J. Meteor. Res.  2019, Vol. 33 Issue (2): 236-250 PDF
http://dx.doi.org/10.1007/s13351-019-8145-7
The Chinese Meteorological Society
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Article Information

MA, Minjin, Yue CHEN, Fan DING, et al., 2019.
The Representativeness of Air Quality Monitoring Sites in the Urban Areas of a Mountainous City. 2019.
J. Meteor. Res., 33(2): 236-250
http://dx.doi.org/10.1007/s13351-019-8145-7

Article History

in final form December 26, 2018
The Representativeness of Air Quality Monitoring Sites in the Urban Areas of a Mountainous City
Minjin MA1, Yue CHEN1, Fan DING2, Zhaoxia PU3, Xudong LIANG4
1. College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000, China;
2. College of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, China;
3. Department of Atmospheric Sciences, University of Utah, Salt Lake City, UT 84112, USA;
4. State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China
ABSTRACT: Lanzhou is a typical mountainous city with severe air pollution in northwestern China. This study uses hourly observational data of air pollutants at five air quality monitoring sites in Lanzhou from July to December 2015 to discuss data quality control and the representativeness of the monitoring sites (four urban sites and one suburban site). A fuzzy matrix is applied to study primary air pollutants. The results show that of the six routinely monitored pollutants, the primary pollutant is PM10 during the study period. Based on lag correlation analysis and one-way analysis of variance, it is concluded that there are redundant observations at the four urban sites for the timely diffusion and transport of air pollutants from the same general area. The coefficient of divergence (COD) method is then used to evaluate the spatial distribution differences, and the primary air pollutant PM10 shows differences at each site. COD can be used as a positive indicator to describe site representativeness. To evaluate the overall air pollution in the valley, correlation analysis is performed between the PM10 concentration retrieved from aerosol optical depth satellite data and the concentration from the four urban monitoring sites. Among these, the correlation between the workers’ hospital site data and the retrieval data is the highest, passing the 90% confidence level. A new representative evaluation model for air quality monitoring sites, Rs = 0.77COD + 0.23Rretrieval, is established by using COD and correlation coefficients between routine observations and satellite retrieval products. From this model, it can be concluded that the biological products institute site in Lanzhou is the most representative site for the evaluation of air pollution out of the four urban air quality monitoring sites from July to December 2015.
Key words: mountainous cities     air quality monitoring     site representativeness
1 Introduction

Urban air pollution is an important issue affecting economic development and human health, and its assessment requires accurate data. Air quality monitoring is a direct observational method for obtaining air pollutant concentration data. An air quality monitoring network was established in the mid-1970s in China, and the National Ambient Air Quality Monitoring Network based on urban sites was established by the mid-1980s to provide data support for air pollution studies. However, most cities had only a “five-day method” of monitoring, and it was difficult to provide full and accurate data to reflect the distribution and transmission of regional air pollution, as data were updated very infrequently, the layout of the monitoring sites did not conform to scientific normative standards, and the observational coverage and representativeness of the sites were insufficient (Zhong et al., 2007). With taller urban buildings and the expansion of urban areas, observational conditions have changed and the representativeness of observational data from air quality monitoring sites has become an important issue in data quality control (Ott and Eliassen, 1973; Chan and Hwang, 1996; Liu et al., 2015). Owing to the continuous heavy air pollution in urban areas in recent years in China and the increased demand for monitoring data for urban studies (Yuan et al., 2009; Gao et al., 2014), the Ministry of Environmental Protection has increased the number of air quality monitoring sites to 1436, covering 367 cities across the country. This raises the question of whether the coexistence of monitoring sites in a city could lead to overlapping information in site observations; therefore, the representativeness of monitoring sites for urban air quality is still an important research topic.

Lanzhou, a base for the heavy chemical industry in northwestern China, has some of the most serious air pollution in China (Yang and Chen, 2002), partly because of its topography. Lanzhou is located in a narrow valley basin surrounded by mountains to the north and south, forming a semi-closed dumbbell. It is a typical valley city with heavy pollution incidents, and particulate matter is the primary pollutant mainly in winter and spring. Among these incidents, those occurring in spring are characterized by a “steep peak” and are related to dust (Wei et al., 2006; Tao et al., 2007; Liu et al., 2012), and in winter are characterized by “slow accumulation” (Liu et al., 2006), caused mainly by local particular meteorological conditions. The heaviest O3, CO, and NOx pollution occurs in winter in Lanzhou (Wang et al., 1994). Compared with Nanjing, Wuhan, Guangzhou, and Chongqing, the level of particulate matter < 2.5 μm and < 10 μm (PM 2.5 and PM10) pollution in Lanzhou is significantly higher in winter (Liu et al., 2006). The meteorological conditions are characterized by low wind speed and a stable atmosphere, which are not conducive to the spreading of air and vertical turbulence, resulting in the continuous accumulation of local source emissions that are likely to cause serious air pollution (Zhao et al., 2015). The topographic barriers and valley circulation have important effects on the air pollution in the valley (Ren and Li, 1978; Shi, 1980; Hu and Zhang, 1999; Zhang, 2001; Xie et al., 2010). However, urbanization is an important cause of air pollution, because of the rapid continuous expansion of the urban canopy and the continually increasing population. It is a challenge for urban air quality monitoring to reflect these changes. Before 2012, there was only one air quality site (Lanlian hotel site) that collected daily data, and four sites (workers’ hospital site, railway design institute site, biological products institute site, and Yuzhong campus of Lanzhou University site) that collected weekly data. After the issuance of the “national environmental air monitoring network (prefecture level or above) scheme” by the Ministry of Environmental Protection in 2012, five air quality monitoring sites were set up for hourly monitoring of six pollutants (PM2.5, PM10, CO, NO2, SO2, and O3); four of these sites (workers’ hospital site, Lanlian hotel site, railway design institute site, and biological products institute site) are in the most urban areas of the city, and the other site (Yuzhong campus of Lanzhou University site) is in the suburbs. These five automatic air quality monitoring sites provide observational data to support air pollution studies, alleviating the past problem of a lack of data. However, due to the proximity of these sites, there may be redundancy in the synchronous observational data. In addition, the spatial representativeness of the observational data at a given site and the relationships among the site observations are important topics for discussion.

