## 4 Summary and Discussion  
In this study, simple and flexible analytical expressions of mass extinction (scattering; absorption) efficiencies taking into account the effects of sizes and chemical compositions of aerosol particles were developed without losing accuracy compared with the Mie theory-based calculations. The polydispersed size range (i.e., geometric volume-mean diameters of up to 10 \(\upmu\)m and geometric standard deviations of 1.5, 2.0, and 2.5) of aerosol particles was considered with lognormal size distributions for ammonium sulfate, ammonium nitrate, sea salt, and elemental carbon aerosols. The MEE (MSE and MAE) of each aerosol chemical composition was first determined by the separate fitting of the Mie theory-based calculations for small (MEE\({}_{S}\)) and large (MEE\({}_{L}\)) size ranges in the form of power-law relationships. The coefficients of the power-law relationships were represented as linear expressions of geometric standard deviation, which allowed flexible parameterizations of various size distributions. The MEE for the intermediate size range was determined using the MEE\({}_{S}\), MEE\({}_{L}\), and harmonic mean-type approximation. To test the accuracy of the newly developed MEE approximation, the simple forcing efficiency of aerosol was also examined. The calculated MEE and simple forcing efficiency using the newly developed method showed high correlations with those determined using the Mie theory-based calculations. Conventional methods that calculate the aerosol extinction coefficient based on observations and outputs of numerical models depend exclusively on the reconstruction methods and their modifications. However, such methods do not take into account the effects of sizes and compositions of aerosol particles, while the newly developed method proposed in this study does. The flexible and convenient parameterizations of MEE developed in this study can be readily used to process in situ observations and adopted in large-scale numerical models. This method would be especially well suited to study the  
Figure 8: Comparison between the simple forcing efficiency (SFE) calculated using analytical approximation and those using Mie theory-based calculation for (**a**) ammonium sulfate (AMS), (**b**) ammonium nitrate (AMN), (**c**) sea salt (NaCl), and (**d**) elemental carbon (EC) with geometric standard deviations (GSD) of 1.5, 2.0, and 2.5. The correlation coefficient (\(r^{2}\)) and root mean square error (RMSE) are embedded in each panel. The black dotted line in each panel is a 1:1 line. aerosol measurement in the ocean. A subsequent study will examine how the realistic non-spherical shapes of aerosol particles affects calculations of MEE and extinction coefficient and attempt to reduce errors in results between the reconstruction methods and the Mie theory-based calculations. The scattering enhancement factor \(f\)(RH) is of great interest and should be improved [22]. Conceptualization: [PERSON] and [PERSON]; Validation: [PERSON], [PERSON], [PERSON] and K.M.H. ; Formal analysis: [PERSON] and W.J.C. ; Investigation: Y.P.K. and C.-H.K. ; Data curation: [PERSON], [PERSON] and S.J. ; Writing--original draft preparation: [PERSON], [PERSON] and [PERSON]; Visualization: [PERSON], [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript. This research was supported by the Technology Development Program to Solve Climate Changes through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (2019M1A2A2103953), KOPRI program (PN20081) by the National Research Foundation of Korea Grant (NRF2016M1A5A1901786), Basic Science Research Program through the NRF by the Ministry of Education (NRF2018R1D1A1A09083227) and by the National Strategic Project--Fine particle of the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (MSIT), the Ministry of Environment (ME), and the Ministry of Health and Welfare (MOHW) (NRF2017M3D8A1092022).