Using a Two-Stage Scheme to Map Toxic Metal Distributions Based on GF-5 Satellite Hyperspectral Images at a Northern Chinese Opencast Coal Mine

Abstract

Toxic metals have attracted great concern worldwide due to their toxicity and slow decomposition. Although metal concentrations can be accurately obtained with chemical methods, it is difficult to map metal distributions on a large scale due to their inherently low efficiency and high cost. Moreover, chemical analysis methods easily lead to secondary contamination. To address these issues, 110 topsoil samples were collected using a soil sampler, and positions for each sample were surveyed using a global navigation satellite system (GNSS) receiver from a coal mine in northern China. Then, the metal contents were surveyed in a laboratory via a portable X-ray fluorescence spectroscopy (XRF) device, and GaoFen-5 (GF-5) satellite hyperspectral images were used to retrieve the spectra of the soil samples. Furthermore, a Savitzky–Golay (SG) filter and continuous wavelet transform (CWT) were selected to smooth and enhance the soil reflectance. Competitive adaptive reweighted sampling (CARS) and Boruta algorithms were utilized to identify the feature bands. The optimum two-stage method, consisting of the random forest (RF) and ordinary kriging (OK) methods, was used to infer the metal concentrations. The following outcomes were achieved. Firstly, both zinc (Zn) (68.07 mg/kg) and nickel (Ni) (26.61 mg/kg) surpassed the regional background value (Zn: 48.60 mg/kg, Ni: 19.5 mg/kg). Secondly, the optimum model of RF, combined with the OK (RFOK) method, with a relatively higher coefficient of determination (R²) (R² = 0.60 for Zn, R² = 0.30 for Ni), a lower root-mean-square error (RMSE) (RMSE = 12.45 mg/kg for Zn, RMSE = 3.97 mg/kg for Ni), and a lower mean absolute error (MAE) (MAE = 9.47 mg/kg for Zn, MAE = 3.31mg/kg for Ni), outperformed the other four models, including the RF, OK, inverse distance weighted (IDW) method, and the optimum model of RF combined with IDW (RFIDW) method in estimating soil Zn and Ni contents, respectively. Thirdly, the distribution of soil Zn and Ni concentrations obtained from the best-predicted method and the GF-5 satellite hyperspectral images was in line with the actual conditions. This scheme proves that satellite hyperspectral images can be used to directly estimate metal distributions, and the present study provides a scientific base for mapping heavy metal spatial distribution on a relatively large scale.

1. Introduction

Soil, an essential part of the terrestrial ecosystem and one of the valuable natural resources for agriculture, is an important base for socioeconomic development and human survival [1]. However, soils have suffered serious toxic metal contamination throughout the world, especially in developing countries under the background of rapid urbanization and industrialization [2]. The major sources of poisonous metals are various smelting and mining activities, as well as the deposition of particulates from mining operations, pesticide utilization, and industrial production [3]. China, the largest coal consumer and producer in the world, is undergoing rapid socioeconomic development [4]. Nevertheless, coal mining activities may impose negative effects on ecosystems and the natural environment, especially on cropland near coal mines [5]. Toxic metals in soils exhibit significantly harm to crops and humans due to to their carcinogenic properties, toxicity, cumulative effects, and non-degradability [6]. What is worse, toxic metals impose negative effects on human health and lead to soil degradation via accumulation in the food chain [7]. For example, gastrointestinal distress, such as abdominal pain, nausea, irritation of the respiratory system, and vomiting, can be generated by inhaling excessive zinc (Zn) [8]. More seriously, fertility and cholesterol balance may be impacted by long-term high-dose exposure to Zn [9]. Additionally, studies indicate that chronic exposure to nickel (Ni) may increase the risk of cancer [10]. Hence, investigating toxic metal contaminations in coal mining areas is strongly desired because the outcomes can be used to identify polluted areas, provide land reclamation strategies, select soil remediation schemes, and propose effective public health prevention measures.