Previous studies have shown that PM10 is the primary pollutant influencing urban air quality, especially in most incidents of continuous heavy pollution (Chan and Yao, 2008; Chen et al., 2010; Yu et al., 2010, 2012; Zhai et al., 2015; Zhang et al., 2017). Much research has been based on observational data taken directly from monitoring sites to analyze air pollution in a city (Kong and Kong, 2017), but the difficulty is in choosing one representative monitoring site among several. As a whole, satellite remote-sensing data can better reflect polluting particulate matter in a city than can local observations at a single site. Normally, the correlation between routine monitoring data and high-precision satellite remote-sensing data is used to evaluate the environmental representativeness of a monitoring site. A series of studies used the relationship between multi-scale, wide-range, and good temporal-resolution MODIS remote-sensing data and observational site data to evaluate the representativeness of the site observations (Liu et al., 2014; Wang et al., 2014, 2017; Chen et al., 2016; Zheng et al., 2017). Considering the problem of redundant observations among urban air quality monitoring sites and the application of high-precision satellite products, a new model to evaluate site representativeness is established in this study to provide a theoretical reference for the layout of urban air quality monitoring sites.

2 Data and methods 2.1 Data

The air pollutant concentration data used in this study are the hourly observational data from five monitoring sites in Lanzhou from July to December 2015, issued by the Ministry of Environmental Protection. According to the “Technical Specification for Location Monitoring of Ambient Air Quality (Trial)” (HJ 664-2013, The Ministry of Environmental Protection, 2013), there are five air quality monitoring sites in Lanzhou (Fig. 1), four of these are in the most urban areas—the workers’ hospital site (WH), Lanlian hotel site (LH), railway design institute site (RD), and biological products institute site (BP)—and one is a background site in the suburbs, on the Yuzhong campus of Lanzhou University (YC). The four pollution monitoring sites in the urban areas are the main focus of this study, with the background site (YC) as a contrast.

 Figure 1 Terrain and distribution of five study sites in Lanzhou. RD: railway design institute site; BP: biological products institute site; LH: Lanlian hotel site, WH: workers hospital site; YC: Yuzhong campus of Lanzhou University.

Terrain data with a resolution of 0.00417° × 0.00417° are the global high-precision Sandwell and Smith terrain data developed by the Scripps Institute of Oceanography at the University of California. The PM10 data are interpolated by the four sets of MODIS secondary products (MYD08_D3 v6): Terra Aerosol Optical Depth 550 nm (Dark Target), Terra Aerosol Optical Depth 550 nm (Deep Blue, Land-only), Aqua Aerosol Optical Depth 550 nm (Dark Target), and Aqua Aerosol Optical Depth 550 nm (Deep Blue, Land-only), with a time resolution of 1 day and a spatial resolution of 1° × 1°.

2.2 Methods

Statistical and objective analyses are applied to analyze the characteristics of air pollutant distribution and variation in Lanzhou. The methods are outlined in Fig. 2 and below.

 Figure 2 Analysis process flow chart.

(1) Fuzzy evaluation model. Qualitative evaluation is transformed into quantitative evaluation by the concept of membership in fuzzy mathematics. It is an overall assessment of an object that is subjected to multiple factors at the same time.

There are six routinely monitored pollutants: PM2.5, PM10, CO, NO2, SO2, O3 (1 h), and O3 (8 h). Although there are two O3 measurements, only the 8-h O3 concentration is considered in the representative analysis of the primary pollutants. According to the data validity rule of Ambient Air Quality Standard (GB3095-2012, The Ministry of Environmental Protection, 2012) (hereinafter abbreviated as standard), the amount of available data used to calculate the daily average must be greater than 20 in one day; therefore, the collected data from the five monitoring sites in Lanzhou are screened and the daily averages of the six pollutants are calculated as indexes in a factor set U = {u1, u2, …, u6}, n = 6. The ambient air functional areas are divided into two types of districts: a nature reserve area (district I) and a mixed commercial, transportation, and residential area (district II). The limits of the daily pollutant concentration of the six routinely monitored pollutants in the quality requirement of the standard are selected as an evaluated level set L = {l1, l2}, m = 2, where the first level is for district I, and the second level is for district II. The limits of the pollutant concentrations at two levels (the first class and the second class) are given in the Appendix (Table A1). Based on this, a relative deviation fuzzy matrix R is established, where the element is ri, j (i = 1, 2, …, 6; j = 1, 2), and its expression is:

