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Article

Spatial Distribution Prediction of Soil Heavy Metals Based on Random Forest Model

by
Shunqi Nie
,
Honghua Chen
*,
Xinxin Sun
and
Yunce An
School of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China
*
Author to whom correspondence should be addressed.
Sustainability 2024, 16(11), 4358; https://doi.org/10.3390/su16114358
Submission received: 2 April 2024 / Revised: 18 May 2024 / Accepted: 20 May 2024 / Published: 22 May 2024
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Abstract

:
Mastering the spatial distribution of soil heavy metal content and evaluating the pollution status of soil heavy metals is of great significance for ensuring agricultural production and protecting human health. This study used a machine learning model to study the spatial distribution of soil heavy metal content in a coastal city in eastern China. Having obtained six soil heavy metal contents, including Cr, Cd, Pb, As, Hg, and Ni, environmental variables such as precipitation, soil moisture, and population density were selected. Random forest (RF) was used to model the spatial distribution of soil heavy metal content. The research findings indicate that the RF model demonstrates a robust predictive capability in discerning the spatial distribution of soil heavy metals, and environmental factor variables can explain 60%, 52.3%, 53.5%, 63.1%, 61.2%, and 51.2% of the heavy metal content of Cr, Cd, Pb, As, Hg, and Ni in soil, respectively. Among the chosen environmental variables, precipitation and population density exert notable influences on the predictive outcomes of the model. Specifically, precipitation exhibits the most substantial impact on Cr and Ni, whereas population density emerges as the primary determinant for Cd, Pb, As, and Hg. The RF prediction results show that Cr and Ni in the study area are less affected by human activities, while Cd, Pb, As, and Hg are more affected by human industrial and agricultural production. Research has shown that using RF models for predicting soil heavy metal distributions has certain significance.

1. Introduction

Soil plays a significant role in ecosystem balance [1], crop yield [2], and human health [3]. With the advancement of modern industry and agricultural activities such as irrigation and fertilization, soil heavy metal pollution has become increasingly severe [4,5]. Characterized by difficulties in degradation, a propensity for accumulation, and significant toxicity, soil heavy metal pollution has emerged as a pressing global environmental concern [6,7,8]. The accumulation of soil heavy metals poses a significant environmental challenge, resulting in various adverse impacts on ecosystems [9]. Excessive levels of soil heavy metals not only impede soil productivity but also pose risks to human and animal health through their inhalation and ingestion pathways [10,11]. Thus, understanding the spatial distribution of soil heavy metal contents and evaluating the status of soil heavy metal pollution are crucial for safeguarding agricultural production and protecting human health [12,13,14,15].
Currently, a considerable amount of research has been conducted on the spatial distribution prediction of soil heavy metal. Classic spatial interpolation methods which are used in soil heavy metal prediction include Kriging and Geographically Weighted Regression (GWR) [16]. In recent years, there has been increasing attention towards utilizing machine learning models, such as the k-nearest neighbors algorithm (KNN) [17], classification and regression tree models (CART) [18], tree models [19], and RF models [20], among others. These methods aid in better understanding and accurately predicting the spatial variability of soil characteristics. In comparison with various machine learning models, the RF model demonstrates advantages due to its resistance to overfitting and insensitivity to multicollinearity [20]. For example, Dharumarajan [21] successfully employed an RF model to predict soil organic carbon, pH, and other soil attributes in southern India. Chagas [22] used an RF model to predict soil surface texture in a semiarid region and found that the RF model performed with higher accuracy than multiple linear regression. Guo [23] discovered their RF model performed better than stepwise linear regression and a generalized additive mixed model in predicting the soil total nitrogen of a rubber plantation. This indicates that an RF model is a more reliable and effective approach for the spatial prediction of soil characteristics. Although RF models have been widely used for the spatial prediction of soil characteristics, current studies have mostly focused on predicting soil heavy metal content in relatively small areas [23,24,25]. This underscores the need to investigate the accuracy of the RF model in predicting soil heavy metal content in large-scale studies.
Multiple environmental factors collectively contribute to the spatial distribution of soil heavy metals [26,27]. Existing research primarily selects environmental factors across both natural and socio-economic aspects. From a natural perspective, soil moisture [28], vegetation coverage [21], organic matter [29,30], elevation, and slope [31] are considered important factors influencing soil heavy metal content. In addition, precipitation also plays an important role in soil heavy metal content through leaching and adsorption processes [32,33,34,35]. As for socio-economic aspects, population density and the distance to transportation were chosen to predict the spatial characteristics of heavy metals in farmland soil [36]. Guo [37] indicated a negative correlation between heavy metals and the distance to roads within a certain range. Liu [38] demonstrated that population density reflects the intensity of living activities, suggesting that areas with a higher population density are likely to induce more heavy metal contamination.
Taking a coastal city in eastern China as the study area, this research utilizes Geographic Information System (GIS) and remote sensing (RS) techniques to extract environmental factor variables including elevation, slope, precipitation, soil moisture, organic matter, NDVI, distance to road, and population density. The field sampling of data is employed, with the content of six heavy metals—Chromium (Cr), Cadmium (Cd), Lead (Pb), Arsenic (As), Mercury (Hg), and Nickel (Ni)—serving as predictive targets. A correlation analysis is conducted to investigate the relationship between the environmental factor variables and the predictive targets. By employing random forest (RF) modeling and selecting optimal model parameters, a predictive model for soil heavy metals is constructed, enabling the prediction of their spatial distribution. The study results are expected to provide a data foundation for the assessment and prevention of soil heavy metal pollution.

