## 4 Experimental Result and Discussion
### Case Study and Analysis  
(1) Beijing  
Figure 3 presents the concentration variation of six pollutants and corresponding air quality evaluation results (chief pollutant and level) of Beijing in four seasons. Combined pollution is common in Beijing and O\({}_{3}\) is dominant in late spring, summer and early autumn. Regional pollution transport and local traffic pollution make PM\({}_{2.5}\) and NO\({}_{2}\) major air pollutants throughout the year, while PM\({}_{10}\) is more notable in spring mainly from dust transport upstream. In general (Figure 3), there is an increase in daily concentration during weekends and holidays, which can be attributed to the strict traffic restriction on weekdays and celebration fireworks during festivals. For hourly concentration (Figure 4A-D), ozone has one peak in the period from 14:00 to 16:00 every day, while two peaks at 8:00 and 20:00 are apparent for other pollutants, which are in accordance with traffic peaks. Referring to pollutant concentration (Figure 3), it is clear from evaluation results that the AQFCE accurately reflects pollution features and trends under different pollution conditions (lighter pollution, heavier pollution, pollution process), and it is sensitive to sudden and significant changes of concentration. As a statistical indicator, the Consistent Rate (CR) and Kendall Correlation Coefficient (T) are applied to compare the AQI with AQFCE on chief pollutants and air quality level (ordered categorical variable). Furthermore, specific examples will provide empirical support for the comparative analysis. For daily reports (Figure 3), the CR between the AQI and AQFCE are 82.47% and 58.08% on chief pollutant and air quality level, respectively. The chief pollutant has an important purpose and significantly influences the subsequent evaluation on air quality level. So, accurate identification of the chief pollutant is the premise of air quality evaluation, and both methods have high consistency on this point. In view of their middle consistency of level, differences are further analyzed by specific examples. On 2 March 2019 (Figure 3), concentration values of SO\({}_{2}\), NO\({}_{2}\), CO, O\({}_{3}\), PM\({}_{2.5}\) and PM\({}_{10}\) were 3, 14, 0.4, 77, 40 and 157, which means values of five pollutants are far below or close to the limit of I and one pollutant's value is close to the limit of II. The AQI and AQFCE determine the same chief  
Figure 4: Hourly pollutant concentration variation and air quality evaluation result of chief pollutant and level of Beijing. For hourly reports (Figure 4A-D), the incomplete criterion of the AQI is really a problem for not only the comparison but also AQI's own evaluation. This is because in the hourly report of the AQI PM\({}_{2.5}\) and PM\({}_{10}\) use daily criterion while other pollutants use hourly criterion, which is unreasonable. This leads to an exaggerated hazard of PM\({}_{2.5}\) and PM\({}_{10}\), and they are more likely to be chosen as chief pollutants even if they are not the biggest hazard. The AQI's level is decided by the chief pollutant alone, so a questionable chief pollutant may give a meaningless air quality level. Experimental results prove this and there are antinomies in the results of the AQI. For example, on 23 October 2018, the chief pollutant of the hourly report was PM\({}_{10}\) in every hour but the daily report's chief pollutant was NO\({}_{2}\), which is contradictory. The AQFCE is complete in hourly reports, and there is a marked drop of CR compared with the daily report as expected--63.04% and 45.49% for the chief pollutant and level. PM\({}_{2.5}\) and PM\({}_{10}\) without hourly criterion really disturb the comparison, but CR increase significantly to 89.74% and 97.39%, respectively, after eliminating their influence, which means AQI with appropriate concentration limits is similar to the AQFCE. Actually, an hourly report of the AQI is severely affected by its criterion, and the AQFCE is robust for use in various tasks.