# An Ambient Air Quality Assessment Model Based on Improved Evidence Theory

### Data

To validate the performance of the proposed DCreWeight model, select hourly air pollution data for Xi’an from June 1, 2014 to May 1, 2016. Years are randomly selected. In this article, null values ​​are treated using the linear interpolation method. According to the proposed DCreWeight model, the results of the one-day comprehensive air quality assessment are as follows (see Fig. 2).

### Evaluation indicators

1. (1)

AQI-based assessment indicators

National AQI standard (HJ633-2012[Z]) describes the level of air quality. The AQI standard states that the highest pollutant concentration determines the level of air quality. It highlights the contribution of a pollutant. Equation (20) shows the calculation of the AQI. It sets 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 the pollutant P.

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

Defined AQI_MAE, AQI_RMSE and AQI_an agreement index as evaluation indicators. The above assessment indicators based on the 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)

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

(23)

where n is the number of samples, (y_{i}) is the real value of the AQI of the ith day, (Salvation}) is the evaluation result of a model.

1. (2)

Evaluation indicators based on the AQCI

The national AQCI takes into account the overall impacts of several pollutants on air quality. It highlights the contribution of six pollutants. AQCI is shown in the equation. (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).

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

### Analysis and comparison of valuation methods

Take the national AQI and AQCI as the pollution standards. Comparisons of the DCreWeight model with the D–S, KCre-Sun, Hybrid-Rule and FSE models are shown in Fig. 4. For clarity of the image, select four months from June 1, 2014 to March 31, 2015, which can represent approximately 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 PMten were primary pollutants during 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’s because the low light made O3 the concentration decreased and the combustion of coal for heating increased SO2 in winter. This is because weak light reduces the O3 concentration while burning coal for heating increases SO2 focus in winter. Take the national AQI and AQCI as the pollution standards, the assessed air quality levels of the D–S, KCre-Sun, Hybrid-Rule and FSE methods are mostly lower than the AQI. The evaluated results of the above models deviate significantly 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 agreement index, AQCI_MAE, and AQCI_RMSE as evaluation indicators. The results of the comparison of the performance of the evaluation methods according to the AQI and AQCI standards are presented in Fig. 5.

According to Figure 5, the DCreWeight model has the minimum MAE, RMSE according to AQI and AQCI standards and its agreement index 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 was validated based on air pollutant data in Xi’an in the section “Analysis and comparison of assessment methods”. To better verify whether the model is suitable for other assessments of urban air quality, we also selected 2014 hourly air pollution data from June 1, 2014 to May 31, 2015, in Shanghai and in Beijing. Initially, the null data was processed by the linear interpolation method. Next, we applied the DCreWeight model to the two cities and compared the air quality between Shanghai and Beijing according to national AQI and AQCI standards.

Figure 6 shows the assessment results of the DCreWeight model in summer, from June 1, 2014 to June 31, 2014. The left vertical axis represents the air quality assessment level and the right vertical axis represents the AQCI value. The national AQCI represents the overall degree of pollution. To clearly verify the accuracy of the DCreWeight model, sort the days by AQCI.

According to Figure 6, the AQI level fluctuates as the AQCI value decreases. Indeed, the AQI level depends on the individual pollutants. However, with the decrease in AQCI, the evaluation results of the DCreWeight model essentially decrease in steps. It indicates that the model assessment is consistent with the actual global pollution. Compared to the AQCI, the proposed model describes air quality levels more intuitively.

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