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For the source apportionment of PM_2.5 mass, the Positive Matrix Factorization (PMF) model (Hopke et al., 2003) was applied to the PM_2.5 chemical component dataset. The PMF model is a receptor model based on a multivariate analysis technique that uses measurement error of the measured data to provide weights in the fitting process. The PMF model provides a solution that minimizes an object function, the Q value, based on the uncertainties of each observation (Polissar et al., 1998). We referred to Kim et al. (2003) for detailed descriptions of the PMF technique, and we used EPA-PMF3.0 for calculation (Norris et al., 2008).

When a source is near the sampling site, source contributionvariationsuggests a close relation to the wind direction surrounding the sampling site. The conditional probability function (CPF) (Kim et al., 2003) was performed to estimate the association of a local source and source contributions estimated from the PMF model coupled with the wind direction data. The CPF value is calculated using the following equation:

where m_Δθ is the number of occurrences from wind sector Δθ that exceeded the threshold criterion, and n_Δθ is the total number of data from the same wind sector. In this study, 16 sectors (Δθ=22.5°) were chosen; calm winds (≤1 m/s) were excluded from this analysis. In this study, the threshold criterion was set at the upper 10th percentile value of the fractional source contributions for each source.

The potential source contribution function (PSCF) (Hopke et al., 1995; Ashbaugh et al., 1985) is utilized to estimate likely locations for long-range transportation of aerosols and secondary aerosols. The PSCF was calculated using the daily source contributions estimated by the PMF model, and the backward trajectories were calculated using the Hybrid-Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model and the NCEP/GDAS global meteorological data (Draxler and Rolph, 2003). The PSCF is a conditional probability that an air parcel that passes through an area will have a concentration exceeding the threshold criterion upon arriving at the sampling site. The sources were likely to be located in areas that had high PSCF values. The PSCF value is calculated using the following equation:

where the n^ij is the total number of passages in the ijth grid cell, and m_ij is the number of passages in the same grid cell that are associated with samples that exceeded the threshold criteria. In this study, the threshold criterion was set at the upper 25th percentile value of the fractional source contributions for each source. Backward trajectories, starting every hour at heights of 1,300 and 1,800 m above ground level, were computed using the vertical velocity model for every sample day, producing 120 hourly trajectory end points per sample. The geophysical region covered by the trajectories was divided into 3,500 grid cells of 1°×1°latitude and longitude. To minimize the effect of small nij values that result in high PSCF values with high uncertainties, an arbitrary weight function W(n_ij) was applied to downweight the PSCF values for cells in which the total number of end points was less than three times the average number of passages per grid cell (Wan et al., 2009; Polissar et al., 2001; Hopke et al., 1995). W(nij) is defined by the following equation depending on nij:

A summary of statistics for the PM_2.5 mass concentration and chemical species is shown in Table 2. An outlier of the PM_2.5 mass concentration is difficult to reconstruct with the PMF model. Therefore, data deviating from the average-concentration range need to be examined using a method of analysis other than the PMF model. In this report, data with analytical precision problems were excluded using the ion balance and the chemical mass closure (CMC) model (Harrison et al., 2003). First, data in which the ratio of the anion equivalence concentration and the cation equivalence concentration did not fall within the ranges of 0.8-1.2 were excluded by confirming the ion balance of each sample. Second, the CMC model was used to determine the concentration of the chemical species of the data in which the ion balance was adequate. The CMC model is a method of estimating the mass concentration (EMC) of the ambient particulates from the concentration of the chemical species. The CMC model is expressed in the following equation:

Data in which the ratio of the EMC and the actual concentration measurement did not fall within the range of 0.8-1.2 were excluded from the PMF analysis. As a result, 165 samples were adopted for the PMF model. Furthermore, an ion and an element such as K⁺ and K (Ca²⁺ and Ca) overlapped. A lower percentage of below the detection limit (K and Ca²⁺) was adopted in order to reduce the loss of data used for PMF analysis. Concentrations below the detection limit level were replaced with a level half that of the detection limit (Polissar et al., 1998). A titanium (Ti) and chrome (Cr) proportion of more than 15% below the detection limit level was excluded from the calculation using the PMF model.

