Limitations in the enhancement of visible light absorption due to mixing state
Abstract
[1] Absorption by light-absorbing carbon (LAC) particles increases when the carbon is mixed with other material, and this change affects climate forcing. We investigate this increase theoretically over a realistic range of particle sizes. Perfect mixing at the molecular level often overestimates absorption. Assuming that LAC is coated by a concentric shell of weakly absorbing material, we calculate absorption by a range of realistic particle sizes and identify regimes in which absorption behaves similarly. We provide fits to amplification in five regions: (1) small cores and (2) intermediate cores, both with large shells; (3) small to intermediate cores with intermediate shells; (4) cores with growing shells; and (5) intermediate to large cores with large shells. Amplification in region 1 is highest but is physically implausible. Amplification in region 5 is constant at about 1.9 and represents an asymptote for particles with broad size distributions. Because absorption by aggregates is amplified by about 1.3 above spherical particles, and that factor is lost when particles are coated, we suggest that absorption by aged aerosol is about 1.5 times greater than that of fresh aerosol. The rate at which particles acquire sufficient coating to increase their original diameter by 60% is important in determining total absorption during their atmospheric lifetimes. Fitted amplification factors are not very sensitive to assumed refractive index of LAC and can be used even in simple models.
1. Introduction and Background
[2] Atmospheric particles, especially the submicrometer particles that have relatively long atmospheric lifetimes, have important effects on the Earth's radiative balance. Both the magnitude and sign of radiative forcing by anthropogenic aerosols depend on their relative amounts of absorption and scattering. Only a few aerosol components absorb light, with the most powerful actors being strongly absorbing carbon particles, herein called “light-absorbing carbon.” Although these particles are a small fraction of the aerosol mass, their absorptive properties and strong extinction make them important in determining aerosol effects on climate.
[3] In earlier work [Bond and Bergstrom, 2006], we reviewed measurements of light absorption by carbonaceous particles. Here, we continue using the term light-absorbing carbon (LAC) to denote the black-appearing substance known to combustion scientists as “soot” and to climate modelers as “black carbon.” We do not address light absorption by weakly absorbing organic carbon, and we focus on visible wavelengths. Bond and Bergstrom [2006] suggested that measurements of carbon particles with strong light absorption tended toward consistent values of absorption and refractive index. We summarized measurements showing that mass absorption cross section for LAC was 7.5 m2/g at 550 nm. That value is about 30% higher than calculations based on Mie theory or aggregate relationships, a phenomenon that may be explained by the interactions between the spherules that form the aggregate [Iskander et al., 1991; Fuller et al., 1999; Liu and Mishchenko, 2005]. We also acknowledged that absorption cross section would change as other substances coagulate or condense with LAC, but we deferred the investigation of that phenomenon to a later paper. That discussion is given here.
[4] Modeled absorption depends on whether the strongly absorbing substance is assumed to be externally mixed—that is, located in particles that are physically separated from other, weakly absorbing material—or internally mixed—that is, contained in the same particle as weakly absorbing material. In this paper, we use the nomenclature of Bond and Bergstrom [2006] to describe particle mixing state. The term volume mixture refers to LAC that is perfectly mixed with other material at the molecular level, and the term encapsulated implies that the LAC particle remains solid, but is covered with other material. Jacobson [2000] pointed out that encapsulated geometries are more realistic.
[5] A major goal of global radiative transfer models is estimating climate forcing, or the change in energy balance at the tropopause. Because aerosols are not well mixed throughout the atmosphere, simulations are one of the only methods of estimating their average climate effect, the other method involving interpretation of satellite measurements [e.g., Christopher et al., 2000; Bellouin et al., 2005]. Both methods require assumptions about absorption and scattering by particles. Table 1 summarizes forcing estimates from global models that examined both externally mixed LAC and either encapsulated or volume-mixed particles. The values vary for many reasons, including emission rate and aerosol lifetime [Bond and Sun, 2005], but the comparison shows that mixing assumptions are also critical: they affect forcing by factors of 1.6 to 2.9. Partly because of this uncertainty, net forcing by pollution aerosol—which includes both sulfates and carbonaceous aerosols—could be either positive or negative. Other studies [e.g., Rosen and Hansen, 1984; Riemer et al., 2003; Chandra et al., 2004] have discussed the importance of mixing assumptions on regional radiative balances.
| External Mixture | Core and Shellb | Volume Mixtureb | Citation |
|---|---|---|---|
| 0.20 | 0.36 (1.8) | Haywood et al. [1997] | |
| 0.16 | - | 0.42 (2.6) | Myhre et al. [1998] |
| 0.20 | - | 0.40 (2.0) | Penner et al. [1998] |
| 0.27 | 0.54 (2.0) | 0.78 (2.9) | Jacobson [2001b] |
| 0.51 | - | 0.80 (1.6) | Chung and Seinfeld [2002] |
| 0.33 | - | 0.60 (1.8) | Chung and Seinfeld [2005]c |
- a Units are W/m2, globally averaged.
- b Ratio is given in parentheses.
- c Values result from different emission inventory.
[6] Because assumed mixing state affects absorption and radiative forcing, atmospheric simulations need to represent how LAC particles are mixed with other substances. This is not a trivial task, requiring some method of explicitly representing aerosol size [e.g., Jacobson, 2001a; Adams and Seinfeld, 2002; Liu et al., 2005]. These simulations may track coagulation and condensation realistically, providing enough input for detailed models of absorption and scattering. However, even these models may be sensitive to input parameters, such as varying particle sizes, and their complexity may preclude sensitivity calculations. Other models cannot afford the computational time required to simulate aerosol dynamics or differing geometries, particularly when those models also include representations of ocean and land surface. Measurement of mixing state is not simple, either; it must be accomplished with single-particle methods, either in real time [e.g., Hughes et al., 2000] or by microscopy [Pósfai et al., 1999; Johnson et al., 2005].
