## 2 Numerical Model and Simulation Setup
### Model Validation  
For the T2M case close to the realistic configuration (most of the trees around the school were shrubs), we validated the CFD model against the wind directions and speeds measured by the 3D sonic anemometer and PM\({}_{2.5}\) concentrations measured by the sensor network around the school [25]. For the wind validation, we coupled the CFD model with the local data assimilation and prediction system (LDAPS), one of the numerical weather prediction systems operated by the Korea Meteorological Administration. The coupled model was integrated from 00 LST to 23 LST on 23 June 2020. The LDAPS provided the horizontal wind components (U and V) for the CFD model. We used the 1-h averaged PM\({}_{2.5}\) concentrations measured at the AQMS 221112 as the background concentrations. During the validation period, the emission rate of PM\({}_{2.5}\) was estimated using the method \begin{table}
\begin{tabular}{c c c c} \hline
**Wind Direction** & **Wind Speeds (m s\({}^{-1}\))** & **PM\({}_{2.5}\) (\(\mu\)g m\({}^{-3}\))** & **Wind Direction Frequency (\%)** \\ \hline northerly (N) & 2.66 & 28.32 & 5.55 \\ north–northeasterly (NNE) & 2.79 & 22.02 & 4.41 \\ northeasterly (NE) & 2.69 & 18.45 & 12.05 \\ east–northeasterly (ENE) & 2.08 & 20.83 & 7.33 \\ easetly (E) & 2.14 & 23.95 & 6.73 \\ east–southeasterly (ESE) & 2.34 & 26.47 & 6.47 \\ southeastly (SE) & 2.19 & 27.70 & 3.10 \\ south–southeasterly (SSE) & 1.89 & 28.77 & 1.50 \\ south–southeasterly (SSW) & 3.04 & 28.96 & 4.14 \\ south–southesterly (SSW) & 3.87 & 33.05 & 11.55 \\ southwesterly (SW) & 4.65 & 28.55 & 8.30 \\ west–southwesterly (WSW) & 3.96 & 29.48 & 6.12 \\ west–westerly (W) & 3.52 & 27.57 & 6.23 \\ west–northwesterly (WNW) & 3.21 & 25.68 & 5.87 \\ north–southwesterly (NW) & 2.46 & 26.21 & 4.59 \\ north–northwesterly (NNW) & 2.69 & 28.16 & 6.04 \\ \hline \end{tabular}
\end{table} 
Table 2: Average wind speed (ASOS 159) and PM\({}_{2.5}\) concentration (AQMS 221112) for each wind direction. Wind speeds (2011–2020) and PM\({}_{2.5}\) concentrations (2015–2020) are averages over school hours (07 LST to 18 LST). described in Section 2.2 (Figure 2). The emission rate had two peaks, which were not distinct, at 07 and 17 LST. It was less than 10\({}^{-6}\) kg m\({}^{-2}\) h\({}^{-1}\) in the early morning (01 LST and 04 LST) and had its maximum (3.64 \(\times\) 10\({}^{-6}\) kg m\({}^{-2}\) h\({}^{-1}\)) at 17 LST. For statistical validation, we used the root mean square error (RMSE), normalized root mean square error (NRMSE), geometric mean variance (VG), geometric mean bias (MG), fractional bias (FB), correlation coefficient (R), and fraction within a factor of two (FAC2) [26]:  
\[\text{RMSE}=\sqrt{\overline{\left(\text{C}_{\text{o}}-\text{C}_{\text{P}} \right)^{2}}} \tag{10}\]  
\[\text{NRMSE}\ =\sqrt{\overline{\frac{\left(\text{C}_{\text{o}}-\text{C}_{\text{P}} \right)^{2}}{\overline{\text{C}}_{\text{o}}^{\ast}\overline{\text{C}}_{\text{P} }^{\ast}}}} \tag{11}\]  
\[\text{VG}=\ \exp\left[\left(\text{ln}\,\text{C}_{\text{o}}-\text{ln}\,\text{C}_{ \text{P}}\right)^{2}\right] \tag{12}\]  
\[\text{MG}=\exp\left[\text{ln}\,\text{C}_{\text{o}}-\text{ln}\,\text{C}_{ \text{P}}\right] \tag{13}\]  
\[\text{FB}=\frac{\left(\overline{\text{C}_{\text{o}}}-\overline{\text{C}_{ \text{P}}}\right)}{0.5\,\left(\overline{\text{C}_{\text{o}}}+\overline{\text{ C}_{\text{P}}}\right)} \tag{14}\]  
\[\text{R}=\frac{\overline{\left(\text{C}_{\text{o}}-\overline{\text{C}_{\text {o}}}\right)\left(\text{C}_{\text{P}}-\overline{\text{C}_{\text{P}}}\right)} }{\sigma_{\text{C}_{\text{o}}}\cdot\sigma_{\text{C}_{\text{P}}}} \tag{15}\]  
\[\text{FAC2}=\ \text{fraction of data that satisfy 0.5 }\leq\ \frac{\text{C}_{\text{P}}}{\text{C}_{\text{o}}}\leq 2.0, \tag{16}\]  
where \(\text{C}_{\text{o}}\), \(\text{C}_{\text{P}}\), \(\overline{\text{C}}\), and \(\sigma_{\text{C}}\) denote the measurements, model predictions, average across the dataset, and standard deviation across the dataset, respectively.