In the PMF analysis, dispersion of Q provided by a calculation repeatedly is small, and the number of factors nearby is most suitable for the theoretical value of Q (Q_Theory), where the value of Q is calculated using the following equation:

where n is the number of samples, and m is the number of components. The average and relative standard deviations (RSD) of the Q value provided by calculations repeated 20 times of each factor number with the Q_Theory are shown in Fig. 2. In this figure, Q_True is the value calculated using all data, and Q_Robust is the value calculated excluding outliers. The RSD of the Q_True and the Q_Robust had a small range of 5-9 factors, and the Q_True and Q_Robust of the 9 factors were nearest in the Q_Theory. Therefore, it was judged that the 9 factors were most suitable. To prove the validity of this result, the robustness and rotational freedom of the final solution were verified using a bootstrap run and an Fpeak run, respectively. The solution with 9 sources and Fpeak=-0.1 was the most reasonable. Furthermore, in the bootstrap run, all factors mapped at more than 80%.

Fig. 2 
Q value and the relative standard deviation of the Q value for the different factor numbers.

Correlation between the reconstructed mass concentrations from the factors extracted by PMF analysis and the measured value of the PM_2.5 mass concentration is shown in Fig. 3. The slope of the regression line is 0.78, and the correlation coefficient is 0.96; the PM_2.5 mass concentration is reconstituted well by extracted factors. The PMF-deduced source profiles and source contributions are presented in Fig. 4 and Fig. 5, respectively. In addition, the estimated source of each factor profile and the average contribution of each factor to the PM_2.5 mass concentration are summarized in Table 3.

Fig. 3 
Scatter plots of PM_2.5 mass versus the predicted PM_2.5 mass.

Fig. 4 
Source profiles based on PMF analysis. The vertical axis expresses the percentage of each species among factors.

Fig. 5 
Source contributions (μg/m³) to the PM_2.5 mass concentrations.

Factor 1 contained large fractions of a host of metals. High concentrations of Zinc (Zn), lead (Pb), nickel (Ni), and cadmium (Cd) are mainly contributed by industrial activities such as coal and waste combustion (Marcazzan et al., 2001). Zn and Ni are also associated with steel mills and other metallic industrial activities (Song et al., 2001). The CPF plot for factor 1 is presented in Fig. 6(a). The CPF value of factor 1 was high from south-southwest to west-southwest. Since there are steel mills approximately 4.5 km westsouthwest and approximately 1.0 km south-southwest of the sampling site, it suggests that this factor was affected by the steel mills in the vicinity of the sampling site. The average contribution of factor 1 is 7.8%. This factor is categorized as “steel mills.”

Fig. 6 
Conditional probability function (CPF) plot. (a) steel mills, (b) sea salt, (c) traffic, (d) coal combustion, (e) heavy oil combustion.

Factor 2 contained significant fractions of the nitrate ion (NO₃ ^-) and chloride ion (Cl^-) with few other component fractions. Furthermore, because the ion balance in factor 2 was 1.03, factor 2 was interpreted as the factor whose expressed contribution of ammonium chloride and ammonium nitrate was semi-volatile. In addition, factor 2 showed a higher trend during low ambient temperature seasons such as autumn and winter (Fig. 5). The average contribution of factor 2 is 7.0%. This factor is categorized as “secondary chloride and nitrate.”

Factor 3 contained typical soil components of the soil, such as Ca²⁺, Al, and Fe. Airborne soil particles could have been resuspended in the air from road traffic, construction sites, and windblown soil dust. Factor 3 appeared in a high concentration in the spring season of 2011 (Fig. 5). The backward trajectories on May 15, 2011, are shown in Fig. 7. Backward trajectories of this day point to eastern Mongolia and the Gobi Desert as sources of the yellow sand found at the sampling site. Furthermore, yellow sand was observed across a broad area of Japan on this day (Japan Meteorological Agency, 2012). Therefore, this high concentration was attributed to dust transported in yellowsand events that had occurred in eastern Mongolia and the Gobi Desert. The average contribution of factor 3 is 5.0%. This factor is categorized as “soil.”

