# Finding Optimal Stations Using Euclidean Distance and Adjustable Surrounding Sphere
## 4 Proposed Methods
### Euclidean Distance + Fixed Surrounding Sphere (ED + FSS)
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & 4 Stations & 5 Stations & 6 Stations & 7 Stations \\ \hline M3: ED + FSS & & & \\ \hline  & COV: 76\% & COV: 87\% & COV: 91\% & COV: 94\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Location of stations within the cities and coverage percentage. has a higher coverage percentage and is better than M3: ED + FSS. Clearly, M4: ED + ASS is better than M3: ED + FSS to better cover the percentage and balance of stations. #### 6.2.4 Flexibility to Apply Our Methods for Different Cities

The M4: ED + ASS shows good spatial coverage and balance of stations based on a specified number of stations. For this section, we compared our method's capability to apply to different sizes of cities and evaluated balancing and distribution of the stations in cities. We used M3: ED + FSS and M4: ED + ASS in Bangkok, Sejong, and Bonn. The cities in that list are in descending order by size. Table 6 (bkk-1), (sj-1), and (bo-1) shows the existing stations and current coverage percentages. There are twelve stations in Bangkok, four stations in Sejong, and one station in Bonn. The result of M3: ED + FSS in Table 6 (bkk-2) shows an imbalance of stations. On the other hand, the stations from M4: ED + ASS in Table 6 (bkk-3) are evenly distributed over the city. One benefit of balancing locations and overlapping areas is that the network can better support the future urban expansion and provide better air pollution monitoring. Although in Table 6, (sj-3) and (bo-3) cannot clearly show the balancing of stations when compared with Table 6 (sj-2) and (bo-2), the COV values of M4: ED + ASS are higher than M3: ED + FSS and show significantly increased rates of 56%, 22%, and 37%, in Bangkok, Sejong, and Bonn, respectively. These results allow us to conclude that our M4: ED + ASS is more flexible than M3: ED + FSS for designing new station networks in any city size. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Country/Methods** & **Bangkok, Thailand** & **Sejong, Korea** & **Bonn, Germany** \\
**(1568.7 km\({}^{2}\))** & **(465.23 km\({}^{2}\))** & **(141.06 km\({}^{2}\))** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Locations of stations within the cities and coverage percentages: (bkk-1), (sj-1), (bo-1) depict current stations, (bkk-2), (sj-2), (bo-2) depict station networks using M3: ED + FSS, and (bkk-3), (sj-3), (bo-3) depict station networks improved using M4: ED + ASS, in Bangkok, Sejong, and Bonn, respectively. ### Assessment of Scenario 2: Finding Additional Stations to Improve the Current Network

For this section, we applied M4: ED + ASS to add one station into the network. Then, we evaluated the results with our proposed criteria: COV and WCD. In Table 7, triangle symbols indicate the existing stations, and star symbol indicates the additional station. The additional stations show the performance of our proposed method and evaluation criteria. They can improve coverage percentages by 39%, 34%, and 130% in Bangkok, Sejong, and Bonn. One of the key limitations of our study is the appropriate ratio of spatial coverage satisfaction versus confidence area. As shown in Figure 8, the dashed line plot graph compares coverage percentage and the number of stations. The 6 th stations show the most coverage percentage of 90%. Increasing the number of stations from 7 up to 12 does not significantly increase coverage. Thus in future work, a change of strategy is needed after achieving the spatial coverage to increase the overlapped regions. ## 7 Conclusions

Increasing spatial coverage of AQMN gives effective environmental management. Especially in setting up a network in cities that lack historical pollution data, adding stations in cities with an existing network that face urbanization can make it challenging to design adequate spatial coverage and effective AQMN. Our experimental results proved the ability of the proposed method to provide maximum spatial coverage based on a given number of stations. The results showed that ED + ASS achieved effectiveness both in