Table A1 Concentration limits for basic items of ambient air pollutants
 Sequence number Pollutant Average time Concentration limit Unit First class Second class 1 SO2 Annual mean 20 60 μg m–3 24-h average 50 150 1-h average 150 500 2 NO2 Annual mean 40 40 24-h average 80 80 1-h average 200 200 3 CO 24-h average 40 4 mg m–3 1-h average 10 10 4 O3 Daily maximum 8-h average 100 160 μg m–3 1-h average 160 200 5 Particulate matter (PM10) Annual mean 40 70 24-h average 50 150 6 Particulate matter (PM2.5) Annual mean 15 35 24-h average 35 75

j = 1,

 ${r_{i, 1}} = \left\{ {\begin{split} & \;\;{1, \quad\quad\quad\quad \quad\quad\quad \;\;\;\;\;\;\;\;{x_i} < {s_{i, 1}}} \\ & \;\; {\dfrac{{{s_{i, 1}} - {x_i}}}{{{s_{i, 1}} - {s_{i, 2}}}}, \quad\quad\quad {s_{i, 1}}\; \leqslant {x_i} < {s_{i, 2}}} \\ & \;\; {0, \quad \quad\quad\quad \quad\quad\quad\;\;\;\;\;\;\;\;{x_i} \geqslant {s_{i, 2}}} \end{split}} \right. ;$ (1)

j = 2,

 {r_{i, 2}} = \left\{ {\begin{align} & \;\; {0, \quad\quad\quad \quad\quad\quad \quad\;\;\;\;\;\;\;\;{x_i} < {s_{i, 1}}} \\ & \;\; {\dfrac{{{s_{i, 2}} - {x_i}}}{{{s_{i, 2}} - {s_{i, 1}}}}, \quad\quad\quad {s_{i, 1}}\; \leqslant {x_i} < {s_{i, 2}}} \\ & \;\; {1, \quad \quad\quad\quad \quad\quad\quad\;\;\;\;\;\;\;\;{x_i} \geqslant {s_{i, 2}}} \end{align}} \right.. (2)

In the above formula, xi represents the monitored value of the ith pollutant, and si, j represents the standard concentration of the jth level of the ith pollutant in a certain sample. After the matrix R is obtained, the weight wi (i = 1, 2, …, 6) of each evaluation index is established, and the results can be used to calculate the coefficient of variation (CV). The weight wi of each evaluation index is given by

 $v{}_i = \dfrac{{{s_i}}}{{\bar x{_i} }},\; {w_i} = \dfrac{{{v_i}}}{{\sum\nolimits_{k = 1}^6 {{v_k}} }},$ (3)

where $\bar x{_i}$ stands for the average concentration of the ith pollutant, and si represents the average value of the two-level standard concentration of the ith pollutant. The weight coefficients of each index can be calculated after substituting monitoring data.

(2) Analysis of variance (ANOVA). ANOVA is a significance test for differences in the mean of two or more samples.

Before applying this method, three assumptions are made: (a) each sample is a random sample that is mutually independent of the others; (b) each sample is from a normal distribution; and (c) the overall variance of each sample is equal, as determined by the homogeneity of the variance. Therefore, the variance homogeneity of the six pollutants at the five sites is first tested in pairs. When P (FFCritical) is larger than α (α = 0.05, FCritical is the critical value of test statistic F), the overall variance of the two samples is homogeneous; that is, the precondition of variance analysis is satisfied. Therefore, ANOVA can be performed on the two groups to determine whether they are from the same general area.

ANOVA considers that the factors causing fluctuations in the research data can be divided into two categories. One category is the uncontrollable random factor, and the resulting difference is called the difference within the group. The other category is the controllable factor that influences the result, which is expressed as the difference between groups. The difference between groups is expressed as the sum of deviation squares between the total mean value and the mean value of each group, recorded as SSb, and the degree of freedom between groups is recorded as dfb. The difference within the group is expressed as the sum of deviation squares between the mean value of each group and the value of the variable within the group, denoted as SSw. The degree of freedom within the group is recorded as dfw. The total sum of the deviation squares is expressed as SSt = SSb + SSw.

 ${\rm{MS_w = }}\dfrac{{{\rm{SS_w}}}}{{{\rm{df_w}}}} = \dfrac{{{\rm{SS_w}}}}{{n - m}}, \; {\rm{MS_b = }}\dfrac{{{\rm{SS_b}}}}{{{\rm{df_b}}}} = \dfrac{{{\rm{SS_b}}}}{{m - 1}},$ (4)

where n is the total number of samples and m is the number of groups. The mean square MSw and MSb can be calculated from the above formula. There are two situations:

(a) The treatment did not work. The samples from each group are from the same general area, namely, MSb/MSw ≈ 1;

(b) The processing is effective, and the mean square between groups is the result of error and different processing. The samples from each group are from different general areas, namely, MSb >> MS w.

