## 3 Results and Discussion
### Soil Heavy Metal Source Apportionment
#### 3.2.2 PMF Analysis and Source Apportionment  
To further identify and quantify the pollution sources and the contribution rates of the heavy metals in the soil of the study area, we conducted a quantitative source apportionment using the EPA_PMF 5.0 software. The PMF model is employed to quantify the sources of metals in the area. By performing 100 test runs for each scenario, we ultimately determined the source factors based on the lowest \(Q\) value obtained between the various test factors [47]. Before applying PMF, the dataset was inspected, and outliers were removed according to the interquartile range and histograms, as outliers can significantly affect PMF results [29]. In this study, outliers were defined as any observations outside the range of \([Q_{1}-1.5 IQR,Q_{3}+1.5 IQR]\), where \(Q_{1}\) and \(Q_{3}\) are the first and third quartiles, respectively, and \(IQR=Q_{3}-Q_{1}\)[49]. The soil heavy metal data and their associated uncertainties were initially imported into the software. The signal-to-noise ratio (\(S/N\)) for the twelve analyzed elements was found to exceed 1, indicating a strong category and confirming that the data met the requirements for PMF model calculations. Given the low coefficient of determination (\(r^{2}\)) for Se and moderate \(r^{2}\) values for V (\(r^{2}=0.29\)) and Pb (\(r^{2}=0.23\)), Se was categorized as \"bad category\", while V and Pb were classified as \"weak category\" [50]. The \(r^{2}\) values for the remaining heavy metals ranged from 0.51 to 0.99, with particularly high values for Hg (\(r^{2}=0.99\)) and As (\(r^{2}=0.97\)), indicating a high correlation between variables and the effectiveness of the PMF model in quantitative source apportionment studies [48]. The fitting results show that the relative contribution rates of factor 1, factor 2, factor 3, and factor 4 are 17.62%, 18.5%, 28.35%, and 35.56%, respectively. The contribution plots for the four factors are shown in Figures 9 and 10. Factor 1 is primarily weighted by As at 73.9%, with secondary contributions from Co at 27.4% and Mn at 20.5%. There is no significant correlation between As and other heavy metals; however, a moderate correlation exists between As and Co (\(r=0.47\), \(p\leq 0.01\)**) (Figure 8), indicating that As has a relatively independent source [51]. As is a toxic element, yet the average concentration of As in this study area is 0.67 times the background value. The As concentration in this region is significantly lower than the local soil background values, suggesting minimal impact from human activities. Additionally, numerous studies have indicated that the sources of As and Cr in soils are derived from the parent  
Figure 9: Contributions of sources to each heavy metal (factor 1 (natural source), factor 2 (coal combustion and atmospheric pollution source), factor 3 (non-ferrous metal smelting and paper industry industrial pollution source), and factor 4 (traffic emission pollution source) are the main sources identified by PMF). material [51; 52]. The high contribution rate of As suggests that factor 1 may be related to these natural processes. Its significant contribution implies that factor 1 may be associated with natural sources. Therefore, factor 1 is likely of natural origin. Factor 2 is primarily weighted by Hg at 92.4%, with secondary contributions from As at 16.4% and Cu at 15.8%. Hg is the main contributor to factor 2. As a typical heavy metal pollutant, Hg is a primary raw material in the production of electronic products [53]. It primarily originates from coal-fired power plants, industrial wastewater, the chlor-alkali industry, and processes that utilize Hg, such as battery manufacturing, fluorescent light production, and electronics [53]. Compared to other metals, the contribution of coal combustion to Hg levels is significantly higher. Coal combustion is widely regarded as the most important source of Hg emissions in China [54; 55]. Hg is almost classified as an isolated factor.