The contribution of soot aerosols to radiative forcing and climate change depends on their optical properties. Since these aerosols are agglomerates composed of quasi-spherical primary particles (usually small with respect to the radiation wavelength), their properties can be calculated following the Rayleigh-Debye-Gans approximation, which considers primary particles as independent absorbers and scatterers, with corrections made to account for multiple scattering and absorption within the agglomerate. A variety of equations can be used for particles small compared to the wavelength. In this study, results of the Rayleigh, Bohren and Huffman, simplified Bohren and Huffman, and Dobbins and Megaridis equations have been compared to the results from the exact Mie equations for the absorption efficiency. This comparison has been made for individual particles with different diameters and for an ensemble of primary particles composing an agglomerate. It has been shown that some of the largest primary particles of a typical agglomerate may not behave as Rayleigh absorbers at short wavelengths, contributing to errors in the estimation of the absorption efficiency. Both Bohren and Huffman and Dobbins and Megaridis equations are useful to extend the application range of the Rayleigh equation, thus reducing the accumulated error in the estimation of the agglomerate absorption efficiency. This analysis has been performed for several complex refractive index spectra. To choose the best equation for a particular application, the wavelength spectrum of the radiation and the range of primary particle sizes should be considered, aiming for a compromise between simplicity and accuracy.

烟尘气溶胶对辐射强迫和气候变化的贡献取决于其光学性质。由于这些气溶胶是由准球形初级颗粒（通常相对于辐射波长而言很小）组成的团块，因此可以按照瑞利-德比-甘斯近似方法（其将初级颗粒视为独立的吸收剂和散射剂）进行计算，并对其进行校正。考虑到团块内的多次散射和吸收。对于与波长相比较小的粒子，可以使用多种方程式。在这项研究中，将Rayleigh，Bohren和Huffman，简化的Bohren和Huffman以及Dobbins和Megaridis方程的结果与精确Mie方程的结果进行了吸收效率的比较。已经对具有不同直径的单个颗粒和构成团聚物的初级颗粒的集合进行了这种比较。已经显示出，典型附聚物的一些最大的初级颗粒在短波长下可能不表现为瑞利吸收剂，从而导致吸收效率估算中的误差。Bohren和Huffman以及Dobbins和Megaridis方程都可用于扩展Rayleigh方程的应用范围，从而减少聚集体吸收效率估算中的累积误差。已经针对多个复数折射率光谱执行了该分析。为了为特定应用选择最佳方程，应考虑辐射的波长光谱和一次粒径的范围，