The ratio of MSb/MSw constitutes the F distribution. Comparison of the F-value with its critical value is done to determine whether the samples are from the same population. The F-value can be calculated as

 $F = \dfrac{{{\rm{MS_b}}}}{{{\rm{MS_w}}}} = \dfrac{{n - m}}{{m - 1}} \cdot \dfrac{{{\rm{SS_b}}}}{{{\rm{SS_w}}}}.$ (5)

(3) COD (coefficient of divergence). This evaluates the degree of air pollutant concentration difference between two different monitoring sites.

The difference between the two types of sites is smaller when the value approaches 0, and greater when it approaches 1. The COD formula is as follows:

 ${\rm CO}{{\rm D}_{fh}} = \sqrt {\dfrac{1}{n}\sum\limits_{i = 1}^n {{{\left({\dfrac{{{x_{if}} - {x_{ih}}}}{{{x_{if}} + {x_{ih}}}}} \right)}^2}} },$ (6)

where xif and xih are the concentrations of the same pollutant at different sites (denoted as f and h), and n is the total sample number for comparison.

(4) Entropy weight method. Entropy describes the uncertainty of information. The degree of dispersion of an index can be judged by an entropy value. A greater dispersion degree of an index means a greater influence of the index on the comprehensive evaluation of multi-index elements, so the greater weight of the index will be used.

For n samples and m indexes, xij is the normalized value of the jth index of the ith sample (i = 1, …, n; j = 1, …, m), and the method to calculate weights using the entropy weight method is shown in Table 1.

Table 1 Measures of calculating weight coefficient using entropy weight method
 Computational procedure Mathematical expression To calculate the proportion of the ith sample of the jth index $p_{i.\ {j}} = \dfrac{x_{i,\ j}}{{\sum\nolimits_{i = 1}^n {{x_{i,\ j}}} }}, \ i = 1, ..., n; \ j = 1, ..., m$ . To calculate the entropy value of the jth index ${e_j} = - k\sum\limits_{i = 1}^n {{p_{i, \ j}}\ln \left({{p_{i, \ j}}} \right)}, \ j = 1, ..., m$ . To calculate the information entropy redundancy ${d_j} = 1 - {e_j}, \ j = 1, ..., m$ . To calculate the weight coefficient of the jth index ${w_j} = \dfrac{{{d_j}}}{{\sum\nolimits_{j = 1}^m {{d_j}} }}, \ j = 1, ..., m$ .
3 Analysis of air pollution characteristics

The five air quality monitoring sites in Lanzhou can be divided into two groups according to their spatial distribution, urban and suburban, to analyze and compare them. The urban sites (WH, LH, RD, and BP) are compared to the suburban site (YC). Site monitoring of PM2.5 and O3 as routine indicators was added to the traditional observations after 2012. The five automatic monitoring sites provide eight routine observation items, including the air quality index (AQI) and pollutant concentrations in Lanzhou. In this study, the monitoring data for six air pollutant concentrations (PM2.5, PM10, CO, NO2, SO2, and O3) from the five monitoring stations are used to analyze the pollutant variation from July to December 2015.

3.1 Characteristics of daily variation

The daily mean of hourly pollutant concentration data from July to December 2015 is used to describe the daily variation of air pollution at the five sites in Lanzhou, as shown in Fig. 3. The concentration value of PM10 is the highest among the all pollutants, and the maximum value appears at BP in December. SO2 shows the lowest concentration throughout the year, below 50 μg m–3, except in late December. Concentrations of PM2.5, PM10, CO, NO2, and SO2 from July (summer) to December (winter) show slow growth, which is likely related to cold weather and the resulting increase in coal burning emissions, as well as a stable boundary layer that is not conducive to pollutant diffusion (Yu et al., 2010b). The O3 concentration trend from July to December shows a decline, which is related to the highest concentration of O3 in summer caused by NOx and HC (black charcoal) compounds produced by the industrial discharge of the Xigu District (Tang et al., 1984), as well as high temperatures and solar radiation. Both are conducive to the photochemical reaction that generates O3 (Yang and Li, 1999).

 Figure 3 (Continued).
 Figure 3 Daily average of pollutant concentrations at the five sites in Lanzhou from July to December 2015. (a) WH, (b) LH, (c) BP, (d) RD, and (e) YC. The left vertical axis represents PM2.5, PM10, NO2, SO2, and O3 (8 h) concentrations (μg m–3), and the right vertical axis represents CO concentration (mg m–3).
3.2 Primary pollutants at the monitoring sites

The AQI and the air pollution index (API, replaced by AQI in practical application) are important indexes that are generally used globally for evaluating air quality. However, due to many factors, the AQI used in China often shows inconsistencies with other environmental monitoring indicators (Wu and Wang, 2012). Especially for areas where there are significant differences in climatic conditions and topography, the use of uniform standards to determine pollution levels and primary pollutants may lead to inaccurate conclusions. A fuzzy-gray clustering evaluation model has been applied to achieve a quantitative assessment of urban air quality, and the results showed more consistency with the actual situation than the API evaluation (Ding et al., 2013). Therefore, a fuzzy comprehensive evaluation model is used in this study to quantitatively compare air quality and analyze primary pollutants at the five sites in Lanzhou.

