## 2 Data and Methods
### Estimation Methods for AOD  
#### 2.2.1 IMPROVE and Its Uncertainty  
The Malm [15] Interagency Monitoring of Protected Visual Environments (IMPROVE) equation is a commonly used WRF-CMAQ diagnosis approach [15; 34; 35; 36]. Two aerosol extinction coefficients are critical for diagnosing AOD [15], as follows:  
\[\text{AOD}=\sum_{i=1}^{N}\bigl{(}\sigma_{sp}+\sigma_{ap}\bigr{)}_{i}\;\Delta Z_{i} \tag{1}\]  
where \(N\) is the number of vertical layers in the numerical model, \(\Delta Z_{i}\) is the thickness of each layer, and \(\sigma_{sp}\) and \(\sigma_{ap}\) are the aerosol extinction coefficients of scattering and absorption by particles, respectively. In Equation (1), \(\sigma_{sp}\) and \(\sigma_{ap}\) are calculated using the following relation:  
\[\sigma_{sp}=0.003\times\text{f(RH)}\times\bigl{[}\text{NH}_{4}^{+}+\;\text{SO} _{4}^{-}+\;\text{NO}_{3}^{-}\bigr{]}+0.004\times\bigl{[}\text{Organic Mass}\bigr{]}+0.001\times\bigl{[}\text{Fine soil}\bigr{]} \tag{2}\]  
\[+0.0006\times\bigl{[}\text{Coasre Mass}\bigr{]}\]  
\[\sigma_{ap}=0.01\times\bigl{[}\text{Light Absorbing Carbon}\bigr{]} \tag{3}\]  
The unit of air pollutants in is mg m\({}^{-3}\), and the unit of each coefficient (0.003, 0.004, 0.001, 0.0006, and 0.01) is m\({}^{2}\) mg\({}^{-1}\); f(RH) is a function that depends on relative humidity and is calculated as follows:  
\[\text{f(RH)}=b_{0}+b_{1}\biggl{(}\frac{1}{1-\text{RH}}\biggr{)}+b_{2}\biggl{(} \frac{1}{1-\text{RH}}\biggr{)}^{2} \tag{4}\]  
where \(b_{0}\), \(b_{1}\), and \(b_{2}\) are correlation parameters that vary seasonally, as listed in Table 2. It should be noted that f(RH) applies to the inorganic aerosol (\(\bigl{[}\text{NH}_{4}^{+}+\text{SO}_{4}^{-}+\text{NO}_{3}^{-}\bigr{]}\)) only. According to previous studies, a non-negligible fraction of organic aerosol is water-soluble [37; 38]. Moreover, a substantial fraction of water-soluble organic aerosol is known to be composed of humic-like substances (HULIS), associated with light-absorbing brown carbon aerosol. However, lot of complexities and uncertainties exist in the characterization of organic aerosol. In this study, we assumed that organic aerosol is non-hygroscopic and non-absorbing aerosol [39]. A drawback of Equation (4) is that it is unable to consider the size dependence of f(RH) [40]. A practical issue in Equation (4) is the formulation of the denominator using relative humidity. A problem arises when the value of f(RH) becomes  
Figure 1: (**a**) Domain of the National Institute of Environmental Research (NIER) operational forecast model. Shadings represent the terrain height (m). The red box and red-colored dots represent Geostationary Ocean Color Imager (GOCI) coverage and the locations of Aerosol Robotic Network (AERONET) sites in East Asia. (**b**) Domain 2 and (**c**) domain 3 of NIER operational forecast system are shown with PM\({}_{2.5}\) observation sites (blue dots) of Air Korea in the Seoul metropolitan area and Yonsei AERONET site (red dot).  
unrealistically large (when RH approaches 1). Therefore, the maximum RH value is limited. The uncertainties and sensitivities are shown in Figure 2. Figure 2 displays the horizontal distribution of GOCI AOD at 01:00 UTC 24 May 2016, along with estimated AODs from the NIER operational model following Equations (2)-(4) with maximum RH values of 93%, 96%, and 98% to avoid infinite values from Equation (4). GOCI AOD does not appropriately represent the AOD value in the area with clouds (Figure 2a); the estimated AODs from the operational model show a large sensitivity to cloud area depending on the maximum RH from Equation (4) (Figure 2b-d). In the broad cloud region, estimated AODs more than doubled as the value of the maximum RH increases from 93% to 98%.