The rapid and accurate measurement of heavy metal concentrations is the prerequisite to obtaining its spatial distribution. Traditionally, ground-level soil sampling and laboratory surveying, including inductively coupled plasma (ICP), X-ray fluorescence spectroscopy (XRF), and atomic absorption spectrometry (AAS), [11,12,13,14,15], have commonly been adopted to measure toxic metal contents in soil. Moreover, the spatial distribution of heavy metals can also be obtained via geostatistical methods, which can infer heavy metal concentrations in unsampled locations [16]. Nevertheless, traditional approaches are labor and time-consuming and may lead to secondary contamination due to extra chemicals used in the laboratory process. Moreover, the above methods, showing low efficiency, have difficulty meeting the need for the rapid investigation of heavy metal distributions at a relatively large scale [17]. Additionally, geostatistics mainly depends on the assumptions of spatial autocorrelation, whereas the actual heavy metals may demonstrate significant spatial heterogeneity due to the diverse chemical and physical properties of the soils and the environment [18].

Recently, hyperspectral remotely sensed technology (RST) has been used to rapidly and accurately estimate soil heavy metal concentrations in large areas [19]. Currently, estimating heavy metal contents with RST can be divided into two types: one uses multi-spectral data, combining auxiliary variables such as the chemical and physical properties of soils, topography elements, and environmental factors to infer the distribution of heavy metals [20,21,22,23,24]; the other type takes advantage of hyperspectral RST to fit a quantitative model between soil heavy metal concentrations and the spectra of soil samples, inferring the metal distributions [25,26,27]. However, the capacity and sensitivity of multi-spectral RST are relatively inadequate. In addition, auxiliary variables for inferring soil heavy metal contents with multi-spectral RST vary according to sampling locations and the lack of universality [28]. Hyperspectral RST can be used to infer heavy metal concentrations because metals have a stronger direct response to organic matter and clay signals when the metals are attached to exchange sites.

Although hyperspectral RST showed convenience and feasibility for predicting heavy metal concentrations, to some extent, some uncertainties and deficiencies still exist [29]. Hyperspectral images can be collected by airborne and space-borne platforms [30]. However, the spectral resolution of some sensors, with a low signal-to-noise ratio (SNR), is coarse. For instance, Hyperion, the short-wave infrared (SWIR) spectral channel with a low SNR, was decommissioned in 2017. Compact High-Resolution Imaging Spectrometer (CHRIS) with the visible-to-near infrared (VNIR) spectral range (415–1050 nm) can hardly be used to inverse heavy metals because the spectral cover is not large enough [31]. Fortunately, the SWIR Advanced Hyperspectral Imager (AHSI), covering 330 bands to reflect solar reflection during 350–2500 nm, with a narrow swath width of approximately 60 km, one of the main payloads onboard the GaoFen-5 (GF-5) satellite, supplies a probability for retrieving heavy metal contents from a relatively large region [32]. The spectral resolution for VNIR and the SWIR is about 5 nm and about 10 nm, respectively, and the maximum SNR is 500 [33]. Hence, the feasibility of utilizing GF-5 satellite data to retrieve toxic metal contents requires further evaluation.

For the soil heavy metals prediction model, a series of data-driven methods, including the extreme learning machine (ELM), partial least squares regression (PLSR), support vector machine (SVM), random forest (RF), and back propagation neural networks (BPNN) methods, have recently been widely used [34,35]. Although the issue of linear fitting can be solved by machine learning methods, it shows some drawbacks regarding model robustness and efficiency, as well the tendency to overfit. Furthermore, the spatial distribution of toxic metals was affected by both physical factors—topography factors, wind orientation, and precipitation, and by anthropogenic activities—air pollution emissions, contamination sources, and industrial production [36]. The use of machine learning methods, such as RF, often exhibit difficulty in reflecting the residuals caused by a random process and other factors, leading to the necessity of the precision inherent in the data-driven methods in estimating soil heavy metal contents, which require further improvement [37]. Previous studies have confirmed that using multi-spectral data, as well as auxiliary variables via a machine learning model combined with geological statistical models, can enhance the precision in predicting soil heavy metal concentrations [38]. However, the possibility and reliability of using hyperspectral images and a machine learning model combined with a geological statistical model to predict soil heavy metal contents have not been assessed previously.

Therefore, the purpose of this study is (1) to verify the feasibility of using GF-5 image and RF, combined with geological statistical models, including ordinary kriging (OK) and inverse distance weighting (IDW), in predicting Zn and Ni concentrations at an opencast coal mine; (2) to obtain the optimal inversion model for Zn and Ni; and (3) to clarify the spatial distribution features of Zn and Ni in the study area.

