[21] We seek to more carefully explore the implications of the coagulation of EC onto dust particles on shortwave absorption. Our observations are limited by large uncertainties (Figure 4), which leads us to turn to model simulations. We stress that our main intention is to address relative changes in absorption and scattering caused by the coagulation of dust and soot, rather than absolute numbers of, for example, dust singlescattering albedo, which is the subject of much current research [e.g., Kaufman et al., 2001].
4.1. DDA Model Calculations
[22] Mie theory is often used to calculate scattering and absorption by atmospheric aerosols. It is, however, generally applicable to spherical, homogeneous particles, although extensions of Mie theory exist for other idealized particles such as those composed of spherically symmetric shells. Dust particles, on the other hand, are known to be very different from spheres. Electron micrograph images of dust particles from various regions of the world, including dust from China, show this clearly. Gao and Anderson [2001] analyzed such images for a parameter they termed “circularity” which is the ratio of the square of the perimeter to 4π times the twodimensional area of the image. Using this measure, a spherical particle would have a circularity of 1.0, with other shapes exhibiting higher circularities (e.g., a square has a circularity of 1.27). For a location in China dominated by aeolian dust (Mt. Waliguan), almost all particles were found to exhibit circularities larger than 1. The distribution is broad, with a mean circularity of about 2. To further complicate matters, soot has a refractive index very different from that of common minerals, and therefore this heterogeneity in optical properties further rules out the use of Mie theory calculations for our purposes here.
[23] The discrete dipole approximation (DDA) technique was used for simulating the radiative properties of dust and soot aerosols [Draine and Flatau, 1994; Purcell and Pennypacker, 1973], using the publicly available software DDSCAT (B. T. Draine and P. J. Flatau, User guide for the Discrete Dipole Approximation Code DDSCAT (Version 5a10), unpublished manuscript, 2000) (available at http://arxiv.org/abs/astroph/0008151v4). Briefly, this model approximates the particle as an array of discrete polarizable points on a cubic lattice. Scattering and absorption crosssections from nonspherical particles and particles with nonhomogeneous compositions are then calculated (see B. T. Draine and P. J. Flatau (unpublished manuscript, 2000) for more details).
[24] Using this model, the absorption and scattering for a population consisting of a number of soot particles and one dust particle, all separate (i.e., an external mixture), is calculated and compared with the case where all the particles in the above population have coagulated such that all the soot particles are deposited on the surface of the dust particles. The dust particles are modeled using three idealized shapes (as shown in Figure 7): a cube (geometry A); a nearly square rod (geometry B); and a flat square (geometry C). Such regular shapes do not exactly model real dust particles, but in examining images of dust particles from the east Asian region, they do seem to reasonably span the range of particle shapes. For the purposes of coagulation with the dust, soot was modeled using two idealized geometries (Figure 7), one a packed matrix, and a second an Xshaped particle, which is intended to be a more physically realistic picture of what a soot agglomerate might look like in the atmosphere, with a larger fractal dimension than the packed matrix.
[25] The light scattering and absorption were modeled to examine the difference between (a) an external mixture of multiple soot particles and a single dust particle, and (b) a particle where the soot particles are all attached to the surface of the dust particle. First, the light scattering from the dust along for geometries A, B, and C were calculated. For all cases, the dust had an effective diameter (defined as the diameter of the equivalentvolume sphere) of 1.12 μm, and the wavelength of light was 550 nm. The grid spacing was 0.03 μm, and therefore each dust particle was composed of 27,000 dipoles. Each soot particle was represented as 9 dipoles, leading to an effective particle diameter of 0.078 μm. The 0.03 μm dipole spacing leads to a primary soot particle diameter in geometry E of 0.037 μm, a reasonable value. To calculate C_{ext} and C_{abs} for each modeled particle, between 300 and 1000 orientations of the particle with respect to the incident radiation are averaged. Performing such orientation averaging is important for understanding the average optical behavior of particles in the atmosphere. Two values of the refractive index m = n + ik were used (a) one representative of a mineral which is somewhat absorbing (e.g., hematite), m = 1.6 + 0.007i, and (b) a mineral with the same real refractive index but exhibiting almost no absorption, m = 1.6 + 10^{−5}i. The observations suggest that the dust observed at Gosan was slightly absorbing (section 3.2), although not very conclusively. We believe that these two cases represent bounding values of refractive index, and that the observed cases lie somewhere in between. EC was assigned a refractive index of m = 1.96 + 0.66i. All refractive indices are from Seinfeld and Pandis [1998]. Using these parameters, the scattering and absorption cross sections C_{scat} and C_{abs} were modeled, from which the specific mass absorption efficiency can be calculated using equation (1).
