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Article

Positive Matrix Factorization as Source Apportionment of Paddy Soil Heavy Metals in Black Shale Areas in Western Zhejiang Province, China

1
Technology Innovation Center of Ecological Evaluation and Remediation of Agricultural Land in Plain Area, MNR, Hangzhou 311200, China
2
Zhejiang Institute of Geosciences, Hangzhou 310007, China
3
School of Earth Sciences and Resources, China University of Geosciences Beijing, Beijing 100083, China
4
College of Environmental Science and Engineering, Yangzhou University, Yangzhou 225009, China
*
Authors to whom correspondence should be addressed.
Sustainability 2023, 15(5), 4547; https://doi.org/10.3390/su15054547
Submission received: 16 December 2022 / Revised: 17 February 2023 / Accepted: 23 February 2023 / Published: 3 March 2023
(This article belongs to the Special Issue Environmental Effects and Remediation of Soil Pollution)

Abstract

:
The source apportionment of pollutants is the key to preventing and controlling the pollution caused by heavy metals in soils. The aim of this study was to investigate the main sources of heavy metals in the soils of black shale areas in western Zhejiang, China. Based on geostatistical spatial analysis, this research employed positive matrix factorization (PMF) for the source apportionment of heavy metals in paddy soil. The results showed that contaminated arable soils were concentrated in the western and southern study areas. At least five major sources of heavy metals were screened in this study: natural sources (39.66%), traffic emissions (32.85%), industrial emissions (9.23%), agricultural activities (9.17%), and mining (9.10%). To be specific, Cd was mainly from mining; As originated from agricultural inputs such as fertilizers and pesticides; and Hg, as an industrial pollutant, was transported by atmospheric deposition in the study area. The accumulation of Pb, Zn, and Cu was mainly influenced by natural sources and anthropogenic sources, i.e., traffic emissions, while that of Cr and Ni was controlled by natural sources.

1. Introduction

Since the outbreak of the Coronavirus disease 2019 (COVID-19), food security faces enormous challenges worldwide. The prevention and control of heavy metal pollution in farmland soils is essential in order to improve food quality and safety in many countries. In 2014, the China Soil Pollution Survey Report showed that the heavy metal contents of China’s arable soils exceeded corresponding background values by 19.4%, and the soil environmental quality was not optimistic [1,2,3]. Heavy metals are primary pollutants due to their toxicity, bioaccumulation, and degradation resistance [4]. Moreover, excessive quantities of heavy metals can damage soil physicochemical properties, quality, productivity and the microbial activities of the soil environment. Due to slow transportation, which decreases with the natural degradation of the soil [5,6], heavy metals can also accumulate through the food chain of “soil–crops–human body”, threatening human health [7]. In crop production and ecological risk assessment, heavy metals generally refer to the elements that have acute biological toxicity, such as cadmium (Cd), arsenic (As), lead (Pb), chromium (Cr) and mercury (Hg), etc. Moreover, although copper (Cu), zinc (Zn) and nickel (Ni) are essential trace elements and are necessary for human growth when under a very low threshold, they are difficult to decompose and easily accumulate [8]. It is widely believed that Cu, Zn and Ni are also harmful elements to humans when beyond the specific threshold. Eight heavy metals, including Cd, As, Pb, Cr, Hg, Cu, Zn and Ni, are listed by the United States Environmental Protection Agency (USEPA) as pollutants in need of preferential control [9]. Therefore, investigating accurate pollution source apportionment and its contribution level is crucial in the prevention and control of the heavy metal pollution of soils, and also necessary for regional ecological safety and residents’ health.
In terms of the source apportionment of heavy metals in soils, the most widely used method is the receptor model analysis with the contaminated area as the target [10]. Existing source apportionment can be classified into source identification and source quantification [11,12]. Currently, the commonly used receptor models include the principal component analysis/absolute principal component analysis (PCA/APCS), the chemical mass balance (CMB), UNMIX, and positive matrix factorization (PMF) [13,14,15,16]. In particular, the PMF model is a new source analysis method that features simple and effective operation because it does not require the determination of complex original spectra. Moreover, it can limit the factor matrix to non-negative values and handle missing and inaccurate data. This model makes full use of the error analysis of data and applies non-negative constraints to the results of the factor matrix decomposition in processing. Thus, the source component spectrum and the source contribution rates obtained from this process highlight a more practical significance [17]. At first, the PMF model was mainly used for the source apportionment of pollutants in the atmosphere, water, and sediments [18,19,20]. In recent years, it has been increasingly used for the source apportionment of soil pollution [10,21,22,23].
The study area is located in the western region of Zhejiang, where the black shale series is widely developed in the lower reaches of the Yangtze River. The black shale series was formed mainly in a stagnant water environment featuring poor circulation, enriched organic material, sulfide minerals such as pyrite, multiple heavy metals, and other trace elements [24,25]. When exposed to the air, the black shale series can be easily decomposed by weathering, and acidic wastewater is produced. In the course, heavy metals are released into the surrounding environment and thus contaminate the arable soils [26,27]. In addition, with the rapid economic development, heavy metal pollutants generated by various human-made pollution sources, such as domestic waste, traffic emissions, agricultural fertilizers and pesticides, and the emission of mining and industry’s “three wastes”, that is, wastewater, gas, and residue, have entered the soil via various ways and further aggravated the soil’s heavy metal pollution [28,29]. However, a review of the literature revealed that there are few studies that have conducted an accurate source analysis of heavy metal pollution from typical geological backgrounds. This includes, for example, studies on the extent of the contribution of the black shale system to Cd in soil. Given the above problems, 463 pieces of rice rhizosphere soil and synergistic grain samples were systematically collected in this study. Based on the analysis of the heavy metal content characteristics, correlation analysis and PMF were applied to identify the pollution sources and apportion the source contributions to the arable soils of the study area. The results obtained from this study may provide a scientific basis for preventing and controlling heavy metal pollution in the regional farmland.