2. Materials and Methods

2.1. Study Area

The study area is a coastal city in eastern China, which is located in a hilly region characterized by continuous hills and crisscrossing ravines, with higher terrain in the northeast, central, and western parts (Figure 1). The soil types in the study area are brown soil, skeletal soil, and cinnamon soil, with metamorphic rock as the underlying geology. It has a temperate continental climate, with an average annual temperature of 11.5 °C and an average annual rainfall of 671.1 mm. The average elevation is 136 m. The population density in the study area is 395 people per square kilometer, with a road length of approximately 2300 km. Planning one sampling point per 1 km × 1 km, we followed the principle of comprehensive distribution in terms of soil, land use type, and spatial coverage. This guaranteed that each type of soil and land use in the study area had surface sampling points, achieving complete spatial coverage and avoiding large unsampled areas within the region. Soil samples were collected from the surface layer, with a sampling depth of 0–20 cm. The northwestern part of the study area has sparse sampling points, mainly due to its mountainous terrain, sparse population, and predominant land use type being forested areas, where the heavy metal content in the soil is less influenced by environmental factors, hence resulting in fewer sampling points.

2.2. Data

According to the “National Standard of the People’s Republic of China for Soil Environmental Quality Risk Control Standard for Agricultural Land Soil Pollution (Trial)” (GB 15618-2018) [39], Cr, Cd, Pb, As, Hg, and Ni have been selected as the six heavy metal elements for spatial interpolation.
In this study, soil heavy metal content data for Cr, Cd, Pb, As, Hg, and Ni were obtained using an Olympus handheld XRF soil heavy metal analyzer in the study area. After data cleaning, a total of 748 sampling points were obtained. Additionally, environmental factor variables for the study area were collected, including the soil organic matter, Digital Elevation Model (DEM), annual average precipitation [40], annual average soil humidity [41], slope, Normalized Difference Vegetation Index (NDVI) [42], land use type, population density [43], distance to roads, and distance to residential areas. The sources of these environmental variables are as follows: The DEM and slope data were obtained from the Geographic Spatial Data Cloud Platform, with a spatial resolution of 30 m. The annual average precipitation and annual average soil humidity data were obtained from the National Tibetan Plateau Data Center, with a spatial resolution of 1 km. NDVI data were obtained from the National Ecological Science Data Center, with a spatial resolution of 30 m. The population density data were obtained from the WorldPop dataset, with a spatial resolution of 1 km. Road data were obtained from OpenStreetMap. The distance to residential areas was calculated using ArcGIS proximity analysis with the “residential areas” category as the land use type, determining the distance from each sampling point to the nearest residential area. (See Table 1).

