A method for spatio-temporal process assessment of eco-geological environmental security in mining areas using catastrophe theory and projection pursuit model

Abstract

It is a universal problem that the eco-geological environment has been damaged by mineral resources exploitation. The accurate evaluation of eco-geological environmental security (EES) in mining areas is essential for restoring the environment of the mining area. However, a robust approach to obtaining an accurate evaluation of ESS has not yet been produced due to the complex spatio-temporal process of EES. Here, we developed a new method for enabling the quantitative evaluation of the EES spatio-temporal process. The EES evaluation index system of mining areas was established from both natural and anthropogenic aspects. The EES evaluation method was developed by combining the catastrophe theory and projection pursuit model (PPM). Then, with the support of remote sensing (RS) and a geographic information system (GIS), the method was applied to evaluate the spatio-temporal process of EES in Panxi mining area. The bifurcation curve and receiver operating characteristic curve were used to verify the developed method. The results showed that this method could accurately evaluate the spatio-temporal process of EES in a mining area and could successfully recognise the threshold value to distinguish the safe status and unsafe status. Strong spatio-temporal variations of EES in Panxi area were found, which may be the result of the combined effect of multiple factors (e.g. mineral resource exploitation, soil erosion, and ecological restoration). In summary, the combination of catastrophe theory and PPM with RS and GIS to quantitatively evaluate the spatio-temporal process of EES in mining areas is a robust method.

Keywords

Eco-geological environmental security catastrophe theory projection pursuit model mining areas spatio-temporal process assessment

I Introduction

The pressure of anthropogenic activities on the eco-geological environment (EGE) has increased in recent decades, and the contradiction between humans and nature has intensified (Messerli et al., 2000; Zwier et al., 2018). Although great progress has been made in EGE protection, it is still being deteriorated (Tost et al., 2018). EGE degradation poses a larger threat to regional development and national security (Rockström et al., 2009). Therefore, eco-geological environmental security (EES) has been an important concern in all countries around the world (Jordan, 2009). Mineral resources are the necessary material basis for the survival and development of human society (Besser et al., 2009). The demand for all kinds of mineral resources has sharply increased, which has accelerated mine exploitation (Habib and Wenzel, 2014). The EGE issues induced by the over-exploitation of mineral resources are globally severe (Leppänen et al., 2017). In China, more than 95% of primary energy, 80% of industrial raw materials, and 70% of agricultural production supplies originate from mineral resources (Xu, 2008). However, long-term and high-intensity exploitation of mineral resources has also led to a series of EGE issues, such as geological disasters, land destruction, vegetation deterioration, and topographic landscape damage (Omotehinse and Ako, 2019). In recent years, the Chinese government has made great efforts in mining restoration (Lan, 2016). Nevertheless, the assessment of EES status in mining areas is a prerequisite for devising an efficient EGE restoration plan (Kapustka et al., 2016).

