by the subscriptλ. Over the years, the litera-ture has reported a large range for values ofαλ, from as lowas 2 m2/g to as high as 25 m2/g (e.g., Waggoner et al., 1981;Horvath, 1993; Liousse et al., 1993; Petzold et al., 1997;Penner et al., 1998; Moosmuller, 1998; Marley et al., 2001;Arnott et al., 2003; Schuster et al., 2005). As suggested byLiousse et al. (1993) this wide variation may be caused bydifferences in the aerosol mixing state, with the smaller val-ues favoring external mixtures, while larger values indicateinternal mixing of BC. Estimates of aerosol radiative forcingattributable to BC are influenced dramatically by the mixingstate of BC, and because of the relationship between mixingstate andαλ, these estimates depend on the value ofαλ aswell (e.g., Ackerman and Toon, 1981; Chylek et al., 1995;Fuller et al., 1999; Jacobson, 2000; Jacobson, 2001; Chungand Seinfeld, 2002; Lesins et al., 2002; Riemer et al., 2003;Sato et al., 2003).

Because of the importance ofαλ in determining the magni-tude of aerosol radiative forcing, atmospheric measurementsof this quantity are critical. In this paper, we present esti-mates ofαλ based on the observed shortwave radiation field,made within the Mexico City basin during the MCMA fieldcampaign undertaken in April and May of 2003. This basinis an ideal place to study BC aerosols because of the highBC emissions; the high altitude, which enhances the aerosolscattering signal over that of molecular scattering; significant

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

1646 J. C. Barnard et al.: Black carbon specific absorption in Mexico City

variations in relative humidity, from very dry to saturatedconditions; and the unique meteorology of the Mexico Citybasin, which under the right meteorological conditions, mayflush pollutants out of the basin on a daily basis (Fast andZhong, 1998; Gaffney et al., 1999; Whiteman et al., 2000;Molina et al., 2002).

2 Methodology

2.1 Measurements

The primary instrument used for this analysis is the Multi-Filter Rotating Shadowband Radiometer (MFRSR, Harrisonet al., 1994). This instrument, as well as most of the other in-struments involved in the MCMA campaign, was deployed atthe National Center for Environmental Research and Train-ing (Centro Nacional de Investigacion y Capacitation Am-beintal, abbreviated as CENICA), on the Iztapalapa campusof the Unversidad Autonoma Metropolitana (UAM). Thissite is located at a latitude and longitude of 19.36 N and99.07 W, respectively, and is atop a building and removedfrom direct exposure to automobile exhaust. As noted byJohnson et al. (2005), this site is in a mixed commercial-residential area with relatively few industries or congestedroads. It is about 9 km southeast from La Merced, a marketarea often filled with dense traffic, and 2 km south of a largefood market frequented by delivery trucks in the morninghours. Given the apparent lack of major aerosol sources inthe near vicinity of the site, we assume that the BC aerosolsobserved here will have had some chance to age compared tothose freshly emitted in traffic.

The MFRSR is, as the name implies, a shadowband ra-diometer that measures two components (diffuse and total)of the shortwave radiation field at the six wavelengths: 415,500, 615, 673, 870, and 940 nm. The third component of thefield – the direct component – is found from the total and dif-fuse components by subtraction combined with a correctionfor the cosine response of the instrument. Because all threeradiation components are measured with the same sensor, ifone component can be calibrated accurately, the other twocomponents will share similar calibration accuracies. Typi-cally, the direct component of the irradiance is calibrated inthe field using the Langley method with a calibration accu-racy that approaches 1% (Michalsky et al., 2001).

Aerosol optical thicknesses,τλ, are derived from the directcomponent, provided that the path between the sun and theinstrument is not obscured by clouds. Whether this criterionis met is easily determined using theAngstrom exponent,a(Seinfeld and Pandis, 1998; Schuster et al., 2006). The sin-gle scattering albedo, 0,λ, is the probability (0≤ 0,λ≤1)that an aerosol scatters, rather than absorbs, a photon thatimpinges on it. Formally it is the ratio of the aerosol scat-tering coefficient,bscat (m−1), to the aerosol extinction co-efficient, which is the sum of thebscat and absorption coef-

ficient, babs (m−1), or 0,λ=bscat/(bscat+babs). The singlescattering albedo can be retrieved from the diffuse and totalirradiances using the algorithm of Petters et al. (2003), Kas-sianov et al. (2005), or Goering et al. (2005). These algo-rithms work best for large optical thicknesses (e.g.,τλ>0.25at 500 nm), a condition that is frequently met in the MexicoCity basin. For the work reported here, we tested both thePetters and Kassianov algorithms and obtained nearly simi-lar results for retrieved single scattering albedos, suggestingthat the results presented below are independent of the algo-rithm chosen. These algorithms can only be used if the skyis completely free of clouds, a criterion that was verified us-ing the method of Long and Ackerman (2000). During theentire MCMA campaign, there were only seven periods thatsatisfied the cloud-free criterion. The dates and time of theseperiods are listed in the first column of Table 1.

