# An ambient air quality evaluation model based on improved evidence theory

### Data

To validate the performance of the proposed DCreWeight model, select hourly air pollution data in Xi’an from June 1, 2014, to May 1, 2016. The years are randomly selected. In this paper, the null values ​​are processed using the linear interpolation method. According to the proposed DCreWeight model, the comprehensive air quality evaluation results on a day are as follows (see Fig. 2).

### Evaluation indicators

1. (1)

Evaluation indicators based on AQI

The national AQI standard (HJ633-2012[Z]) describes the air quality level. AQI standard denotes that the highest pollutant concentration determines the air quality level. It highlights the contribution of one pollutant. Equation (20) shows the calculation of AQI. It defines the concentration limits [BPLo, BPHi] and IAQI limits [IAQIHi, IAQILo].

$${ text {AQI}} = { text {max}} left ({ left ({{ text {IAQI}} _ {{{ text {Hi}}}} – { text {IAQI }} _ {{{ text {Lo}}}}}} right) * left ({{ text {C}} _ ​​{{ text {P}}} – { text {BP}} _ { {{ text {Lo}}}}} right) / left ({{ text {BP}} _ {{{ text {Hi}}}} – { text {BP}} _ {{{ text {Lo}}}}} right) + { text {IAQI}} _ {{{ text {Lo}}}}} right)$$

(20)

where CP is the concentration of pollutant P.

Taking the national AQI as the pollution standard, the indicator MAE, RMSE and an index of agreement can be calculated to analyze the performance of evaluation models. Count the number of days when AQI is equal to the evaluation level of models, and define it as right_num.

Defined AQI_MAE, AQI_RMSE and AQI_an index of agreement as evaluation indicators. The above evaluation indicators based on AQI can be calculated as follows:

$${ text {AQI}} _ { text {MAE}} = frac {1} {n} mathop sum limits_ {i = 1} ^ {n} left ({h_ {i} – y_ {i}} right)$$

(21)

$${ text {AQI}} _ { text {RMSE}} = sqrt { frac {1} {n} mathop sum limits_ {i = 1} ^ {n} left ({h_ {i} – y_ {i}} right) ^ {2}}$$

(22)

$${ text {AQI}} _ { text {an}} ; { text {index}} ; { text {of}} ; { text {agreement}} = frac {{ { text {right}} _ { text {num}}}} {n}$$

(23)

where n is the number of samples, (y_ {i} ) is the actual AQI value of the i-th day, (h_ {i} ) is the evaluation result of a model.

1. (2)

Evaluation indicators based on AQCI

The national AQCI considers the comprehensive impacts of multiple pollutants on air quality. It highlights the contribution of six pollutants. AQCI is shown in Eq. (24).

$${ text {AQCI}} = { text {sum}} left ({{ text {C}} _ ​​{{ text {P}}} / { text {S}} _ {{ text {P}}}} right)$$

(24)

where SP is the second concentration limit of pollutant P in the Ambient Air Quality Standards (GB 3095-2012).

Taking the national AQCI as the pollution standard, the indicator AQCI_MAE and AQCI_RMSE can be calculated by Eqs. (21) and (22) in the same way.

### Analysis and comparison of evaluation methods

Take national AQI and AQCI as pollution standards. The comparisons of the DCreWeight model with the D – S, KCre-Sun, Hybrid-Rule, and FSE models are in Fig. 4. For the clarity of the image, select four months from June 1, 2014 to March 31, 2015, which can roughly represent four seasons. Spring is represented by March. Summer represented by June. Autumn is represented by September. Winter is represented by December.

According to Figs. 3 and 4, the air pollution situations were Winter> Spring> Summer> Autumn. PM2.5 and PM10 were primary pollutants in the four months. In Winter, the weight of SO2 was greater than that of O3. But in the other three months, it was smaller than that of O3. It is because that the weak light made O3 concentration decreased, and coal burning for heating made an increase of SO2 in Winter. It is because the weak light reduces the O3 concentration while coal burning for heating increases SO2 concentration in Winter. Take national AQI and AQCI as pollution standards, the evaluated air quality levels of D – S, KCre-Sun, Hybrid-Rule, and FSE methods are mostly lower than AQI. The evaluated results of the above models deviate greatly from the AQI and AQCI, while the evaluated results of the DcreWeight model are closest to the national AQI and AQCI.

To validate the superiority of the models, take AQI_MAE, AQI_RMSE, AQI_an index of agreement, AQCI_MAE, and AQCI_RMSE as evaluation indicators. The performance comparison results of the evaluation methods under the AQI and AQCI standards are shown in Fig. 5.

According to Fig. 5, the DCreWeight model has the minimum MAE, RMSE under the AQI and AQCI standards and its index of agreement is the highest, which is superior to the D – S, KCre-Sun, Hybrid-Rule, and FSE methods .

### The application in Shanghai and Beijing

The superiority of the model has been validated according to air pollutants data in Xi’an in “Analysis and comparison of evaluation methods” section. In order to better check whether the model is suitable for other urban air quality assessments, we also selected hourly air pollution data from 2014 from June 1, 2014, to May 31, 2015, in Shanghai and Beijing. Firstly, the null data were processed using the linear interpolation method. Then, we applied the DCreWeight model to the two cities and compared the air quality between Shanghai and Beijing under the national AQI and AQCI standards.

Figure 6 shows the evaluation results of the DCreWeight model in Summer, from June 1, 2014, to June 31, 2014. The left vertical axis represents the air quality evaluation level, and the right vertical axis represents the AQCI value. National AQCI represents the comprehensive pollution degree. To clearly check the accuracy of the DCreWeight model, sort the days according to AQCI.

According to Fig. 6, the AQI level fluctuates as the AQCI value decreases. This is because the AQI level depends on individual pollutants. However, with the decrease of AQCI, the evaluation results of the DCreWeight model basically decline in steps. It indicates that the evaluation of the model is in line with the actual comprehensive pollution. Compared with AQCI, the proposed model describes air quality levels more intuitively.

Next, compare the air quality between Shanghai and Beijing, as shown in Fig. 7.