[26] To establish the optical properties of externally mixed dust and soot, C_{scat} and C_{abs} were modeled for both pure dust particles and pure soot aerosol. To verify the lowresolution sootonly calculations, additional runs were performed for geometries where the soot particle is represented as a single sphere (550 dipoles), and one where it is a chain of three spheres joined in a straight line (4224 dipoles). A comparison of the scattering and absorption cross sections for all of the soot geometries are in very reasonable agreement, implying that the results are not very sensitive to the choice of geometry, nor the number of dipoles used. Next, 22 soot particles were randomly deposited on the surface of each dust geometry. This was the number necessary to lead to a EC mass fraction of 0.4%, as derived from the coarse particle phase measurements at Gosan during the Kosa episodes. Soot geometry D was used for all three dust geometries, and soot geometry E was used with dust A to determine whether or not the results are sensitive to the soot geometry.
4.2. DDA Model Results
[27] Figure 8 shows the results for the dust particles only (no soot added) for both the absorbing and nonabsorbing dust cases. The differences in scattering and absorption are strictly a result of the different dust geometries A, B, and C that were used. The model calculations predict that large differences in scattering (greater than a factor of 3 between geometries A and B), can result simply from changing the dust geometry. These results qualitatively agree with one recent study that found significant differences in extinction coefficient as a function dust geometry [Kalashnikova and Sokolik, 2002]. Note, however, that the amount of absorption that occurs is a much weaker function of geometry for the absorbing dust (at most a 20% difference among the three geometries). This leads to a wide range in dustonly singlescattering albedo ω (where ω = C_{scat}/C_{ext}) between 0.876 and 0.962, as seen in Figure 8. For the nonabsorbing dust, the model predictions show a very similar pattern in scattering efficiencies, but of course the singlescattering albedo remains nearly unity (not shown) because of the very small value of k.
[28] When soot is added to the dust particles, the model calculations yield results shown in Figure 9. Relative to pure dust, absorption increases by adding soot, as expected. At the same time, dust particle extinction changes very slightly because of the addition of the soot particles. For geometry A, extinction actually decreases by about 2%, a result of scattering decreasing by an amount slightly greater than the increase in absorption. For geometries B and C, extinction increases and decreases, respectively, but by less than 0.5%. The values of ω therefore decrease (because the change in absorption is the strongest effect) as shown in Figure 9. For the absorbing dust case, the new range of ω is 0.846 to 0.948, a decrease of between 2 and 3%, while the nonabsorbing dust shows a decrease in ω from unity to between 0.961 and 0.985. These predictions of singlescattering albedo could be important for understanding the optical properties of aeolian dust in this region, which may have important implications for remote sensing measurements in addition to radiative forcing.
[29] For the purposes of understanding the radiative forcing by aerosols, the overall population singlescattering albedo (as opposed to that for only the dust particles) is the relevant parameter. By assuming that the EC particles were purely composed of EC and therefore externally mixed prior to coagulation, the amount of absorption for the entire population can be predicted, and then compared to that for the case where all these particles are coagulated into one larger particle; that is, we compare the absorption cross section due to unpolluted dust separate from 22 soot particles (our base case), with that when dust and 22 soot particles are coagulated together as one composite particle. The change in absorption is shown in Table 1 for the nonabsorbing dust geometries. The results show that coagulation leads to an enhancement in the absorption crosssection, and therefore in the total amount of absorbed energy by a factor of between 18% and 58%. Extinction again remains very nearly constant, in all cases changing by less than 2%. This translates directly into a 18 to 58% increase in the specific mass absorption efficiency. The net effect of coagulating externally mixed EC with nonabsorbing dust, therefore, is an increase in absorption (and therefore in α_{a}), a slight decrease in scattering, and leading to a small net decrease in extinction, which leads to a net positive radiative forcing both at the top of atmosphere, and at the Earth's surface. For the absorbing dust cases, however, the results (Table 1) are somewhat different. Very little change in absorption occurs, as the absorption cross section of the soot is much smaller than that for the dust itself, and therefore very little net change occurs due to the coagulation of soot and dust.