The average value of 0,λ over these seven cases is0.90. For the same days, the average 0,λ derived from theAERONET (Aerosol Robotic Network; Holben et al., 1998)sun photometer located in Mexico City is 0.89 at 500 nm,as determined by linear interpolation between inferred singlescattering albedos at 441 nm and 673 nm. It is also possi-ble to derive 0,λ from surface measurements. Baumgart-ner et al. (2000) measuredbscatandbabsusing a nephelome-ter and particle soot absorption photometer (PSAP), respec-tively. Before these measurements were made, the aerosolswere heated to ensure that the relative humidity was less than40%. Atmospheric soundings that bracket the time periodover which inferences of 0,λ were made indicate that theboundary layer was quite dry, with relative humidities belowthe aerosol mixing height generally less than 30%. For suchlow humidities, the aerosol is likely to be dry. This dry con-dition permits the use of Baumgartner et al.’s surface mea-surements without concern for humidity effects. Using thesemeasurements, given in Fig. 2 of Baumgartner et al. (2000),and including only values for relative humidities less than30%, 0,λ is found to be 0.88 at 550 nm. The agreementbetween these three different ways of finding 0,λ suggeststhat our 0,λ are credible.

2.2 Determination ofαλ

The method used here to estimateαλ is based on a techniquefirst discussed by Schuster et al. (2005), with an importantdifference mentioned below. The method relies on the simpleequation:

αλ =(1 − 0,λ)τλ

MBC=

τλ,abs

MBC(1)

whereτλ,absis the aerosol absorption optical depth. The ma-jor assumption underlying this equation is that BC is the onlyatmospheric absorber at the wavelengthλ, which is generallyvalid outside the UV and near-UV spectral ranges (Heintzen-berg et al., 1997). The aerosol optical thickness is inferredfrom the MFRSR direct normal irradiances, and0,λ is

Atmos. Chem. Phys., 7, 1645–1655, 2007 www.atmos-chem-phys.net/7/1645/2007/

J. C. Barnard et al.: Black carbon specific absorption in Mexico City 1647

Table 1. The seven case studies selected for retrievals ofαλ (for λ=500 nm) and the results from BC physical and optical parameter sets Iand II.

Date,time period (hours,LST)

τλ a 0,λ CV =Cf +Cc

(µm3/µm2)

fV

III

MBC(mg/m2)

I/II

αλ

(m2/g)I/II

Re[ms ]I/II

14 April 2003(08:26–10:19)

0.313 1.73 0.901 0.1443 0.011360.01369

3.3/4.0 9.5/8.7 1.33/1.33

15 April 2003(07:33–10:26)

0.331 1.50 0.889 0.1350 0.016000.01936

4.3/5.2 8.5/7.8 1.40/1.40

16 April 2003(08:02–10:27)

0.375 1.57 0.859 0.1569 0.019380.02347

6.1/7.4 8.7/8.0 1.39/1.39

18 April 2003(08:19–10:32)

0.267 1.48 0.965 0.1461 0.003750.00448

1.1/1.3 8.5/7.9 1.32/1.32

26 April 2003(07:36–10:40)

0.390 1.69 0.901 0.1300 0.016210.01971

4.2/5.1 9.2/8.4 1.46/1.46

27 April 2003(07:49–11:59)

0.310 1.69 0.924 0.1354 0.009840.01191

2.7/3.2 8.8/8.1 1.39/1.39

30 April 2003(07:54–11:00)

0.335 1.58 0.886 0.1208 0.017240.02093

4.2/5.1 9.2/8.4 1.44/1.44

average 0.332 0.904 3.7/4.5 8.9/8.2 1.39/1.39

found from the diffuse and total MFRSR irradiances and thesingle scattering albedo algorithms mentioned above. It thenremains to findMBC.

To find this quantity, we must make the following assump-tions: (1) the aerosol is spherical and internally mixed ina shell/core manner (Jacobson, 2000; Bond et al., 2006),with the core of the aerosol consisting of BC. This shell/coreconfiguration differentiates our method from that of Schus-ter et al. (2005), which handled internal mixing using theMaxwell-Garnett approximation; (2) the physical and opti-cal properties (density,ρBC; refractive index,mBC) of theBC are known; (3) the shell is non-absorbing; (4) the colum-nar aerosol volume distribution of the aerosol is known; and(5) the mass fractions of the various aerosol chemical con-stituents do not vary with the aerosol size. The first assump-tion of an internal mixture is difficult to verify although elec-tron micrographs of the aerosol, as well as a single-particlechemical analysis of the aerosols, indicate that the soot is in-ternally mixed with other substances (Johnson et al., 2005).Given the complexity of aerosol shapes and mixing config-urations depicted in Johnson et al., the spherical shell/coremodel of internal mixing is a simplification but is necessaryfor conventional Mie theory calculations of the aerosol’s op-tical properties. In regard to the second assumption, the re-ported values for the physical properties and optical of BCvary widely, as reported by Bond and Bergstrom (2006) andFuller et al. (1999). Lacking in situ measurements we as-sume plausible values for these properties, discussed below.Assumption three, that the shell does not absorb, is tanta-mount to assuming that BC is the only absorber at 500 nm.As mentioned above, this is consistent with the assertion ofHeintzenberg et al. (1997).

