## 2 Materials and Methods
### Aerosol Size Distribution Function  
Because atmospheric aerosols occur over a large size range, particle size distribution was represented by a mathematical description to accurately calculate the aerosol concentration. The aerosols were assumed to be spherical with the same optical properties. Assuming that \(dN=n_{N}\big{(}D_{p}\big{)}dD_{p}\) represents the number of particles in the size range \(\big{(}D_{p},\ D_{p}+dD_{p}\big{)}\), the aerosol number distribution \(n_{N}\big{(}D_{p}\big{)}\) and mass distribution \(n_{m}\big{(}D_{p}\big{)}\) can be expressed according to Equations (1) and (2):  
\[n_{N}\big{(}D_{p}\big{)}=\frac{dN}{dD_{p}} \tag{1}\]  
\[n_{m}\big{(}D_{p}\big{)}=\frac{\rho_{p}}{10^{6}}\frac{\pi}{6}D_{p}{}^{3}n_{N} \big{(}D_{p}\big{)} \tag{2}\]  
where \(N\) is the number of particles per unit volume (cm\({}^{-3}\)) and \(D_{p}\) is the diameter of the particles (\(\mu\)m) [30]. The density \(\rho_{p}\) (g-cm\({}^{-3}\)) of the particles generally has a value between 1 and 2 [31] and is affected by particle size, type, season, and region. Because this study primarily analyzed atmospheric particles observed during spring, a density of 1.6 suggested by [PERSON] et al. [32] was considered. Equations (3) and (4) are the common logarithm of Equations (1) and (2):  
\[\frac{dN}{dlogD_{p}}=2.303D_{p}n_{N}\big{(}D_{p}\big{)} \tag{3}\]  
\[\frac{dM}{dlogD_{p}}=2.303D_{p}n_{m}\big{(}D_{p}\big{)} \tag{4}\]  
The hourly observation data were calculated to obtain the descriptive statistics, including the following: mean, standard deviation (SD), 25 and 75 percentiles (Q1 and Q3), interquartile range (IQR), median absolute deviation (MAD), skewness, and kurtosis to examine the distributions of the variables.  
To statistically examine the concentration distribution according to particle size, the optimal probability density function for high-concentration aerosol phenomena was derived using mass concentration data by diameter. The mass concentration per unit volume was converted to a lognormal distribution based on diameter, and statistical variables were estimated from the measured data.  
To statistically examine the distribution of mass concentrations according to particle size, two optimum lognormal distribution functions were used (Equation (5)):  
\[\frac{dM}{dlogD}=A_{1}exp\left[-\frac{\left[logD-D_{g1}\right]^{2}}{2\left[log \sigma_{g1}\right]^{2}}\right]+A_{2}exp\left[-\frac{\left[logD-D_{g2}\right]^{ 2}}{2\left[log\sigma_{g2}\right]^{2}}\right] \tag{5}\]  
where \(A_{1}\) and \(A_{2}\) are the amplitudes, \(D_{1}\) and \(D_{2}\) are the geometric mean mass diameters, and \(\sigma_{1}\) and \(\sigma_{2}\) are the geometric standard deviations of Modes 1 and 2, respectively. Mode 1 indicates a section where the aerosol size is relatively small, and Mode 2 indicates a relatively large section. The lognormal distribution constants, total mass concentration  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Contents** \\ \hline _Light collection_ & Wide-angle light collection by the ellipsoidal mirror \\ _Light source_ & Laser diode \\ _Particle diameter_ & \(<\)10.0 \(\mu\)m \\ _Size channels_ & 0.3, 0.5, 1.0, 3.0, 5.0, and 10.0 \(\mu\)m \\ _Sample flow rate_ & 28.3 L-min\({}^{-1}\) \\ _Power supply_ & Ni-Cd Battery with AC adaptor (standard) dry cell \\  & battery/U2X9 (optional) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specification of the laser particle counter (LPC).  
(\(M_{t}\)), geometric mean diameter (\(D_{S}\)), and geometric standard deviation (\(\sigma\)) values were calculated for meteorological phenomena through the function.