Analysis of Chemical Composition Characteristics and Source of PM 2.5 under Different Pollution Degrees in Autumn and Winter of Liaocheng, China

: Analysis of chemical composition characteristics of PM 2.5 under different pollution degrees can reveal the changes of pollution sources. In order to make clear the evolution process of PM 2.5 compositions in autumn and winter, PM 2.5 samples were continuously collected and analyzed at Liaocheng city, China. The collected samples were classiﬁed as clean days (CLD), mild-moderate pollution days (MMD) and severe-serious pollution days (SSD). It was concluded that with the increase of pollution degrees, the concentrations of water-soluble ions and carbon components increased signiﬁcantly, while elements only increased slightly. In addition, as the pollution degrees increased, the percentage of NO 3 − , SO 42 − and NH 4+ increased signiﬁcantly, from 23.0% in CLD to 49.0% in SSD, while the percentage of other components decreased, especially crust material. The PMF analyzed results showed that secondary transformation (36.7%), combustion sources (20.4%), secondary organic aerosols (SOA) (11.7%), vehicle sources (11%), dust (10.5%) and industrial processes (9.7%) were the main sources of PM 2.5 during autumn and winter in Liaocheng. The contribution of secondary transformation reached 57% at the SSD level, which indicated that it was the main reason for the increase of PM 2.5 concentrations. The air mass mainly came from ﬁve paths to Liaocheng. The secondary transformation contribution of the air mass with short transmission distance was higher, while the contribution of the dust was higher from the long distance.


Introduction
In recent years, China has experienced rapid economic developments along with serious air pollution problems, especially extreme haze episodes. Since 2013, with the formulation and implementation of a number of air pollution prevention and control measures, such as "Air Ten" and "Winning the Battle to Protect the Blue Sky" [1,2], the emission of air pollutants in China has decreased significantly, and the air quality has improved, but PM 2.5 is still the primary pollutant in most cities [3]. The chemical composition of PM 2.5 is very complex and has an important impact on visibility, climate and human health. At present, numerous analyses of chemistry compositions and source appointment of PM 2.5 have been carried out in typical polluted areas in China like Beijing-Tianjin-Hebei and surrounding areas [4], the Yangtze River Delta [5] and the Pearl River Delta [6] and lots of cities like Beijing [7], Tianjin [8], Shijiazhuang [9], Xingtai [10], Jinan [11], Shanghai [12] and Guangzhou [13]. Sulfate, nitrate and ammonium were found to be the major components of water-soluble inorganic ions, which accounted for 30-80% of PM 2.5 . Carbonaceous components are also important constituents of PM 2.5 , and OC contains a large number of carcinogenic, teratogenic and mutagenic components [14]. Elements were divided into crustal elements and anthropogenic pollution elements, including trace heavy metals, although their concentration is relatively low but harmful to the human body [15]. An analytical model of particulate matter receptor method is one of the common tools in the study of source appointment [16]. The positive definite matrix (PMF) and its analytic results are also objective sources of information. Additionally, the PMF model can provide the time series of various pollution sources' contributions. Therefore, the PMF model was selected in this paper to analyze the sources of PM 2.5 in Liaocheng.
Shandong Province is an area with a high concentration of air pollutants and frequently encountered haze episodes. Liaocheng is located at the northwest inland area of Shandong Province, and it is one of the important transport channels of air pollution in the "2 + 26" cities area. The air pollution problem of Liaocheng has been widely concerned because of its low ranking in the Shandong province. Currently, the research of PM 2.5 in Liaocheng mainly focuses on the analysis of the characteristics of chemical components and sources [17][18][19], but there was no report on the characteristics and source apportionment of PM 2.5 under different pollution degrees, as well as research in the whole autumn and winter period. Therefore, this study analyzed the characteristics and sources of PM 2.5 under different pollution degrees in the autumn and winter of Liaocheng in order to provide data support and scientific support for air pollution control in Liaocheng.  2.5 was collected at the campus of Liaocheng University, located east of Liaocheng (34.43 • N, 115.99 • E) and is shown in Figure 1. The instruments used in this study were installed on the rooftop (15 m above ground) of NO.4 Experimental Building. There were no tall buildings and obvious pollution sources around the sampling site, which could objectively reflect the air pollution situation in Liaocheng. Two high-volume samplers (TH-150C, Tianhong Instrument Co. Ltd., Wuhan, China) were used to collect PM 2.5 samples, and the flow rate was set to 100 L·min −1 during the sampling process. Quartz and polypropylene films were loaded to capture PM 2.5 , and both were 90 cm in size. After sampling, the filter samples were placed in the refrigerator at −4 • C for preservation. The sampling time was 109 days, from 15 October 2017 to 31 January 2018, while the sampling duration for each sample was 23.5 h, from 10:00 a.m. to 9:00 a.m. the next day, and a total of 109 PM 2.5 samples were collected. During sampling periods, the machine failure period and invalid data were removed, and a total of 105 groups of effective samples were obtained.