The columnar aerosol volume distribution, required by thefourth assumption, is obtained from the AERONET databasefor the specific days in question. The volume distributionfound by the AERONET algorithm is expressed asdV/dlnrwith units (µm3/µm2), such that the integration over allaerosol radii (or more properly, the logarithm of the aerosolradius) yields the total volume concentration of the aerosolper unit area of the atmospheric column,CV (with unitsµm3/µm2). The inversion method leading to the aerosol vol-ume distribution, as well as the assumptions inherent to theinversion (e.g., spherical particles, various smoothing con-straints), have been discussed in Dubovik and King (2000).Formally, the volume distribution is the sum of two lognor-mal distributions that represent the fine (f ) and coarse modes(c) of the total distribution (Dubovik et al., 2002),

dV (r)

d ln r=

CV,f√2πσf

exp

[

−(ln r − ln rV,f )2

2σ 2f

]

+CV,c√2πσc

exp

[

−(ln r − ln rV,c)

2

2σ 2c

]

(2)

In this equation,r is the particle radius, andrV and σ

are the volume median particle radius and the standard de-viation, respectively, for either the fine or coarse mode.(The conventional geometric standard deviation,σ g, is re-lated to the standard deviation listed above by the re-lationship, σ=lnσ g.) Typical values of these quantitiesfor the MCMA field experiment are for the fine mode:CV,f =0.075µm3/µm2, rV,f =0.13µm,σ f =0.43; and for thecoarse mode:CV,c=0.063µm3/µm2, rV,c=3.6µm,σ c=0.62.

The fifth assumption – constant aerosol composition re-gardless of aerosol size – is at least partially satisfied. Black

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carbon emitted from traffic sources is submicron in size. Thatthese small soot particles make their way to larger particles isclearly seen in the scanning electron micrographs shown inFig. 5 of Johnson et al. (2005), which show internally mixedsoot contained in particles that are larger than 1µm in size.

FindingMBC begins with the equations

(1 − 0,λ)τλ =∞

∫

0

dn(r)

drσabs(ms, mBC, r, fV )dr (3)

and

τλ =∞

∫

0

dn(r)

drσext(ms, mBC, r, fV )dr (4)

where dn(r)/dr is columnar number distribu-tion obtained from the volume distribution (e.g.,dV/dlnr=r(4/3πr3)dn(r)/dr); σabs(ms, mc, r, fV ) andσext(ms, mc, r, fV ) are the absorption and extinction crosssections as a function of the (complex) refractive indices ofthe shell,ms , and the BC core,mBC; r is the total radius ofthe particle, andfV (0≤fV ≤1) is the volume fraction of theaerosol that consists of BC. Invoking assumptions two andthree mentioned above, we assume values formBC and thecomplex part ofms , denoted as Im[ms ] (these values will bediscussed below);dn(r)/dr is known from the AERONETretrievals, and from the MFRSR measurements we can inferτλ and 0,λ. With these known factors, Eqs. (3) and (4)become integral equations forfV and the real part ofms ,Re[ms ]. Once fV is known, MBC follows immediately,MBC=CV fV ρBC, where again, we use assumption (2) andchoose a plausible value forρBC, discussed below.

Solving Eqs. (3) and (4) forfV and the real part ofms

is a straightforward, iterative process. First, we take Im[ms ]as−10−7i. The small imaginary part of the shell refractiveindex implies negligible absorption and is representative ofa sulfate-like compound (Toon et al., 1976), and/or organiccompounds that do not absorb at 500 nm. Next, the shell/coreMie code of Ackerman and Toon (1981) is used to computeσabs(ms, mc, r, fV ) and σext(ms, mc, r, fV ) for ranges ofrthat encompass the limits ofdn(r)/dr and plausible values offV . Equation (3) and (4) are integrated numerically, com-pared with (1− 0,λ)τλ andτλ, respectively, and this pro-cess is repeated until the left- and right-hand sides of theequations are equal. This iteration is robust and convergesrapidly.

When solving Eqs. (3) and (4), assumptions regarding spe-cific values ofmBC andρBC must be made. Measurements ofthe density of diesel soot (Park et al., 2004; Wu et al., 1997),and the discussion provided in Fuller et al. (1999) and Schus-ter et al. (2005) suggest a plausible range ofρBC from 1.7 to2.1 g/cm3. Bond and Bergstrom (2006) suggest a more lim-ited range of 1.7 to 1.9 g/cm3. Although measured densityvalues less than 1.7 g/cm3 have been reported, an important

consideration favoring the higher density values is the needto correlate carbon mass emissions with climate impact. Asnoted by Fuller et al. and references therein, for this cor-relation to be meaningful, the density of the tiny spherulesthat compose soot clusters is important, and not some aver-age density of a soot cluster, which contains voids. Withinthe 1.7 g/m3 to 2.1 g/m3 range, however, we cannot pretendto know the density exactly and consequently, we chose thevalue, 2.0 g/m3, so the results may be compared with Schus-ter et al. (2005). For this same reason we takemBC=2.0–1.0i(Soot G, Fuller et al., 1999).

