## 2 Methods
### Extinction Coefficient (\(b_{ext}\)) Calculations for Polydisperse Aerosols
A physical relationship between light extinction and atmospheric particle composition for externally mixed aerosol can be expressed by the following equations with respect to a given particle concentration, size distribution, refractive indices, and densities of each chemical species [3,16,21]:  
\[b_{ext}=\sum_{i}b_{ext,i} \tag{1}\]  
\[b_{ext,i}=\frac{\pi d_{p}^{2}}{4}Q_{ext,i}\big{(}d_{p},\lambda,m\big{)}n\big{(} d_{p}\big{)} \tag{2}\]  
where \(b_{ext,i}\) is the extinction coefficient associated with the \(i\)th species; \(n(d_{p})\) is the number distribution; \(Q_{ext,i}\big{(}d_{p},\lambda,m\big{)}\) is the extinction efficiency of a particle with a diameter, \(d_{p}\) and a refractive index, \(m\), at a specific wavelength, \(\lambda\), for the \(i\)th species. It should be noted that \(b_{ext}\) can be expressed as a function of particle size. For a given mass concentration, the overall extinction coefficient expressed in Equations (1) and (2) can be simplified as follows:  
\[b_{ext}=\sum_{i}b_{ext,i}=\sum_{i}[C_{i}\times MEE_{i}] \tag{3}\]  
where \(MEE_{i}\) is the mass extinction efficiency in m\({}^{2}\) g\({}^{-1}\), and \(C_{i}\) is the mass concentration of the \(i\)th chemical species (in \(\upmu\)g m\({}^{-3}\)). In this study, the resultant expression of \(b_{ext}\) and \(b_{abs}\) for a dry aerosol can be expressed as follows:  
\[b_{ext}=\text{MEE}_{[ Inorganic]}\text{ C}_{[ Inorganic]}+\text{MEE}_{[OM]}\text{ C}_{[OM]}+\text{MEE}_{[NaCl]}\text{ C}_{[NaCl]}+\text{MEE}_{[Crus]}\text{ C}_{[Crusst]}+\text{MEE}_{[EC]}\text{ C}_{[EC]} \tag{4}\]  
where the MEE for each species is usually considered constant. However, for polydisperse aerosols, we must use size-dependent MEEs. We obtained the MEE using Equation (5) from the \(b_{ext}\) and mass concentration. The MEE is defined as the ratio between the aerosol extinction coefficient and the aerosol mass concentration in a unit volume of air [7,22]. \[MEE_{i}=\frac{b_{ext}}{C_{i}} \tag{5}\]  
We assumed that aerosols follow a log-normal size distribution, which is expressed as a function of d\({}_{\text{g}}\) and the GSD. Figure 2: Sensitivity of (**a**) the mass extinction efficiency (MEE), (**b**) mass scattering efficiency (MSE), and (**c**) mass absorption efficiency (MAE) for internally mixed aerosol as a function of the geometric mean diameters (d\({}_{\text{g}}\)) in the range of 0.1–2.5 \(\upmu\)m and geometric standard deviations (GSD) in the range of 1.5–2.5. Figure 3 shows the size-resolved MEEs for different chemical species and GSDs. A d\({}_{\text{g}}\) range of 0.1-2.5 \(\upmu\)m was considered, and GSDs of 1.5, 2.1, and 2.5 were compared. As shown in Figure 3, the MEEs had different distributions that depended on the chemical species, which were characterized by different size distributions. According to [PERSON] et al. [23], the MEE values for inorganic ion, OM, NaCl, crust, and EC are 3.0, 4.0, 1.7, 1.0, and 10.0 m\({}^{2}\) g\({}^{-1}\), which represent constants at specific conditions among the widely distributed MEEs. Figure 3 implies that the MEEs for polydisperse aerosols are influenced by many factors, including emissions, chemical signature, and meteorology. This suggests that we must pay careful attention when applying MEEs from previous studies that may have used different spatiotemporal conditions.