2. Materials and Methods

2.1. Study Area and Sampling

The study area is located in the west of Zhejiang Province, China (118°51′ E~120°22′ E and 29°35′ N~30°44′ N). It belongs to the subtropical monsoon zone, featuring four distinct seasons and plenty of light. The terrain consists of hills and mountains, and slopes stretching from southwest to northeast. The soils in the study area can be classified into the following groups: red earth, paddy soil, limestone soil, purplish soil, fluvo-aquic soil, and skeletal soil. Among them, the red earth and the paddy soil are the two main types of soil, with major crops such as rice, vegetables and pecans planted in them.
In the study area, 463 pieces of rice rhizosphere soil and synergistic grain sample were systematically determined by GPS (Figure 1). Soil samples (0–20 cm in thickness) were set in cultivated land according to the method of map spots combined with grid density, with a density of 4 to 16 sampling points per square kilometer. Each sample was collected using the 5-grid-based sampling method; one main grid was selected then four sub-grids were taken at equal distances to it, and evenly mixed. In addition, ridges and obvious man-made polluted areas were avoided in the sampling. Soil samples were collected in cloth bags, air-dried to remove the remaining roots, insects and rocks, and cracked by a rubber hammer for analysis in the laboratory.

2.2. Chemical Analysis and Quality Control

Soil samples were pre-processed and analyzed in the laboratory of Zhejiang Institute of Geology and Mineral Resources, China; sample handling and testing met international standards [30,31,32]. Below is a detailed summary of the process. The soil pH was measured using a pH meter with a glass electrode. For the determination of the concentrations of Cd, Cu, Cr and Ni, 0.1–0.25 g of soil sample was digested with three mixed acids (2 mL HF + 10 mL HNO3 + 5 mL HCLO4), the residues were diluted with 3% HNO3, and measured by the inductively coupled plasma mass spectrometer (ICP-MS), Thermo X SeriesⅡ, produced by Thermo Electron Corporation, USA. For the determination of the concentrations of Pb and Zn, 4 g of soil sample was put into a plastic ring and pressed to make a thin section under 10 MPa of pressure. The section was then put on the sample platform of the X-ray fluorescence spectrometry (XRF) (ZSX100e, Rigaku Corporation, Tokyo, Japan) equipment for determination. In total, 0.25 g of soil sample was digested with 50% aqua regia at 100 °C in a water bath for 1 h, followed by the addition of potassium borohydride as a reducing agent. It was again reduced by thiourea-ascorbic acid and then put into the hydride generation atomic fluorescence spectrometer (HG-AFS) (AFS-9800, Institute of Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences) for measuring the concentration of As. Then, 0.5 g of soil sample was digested with 50% aqua regia at 100 °C in a water bath for 1 h, followed by the addition of KMnO4 solution; this was kept for 30 min, then diluted with oxalic acid solution and put into a cold vapor-atomic fluorescence spectrometer (CV-AFS) (XGY-1011A, Institute of Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences) for measuring the concentration of Hg.