[7] Many investigators have calculated how mixing configurations affect absorption. Some of these calculations have been limited to a few instructive particle sizes. We seek a more general approach, exploring a wide range of plausible particle sizes, as a contribution to bounding the uncertainties in forcing by LAC. This investigation will also be relevant to interpreting measurements that rely on absorption to infer LAC mass. Such measurements either collect particles on filters and measure the change in transmittance [Lin et al., 1973; Horvath, 1993a; Bond et al., 1999] or invert sky radiance to infer absorption [Dubovik and King, 2000]. Changes in absorption affect the inferred amount of absorbing material, and consequently affect model-measurement comparisons. For example, Sato et al. [2003] reported discrepancies of about a factor of two between modeled particulate absorption and that measured by Sun photometers. These discrepancies might result from underestimated emissions, but they could also be caused by incorrect assumptions about absorption-to-mass ratio. The purpose of our investigation is to answer the questions, “What amount of discrepancy between measured and modeled LAC might be caused by differences in absorption-to-mass ratio?” and “What is the likely range of absorption by LAC?” The latter question is directly relevant to calculations of direct climate forcing. Absorption is not directly proportional to positive climate forcing, but is closely related to it. If mixing increases single-scattering albedo (scattering divided by absorption plus scattering) and leaves backscatter ratio approximately constant, then absorption enhancement is an upper limit on positive forcing enhancement.
[8] In 3, we show how absorption enhancement can be produced artificially by common assumptions made in models; these should be avoided. 6 discusses shell-and-core geometries and parameterizations of absorption by mixed aerosol. 15 presents sensitivity calculations, and 16 summarizes our recommendations.
[9] We are interested in absorption by a given mass of particulate light-absorbing carbon. Throughout this document, following Schnaiter et al. [2005], we will use the term “absorption amplification” to denote the ratio of absorption by a mixed particle to absorption by a pure particle when both particles contain the same amount of light-absorbing carbon mass. For the pure material, we use a refractive index of 1.85 − 0.71i, which is in the middle of the range suggested by Bond and Bergstrom [2006].
2. Foundation
[10] Some of the results in 3 depend on understanding the nature of absorption as particle size changes. This relationship is so germane to the following discussions that we present the main relationships with the aid of Figure 1. In this paper, we will use the terms small, intermediate, and large to indicate sizes relative to the wavelength of incident radiation. The relative size is indicated by the size parameter, x = πd/λ, where d is particle diameter and λ is the wavelength of incident radiation. The size parameter x is much less than one for small particles, near one for particles of intermediate size (about 100 nm for 550-nm radiation), and much greater than one for large particles. Figure 1 demonstrates the following relationships:
[11] 1. For very small particles, mass-normalized absorption cross section is constant because the entire particle mass participates in absorbing light.
[12] 2. For larger particles, absorption cross section decreases with the inverse of the diameter because only the surface of the particle participates in absorbing light.
[13] 3. The peak in absorption at intermediate sizes results because the denominator in one of the series terms becomes small [Bohren and Huffman, 1983, section 11.5.4]. This occurs when the frequency of the forcing (incident radiation) is near a characteristic frequency of the system (governed by the size), so an engineer might think of this as resonance.
[14] Not demonstrated in Figure 1, but also important to this discussion, is the relationship between absorption and refractive index. For small particles with refractive indices typical of LAC, absorption increases with greater imaginary refractive index and decreases with greater real refractive index [Bond and Bergstrom, 2006].
3. Artificial Enhancement
3.1. Effect of Mixing Rules on Refractive Index
[15] The simplest way to represent a particle containing multiple components is to assume a single (“effective”) refractive index for the entire particle, and to use that value in Mie calculations. Many rules for such effective refractive indices have been suggested. The most common approach to calculating the refractive index in climate models is volume mixing, a separate weighting of real and imaginary refractive indices by volumetric fraction. Of the models listed in Table 1, only that of Jacobson [2001b] used core and shell absorption as opposed to volume mixing. Jacobson [2000] pointed out that the volume mixture model does not represent absorbing carbon particles that do not dissolve. We have explained elsewhere how strong light absorption by carbonaceous particles depends on the size of contiguous sp2-bonded carbon structures [Bond and Bergstrom, 2006]. Distributing the material evenly throughout the particle would disrupt the medium-range order that governs absorption. Both considerations suggest that the simple volume mixture approach is not physically reasonable.
[16] Other mixing rules are also based on volume-weighting different properties of the components [Born and Wolf, 1959; Graham, 1974; Heller, 1965; Medalia and Richards, 1972; Chýlek et al., 1981; Felske et al., 1984; Lesins et al., 2002]. These include: (1) the refractive index minus one [Gladstone and Dale, 1863]; (2) the dielectric constant ɛ = m2 (mentioned but not used by Chýlek et al. [1981], (3) the quantity (m2 − 1)/(m2 + 2), known as the Lorentz-Lorenz formula); or (4) deriving the average dielectric function from geometric considerations, resulting in the Maxwell Garnett or Bruggeman effective medium approximations. Equations for most of these relationships may be found in work by either Heller [1965] or Bohren and Huffman [1983, chapter 8]. All of them assume that the variation in molecular structure occurs on scales smaller than the wavelength of light; that is, if two substances are present in discrete packets, those packets must be smaller than the wavelength. A formula similar to the Lorentz-Lorenz equation, using only the real part of the imaginary refractive index, is discussed by Stelson [1990] and often used to interpret atmospheric data [e.g., Quinn et al., 2002].
[17] The choice of mixing model affects optical predictions greatly, not only for absorption but also for scattering and single-scattering albedo [Mackowski et al., 1990]. Felske et al. [1984] argue that the Bruggeman approximation is most applicable for void-containing soot pellets, and Lesins et al. [2002] suggest that the Maxwell Garnett approximation is appropriate for small black particles suspended in water. Figure 2 shows absorption amplification predicted by several of these mixing rules, for carbonaceous particles mixed both with air (Figure 2a) and with sulfate (m = 1.55 − 0.001i, Figure 2b). Videen et al. [1994] showed similar relationships for varying refractive index. Lesins et al. [2002] show that the choice of model used to represent the effective refractive index often affects the imaginary part of the effective refractive index more than the real part. Schuster et al. [2005] found that volume mixing resulted in a refractive index 13–30% greater than the Maxwell Garnett approximation. The choice of mixing rule affects both real and imaginary parts of the refractive index, however, so we show the change in absorption by small particles, rather than just the change in imaginary refractive index. We include mixing with air for comparison with the results of Chýlek et al. [1981] and Horvath [1993b], and our results agree with their findings: the amplification is as high as 2 when the volume fraction of carbon is small. Much of the enhancement comes from reducing the effective real refractive index of the particle. For particles mixed with sulfate-like material, the real refractive index is not as greatly altered and the absorption amplification is lower.
