## 2 Materials and Methods
### Data Processing  
The SMPS measured the number size distribution of the aerosol particles every 3 min. The hourly-averaged values of \(N_{\rm CN}\) and the size distributions were used in the following analyses. The CCN counter measured \(N_{\rm CCN}\) every second. It was operated at 6 different \(SS\) conditions and each \(SS\) condition continued for 10 min. Thus, it took 1 h to complete one cycle. Averaged values of \(N_{\rm CCN}\) at each \(SS\) condition were calculated for every hour. The \(N_{\rm CCN}\) data obtained at the 0.16, 0.21, 0.36 and 0.55% \(SS\)s were used for the following analysis. The FM measured the \(N_{\rm CD}\) every 10 s and hourly-averaged values of \(N_{\rm CD}\) were used for the following analyses.  
When aerosol particles are mixed well internally, the particles with diameters larger than the activation diameter (\(d_{\rm a}\)) can activate as CCN at a given \(SS\). Then, \(N_{\rm CCN}\) can be written as:  
\[N_{\rm CCN}=\int_{d_{\rm a}}^{d_{\rm max}}n(\log d)\mathrm{d}\mathrm{log}d, \tag{1}\]  
where \(d\) and \(n(\mathrm{log}d)\) are the dry diameter and the number size distribution of the aerosol obtained by SMPS, respectively. Then \(d_{\rm a}\) can be obtained by integrating the particle size distributions. The maximum particle size measured by SMPS, 500 nm, was used as \(d_{\rm max}\).  
The relationship between the saturation ratio, \(S\), and the droplet diameter is described by the [PERSON] theory (2016). The theory can be re-written by using the hygroscopicity parameter \(\kappa\)([PERSON], 1970) as follows:  
\[S=\frac{d_{\rm drop}^{3}-d^{3}}{d_{\rm drop}^{3}-d^{3}(1-\kappa)}\exp\left( \frac{4\sigma_{\rm s/a}M_{\rm w}}{RT\rho_{\rm w}d_{\rm drop}}\right), \tag{2}\]  
where \(d_{\rm drop}\) is the droplet diameter, \(\sigma_{\rm s/a}\) is the surface tension at the solution-air interface, \(M_{\rm w}\) is the molecular weight of water, \(R\) is the universal gas constant, \(T\) is the droplet temperature, and \(\rho_{\rm w}\) is the density of pure water. Note that the relationship between supersaturation, \(SS\), and saturation ratio, \(S\), is as below:  
\[SS=(S-1)\times 100\%. \tag{3}\]  
Equation (2) can be simplified as follows ([PERSON], 1970; [PERSON], 1970):  
\[S=\exp\left(\sqrt{\frac{4A^{3}}{27\kappa d^{3}}}\right), \tag{4}\]The parameter \(A\) represents [PERSON]'s term and can be written as:  
\[A=\frac{4\sigma_{\text{s/a}}M_{\text{w}}}{RT\rho_{\text{w}}}, \tag{5}\]  
In Equation (5), \(A\approx 0.66/T\) (in mm) can be used [29]. The \(\kappa\) of ambient aerosol was then calculated for each \(SS\) condition (0.16, 0.21, 0.36 and 0.55%) of the CCN counter by using \(d\) as \(d_{\text{a}}\) in Equation (4):  
\[\kappa=\frac{4A^{3}}{27d_{\text{a}}^{2}\ln^{2}S}. \tag{6}\]  
By applying Equation (1) and replacing \(N_{\text{CCN}}\) by \(N_{\text{CD}}\), the activation diameters (\(d_{\text{a, CD}}\)) under ambient \(SS\) conditions were calculated based on the aerosol size distributions:  
\[N_{\text{CD}}=\int_{d_{\text{a,CD}}}^{d_{\text{max}}}n\left(\log d_{\text{p}} \right)\,\text{dlog}d_{\text{p}}. \tag{7}\]  
To estimate the \(SS_{\text{eff}}\) of the clouds observed at the MFRS, we used the regression curve of the relationship between mean \(d_{\text{a}}\), calculated by Equation (1), and \(SS\) obtained by the CCN measurements. Using the data collected by the FM, the liquid water content (\(L\)WC) and the effective radius (\(R_{\text{eff}}\)) of the cloud droplets were calculated using the following equations [15], respectively:  
\[LWC=\frac{\pi}{6}\rho_{\text{w}}\sum_{\text{i}}n_{\text{i}}d_{\text{i}}^{3}, \tag{8}\]  
\[R_{\text{eff}}=\frac{1}{2}\sum_{\text{i}}n_{\text{i}}d_{\text{i}}^{3}/\sum_{ \text{i}}n_{\text{i}}d_{\text{i}}^{2}, \tag{9}\]  
where, \(n_{\text{i}}\) is the number concentration of cloud droplets and \(d_{\text{i}}\) is the geometric mean diameter of each size bin set by the FM.