## 3 Results and Discussion
### Derivation of Optimal Probability Density Function  
In general, the particle size distribution of atmospheric aerosols showed a bimodal distribution, with two peaks on either side of the fine and coarse particle areas (\(\sim\)1-2 m) due to the influence of various anthropogenic and natural sources [37].  
To statistically examine the mass concentration distribution according to measured particle size data, an optimal probability density function with two peaks was calculated using Equation (5). The function was optimized for each of the five weather conditions, and the lognormal distribution constants, \(M_{t}\), \(D_{g}\), and \(\sigma\) values were calculated (summarized in Table 4). Figure 8 shows the probability density function of the aerosol mass concentration distribution for each phenomenon, indicating their bimodal lognormal distributions.  
During AD events, the total mass concentrations in fine and coarse modes were estimated as 1.76 \(\upmu\)g\(\cdot\)m\({}^{-3}\) and 4.03 \(\upmu\)g\(\cdot\)m\({}^{-3}\), with average diameters of 0.42 \(\upmu\)m and 5.10 \(\upmu\)m, respectively. Compared with other phenomena, the total mass concentration of Mode 2 (larger mode) showed a very high value and was estimated to be the most pronounced bimodal distribution. The largest average diameter was observed in Mode 1, whereas the SD of Mode 2 was 1.52 \(\upmu\)m, showing the largest value among the various studied phenomena. For HZ events, the total mass of smaller particles (Mode 1) was larger than that of the larger particles (Mode 2), estimated as 3.00 and 0.53 \(\upmu\)g m\({}^{-3}\) (mean diameters of 0.38 and 5.14 \(\upmu\)m), respectively, whereas MI cases displayed concentrations of 3.79 and 0.36 \(\upmu\)g\(\cdot\)m\({}^{-3}\) (mean diameters of 0.40 and 5.28 \(\upmu\)m), respectively. Although the mass concentration in Mode 1 was the highest, the SD was the lowest (1.28 \(\upmu\)m).  
Furthermore, the concentration of Mode 2 showed the lowest value (0.36 \(\upmu\)g\(\cdot\)m\({}^{-3}\)) observed during PR events. Moreover, the largest mean diameter for PR events was observed in Mode 2 (5.49 \(\upmu\)m), whereas the greatest mass concentration was recorded in Mode 1 (1.44 times higher than that during AD). During CD observations, the total aerosol numbers were estimated as 2.14 and 0.62 \(\upmu\)g\(\cdot\)m\({}^{-3}\), and the mean diameters were 0.36 and 5.24 \(\upmu\)m in Modes 1 and 2, respectively.  
The results were compared with those of [PERSON] and [PERSON] [19], who analyzed the mass concentration characteristics of aerosol values in Seoul, producing mean diameters for AD events of 0.89 (\(\pm\)2.4) and 9.12 (\(\pm\)2.14) \(\upmu\)m, respectively. During non-AD events, mean diameters of 0.6 (\(\pm\)1.78) and 8.51 (\(\pm\)2.14) \(\upmu\)m were observed, respectively. Accordingly, during AD events, the corresponding results showed a clearer concentration distribution in Mode 2 than in Mode 1, although the mean diameter differed by approximately 4 \(\upmu\)m. The smaller mean diameter observed in the present study compared to other cases may be due to the regional differences between Seoul and Busan, and the corresponding reduction in coarse mode particles according to the distance from the Asian dust source.  
Figure 7: Meteorological factor distributions for each phenomenon: (**a**) temperature and relative humidity, (**b**) pressure and wind speed. AD: Asian dust, HZ: haze, MI: mist, CD: clear days, and PR: precipitation.