[18] Volumetric weighting of refractive indices results in the second-highest enhancement of all the mixing models. The Lorentz-Lorenz formula weights a quantity that is directly proportional to absorption for small particles, and results in no amplification. The Bruggeman formula predicts intermediate values compared to the other rules, limited to a maximum of about 1.5. The Maxwell Garnett rule agrees closely with the Bruggeman formula for sulfate-like material and suggests no enhancement for mixing with air voids. Simply weighting refractive indices predicts one of the highest enhancements, but it is physically incorrect.
3.2. Mie Theory and Volume Mixing
[19] Figure 2 suggests that absorption amplification predicted by volume mixing should be limited to about 1.7 for soot-sulfate mixtures of small particles. Yet Table 1 shows that some models predict changes in radiative forcing that are greater than a factor of two. This change cannot be explained by the difference between absorption and forcing, unless mixing results in a very large decrease in particle scattering, which it does not. The difference can be understood only by considering particles larger that those for which cross section is constant. To demonstrate, we followed the volume-mixing procedure to produce Figure 3. For each calculation, we assumed a volume fraction of absorbing material. We calculated volume-weighted refractive indices and performed Mie calculations with them. We then normalized the resulting absorption cross section to the volume of absorbing material, and this quantity is shown in Figure 3.
[20] Along the top of Figure 3, the volume fraction of absorbing material is unity; this is the absorption of pure light-absorbing material. Features similar to those in Figure 1 appear in Figure 3. For particles smaller than about 80 nm, the normalized absorption cross section is almost constant with diameter. For larger particles, there is a decrease in absorption with particle size. The distorted portion in the middle of Figure 3 results from the resonance peak, although its position and width change depending on the fraction of absorbing material. The arrow on Figure 3 shows how absorption per mass of LAC appears to change for a particle of given size, as the fraction of absorbing material is reduced. We will consider mixing by three particles, with diameters of 20, 200, and 500 nm.
[21] For the smallest particle (20 nm), a size selected in many global models, normalized absorption changes very little as the particle is mixed. However, this particle size is unrealistically small [Bond and Bergstrom, 2006, section 7.7]. In the future, models will probably begin using more accurate particle sizes.
[22] For the largest particle (500 nm), absorption of a pure particle is about 3 m2/g. These large particles are in the region where absorption decreases with diameter. When this particle contains only 20% absorbing material, the normalized absorption cross section increases to about 8 m2/g. Physically, the material at the pure particle's center could not participate in absorption because the outer part of the particle shields it. Spreading the material thinly throughout the particle allows more of the absorbing material to interact with light. In reality, this distribution does not occur. Any material added to an absorbing particle causes its size to increase. A trajectory through Figure 3 that represents a more physical process, moving toward the right as well as down, does not increase normalized absorption.
[23] For the medium-sized particle (250 nm), the absorption cross section of a pure particle is about 5 m2/g. The normalized cross section of this material is about 11 m2/g when the particle contains 20% absorbing material. Absorption increases partly because the mixed particle is in the resonant portion of the curve. Resonance peaks, however, result from induced currents along the particle's surface [Bohren and Huffman, 1983]. This conductivity requires mobile electrons, but perfect molecular mixing would eliminate the conjugated sp2 bonds that enable electron mobility. Thus resonance would not occur if absorbing material were spread throughout a particle, making the high values in the lower portion of Figure 3 unlikely.
[24] In summary, theoretical calculations can predict absorption enhancement for volume-mixed particles that is not physically reasonable. These predictions result largely from artifacts that disappear when they are examined closely. The approximations we examined are not physically realistic, and the results would be of little interest except for the fact that they may result from procedures that are presently applied in climate models. This finding is probably well known to those who routinely examine optics of real particles, but we hope to bring it to the attention of those who invoke these approximations to model radiative transfer in the atmosphere. We emphasize: Volume-weighted mixing approximations can, and often do, produce unjustified overestimates of absorption.
4. Core-Shell Particles
[25] Although LAC cannot be homogeneously mixed within a particle, uneven distribution of different compounds throughout a single particle is common [e.g., Liousse et al., 1993; Pósfai et al., 1999; Naoe and Okada, 2001]. Jacobson [2000] pointed out that the concentric sphere geometry is more plausible; it could be produced by organic or ionic species condensing on insoluble LAC cores. He predicted that most absorbing particles would be mixed with nonabsorbing species within a few days after emission [Jacobson, 2001b]. After nonabsorbing species have condensed, they may interact with water, causing the particles to increase in size, as modeled by Redemann et al. [2001]. We examine the range of absorption that these core shell particles could produce.
[26] Many calculations for coated, concentric spheres have been reported [Fenn and Oser, 1965; Kattawar and Hood, 1976; Ackerman and Toon, 1981; Bhandari, 1986; Mackowski et al., 1990; Fuller, 1995]. The concentric-shell-and-core model predicts an increase of absorption above the pure absorbing particle. That is, depositing a shell of nonabsorbing material around a pure LAC particle increases the absorption of the pure particle. In laboratory experiments, Schnaiter et al. [2003] observed amplification of about 1.35 for soot particles thinly coated with secondary organic aerosol. Later experiments producing thicker coatings of organic material showed a maximum amplification of 1.8–2.1 [Schnaiter et al., 2005]; these authors also calculated similar results using Mie theory combined with measured particle sizes.
