Abstract. The absorption Ångström exponent (AAE) is an important aerosol optical parameter used for aerosol characterization and apportionment studies. The AAE of black carbon (BC) particles is widely accepted to be 1.0, although observational estimates give quite a wide range of 0.6–1.3. With considerable uncertainties related to observations, a numerical study is a powerful method, if not the only one, to provide a better and more accurate understanding on BC AAE. This study calculates BC AAE using realistic particle geometries based on fractal aggregate and an accurate numerical optical model (namely the multiple-sphere T-matrix method), and considers bulk properties of an ensemble of BC particles following lognormal size distributions. At odds with the expectations, BC AAE is not 1.0, even when BC is assumed to have small sizes and a wavelength-independent refractive index. With a wavelength-independent refractive index, the AAE of fresh BC is approximately 1.05 and relatively insensitive to particle size. For BC with geometric mean diameters larger than 0.12 µm, BC AAE becomes smaller when BC particles are aged (compact structures or coated by other non-absorptive materials). For coated BC, we prescribe the coating fraction variation based on a laboratory study, where smaller BC cores are shown to develop larger coating fractions than those of bigger BC cores. For both compact and coated BC, the AAE is highly sensitive to particle size distribution, ranging from approximately 0.8 to even over 1.4 with wavelength-independent refractive index. When the refractive index is allowed to vary with wavelength, a feature with observational backing, the BC AAE may show an even wider range. For different BC morphologies, we derive simple empirical equations on BC AAE based on our numerical results, which can serve as a guide for the response of BC AAE to BC size and refractive index. Due to its complex influences, the effects of BC geometry is better to be discussed at certain BC properties, i.e., known size and refractive index.

The absorption Ångström exponent of black carbon: from numerical aspects