2. Materials and Methods

Figure 1 is a workflow that shows all methods and describes the main steps followed in the study. The flow chart is composed of four parts: data preparation, spectra pretreatment and feature selection, model calibration and validation, and mapping heavy metal concentrations.

First, the remote sensing images of GF-5 are preprocessed, which consists of radiometric calibration, atmospheric correction, and mixed pixel decomposition. It also covers soil sample preprocessing and heavy metal contents determination.

The second part is spectral data processing, mainly including Savitzky–Golay (SG) smoothing and continuous wavelet transform (CWT) of GF-5 image data, as well as spectral reflectance extraction using ArcGIS 10.0 for constructing the spectral database. The spectral reflectance of GF-5 and soil heavy metal contents were defined as independent variables and dependent variables, respectively, then the adaptive reweighted competitive sampling (CARS) method and Boruta algorithms were used to select the characteristic bands.

Third, RF models were fitted based on independent variables and dependent variables to determine the optimum model for heavy metal concentrations. The predicted heavy metal contents obtained from the optimum model deduced the actual heavy metal contents surveyed in the lab to determine the residual. Then residual was interpolated using OK and IDW to obtain residual distribution maps.

Fourth, the final heavy metal contents map was generated by overlaying the residual distribution maps and metal distribution maps obtained from the optimum model.

2.1. Study Area

The research site is adjacent to an open-pit mine located in the Ordos Plateau, Inner Mongolian, China (Figure 2). The topography is generally flat in the east and high in the west, with an altitude range of 850 m to 2149 m. The typical annual precipitation and temperature range from 170 mm to 450 mm and 5.3 °C to 8.7 °C, respectively. The coal resources of the Ordos Plateau are rich [39]. Moreover, the coal industry is very important for the economic growth of the Ordos. Nevertheless, mining activities generate obvious passive influences on the natural environment. Recently, heavy metal pollution around the coal mine, especially in the nearby cropland, has aroused wide concerns.

2.2. Soil Sample Collection and Measurement

A total of 110 soil samples, with a depth of about 20 cm, were collected in February 2020 according to the procedure listed in the FOREGS Geochemical Mapping Field Manual [40]. The soil sample sites were distributed in the farmlands of the coal mine areas to eliminate human influences and to ensure a reasonable distribution, as much as possible. Additionally, to obtain the precise geographic location of each soil sample, the global navigation satellite system (GNSS) with the real-time kinematic (RTK) method and the Continuous Operating Reference Station (CORS) signals were used to determine each sampling site’s position. The China Geodetic Coordinate System 2000 (CGCS2000) was defined as the coordinate system of the current project.

In the laboratory, the samples were first air dried. Then, the samples were ground using grinding rods, and other foreign matter was removed. Third, all soil samples were placed into an oven until dry, without changing the weight. Fourth, the samples were sieved using a 0.7 mm nylon aperture sieve and put into clean polyethylene bags for analysis [8].

For quality control and quality assurance (QC/QA), the contents of toxic metals were surveyed using a SPECTRO xSORT X-ray device. The SPECTRO xSORT had been calibrated using the geochemical reference standards and the GSS series from the GSD series (China Institute of Geophysical and Geochemical Survey, Langfang, China) to ensure that the relative standard deviation was in the range of 3% to 5% [9].

2.3. Hyperspectral Remotely Sensed Data Collection and Pretreatment

2.3.1. Acquisition and Processing of GF-5 Data

The AHSI sensor is included in the GF-5 and can be obtained at https://www.cheosgrid.org.cn/index.htm (accessed on 5 April 2020). The GF-5 image, with a spatial resolution of 30 m and a sweep width of 60 km, covers 330 wavelength bands, including the VNIR and SWIR bands regions from 390 to 2513 nm. Specifically, the spectral resolutions of the VNIR and SWIR bands were 4.28 nm and 8.42 nm, respectively, and the SNR in the VNIR and SWIR regions was about 700 and 500, respectively. Several methods, including radiometric calibration, atmospheric correction, and orthorectification, were adopted to process the GF-5 image. The spectral data of the sample sites can be extracted via ArcGIS 10.0, and detailed information in terms of GF-5 data processing was exclusively stated in the published paper [41]. Therefore, this paper does not desecribe the processes again.