Quality Assurance and Quality Control of Sampling
The samplers were calibrated before the sampling process, the flow-rate range of the samplers was from 60 to 150 L/min with an accuracy of ±2.5%, and the relative error of the flow rate was less than 2%. The quartz films were first calcined at 450 • C for 5 h, and polypropylene films at 60 • C for 3 h in order to remove the organics and other impurities on the films. Then, the films were packed into aluminum foil papers and placed in a constant temperature and humidity chamber at 25 • C and 50 • C of 5% relative humidity for 24 h. Then, the films were sealed in film boxes at a temperature of 20 • C. Three blank films were reserved as the blank samples to correct the data of each sample in order to guarantee the accuracy and reliability of the analyzed data of the collected samples. Before analysis, polypropylene films were extracted ultrasonically by 20 mL of ultrapure water for 20 min, and then water-soluble matter was filtrated and stored at 4 • C. Ion chromatography (Universal ICS-90, Metrohm Company, Herisau, Swiss) was used to analyze the inorganic ions, which included chloride (Cl − ), nitrate (NO 3 − ) and sulfate (SO 4 2− ), sodium (Na + ), ammonium (NH 4 + ), potassium (K + ), magnesium (Mg 2+ ), calcium (Ca 2+ ) and fluoride (F − ) [20][21][22].

Inorganic Element
Six quartz filters (10.9 cm 2 each) were placed in a high-pressure Teflon digestion vessel, digested with a mixture of ultra-high purity acids (11.1% HNO 3 /33.5% HCl) and then heated in a microwave system. The microwave system was ramped to 200 • C and was retained at this temperature for 30 min. After the digestion process, metal components, such as Li, Be, Mg, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Mo, Cd, Sn, Sb, Ba, Hg, Pb, Bi, Ca, K, Mg, Na, were determined using Inductively Coupled Plasma-Mass Spectrometry (7700 Series ICP-MS, Agilent Technologies Inc., Palo Alto, CA, USA). In addition, the concentrations of Al and Si were determined by Inductively Coupled Plasma Atomic Emission Spectrometry (8300 ICP-AES, PerkinElmer company, Boston, MA, USA) [27][28][29][30].

Quality Assurance and Quality Control of Chemical Components Analysis
Strict quality control and quality assurance measures were used in the chemical components analysis process. A three field blank was collected, and the laboratory blank was also analyzed. For each batch of samples, a blank addition criterion was added (watersoluble ions and inorganic elements). Recovery as well as calibration and quantification were performed using external standard solutions, the recovery rate of calibration was between 80% and 120%. The correlation coefficients of standard curves were all higher than 0.99. For every 10 samples, a calibration median point was analyzed. If the deviation of the calibration median point was greater than 20%, the curve was redrawn.
For carbonaceous species, the background contamination was regularly monitored by blank tests, which were used to validate and correct the corresponding data. Calibration of the analyzer was done before and after sample analysis every day. The first sample was analyzed every ten samples again, and the precision had to be less than 5%.

