Does optically effective complex refractive index of internal-mixed aerosols have a physically-based meaning?

It is documented that some unreasonable low real parts of aerosol complex refractive index (ACRI) are retrieved from measured particle optical properties, and whether the optically effective ACRI has a physically-based sense is still an open question. Numerical determination of the optically effective ACRI from accurately calculated scattering and absorption properties of polydisperse coated BC particles by the core-shell Mie, representing some internal-mixed aged BC particles under polluted urban environments, is performed with a Mie theory based data analysis scheme. After getting rid of retrieval uncertainties (such as altered shapes), the look-up tables without limiting ACRI ranges based on known particle compositions could theoretically result in some unreasonable extreme real parts of optically effective ACRI of coarse coated BC with some shell/core ratios. Based on limited look-up tables with aerosol compositions considered, the retrieved imaginary parts of optically effective ACRIs of coarse coated BC, showing smooth as a function of shell/core ratio, are significantly lower than those approximated by the volume weighted average (VWA) method by a factor of nearly 3. Although the VWA shows acceptable performances for coated BC in the Aitken or accumulation modes, it could overestimate the absorption of coarse coated BC by a factor of ~2 for large shell/core ratio. This may be one of the reasons why modelled aerosol optical depth is 20% larger than observed. Our study indicates that the optically effective ACRI of internal-mixed BC particles does have a physically-based meaning like real ACRI, unless limited ACRI look-up tables considering aerosol compositions are applied for retrieval. We suggest that the optically effective ACRI, rather than the ACRI given by the VWA, should be considered for coarse internal-mixed particles in the state-of-the-art aerosol-climate models.