Fig. 7 
Backward trajectories of samples arriving at the sampling site on May 15, 2011 (JST 3:00, 9:00, 15:00, and 21:00).

Factor 4 shows enhanced fractions of Cl^-, sodium ion (Na⁺), and magnesium ion (Mg²⁺). These tracers are mainly associated with sea salt particles. The CPF plot for factor 4 is presented in Fig. 6(b). The CPF value of factor 4 was high from southeast to southsoutheast because the sampling site was located on the north side of the Seto Inland Sea (Fig. 1). The average contribution of factor 4 is 3.8%. This factor is categorized as “sea salt.”

Factor 5 contained a large fraction of OC, EC, and antimony (Sb); there were few other component fractions. The large contribution of OC and EC indicates fuel combustion; and Sb is associated with brake pad wear (Iijima et al., 2009). The CPF plot for factor 5 is presented in Fig. 6(c). The CPF value of factor 5 was high from north-northeast to northeast. National Route 2 runs approximately 1.4 km to the north-northeast and National Route 250 runs approximately 0.5 km south-southwest of the sampling site. As indicated above, the average daily traffic volume and the proportion of heavy vehicles to the traffic volume on National Route 2 are heavier than those of National Route 250. Furthermore, the major arterial roads are concentrated northeast of Himeji City (Ministry of Land, Infrastructure, Transport and Tourism, 2010). Therefore, factor 5 shows the traffic and exhaust gas of vehicles on the nearby road. The average contribution of factor 5 is 20.8%. This factor is categorized as “traffic.”

Factor 6 constituted a significant fraction of the sulfate ion (SO₄ ^2-) and ammonium ion (NH₄ ^{+ + +}). Furthermore, because the ion balance in factor 6 was 1.04, factor 6 was interpreted as the factor that expressed the contribution of ammonium sulfate. In addition, this factor contains a fraction of OC, EC, vanadium (V), and arsenic (As). Ammonium sulfate is produced by sulfur dioxide (SO₂) exhausted into the atmosphere by the combustion of fossil fuels such as oil and coal. At first, sulfur dioxide is oxidized to sulfuric acid; the sulfuric acid is neutralized by ammonia and converted to ammonium sulfate. Because ammonium sulfate is stable in the atmosphere for a long time, it is transported great distances. Therefore, it suggests that the SO₂ occurring at a great distance changes during transportation to ammonium sulfate before arriving at the sampling site. The average contribution of factor 6 is 20.9%. This factor is categorized as “secondary sulfate 1.”

Factor 7 contained a large fraction of potassium (K). K (or K⁺) is considered to be an index of burning biomass fields (Zhang et al., 2010) and fireworks (Tsai et al., 2012). Furthermore, this factor contains a fraction of NO₃ ^-, SO₄ ^2-, and Pb, suggesting fossil fuel combustion. The average contribution of factor 7 is 8.0%. This factor is categorized as “secondary sulfate 2.” In addition, we considered the sources of secondary sulfate 1 and secondary sulfate 2, which contribute highly to the sulfate in section 3.3.

(Cu). Generally, the As contained in atmospheric particles traces back to coal combustion in Japan (Mamuro et al., 1979). Furthermore, this factor contains a fraction of EC, suggesting combustion. The CPF plot for factor 8 is presented in Fig. 6(d). The CPF value of factor 8 was high from south-southwest to west-southwest. Since the coal-fired power plant (total output: 133,000 kW, Kansai Electric Power Co., Inc., 2013) is approximately 4.5 km west-southwest of the sampling site, it suggests that this factor was affected by the coal-fired power plant in the vicinity of the sampling site. The average contribution of factor 8 is 2.3%. This factor is categorized as “coal combustion.”