2.3.2. Smoothing and Enhancing Spectra

To eliminate noise from the spectrum data, as well as to separate overlapping samples owing to the “burr” phenomenon, SG smoothing is carried out for the raw spectra. The SG method, with 21 window lengths, was selected to obtain a quadratic polynomial [42]. We have supplemented the experiment for determining the best smoothing window of SG (Figure S1). Furthermore, we have added necessary experiments for evaluating the two methods, and we found that the results for using both SG and CWT were better than those obtained using only CWT (Table S1). Thus, the SG smoothed spectra were enhanced by CWT.

The soil spectral absorption characteristics are close to the Gaussian function, so the Gaussian 4 function, with ten decomposition scales, was selected as the mother wavelet function. We used L1–L10 to represent ten decomposition scales, including 2¹, 2², 2³, 2⁴, 2⁵, 2⁶, 2⁷, 2⁸, 2⁹, and 2¹⁰, respectively [43].

2.4. Characteristic Bands Selection

If all hyperspectral data are directly used to fit the models, the performance of the models will be affected due to redundant data. In this paper, the CARS and Boruta algorithms are introduced to eliminate the redundancy of the hyperspectral data. CARS, which eliminates redundant and irrelevant variables while preserving informative variables, is one of the feature selection strategies employed in this study [44]. The Boruta method, which provides an intrinsic measure of each variable’s significance, known as the Z-score, was also used in this study to carry out the selection of spectral features [45]. All characteristic bands selected by the CARS and Boruta methods were tested to determine the optimal model (Figure 1). One significant point must be clearly clarified. We did not use testing data for feature selection. Only training datasets were used for feature selection in this study.

2.5. Two-Staged Schemes

The two-staged schemes, the first stage consisting of fitting the data using the random forest method to determine the optimal model, and the second stage consisting of correcting the heavy metal map obtained from the optimum model by overlaying the residual, are described as follows.

2.5.1. Random Forest (RF)

RF, one of the bagging-based integrated learning techniques, is widely used for solving classification and regression issues [46,47,48,49,50,51]. The number of decision tree classifiers (ntree), the maximum number of features (mtry), and the minimum number of samples of the leaf nodes significantly affect the model performance. In this study, a round-robin approach was used to determine the optimal mtry and ntree, and the ranges of ntree and mtry are 1 to 100 and 1 to P − 1, respectively. P is the number of independent variables, and the interval for both mtry and ntree is 1.

2.5.2. Interpolation Methods

Both the OK and the IDW models were used to spatialize the residual generated by the optimal model in the section. OK interpolation is one of the widely used kriging interpolation techniques, which assumes that every point in space has the same expected value and variance [52,53,54,55]. Meanwhile, to select the best interpolation method for estimating heavy metal contents, the IDW was also introduced to interpolate the residual, which is essentially a weighted moving average technique [56,57].

2.5.3. Overlay Methods

Firstly, we selected ten scales including 2¹, 2², 2³, 2⁴, 2⁵, 2⁶, 2⁷, 2⁸, 2⁹, and 2¹⁰ as wavelet scales, according to the methods used in previous studies. Secondly, we conducted feature selection using the spectra after L1-L10 wavelet transformation. Thirdly, we fitted models using the feature bands of each wavelet scale, and the precision was evaluated by R², RMSE, and MAE. Then, the best wavelet scale with the highest precision was used in building the final model. Finally, the second stage aimed to correct the heavy metals map obtained from the optimum model by overlaying the residual map generated by the interpolation methods. The optimum model of RF, combined with OK (RFOK) and with IDW (RFIDW), was used in this study to determine the final heavy metal concentrations map [58].

2.6. Accuracy Evaluation

In this study, 70% of the samples are model calibration sets, and the other 30% are model validation sets [59]. Not all validation set samples were used in the RF model fitting. Three metrics were selected, including the coefficient of determination (R²), root-mean-square error (RMSE), and mean absolute error (MAE), to evaluate the model accuracy. The calibration sets (training dataset) were only used for model fitting and model parameter optimization. The validation sets (testing datasets) were only used for performance evaluation.

The equations corresponding to the above three metrics can be found in previous studies, so they have not been inlcuded again in this paper [60].

3. Results and Discussion

3.1. Descriptive Statistics for Heavy Metal Contents

The risk screening values for Zn and Ni are 200 mg/kg and 190 mg/kg, based on the soil environmental quality risk control standard for the soil contamination of agricultural land in China [61]. Clearly, neither Zn nor Ni’s mean value in this work surpasses the national risk screening value (

Table 1. Descriptive statistics for heavy metal concentrations in the study area.