Online Data Source
Air quality data were obtained from China's air quality online monitoring and analysis platform (http://www/aqistudy.cn/historydata, accessed on 18 July 2021), and meteoro-logical data were obtained from the National Oceanic and Atmospheric Administration (ftp://arlftp.arlhq.noaa.gov/pub/archives/gdas1/, accessed on 18 July 2021), which are open-source databases for research.

Analysis of Secondary Pollution
Secondary formation is an important reason for PM 2.5 pollution. Sulfate and nitrate are the main products of secondary inorganic formation in PM 2.5 , and their components are related to the oxidation efficiency of SO 2 and NO 2 . Usually, secondary formation rates of SO 2 and NO 2 are characterized by SOR (sulfate oxidation rate) and NOR (nitrate oxidation rate) [31,32], which can be calculated by the following Equations (1) and (2) Secondary organic carbon in the atmosphere is formed by photochemical reactions or gas-particle conversion of volatile and semi-volatile organic compounds. The degree of secondary carbon pollution can be characterized by indicators like OC/EC and SOC/OC. The higher the ratio, the more serious the secondary pollution. SOC concentrations were determined by the EC tracer method following Equations (3) and (4) [33,34].
where OC and EC are measured concentration, (OC/EC) min is the minimum OC/EC ratio in the sampling period, POC and SOC represent the estimated primary OC and secondary OC, respectively.

Positive Matrix Factorization Analysis
Positive Matrix Factorization (PMF) is a multivariate factor analysis tool that decomposes a matrix of sample data into two matrices: factor contributions and factor profiles [35,36]. With measured source profile information and emission inventories, the source type is determined. In this study, the EPA PMF 3.0 program was used for PMF analysis. The PMF model can be expressed as: where X ij is matrix X of i by j dimensions, i is the number of samples and j is the number of chemical species, p is the number of factors, f is the species profile of each source, g is the amount of mass contributed by each factor to each individual sample, and e ij is the residual for each sample/species. Q is an object function, and a criterion for the model, which is defined as: where u ij is the uncertainty of the j th component in the i th sample.

Back Trajectory and Clustering Analysis
The 24 h backward trajectories of air mass during the pollution processes were investigated by the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) (http://ready.arl.noaa.gov/HYSPLIT.php, accessed on 12 July 2021) model developed by the National Oceanic and Atmosphere Administration (NOAA), and the ARL archives of the NOAA were used as the meteorological input data in this study. In this study, the model started at a height of 100 m above ground level with a time interval of one hour and set hourly 72 h back trajectory starting from the sampling site. Based on the results of the backward trajectory analysis, the trajectories and pollution concentrations were used for cluster analysis by MeteoInfo Map, which is an open-source geographic information system and scientific computing environment software.
Cluster analysis is an objective classification method to study multiple elements (or variables). It looks for a statistical quantity that can objectively reflect the distance relationship between samples and then divides samples into several categories according to the statistical quantity. The clustering method based on airflow trajectory is to group a large number of airflow tracks according to their spatial similarity (transmission velocity and direction). In this study, the Angle Distance algorithm provided by TrajStat software was used to cluster the airflow trajectory, and total spatial variance (TSV) was used to judge the classification quality. The principle is as follows: the TSV of the first several classification steps increases rapidly and then increases slowly. When the categories are divided to a certain number, TSV increases rapidly again, indicating that the merged categories are different. The classification merger is over, and the categories before the merger are the classification results. The average trajectories of these categories are the main flow trajectories of the target point in the analysis periods.