It is instructive, however, to repeat the specific absorptioncalculations using the refractive indices and densities as re-ported by Bond and Bergstrom (2006). In this paper, an ex-haustive review and analysis of the literature was undertakento determine suggested ranges of these quantities. Consider-ing these ranges to be the most credible and updated valuesfor use in radiative transfer calculations, we again findαλ bytakingρBC to be 1.8 g/m3 andmBC as 1.95–0.79i. The den-sity is the midpoint of the suggested range of 1.7 to 1.9 g/m3,while mBC is the highest of the suggested values and impliesa minimal void volume in the carbon. To distinguish betweenthese two sets of calculations, we label them as I – for com-parison with the results of Schuster et al. (2005); and II –using Bond and Bergstrom “best estimate” values. For thesake of explicitness, the refractive indices and densities ofthese two sets of calculations are shown in Table 2.

2.3 Specific absorption values

The technique described above was applied to 7 cases duringwhich the sky was free from clouds. Table 1 shows the resultsfor both sets I and II, as well as values ofτλ , a, and 0,λ

averaged over the indicated clear sky periods. All results arefor a wavelength of 500 nm. It is again important to reiteratethat the derived values ofαλ are only appropriate for the timeperiods when the skies are clear because this requirement isnecessary to derive 0,λ. These time periods occur in themorning hours, before a convective boundary layer developsthat encourages the development of convective cloudiness.

For the seven cases considered here and for the BC pa-rameter sets I and II, the eighth column in Table 1 showsαλ,while the last column shows Re[ms ]. The specific absorp-tions are depicted by the bar chart in Fig. 1, which showsthat the results of set I are larger than set II, but nonethelessfairly close. When averaged over the 7 cases, the averagedvalues, shown in the bottom row of Table 1, are 8.9 m2/g and8.2 m2/g, for sets I and II respectively, a difference of about9%.

When averaged over all days, Re[ms ] is equal to 1.39 forboth sets. That Re[ms ] is virtually the same for both setsis related to the fact that the extinction (τλ) depends mostlyon the real part of the (effective shell/core) refractive index(King et al., 1978). Furthermore, our value is quite closeto the real part of the refractive index obtained from the



Table 2. BC properties used in the two sets of calculations considered here.

Set I – for comparison withthe results of Schuster etal. (2005)

Set II – using “best es-timate” values from Bondand Bergstrom (2006)

Refractive index of BC,mBC 2.0–1.0i 1.95–0.79iDensity of BC,ρBC 2.0 g/m3 1.8 g/m3

AERONET retrievals, 1.40, when averaged over the samedays. An effective shell refractive index of this magnitudesuggests the presence of water in the shell, but the bound-ary layer was very dry and the aerosols were likely to bedry. However, a Re[ms ] of this magnitude may be congruentwith the large organic carbon (OC) content of the MCMAaerosol. As noted in Salcedo et al. (2006), the average masscomposition of OC in the aerosol was about 55%. We do notknow exactly which compounds compose the OC content ofthe MCMA aerosol, nor do we know their refractive indices.To get around a similar problem, Schnaiter et al. (2003) esti-mated the refractive index of secondary organic aerosols byusing known refractive indices of two OC compounds sim-ilar to those that might be found in these aerosols. Thesetwo values reported by Schnaiter et al. are 1.43 to 1.45. Ja-cobson (1999) has tabulated the real part of refractive indexof many organic compounds; these range from about 1.33 to1.63. Given these range of values, Re[ms ] is consistent witha significant OC component in the MCMA aerosol.

Schuster et al. (2005) report values ofαλ at manyAERONET locations using retrievals of aerosol propertiesfrom the AERONET sun photometers. The methodology be-hind their results closely parallels our method, and our set Iassumes the same values for the physical properties of BC.The major difference between the two methods is our useof a shell/core model to represent aerosol mixing propertiesversus Schuster et al.’s use of the Maxwell-Garnett (MG) ef-fective medium approximation (Lesins et al., 2002; Bohrenand Huffman, 1983) to find an “effective” refractive index ofthe aerosol mix. When Schuster at al. used this approxima-tion, the volume fractions of BC and ammonium sulphate,contained in a water host, are iterated until the difference be-tween the calculated and observed (AERONET) values of theindex of refraction is minimized. Once the volume fractionis known,MBC is easily calculated.

For Mexico City, Schuster et al. (2005) quote a value ofαλ of 9.5±0.9 m2/g when averaged over the years 2000 and2001, for a wavelength of 550 nm. Recall that for set I, weused the same BC physical parameters as Schuster et al. Forthis set, our value 8.9 m2/g has been derived for a wavelengthof 500 nm, and to compare these two values, we must adjustour value to a wavelength of 550 nm. From measurements ofaerosol absorption taken at different wavelengths, Bergstromet al. (2002) show that the wavelength dependence of BC

4/1

3/0

34/1

4/0

34/1

5/0

34/1

6/0

34/1

7/0

34/1

8/0

34/1

9/0

34/2

0/0

34/2

1/0

34/2

2/0

34/2

3/0

34/2

4/0

34/2

5/0

34/2

6/0

34/2

7/0

34/2

8/0

34/2

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34/3

0/0

35/1

/03

date

0

1

2

3

4

5

6

7

8

9

10

11

12

13

α λ=500

nm

Set I

Set II

Fig. 1. Bar chart summarizing the values ofαλ, for λ=500 nm, overthe course of the MCMA field campaign. Results from sets I and IIare shown.

absorption is best described by the well-known relationshipλ−1 over a wavelength range of 0.4 to 1.0µm. Kirchstet-ter et al. (2004) suggest that, for motor vehicle aerosols thathave a relatively large BC component, the wavelength de-pendence is also aboutλ−1 in the visible range. These stud-ies indicate that, for our wavelength extrapolation from 500to 550 nm, the relationshipλ−1 is appropriate. With this inmind, converting our “set I” value to 550 nm gives 8.1 m2/g[=8.9 m2/g(550 nm/500 nm)−1], which is lower than Schus-ter et al.’s value by about 15%. Our set II value at 550 nm is7.4 m2/g.