2.3. The Random Forest Model Based on Environmental Factors

RF is an ensemble classification algorithm, with the core idea of reducing the overfitting risk of individual decision trees by constructing multiple decision trees. By employing an RF model, significant improvements in prediction accuracy can be achieved, while also mitigating issues such as overfitting, missing values, or multicollinearity. Furthermore, this model can easily address complex qualitative and quantitative problems. A variance inflation factor (VIF) was used for the multicollinearity issue, with a threshold of 5. The multicollinearity issue was not severe in our study (VIF < 5). This study utilizes the Python package “sklearn.ensemble.RandomForestRegressor” for modeling. The configuration of the RF model is determined by two adjustable parameters: the number of decision trees (ntree) and the maximum depth of trees (max_depth).
The experimental setup is outlined as follows (Figure 2):
(1)
The environmental factor variables of the sampling points are acquired and combined with heavy metal element contents at the sampling points to form a dataset.
(2)
The dataset is divided into a training set and a validation set in a 7:3 ratio. The training set is used to train RF models with different parameters, and the validation set is utilized for accuracy validation to select the optimal model.
(3)
Construction of the RF model: Utilizing the Bootstrap resampling method, n samples are randomly drawn from the training set to form a new training sample set. With the dataset containing nine feature factors, a random subset of m (where m ≤ 9) features is selected to form a feature subset. Decision trees are constructed on the new sample set and feature subset, selecting the best splitting attribute during the tree-growing process for node splitting. This process is repeated multiple times to construct decision trees and obtain base estimators. These decision trees are then combined to form the RF.
(4)
Using the “Fishnet” tool in ArcGIS 10.8, a 500 m grid of points was created for the study area. The “Extract Values to Points” tool in ArcGIS 10.8 was then used to extract nine environmental covariates for the grid points.
(5)
The RF model was applied to predict the Cr, Cd, Pb, As, Hg, and Ni contents at each grid point. The experimental results are used to generate spatial distribution prediction maps of heavy metal elements using the “Point to Raster” tool in ArcGIS 10.8.

2.4. Parameter Settings for Random Forest Model

Through sequential experiments, the optimal values for the parameters ntree and max_depth in the RF model can be determined [44]. In Table 2, max_depth and ntree are selected as 10, 20, 30, and 500, 800, 1000, respectively. Then, three groups of nine experiments were conducted for each setting, and the results are presented in Table 2. To avoid overfitting, this study compares the R2 values between the training set and validation set, selecting the parameters with the most similar results as the optimal predictive model. The results indicate that when ntree is set to 800 and max_depth is set to 20, the R2 values for both the training set and validation set of each metal prediction model are relatively close and relatively large. This suggests that the model exhibits the best stability and robustness with this configuration, providing the most reliable predictions.

2.5. Accuracy Evaluation

By employing three parameters, Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and coefficient of determination (R2), the accuracy of the model can be effectively measured. Lower values of MAE and RMSE indicate the higher accuracy of the model, while the R2 of the test set is used to evaluate the model’s predictive accuracy and generalization ability. The calculation formulas are as follows:
R M S E = 1 n ∑ i = 1 n p i − o i 2
M A E = 1 n ∑ i = 1 n p i − o i
R 2 = 1 − ∑ i = 1 n p i − o i 2 ∑ i = 1 n p i − o ^ i 2
In these formulas, p i and o i represent the predicted and observed values, respectively. o ^ i is the mean of the observed values.

3. Results

3.1. Statistical Characteristics of Heavy Metal Content in Soil

Table 3 and Table 4 present the statistical results of the soil heavy metals in the training set and validation set at the sampling points, respectively. Skewness and kurtosis are used to describe the normal distribution of the data, where smaller values typically indicate a closer fit to the normal distribution. The coefficient of variation is a relative statistical measure of data variability, calculated as the ratio of the standard deviation to the mean. Generally, a smaller coefficient of variation indicates lower data variability, while a larger coefficient of variation suggests higher variability. From the tables, it can be observed that the data on the six heavy metal elements collectively follow a normal distribution. However, the coefficient of variation for Hg is relatively high, indicating its poorer stability.

