# Improving PM2.5 Concentration Forecast with the Identification of Temperature Inversion
## 4 Experimental Results and Comparative Performances
### Pm\({}_{2.5}\) Concentration Estimation
CNN showed the best MAE result with six days in 2018 and 2019, while AllNormal gave the best 2019 MAE performance when the length of short-term training was set to five days. Considering the overall comparative performances, a seven-day short-term training dataset was employed in our models. (2) In most cases, Expert, CART and CNN outperformed AllNormal and AllTemp on both RMSE and MAE, meaning that the classification of the test day for temperature inversion did improve the performance of the subsequent PM\({}_{2.5}\) forecast. If we compare the mean performance of Expert, CART and CNN, which consider the temperature inversion, to that of AllNormal, the forecast error was reduced by 4-9% and 2-7% in terms of RMSE and MAE. The improvement made by temperature inversion classification was significant. (3) It can be seen that AllNormal surpassed AllTemp on all cases in terms of both RMSE and MAE. This was because the number of days deemed to be under temperature inversion phenomenon was less than one third of all days in the entire year, and AllNormal made more correct classifications than AllTemp and thus obtained better forecast results. (4) It is natural to assume that the forecast assisted by human experts is likely to be superior to that by CART or CNN, because we consider the results of experts as our ground-truth values. This assumption is quite true in 2018 and 2019, but if we look at the forecast result in 2017, CNN makes the best forecasts, while CART and Expert are comparable. With a further investigation, we found that in 2017 Puli township had significantly more pollution days than in 2016, 2018 and 2019. Some of the pollution days were due to external sources instead of temperature inversion as will be noted. These cases incurred large forecast errors for the experts. On the contrary, CART and CNN were not perfect classifiers like Expert; they sometimes misclassified external sources as temperature inversion, which unexpectedly resulted in a better forecast. However, we cannot consider CART and CNN as better classifiers than Expert just based on 2017 results because the Expert was the ground-truth for training the classifiers. The reason for employing CART and CNN was that they can reduce the manual effort of experts labeling the records, and make the recognition of temperature inversion automatic. One of the typical events caused by external pollutions was on 10 March 2017. We observe there existed a high correlation between the pollution events in Puli and Lunebi (see Figure 3a). Lunebi is near to a large petrochemical complex and it is 65 km southwest of Puli. A river goes between the two townships and forms a potential tunnel for pollution transportation. Table 5 shows the hourly PM\({}_{2.5}\) concentration (\(\mu\)g/m\({}^{3}\)) for both townships and the wind speeds (m/s) and wind directions (in 360 degrees) observed at Lunebi in the same day. It is seen that the PM\({}_{2.5}\) concentration measured at Lunebi rose since from hour 0 and reached its daily high 119 \(\mu\)g/m\({}^{3}\) at hour 9. It then gradually decreased to normal at hour 17. The PM\({}_{2.5}\) concentration measured at Puli showed similar trends but with a time lag of about 10 h. The concentration rose from hour 14 and reached its daily high of 127 \(\mu\)g/m\({}^{3}\) at hour 20 and 21. It remained above 100 \(\mu\)g/m\({}^{3}\) until midnight. The main wind direction observed at Lunebi during hour 10 and hour 12 was west or southwest with speeds between 0.9 and 2.2 m/s. If we divide the straight distance (65 km) between the two townships by the time lag (10 h), the transportation speed is 1.64 m/s, which is close to the wind speed during the same period. Actually, the transportation speed was a bit higher than 1.64 m/s since the river valley is a curved route, so the two phenomena highly coincided with each other.