[27] Computer codes to calculate absorption and scattering of these particles are freely available (see Bohren and Huffman [1983], “BHCOAT”), and we used an implementation of these algorithms in MatLab [Mätzler, 2002]. Figure 4 shows absorption amplification for a wide range of core and shell thicknesses that might be expected for atmospheric aerosol; Figure 4 represents nearly 1500 results of core-shell calculations on lognormal distributions, each with geometric standard deviation of 1.1. The results are consistent with those of Fuller [1995] and Fuller et al. [1999]. Figure 4a, a surface plot of log10(amplification), provides the following insights: (1) Amplification is always greater than or equal to one—that is, coatings always increase absorption, never decrease it; (2) enhancement by encapsulated droplets can be extremely high for small cores; and (3) for cores larger than about 150 nm, amplification is nearly constant. Figure 4b, a contour plot of amplification, shows the same data as Figure 4a, demonstrating that amplification above 5 is confined to a narrow range of conditions.
[28] Figure 4b also demonstrates some distinct regimes. These are identified in Figure 5, summarized in Table 2, and discussed in the following subsections. Table 2 provides fits to the amplification when the core and shell diameters are known. Kerker [1969] discussed some limiting cases of the core-shell calculations, but most of them do not describe atmospheric particles. The regimes shown in Figure 5 are likely related to limits in the core-shell solutions. However, we have found it simpler to use the computational results. Figures 4 and 5 presented physical particle dimensions and assumed a wavelength of 550 nm, because diameters are sometimes easier to visualize. The calculations are valid for all equivalent size parameters, so Table 2 presents relationships in that form.
| xcore | xshell | Fit | RMS Error | |
|---|---|---|---|---|
| 1 | <0.3 | >3 | 2.52 exp(0.0144 ts) | 1.3 |
| 2 | 0.3–1 | >3 | 5.69 exp(−1.1xcore) | 0.2 |
| 3 | <1 | <3 | 0.8 − 0.2 xcore + 1.7 xshell − 1.2 xcore xshell | 0.2 |
| 4 | all | <1.6 xcore | 1 + ts (0.54 xcore + 0.46) | 0.03 |
| 5 | >1 | >1.6 xcore | 1.93 | 0.05 |
- a Size parameter, x, is πd/λ. Relative shell thickness, ts, is (xshell – xcore)/xcore. See 11 for comment on fit to region 1.
4.1. Particle Sizes
[29] The discussions that follow will benefit from a summary of particle sizes commonly found in atmospheric aerosol, because our interest is in determining the ranges of possible core and shell sizes. Table 3 summarizes size distributions measured at or near combustion sources. After emission, LAC particles may grow by coagulation or condensation. Thus measurements at sources provide a lower bound on the sizes of these particles. The measurements summarized in Table 3 include sources that contribute most to global emissions of LAC [Bond et al., 2004]. In most of the studies, exhaust was diluted so that organic vapors would condense.
| Combustion Source | Fuel | Measurement | CMD, nm | MMD, nm | GSD | Citation |
|---|---|---|---|---|---|---|
| Middle-Distillate Vehicles | ||||||
| Two heavy-duty trucks | diesel | EAA | 100 | 200 | 1.6 | Hildemann et al. [1991] |
| One vehicleb,c | diesel | SMPS | 70–76 | 150–220 | 1.6–1.8 | Maricq et al. [1999] |
| Automobile, light truckb,c | diesel | SMPS | 63–82 | 130–320 | 1.6–2.0 | Maricq et al. [2001] |
| Four vehiclesb,c | three diesel, one JP8 | SMPS, MOUDI | 22–83 | 80–270 | 1.7–2.0 | Rogers et al. [2003] |
| Three vehicles, two enginesb,c | diesel | SMPS | 60–120 | 130–170 | 1.4–1.7 | Harris and Maricq [2001] |
| Four military vehiclesb,c | diesel | SMPS | 29–88 | 38–170 | 1.3–1.6 | Kelly et al. [2003] |
| Light-Distillate Vehicles | ||||||
| Catalytic vehicles | gasoline | EAA | 174 | 200 | 1.2 | Hildemann et al. [1991] |
| Noncatalytic vehicles | gasoline | EAA | 18 | 100 | 1.4 | Hildemann et al. [1991] |
| Eight trucks, 11 autos (one DI), three FTP phases eachb | gasoline | SMPS | 67 ± 17 | 250 ± 260 | 1.8 ± 0.4 | Maricq et al. [1999] |
| Three vehicles, one engineb,c | gasoline | SMPS | 20 | 40 | 1.6 | Harris and Maricq [2001] |
| One DI engineb,c | gasoline | SMPS | 50–150 | 470–1500 | 2.4 | Harris and Maricq [2001] |
| One truckb,c | gasoline | SMPS | 20–50 | 20–170 | 1.2–1.9 | Maricq et al. [2001] |
| One vehicleb,c | gasoline | SMPS, MOUDI | 18 | 25 | 1.6 | Kelly et al. [2003] |
| Three catalytic vehiclesb,c | gasoline | OPC, DMA, MOUDI | 100 | 150 | 1.5 | Kleeman et al. [2000] |
| Small Solid Fuel Combustors | ||||||
| Fireplaceb,d | wood (pine, oak, eucalyptus) | MOUDI | 70–110 | 150–200 | 1.5–1.7 | Kleeman et al. [1999] |
| Fireplace, steady stateb,d | wood (pine, oak) | EAA | 19–30 | 100 | 1.8–2.1 | Hildemann et al. [1991] |
| Cooking stovesc | acacia wood | MOUDI | 120–600 | 470–780 | 1.3–2.0 | Venkataraman and Rao [2001] |
| Cooking stovesc | dried cattle manure | MOUDI | 270–600 | 600–780 | 1.3–1.7 | Venkataraman and Rao [2001] |
| Heating and cooking stovesc,e | coal briquettes | DMPS | 5 | 2.6 | Bond et al. [2002] | |
| Heating and cooking stovesc,e | bituminous coal | DMPS | 25 | 3.0 | Bond et al. [2002] | |
| Heating and cooking stovesc,e | lignite | DMPS | 81 | 2.2 | Bond et al. [2002] | |
| Cooking stovesd | wood, two burn rates | MOUDI | 60–550 | 420–1050 | 1.6–2.2 | Habib (2006)f |