Many methods have been applied to EES assessment (Sokolenko et al., 2017). Ecological models are developed depending on resource and environmental carrying capacity, and mainly include the ecological footprint model and the energy value analysis method (Chu et al., 2017; Veettil and Mishra, 2020), which can quantitatively measure the ecological carrying capacity status with fewer indexes. However, these models do not consider the interactions between factors affecting ecological carrying capacity, whose levels were only analysed from the perspective of anthropogenic possession and the utilisation of natural resources. The landscape ecology model mainly assesses the current status and dynamic trends of multi-scale EES and can easily store information due to the presence of landscape structure components (Dalloz et al., 2017). However, the landscape pattern indexes cannot better reflect EES, which leads to unreliable evaluation results. Mathematical methods generally include a comprehensive index, grey correlation, matter-element extension, principal component analysis, and artificial neural networks. The comprehensive index method reflects the comprehensiveness, integrity, and hierarchy of EES assessment (Mapar et al., 2020). However, this method simplifies the problem and cannot reflect the essence of EES. The grey correlation method does not require high-quality ecosystem parameters and adapts more to the EES systems that are not yet uniform, but the determination of the discrimination coefficient is more subjective (Sahoo et al., 2016). The matter-element extension method is extensible and flexible, but the associative function is not well defined and difficult to generalise (Wang et al., 2019). Principal component analysis overcomes the overlapping problem among elevation indicators, but the actual meaning of the indicators is not considered, and the index weight may not reflect the actual importance of the indicator (Uddin et al., 2019). For the artificial neural network method, the weights of evaluation indicators are automatically adjusted and thus have strong adaptability (Alizadeh et al., 2018). However, it may induce overtraining or undertraining, and the results may fall into local minimum and may not match reality. The aforementioned methods also suffer from several problems. The first is that these methods all evaluate the EES status at a given moment. However, EES is a process function of time and space. When the value exceeds a threshold, the EGE undergoes irreversible mutations. The methods cannot effectively depict the EES dynamic process, which limits the objective understanding of EES (Rouge et al., 2015). Second, the evaluation process and results of these methods are strongly influenced by human disturbance, and the degree of objectivity is weak. Therefore, a method to objectively depict the EES dynamic process is urgently required.

Catastrophe theory is used to describe the shift of a natural or social process from a gradual and quantitative status to a sudden and qualitative status (Thom, 1977; Zeeman, 1979). It has been frequently used to predict the plugging pressure of lost circulation control in fractured reservoirs, cognitive workload and fatigue in teams, flood susceptibility mapping, and potential consequences of dam breach (Al-Abadi et al., 2016; Ge et al., 2019; Guastello et al., 2014; She et al., 2020). The projection pursuit model (PPM) is used to project high-dimensional data to low-dimensional subspaces (Guastello et al., 2019). The data are then analysed to find a projection that reflects the structure or features of the original high-dimensional data. It has been widely used in EGE assessment because of its strong resistance to anthropogenic disturbance, good robustness, and high accuracy (Allahbakhshian et al., 2020). Nevertheless, the integration of catastrophe theory with PPM has scarcely been applied to EES evaluation. Analysing the spatial and temporal changes of EES in mining areas by combining timely remote sensing (RS) data, geographic information system (GIS) techniques, and mathematical models has become a crucial research direction (Hinton, 1996).

In this regard, the present study developed an EES evaluation method by combining catastrophe theory with PPM based on RS and GIS. The Panxi area was chosen as a research prototype to (1) validate the feasibility of the method developed and (2) analyse the spatio-temporal process of EES in mining areas.

II Method

The development of the EES assessment method contains the following steps (Figure 1): (1) the index system of EES assessment in the mining area is established according to the characteristics of EGE; (2) the EES spatio-temporal process evaluation model is developed by integrating catastrophe theory and PPM; and (3) the validity of the method developed in the mining area is verified using a bifurcation curve and receiver operating characteristic (ROC) curve.

Figure 1.

Flowchart used to build EES assessment method in mining areas.

1 Establishing an assessment index system

Based on previous studies (Ramadhan et al., 2020), the EES evaluation index system in mining areas is developed by including natural and anthropogenic influencing factors. The natural influencing factors are elevation, slope, lithology, seismic acceleration, geological hazard density, temperature, precipitation, soil type, and vegetation coverage. The anthropogenic influencing factors are mining scale, mining mode, mining regreening, mining density, land cover, gross domestic product (GDP), and population density. The principles for selecting the evaluation indices are described in Table 1 (Sun et al., 2020).

Table 1.

Reasons for indicator selection for EES assessment in mining areas.