Analysis of Mass Concentrations of PM 2.5 and the Meteorological Conditions
The daily average concentrations of PM 2.5 and the meteorological conditions are shown in Figure 2 and Table 1, respectively. The average concentration of PM 2.5 was 109.7 µg/m 3 , ranging from 26.7 to 286.3 µg/m 3 with a standard deviation of 56.8 µg/m 3 . Compared with the Chinese National Ambient Air Quality Standard (NAAQS) (daily standard: 75 µg/m 3 ), this value exceeded NAAQS 0.46 times, and the peak concentration appeared in December 29, exceeding the standard 2.82 times. Liaocheng is one of the "2 + 26" cities which are heavily polluted in China. The PM 2.5 concentrations of Liaocheng in autumn and winter were comparable to those of Yuncheng [37] and Xingtai [38], but were higher than those of Beijing [39], Heze [40], Puyang [41] as well as Central Plains City Group cities [42] like Zhengzhou, Luoyang, Anyang and Xinxiang.
According to the calculation method of PM 2.5 sub-index in the Ambient Air Quality Index (AQI) Technical Regulation (Trial) (HJ 633-2012), the days during the sampling period were divided into three types: clean days (CLD) (PM2.5 < 75 µg/m 3 ), mild-moderate pollution days (MMD) (75 µg/m 3 < PM 2.5 < 150 µg/m 3 ) and severe-serious pollution days (SSD) (PM 2.5 > 150 µg/m 3 ). There were 34 CLD, 51 MMD and 20 SSD during the sample period, and the pollution days accounted for 67.6% of all sampling days. The average concentrations of PM 2.5 were 55.2 ± 12.3 µg/m 3 , 109.5 ± 21.8 µg/m 3 , 202.8 ± 41.5 µg/m 3 at CCD, MMD and SSD, respectively, which indicated that PM 2.5 pollution degree was still serious in the Liaocheng area, and stricter strategies should be used to reduce the pollution situation.
The specific meteorological parameters during the sample period are shown in Table 1. As seen in this table, the dominant wind direction was northwest, the overall wind speed was low with a mean value of 1.37 m/s and ranged from 0.52 to 2.71 m/s. The average temperature was 5.80 • C and ranged from −5.24 to 18.59 • C with a standard deviation of 6.22 • C, and relative humidity (RH) ranged from 21.0% to 81.0% with an average value of 44.15%. As pollution degree increased, the wind speed showed a decreasing trend and decreased from 1.44 m/s in CLD to 1.33 m/s in SSD, while the air pressure also decreased to a certain extent. RH showed a contrary trend compared with that of wind speed and increased from 28.38% in CLD to 53.56% in SSD. Generally, when the wind speed is low and air pressure is stable, the diffusion conditions are unfavorable, and pollutants easily accumulate. In addition, high RH is conducive to the secondary conversion of gaseous precursors such as SO 2 and NOx in the ambient air, which promotes moisture absorption growth and increase of particulate matter concentration.

Analysis of Chemical Components
The time variation of concentrations of water-soluble ions, carbon components and elements in PM 2.5 during sampling is shown in Figure 3. On the whole, water-soluble ions were the main component of PM 2.5 with a concentration of 50.4 µg/m 3 and accounted for 46.0% of PM 2.5 during the sampling period. The concentrations of OC and EC were 15.2 µg/m 3 and 6.66 µg/m 3 and accounted for 13.9% and 6.1% of PM 2.5 , respectively. The concentration of elements was relatively low with a concentration of 12.21 µg/m 3 , accounting for 11.1% of PM 2.5 , therefore, water-soluble ions and OC were the key points of PM 2.5 pollution control.