3.2. Correlation Analysis of Factors Affecting Heavy Metals in Soil

Using the “Correlate” module in SPSS Statistics 25 software, a correlation analysis was conducted to investigate the influence of different environmental variables on soil heavy metal content [46]. By conducting a correlation analysis on the data, we can determine the degree of association between different variables, with smaller p-values indicating stronger correlations. According to the correlation analysis results presented in Table 5, it is evident that annual average precipitation, elevation, and population density exhibit significant correlations with all heavy metals. Additionally, soil organic matter and the distance from the sampling points to residential areas are correlated with Cd, Pb, As, and Hg. Slope is only correlated with Cr and Pb. Soil humidity and the distance from sampling points to roads show no significant correlation with any of the heavy metals.
The results indicate significant correlations as follows: Cr exhibits significant correlations with annual average precipitation, elevation, slope, and population density. Cd shows significant correlations with soil organic matter, annual average precipitation, elevation, slope, distance from sampling points to residential areas, and population density. Pb demonstrates significant correlations with soil organic matter, annual average precipitation, elevation, slope, distance from sampling points to residential areas, and population density. As displays significant correlations with soil organic matter, annual average precipitation, elevation, distance from sampling points to residential areas, population density, and NDVI. Hg indicates significant correlations with soil organic matter, annual average precipitation, elevation, distance from sampling points to residential areas, distance from sampling points to roads, and population density. Ni shows significant correlations with annual average precipitation, elevation, and population density.

3.3. Importance Analysis of Environmental Variables in Random Forest Model

Utilizing the RF model, the importance of influencing factors in predicting various metals was ranked and analyzed [47]. As depicted in Figure 3, for Cr, the most important factors are population density, annual average precipitation, and elevation. For Cd, the significant factors include annual average precipitation, soil humidity, and soil organic matter. Pb is primarily influenced by annual average precipitation. As is significantly influenced by annual average precipitation and soil organic matter. Hg is notably influenced by annual average precipitation, elevation, and soil organic matter. Ni is significantly affected by population density, annual average precipitation, and slope. This analysis suggests that precipitation may have a diluting effect on soil heavy metals, leading to a significant relationship between precipitation and soil heavy metal content.

3.4. Precision Analysis of Heavy Metal Content Prediction Based on Random Forest Model

By calculating evaluation metrics such as the RMSE, MAE, and R2, and undergoing multiple rounds of parameter tuning, it was found that the RF model exhibited the best performance. Therefore, we selected this as the most stable model. According to Table 6, (1) the coefficient of determination (R2) of the RF model closely matches that of the validation set, indicating its ability to effectively avoid overfitting. (2) Based on R2 values, the prediction performance, from highest to lowest, is as follows: As, Hg, Cr, Pb, Cd, Ni. (3) For soil heavy metal content prediction, the models for As, Hg, Cr, Pb, and Cd exhibit high fitting and generalization capabilities. Both the R2 values for the training set and the validation set are above 0.5 and are relatively close, indicating stable models. The R2 value for Ni in the validation set is slightly lower than 0.5, suggesting a relatively poorer prediction accuracy. (4) The analysis of MAE and RMSE reveals that the MAE and RMSE values of the training set are smaller than those of the validation set, indicating the overall higher prediction accuracy of the model. This indicates that, within the study area, the RF model performs well in predicting soil heavy metal content.

3.5. Spatial Distribution Prediction of Soil Heavy Metals Based on Random Forest Model

The RF model was utilized to predict the soil heavy metal contents of Cr, Cd, Pb, As, Hg, and Ni in the study area, respectively, and spatial distribution maps were obtained for each soil heavy metal. From Figure 4, it is evident that the distribution of Cd, Pb, As, and Hg in the study area shows higher concentrations in the central and northern regions. Specifically, Cd and As exhibit relatively higher concentrations in the northwest region compared to other areas, while Pb shows higher overall concentrations in the northern region and lower concentrations in the southern region. Hg is predominantly concentrated in a small portion of the central-to-northern region, with lower concentrations in other areas. Conversely, Cr exhibits lower concentrations primarily in the northwest region, with higher concentrations in other areas. Ni shows higher concentrations in the southern region, with distributions in other areas as well. Both Cr and Ni demonstrate higher concentrations in the southern region.