Element	Max (mg/kg)	Min (mg/kg)	Mean (mg/kg)	Std. (mg/kg)	CV(%)	Chinese Soil Criteria (mg/kg)	Inner Mongolian Criteria (mg/kg)
Zn	157.00	30.05	68.07	22.56	33.14	200.00	48.60
Ni	47.92	15.37	26.61	5.57	20.93	190.00	19.50

). However, both Zn and Ni mean values exceed the local risk screening value. The results indicated that Zn, with a 33.14% coefficient of variation (CV), exhibits a skewed distribution, which shows that Zn has accumulated, to some extent, in the study area under the influence of long-term human activities and mining practices. However Ni, with 20.93% CV, represents a nearly normal distribution (Table 1 and Figure 3).

3.2. Analysis of Soil Spectral Characteristics

The original spectra for the entire 110 sample sites are shown in Figure 4a. Overall, the organic matter and iron ions lead to the soil spectral curve exhibiting an increasing trend between 350 and 1400 nm [62]. The reflection peaks caused by sensor noise are noticeable at positions between 900 and 1100 nm. Additionally, the absorption troughs at 1400, 1900, and 2200 nm are caused by the composition of water and adsorbed minerals [63]. The raw spectral reflectance was smoothed by SG smoothing, and the SG effectively eliminated noise and removed the “burr” phenomena (Figure 4b).

The CWT-transformed spectra are shown in Figure 4c–l, labeled with L1–L10 for each of the 10 scales. From this figure, we can outline four general properties of wavelet spectra. The width and position of the narrow spectral features were captured in the L1–L3 spectrum, and feature identification is considerably improved using these three spectrum scales compared to the original reflectance. The L4–L6 spectrum captured properties of the continuum and retained the overall amplitude of the original reflectance spectrum. The relative strength of the features in the reflectance was preserved and enhanced in the L4–L6 spectra. In the L7–L10 spectrum, the spectral information was continuously eliminated, resulting in a flattening of the spectral curve and the loss of the majority of the spectral information [64].

In summary, it is necessary to first reduce noise from the raw spectrum data before highlighting reflection peaks and absorption valleys in the smoothed spectral data in order to gain additional spectral information. Published research has shown that the wavelet transform scale is not as broad as it could be, and as the scale increases, the spectral information gradually disappears [65,66]. As a result, the spectral curve in this study is unable to display the typical spectral features beyond the L7 scale.

3.3. Analysis of Spectral Feature Bands for Both Zn and Ni

In this work, two techniques, including the CARS and Boruta algorithms, were adopted to select the spectral feature bands. CARS uses cross-validation to choose the feature bands with the fewest root mean square errors (RMSECV), and the Boruta algorithm sieves the feature bands based on their Z-score.

The feature bands for both Zn and Ni are essentially distributed in the 300–700 nm, 1100–1400 nm, and 2300 nm ranges (Figure 5 and Figure 6). It should be noted that the distribution maps of Zn and Ni concentrations in this study were indirectly obtained from variations of SOC and clay because heavy metals have a close relationship with these types of soil.

For the Zn element, the feature bands were primarily located in the ranges of 400–650 nm, 1190–1520 nm, and 2340–2380 nm (Figure 5a and Figure 6a), and these results are largely in line with those of earlier investigations [67,68,69]. Zn and clay minerals exhibit a strong association, and the OH bonds in clay minerals react spectrally in this wavelength range; thus, clays have high reflection peaks around 400–600 nm, 1900 nm, and 2200 nm [70].

In contrast, Ni exhibits a significant spectral response in the region of 840–900 nm, 1330–1540 nm, and 2130–2370 nm (Figure 5b and Figure 6b). In the clay minerals, the location of these spectral feature bands is dominated by the secondary absorption peak of the Al–OH group [61,62,63,64,65,66,67,68,69,70,71,72,73]. Additionally, the organic matter exhibits a strong correlation with Ni, and the clay minerals, including kaolinite and vermiculite, also absorb Ni in this wavelength region. Clearly, spectral feature bands for both Zn and Ni demonstrate close relationships with the organic matter and clay minerals.