Evaluation indicator		Reasons for indicator selection
Natural Influencing factors	Elevation and slope	Elevation and slope, the basic geomorphological indicators, are the crucial factors affecting surface runoff and soil erosion, which have an essential impact on EES in mining areas.
	Lithology	Rocks are the material basis for the formation of landforms and soil. The rock structure determines the characteristics of geotechnical strength and self-stability, which is an internal factor describing EES in mining areas.
	Seismic acceleration	Seismic acceleration, the basis for determining the intensity, refers to the acceleration of ground motion during an earthquake, which has an important influence on EES in mining areas.
	Geological hazard	Geological hazards, with a significant impact on EES, refer to the movement of rocks and soils on the earth’s surface that severely damage human lives, property, and the living environment. This study applies the density of geological hazards per unit area to be EES evaluation indicators.
	Temperature and precipitation	Temperature and precipitation are the kinetic energy factors to compose natural environment and the energy basis of the ecosystem. When their energy characteristics and transmission transformation are not coordinated with other factors in space and time, it will lead to ecological degradation. Therefore, temperature and precipitation have important impacts on EES in mining areas.
	Soil type	Soil is a crucial condition for maintaining the ecological balance of the land. Different types of soil gain different degrees of erodibility, which is an important factor affecting EES in mining areas.
	Vegetation coverage	The status of surface vegetation coverage directly affects and even determines the status and functions of ecosystems such as primary biological production, ecological carrying capacity, and soil erosion intensity in the regional ecological environment, and has important indications for EES in mining areas. In this study, the normalised vegetation index (NDVI) is used as an indicator of vegetation coverage.
Anthropogenic influencing factors	Mining scale	The scale of mining is a direct influence factor of EES in mining areas.
	Mining mode	The mining mode is an important factor influencing EES in the mining area.
	Mining regreening	The degree of mine regreening is an important factor affecting EES in mining areas.
	Mining density	Different mine densities give rise to different degrees of damage to the ecological and geological environment of the mining area, which is an essential factor affecting EES in mining areas.
	Land cover	Regional soil erosion and reduction, and forest vegetation are correlative with land use patterns. Therefore, land cover and its changes are important factors affecting EES in mining areas.
	Economic development level	Economic development is closely related to the ecological geological environment. Mastering the economic development status of mining areas is important to evaluate EES. In this study, GDP is used as an indicator of economic development level for EES assessment in mining areas.
	Population density	The population is a fundamental indicator that affects the regional sustainable development and EES. The paper applies population density to characterise the impact of population on EES in mining areas.

2 Development of the assessment method

2.1. Establishment of the potential function

The EES assessment index system influences can be described by the cusp catastrophe model (CCM) of catastrophe theory. According to catastrophe theory, the ideal system potential function of CCM for EES is as follows (Mostafa, 2019):

f (x) = x^{4} + m_{1} x^{2} + m_{2} x

where f is the ideal system potential function; x is the EES status variable; m₁ is the natural influencing factors control variables (N); m₂ is the anthropogenic influencing factors control variable (H); and the functional relationships between m₁ and the nine natural influencing factors are established by using PPM as well as m₂ and the seven anthropogenic influencing factors (Wang and Ni, 2008). The method is as follows:

(1) Linear projection: assume that $\vec{u}$ is the unit projection direction vector in the t-dimensional space, and $V_{i j}$ is the eigenvalue of projection of $W_{i j}$ in linear one-dimensional space. Thus, $V_{i j}$ can be described as follows:

V_{i j} = \sum_{j = 1}^{t} \vec{u} W_{i j}

where $V_{i j} (i = 1, 2, 3 \dots s; j = 1, 2, 3 \dots t)$ is the j-th evaluation indicator of the i-th sample, s is the number of evaluation samples, and t is the number of evaluation indicators.

(2) Establishing projection indices: the index classification is used to find the maximum distribution structure in both inner-class density $Q (\vec{u})$ and between-class distance $P (\vec{u})$ . The projection index R is defined as:

R = Q (\vec{u}) \times P (\vec{u})

$Q (\vec{u})$ is calculated using the distance between two projected eigenvalues with the following equations:

Q (\vec{u}) = \sum_{i = 1}^{S} \sum_{j = 1}^{S} (C - D_{i l}) \times f (C - D_{i l})

D_{i l} = |V_{i} - V_{j}|, (l = 1, 2, 3 \dots s)

where C represents the width of the estimated local scatter density. The range of C is $\max (D_{i l}) + \frac{t}{2} \leq C \leq 2 t$ , and $C = t$ is available.

