Numerical accuracy of “equivalent” spherical approximations for computing ensemble-averaged scattering properties of fractal soot aggregates

Numerical accuracy is quantitatively assessed in conjunction with the application of four “equivalent” spherical approximations in the computation of the optical properties of small aggregate soot particles. The approximations are based on equal volume, equal surface area, the radius of gyration, and a collection of independent spheres with the same volume and the same volume-to-projected area ratio as the original nonspherical particle. A diffusion-limited cluster-cluster aggregation algorithm is used to specify the geometries of soot particles. Furthermore, the Generalized Multi-particle Mie (GMM) method is utilized to compute the single-scattering properties of individual soot aggregate particles assumed to be randomly oriented in space. The ensemble-averaged single-scattering properties of the particles are obtained by accounting for the probability distribution functions (PDF) of the number of monomers per aggregate at two wavelengths, 0.628 and 1.1 μm. It is shown that all of the aforementioned equivalent-spherical approximations lead to large errors in the computation of the phase function.