Water Soluble Ions Analysis
The concentration of various chemical components of PM 2.5 in Liaocheng in autumn and winter as well as concentrations at different pollution degrees are shown in Table 2 [44][45][46]. The concentration of Cl − was 3.85 ± 2.58 µg/m 3 , accounting for 7.6% of water-soluble ions. Cl − in the atmosphere mainly comes from fossil fuel combustion and biomass combustion [47], and may partly come from sea salt. However, Liaocheng is an inland city and is thus more related to a combustion source than sea salt. In addition, K + is usually used as the indicator ion of biomass combustion source [48], and its concentration was 1.11 ± 0.46 µg/m 3 during the sampling period. With an increase of pollution degree, both Cl − and K + concentrations increased to a certain extent. The average concentration of Ca 2+ was 2.10 ± 1.12 µg/m 3 , and the concentration gradually decreased with an increase of pollution degree, from 2.20 µg/m 3 in CLD to 1.83 µg/m 3 in SSD. Ca 2+ is mainly derived from dust [49], indicating that with the increase of pollution, the influence of dust gradually increases. The concentration of Mg 2+ , which is also a representative ion of dust, was low and changed little with the change of pollution degree. Na + and F − concentrations were relatively lower, with 0.41 ± 0.18 µg/m 3 and 0.11 ± 0.08 µg/m 3 , respectively. With an increase of pollution degree, the concentration of Na + increased, while the concentration of F − had no significant change. The main source of Na + may be soil dust because of its inland location, and the variation trend was similar to that of Ca 2+ . In addition, the concentration of F − was low and stable, indicating that its source was relatively stable. The analysis above shows that SO 4 2− and NO 3 − were important components of water-soluble ions and PM 2.5 . NOR and SOR are the indicators of secondary aerosols in the atmosphere, and it is generally believed that the secondary transformation of SO 2 and NOx occurs when SOR and NOR are greater than 0.1 [50]. The average values of NOR and SOR were 0.26 and 0.22 in autumn and winter of Liaocheng, and the maximum values were 0.76 and 0.52, respectively, suggesting that the phenomenon of atmospheric secondary transformation was obvious during autumn and winter in Liaocheng. SOR and NOR were significantly different at different pollution degrees. They were 0.06 and 0.05 at CLD, which suggested no obvious secondary transformation, but increased to 0.26 and 0.23 at MMD and to 0.47 and 0.36 at SSD, 8.0 and 7.0 times those of CLD, respectively. SOR and NOR increased significantly with the increase of pollution degree, suggesting that the increase of PM 2.5 concentrations was greatly affected by the conversion of sulfate and nitrate. In addition, SOR and NOR are greatly affected by meteorological conditions, especially temperature and RH, and their relationship between temperature and RH is shown in Figure 4. SOR and NOR were positively correlated with RH (R 2 were 0.69 and 0.59, respectively), but the correlation with temperature was complex. SOR and NOR were correlated positively with the temperature when the temperature was above 10 • C, but relatively poorly when the temperature was low.

OC and EC Analysis
Carbonaceous species were found to contribute significantly to the formation of fine particles which mainly include EC and OC. EC is a good indicator of primary anthropogenic pollutants and it is one of the main light-absorbing species in fine particles. It is also the medium of gas-solid reaction for SO 2 and NOx [51]. While the source of OC is more complex, besides the primary emissions from fuel combustion, industrial production and natural sources, there is secondary organic carbon (SOC) produced by photochemical reactions of gaseous precursors in the atmosphere. The mean concentrations of OC and EC were 15.20 ± 7.02 µg/m 3 and 6.66 Usually, the OC/EC value is often used to judge a pollution source preliminarily. The relevant studies show that OC/EC between 1.0 and 4.2 indicates the presence of vehicle exhaust emissions [52]; OC/EC between 2.5 and 10.5 indicates the presence of coalburning emissions [34] and OC/EC between 3.8 and 13.2 indicates the presence of biomass combustion emissions [53]. Chow [54] considered that when OC/EC exceeds 2, there is a secondary organic carbon presence. Through calculation, the average OC/EC value during the sample period was 2.28, therefore, secondary pollution more likely happened in the autumn and winter in Liaocheng, and the main source may be vehicle exhaust. Moreover, the concentrations of SOC could also reflect the level of secondary pollution and were also calculated. The concentration of SOC was 8.01 ± 5.95 µg/m 3 and accounted for 52.7% in OC. As the pollution degree increased, the concentration of SOC increased gradually from 5.43 µg/m 3 at CLD to 11.65 µg/m 3 at SSD, but its proportion in OC decreased from 53.1% to 50.8%. The correlations between PM 2.5 and OC, EC and SOC are shown in Figure 5. As seen in Figure 5, OC, EC and SOC were significantly correlated with PM 2.5 , and the R 2 (Pearson coefficient) were 0.52, 0.30 and 0.23, respectively, suggesting that PM 2.5 concentrations were affected by organic matter to some extent, but secondary organic pollution was not the main reason for the increase of PM 2.5 concentrations.