All values mentioned above are less than 10 m2/g, a valuecommonly accepted forαλ at a wavelength of 550 nm. Bondet al. (2006) suggest that aged (i.e., coated) BC aerosolshave an (specific) absorption amplification factor of up to1.5. (Larger values are possible but only for conditionswhich are unlikely to occur in the atmosphere.) Using Bond



and Bergstrom’s (2006) uncoated value of 7.5±1.2 m2/g(550 nm), the range inαλ from uncoated to coated extendsfrom 7.5±1.2 m2/g up to 11.3±1.8 m2/g, and our values,as well as those of Schuster et al. (2005) lie in this range.Our values are also consistent with Fuller et al. (1999) whosuggest that the “canonical” value of 10 m2/g is too large.They arrived at this conclusion by explicitly calculatingαλ

for randomly spaced BC occlusions within a host sulphateaerosol, and over a wide range of plausible BC mass mix-ing ratios, the calculations indicate thatαλ>10 m2/g occursonly when two conditions are met: most of the BC is in-ternally mixed, and the host aerosols are sufficiently large,defined asRg>0.06, whereRg is the geometric mean radiusof the size distribution. Our retrievals ofRg for the MCMAbased on the algorithm of Kassianov et al. (2005), indicatethatRg is about 0.035µm. Alternatively, using the fine com-ponent of the AERONET volume distribution yields anRg

of about 0.032µm. Both of these radii are smaller that the0.06µm limit, suggesting thatαλ should be less than 10 m2/gat 550 nm.

2.4 MBC, fv

In addition to αλ, Table 1 provides other aerosol charac-teristics that are derived from our methods, such asMBC.For both sets I and II the averagedMBC values are about4 mg/m2. These are large BC loadings. As shown in Schuster(2004), columnar BC concentrations in an urban area (God-dard Space Flight Center [GSFC] near Washington, D.C.,USA) inferred from AERONET measurements, can range ashigh as about 7 mg/m2, although most values are less than3 mg/m2. That the BC columnar concentrations are largerthan those typically found at the GSFC seems intuitivelycredible, given the very large population and emissions ofthe MCMA.

2.5 Uncertainties

Quantification of the uncertainties associated with themethod described here is possible, but still subject to someeducated guesswork. Because our method is similar to thatdiscussed by Schuster et al. (2005), much of the uncertaintyanalysis contained in Schuster et al. is applicable to ourmethod as well. The sources of uncertainty discussed inSchuster at al. include the obvious ones: the physical andoptical properties of carbon and the host aerosol, mixing as-sumptions, and the contamination of the results by absorbingspecies other than BC. Because these various sources of un-certainty have already been thoroughly discussed in Schusteret al., we will summarize them here. We will also estimatethe uncertainty due to the error in the retrieved volume dis-tributions, the departure of the aerosol shape from spherical,and errors in the retrieval of 0,λ and τλ. In the discus-sion below, we shall just consider the uncertainties associatedwith set I; similar arguments would hold for set II. Although

the magnitude of the uncertainties might be somewhat dif-ferent between each set, we must be mindful that these un-certainties cannot be pinned down with exactitude, and anuncertainty estimated for either set is likely to representativeof the other set as well.

2.5.1 Density of BC

Considering the discussion of Fuller et al. (1999) plausi-ble bounds for BC density range from 1.7 g/m3 to 2.1 g/m3.Bond and Bergstrom (2006) state that the upper end of theplausible range is only 1.9 g/m3. For our set I calculations,we assume a value of 2.0 g/m3 for comparison of the resultsof Schuster et al. (2005). Assuming that the density of BCin the MCMA is bracketed by 1.7 g/m3 to 2.1 g/m3, the errorbounds onαλ are +18% to−5%. That is,αλ could be 18%higher or 5% lower than the values we calculate. Schuster etal. estimated±5%; we think this is a little too low.

2.5.2 Optical properties of BC

The value chosen for the refractive index is 2.0–1.0i, andthis is somewhat above the upper end of reported refractiveindices (Bond and Bergstrom, 2006) for both the real andimaginary parts. Reducing either the real or imaginary partof the refractive index from the chosen value reduces the cal-culated value ofαλ. For example, using a refractive index of1.85–0.71i (a value employed by Bond et al., 2006, and inthe middle of the range suggested by Bond and Bergstrom,2006), in place of 2.0–1.0i , reduces theαλ by about 22%.Even lower values for the imaginary part of the refractive in-dex can significantly reduceαλ. As noted by Schuster at al.,using the OPAC (Optical Properties or Aerosols and Clouds)refractive index for soot, 1.75–0.44i, lowersαλ by a factor oftwo, outside the range which is thought plausible. Additionalevidence suggests that the OPAC refractive index is not “darkenough” and should be retired (Bond and Bergstrom, 2006),and our results support this assertion. Because the chosenvalues of both the real and imaginary parts of the refractiveindex are near the upper bounds thought likely, we estimatea possible positive uncertainty of +10%.