| Crop waste, three typesd | wood, two burn rates | 50–1000 | 440–1300 | 1.3–2.4 | crop waste, three types | Habib (2006)f |
| Dried cattle manured | wood, two burn rates | 250 | 860 | 1.9 | dried cattle manure | Habib (2006)f |
| Large Stationary Sources | ||||||
| Industrial boiler | fuel oil | EAA | 20 | 50 | 1.7 | Hildemannet al. [1999] |
| Small industrial boilerc,g | lignite, Aitken | TDMA | 48–53 | 74–79 | 1.4–1.5 | Wehner et al. [1999] |
| Small industrial boilerc,g | lignite, accum | TDMA | 280–400 | 540–780 | 1.6 | Wehner et al. [1999] |
| Firetube boilerb,d,h | residual oil | SMPS | 20–25 | 70 | 1.4–1.5 | Miller et al. [1998] |
| GE fuel evaluation facilityc,i | coal | SMPS | 40–71 | 60–140 | 1.5–1.7 | Chang et al. [2004] |
| GE fuel evaluation facilityc,i | fuel oil | SMPS | 80–100 | 120–150 | 1.4 | Chang et al. [2004] |
| Small industrial boilerc,g | natural gas, Aitken | TDMA | 40–59 | 113–166 | 1.8 | Bond et al. [2006] |
| Same study | accumulation mode | TDMA | 200 | 380–480 | 1.6–1.7 | Same as above |
| Small industrial boiler | fuel oil, Aitken | TDMA | 35–60 | 70–170 | 1.4–1.6 | Bond et al. [2006] |
| Same study | accumulation | TDMA | 89–200 | 120–390 | 1.4–1.6 | Same as above |
- a CMD is count median diameter, MMD is mass median diameter, and GSD is geometric standard deviation. Abbreviations: DI, direct injection; DMPS, differential mobility particle sizer; EAA, electrical aerosol analyzer; FTP, federal testing protocol; MOUDI, micro-orifice uniform deposition impactor; OPC, optical particle counter; SMPS, scanning mobility particle sizer.
- b GSD is calculated from graph.
- c MMD is calculated using equation in text.
- d CMD is calculated using equation in text.
- e GSD is given for averaged distribution, so no MMD was calculated.
- f G. Habib et al. (unpublished data, 2006).
- g Ultrafine mode around 6 nm was also observed.
- h Supermicron particles were also observed, thought to be mineral matter.
- i Value depends on sampling dilution ratio.
[32] CMD of particles emitted from diesel vehicles ranged from 22 to 120 nm. Gasoline engines emit particles of similar size, 18–150 nm in diameter. Several modes can be emitted simultaneously from industrial boilers burning gaseous and liquid fuels. The CMD of the smallest modes is 5–10 nm. A slightly larger (Aitken) mode appears at 50 nm, and accumulation mode particles are 60–200 nm. Particles from coal boilers may be even larger, up to 400 nm. In contrast to vehicular and industrial boilers, biofuel combustion in cooking stoves may emit somewhat larger particles with CMD ranging from 240–1040 nm. Small particles come from some woody cooking fuels at low burn rates and from fireplace combustion. We note that the larger particles have been measured with cascade impactors rather than electrical mobility. Overall, emitted particles are found at small and intermediate sizes, with a few sources producing larger particles. Size distributions in freshly emitted biomass smoke plumes are of intermediate size, with CMD between 120 and 150 nm. Smaller particles are emitted from flaming biomass combustion [Reid et al., 1998].
[33] In the atmosphere, particles increase in size as they coagulate and as material condenses on them. Table 4 tabulates size information on fine particles (diameters less than 1 μm) measured in some major field campaigns. Measurements near highways show CMD ranging between 14 and 100 nm, indicating that particles do not grow immediately after emission. Very small particles with diameters 10–20 nm appear to be lost rapidly after emission [Kittelson et al., 2004]. Particles from biomass combustion, measured in aged plumes, do show growth due to condensation and coagulation, with CMD increasing to 110 to 210 nm [Reid et al., 1998].
| Experiment | Comments | Measurement | CMD | MMD, nm | GSD, nm | Reference |
|---|---|---|---|---|---|---|
| Very Near Source | ||||||
| Minnesota, USA highwaysa,b | 32–80 km/h; dominated by diesel vehicles | SMPS (8–300 nm) | 14–25 | 24 | 1.5 | Kittelson et al. [2004] |
| Highway tunnela,b | Nucleation mode | SMPS | 12–18 | 19–38 | 1.5–1.6 | Abu-Allanban et al. [2004] |
| Same study | Accumulation mode | SMPS | 87–100 | Same as above | ||
| Brazila,b | Biomass burning | DMPS, PCASP | 90–150 | 282–380 | 1.6–1.9 | Reid et al. [1998]; Martins et al. [1998] |
| Continental Plumes | ||||||
| Indian Ocean (INDOEX)c | Cascade impactor | 450–500 | 490–560 | 1.1–1.3 | Chowdhury et al. [2001] | |
| Western Pacific (ACE-Asia)c | Air mass from Korea and Japan | Cascade Impactor | 190–360 | 400–450 | 1.4–1.7 | Quinn et al. [2004] |
| Eastern Atlantic (ACE-2) | Polluted boundary layer | DMA, PCASP, FSSP | 170 | Collins et al. [2000] | ||
| Eastern Atlantic (ACE-2) | Polluted free troposphere | DMA, PCASP, FSSP | 91 | Collins et al. [2000] | ||
| Western Atlantic (NEAQS 2002)a,b | DMPS | 75–100 | 164–185 | 1.6–1.7 | NOAA-PMELd | |
| Brazila,b | Dominated by biomass burning | DMPS, PCASP | 110–180 | 320–480 | 1.6–1.8 | Reid et al. [1998] |
- a GSD is calculated from graph.
- b MMD is calculated using equation.
- c CMD is calculated using equation.
- d National Oceanic and Atmospheric Administration, Pacific Marine Environmental Laboratories (data available at http://saga.pmel.noaa.gov/data/).