Following the new standard issued by the Ministry of Environmental Protection in 2012, the regulations for classification of environmental air functional zones have been implemented nationwide since 1 January 2016, as well as standard classification, pollutant items, average time and concentration limits, and data validity regulations. Therefore, the new grading standard is adopted to conduct fuzzy evaluation of the pollutant concentration data from July to December 2015, and to compare the weighted coefficients to obtain primary pollutants at the five sites in Lanzhou.

Using observational data from the five air quality monitoring sites in Lanzhou from July to December 2015, the monthly variation of the weight coefficients of the six environmental pollutants over time is calculated (Fig. 4). At all five sites, PM10 has the highest frequency of predominance during the analysis period, with a four times greater frequency at the four urban sites than at the suburban site. Therefore, PM10 can be considered the main pollutant at the five sites during the analysis period. Overall, PM10 can be considered the primary pollutant in Lanzhou, with PM2.5 as the secondary pollutant, while SO2 has the least impact on the air quality in Lanzhou. Therefore, the primary pollutant PM10 will be used as the example for site representativeness in the following analysis. But first, the correlation among the air pollutants at the different sites is investigated.

 Figure 4 Variation of weight coefficients of air pollution factors at the five monitoring sites (WH, LH, BP, RD, and YC) in Lanzhou from July to December 2015.
4 Correlation of the air pollutant concentrations between the monitoring sites

Owing to the distance between the sites, there are differences in the temporal and spatial variation of pollutants among the monitoring sites. The spatial and temporal correlations between the sites are investigated separately to discern whether there is overlapping information in the observations of the six pollutants at the five sites.

4.1 Temporal correlation

To investigate pollutant transmission at the five monitoring sites, the concentrations of the six pollutants are averaged hourly from July to December 2015 to analyze the lag correlation between the five sites, with a significance level of 0.05 (Fig. 5). The correlations between each of the four urban sites and the one suburban site generally do not pass the significance test, indicating that there is a significant difference in pollutant distribution between the two areas. This difference will be discussed in detail in Section 4.2. The correlation coefficient of particle pollutants lagging ±1 h among the four urban sites is above 0.6, indicating that there is diffusion and transport of pollutants between the urban sites. Owing to the prevailing lag correlation of the primary pollutant PM10, it can be inferred that the transport between sites has an impact on the PM10 concentration at each site. Thus, the spatial correlation between sites will be further analyzed.

 Figure 5 Lag correlation analysis of PM10 concentration between different sites in Lanzhou in the second half of 2015 (α = 0.05). Solid lines indicate that the significance test is passed, and dotted lines indicate that the test is not passed. (a) WH and LH, (b) WH and BP, (c) WH and RD, (d) WH and YC, (e) LH and BP, (f) LH and RD, (g) LH and YC, (h) BP and RD, (i) BP and YC, and (j) RD and YC.
4.2 Data reproducibility test in urban sites

ANOVA is a test of the significance of differences in the mean of two or more samples.

For each pollutant, under the premise of a significance level of α = 0.05, the hypothesis is that there is no significant difference in the PM10 concentration between the five sites in pairs.

One-way ANOVA is performed for each set of the data. The results in Table 2 show that the PM10 concentration monitoring data from the four urban sites in Lanzhou can be considered to be from the same general area from July to December. Therefore, there are some redundant observations at these four sites. It is necessary to select a representative site among them.

Table 2 Univariate analysis of variance of PM10 concentration at four urban sites in Lanzhou from July to December 2015
 Variance source SS df MS F P-value FCritical Variation between groups 664.4243 3 221.4748 0.366135 0.778191 3.098391 Variation within group 12097.97 20 604.8986 Total 12762.4 23
4.3 Spatial correlation

The COD method is used to evaluate the spatial distribution differences of pollutant concentrations monitored by the urban and suburban sites in Lanzhou.

COD is calculated and compared among the six pollutant concentrations monitored by the five sites in Lanzhou. It can be found that the COD among the four urban sites is relatively small (table omitted), while the COD between the urban sites and suburban site is large.

The study period is divided into three periods: July–August, September–October, and November–December. The spatial disparity of pollutants between the urban and suburban sites is analyzed from July to December (Table 3). The CODs for PM10, CO, NO2, and O3 show an increasing trend, the COD for PM2.5 changes smoothly, and that for SO2 tends to decrease. The COD of the particulate pollutants between the urban and suburban sites is generally smaller than that of gaseous pollutants (except CO). Combined with the characteristics of the stable boundary layer in Lanzhou in winter, it is known that the distribution and transport of gaseous pollutants are more easily affected by airflow. In addition, the greatest fluctuation of the COD of PM10 and SO2 occurs during different time periods, with PM10 increasing from around 0.07 in July–August to around 0.40 in November–December, and SO2 decreasing from around 0.70 in July–August to around 0.35 in November–December.

