# A Spatial-Temporal Approach for Air Quality Forecast in Urban Areas
## 4 Experimental Evaluations
### Performance  
To show the performance of our proposed approach, we modified two methods based on two well-established measurements and tried some simple methods. The first was the  
Figure 12: Comparison of the best \(r\) and \(s\) combinations.  
Figure 13: PM2.5 RMSE of different parameters of \(n\).  
PCC-based method. The temporal weather similarity was calculated using PCC instead of using recent and similar references. The idea was that the PM2.5 time series was highly correlated to the weather conditions. Hence, the first method modified PCC to calculate weather similarities between the historically continuous 48 h and the target 48 h. The PM2.5 time series of the continuous 48 h with the highest weather similarity in the historical data would be extracted to forecast the target PM2.5. Due to the air quality being continuous data, the forecast value would increase or decrease based on the variety of the extracted PM2.5 time series, instead of the value of the extracted PM2.5 time series. To compare this method, we also tried to forecast using the extracting continuous 48 h PM2.5 in historical data randomly. For the second, IDW-based method, we used IDW to average the forecast time series value for the spatial inference. The temporal inference of this method and our approach was the same, but this method selected six nearby devices around the target device, selected as in Section 4.2.2 and used IDW to average the PM2.5 values as the final forecast result of PM2.5. To check our method, we did not require too many parameters, \"r\" and \"s\", and it was forecasted using the mean weather. The results of the mean weather are shown below. We also tried to compare this with the results of the forecast from the same hour over the previous 90 days. Figure 14a shows the results of different methods in terms of RMSE and MAE. Our method was better than other methods used. Figure 14b shows the RMSE of the methods for each forecasted hour. The result shows that our proposed approach can converge and stably forecast future hours. However, after about 30 h, the 90-day results narrowly win. In Figure 14c, results from different days are compared. The results are better when they refer to more days, and the results converge within 30 to 90 days. In Figure 14d, except the result from the afternoon, our results were more accurate for more periods, and the results show that the PM2.5 in the afternoon is harder to forecast.  
The acceptable error of PM2.5 forecast is introduced. Table 2 shows the grade of PM2.5 from Environmental Protection Administration Executive Yuan (R.O.C.). Given that the range of each grade is different (Table 2), the acceptable error is different in each grade. In  
Figure 14: Evaluation of the PM2.5 forecast error for (**a**) different methods in RMSE and MAE, (**b**) different methods in various hours, (**c**) different days methods in various hours, and (**d**) different methods in various hours in days.  
Figure 15, the bar is the standard deviation (STD) of our results in each grade. PM2.5 in data are within 150, so there are no data in grade \"Very Unhealthy\". This shows that our results are within the acceptable error in each grade.