To guarantee the quality of analysis, a standard soil sample was used. The deviation between the measured values of heavy metals and the reference values of those in the standard sample was less than 5%. To improve the analysis, the concentrations of heavy metals in some soil selected randomly during the analysis process were measured several times. In the end, the relative standard deviation (RSD%) for the duplicated measurements ranged from 1.65% to 9.95%.

2.3. Positive Matrix Factorization

The PMF model is an improved factor analysis method proposed by Paatero and Tapper in 1994 [20]. The PMF model has similarities with the response surface methodology (RSM) in that the objective function is applied to obtain the desired results and in that fitting coefficients (R2) are used to test the applicability of the model. However, RSM generally uses a second-order polynomial to fit the objective function, while PMF is based on the least squares method for qualifying and iteratively calculating the minimum of the objective function [33,34]. The concentration data can be regarded as a data matrix X of dimensions i by j ; this is then decomposed into two matrices, including the factor contributions (G) and the factor profiles (F). The equation is shown as follows:
x i j = k = 1 p g i k f k j + e i j
where x i j refers to the concentration matrix of the j th chemical species in the i th sample; g i k refers to the contribution matrix of the k th source factor to the i th sample; f k j refers to the concentration matrix of the j th chemical species in the k th source; and e i j refers to the residual for each sample.
The factor contributions and the source profiles can be obtained by minimizing the objective function Q in the PMF model, which can be calculated as follows:
Q = i = 1 n j = 1 m ( x i j k = 1 p g i k f k j u i j ) 2 = i = 1 n j = 1 m ( e i j u i j ) 2
where j th refers to the chemical species for the i th sample and u i j refers to the uncertainty, which can be calculated as follows:
u i j = { 5 6 × MDL   c MDL ( δ × c ) 2 + ( 0.5 × MDL ) 2   c   > MDL  
where δ refers to the error fraction in the chemical species analysis; c refers to the concentration of the chemical species; and MDL refers to the method detection limit.
In this study, the soil pollutant source apportionment adopted the PMF receptor model, as recommended by the United States Environmental Protection Agency (USEPA) [35]. With the data imported into EPA PMF 5.0, the number of factors was set in order to run the software. Since randomicity can cause errors in the analysis results to varying extents, the data were verified 20 times by PMF with random seeds and different factors (ranging from 3 to 7). The trial algorithm used different factor numbers to compare Q/Qexp. Qexp is calculated for each scenario, equal to (number of non-weak data values in X) −(number of elements in G plus those of F). For example, for four factors matched with 463 samples and 8 strong species, the formula can be written as (463 × 8) − ((4 × 463) + (4 × 8)), that is, 1820. When Q/Qexp fluctuates more slowly with increasing factors, this indicates that there are too many suitable factors. In this paper, the optimal number of factors was 5, found by determining the inflection point of Q/Qexp.

2.4. Statistical Analysis

The data were organized and analyzed in Excel 2019. The correlation analysis was conducted with IMB SPSS software. ArcGIS 10.4 was applied to map the distribution of sampling grids and the geostatistical analysis. The source apportionment was completed with EPA PMF 5.0.