Table 3 CODs of six pollutant concentrations between the four urban sites and the suburban site in Lanzhou City from July to December in 2015
 Period (2015) Site Pollutant PM2.5 PM10 CO NO2 SO2 O3 (1 h) O3 (8 h) Jul–Aug WH 0.2854 0.0839 0.2609 0.3261 0.2965 0.3636 0.3305 LH 0.2896 0.0707 0.3193 0.3632 0.7086 0.3651 0.3271 BP 0.2372 0.0690 0.3462 0.3600 0.5959 0.3946 0.3525 RD 0.2546 0.0845 0.3156 0.4296 0.5857 0.3708 0.3344 Sep–Oct WH 0.3066 0.2958 0.1926 0.4198 0.5261 0.3618 0.3088 LH 0.3047 0.2923 0.2380 0.4748 0.5010 0.3918 0.3258 BP 0.2251 0.2488 0.1888 0.3862 0.3633 0.3805 0.3145 RD 0.2622 0.2659 0.2537 0.5098 0.4024 0.3908 0.3326 Nov–Dec WH 0.2889 0.3622 0.4112 0.4526 0.3614 0.5219 0.4773 LH 0.3534 0.4003 0.2468 0.4595 0.4791 0.6325 0.5608 BP 0.2499 0.3223 0.2894 0.4476 0.3416 0.6557 0.6252 RD 0.2532 0.3068 0.3783 0.4889 0.4651 0.6829 0.6671

The spatial distribution of the primary pollutant PM10 also shows differences among the urban sites. The COD of PM10 in the urban sites, which gradually increases from July to December, shows obvious monthly changes. In July–August (summer), the COD between the sites is generally less than 0.1. It increases sharply to around 0.25–0.3 after September and exceeds 0.3 at all sites after November. The maximum COD within the urban area occurs at LH (0.4003) in November–December, and the minimum value appears at BP (0.0690) in July–August. A greater COD value means less redundancy of the monitoring data between the sites, indicating higher representativeness. Therefore, the COD can be used as a positive indicator to describe site representativeness.

From the above analysis, the COD between the four urban sites and the suburban reference site can be used as a weight coefficient to obtain a more complete set of hourly averaged PM10 data for Lanzhou, which will be used for further correlation analysis with aerosol optical depth.

5 Retrieval analysis of primary air pollutant concentrations from satellite data

To investigate the redundancy of the observational data, the correlation between routine monitoring data and high-precision observational data is an important indicator of site representativeness. Owing to the lack of automatic monitoring data, more complete daily mean data for the pollutants in Lanzhou can be obtained by satellite data with relatively good continuity. In addition, the satellite observations represent local city air pollution overall. Therefore, it is of great significance to select the air quality monitoring station in Lanzhou with the highest relevance to the aerosol optical depth (AOD) of MODIS.

First, a linear regression analysis is conducted by using four sets of AOD daily data and the daily average PM10 concentration weighted by COD. The correlation coefficients are generally very low between the MODIS AOD and the raw PM10 concentration in the urban area during the study period to describe the actual relationship well (Table 4), and the significance levels are also not high enough. Therefore, the method needs to be revised.

Table 4 Linear regression analysis between unprocessed PM10 and MODIS AOD data (α = 0.05)
 MODIS product Terra deep blue Terra dark target Aqua deep blue Aqua dark target Regression equation y = 22.62x + 103.68 y= –35.53x + 109.36 y = –27.94x + 110.81 y = –70.82x + 113.23 Correlation coefficient (R2) 0.00408 0.0135 0.00283 0.0464

According to Cheng’s method, the relation between PM10 concentration and AOD is revised by using the following two steps (Cheng, 2014). First, humidity revision is performed on the PM10 concentration. Ground monitoring stations generally measure PM10 concentration in dry air at high temperatures. The monitoring result is the mass concentration of dry particles. The AOD is obtained by satellite remote sounding under the environmental background. Relative humidity has a significant effect on the aerosol particle size, so that the extinction coefficient of hygroscopic aerosol particles increases significantly after moisture absorption and expansion. The humidity influence factor is defined as:

 $f\left({\rm RH} \right) = \dfrac{1}{{1 - \dfrac{{\rm RH}}{{100}}}},$ (7)

where RH is relative humidity, and the mass concentration of PM10 is multiplied by $f\left({{\rm{RH}}} \right)$ at the corresponding time to obtain a revised humidity value $C\left({{\rm{P}}{{\rm{M}}_{{\rm{10}}}}} \right) \times f\left({{\rm{RH}}} \right)$ as a substitute for the raw PM10 concentration.

Second, aerosol scale height revision is performed on the four sets of AOD data. The AOD represents the integral of the extinction coefficient of the whole atmosphere in the vertical direction. The aerosol scale height is an important parameter to measure the main vertical distribution of the aerosol concentration. It basically reflects the mixed layer height except when it is relatively large in spring due to dust (Chen et al., 2013). To increase the credibility of the AOD data, it is necessary to revise the aerosol scale height. The Peterson model is used to describe the relationship between the aerosol scale height, atmospheric visibility, and AOD. The model is expressed as follows:

 $\tau = H \times \left({\dfrac{{3.0}}{V} - 0.0146} \right),$ (8)

where τ represents the AOD, H represents the aerosol scale height (m), and V represents the horizontal visibility (m). In contrast, the daily aerosol scale height can be calculated by using the daily satellite-retrieved optical depth and the daily surface horizontal visibility data. In consideration of the inadequate effect of the vertical correction for seasonal average scale height (Cheng, 2014) and the short study period in this paper, the monthly average scale height and the Peterson model are used to revise the daily AOD data from July to December 2015.