2.5.3 Mixing assumptions and aerosol shape

Scanning electron micrographs of soot-containing particlesshown in Johnson et al. (2005) show that the soot is inter-nally mixed. The particles shapes are tortured, and are any-thing but perfect spheres. Because it is impossible to modelthe optical properties of such aerosols exactly, we must per-force approximate the aerosols as spheres. Given that we as-sume a spherical shape, a concomitant issue is the rules thatgovern the mixing of the BC within the sphere. In our case,we chose a concentric sphere (CS) model with carbon in thecenter. Other mixing scenarios are possible. Some lead tounrealistic results; for example, Bond et al. (2006) stronglyadvise against using volume averaging of refractive indices



because this mixing model overestimates absorption. For in-ternal mixtures, Lesins et al. (2002) examined shell/core con-figurations and refractive index mixing rules such as MG.Optical properties derived from these two scenarios, for thesame volume fraction of BC, were typically within 5% ofone another. For thefV of the MCMA aerosol, less than0.03, calculations done by Fuller et al. (1999) of BC absorp-tion – and shown in their Fig. 12 – indicate that the CS modelprovides nearly identical absorption to a case where the BCinclusion is randomly distributed throughout the host aerosol,or when the inclusion is located just below the surface. Usingthis as a guide, we estimate any error in using a CS modelto be slightly negative (i.e., the actual absorption could beslightly less than our calculations), but close to zero. Thisestimate is only justifiable for small BC mixing ratios andspherical aerosols.

That the aerosols are not spherical induces some error intoour calculation. Recent work using exact calculations ofthe optical properties of fractal-like soot aggregations in ran-dom orientations (Liu and Mishchenko, 2005) provides someguidance on the extent that aerosol morphology influencesαλ. For example, when the fractal dimension varies from1.5 (chain-like structures) to 2.4 (more compact and sphere-like), αλ decreases by about 10%. These results are notstrictly applicable to our study because, among other things,Liu and Mishchenko focused only on aggregations of sootmonomers, and not the more realistic situation of soot mixedwith other compounds. Nonetheless, given these results, wespeculate that aerosol shape issues introduce an uncertaintyof about±10%.

2.5.4 Contamination of results by other absorbing species

The air and aerosols in the MCMA contain substances, asidefrom BC, that absorb sunlight. Surface observations of NO2concentrations that occur in the morning hours in MexicoCity (Rainer Volkamer, personal communication) show thatit is large enough (>40 ppb) to be a significant absorber.These high concentrations would contaminate the retrievalsof 0,λ at wavelengths where there is significant NO2 ab-sorption (440 nm for the AERONET sun photometer and415 nm for the MFRSR). The effect of this absorption is toreduce the inferred value of 0,λ compared to the value thatwould be inferred if the NO2 absorption were properly takeninto account. The OC content of the MCMA aerosol is sig-nificant (Salcedo et al., 2006) and this large amount of OCcould contribute to increased absorption at the UV and near-UV wavelengths (Jacobson, 1999; Kirchstetter et al., 2004),adding to the contamination of 0,λ retrievals. Similarlydust is known to absorb in the UV and near-UV wavelengths(Sokolik and Toon, 1999). The net effect of this contami-nation, if not accounted for, is to attribute the absorption ofNO2, OC, and dust to BC. This would tend to increase ourretrieved values ofαλ.

We have been able to minimize this error by making re-trievals at a wavelength equal to 500 nm, where the absorp-tion of NO2 is small, and the absorption of OC is expectedto be very small (Jacobson, 1999; Kirchstetter et al., 2004).Plots of single scattering albedo versus wavelength reveal adefinite dust signature in dusty areas (Dubovik et al., 2002),and this signature is absent in the MCMA data, indicatingthat dust absorption is not likely to be large. Schuster esti-mated the total contamination bias to be about−10%, thatis, the trueαλ values could be lower than calculated by upto this amount. In our case, we estimate that the error is lessthan−5% because of the use of the 500 nm wavelength, andthe apparently small dust loading of the MCMA.

2.5.5 Uncertainties in volume distribution retrievals

According to Dubovik et al. (2002), for intermediate parti-cles sizes where the bulk of the particles reside, the retrievalerrors of the volume distribution do not exceed 10% in themaxima of the volume distribution. If we assume that theuncertainty of the retrieved aerosol volumes (i.e., integrationof the volume distribution) is the same magnitude, then thederived volumes listed in column five, Table 2 would be un-certain to±10%. (This is a conservative estimate of the errorbecause it does not account for canceling errors during theintegration of the volume distribution.) If we again do thecalculations and vary the aerosol volume by±10%, the cal-culated specific absorptions change by about 4%.