3. Results and Discussion

3.1. Spatial Distribution of Heavy Metals in Soils

For arable soils in the study area, the descriptive statistics of the contents of 8 heavy metals and the pH of 463 samples are provided in Table 1. Most of these soils were slightly acidic, with the soil pH in a range of 4.43–8.24. The mean contents of Cd, As, Pb, Cr, Hg, Cu, Zn and Ni in the soils covered in this study were 0.53, 9.62, 34.46, 55.02, 0.14, 27.39, 105.02, and 25.27 mg kg−1, respectively. Except for the negative skewness of Cr, all the heavy metals showed a positive skewness distribution. The Geochemical baseline values of all the heavy metals were higher than the background values of the soil in China, except As [36], which indicates that these elements were significantly influenced by the geological background. The coefficients of variation (CV) in the 8 heavy metals in the samples could be expressed by Cd > As > Hg > Ni > Zn > Cu > Cr > Pb. All the heavy metals were highly variable, except for Pb, which was moderately variable [37]. In particular, the CV of Cd was the largest, at 146.91%, which indicates that human activities accelerated the continuous accumulation of Cd and other heavy metals in the soils; this will probably threaten the ecological environment.

3.2. Source Apportionment of Heavy Metals

3.2.1. Correlation Analysis

Heavy metals in soils are mainly derived from the process of soil formation and anthropogenic activities, and those from the same source were mutually correlated. According to the correlation analysis, the consistency of soil heavy metals sources can be inferred [38]. The Pearson correlation analytical results of 8 heavy metals in the study area are given in Table 2, indicating that there were significant correlations among most heavy metals. Among them, the correlation between Cr and Ni was the strongest, with a coefficient of 0.793 (p < 0.01), followed by Cu and Zn with a coefficient of 0.636 (p < 0.01), indicating that Cr–Ni and Cu–Zn had strong homologies. In addition, Cu–Zn was positively correlated with both Pb and Cr–Ni (p < 0.01), while there was a non-significant correlation between Pb and Cr–Ni, indicating that Cu and Zn may derive from multiple channels. Cd was found to be negatively correlated with Cr and Hg. Meanwhile, Cr and Hg passed the significance test at a 0.05 level and had a low correlation coefficient (r = 0.114), possibly showing that Cd, Cr and Hg were from different primary sources. In addition, the negative correlation between As and Hg suggests that their primary sources might be different. All of the above results indicate that the sources of heavy metal pollutants in the study area are complex, demanding further analysis.