[34] For measurements far from sources, we have tabulated only experiments that measured continental plumes. Particles in these locations are older, and therefore have grown more, than particles in urban areas. Our interest is in determining the boundaries of core and shell sizes that are most likely to exist in the atmosphere, and the continental plume aerosol is closer to an upper size limit. The field campaigns summarized in Table 4 show intermediate and large particles. CMD ranges from 190 to 360 nm for regions near Japan and Korea, which are thought to be dominated by fossil fuel emissions [Quinn et al., 2004]. These large particles were not observed near source regions, suggesting that they had grown since emission. CMD of polluted plumes in the Atlantic Ocean, containing outflow from both North America and Europe, was about 80–200 nm. Particles measured in the plume from the Indian subcontinent were larger (CMD 450 to 500 nm; GSD 1.1–1.3) than those in the east Asia region. These large particles might be attributed to the dominance of biofuel combustion in Indian region, but we cannot confirm this without detailed modeling of particle emission and dynamics.
4.2. Region 1: Small Cores (xcore < 0.3) and Large Shells (xshell > 3)
[35] Region 1, with xcore below 0.3, is the only one in which extremely high enhancement occurs. The amplification requires nonlinear fits, and the relationships are complex: even an exponential fit can differ from the model results by up to 40%. If small-particle absorption increases like those in region 3 are physically realistic, then absorption by LAC might be almost unlimited, and its value would be quite sensitive to the exact sizes of cores and shells.
[36] This region might contribute little to absorption for several reasons. First, amplification greater than 10 requires a core diameter no larger than 10 nm and a shell diameter over 1000 nm. Even if atmospheric LAC did exist as 10-nm particles, the volume of nonabsorbing material in the atmosphere would have to be 106 times greater than the volume of absorbing material. There simply isn't enough organic or ionic material available to coat all available tiny LAC particles. These small particles could be located in cloud droplets, although they still might not achieve the absorption shown in Figure 4; 11 discusses this possibility.
[37] Second, very little mass is present at sizes below 50 nm. Even if the count mean diameter of a lognormal distribution is around 50 nm and the geometric standard deviation is 1.5, as Table 3 suggests it might be, about 12% of the particle mass lies below 50 nm and less than 0.03% of the mass has diameters smaller than 20 nm. Because absorption is proportional to mass for small particles, particles smaller than 20 nm could increase absorption by only about 5% of the total absorption (0.05% times amplification of 100).
[38] Third, very small particles are lost by coagulation within a few meters of the source [Zhu et al., 2002; Kittelson et al., 2004], so these particles do not have long atmospheric lifetimes. These very small particles are thought to be volatile, and not LAC [Sakurai et al., 2003]. We suggest that the contribution of this range is insignificant, despite its dramatic appearance in Figure 4a.
4.3. Regions 2 and 5: Large Shells (xshell > 3) and Intermediate Cores (xcore > 0.3)
[39] Absorption amplification by cores with larger shells (regions marked “2” and “5” in Figure 5) depend strongly on core diameter and very little on shell diameter. Region 2 contains intermediate cores, with xcore between 0.3 and 1; these cores can have the highest amplification after those in region 1. An exponential decay curve in xcore fits the modeled amplification within 10%, as shown in Table 2. Region 5 contains large shells and larger cores (xcore > 1), and amplification is constant within 2% over a wide range of cores and shells. These two regions represent the maximum amplification after condensable material is very thickly deposited onto an LAC core. As shown in Table 2, amplification depends on core size alone after xshell becomes greater than 3. Laboratory experiments by Schnaiter et al. [2005] confirm that amplification does not appear to increase beyond a value of about 2.
[40] Unlike the case of small cores and large shells discussed earlier, some of the combinations in region 2 are plausible. Shells considered large for these purposes are about 500 nm for 550-nm radiation, near the mass median diameters observed in the Indian Ocean. For the smallest shells and largest cores, the shell volume would be about 8 times greater than the core, and this ratio is observed in ambient aerosol.
[41] Calculations for Figures 4 and 5 assumed narrow size distributions to illustrate the effects of particle size; real atmospheric distributions are usually broader. Again, core size and not shell size governs amplification in these regions, so the precise amount of absorption depends on the fraction of core mass at each size. Figure 6 shows calculations of amplification for three different geometric standard deviations. As the distributions become broader, larger particles form a greater part of the mass, and the overall amplification approaches the asymptote of about 1.9. Table 3 shows that GSD around 1.6–1.8 is most commonly observed at sources.
4.4. Region 4: Shells on New Particles (xshell < 1.6 xcore)
[42] The next region of interest is marked “4” in Figure 5, and covers all the core sizes modeled. This region corresponds to shells growing by condensation. Figure 7 expands the portion of Figure 4b that contains this region, but this time amplification is shown as a function of increased particle diameter. Amplification is not quite linear in fractional diameter increase; it also has a slight dependence on particle size. Nevertheless, Figure 7 shows that absorption increases immediately after substances condense on LAC cores, and continues to increase with additional shell growth. It reaches 20% when the particle's diameter has grown by 20%, corresponding to a volume increase of about 70%. As shown in Table 2, this relationship can be modeled quite well by a simple function that combines the core size parameter, xcore, with the relative shell thickness ts, defined as (xshell − xcore)/xcore.
4.5. Region 3: Growing Shells (xshell < 1, xcore < 3)
[43] Region 3 in Figure 5 encompasses the remainder of the particles. In this region, amplification increases with thickening shells, and also depends on core diameter. A relationship involving both shell and core sizes is needed to represent amplification in this region. Amplifications reach as high as a factor of 5, but again the highest amplification is associated with smaller particles and has little effect on total absorption. However, particles in this region could possibly have enhancements as high as 3.
4.6. Concentricity
[44] Thus far, we have assumed that the absorbing core is concentric within the less-absorbing shell. This may not always be true. Small carbon particles are not constrained to concentric locations at the center of a particle. Thermodynamic considerations may favor locations near the surface; that scenario is quite plausible for particles that are originally hydrophobic. LAC particles that have coagulated with inorganic particles are not expected to have concentric geometry, either.
