The dependence of the specific attenuation cross-section on black carbon mass fraction and particle size

The specific attenuation cross-section σ(ATN) which relates the attenuation of light by a particle-loaden quartz fiber filter to the black carbon (BC) content of deposited fine dust is the most important parameter for optical BC determination using an aethalometer. A simple model is presented to describe the effects of light scattering particles on the specific attenuation cross-section. It is found that σ(ATN) varies with the BC fraction of total mass f according to σ(ATN) = σ(abs) + (f^-1 - 1) (σ(scat)). The average specific scattering cross-section σ(scat) depends on the light scattering dry fraction of fine dust particles, while the specific absorption cross-section σ(abs) is determined by the light absorbing BC particles. The application of the model to an externally mixed BC-NaCl aerosol shows excellent agreement between the proposed theory and our experiments. The suitability of the outlined model is confirmed by analyses of attenuation data sets obtained from several measuring sites in Germany. For the examined data sets the average attenuation cross-section σ(abs), of ambient BC varies between 8 m²g^-1 (rural sites) and 19 m²g^-1 (street crossing). These variations can be explained by assuming a site-independent BC absorption cross-section σ(ATN)= 4 m²g^-1 which is derived from experiments with a BC test aerosol, and by varying the σ(abs) value From 0.45 m² g^-1 (rural sites) to 1.2-1.4 m²g^-1 (urban areas). Finally, the particle size dependence of the specific absorption cross-section σ(abs) is examined for a particle size range from 0.05 μm to 1.1 μm. As it is suggested by the fractal nature of BC particles no size dependence of σ(abs) with respect to the used BC test aerosol is found.