3.2.2. PMF Model Analysis

The PMF model performed the source apportionment, and the R2 between the observed and the predicted values of heavy metals are listed in Table 3. The R2 of Cd, As, Cr, and Hg were greater than 0.9, and the remaining heavy metals were close to or greater than 0.7. On this basis, it is revealed that the overall analysis of the PMF model was effective and that the model results were suitable for interpreting the information contained in the initial data.
The analysis results of the PMF model are illustrated in Figure 2. The contributions of Factor 1 to Cr, Ni, Cu, and Zn were relatively high, with a contribution ratio of 69%, 68%, 45%, and 28%, respectively. Meanwhile, Factor 1 also contributed to Pb, As and Cd, with 19%, 9% and 4%, respectively. The average concentrations of Cr, Cu, Ni, and Zn were close to the background values, where the mean of Cr, Cu, and Ni was slightly lower than the background values; meanwhile, Zn was slightly higher than the background value. As shown in Figure 3, the spatial distribution of Cr, Cu, Ni, and Zn was consistent with the overall trend seen in the black shale series, and the high-value areas were distributed in the exposed area of the black shale series or at a certain distance downstream from it, indicating that the concentrations of these elements were mainly controlled by the geological background. Furthermore, the relevant research in this area also demonstrates that the concentrations and distributions of As, Cd, Cr, Cu, Ni, Pb, and Zn in soils were influenced by the geological background of the black shale series [39,40]. Thus, Factor 1 was mainly derived from natural sources.
Factor 2 contributed 67% of Cd, and the average concentration of Cd was 3.3 times higher than the background value; and CV was 146.91%, with an extremely variable spatial distribution. As shown in Figure 4, shale mining, limestone mining and metal mining were present in the study area. Black shale was widely exposed by shale mining, and, because it was often interbedded with limestone, it was also exposed by lime mining activities [41]. The weathering of black shale could release acidic water binding with several heavy metal elements, and the exhalation rate of Cd among the leached heavy metals was relatively high [42,43]. The lower pH could activate Cd, enhancing its capacity for transportation in the environment, which resulted in the contamination of Cd in overlying soils [44,45,46]. In addition, the metal mining caused the strong horizontal and vertical migration of heavy metals in the slag and waste rock, and the well-developed water system in the study area further aggravated the migration and enrichment of heavy metals [47]. Therefore, Factor 2 could be interpreted as a mining source.
Factor 3 contributed 71% of Hg, with an average concentration slightly higher than that of the local background value; the CV was 56.52%, with a higher variation. Figure 3 indicates a scattered distribution of Hg in the high-value areas, mainly in clustered areas such as basins and towns, which was remarkably influenced by anthropogenic activities. The two pillar industries in the study area, cement manufacturing, and chemical manufacturing, heavily relied on burning coal for long-term production; this was considered to be the main contributor to Hg pollution in the atmosphere [48,49]. The atmosphere, soil and water circulate and interact mutually; as a result, heavy metals in the atmosphere enter the surface soils via dry and wet deposition. In this sense, the source of atmospheric heavy metal pollution should be adopted as one of the indicators for analyzing the quantities of heavy metal pollutants in soils [50]. The main topography of the study area involved hills, basins, and mountains, which is more beneficial to pollutants entering the soil through atmospheric dust fall. Therefore, Factor 3 could be regarded as an anthropogenic component of industrial emissions.
Factor 4 was dominated by As with a high contribution (79.2%). The average concentration of As was 1.4 times higher than the background value, which suggests that there was some exogenous influence on the arable soils. Indeed, inorganic arsenic compounds such as Na₃AsO₄, Pb₃(AsO₄)₂, and Ca₃(AsO₄)₂ are vital components of pesticides, and are mainly used in herbicides, insecticides, and other pesticides [51,52]. Generally, the content of As in the phosphate fertilizers is 20–50 mg kg−1, while there are also some situations in which As content in phosphate fertilizers is as high as several hundred milligrams per kilogram [53,54]. It was found that the study area was one of the major pecan-producing areas in China with high agricultural activities. In recent years, the planting area of pecans has been expanding to meet the unceasing market demand. The large-scale planting of monoculture trees has resulted in unbalanced vegetation and anabatic insect attack. Farmers automatically began to rely on chemical fertilizers and pesticides to maintain agricultural production, which inevitably brings the pollution risk of As to croplands. Hence, Factor 4 could be considered as agricultural activities.
Factor 5 was associated with the accumulation of Pb, Zn, Cu, and Cd, with contributions at 54%, 48%, 28%, and 20%, respectively; these were the main components of motor vehicle emissions [55,56]. All the gasoline additives, brake pads, car engine starting and fuel-burning led to the emission of Pb [57,58]. Zn is usually used as an additive fuel for the automotive engine, and this is its primary source of atmosphere pollution; in addition, tire wear and road infrastructure are important sources of Zn atmosphere pollution that cannot be ignored. As a consequence, Zn can enter the soil with atmospheric dust via both of these channels [59,60]. The module wear of the engine and the leak of gasoline or fuel may be the cumulative sources of Cu [61]. As shown in Figure 3, the study area has a dense network of major roads, and extensive arable soils in the study area are distributed along the busy roads. Frequent traffic activities lead to the accumulation of heavy metals such as Pb and Zn in arable soils. Therefore, Factor 5 could be interpreted as traffic emissions.
In summary, the accumulation of heavy metals in the arable soils covered in this study was mainly influenced by natural sources, traffic emissions, industrial emissions, agricultural activities, mining, etc. According to the PMF calculation results shown in Figure 5, natural sources exerted the most significant impact on the quantity of heavy metals in the soils of the study area, accounting for 39.66% of all contributions; this was followed by traffic emissions, at 32.85%. In comparison, industrial emissions, agricultural activities, and mining contributed less, at 9.23%, 9.17%, and 9.10%, respectively. The results of the source apportionment indicate that the accumulation of Cd and other heavy metals in paddy soils was aggravated by the superposition of anthropogenic activities in the background area of the black shale series.