4. Discussion

Analyzing the sources of high concentrations of different heavy metals is essential for soil pollution prevention. This study revealed significant accumulations of Pb and Hg in the central-to-northern region of the study area, coinciding with the presence of multiple economic development zones and industrial parks [48]. Several studies [49,50,51] have indicated that industrial emissions are a major source of pollution for Pb and Hg. These pollutants can accumulate in the soil through solid waste, industrial wastewater, or dust deposition from industrial emissions. Therefore, the relatively high concentrations of Pb and Hg in the central to northern parts of the study area are primarily due to industrial production. Furthermore, Cd and As are highly concentrated in the northern region of the study area, which is correlated with agricultural land. Ji [52] showed that there is a significant presence of crops in the northwest part of the study area. Agricultural inputs such as fertilizers and pesticides contain elements such as Cd and As, leading to their accumulation in the soil [53,54]. Our study also found that there are similar distributions of Cr and Ni in the southern parts of the study area, where human activities are relatively limited. Research by Wang [55] has demonstrated a strong homogeneity between Cr and Ni, indicating that their primary sources are natural sources.
Although feature selection is regarded as an important step in the RF model [56], all environmental factors selected in our study were used to train the model. The current study has shown that all these factors are correlated with soil heavy metals. We think the existing factors can provide more comprehensive environmental information, which is important for the spatial prediction of soil heavy metal. Precipitation and population density highly relate to soil heavy metal contents, a fact which is supported by the study of Zhu [32]. Agricultural and industrial activities in human settlements are important factors affecting soil heavy metal content, thus leading to a significant correlation between population density and soil heavy metal content. Furthermore, there are additional environmental factors that may impact soil heavy metal content. For example, slope direction, various bands of remote sensing imagery, and the distance from sampling points to rivers were included as environmental variables for the prediction of As’s distribution in soil [57]. Liu [58] took into account the pH when assessing soil heavy metal pollution, while Jiang [59] considered PM2.5, GDP, and the duration of nighttime lighting in the Yangtze River region.
Geographically Weighted Regression (GWR), Support Vector Machine (SVM), and other machine learning algorithms can also be used to predict soil heavy metal contents [24,60], but the RF model was chosen in our study due to its strong robustness, resistance to overfitting, and insensitivity to multicollinearity [20]. Ma [24] also used an RF model to predict soil heavy metal hyperspectral data, showing that the RF algorithm can achieve higher accuracy results compared to the ELM (Extreme Learning Machine) and SVM algorithms.
Although the spatial distributions of various soil heavy metals were obtained in our study, there are still some limitations. The R2 in our study is common in the spatial prediction of soil heavy metals using the RF model [24,61,62], especially in large-scale studies. But our prediction accuracy can be further improved in some respects. First, more environmental factors can be included to provide additional information and enhance prediction accuracy. Azizi [63] proved that increasing the number of environmental factors continuously can raise the R2 from 0.24 to 0.63 in soil heavy metal prediction. Second, more parameter optimization experiments can enhance prediction accuracy. Additionally, although excessive levels of heavy metals such as Cuprum (Cu) and Zinc (Zn) can also impact both soil ecosystems and human health, these elements are essential for plant growth and maintaining human physiological functions [64]. Therefore, our study did not conduct spatial distribution predictions for these soil heavy metal elements. In subsequent experiments, more environmental factors will be considered, and various prediction methods will be compared for mapping the spatial distribution of soil heavy metals.

5. Conclusions

The use of the RF model in this study for predicting the spatial distribution of soil heavy metals holds significant importance in improving prediction accuracy. The research findings are as follows:
(1)
The modeling results of the RF model indicate that environmental variables play a significant role in explaining the variations in the soil heavy metal content of Cr, Cd, As, Pb, Hg, and Ni within the study area. The close similarity between the R2 values of the training and validation sets suggests that the RF model exhibits reduced overfitting issues and higher stability in predicting the spatial distribution of heavy metals in the soil within the study area. Therefore, the RF model demonstrates a favorable performance in predicting the spatial distribution of soil heavy metal content.
(2)
For the soil heavy metal content in the study area, annual precipitation and population density are identified as major influencing factors. Specifically, Cd and Hg are primarily water-soluble components, while Cr, As, Pb, and Ni mainly exist in insoluble forms in water. Therefore, precipitation plays a significant role in soil heavy metal dynamics due to its dilution and dissolution effects. Consequently, there is a substantial relationship between precipitation and soil heavy metal content. Additionally, human activities are significant factors influencing soil heavy metal content. Hence, there is a notable correlation between population density and soil heavy metal content.
(3)
Based on the predicted distribution maps and the natural and social environmental conditions of the study area, it is evident that industrial activities can lead to elevated levels of Pb and Hg in the soil. The use of agricultural products in agricultural production can result in increased levels of Cd and As in the soil. Cr and Ni are primarily influenced by natural environmental factors and precipitation, with less influence from human activities.
From the research findings, it is evident that the RF model can accurately predict the distribution of soil heavy metals. Subsequently, it would be beneficial to explore the integration of the RF model with other machine learning methods for predicting the spatial distribution of soil heavy metals. This integration could potentially yield even more precise results, thereby providing more reliable insights for environmental management and protection.