2.5.6 Uncertainties in the retrieval of0,λ andτλ

The uncertainty in the retrieval of 0,λ, 1 0,λ, and anuncertainty inτλ, 1τλ, contribute directly to the overalluncertainty ofαλ, 1αλ, in the following manner:αλ +1αλ=(1−( 0,λ+1 0,λ))( τλ+1τλ)/MBC, where the un-certainties in 0,λ andτλ can be of either sign. Michalskyet al. (2001) states that1τλ is ±0.01, while1 0,λ is about±0.03 (Dubovik et al., 2002; Georing et al., 2005). Assum-ing that the real 0,λ is about 0.9, and the realτλ is about0.33 (the average values for the MCMA campaign), we ob-tain uncertainties of about±30%. For single scattering albe-dos that approach one (e.g., the case of 18 April 2003 with 0,λ=0.965), the uncertainty would be much larger.

2.5.7 Summary of errors

Considering all these factors except particle shape, Schus-ter et al. (2005) estimated the overall error inMBC retrievalsto range from−40% to +15% by simply summing the in-dividual uncertainties together. That is,MBC may be over-estimated by 40% or underestimated by 15% and (approxi-mately) visa versa forαλ because of the inverse relationshipbetweenMBC andαλ. Summarizing our uncertainty anal-ysis forαλ gives the following values: (a) density,−5% to18%; (b) optical properties of BC, +10%; (c) mixing assump-tions and particle shape,±10%; (d) contamination by other



6 7 8 9 10 11 12 13 14 15 16 17 1

time (hours, LST)8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

AO

T (

500

nm

)

AERONET

MFRSR

Fig. 2. Aerosol optical thickness (AOT) at 500 nm derived from theMFRSR and AERONET sun photometer in Mexico City. The dateis 27 April 2003.

species,−5% to 0%; (e) uncertainties in the retrievals of thevolume distribution,±4%; and (f) uncertainties in the re-trievals of 0,λ andτλ, ±30%. A simple addition of theseuncertainties, which emphasizes the worst case scenario be-cause no errors are allowed to cancel, yields an overall un-certainty of from about−55% to about +75%. For conve-nience, we simply take uncertainty to be±70%. For a spe-cific absorption of 8.9, this maps into error bars of magnitudeof about±6.2 m2/g. Most of the overall uncertainty stemsfrom the large uncertainty in retrieving the single scatteringalbedo.

3 Discussion

When theαλ values are converted to 550 nm using the con-version rule,λ−1, and when averaged over all seven cases,our method yields 8.1 m2/g and 7.4 m2/g for sets I and II,respectively. On the other hand, Schuster et al. (2005) de-rived a value of 9.5 m2/g. Baumgartner et al. (2002) mea-suredαλ at 550 nm equal to 7.0±0.5 m2/g at the surface usingoptical methods to measure aerosol absorption and thermalmethods to determine EC mass. These values span a plau-sible range as enunciated in Fuller et al. (1999) and Bond etal. (2006). Fuller et al. states that for isolated carbon spheres,αλ is about 5 m2/g, while for aggregates of graphitic carbongrains,αλ is about 7 m2/g or less, and for occluded carbon,αλ is unlikely to exceed 10 m2/g, except for large, internallymixed aerosols. (Of course, the exact values of these bound-aries depend on the size distribution of the aerosol, as well as

the optical constants assumed for BC.) As mentioned above,assuming an absorption amplification factor of 1.5 (Bondet al., 2006), it can be inferred from Bond and Bergstrom(2006) that the range inαλ extends from 7.5±1.2 m2/g (un-coated) to about 11.3±1.8 m2/g. The evidence from John-son et al. (2005) suggests that the aerosols are internallymixed, yet the aerosols over the MCMA are probably notlarge enough to expectαλ>10 m2/g. Our results, along withthose of Schuster et al. and Baumgartner et al., all lie in arange of about 7–10 m2/g at 550 nm and are therefore con-sistent with the findings of Fuller et al. (1999) and Bond etal. (2006).

The difference inαλ values between the results of Schus-ter et al. (2005) and our method is not large compared to therange of values reported in the literature. However, becauseour method uses the same BC physical/optical constants andthe same volume distributions as Schuster et al., it is inter-esting to investigate why the observed difference exists. Itcannot be completely explained by the different ways of deal-ing with the internal mixture, e.g., shell/core versus MG. Us-ing an aerosol volume distribution appropriate for the GSFC,Schuster et al. found that shell/core and MG approaches aresimilar, except for lower volume fractions of BC,fV <0.2.For very smallfV (<0.05), the shell/core method gave higherspecific absorptions than MG by at least 10%. These findingsindicate that our results should be about 5–10% larger thanShuster et al.’sαλ values. However, our shell/core values aresmaller than Schuster et al.’s values.