$D_{i l}$ is the distance between two projected eigenvalues. $f (C - D_{i l})$ is a step function: if $C = D_{i l}$ , then $f (C - D_{i l}) = 1$ ; otherwise, $f (C - D_{i l}) = 0$ . When the value of $Q (\vec{u})$ is larger, the clustering is more obvious.

$P (\vec{u})$ is calculated based on the variance of the projected eigenvalues of the evaluation indexes with the following equation:

P (\vec{u}) = {[\sum_{i = 1}^{s} \frac{V_{i} - \bar{V}}{s}]}^{1 / 2}

where $\vec{u}$ is the average value of the projected eigenvalues. When the value of $P (\vec{u})$ is larger, the scatter is more obvious.

(3) Projection orientation optimisation: projection orientation is optimised based on projection index R. Projection direction vector $\vec{u}$ is the best direction when R is the maximum. Thus, the optimal direction can be described as follows:

\{\begin{matrix} max R \\ ‖u‖ = 1 \end{matrix}

A genetic algorithm is used to find the optimal projection direction (Espezua et al., 2014). The maximum value of each component in the optimal projection direction represents the contribution and direction (positive or negative correlation) of the corresponding indexes. The comprehensive value of N (or H) can be calculated as follows:

C I = \sum_{i = 1}^{n} K_{i} T_{i} = K_{1} T_{1} + K_{2} T_{2} + \dots + K_{n} T_{n}

where $C I$ is the comprehensive result of N or H; K_i is the standardised value of the i-th index; and T_i is the best weight of this indicator. A higher value of $C I$ indicates a greater influence on EES.

2.2 Development of equilibrium surface formula for EES

According to the cusp catastrophe theory, the ideal equilibrium surface and the ideal bifurcation set can be described as follows:

f (x) = 4 x^{3} + 2 m_{1} x + m_{2} = 0

8 u_{1}^{3} + 27 u_{2}^{2} = 0

Based on equation (9), EES can be expressed by a phase point $(E E S, N, H)$ in a three-dimensional coordinate space. The root number of equation (10) can be used to judge whether EES changes in mining areas. According to the Cardano formula (Wituła and Słota, 2010), the discriminant of equation (10) is defined as

B = 8 u_{1}^{3} + 27 u_{2}^{2}

EES is assessed by the coordinate transformation between the three-dimensional coordinate $(x, m_{1}, m_{2})$ in the ideal equilibrium surface of the CCM and the EES equilibrium surface $(E E S, N, H)$ defined by the state variable (EES) and control variables (N, H).

To accurately simulate the mapping between the control variables (N and H) and the state variable (EES), all coefficients in equation (9) are set as non-zero constants, and the equation of the equilibrium surface is as follows:

m_{2} = a x_{1}^{3} + b m_{1} x_{1}

In equation (12), if $x_{1} = x_{0}$ , then $m_{2} = a x_{0}^{3} + b m_{1} x_{0}$ . m₁ and m₂ are formed into a linear relationship when x₁ is a fixed value. Therefore, the equilibrium surface is composed of lines that are parallel to the plane $m_{1} o m_{2}$ (Figure 2).

Figure 2.

Equilibrium surface formed by straight lines.

Then, the three-dimensional coordinate $(x, m_{1}, m_{2})$ in the ideal equilibrium surface is transformed into the equilibrium surface ( $E E S, N, H$ ). The spatial translation is set as $(x_{11}, m_{11}, m_{22})$ , and the rotation angle around the Z-axis is α (Figure 3). Then, the coordinate conversion relationship between the three-dimensional coordinate $(x, m_{1}, m_{2})$ in the ideal equilibrium surface and the new coordinate ( $E S S, N, H$ ) is defined as

\{\begin{matrix} x_{1} = E E S + x_{11} \\ m_{1} = N c o s α + H s i n α + m_{11} \\ m_{2} = - N s i n α + H c o s α + m_{22} \end{matrix}

Figure 3.