Elemental Analysis
Elements were mainly divided into two groups: (1) crustal elements like Si, Ca, Mg, Al and Fe, which were considered as the main indicators of crustal dust; (2) anthropogenic elements including Mn, Ni, Cu, Zn, As, Se, Cd, Sb, Pb, et al., which probably originated from fossil fuel combustion, industrial metallurgical processes and vehicle emissions [55,56]. The total concentration of elements in the study was 12.21 ± 4.84 µg/m 3 and accounted for 11.1% of PM 2.5 mass. With increased pollution degree, the elements' concentration increased from 11.81 µg/m 3 at CCD to 12.6 µg/m 3 at MMD, while the proportion in PM 2.5 decreased significantly from 21.4% to 6.2%, which indicates that elements were not the cause of the PM 2.5 concentration increase. The concentrations of element species follow the order of Si > Ca > Al > K > Fe > Na > Mg > Zn > Pb > Ti > Mn > Cu > Ba > Cr > As > Sn > Sb > Ni > V > Cd > Li > Co, and Si, Ca, Al, K and Fe were the abundant elements quite possibly coming from crustal dust with the average concentrations of 3.99 ± 2.03, 2.74 ± 1.37, 1.53 ± 0.79, 1.47 ± 0.60 and 1.10 ± 0.49 µg/m 3 , respectively. With the increase of pollution degree, the concentrations of Si, Ca, Mg and Ti gradually decreased, while the concentrations of other elements basically showed a gradually increasing trend, indicating that with the pollution increase, the natural sources of elements decreased, while the influence of anthropogenic source increased to some extent.