3.4. Prediction Model Performance Evaluation and Heavy Metal Concentrations Map Accuracy Analysis

In this study, R², RMSE, and MAE were adopted to evaluate the RF prediction model performance, and 30% of the soil samples were defined as the validation set.

For the Zn element, the optimal RF prediction model with the highest R² (0.4258), lowest RMSE (15.4994 mg/kg), and MAE (12.7899 mg/kg) was determined by the CARS feature selection at the L1 scale of the CWT (Figure 7a).

For the Ni element, the best RF prediction model with the highest R² (0.2615), lowest RMSE (4.0933 mg/kg), and MAE (3.4126 mg/kg) was determined by the Boruta feature selection at the L2 scale of the CWT (Figure 7d).

The final mapping accuracy is shown in Figure 8.

The heavy metal concentrations maps were generated by the optimum RF prediction model using GF-5 AHSI imagery via Matlab and ArcGIS10.0 (Figure 9a and Figure 10a). The specific processes of generating heavy metal concentrations distribution maps are expressed as follows. Firstly, the optimum model exhibiting feature bands of the best wavelet scale was determined. Secondly, the GF-5 remote sensing image was processed via SG and wavelet methods. Thirdly, the corresponding feature bands of the GF-5 remote sensing images were sieved and inputted into the optimum model to calculate the continuous distribution of heavy metal concentrations. Finally, the heavy metal concentrations map was designed and outputted based on ArcGIS 10.0. Then, the residuals obtained from the optimum RF prediction model were interpolated to heavy metal concentration residual maps by OK and IDW. Furthermore, an overlay process was conducted to obtain the RFOK and RFIDW (Figure 9b,c and Figure 10b,c) heavy metal concentration maps, based on Figure 9a and Figure 10a. Meanwhile, we also used the actual heavy metal concentrations of 70% of the soil samples to map the distribution of metals, using OK and IDW for comparison (Figure 9d,e and Figure 10d,e).

In this study, R², RMSE, and MAE were adopted to evaluate heavy metal concentration map accuracy, and 30% of soil samples were defined as the validation sets (

Table 2. Heavy metal concentrations map accuracy evaluation.

Element	Method	${\mathit{R}}_{\mathit{v}}^2$	$\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{c}}$ mg/kg	$\mathit{M}\mathit{A}{\mathit{E}}_{\mathit{c}}$ mg/kg	${\mathit{R}}_{\mathit{v}}^2$	$\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{v}}$ mg/kg	$\mathit{M}\mathit{A}{\mathit{E}}_{\mathit{v}}$ mg/kg
Zn	RF	0.8380	12.4158	9.3794	0.4258	15.4994	12.7899
	ELM	0.9513	4.7416	3.4512	0.3675	92.9663	70.0457
	SVM	0.3643	20.1904	13.2935	0.0357	21.542	16.094
	BPNN	0.2442	15.5495	16.7292	0.0998	21.2185	20.8124
Ni	RFOK	/	/	/	0.6029	12.4515	9.4730
	RFIDW	/	/	/	0.4878	13.9629	10.9129
	OK	/	/	/	0.2667	17.7032	14.8138
	IDW	/	/	/	0.2986	17.7784	14.4651
	RF	0.9292	2.3910	1.7828	0.2616	4.0883	3.4138
	ELM	0.3941	4.2316	3.2805	0.2179	7.8697	5.7294
	SVM	0.4955	4.325	2.625	0.1128	4.866	3.864
	BPNN	0.2895	5.4073	3.8706	0.1116	5.8028	4.0719
	RFOK	/	/	/	0.3038	3.9765	3.3112
	RFIDW	/	/	/	0.2258	4.3660	3.5848
	OK	/	/	/	0.2251	4.2641	3.3180
	IDW	/	/	/	0.1180	4.5961	3.5455

).

Clearly, the RFOK method demonstrated the best accuracy with the highest validation R² (0.6029 for Zn, 0.3038 for Ni) and the lowest validation RMSE (12.4515 mg/kg for Zn, 3.9765 mg/kg for Ni) and MAE (9.4730 mg/kg for Zn, 3.3112 mg/kg for Ni) for both Zn and Ni (Table 2 and Figure 8).

Hence, the RFOK was selected as the final method to map the heavy metal concentrations in this study (Figure 9c and Figure 10c).