Author Contributions

Methodology, S.N.; Formal analysis, S.N.; Resources, H.C.; Data curation, X.S.; Writing—original draft, S.N.; Supervision, Y.A.; Funding acquisition, H.C. All authors have read and agreed to the published version of the manuscript.

Funding

This study was funded by the National Natural Science Foundation of China (42101430).

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Study area and sample points.
Figure 1. Study area and sample points.
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Figure 2. Workflow of prediction of spatial distribution of heavy metal elements based on RF model.
Figure 2. Workflow of prediction of spatial distribution of heavy metal elements based on RF model.
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Figure 3. Importance of environmental factors. PD: population density; Prep: precipitation; Ele: elevation; OM: organic matter; Hum: humidity; Slp: slope; DtL: distance to living area; DtR: distance to road.
Figure 3. Importance of environmental factors. PD: population density; Prep: precipitation; Ele: elevation; OM: organic matter; Hum: humidity; Slp: slope; DtL: distance to living area; DtR: distance to road.
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Figure 4. Spatial distribution of soil heavy metals based on RF model.
Figure 4. Spatial distribution of soil heavy metals based on RF model.
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Table 1. List of environmental indicators.
Table 1. List of environmental indicators.
Name of IndicatorsUnitData SourcesCalculation Method
Elevationmwww.gscloud.cn (accessed on 1 October 2023)/
Slopedegreewww.gscloud.cn/
Precipitationmmhttps://doi.org/10.5281/zenodo.3185722 (accessed on 1 October 2023)/
Humiditydm3/m3https://cstr.cn/18406.11.Terre.tpdc.272415 (accessed on 1 October 2023)/
Organic Mattermg/kghttps://doi.org/10.11888/Soil.tpdc.270281 (accessed on 1 October 2023)/
NDVI/https://cstr.cn/15732.11.nesdc.ecodb.rs.2021.012 (accessed on 1 October 2023)/
Distance to Living Aream/The distance from sampling points to residential areas is calculated based on the land use type by a “proximity analysis” in ArcGIS 10.8.
Distance to Roadmhttps://www.openstreetmap.org (accessed on 1 October 2023)The distance from sampling points to roads is calculated by a “proximity analysis” in ArcGIS 10.8.
Population Densityperson/km2www.worldpop.org (accessed on 1 October 2023)/
Table 2. Selection of optimal parameter values for the RF model.
Table 2. Selection of optimal parameter values for the RF model.
ntreemax_
Depth		CrCdPb
Training Set (R2)Validation Set (R2)Training Set (R2)Validation Set (R2)Training Set (R2)Validation Set (R2)
Test 150010 0.556 0.507 0.517 0.496 0.521 0.511
50020 0.599 0.539 0.518 0.498 0.527 0.521
50030 0.599 0.538 0.516 0.497 0.526 0.520
Test 280010 0.559 0.508 0.517 0.499 0.522 0.517
80020 0.600 0.542 0.523 0.504 0.535 0.527
80030 0.600 0.541 0.522 0.503 0.534 0.526
Test 3100010 0.558 0.507 0.517 0.498 0.521 0.517
100020 0.599 0.540 0.521 0.501 0.534 0.524
100030 0.599 0.540 0.520 0.500 0.533 0.523
ntreemax_
Depth		AsHgNi
Training Set (R2)Validation Set (R2)Training Set (R2)Validation Set (R2)Training Set (R2)Validation Set (R2)
Test 150010 0.622 0.618 0.605 0.573 0.473 0.454
50020 0.627 0.622 0.607 0.579 0.511 0.481
50030 0.626 0.621 0.606 0.578 0.510 0.480
Test 280010 0.629 0.625 0.610 0.582 0.472 0.452
