# Optically effective complex refractive index of coated black carbon aerosols: from numerical aspects

Aerosol complex refractive index (ACRI) is an important microphysical parameter used for the studies of modeling their radiative effects. With considerable uncertainties related to retrieval based on observations, a numerical study is a powerful method, if not the only one, to provide a better and more accurate understanding of retrieved optically effective ACRIs of aged black carbon (BC) particles. Numerical investigations of the optically effective ACRIs of polydisperse coated BC aggregates retrieved from their accurate scattering and absorption properties, which are calculated by the multiple-sphere T-matrix method (MSTM), without overall particle shape variations during retrieval, are carried out. The aim of this study is to evaluate the effects of aerosol microphysics, including inline-formulashell∕core ratio inline-formulaDpDc, BC geometry, BC position inside coating, and size distribution, on retrieved optically effective ACRIs of coated BC particles. At odds with expectations, retrieved optically effective ACRIs of coated BC particles in coarse mode are not merely impacted by their chemical compositions and inline-formulashell∕core ratio, being highly complicated functions of particle microphysics. However, in accumulation mode, the coated BC optically effective ACRI is dominantly influenced by particle chemical compositions and the inline-formulashell∕core ratio. The popular volume-weighted average (VWA) method and effective medium theory (EMT) provide acceptable ACRI results for coated BC in accumulation mode, and the resulting uncertainties in particle scattering and absorption are both less than approximately 10 %. For coarse coated BC, the VWA and EMT, nevertheless, produce dramatically higher imaginary parts than those of optically effective ACRIs, significantly overestimating particle absorption by a factor of nearly 2 for heavily coated BC with a large BC fractal dimension or BC close to the coating boundary. Using the VWA could introduce significant overestimation in aged BC absorption analysis studies, and this may be one of the reasons why modeled aerosol optical depth is 20 % larger than observed, since it is widely employed in the state-of-the-art aerosol–climate models. We propose a simple new ACRI parameterization for fully coated BC with inline-formula $M5inlinescrollmathml{D}_{\mathrm{normal p}}/{D}_{\mathrm{normal c}}\ge normal 2.0$ 61pt16ptsvg-formulamathimg0bbe304f427773da1f33f8ddbb94af0a acp-19-7507-2019-ie00001.svg61pt16ptacp-19-7507-2019-ie00001.png in coarse mode, which can serve as a guide for the improvement of ACRIs of heavily coated BC, and its scattering and absorption errors are reduced by a factor of nearly 2 compared to the VWA. Our study indicates that a reliable estimate of the radiative effects of aged BC particles in coarse mode would require accounting for the optically effective ACRI, rather than the ACRI given by the VWA, in aerosol–climate models.

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Zhang, Xiaolin / Mao, Mao / Yin, Yan: Optically effective complex refractive index of coated black carbon aerosols: from numerical aspects. 2019. Copernicus Publications.

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