Factor 9 contained a significant fraction of V and a large fraction of nickel (Ni). Generally, V and Ni contained in atmospheric particles trace back to heavy oil combustion in Japan (Mamuro et al., 1979). Typical oil combustion sources are ships and boilers, such as thermal power plants using heavy oil. Although two thermal power plants exist near the sampling site (Fig. 1(b)), the thermal power plants have a small effect because their main fuel is liquefied natural gas (Kansai Electric Power Co., Inc., 2013). A recent study showed that V is definitely the index of ships (Zhao et al., 2013); in addition, inland shipping can also be considered a source of particulate matter (Vallius, 2005). The CPF plot for factor 9 is presented in Fig. 6(e). The CPF value of factor 9 was high from south-southeast to southwest. Since the Port of Himeji, an international hub port, is approximately 4.0 km south-southeast of the sampling site, it suggests that this factor was affected by ship traffic in the vicinity of the sea. The average contribution of factor 9 is 3.8%. This factor is categorized as “heavy oil combustion.”

When it is calculated as seven factors, factors 6 and 7 do not appear; the loading of those factors is allocated to other factors (Fig. 8). Therefore, factors 6 and 7 may have collinearity with other factors. Furthermore, as compared with factor 9, the load of SO₄ ^2- in heavy oil combustion was increased, and the load of As and Pb in secondary sulfate 1 was increased in the case of factor 7. Therefore, a source of SO₄ ^2- suggests heavy oil combustion as an index of V and coal combustion as an index of As and Pb. Yamagami et al. (2013) extracted eight factors by applying the PMF component concentrations of PM_2.5 that were collected at six points in Nagoya City. The results show that the load of SO₄ ^2- is large in “coal combustion” and “heavy oil combustion;” therefore, “coal combustion” and “heavy oil combustion” have been estimated to be major sources of SO₄ ^2-. Since, in this analysis, similar results have been observed when seven factors have been calculated, “coal combustion” and “heavy oil combustion” are considered sources of SO₄ ^2-. However, the survey site in this study is one point in the industrial area; it is possible that its location strongly influenced the sources in the nearby survey site. On the other hand, the number of survey sites in the reporting of Yamagami et al. is a six survey points, including the general environment point, has been analyzed as the same number of sources the number of each point. Therefore, it is possible that the influence of the source in the survey site vicinity has not yet been extracted.

Fig. 8 
Comparison of the source profile by 9 factors and 7 factors. The vertical axis expresses the percentage of each species among factors.

On the other hand, factor 8 is speculated to be caused by coal combustion because the load of As is large; factor 9 is speculated to be caused by heavy oil combustion because the load of V is large. However, the load of SO₄ ^2-, as compared with factors 6 and 7, is small. The reason is that the distance between the source and the survey site is close. Since a conversion rate to SO₄ ^2- from SO₂ is estimated to be 0.9-3.7%/hr (An et al., 2003; Sasaki et al., 1988; Uno et al., 1997), if located near the source, the factor representing heavy oil combustion or coal combustion, SO₄ ^2-, there is a possibility of a small loading. As with China, Japan has heavy oil combustion facilities and coal-fired facilities. In particular, coal-fired power plants and steel mills, coke ovens, and ports are also present in the areas surrounding survey sites. Therefore, factors 8 and 9 represent the impact of fossil fuel combustion in the vicinity, and factors 6 and 7 represent the impact of fossil fuel combustion at a distance. However, due to the differences in distance between the survey sites, they are believed to have been extracted as different factors.

Sulfate accounts for 26.4% of the mass concentration of PM_2.5 at this sampling site. Therefore, it is important to identify the source of sulfate to reduce PM_2.5. In this study, two different types of secondary sulfate were identified by PMF analysis. Secondary sulfate 1 and secondary sulfate 2 account for 20.9% and 8.0%, respectively, of the PM_2.5 mass concentration. Secondary sulfate 1 is characterized by its high concentration of SO₄ ^2- and NH₄ ^{+ + +}. Secondary sulfate 2, on the other hand, is characterized by its high contribution of potassium (K). Furthermore, secondary sulfate 1 shows a high seasonal variation in the spring and summer that is associated with high photochemical activity (Fig. 5); secondary sulfate 2 has a weak summer-low seasonal variation (Fig. 5). Therefore, it suggests that these sources were greatly different.

