## 2 Methods
### Methods for Calculating Indices of Soil Pollution and Risks to Public Health  
[PERSON] [55] developed the geoaccumulation index (I\({}_{geo}\)), which is widely used in European studies of trace metals [56]. This method estimates environmental pollution by comparing the difference between current and pre-industrial concentrations. It was first developed for the assessment of the quality of bottom sediments of rivers and was used to assess soil pollution [57]. To calculate \(\mathrm{I_{geo}}\) for the soils of the surveyed plots, the following equation is proposed:  
\[\mathrm{I_{geo}}=\log_{2}\left(\frac{\mathrm{C_{n}}}{1.5\mathrm{B_{n}}}\right) \tag{4}\]  
where \(\mathrm{C_{n}}\) is the measured concentration of each heavy metal found in the studied soil (mg/kg) and \(\mathrm{B_{n}}\) is the geochemical background value of heavy metals in soil for different provinces (mg/kg). The constant 1.5 is used due to possible variations in the initial data [57]. The geoaccumulation index consists of 7 classes or points, among which the highest 6 classes reflects 100-fold enrichment compared to background values [58]. The USEPA health risk assessment model is used to assess the non-carcinogenic and carcinogenic impact on humans exposed to heavy metals [59]. Average daily intake (ADI) is calculated using the following expression [59]:  
\[\mathrm{ADI}=\frac{\mathrm{C}\times\mathrm{IR}\times\mathrm{EF}\times\mathrm{ ED}}{\mathrm{BW}\times\mathrm{AT}} \tag{5}\]  
where ADI is an average daily intake (mg/kg per day), \(\mathrm{C}\) is the concentration of heavy metals in a particular exposure medium (mg/kg), IR is the ingestion rate (kg/day), EF is the exposure frequency (day/year), ED is the exposure duration (year), BW is body weight (kg), and AT is the time period over which the dose is averaged (day). For non-carcinogenic effects AT = ED \(\times\) 365 (days) and for carcinogenic effects AT = 25,550 (days) (70 years \(\times\) 365 days/year). Considering the characteristics of soil pollution with heavy metals, two pathways of exposure are often considered [59]:  
1. Ingestion: \[\mathrm{ADI_{ing}}=\frac{\mathrm{C_{S}}\times\mathrm{IR_{S}}\times\mathrm{EF} \times\mathrm{ED}}{\mathrm{BW}\times\mathrm{AT}}\] (6) where \(\mathrm{ADI_{ing}}\) is the average daily intake from ingestion (mg/kg per day), \(\mathrm{C_{S}}\) is the heavy metal concentration in the soil (mg/kg), and \(\mathrm{IR_{s}}\) is the ingestion rate of soil (kg/day). 2. Dermal absorption: \[\mathrm{ADI_{dermal}}=\frac{\mathrm{C_{S}}\times\mathrm{SA}\times\mathrm{AF} \times\mathrm{ABS}\times\mathrm{EF}\times\mathrm{ED}}{\mathrm{BW}\times \mathrm{AT}}\] (7) where \(\mathrm{ADI_{dermal}}\) is the average daily intake from dermal absorption (mg/kg per day), \(\mathrm{C_{S}}\) is the heavy metal concentration in the soil (mg/kg), SA is the exposed skin surface area (cm\({}^{2}\)), AF is the adherence factor (mg/cm\({}^{2}\) per day), and ABS is the dermal absorption index (unitless). Non-carcinogenic risk is assessed by calculating hazard quotient (HQ) values. For composite heavy metal pollution, a hazard index (HI) is used to assess the overall non-carcinogenic risk, which summarizes the HQ for each heavy metal [59]. It is assumed that the exposed population has no potential risk when the HI is below one. \[\mathrm{HQ}=\frac{\mathrm{ADI}}{\mathrm{RfD}} \tag{8}\]  
\[\mathrm{HI}=\sum\mathrm{HQ} \tag{9}\]  
where HI is the estimated non-carcinogenic health index and RfD is the reference dose of certain heavy metal (mg/kg per day). Due to the lack of reference doses for the assessment of dermal absorption, USEPA has developed a method for extrapolating oral toxicity values for use in dermal risk assessment [59]. \[\mathrm{RfD_{ABS}}=\mathrm{RfD_{0}}\times\mathrm{ABS_{CI}} \tag{10}\]where RfD\({}_{\text{ABS}}\) is skin contact reference dose (mg/kg per day), RfD\({}_{0}\) is the oral reference dose (mg/kg per day), and ABS\({}_{\text{GI}}\) is the gastrointestinal absorption factor (unitless).