It is possible that the short sample period of 7 days duringthe field campaign does not allow us to sample the full rangeof conditions found in Schuster et al.’s analysis. Had we beenable to perform the analysis over several years as was donein Schuster at al., our values may have become closer to theirvalues. We also must be cognizant of spatial sampling dif-ferences. The spatial sampling could be problematic becausethe distance between the MFRSR and the AERONET instru-ments is about 16 km, and the possibility that the instrumentsobserve different types of aerosols, different aerosol size dis-tributions, etc., cannot be dismissed. For example, Fig. 2shows simultaneous observations of aerosol optical thicknessat 500 nm, taken at the MFRSR and AERONET sites on 27April 2003. In the morning hours, these optical thicknessesare similar, but diverge as the day progresses. This increas-ing discrepancy can be explained by the meteorology of theMCMA (modelled by Fast and Zhong, 1998): the winds thatarise during the morning often blow the pollution towards theAERONET site, and this pollution runs into the mountainsand would tend to be recirculated over the site, thus increas-ing the optical thickness at this site over that at the MFRSRsite. Whether this increasing optical thickness is associatedwith a change in aerosol intensive properties (e.g., 0,λ)

cannot be determined without additional measurements.



4 Conclusions

Using data from the MFRSR, as well as aerosol volume dis-tributions obtained from the AERONET sun photometer, wecalculatedαλ during the MCMA-2003 field campaign, fora wavelength of 500 nm. The method described here usesinferences of the aerosol optical thickness,τλ, and aerosolsingle scattering albedo, 0,λ, obtained from the MFRSRto estimate the absorption optical thickness,τλ,abs . Oncethis quantity is estimated, all that is needed is an estimateof columnar concentration of BC,MBC. This method alsorelies on the AERONET volume distribution appropriate forthe day in question, the assumption of a shell/core model ofinternal mixing, and specific choices of BC density and re-fractive index to findMBC. For these quantities, we chosetwo sets (I and II) of values as listed in Table 2. For set I, theBC physical and optical properties are those stated in Fulleret al. (1999) under the category “Soot G”. These values werechosen so that our results could be compared with those ofSchuster et al. (2005). The second (II) comes from “bestestimates” of these quantities found in Bond and Bergstrom(2006), as listed in Table 2. When averaged over 7 clear peri-ods of the MCMA-2003 field campaign, consisting of a totalof about 10 h in the morning over the month of April 2003,the values ofαλ are 8.9 m2/g (I) or 8.2 m2/g (II) at 500 nm.The estimated level of worst case uncertainty for our methodis ±70%. This estimate assumes all errors are additive andof the same sign.

When converted to a wavelength of 550 nm using aλ−1

conversion rule, the values ofαλ are 8.1 m2/g and 7.4 m2/g,for sets I and II, respectively. For the aerosol size dis-tributions observed in the MCMA, these values lie withinthe range of likelyαλ values as demarcated by Fulleret al. (1999), Bond and Bergstrom (2006), and Bond etal. (2006).

Schuster et al. (2005) have derived anαλ value of 9.5 m2/gat 550 nm using methods similar to our method, and Baum-gartner et al. (2002) report a surface value of 7.0±0.5 m2/gat 550 nm, obtained using an entirely different technique. Allreported values, including our own, lie in a range betweenabout 7 and 10 m2/g for aerosols that are moderately aged.Refining the optically basedαλ values discussed in this pa-per will require more precise information about the refractiveindices and densities of BC, and/or a method of finding theBC load throughout the vertical extent of the atmosphere. Asnoted by Schuster et al. results such as those presented herehave not been validated by elemental carbon measurementsthroughout the atmospheric column.

It cannot be underemphasized that these results can onlybe considered as effective, “radiatively correct” results,meaning that given the assumptions discussed in Sect. 2.2,the αλ and MBC values are those required to force calcu-lated irradiances to be identical with measured irradiances at500 nm. Using a different set of assumptions would result indifferent values ofαλ andMBC, but these values would still

be consistent with the requirement that calculated and mea-sured irradiances match. It must be noted, however, that toobtain specific absorption values far outside the range speci-fied above would require rather dubious assumptions regard-ing the physical and optical properties of BC. For example,if for case 6 (αλ=8.8 m2/g), we assume that the refractiveindex is 2.1–1.2i in place of 2.0–1.0i, then to obtain a spe-cific absorption at the upper end of the expected range (about13 m2/g), the chosen density value would have to be about1.4 g/m3 (assuming no other source of uncertainties). Thisvalue, as well as the refractive index value, lie outside theranges thought plausible.

Acknowledgements. The authors are grateful to the other par-ticipants in the MCMA-2003 field campaign for their usefuldiscussions regarding this work. The authors also thank J. Hubbefor setting up the MFRSR in Mexico City and Ben deFoy of MITfor providing us the relative humidity sounding data. We wouldalso like to thank the AERONET program for the collection andanalysis of sun photometer data, which led to the aerosol volumedistributions and aerosol single scattering albedos used in thisstudy. Discussions with C. Doran and G. Schuster are also greatlyappreciated. The comments of the reviewers were also very useful.This research was sponsored in part by the U.S. Department ofEnergy’s Atmospheric Science Program (ASP) under ContractDE-AC06-76RLO 1830 at Pacific Northwest National Laboratory.The Pacific Northwest National Laboratory is operated for the U.S.Department of Energy by the Battelle Memorial Institute. TheMIT team would like to acknowledge financial support from theNational Science Foundation (Award No. ATM-0308748) and theMexico City Environmental Commission.

Edited by: U. Poschl

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Estimation of a ”radiatively correct” black carbon ...

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