## 4 Conclusions  
We investigated the effects of wall- and tree-type fences on the airflows and PM\({}_{2.5}\) concentrations in a school from an aerodynamics perspective using an RNG \(k\)-\(\epsilon\) CFD model. The CNTL case assumed the absence of fences, and the wall and tree heights considered in the wall-type fence (W2M and W4M) and tree-type fence (T2M and T4M) cases were 2 m and 4 m.  
To validate the simulated results against the measured wind speeds, wind directions, and PM\({}_{2.5}\) concentrations, the CFD model coupled with the LDAPS was integrated from 00 LST to 23 LST of 23 June 2020, for the T2M cases. The background PM\({}_{2.5}\) used was the measured PM\({}_{2.5}\) concentration at AQMS 221112. We calculated the PM\({}_{2.5}\) emission rate from the CAPSS based on the monthly, daily, and hourly emission factors. Although the CFD model underestimated the PM\({}_{2.5}\) concentrations from 00 LST to 08 LST, we concluded that the model simulated the wind speeds, wind directions, and PM\({}_{2.5}\) concentrations in the daytime well. The CFD model satisfied the recommended criteria (NRMSE, VG, MG, FB, and FAC2 criteria) for wind speeds and PM\({}_{2.5}\) concentration. We evaluated the wall- and tree-type fence effects for 16 inflow directions by conducting numerical simulations with different fence types and heights. With the east-southeasterly inflow, in the CNTL case, relatively high PM\({}_{2.5}\) levels on the road were transported to the school from the east school boundary. The wall-type fence on the east school boundary prevented the incoming flow to the school from the east road, and the PM\({}_{2.5}\) concentrations decreased significantly in the downwind region of the fence because the fence restricted the emitted pollutants. However, the PM\({}_{2.5}\) concentrations increased in the school ground as a result of pollutants coming over the fences. With the east-northeasterly inflow, in the CNTL case, the ambient wind was descended by \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **First Floor** & **Second Floor** & **Third Floor** & **Fourth Floor** \\ \hline \multirow{3}{*}{School ground} & W2M & \(-0.35\) (0.45) & \(-0.27\) (0.38) & \(-0.22\) (0.30) & \(-0.17\) (0.25) \\  & W4M & \(-0.79\) (0.29) & \(-0.58\) (0.25) & \(-0.47\) (0.24) & \(-0.34\) (0.17) \\  & T2M & \(-1.01\) (0.55) & \(-0.60\) (0.40) & \(-0.37\) (0.20) & \(-0.26\) (0.15) \\  & T4M & \(-1.10\) (0.78) & \(-0.68\) (0.62) & \(-0.43\) (0.34) & \(-0.28\) (0.28) \\ \hline \multirow{3}{*}{School boundary} & W2M & \(-3.11\) (1.23) & \(-1.10\) (0.47) & \(-0.54\) (0.38) & \(-0.28\) (0.28) \\  & W4M & \(-8.47\) (2.97) & \(-3.30\) (0.55) & \(-1.44\) (0.46) & \(-0.71\) (0.25) \\ \cline{1-1}  & T2M & \(-1.45\) (0.56) & \(-0.83\) (0.42) & \(-0.54\) (0.28) & \(-0.35\) (0.19) \\ \cline{1-1}  & T4M & \(-1.78\) (0.77) & \(-0.95\) (0.51) & \(-0.55\) (0.40) & \(-0.36\) (0.22) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Change rate of PM\({}_{2.5}\) concentration by the school building floor for each case compared to the CNTL case (%). The parentheses indicate the standard deviations of the PM\({}_{2.5}\) concentration calculated for 16 inflow directions. the northwest (south) school buildings, resulting in westerly (southerly) flows around the northwest (south) school ground. Upward flows appeared due to convergence of the opposite flows (westerly and southerly) in the school ground. The PM\({}_{2.5}\) concentrations in the upward flow regions were relatively low. In the T4M case, the trees in the school ground greatly decreased the horizontal wind speeds due to drag, resulting in a shift of the flow convergence region to the southeast region. The PM\({}_{2.5}\) concentration in the north school ground increased as the upward flow weakened. The PM\({}_{2.5}\) concentration in the south school ground decreased in the upward flow region because the number of transported pollutants from the background to the surface decreased due to the upward flows.