Fig. 9 shows the PSCF plots for secondary sulfate 1 and secondary sulfate 2. Potential source areas and pathways where the secondary sulfates were formed are likely to be located in the high-PSCF-value areas. As shown in Fig. 9(a), the PSCF plot of secondary sulfate 1 shows the influence of the industrial area of the east coastal region of China, the Eastern China Sea, and the Kyushu region of Japan. The Yangtze Delta region of the eastern coastal industrial region of China includes Shanghai, Chiangsu, and Zhejiang. In recent years, the economic growth rate of the Yangtze Delta region has greatly exceeded the national average, and its economic growth is remarkable. It was suggested that SO₂ emissions from the thermal power plant and industries located in the eastern coastal industrial region of China were related to what was converted to high PSCF values in the process of transportation. The Eastern China Sea has a great deal of marine traffic by ships. Yang et al. (2007) have developed an emission inventory from marine ships, in which the SO₂ from ships accounts for 9.5% of all sources in Shanghai in 2003. In addition, Zhao et al. (2013) report a major link between the peak of SO₂ measured in the Yangshan Port of Shanghai and the ships’ exhaust. This suggests that the high PSCF values in the Eastern China Sea are affected by the SO₂ emission from ships. There are many active volcanoes in Kyushu region of Japan. In particular, there were many SO₂ emissions from the Sakurajima volcano; emissions in 2011 and 2012 were 300-3,200 tons/day and 1,200-5,700 tons/ day, respectively (Fukuoka District Meteorological Observatory, 2012, 2011). This suggests that the SO₂ exhausted from various sources changed to sulfate in the transportation process.

Fig. 9 
Potential source contribution function (PSCF) plot. (a) secondary sulfate 1, (b) secondary sulfate 2.

The high contribution of potassium (K) in secondary sulfate 2 suggests a strong influence of burning biomass fields (Zhang et al., 2010). Kumagai et al. (2010) measured the levoglucosan and potassium ions that are indices of burning biomass on the Kanto Plain of Japan and reported that the contribution of biomass burning is high in the winter; the average contribution of burning biomass to the fine particulate mass was 20% in the winter. Biomass burning in the report of Kumagai et al. was similar to a characteristic of secondary sulfate 2 in this study; this supports the influence of biomass burning at this sampling site. However, this factor contains a fraction of NO₃ ^-, SO₄ ^2-, and Pb, suggesting the combustion of fossil fuel. As shown in Fig. 9(b), although the PSCF plot of secondary sulfate 2 shows the influence of the border area between Russia and Mongolia where forest fires are frequent (Heo et al., 2009), the PSCF value of the urban areas of China, such as Beijing, Hebei, and western Inner Mongolia, is high. In Chinese urban areas and Inner Mongolia, coal central heating systems are used in the winter, generating serious atmospheric pollution (Zhao and San, 1986). This suggests that secondary sulfate 2 was affected by particles derived from the combustion of fossil fuels, such as coal, in addition to biomass burning. On the other hand, the day with the highest contribution concentration of secondary sulfate 2 (9.5 μg/m³) was January 25, 2012. January 23 and 22, 2012, were the Chinese New Year and New Year’s Eve, respectively - a most important festival in China. During this event, people use a large quantity of fireworks. Previous studies have shown that fireworks aerosols are rich in K (Tsai et al., 2012). Therefore, the increased contribution of this factor on January 25, 2012 and the next several days may have been affected by the long-distance transportation of fireworks aerosols.

Heo et al. (2009) reported the results of source identification and apportionment by PMF and PSCF analyses of PM_2.5 in Seoul, Korea, from March 2003 to December 2006. In their report, nine factors were extracted by PMF analysis; the contribution of a factor categorized as “secondary sulfate” was 20.5%. Furthermore, the PSCF plot of “secondary sulfate” conformed to the result of the PSCF plot of secondary sulfate 1. Their report strongly supports the results of this study. Higo et al. (2013) extracted seven factors by applying the PMF component concentrations of PM_2.5 that were collected at two general environmental points in Fukuoka City. Their results show that the load of SO₄ ^2- and the impact of cross-border transport are large for “coal combustion” and “oil combustion.” Furthermore, in the reports, “oil combustion” and “coal combustion” indicate high concentrations in spring and winter, respectively. Therefore, we estimated that secondary sulfate 1 and secondary sulfate 2 were extracted as other factors, as is the case with the reporting of Higo et al., that high concentrations differed seasonally.