Theoretical studies of the optical scattering and absorption properties of fractal aggregates generated from combustion sources

Aerosols generated from combustion are a primary source of carbonaceous particles in the earth's atmosphere and their absorption and scattering properties play a significant role in assessing climate affects at both regional and global levels. Yet the chemistry, size, and morphology of these aerosols can vary over an exceedingly wide dynamic range, resulting in absorption/scattering efficiencies and their albedos that may easily vary by factors of two to three, thus producing significant uncertainties in their contribution to climate forcing. To quantify these effects, detailed theoretical and experimental investigations were undertaken that encompass a large range of aerosol properties generated from various combustion sources relevant to radiative transfer with the intent of validating or defining the regions of applicability of commonly accepted approximations, such as Rayleigh-Debye-Gans, used in many climate forcing models. This paper discusses some of the initial results of the theoretical portions of the research. Aerosols generated from most combustion sources appear as fractal aggregates with fractal dimensions, Df, that typically vary from a low value of around 1.6 to maximum values in the range of 2.1 to 2.3 depending upon the source and the aggregation mechanisms. Fractal aggregates generated from well-ventilated flaming combustion are generally categorized as black carbon with high percentages of carbon in their composition, fractal dimensions in the range of 1.6 to 1.9, primary particle diameters in the range of 10 to 50 nm, and high values of extinction coefficient in their index of refraction resulting in significant absorption and single particle albedos in the range of 0.15 to 0.30. Fractal aggregates generated from fuel rich and non-flaming combustion contain significantly less carbon, have fractal dimensions in the range of 1.9 to 2.3, primary particles in the range of 50 to 100 nm, and significantly lower values of extinction coefficient in their index of refraction resulting in increased scattering and significantly higher single particle albedos. To quantify the effects of such potentially large differences in the size, chemistry, and morphology of these diverse fractal aggregates detailed numerical computations were performed using the Discrete Dipole Approximation software DDSCAT 7.0 maintained by Professor Bruce Draine at Princeton University. To simulate the effects of carbon content, the extinction coefficient of the index of refraction was varied over the range of 0.25 to 1.25 corresponding to increasing carbon percentages. To simulate the impact of particle morphology on the scattering and absorption the primary particle diameters for a base fractal aggregate (74 spheres and with a fractal dimension of 1.70) were gradually increased resulting in increasing levels of overlap and increasing values of fractal dimension. In another simulation, the diameters of half of the spheres were increased by a significantly larger fraction than the other half of the spheres. Three dimensional drawings of the resultant fractal aggregates were made using AutoCad software which also yielded the radius of gyration and volume equivalent radius for every different fractal calculation. The results of these detailed numerical simulations were compared to those predicted using the simplified Rayleigh-Debye-Gans (RDG) approximation. The results of these comparisons indicated that the accuracy of the RDG approximation worsens both as the extinction coefficient of the refractive index increases, as the primary particle diameter increases and at high levels of particle overlap corresponding to larger fractal dimensions. Based upon these results, a technique was developed using the first and second moments of the fractal aggregate that extended the range of validity of the RDG by roughly 50%-60% and significantly improved the accuracy of the approximation over its normally useful range. The details of the numerical computations and suggested improvements to the RDG approximation are the subject of this paper.