Table 1. Model Predictions of the Change in Total Shortwave Absorption as a Function of Initial Soot Mixing State, Dust Refractive Index, and Dust Geometry^{a}Calculation Parameters  Change in Total Absorption Due to Coagulation 

Soot Initial Mixing State  Dust Refractive Index  Dust A/Soot D Geometry  Dust B/Soot D Geometry  Dust C/Soot D Geometry 


External  absorbing  +2%  +8%  −2% 
External  nonabsorbing  +31%  +58%  +18% 
Internal  absorbing  −14%  −10%  −17% 
Internal  nonabsorbing  −35%  −23%  −42% 
[30] To show that these results are not specific to the size of dust particle chosen, a number of model runs were made with different sizes of nonabsorbing dust using geometry A. Table 2 shows the enhancement in absorption as a function of size. While not constant, this enhancement lies between +15% and +37% across the size range considered, which therefore shows that the results are not peculiar to the dust particle size chosen.
Table 2. Model Predictions of the Change in Mass Specific Absorption Efficiency of EC Due to Coagulation as a Function of Initial Dust Size, Assuming That EC is Initially Externally Mixed and the Dust is Nonabsorbing^{a}Particle Diameter, μm  Change 


0.4  +26% 
0.5  +21% 
0.6  +15% 
0.8  +37% 
1.1  +30% 
[31] Because these enhancement factors assume that the soot is initially externally mixed, the results likely represent the upper bound in the change in absorption due to coagulation. If the soot was initially internally mixed, the initial specific mass absorption efficiency would have been greater as discussed above, and coagulation would therefore lead to a smaller change in absorption enhancement, and possibly even to a decrease in overall energy absorption. To examine this question, the absorption efficiency of soot was increased by a factor of 2 to reflect EC that is initially internally mixed after which the model calculations were reanalyzed. This doubling in absorption efficiency was estimated on the basis of the fact that externally mixed soot has been predicted to have values of α_{a} in the range between 4 and 8 m^{2}/g, whereas the PM1 values observed here (Figure 5) are somewhat greater, mostly in the range between 10 and 16 m^{2}/g. By increasing α_{a} for soot aerosol only, then, the model calculations show a different story (Table 1). For the absorbing dust, coagulation leads to a change in overall aerosol absorption by −10 to −17% whereas before almost no change was seen. For nonabsorbing dust, coagulation is predicted to cause an even larger change in absorption, between −23 and −42%, whereas previously absorption was predicted to change by +18 to +58%. This comparison is not perfect because the model calculations for composite soot plus dust particles were not redone to reflect additional nonabsorptive material internally mixed with EC. However, this is not expected to lead to large changes because scattering will be dominated by the dust particles in the composite particle. Therefore the model predicted net radiative effects of EC coagulating with Asian dust is inconclusive in sign, as it depends strongly on the initial radiative properties of the individual sootcontaining particles.
4.3. Comparison With Observations
[32] To compare these model results with observations, we again examine those four dust days when coarse and fine α_{a} were calculated with reasonable uncertainty (Figure 4). One net effect of the coagulation of soot with dust is a shift of soot from the PM1 fraction, where it has a generally high absorption efficiency, to the coarse particle fraction, where α_{a} is substantially lower. This in turn leads to a decrease in overall shortwave absorption in polluted east Asian dust plumes. Preliminary estimates show that if instead of 39% of the EC mass being in the coarse particle phase as was found during dust events, we assumed that this value was 27% (which is the average for all of the nondust days), then it is estimated that the observed average change in overall aerosol shortwave absorption due to coagulation would be −12% (averaged over the four days with good data). If we assume that 0% of the EC was in the coarse particle phase before coagulation (a comparison more in line with the setup of the model calculations), then the observed decrease in aerosol absorption would be −40%. Our previous model calculations predicted changes in range of −10 to −17% for internally mixed absorbing dust, and −23 to −42% for internally mixed nonabsorbing dust. Given the assumptions used in the calculations and the uncertainties in the observations, one probably should not draw any conclusions about the extent to which the mineral dust was absorbing. However, the fact that both observations and model predictions are consistent in showing similar reductions in absorption due to coagulation strengthens the case for this effect, and we therefore estimate the impact to be −10 to −40%, with values closer to −10% being more likely.