[45] Fuller [1995] and Fuller et al. [1999] investigated the optics of a small carbon inclusion in various locations in sulfate and water droplets, and averaged absorption over several locations and orientations. They found that for particles with very small inclusions, absorption is greatest when the inclusion is exactly at the center, and is strongly reduced when the inclusion moves away from the center. These findings provide another argument against high absorption by particles in region 2 (Figure 5). Even if there were enough cloud water to form shells around all 20-nm LAC, the large amplifications depicted in Figure 4 would occur only if the inclusion remained exactly at the center. Furthermore, large absorption localized in the droplet's center would result in internal convective currents that would displace the inclusion. Videen and Chýlek [1998] showed that location-averaged absorption matched either Bruggeman or Maxwell Garnett effective medium approximations, as long as cores were much smaller than shells. The sizes they investigated correspond most closely to region 1, and we suggest using the effective medium approach for that region, rather than the fits given in Table 2.
[46] For larger inclusions, Fuller et al. [1999] calculated lower absorption amplification, which we confirm. They also reported that the concentric sphere model approximates absorption no matter what the inclusion's location. Thus the concentric sphere model may represent absorption poorly for those arrangements that we find implausible on physical grounds, but it is reasonable for configurations that are more like atmospheric particles.
[47] We have explored only the core-shell configuration in this work. Other calculations have examined mixing between aggregates and nonabsorbing material [Fuller et al., 1999; Mishchenko et al., 2004], but only with a limited number of configurations. A wider range of cases should be examined with these more accurate models, to determine whether the core-shell approximation predicts amplification with sufficient accuracy.
4.7. Absorption by Large Particles
[48] Figure 1 shows that absorption by LAC is lower for particle diameters greater than about 300 nm. Bond and Bergstrom [2006] argued that fresh LAC has a constant absorption cross section because its form is aggregate, not spherical. After they are wetted, particles may collapse [e.g., Hallett et al., 1989; Colbeck et al., 1990] and the spherical assumption may be more appropriate for such particles. In a distribution of spherical particles with CMD of 100 nm and GSD of 1.5, only about 7% of the mass is found in particles with diameters greater than 300 nm. In a larger and broader distribution, say CMD = 200 nm and GSD = 1.8, 85% of the mass appears to be in such large particles, which should decrease absorption far below the fresh aerosol value.
[49] As we mentioned, mobility-based measurements overestimate the mass of large particles [Lall and Friedlander, 2006]. Thus the apparent fraction of mass in large particles is greater when it is assumed that the particles are spherical. We investigated this issue for an apparent (measured) size distribution with CMD = 200 nm, GSD = 1.8. Using the relationships summarized by Lall and Friedlander [2006], we inferred a distribution of aggregates from this apparent size distribution, assuming primary spherules 30 nm in diameter. A 300-nm sphere with void fraction of 0.26, the close-packing ratio for spheres, would contain about 200 primary spherules. Only 5% of the particle mass in our corrected distribution would end up in larger particles. We do not discount the idea that the presence of LAC in larger particles could reduce overall absorption, but the effect is far less than indicated by mobility-measured distributions. This correction affects larger particles more than smaller particles, and does not alter our statements about particle mass below 50 nm in 7.
4.8. Likely Absorption and Forcing
[50] In summary, absorption amplification due to coating with nonabsorbing material appears to approach a constant value of about 1.9 for the refractive indices we used. It depends strongly on inclusion size for values of xcore below 1. It may be somewhat higher than 1.9 if the entire distribution of cores is small. Small cores reach a maximum value of amplification that is independent of shell size. For larger inclusions or cores, enhancement depends on shell thickness until the particle has increased its volume by about six times. After that, no further increase occurs.
[51] In a previous paper [Bond and Bergstrom, 2006], we suggested that absorption enhancement would be about 50%. That value was based on the calculations presented here. We also cited work showing that interactions between small spherules in an aggregate leads to absorption 30% greater than that calculated using Mie theory. Fuller et al. [1999] showed that when these aggregates are encapsulated with less-absorbing material, the enhancement due to interaction disappears. Maximum enhancement is then about 1.9 (for thickly coated particles) divided by 1.3 (for uncoated aggregates), where the values 1.9 and 1.3 are both relative to Mie calculations. The ratio between the two is about 1.5.
[52] The range of absorption we expect in the atmosphere, then, lies between 7.5 m2/g for freshly emitted aerosol [Bond and Bergstrom, 2006] and 1.5 times that value for aged, coated aerosol from the work presented here (11.3 m2/g). This agrees well with the range estimated by Schuster et al. [2005] from Aerosol Robotic Network data (7.7–12.5 m2/g). Atmospheric measurements can result in a much wider range of mass-normalized absorption cross sections, varying from 5 to 25 m2/g [Liousse et al., 1993; Martins et al., 1998; Carrico et al., 2003; Quinn et al., 2004]. Some of the high values may be caused by errors in measuring elemental carbon. Quinn et al. [2004] show a strong mode around 12 m2/g, and we attribute this finding to aerosol mixing state.
[53] Increased absorption does not necessarily result in increased positive forcing, because the effects of scattering also play a role. Larger particles scatter more light, so coating an absorbing sphere with nonabsorbing material increases both scattering and absorption. Schnaiter et al. [2003] found that coating spheres resulted in a greater increase in scattering than in absorption; single-scattering albedo increased and radiative forcing would become more negative. A rigorous estimate of radiative forcing would also account for scattering by nonabsorbing material that condensed in the absence of LAC cores. If LAC cores were not present, would this material condense or coagulate with nonabsorbing particles of size similar to the LAC, so that the total scattering would be comparable? Or does the presence of LAC change the size distribution and hence the scattering in a fundamental manner, as indicated by the fact that aerosol in polluted regions is associated with both lower single-scattering albedo and smaller particle sizes?
[54] Such questions can only be answered with detailed models of aerosol dynamics. The model of Jacobson [2001a] did include aerosol dynamics for size-distributed aerosol, and predicted an increase in positive forcing by a factor of two when core-shell geometry was used instead of externally mixed aerosol. This model did not account for the interactional enhancement within aggregates (about 30%), and the factor of two increase in forcing is consistent with the amplification discussed here. In that model, changes in scattering behavior did not appear to reduce positive forcing.