80020 0.631 0.627 0.612 0.584 0.512 0.482
80030 0.630 0.626 0.611 0.583 0.511 0.481
Test 3100010 0.627 0.624 0.609 0.581 0.475 0.453
100020 0.628 0.625 0.610 0.582 0.509 0.481
100030 0.625 0.621 0.610 0.579 0.510 0.480
Table 3. Basic statistical characteristics of soil heavy metals in training set.
Table 3. Basic statistical characteristics of soil heavy metals in training set.
MetalRange (mg/kg)Mean Value (mg/kg)Standard Deviation (mg/kg)SkewnessKurtosisCoefficient of Variation (%)Background Value [45] (mg/kg)
Cr12.70~144.0057.0120.621.562.9636.17 57
Cd0.0031~0.300.120.0590.680.3549.17 0.117
Pb6.87~57.8023.407.220.731.8130.85 27.2
As2.37~21.807.652.511.003.5732.81 6.4
Hg0.011~1.050.0720.104.9932.06138.89 0.034
Ni4.07~82.8027.7411.031.131.3439.76 24.6
Table 4. Basic statistical characteristics of soil heavy metals in validation set.
Table 4. Basic statistical characteristics of soil heavy metals in validation set.
MetalRange (mg/kg)Mean Value (mg/kg)Standard Deviation (mg/kg)SkewnessKurtosisCoefficient of Variation (%)Background Value [45] (mg/kg)
Cr6.39~147.0058.3524.361.332.0741.75 57
Cd0.0161~0.290.120.0600.680.2050.00 0.117
Pb8.25~56.3023.236.820.982.3529.36 27.2
As2.22~21.807.242.581.325.5035.64 6.4
Hg0.014~0.950.0580.0654.2922.68112.07 0.034
Ni6.07~81.8028.0311.990.880.2442.78 24.6
Table 5. Correlation analysis of soil heavy metal contents and environmental variables.
Table 5. Correlation analysis of soil heavy metal contents and environmental variables.
VariableCrCdPbAsHgNi
Organic Matter−0.0280.226 **0.208 **0.504 **0.349 **−0.030
Precipitation0.150 **−0.188 **−0.218 **−0.288 **−0.224 **0.107 **
Humidity0.022−0.055−0.041−0.034−0.062−0.001
Elevation0.133 **−0.233 **−0.253 **−0.516 **−0.374 **0.081 *
Slope−0.084 *0.0330.099 **0.0440.039−0.056
NDVI0.041−0.058−0.026−0.056 *0.026−0.004
Distance to Living Area0.012−0.115 **−0.102 **−0.227 **−0.152 **0.011
Distance to Road−0.002−0.025−0.0070.0380.058 *0.045
Population Density−0.159 **0.144 **0.229 **0.233 **0.299 **−0.122 **
**, correlation is significant at the 0.01 level (two-tailed). *, correlation is significant at the 0.05 level (two-tailed).
Table 6. Precision of the prediction of soil heavy metal.
Table 6. Precision of the prediction of soil heavy metal.
ElementTraining DatasetsValidation Datasets
RMSE
(mg/kg)		MAE
(mg/kg)		R2RMSE
(mg/kg)		MAE
(mg/kg)		R2
Cr3.840 10.200 0.600 4.055 11.943 0.542
Cd0.190 0.028 0.523 0.205 0.032 0.504
Pb2.047 2.952 0.535 2.164 3.402 0.527
As1.168 0.945 0.631 1.254 1.023 0.627
Hg0.241 0.023 0.612 0.205 0.021 0.584
Ni2.693 5.388 0.512 2.9356.5590.482
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Nie, S.; Chen, H.; Sun, X.; An, Y. Spatial Distribution Prediction of Soil Heavy Metals Based on Random Forest Model. Sustainability 2024, 16, 4358. https://doi.org/10.3390/su16114358

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Nie S, Chen H, Sun X, An Y. Spatial Distribution Prediction of Soil Heavy Metals Based on Random Forest Model. Sustainability. 2024; 16(11):4358. https://doi.org/10.3390/su16114358

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Nie, Shunqi, Honghua Chen, Xinxin Sun, and Yunce An. 2024. "Spatial Distribution Prediction of Soil Heavy Metals Based on Random Forest Model" Sustainability 16, no. 11: 4358. https://doi.org/10.3390/su16114358

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