Black carbon (BC) aerosols strongly absorb solar radiation in the atmosphere and directly or indirectly influence regional and global climate. However, the shape and mixing structures of BC particles are complex, and their optical properties are largely unquantified. Previous studies have used several numerical simulation tools to analyze the optical properties of BC particles, while the mixing structures of BC models in these studies are still quite different from those of the real individual BC particles in the atmosphere. In addition, most studies use only one numerical simulation tool to calculate the optical properties of BC particles. Therefore, the differences in optical results from different numerical simulation tools are still uncertain. In this study, a novel three-dimensional (3D) modeling tool, namely, Electron-Microscope-to-BC-simulation (EMBS), is applied to construct realistic 3D BC models. The EMBS can construct optical models of particles with arbitrary shapes and structures and can be applied in discrete dipole approximation (DDA). Then the influence of complex shapes and mixing structures of atmospheric BC particles on optical characteristics can be estimated. The absorption intensity Eabs, single scattering albedo (SSA), and absorption cross section Cabs of individual BC particles with different fractal dimensions (Df =1.8 and Df =2.6) and mixing structures are calculated by three numerical simulation methods, including DDA, multi-sphere T-matrix (MSTM), and Mie theory. The numerical simulation results obtained by different methods are compared, and the reasons for the difference in the results of different numerical simulation tools are analyzed.
In this study, the EMBS is used to construct BC particle models with different fractal dimensions (Df =1.8 and Df =2.6) and mixing structures. The BC models from the EMBS are applied by the DDA. The Eabs, SSA, and Cabs of BC particles constructed by the EMBS are calculated by the DDA method and then compared with the results from MSTM and Mie methods (Fig. 1). The parameters of individual BC particles (e.g., the radius of BC, Dp/Dc, F, etc.) are identical for the three methods. Each BC aggregate consists of 100 monomers with a radius of 20 nm. The coating thickness Dp/Dc and embedded fraction F are in the range of 1.5-2.7 and 0.10-1.00, respectively. The wavelength of incident light λ is 550 nm. The complex refractive index of BC is m=1.85+0.71i, and that of the BC coating is m=1.53+0i. This study assumes that particles are randomly oriented in the atmosphere, and 1000 incident light directions are used for each particle. The Mie method corresponds to the core-shell BC model and is conducted by the BHCOAT program.
For BC particles with loose structures (Df =1.8) and compact structures (Df =2.6), the Eabs of MSTM model is more sensitive to embedded fraction, while that of DDA model is more sensitive to the coating thickness (Fig. 4). The SSA of DDA and MSTM methods increases with the increase in the coating thickness, and that of DDA method is smaller than that of MSTM method (Fig. 5). In addition, the SSA of DDA and MSTM methods decreases with the increase in F, but the sensitivity of both models to F is not high (Fig. 5). The optical properties calculated by DDA and MSTM methods are still different when the parameters (such as Dp/Dc, F, and fractal dimension) are consistent. The results of this study prove that there are indeed obvious differences between DDA and MSTM in the simulation of optical properties of individual BC particles. The model shape and mixing structures of BC models for DDA method are more flexible, while MSTM has limitations in constructing models. On the one hand, there is the influence of the shape of BC models. For the bare BC model without coating, the relative deviation caused by different shapes of BC aggregates is large. The relative deviations of Cabs and Qabs are 13% and 9%, respectively (Fig. 6). For the fully embedded BC model, the relative deviations of Eabs, SSA, and Cabs reach 20%, 7%, and 23%, respectively (Fig. 7). On the other hand, the relative position of BC aggregate and coating results in a relative deviation of 2%-4% (Fig. 8). The BC models used by the MSTM method are quite different from the real atmospheric BC particles, so the deviation generated by the simulation may be larger than that of the DDA.
It is found that the Eabs results of MSTM method are more sensitive to the embedded fraction, while those of DDA method are more sensitive to the coating thickness. The difference between the two methods mainly results from: 1) differences in the shape of BC aggregates and coating in DDA and MSTM methods lead to the relative deviation of Eabs and Cabs up to 20% and 23%, respectively; 2) relative position and shape of the coating can produce relative deviation in 2%-4%. Due to the differences in BC model shapes and structures between DDA and MSTM methods, the optical simulation results may differ greatly.