5. Uncertainties in Refractive Index
[55] In earlier work [Bond and Bergstrom, 2006], we constrained the refractive index of LAC to a range in which real and imaginary refractive index covaried. We acknowledged that we did not know exactly where the refractive index lay, but we suggested that its exact location did not affect predicted absorption by fresh particles. The same statement may not be true for absorption amplification; different refractive indices may result in differences in predicted amplification. If so, it may become critical to identify the refractive index exactly.
[56] To examine this possibility, we repeated the calculations in Figure 4 with three different refractive indices, applied the same fits found in Table 2, and calculated the errors in predicted amplification. The three refractive indices we chose are commonly found in the literature, even though we have questioned whether they represent atmospheric LAC. Table 5 shows the results. The fits overestimate amplification when real refractive index is lower than our base case, and underestimate it for higher real refractive indices. Even so, amplification is predicted within 0.1 or about 5% for growing particles (region 4) and large particles with constant amplification (region 5). The worst prediction errors are in region 1, which we do not find physically plausible anyway. For the remaining regions (2 and 3), absolute prediction errors are larger than in regions 4 and 5, but on average they are within 15% of the prediction. Thus the relations in Table 2 predict amplification within about 15% for the most plausible refractive indices.
| Refractive Index | Base Case 1.85 + 0.71i | Low m 1.55 + 0.55i | High m 2.0 + 1i | Less Absorbing 1.96 + 0.66i | |||||
|---|---|---|---|---|---|---|---|---|---|
| Description | Region | Bias | MSE | Bias | MSE | Bias | MSE | Bias | MSE |
| Small particles, large shells | 1 | −0.2 | 1.3 | 0.6 | 1.1 | −0.1 | 1.2 | −1.3 | 3 |
| Intermediate particles, large shells | 2 | 0.06 | 0.2 | 0.5 | 0.3 | −0.2 | 0.2 | −0.1 | 0.2 |
| Small particles, intermediate shells | 3 | −0.01 | 0.2 | 0.4 | 0.2 | −0.3 | 0.3 | −0.1 | 0.2 |
| Growing particles | 4 | 0.005 | 0.03 | 0.1 | 0.07 | −0.05 | 0.04 | −0.01 | 0.03 |
| Large particles, large shells | 5 | 0.008 | 0.05 | 0.1 | 0.1 | −0.1 | 0.06 | −0.005 | 0.04 |
- a Positive bias means that the fit is greater than calculated absorption.
6. Summary and Recommendations
[57] For at least 25 years, it has been known that submicrometer light-absorbing aerosols absorb more light when they are mixed with nonabsorbing material, and that this increase affects total climate forcing. We have investigated these increases in absorption theoretically over the range of absorbing particle sizes expected in the atmosphere. Absorption is always increased when mixing occurs, and models that ignore such mixing underestimate positive forcing by LAC. However, perfect mixing at the molecular level often overestimates absorption.
[58] Using a core-shell model, we demonstrated that amplification is slightly sensitive to chosen particle size. Although we calculate high amplifications (up to 4) for particles with size parameter (x = πd/λ) less than one, and very high amplifications for particles with x less than 0.3, these particles contribute a small fraction of mass. We suggest that absorption by aged aerosol is about 1.5 times greater than that of fresh aerosol. We provided amplification factors on the basis of core and shell size, which are not very sensitive to assumed refractive index of LAC. Total absorption during a particle's atmospheric lifetime is sensitive to the rate of mixing with nonabsorbing material.
6.1. Modeling Recommendations
[59] Although climate modelers have recognized that absorption is altered if absorbing and weakly absorbing material are mixed in the same particle, some models continue to calculate forcing without considering mixing. This practice should change. Measurements usually suggest that mixing does occur; as a consequence, external mixing models underestimate absorption and positive forcing. Volume-mixing approximations for refractive index should be avoided. They are unrealistic, they lead to unphysical results, and they overestimate absorption.
[60] Even very simple aerosol models may improve their representations of optics by assuming that absorption increases linearly as nonabsorbing aerosol condenses, and reaches a maximum of 1.5 times greater than its original value when particle volume has increased by a factor of about six. An alternative might involve taking advantage of existing model features. Models often carry two species of LAC, one to represent hydrophobic, freshly emitted aerosol, and the other representing aged, hydrophobic LAC that can be removed by wet scavenging. Perhaps this aging transformation is related to coating; models could apply the optical properties of fresh LAC to the hydrophobic tracer, and those of fully coated LAC to the hydrophilic tracer. We do not suggest that this is a highly accurate representation of absorption, but it would improve on existing assumptions.
6.2. Measurement Confirmation
[61] It is difficult to measure the exact mixing state of particles, meaning the quantity of absorbing and nonabsorbing material in each particle and the location of the absorbing material within the particle. Fortunately, only a few variables appear important in determining absorption. The critical assumptions and limitations identified here should be confirmed with measurements. This are:
[62] 1. For thickly coated particles, absorption is increased by about 90% above that of spherical particles, or 50% above aggregates.
[63] 2. Very little LAC mass is present below 50 nm.
[64] 3. The increase may be higher than 90% (for 550-nm light) when inclusion diameters are lower than 150 nm. The enhancement is a strong function of core size. If this region proves to be important, efforts should be made to identify the absorption and size of cores at these sizes, and to confirm that the absorption amplification may be greater than 2.
[65] Figure 5 shows that consistent relationships between absorption amplification and shell thickness may not exist, depending on the size of cores and shells. It is unwise to rely on correlations between absorption cross section and non-LAC mass to determine whether coated spheres are present.
[66] The average absorption of particles during their lifetimes is of interest; this value strongly affects the amount of warming that might be avoided by reducing emissions of these particles. Because mixing so strongly affects absorption, it is critical to determine how quickly mixing occurs. Both measurements and aerosol simulations on urban to regional scales should be applied to this problem.
Acknowledgments
[67] This work was funded by the National Aeronautics and Space Administration's Earth Observing System under grant NNG04GL91G. We thank NOAA's Pacific Marine Environmental Laboratories for access to size distribution data from recent field studies.