Schematic diagram of coordinate transformation between $(x, m_{1}, m_{2})$ and $(E E S, N, H)$ .

The equation $m_{2} = a x_{11}^{3} + b x_{11} m_{1}$ was set as the N-axis of natural influencing factors, which is the intersecting line of the equilibrium surface and the plane passing through the origin of the new coordinate system. The new coordinate system is derived from the rotation α and translation of the original coordinate system around the EES-axis. Combined with Figure 3, the equation can be established as follows:

t a n α = b x_{11}, s i n α = \frac{b x_{11}}{\sqrt{1 + b^{2} x_{11}^{2}}}, c o s α = \frac{1}{\sqrt{1 + b^{2} x_{11}^{2}}}

The coordinate of point $(E E S_{1}, N_{1}, H_{1})$ in the original coordinate system is $(E E S_{1} + x_{11}, N_{1} c o s α + H_{1} s i n α + m_{11}, - N_{1} s i n α + H_{1} c o s α + m_{22})$ , and the direction vector of the Z-axis is $(0, c o s α, s i n α)$ . Therefore, the equation for the plane that is perpendicular to the Z-axis passing through the origin of the former coordinate system is as follows:

N_{1} + \frac{m_{11}}{\sqrt{1 + b^{2} x_{11}^{2}}} - \frac{b m_{22} x_{11}}{\sqrt{1 + b^{2} x_{11}^{2}}} = 0

As point k $(E E S_{2} + x_{11}, N_{2} c o s α + H_{2} s i n α + m_{11}, - N_{2} s i n α + H_{2} c o s α + m_{22})$ is a catastrophe point, $(N_{2} c o s α + H_{2} s i n α + m_{11}, - N_{2} s i n α + H_{2} c o s α + m_{22})$ is available in equation (11). Moreover, there are three roots of x₁ at this point, including $x_{11}$ , $x_{12}$ , and $x_{13}$ , which means that equation (16) satisfies equation (17):

- N_{2} s i n α + H_{2} c o s α + m_{22} = a x_{1}^{3} + b x_{1} (N_{2} c o s α + H_{2} s i n α + m_{11})

(x_{1} - x_{11}) (x_{1} - x_{12}) (x_{1} - x_{13}) = 0

Whereas point k is included in the collection of singular points, three roots of equations (16) and (17) have two equal roots $(x_{11} = x_{13})$ , which are defined as:

\{\begin{matrix} 2 x_{11} + x_{12} = 0 \\ \frac{b}{a} (\frac{N_{2}}{\sqrt{1 + b^{2} x_{11}^{2}}} + \frac{b H_{2} x_{11}}{\sqrt{1 + b^{2} x_{11}^{2}}} + m_{11}) = x_{11}^{2} + 2 x_{11} x_{12} \\ \frac{- b N_{2} x_{11}}{\sqrt{1 + b^{2} x_{11}^{2}}} + \frac{H_{2}}{\sqrt{1 + b^{2} x_{11}^{2}}} + m_{22} = a x_{11}^{2} x_{12} \end{matrix}

Point k is a catastrophe point of EES, and the EES coefficient increases slowly with the growth of the control variable coefficient within a certain range of this point’s value. Consequently, the EES jumps from $x_{11}$ to $x_{12}$ at point k. The transition amount is expressed as (Song et al., 2015):

x_{11} - x_{12} = 1

By substituting equations (13) and (12) into equation (11), the transformed curved surface $(E E S, N, H)$ is used to calculate the EES. The equation is as follows:

{(E E S + x_{11})}^{3} + \frac{b}{a} (\frac{N}{\sqrt{1 + b^{2} x_{11}^{2}}} + \frac{b H x_{11}}{\sqrt{1 + b^{2} x_{11}^{2}}} + m_{11}) (E E S + x_{11}) + \frac{1}{a} (\frac{b N x_{11}}{\sqrt{1 + b^{2} x_{11}^{2}}} - \frac{H}{\sqrt{1 + b^{2} x_{11}^{2}}} - m_{22}) = 0

Setting $E E S + x_{11}$ in equation (20) as the unknown quantity X, $\frac{b}{a} (\frac{N}{\sqrt{1 + b^{2} x_{11}^{2}}} + \frac{b H x_{11}}{\sqrt{1 + b^{2} x_{11}^{2}}} + m_{11})$ and $\frac{1}{a} (\frac{b N x_{11}}{\sqrt{1 + b^{2} x_{11}^{2}}} - \frac{H}{\sqrt{1 + b^{2} x_{11}^{2}}} - m_{22})$ as constants A and B, equation (20) can be expressed as:

X^{3} + A X + B = 0

Based on the Cardano formula, the discriminant of equation (21) is calculated as follows:

Δ = 9 B^{2} + 4 A^{3}

Then, equation (22) is the EES evaluation equation. Based on CCM, when $Δ > 0$ , equation (22) has only one root, which means EES has a safe status. When $Δ < 0$ , there are three unequal real roots in equation (22), which means EES has an unsafe status. When $Δ = 0$ , there are three equal real roots in equation (22), which means EES has a warning status between safe and unsafe. In order to acquire an overall understanding of EES in mining areas, this study uses natural breaks classification to divide the EES warning status into two levels: mild warning status and severe warning status (Janssen et al., 2012), and EES safe status is divided into relative safety status and good safety status.

The EES assessment model is solved by equations (15), (18), and (19), but there are five equations and six unknowns in the three equations, in which b is an arbitrary constant. Therefore, the function approximation and the trial method commonly used in mathematics are adopted to solve the model (Sawaragi et al., 1971; Wachspress, 1971).

2.3 Model validation

Two methods were used to verify the method developed:

2.3.1 Bifurcation curve

According to equations (23) and (24), the bifurcation curves ( $\overset{´}{o} \overset{´}{g}$ and $\overset{´}{o} \overset{´}{h}$ ) are determined. The values of observation verification points calculated by the proposed method are marked on the bifurcation curve, and the plane coordinates are formed. The method is verified by observing the position relationship between the verification points and the bifurcation curve. If the N and H values of the verification points have a greater impact on the EES, the position on the coordinate map will be farther away from the bifurcation curve, which indicates that the method is feasible.

a {(\sqrt{\frac{- b m_{1}}{3 a}})}^{3} + b m_{1} (\sqrt{\frac{- b m_{1}}{3 a}}) = m_{2}

a {(- \sqrt{\frac{- b m_{1}}{3 a}})}^{3} + b m_{1} (- \sqrt{\frac{- b m_{1}}{3 a}}) = m_{2}

2.3.2 ROC curve

The area under the curve (AUC) value of the evaluation results of the method developed and existing research results is obtained by ROC curve analysis. The larger the AUC value, the higher the similarity between the evaluation results and the reference results.

III Case study in the Panxi mining area

1 Study area

The Panxi area is an important mineral resource base in China, located in the transition zone from the Tibetan Plateau and Yunnan–Guizhou Plateau to the Sichuan Basin, with an area of 11,929 km² (Figure 4). The region is in a subtropical monsoon climate zone, with an average annual temperature of 16–17°C and precipitation of 800–1200 mm. The landform in this area is dominated by high mountains and hills. It is rich in iron, vanadium, titanium, copper, coal, and lead-zinc. Mineral resource exploitation has contributed significantly to the economic development of the Panxi area. However, exploitation has also caused severe EGE problems.

Figure 4.

Location of Panxi mining area and the spatial distribution of mineral resources.