3.3. Influence of Black Shale on the Distribution of Heavy Metals

Numerous studies have shown that black shale is usually enriched with a variety of heavy metals and other trace elements, which may be one of the natural causes of heavy metal contamination in surface soils [24,62,63]. The migration process of heavy metal contamination in the black shale–paddy system had two main pathways: first, the soil developed from the residual deposits of black shale as the parent material may inherit heavy metals from the parent rock [64,65], resulting in the risk of heavy metals in farmland reclaimed in the area. Second, in the process of the surface water–rock interaction, the oxidation and decomposition of sulfide in black shale produced acidic drainage, which leached and activated heavy metals such as Cd to migrate to farmland through the water system [66].
In order to further clarify the influence of black shale on the content of heavy metals in soil, the affected areas of the black shale series in the study area were mapped out and shown in Figure 6, mainly in the west and south of C, northwest of E, west and south of F and north of I. The spatial distribution of the heavy metals in the arable soil showed that the high-value areas of Cd and Zn were mainly distributed in the west and south of F, the high-value areas of As were mainly distributed in the west of C and F, the high-value areas of Pb were mainly distributed in the south of F, and the high-value areas of Cu were mainly distributed in the south of C and F. The high-value areas of five heavy metals, Cd, As, Pb, Cu and Zn, were all located near the black shale areas and its affected areas, and were significantly influenced by black shale, which had significance for the prevention and control of soil heavy metal contamination.

4. Conclusions

Heavy metal pollution is one of the major problems in agricultural soils, and greatly threatens national food security and human health. This study analyzed the pollution sources of heavy metals in agricultural soils through the PMF model in black shale areas in western Zhejiang Province. The results are as follows:
  • Based on the correlation analysis and the PMF model, five sources were apportioned. Cd largely originated from mining, As mostly stemmed from agricultural activities, and Hg was mainly influenced by industrial emissions. In addition, Pb, Zn, and Cu were primarily affected by the mixture of traffic emissions and natural sources, while Cr and Ni were controlled by natural sources.
  • The relative contributions of natural sources, traffic emissions, industrial emissions, agricultural activities, and mining were 39.66%, 32.85%, 9.23%, 9.17% and 9.10%, respectively. Most pollution was contributed by anthropogenic activities, such as mining and the construction of roads and bridges, superimposed on the black shale series.
Our findings in this work accurately reveal that the sources of heavy metal pollution in the study areas should be in favor of implementing more rational policies in order to guarantee the security of agricultural products in the study areas, such as enforcing the tough regulation of anthropogenic activities and adopting effective measures in order to prevent, control, and remediate the transportation and accumulation of heavy metals.