After the above two revision steps, linear, quadratic, and cubic regression tests are performed on the two variables. Twelve sets of tests are executed to find the most significant regression equation, and linear, quadratic, and cubic regression equations are given among the four sets of AOD data revised by the aerosol scale height and the PM10 concentration revised by humidity (Table 5). In these tests, the equation with the best regression significance, y = –354.468x3 + 1046.168x2 – 765.832x + 151.481, is obtained between the Terra Dark Target 550 nm AOD and the daily PM10 concentration in Lanzhou from July to December 2015, where the independent variable x represents AOD and the dependent variable y indicates PM10 concentration.

Table 5 Linear, quadratic, and cubic regression test results among the four groups of AOD data and average PM10 concentrations in Lanzhou urban region
 AOD product Order of regression equation Regression equation Correlation coefficient R2 P-value Terra Deep Blue AOD Linear y = 21.030x + 124.048 0.022 0.089 Quadratic y = 39.290x2 − 10.689x + 119.502 0.025 0.195 Cubic y = 76.512x3 − 61.550x2 + 16.510x + 113.339 0.028 0.314 Terra Dark Target AOD Linear y = 48.844x + 109.607 0.048 0.019 Quadratic y = 91.321x2 − 46.496x + 101.852 0.051 0.056 Cubic y = –354.468x3 + 1046.168x2 − 765.832x + 151.481 0.09 0.016 Aqua Deep Blue AOD Linear y = 23.788x + 124.519 0.026 0.067 Quadratic y = 30.926x2 − 4.416x + 122.767 0.0268 0.184 Cubic y = 46.561x3 − 27.453x2 + 8.322x + 120.245 0.026 0.333 Aqua Dark Target AOD Linear y = 42.563x + 110.157 0.042 0.032 Quadratic y = –36.956x2 + 85.148x + 124.53 0.053 0.055 Cubic y = –366.170x3 + 901.114x2 − 563.659x + 159.424 0.087 0.022

A set of daily PM10 concentration data that satisfy the time continuity can be interpolated from the daily AOD data on the basis of the regression equation obtained from the above analysis. A correlative analysis is then performed between the daily average PM10 concentration observed at the four urban sites and the retrieval concentration to find the site that has the highest correlation with the high-precision satellite data. The correlations between the daily average PM10 concentration at the four urban sites and the satellite-retrieved concentration (Table 6) indicate that the correlation between WH and the retrieval data is the highest, passing the 90% confidence level.

Table 6 Correlation coefficients between PM10 concentration daily data obtained by MODIS AOD and daily average PM10 concentration at the four sites in Lanzhou urban area
 Urban site WH LH BP RD Correlation coefficient 0.9280 0.9162 0.8963 0.9270
6 A new evaluation model for site representativeness

The representativeness of air quality monitoring sites can be measured by determining (1) the redundant observations at sites in urban areas and (2) the correlation of the monitoring data with high-precision data (such as satellite data) in regional analysis. Based on the above two factors, a site representativeness evaluation model is constructed, using Rs for the representativeness of air quality monitoring sites, as follows:

 ${R_{\rm{s}}} = a \cdot {\rm{COD}} + b \cdot {R_{{\rm{retrieval}}}},$ (9)

where COD represents the COD value between each site and the remaining three urban sites, Rretrieval is the correlation coefficient between the PM10 concentration data of each urban site and the MODIS AOD retrieval data, and a and b are undetermined coefficients, indicating the weight coefficients of the above two indexes, respectively.

Index weights reflect the importance of different evaluating indicators in decision-making. Reasonable determination of weight coefficients is key to quantitative evaluation and has a direct impact on the scientific value of the evaluation model (Ni, 2002). In mathematics and other scientific fields, there are two ways to determine index weights. Subjective weighting methods determine the weight of the index using comprehensive treatments based on the subjective judgment of expert experience. Subjective weighting methods include the Delphi method, analytic hierarchy process (AHP) method, and expert scoring method. Objective weighting methods determine the weight of the index directly according to the degree of discretization (Gao, 2003). Objective weighting methods include the entropy weight method, standard deviation method, and criteria importance through the intercriteria correlation (CRITIC) method (Wang et al., 2007). Each method has its advantages and disadvantages. The subjective weighting methods measure indicator weights based on subjective judgments with strong interpretation; however, the limitations of the knowledge and experience of the expert groups that they rely on cannot be eliminated (Wang and Zhang, 2001). The objective weighting methods are usually more accurate, but they sometimes reach a conclusion that is contrary to the actual situation, and it then becomes difficult to give a clear explanation of the results (Cheng, 2010).

To analyze the undetermined coefficients in a target period, a suitable weight calculation method should be chosen for the current period. Although the subjective weighting methods are simpler and easier to implement, there is no expert experience evaluation standard available for the evaluation of air quality monitoring sites in Lanzhou. In practical applications, subjective and objective weighting methods are used in combination to complement each other. Considering the limited number of indicators selected in this study, the comparatively objective entropy weight method is chosen to calculate a and b to ensure that the established indicators reflect most of the original information (Zhang et al., 2010). This method can determine the weight according to the amount of information contained in each indicator without losing the original information (Huang, 2003).