2 Data source and processing of EES assessment indexes

According to the index system, the data sources for each index are shown in Table 2. The data collected were further processed using the following steps. First, thematic data processing: land cover data were interpreted by unsupervised classification combined with manual visual interpretation using Landsat TM, ETM+, and OLI images of the study area. Meanwhile, 200 validation points were selected in the study area to verify the interpretation accuracy, which was higher than 90%. High-resolution RS images were used to extract mining data including mining mode, mining regreening, and the density of mining points. A total of 100 points were selected for field verification, and the verified interpretation accuracy was more than 95%. Elevation and slope data were derived from the digital elevation mode (DEM) data. Spatial data of temperature, precipitation, GDP, and population data were interpolated using ArcGIS software. Second, to ensure good spatial overlap of different data, the Gauss–Kluge projection, 1980 Xi’an coordinate system, and 1985 Yellow Sea elevation system were used. The size of the evaluation cell was 250 × 250 m (Shao et al., 2014).

Table 2.

Data sources for indicators of EES assessment in mining areas.

Evaluation indicators		Data source
Natural influencing factors	Elevation, slope	Geospatial data cloud (http://www.gscloud.cn/)
	Lithology	Geological map of study area (scale is 1:250000)
	Seismic acceleration	Map of peak ground earthquake acceleration in China (GB18306-2015)
	Geological hazard density	China’s census of geographical conditions
	Temperature, precipitation	China Meteorological Data Service Center (http://data.cma.cn/)
	Soil type	National Soil Information Service Platform of China (http://www.soilinfo.cn)
	Vegetation index	Moderate-resolution Imaging Spectrometer (MODIS) data (http://www.gscloud.cn/): Normalised Difference Vegetation Index (NDVI)
Anthropogenic influencing factors	Mining scale, mining mode,	Land resources authority deputy of the study area
	mining regreening, mining density	High-resolution images (e.g. Ikonos, Quick Bird, GF-2)
	Land cover	Landsat TM, ETM+, OLI images (http://www.gscloud.cn), orbit codes: 130042, 131041, 130041
	GDP, population density	Regional statistical yearbook of the study area

Before determining the influence of each indicator on EES, this study normalised the values of each indicator data to a range of –1 to 1. Elevation, vegetation index, seismic acceleration, geological disaster density, precipitation, temperature, slope, GDP, mine density, population density, and mining scale are quantitative data and can be directly normalised. Lithology, land cover, soil type, mining mode, and mining regreening are qualitative data, which need to be quantified, as shown in Table 3. The normalised results of all indexes are shown in Figure 5.

Table 3.

Normalisation methods of qualitative indexes.

Qualitative index	Normalisation method	References
Lithology	Grade 1 (hard rock): granite, metamorphic sandstone, dacite; Grade 2 (harder rocks): dolomitic limestone, marble, slate, dolomite, limestone; Grade 3 (softer rocks): marl, argillaceous, sandstone, siltstone and shale; Grade 4 (soft rocks): mudstone, sand mudstone; Grade 5: quaternary loose deposits.	Chinese engineering rock body classification standards (GB/T50218–2014, 2014)
Land cover	Class 1: river, lake; Class 2: wooded land, high-cover grassland; Class 3: shrublands, open woodland and medium-cover grassland; Class 4: low-cover grassland, cropland; Class 5: urban building land, rural settlement, glacier, mine, bare rock and bare land.	Bai and Tang (2010)
Soil type	The study area is dominated by dark brown soil, lateritic red soil, brown-red soil, red soil, yellow soil, yellow-brown soil, limestone soil, paddy soil, purple soil, and brown soils, whose soil erodible K-values are 0.286, 0.278, 0.283, 0.299, 0.300. 0.297, 0.294, 0.350, 0.330, and 0.291, respectively.	Deng et al. (2003)
Mining mode	Class 1: area without mines; Class 2: abandoned mines; Class 3: underground mining; Class 4: underground and opencut combined mining; Class 5: opencut mining.	Bian et al. (2020)
Mine regreening	Level 1: area without mining activity; Level 2: mines with good regreening; Level 3: mines with medium re-greening; Level 4: mines with general regreening; Level 5: mines with no regreening.	Sun et al. (2020)

Figure 5.