Author Contributions

Conceptualization, C.X., X.L. and Z.C.; software, R.S., L.H. and J.B.; validation, X.L.; formal analysis, C.H., A.G. and W.P.; investigation, C.F. and R.Z.; resources, X.L. and Z.C.; data curation, C.X.; writing—original draft preparation, C.X. and X.L.; writing—review and editing, X.L.; visualization, X.L.; supervision, C.H.; project administration, X.L. and Z.C.; funding acquisition, X.L. and Z.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ22D030003); Key R&D Program of Zhejiang Province, China (Grant No. 2021C04020); Science and Technology Programs of Department of Natural Resources of Zhejiang Province, China (Grant No. 2020006 and No. 2020-45) and the Ecological Environment Scientific Research and Achievement Promotion Program of Zhejiang Province (Grant No. 2021XM0040).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Map of the study area and the sampling sites in the West of Zhejiang Province, China.
Figure 1. Map of the study area and the sampling sites in the West of Zhejiang Province, China.
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Figure 2. Source contribution ratios of heavy metals in soils covered in this study in the West of Zhejiang Province, China.
Figure 2. Source contribution ratios of heavy metals in soils covered in this study in the West of Zhejiang Province, China.
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Figure 3. The spatial distributions of heavy metals in the study area in the West of Zhejiang Province, China.
Figure 3. The spatial distributions of heavy metals in the study area in the West of Zhejiang Province, China.
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Figure 4. Overview map of the study area.
Figure 4. Overview map of the study area.
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Figure 5. Total contribution ratios of different sources in the West of Zhejiang Province, China.
Figure 5. Total contribution ratios of different sources in the West of Zhejiang Province, China.
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Figure 6. Distribution map of black shale in the study area.
Figure 6. Distribution map of black shale in the study area.
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Table 1. Statistical characteristics of heavy metals contents in the study area.
Table 1. Statistical characteristics of heavy metals contents in the study area.
Heavy MetalCdAsPbCrHgCuZnNipH
Min (mg kg−1)0.091.2016.7313.200.025.3045.605.354.43
Max (mg kg−1)8.8850.4086.80114.000.7095.80510.5083.508.24
Mean (mg kg−1)0.539.6234.4655.020.1427.39105.0225.27
Standard deviation (mg kg−1)0.786.958.4220.520.0811.0944.5711.43
Coefficient of variation (%)146.9172.2024.4337.2956.5240.4742.4445.23
Geochemical baseline0.196.7631.5660.690.1125.5793.8824.14
Background values in China (mg kg−1)0.09711.226.0061.000.06522.6074.2026.90
Skewness5.162.281.80−0.192.491.963.750.82
Kurtosis37.917.745.58−0.5611.017.8122.392.36
Table 2. Correlation of heavy metals in the study area.
Table 2. Correlation of heavy metals in the study area.
Heavy MetalsCdAsPbCrHgCuZnNi
Cd1
As0.271 **1
Pb0.437 **0.194 **1
Cr0.0560.322 **0.0061
Hg0.0660.0730.240 **0.114 *1
Cu0.449 **0.395 **0.455 **0.495 **0.125 **1
Zn0.605 **0.299 **0.550 **0.123 **0.0680.636 **1
Ni0.313 **0.467 **0.0370.793 **0.116 *0.579 **0.393 **1
** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed).
Table 3. Results of fitting the observed and predicted values of heavy metals.
Table 3. Results of fitting the observed and predicted values of heavy metals.
Heavy MetalR2Fitting Equation
Cd0.9771y = 0.94x + 0.03
As0.9998y = 1.01x − 0.02
Pb0.8015y = 0.92x + 2.39
Cr0.9174y = 0.98x + 0.45
Hg0.9877y = 0.93x + 0.01
Cu0.6952y = 0.57x + 10.21
Zn0.7238y = 0.58x + 39.63
Ni0.8416y = 0.77x + 4.96
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Xu, C.; Lu, X.; Huang, C.; Sun, R.; Gu, A.; Pan, W.; He, L.; Bao, J.; Zou, R.; Fu, C.; et al. Positive Matrix Factorization as Source Apportionment of Paddy Soil Heavy Metals in Black Shale Areas in Western Zhejiang Province, China. Sustainability 2023, 15, 4547. https://doi.org/10.3390/su15054547

AMA Style

Xu C, Lu X, Huang C, Sun R, Gu A, Pan W, He L, Bao J, Zou R, Fu C, et al. Positive Matrix Factorization as Source Apportionment of Paddy Soil Heavy Metals in Black Shale Areas in Western Zhejiang Province, China. Sustainability. 2023; 15(5):4547. https://doi.org/10.3390/su15054547

Chicago/Turabian Style

Xu, Changyan, Xinzhe Lu, Chunlei Huang, Rui Sun, Anqing Gu, Weifeng Pan, Li He, Jiayu Bao, Ruosong Zou, Cheng Fu, and et al. 2023. "Positive Matrix Factorization as Source Apportionment of Paddy Soil Heavy Metals in Black Shale Areas in Western Zhejiang Province, China" Sustainability 15, no. 5: 4547. https://doi.org/10.3390/su15054547

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