PM 2.5 Mass Reconstruction
The results of PM 2.5 mass reconstruction during CCD, MMD and SSD are shown in Figure 6, including SNA (sum of NO 3 − , SO 4 2− and NH 4 + ), other soluble ions, organic matter (OM), EC, crustal matter (CM), other elements, and non-identified compositions. OM is estimated as OC multiplied by 1.6 for urban areas [57]. The sum of Na + , K + , F − and Cl − concentrations were calculated [58] as other soluble ions, and 20 concentrations of elements (all elements except Al, Si, Ca, Fe and Mg) as other elements. CM is calculated using the crustal species, which can be expressed as Equation (7). Additionally, there were some unknown components in the chemical mass reconstruction results which may come from the other components that cannot be measured, the mass weighing error of PM 2.5 , the measurement error of chemical components and the deviation of conversion coefficient; this part was defined as UD. After reconstruction, PM 2.5 concentrations were significantly correlated with the monitored value, R and average residual were 0.96 and 0, respectively, indicating that the reconstructed data were effective, while the monitoring data and chemical composition analysis data were highly reliable, too. (8) Figure 6. Standard P-P plots of regression normalized residuals.
The reconstruction of PM 2.5 during the sample period and different pollution degrees are shown in Figure 7. SNA, OM and CM were the main chemical components of PM 2.5 . As the pollution degree increased, the total chemical components' concentrations increased significantly, as did SNA, and the concentrations were 13.97, 39.78, 99.48 µg/m 3 and the proportions were 23.0%, 36.3%, 49.0% at CLD, MMD, SSD, respectively, while the ratio of SNA/PM 2.5 at SSD was 6.17 times than that at CLD. SNA mainly came from secondary transformation of SO 2 , NOx and NH 3 . Coal combustion produces lots of pollutants in the autumn and winter in Liaocheng, while vehicle emissions and transit vehicles also have a certain amount of emission. Combined with the relatively stable weather conditions, pollutants were more likely to undergo secondary transformation under low temperature and high humidity conditions [59], resulting in a higher concentration and proportion of SNA. As for OM, the concentrations and proportions were 16.34, 24.72, 36.69 µg/m 3 and 27.1%, 22.6%,18.1% at CLD, MMD and SSD, respectively. With the increase of pollution degree, the concentration increased but the proportion decreased, while the change trend of EC was similar with that of OM. The concentration and proportions of CM were 17.82, 17.59 and 16.36 µg/m 3 at CLD, MMD and SSD, respectively. With the increase of pollution degree, CM concentration decreased slightly, but the proportions decreased significantly. The ratio decreased from 29.6% at CLD to 8.1% at SSD. CM is mainly derived from dust, which indicated that the contribution of dust may have obviously decreased with the increase of pollution degree. Generally, PM 2.5 in autumn and winter in Liaocheng was dominated by SNA, OM and CM, and SNA was the main reason for the increase of PM 2.5 concentrations, so the control of its precursors like SO 2 and NOx was particularly important.  In this study, 26 species including PM 2.5 were used as input data for the PMF model. In general, SOA and SOC data were removed from PM 2.5 and OC, respectively, in order to reduce the SOC influence of the calculation. The factor number performed ranged from 1 to 7, and the five-factor with FPEAK = 0 solution was found to provide the "optimal solution". Under this solution, residuals of the majority of standardized species were between −3 and +3, G-space plots showed data points lying within the source axes. The results of five source factors with clear profile and physical meaning are shown in Figure 8. Factor 1 showed major loadings of POC, EC, As, Cd and K + . Both source profiles measured in the laboratory and the chemical analysis of ambient PM 2.5 samples have indicated that OC and EC can be considered as tracer contents of coal combustion. K + is primarily emitted from biomass burning [49], and As is often used as a marker for coal-fired power plant emissions [60], so Factor 1 has been identified as the combustion-related source.
Factor 2 was significantly loaded on SO 4 2− , NO 3 − and NH 4 + and could be identified as a mixture of secondary aerosols of nitrates and sulfates. In the atmosphere, the formation of secondary ions is mainly from gaseous precursors (SO 2 , NH 3 and NOx) created by anthropogenic activities.
Factor 3 was predominantly loaded on Ni, Zn, Cr, V, Mn and Pb. It is generally believed that Zn, Mn, Cr and Ni are the indicator species of metallurgical emissions [61], and V is usually discharged by oil-fired power plants and steam boilers [62]. Therefore, Factor 3 was identified as the industrial process source related to metal processing.
Factor 4 showed high loadings for POC, EC, Zn, Pb, Mn, Cu and Ni. In general, EC is the characteristic element of vehicles [63], while vehicle brake wear, tire wear and oil drip could result in greater abundance of Zn, Mn and Pb in paved road dust [64]. Zn is also a marker element with Pb for transportation, because utilization of Pb as a fuel additive nowadays has been banned. Therefore, Factor 4 represents the pollution of vehicles.
Factor 5 was significantly loaded on Mg 2+ , Ca 2+ , Ti, Al and Si. Ions like Mg 2+ and Ca 2+ are often used to identify building dust, while Al, Si and Ti are mainly related to dust blown into the atmosphere by soil or rock weathering, so Factor 5 was identified as dust source.
The source of PM 2.5 during the sampling period is shown in Figure 9, according to the result of PMF. It showed that secondary transformation had the most abundant contribution to PM 2.5 (36.7%), followed by combustion-related source (20.4%). The contributions of SOA and mobile sources were not significantly different, accounting for 11.7% and 11%, respectively, while the contributions of dust sources and industrial process sources were 10.5% and 9.7%, respectively (Figure 8). Regarding different pollution degrees, at CLD dust sources contributed the most (22.7%), followed by mobile sources (19.2%) and combustion sources (17%), the contribution of SOA and industrial process sources were 15.7% and 14.9%, respectively, while secondary transformation was the lowest (10.4%). In the case of MMD, the contribution of secondary transformation sources increased significantly (31.4%), while the contribution of combustion sources also increased to a certain extent (23.5%), other sources' contribution decreased with different ranges, especially dust and industrial process, which decreased to 11% and 11.2%, respectively. However, in the case of SSD, the proportion of secondary transformation increased sharply again, reaching 57%, more than five times that at CLD, while the contribution proportion of other pollution sources decreased to some extent. The contribution proportion of combustion sources decreased to 18%, and the contributions of other pollution sources were less than 10%. Generally, as the pollution degree increased, the contribution of secondary transformation increased significantly, that of combustion sources first increased and then decreased, while the contributions of dust sources, mobile sources, industrial process sources and SOA gradually decreased. In autumn and winter, the diffusion conditions were unfavorable when the pollution was heavy, the humidity was also relatively high and secondary transformation was conducive. Therefore, efforts should be made to control the emission of PM 2.5 precursors including NOx and SO 2 , with the focus on coal burning and vehicle exhaust emissions, in order to reduce the generation of secondary inorganic particles.

