# A Spatial-Temporal Approach for Air Quality Forecast in Urban Areas
## 4 Experimental Evaluations
### Impact on Various Parameter Settings
#### 4.2.1 Temporal Parameter  
First, we tested the temporal parameters. This experiment tested the recent data amount (\(r\)) and similar data amount (\(s\)) only. The correlation between parameter \(r\) and PM2.5 forecast at the 6 th, 12 th, 24 th, 36 th, and 48 th hours are shown in Figure 8. The x-axis is parameter \(r\), and the y-axis is the RMSE of the PM2.5 forecast value. It is obvious that as \(r\) becomes larger, the RMSE of PM2.5 value becomes better at the 12 th, 24 th, 36 th, and 48 th hours. However, the degree of decline in RMSE is also small. For the PM2.5 forecast at the 24 th hour, as \(r\) increases from 1 to 30, the RMSE of PM2.5 is only reduced by about 1.5 \(\mathrm{\SIUnitSymbolMicro g}/\mathrm{m}^{3}\). As \(r\) becomes larger, the degree of decline was considered to converge. However, the trend of the 6 th hour is opposite to the other curves in the figure. As \(r\) became larger, the RMSE at the 6 th hour became larger. Air quality is usually highly similar to the last observed value because air quality is continuous data. This is the reason why the RMSE was smaller when there were only recent data selected. In addition, as the forecasting time was further away, the RMSE became larger. Therefore, the farther the forecast hour, the harder it is to forecast. Figure 7: Distribution of AirBoxes and weather stations in or around Taipei. Figure 9 shows the performance of parameter \(s\). The degree of convergence of RMSE is more pronounced than it is with \(r\). However, the RMSE is greater when \(s=1\) than when \(r=1\). When they are both 30, RMSE is better than \(r\). In addition, the degree of decline of a similar reference is greater than the recent reference. This indicates that parameter \(s\) is beneficial for the PM2.5 forecast. According to the experimental results, it was determined that the RMSE results of the forecast results are close every hour. When the forecast is further apart, the reference value of \(r\) becomes smaller, but \(s\) is more decisive. While \(s\) may include recent data, it is possible to select long-term data from the history. This tells us that, when the forecast hour is further away, the RMSE will become larger if we only use similar reference data. Figure 10 shows the experimental results when parameters \(r\) and \(s\) are set to the same value. As the number of references increases, we can see that the RMSE improves and the degree of decline also converges. It is worth noting that the 6 th hour of the RMSE does not improve as the number of references increases. When \(r\) and \(s\) are greater than 7, the RMSE becomes even worse. According to the experimental results, we found that it only takes a few \(r\) to forecast the first 6 th hour, and the RMSE will perform very well. This shows the different combinations of parameters, from 0 to 30, at the 6 th, 12 th, 24 th, 36 th, and 48 th h, in Figure 11. We can see that the RMSE at the 12 th, 24 th, 36 th, and 48 th h becomes smaller as the parameters increase and the convergence is also obvious. The results from the 6 th hour show that it can perform well when there is only one recent reference. When the parameter is larger, its RMSE will not improve. We can see that the impact of recent data is better than the impact of similar data at the 6 th and 12 th h. Similar references performed well at the 24 th, 36 th, and 48 th h. This tells us that the recent reference is more useful in forecasting the most near future time. When we forecast further than an hour into the future, similar references are more important than recent data. Figure 11 shows that when recent and similar reference data are both used for forecasting, the RMSE of the PM2.5 forecast value is better than when only using one of them. Figure 8: The impact on PM2.5 error of parameter \(r\) on the PM2.5 value forecast. Figure 9: The impact on PM2.5 error of parameter \(s\) on PM2.5 value forecast.