A published study has found that several variables, including topography, human activities, and the distribution of pollution sources, may impose effects on the distribution of heavy metals [74].

Although this study only selected spectral data as the independent variables, and the impact of environmental conditions on the distribution of soil heavy metals was ignored, the two-stage scheme compensated for this flaw, to some extent.

The RF model can determine the relationship between heavy metal concentrations and spectral reflectance [75]. However, the influence of environmental factors and topography factors on the heavy metal concentrations was completely ignored by the RF model.

The geo-statistical models, such as OK and IDW, based on the first law of geography, can reflect the relationship between heavy metal contents and environmental factors.

Thus, both RF and geostatistical models were merged in this study, and the results confirmed that this two-stage scheme can be adopted to predict heavy metal concentrations.

3.5. Distribution Feature of Toxic Metals

To compare the reliability of heavy metal concentrations distribution maps, five maps generated by RF, RFIDW, RFOK, OK, and IDW, are shown simultaneously (Figure 9 and Figure 10). Figure 9f and Figure 10f are true-color GF-5 images of the study area.

As demonstrated in Figure 8 and Figure 9, the heavy metal concentrations distribution map based on five methods for both Zn and Ni are comparable, and the spatial distribution features are largely consistent.

Clearly, the concentrations for both Zn and Ni exceeded the local heavy metal concentrations background value, but were lower than the limits contained in the Chinese criteria in most locations of the study area (Figure 9 and Figure 10 and Table 1). Two hotspots for Zn and Ni were detected, respectively, in the southwest and the middle east portions of the study area because the largest opencast coal mine, as well as a number of other coal mines, are mainly distributed in the southwest and the middle east portions of the study area. These results confirmed that the development of the opencast coal mine generated obvious influences on the distribution of heavy metals in the area.

It is clear that the spatial distributions of Zn and Ni were approximately the same, while the detailed descriptions of each map vary to some extent (Figure 9 and Figure 10).

Specifically, the geographical distribution maps generated by the geostatistical models, with discontinuities in the transition zones of heavy metals, are similar (Figure 9d,e and Figure 10d,e). The spatial variability can scarcely be represented by the geographical distribution maps.

By contrast, the RF method can construct a quantitative relationship between heavy metal concentrations and spectral data, and the spatial distribution of heavy metal concentrations can be explicitly described using GF-5 images based on RF at the raster scale.

However, the influence of environmental factors such as geographical location on the predicted results were not considered by the RF. Hence, the two-staged schemes proposed by this study, integrating geostatistical methods with RF, can compensate for the disadvantage of the RF model and improve the overall precision. The distribution maps of heavy metal concentrations generated by RFOK demonstrated more objectivity than other methods, according to performance evaluation (Table 2, Figure 9c and Figure 10c).

4. Conclusions

By combining the heavy metal concentrations at the sampling sites with the GF-5 hyperspectral image, this study proposes a two-stage scheme to directly map the spatial distribution of heavy metal contents without surveying the spectral data. Heavy metal concentration maps were indirectly inferred based on the close relationship between heavy metals and SOC and clay. The findings of this study indicated that it is possible to acquire the spatial distribution of heavy metals using hyperspectral images directly based on the close relationship between heavy metals and related soil materials, such as SOC and clay, over a relatively larger area.

The average concentration of Zn and Ni are 68.07 mg/kg and 26.61 mg/kg in the study area, respectively, which are higher than the concentrations in the regional background values.

Additionally, this study integrates geostatistical methods with RF to develop a two-stage scheme for estimating heavy metal concentrations, and the prediction accuracy improved significantly because both the spectral characteristic of heavy metals and the influence of environmental factors were taken into consideration via the two-stage scheme.

The features of the distribution of the heavy metals estimated by five prediction methods were detected to be close, while exhibiting a significant difference in details. The heterogeneity of heavy metals distribution and the concentrations in the transition regions can be well described by the RFOK model. On the contrary, the capacity and accuracy of the other four methods regarding capturing the detailed spatial variability of toxic metals are relatively weak.

The mechanism of the distribution of heavy metals is quite complicated. Although the two-staged schemes can be carried out to estimate toxic metal concentrations, the inner mechanism is still uncertain. Therefore, we plan to conduct a new quantitative study to explore the sources of heavy metals and the influence of environmental factors regarding heavy metals in the coal mining areas.