## 4 Summary and Conclusions  
AOD retrieval from satellites can provide reliable information, but missing values are problematic when cloud fractions are continually high. Instead of real observations, a numerical model can be used to make up for missing data. In this study, to investigate the consistency of AOD estimations, the AOD calculation ability of the NIER operational numerical forecast model (WRF-CMAQ) was verified through comparative analysis. The greatest uncertainty in the M1 (IMPROVE) method [15] is related to f(RH), which corresponds to the cloud and aerosol hygroscopic growth factor. The AODs are very sensitive to the set value of the maximum relative humidity, especially around cloudy regions where relative humidity is close to 1. To remove this uncertainty, we tested two alternative estimations [29; 30] in which it is not necessary to set the maximum value of relative humidity.  
When comparing GOCI-retrieved and WRF-CMAQ-derived AODs for spring and winter, the M1 estimation with maximum RH = 96% showed the largest values, while those of the M3 method were the smallest. These results are consistent with a single observational analysis for the Seoul Metropolitan. However, the statistics should be treated with caution, since all R values were significantly lower than those in a previous study; identifying the reasons for this requires further study considering local features of AOD with large observational points. Other statistics, such as RMSE and MB, are dependent on model resolution and the analyzed period. AOD estimations are not always improved at high resolution, and their seasonal dependency is apparent. Underestimations and overestimations were reduced during winter compared with springtime for the M3 and other estimation methods, respectively.  
To extend our analysis to a larger domain, we also carried out a statistical investigation for NIER D01 and D02. All AODs performed well, showing small MB values. The values of R in D01 were larger than the single observational values and were comparable to those reported in the literature. However, from the D02 analysis, R was significantly lower than that of D01. For the M3 estimation, values were >0.5, but for all other methods, the values were <0.5. A small number of observations and/or local characteristics of AOD can cause these results and it will be a challenge to investigate this issue in future studies. In general, the R values were highest during summer and lowest during springtime for all methods. Overall, the M3 gave the best scores in the large domain analysis. To the best of our knowledge, M1 is still widely used to derive AOD from WRF-CMAQ. While our results only represent a 1-year data analysis, care should be taken when performing AOD estimation, and empirically reconstructed mass-extinction methods, such as that of M3, offer an alternative solution.  
Conceptualization S.-H.P., H.-J.K., W.J.C. and C.H.J.; methodology, S.-H.P., H.-J.K. and U.S.; software, H.-J.K.; validation, H.-J.K. and U.S.; formal analysis, H.-J.K., J.-H.K., C.H.J., W.J.C. and K.-P.N.; investigation, H.-J.K. and J.-H.K.; resources, W.J.C. and K.-P.N.; writing--original draft preparation, S.-H.P., H.-J.K. and U.S. All authors have read and agreed to the published version of the manuscript.  
This research was supported by a grant from the National Institute of Environment Research (NIER), funded by the Ministry of Environment (MOE) of the Republic of Korea (e.x. NIER-2019-01-02-085). (S-H.P.) This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST; 2021R1A2C1012433) and (in part) by the Yonsei University Future-leading Research Initiative of 2018-22-0021.  
Not applicable.  
We would like to acknowledge the use of the GOCI product ([PERSON]; [PERSON]). We also thank NIER's operational team for developing and maintaining the air-quality forecasting system.  
The authors declare no conflict of interest.