Source Analysis of PM 2.5 Using Back Trajectory and Clustering
Regional transport has important influence of the formation of air pollution. Thus, the transport of PM 2.5 during the sample period was studied. The clustering analysis of the backward flow trajectory of the sampling period was conducted, and the result are shown in Figure 10. It showed that there were five transport paths during the sampling period. The short-distance transport from the northeast and west-northwest (cluster 1 and cluster 2) directions ratio were high, accounting for 29% and 28% of the total trajectory, respectively. The third type of trajectory from southeast to Liaocheng from Anhui Province was the shortest (cluster 3), accounting for 17% of the total trajectory. The fourth and fifth types of trajectories were relatively long, both from the northwest to Liaocheng via Inner Mongolia and Hebei Province, accounting for 15% (cluster 4) and 11% (cluster 5) of the total trajectories, respectively. Source resolution results of atmospheric PM 2.5 are classified according to air mass sources, which is helpful in determining the spatial orientation of atmospheric PM 2.5 pollution sources. PM 2.5 source resolution results corresponding to various trajectories are also shown in Figure 9. The contribution of secondary transformation of clusters 1, 2 and 3 which transmitted in short distance were relatively high, accounting for more than 40% of PM 2.5 and suggesting that the accumulation of local pollutants was conducive to the secondary reaction when the weather was calm and stable. The secondary transformation proportions of cluster 4 and 5 transmitted by long distance were significantly lower, especially cluster 5, but the dust sources' contributions of cluster 4 and 5 were significantly higher. Wind speed was higher during long distance transmission, so it more easily led surface dust pollution. There was little difference in the contribution of industrial sources of every cluster. The contribution of cluster 1 and cluster 3 was slightly higher, accounting for 12.1% and 12.5% respectively. Cluster 1 passed through Shandong Province, while cluster 3 was mainly influenced by cities of Anhui Province, which had more industrial enterprises. As for cluster 4 and cluster 5, mobile sources and SOA contributed more, which may be related to the route crossing Hebei. However, the contribution of combustion sources was the highest, which may be related to the primary pollutants and coal burning in winter in North China.

Conclusions
(1) During the study period, the concentration of PM 2.5 varied from 26.7 to 286.3 µg/m 3 , with an average concentration of 109.7 ± 56.8 µg/m 3 in autumn and winter in Liaocheng, which was 0.46 times higher than the limit value of PM 2.5 concentration CAAQS (GB 3095-2012) (daily standard: 75 µg/m 3 ). Number of pollution days accounted for 67.6% of sampling period.  4) The results of chemical composition reconstruction showed that SNA and OM accounted for a higher proportion of PM 2.5 , which were 39.0% and 22.2%, respectively. The proportion of crustal substances, other ions, EC and trace elements were relatively low, 15.9%, 7.0%, 6.1% and 2.1%, respectively. The proportion of SNA increased significantly with the increase of pollution degree, from 23.0% at CLD to 49.0% at SSD. The proportion of other components decreased, especially crustal materials. (5) Five factors of PM 2.5 have been identified by PMF: secondary transformation sources (36.7%), combustion-related sources (20.4%), SOA (11.7%), vehicle emissions (11%), dust (10.5%) and industrial processes (9.7%). The contribution of secondary inorganic sources, which was the main cause of the PM 2.5 concentration rise, reached 57% in SSD. (6) During the study period, the air mass mainly came from five paths in Liaocheng, and the air mass from the Shandong province and the northeast accounted for a higher proportion. The secondary transformation contribution of the air mass with short transmission distance like that in clusters 1, 2 and 3 were higher, while the contribution of the dust from the long distance, like clusters 4 and 5, were higher. Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.