Shannon proposed that “information is used to eliminate uncertainty” (Shannon, 1948), as well as the concept of “information entropy”, which is a measure not only of the information needed to eliminate uncertainty, but also of the amount of information that the unknown event may contain (Shannon and Weaver, 1949). According to the basic principle of information theory, information is a measure of the degree of order in a system, and entropy is a measure of the degree of disorder in the system. The smaller the information entropy of the indicator, the greater the amount of information provided by the indicator; and the greater the role it plays in the comprehensive evaluation, the higher the weight should be (Wang and Song, 2003).

Both the COD and Rretrieval are positive indicators of a larger index value and higher site representativeness.

For the representativeness of air quality monitoring sites, the number of samples is the number of sites, n = 4, and the number of indicators m = 2. Incorporating the COD and Rretrieval data calculated above, the relative importance of the two indicators in the comprehensive evaluation is measured according to the entropy weight method, and the weight coefficients of the two indicators are shown in Table 7.

Table 7 Weight coefficients of the two indexes calculated by the entropy weight method
 Proportions of each index (pi,j) Entropy (ej) Information entropy redundancy (dj) Index weight (wj) WH LH BP RD COD 0.2453 0.2526 0.2591 0.2429 0.9998 2.34E−04 0.77 Rretrieval 0.2530 0.2498 0.2444 0.2528 0.9999 7.00E−05 0.23

The values of a and b are 0.77 and 0.23, respectively. The representative evaluation model of air quality monitoring sites in Lanzhou from July to December 2015 is determined as follows:

 ${R_{\rm{s}}} = 0.77{\rm{COD}} + 0.23{R_{{\rm{retrieval}}{\rm{.}}}}$ (10)

Substituting the values for the COD and the correlation coefficient of the retrieval in the above model, the evaluation results of the four sites can be obtained (Table 8). The Rs value of BP is 0.2557, which is the highest among the four urban sites. Therefore, the BP site can be considered the most representative of the four urban air quality monitoring sites in Lanzhou during the research period.

Table 8 Results of representative evaluation of four sites in Lanzhou in the second half of 2015
 WH LH BP RD Rs 0.2471 0.2520 0.2557 0.2452

Owing to the length of the research data, the study period is short and does not include the period when the sand dust weather is frequent in spring, so the difference between the results of the four urban sites may be not significant enough. In addition, since the determination of each parameter and weight coefficient in this study is based on the analysis of pollutant concentration observed in the Lanzhou urban area during the study period, the parameters of other cities or regions should be determined by calculating the local monitoring data using the model.

7 Summary and discussion

Current research on the representativeness of air quality monitoring sites focuses on the scope of time and space, and to date there has not been a representative evaluation model of multiple sites within an urban area. This study uses hourly observational data at five monitoring sites from July to December 2015 in Lanzhou issued by the Ministry of Environmental Protection to measure primary pollutants and analyze site representativeness. A representative evaluation model is established from two aspects: (a) minimizing redundant observations, and (b) obtaining optimal correlation with high-precision observational data. The following conclusions are obtained:

(1) Fuzzy matrix analysis applied to obtain primary air pollutants among the six routinely monitored pollutants shows that PM10 is the primary air pollutant, while PM2.5 is the secondary pollutant during the research period. SO2 has the least impact on air quality.

(2) The correlation coefficient of the particulate pollutants and O3 lagging ± 1 h among the four urban sites is above 0.6, and it can be considered that the PM10 concentration data monitored at the four urban sites are derived from the same general area in Lanzhou from July to December 2015. Diffusion and transport of pollutants generally occurs among the sites, and there are redundant observations among these four sites. The COD of PM10 at the four urban sites increases gradually from July to December. The biggest difference exists between the LH site and the other three sites. A greater COD value means smaller redundancy of the monitoring data among the sites. COD can be used as a positive indicator to describe site representativeness.

(3) Correlation analysis is performed between the retrieval of the PM10 concentration from the MODIS AOD data after two revision steps and the PM10 concentration from the four urban monitoring sites. The correlation between the WH site and the retrieval data is the highest, passing the 90% confidence level.

(4) A new model to evaluate the representativeness of air quality monitoring sites, Rs = 0.77COD + 0.23Rretrieval, is established by using the COD and correlation coefficients between routine observations and satellite-retrieved data. The conclusion is that the biology products institute (BP) site is the most representative of the four urban air quality monitoring sites from July to December 2015.

In summary, the new evaluation model for air quality monitoring sites solves the problem of redundancy in regional pollution observations and establishes a connection with remote-sensing data that retrieves city air pollution as a whole. However, due to the length limitation of the research period, the results do not cover all times, in particular, dusty periods in spring.

Acknowledgments. Many thanks are given to website data.epmap.org for the supply of research data. Anonymous reviewers who provided comments and suggestions are also gratefully acknowledged.

Appendix: Quality requirements for environmental air functional zones

According to the data validity rule of Ambient Air Quality Standard (GB3095-2012, The Ministry of Environmental Protection, 2012), the ambient air functional areas are divided into two types of districts, where the first type is a nature reserve area (district I), and the second type is a mixed commercial, transportation, and residential area (district II).

The limit of the daily pollutant concentration of the six routinely monitored pollutants in the quality requirement of the standard are shown in Table A1. The first class concentration limits are used in functional district I, and the second class concentration limits are used in functional district II.

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