## 1 Introduction
Each species has the corresponding dry mass extinction (scattering; absorption) efficiency (m\({}^{2}\)g\({}^{-1}\)), and the terms in the brackets correspond to mass concentrations (mg m\({}^{-3}\)). Although [PERSON]'s reconstruction method [8] is widely used to estimate the extinction coefficient, one of the main weaknesses of [PERSON]'s equations is the assumption of size-independent mass extinction (scattering; absorption) efficiencies. [PERSON]'s reconstruction method uses a constant MEE for each chemical species regardless of particle size, and thus, it does not take into account the size distribution of chemical compositions, which can cause visibility degradation. Thus, the extinction coefficient in Equation (3) is identical for the distributions of aerosol particles as long as their mass concentrations are identical, although there are wide variations in size distributions [9]. Figure 2 shows an example comparison of MEE as a function of geometric volume-mean diameter (\(d_{gv}\)) with varying geometric standard deviations (\(\sigma_{g}\)). For AMS, AMN, sea salt (NaCl), and EC, the corresponding refractive indices and densities of externally mixed aerosols at a wavelength of 550 nm are shown in Table 1. It is clear that MEE has a strong dependence on the size distributions (i.e., different geometric standard deviations), as shown in Figure 2 and also in Figure 1. Thus, to consider the effect of particle size on the aerosol optical properties, [PERSON]'s reconstruction method (i.e., Equation (2)) has often been modified. For example, [PERSON] et al. [6] revised the Interagency Monitoring of Protected Visual Environments equation for fine and coarse particles using the Mie theory. In that study, the bimodal aerosol size distributions for AMS and AMN with two limited geometric mean diameters (geometric standard deviations) of 0.2 \(\upmu\)m (2.2) and 0.5 \(\upmu\)m (1.5) were used to represent fine and coarse modes, respectively. Thus, these modified expressions still could not fully describe the size-dependent mass efficiencies. Table 2 summarizes the constant mass extinction efficiencies determined in the original [PERSON]'s equation [8] and in [PERSON]'s revised method [6]. Figure 1: The calculated extinction efficiency (\(Q_{ext}\), blue) and mass extinction efficiency (MEE, red) as a function of size parameter (\(\pi d_{p}/\lambda\)) for (**a**) ammonium sulfate (AMS), (**b**) ammonium nitrate (AMN), (**c**) sea salt (SS, NaCl), and (**d**) elemental carbon (EC). Mie code [3] was used for these calculations at a wavelength \(\lambda\) = 550 nm, and the corresponding refractive indices and density of aerosols are shown in Table 1.  
Another important factor to reconsider in [PERSON]'s reconstruction method is the size-resolved parameterization of sea-salt particles. In the marine atmosphere, typical background aerosol comprises primarily produced sea-salt particles and secondarily produced particles consisting of non-sea salt sulfate and organic compounds [10]. Sea-salt particles dominate the super-micrometer fraction (\(d_{p}>1\) um) of the aerosol size distributions. However, some primarily produced sea-salt particles contribute significantly to the sub-micrometer fraction of the particle size distribution [11; 12]. In terms of the radiative forcing of the climate, the sub-micrometer size range is most relevant to light scattering because it comprises particles with diameters comparable to the wavelength of visible solar radiation. Measurements of the size-segregated chemical composition of aerosols over the Southern Ocean and the application of Mie scattering theory to those measurements confirmed the important role of sub-micrometer sea-salt particles. Sea-salt particles dominated both the chemical composition and aerosol light scattering of sub-micrometer particles [13; 14]. In [PERSON]'s original reconstruction method [8], sea-salt particles were regarded as coarse-mass particles with the constant MEE of 0.6 as shown in Equation (3).