Normalised evaluation indices of the Panxi area in 2018.

3 Evaluation results and precision

3.1 Model parameter

According to the method developed, the cut-off point for mutation of N $(N_{1}, N_{2})$ and H $(H_{1}, H_{2})$ from 2009 to 2018 could be determined by analysing the values of CI for N or H (Figure 6). The values of a, b, $x_{11}$ , $m_{11}$ , $m_{22}$ , and $x_{12}$ are listed in Table 4. The EES assessment results are shown in Figure 7.

Table 4.

Parameter values of the method developed in Panxi mining area (2009–2018).

Time	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018
x₁₁	1/3	1/3	1/3	1/3	1/3	1/3	1/3	1/3	1/3	1/3
x₁₂	–2/3	–2/3	–2/3	–2/3	–2/3	–2/3	–2/3	–2/3	–2/3	–2/3
a	–0.65	–0.75	–0.71	–0.31	–0.79	–0.75	–0.32	–0.66	–0.64	–0.58
b	1	1	1	1	1	1	1	1	1	1
m₁₁	0.65	0.35	0.42	0.46	0.45	0.52	0.56	0.62	0.64	0.63
m₁₂	–0.28	–0.98	–0.72	–0.54	–1.01	–0.76	–0.59	–0.47	–0.37	–0.34

Figure 6.

Parameter statistics of natural and anthropogenic influencing factors.

Figure 7.

Results of EES evaluation in study area from 2009 to 2018.

3.2 Model validation

3.2.1 Bifurcation curves

In this study, 18 points were selected for annual field verification from 2009 to 2018. The verification points were mainly selected in nine types of areas: metal mining, non-metallic mining, coal mining, geological disaster, urban, agricultural, hydropower development, economic, and grassland areas. According to the results of the field investigation, the N and H values of 18 verification points per year from 2009 to 2018 are marked on a coordinate map according to their sum values (Figure 8). From Figure 8, point sets A and C were far away from the bifurcation curves, and $\overset{´}{o} \overset{´}{g}$ and $\overset{´}{o} \overset{´}{h}$ point sets B were mainly distributed near $\overset{´}{o} \overset{´}{g}$ and $\overset{´}{o} \overset{´}{h}$ . These results demonstrate that the method developed is feasible.

Figure 8.

Verification diagram by the bifurcation curve.

3.2.2 ROC curve

The AUC of the evaluation results of this study and existing studies is 0.855 (Figure 9), indicating a high correlation.

Figure 9.

AUC of evaluation results of this study and existing study (Sun et al., 2020). TPR: Sensitivity; FPR: Specificity.

3.3 EES status’ area and change

According to the EES evaluation results (Figure 10), the good safety status and the relative safety status accounted for the largest area, followed by mild warning status and then severe warning status. Unsafe status occupied the smallest area. Taking the evaluation results of 2018 as an example, good safety, relative safety, mild warning, severe warning, and unsafe status occupied 5321.50 km², 4242.13 km², 1687.94 km², 352.44 km², and 281.69 km², respectively, which accounted for 45.12%, 35.97%, 14.31%, 2.99%, and 1.60%, respectively.

Figure 10.

Area of EES status in the study area each year.

From 2009 to 2018, the areas of the five safety statuses had different changes (Figure 11). Both good safety status and relative safety status had small changes in area. The area with mild warning status had a more complex change process. The areas of both severe warning and unsafe status initially increased and then subsequently decreased.

Figure 11.

Change trend of EES status area in the study area from 2009 to 2018.

IV Discussion

1 Reliability and limitations of the method developed

The assessment and accurate classification of EES in mining areas are the premise for mine EGE restoration. However, current EES classification is generally determined by the threshold value of similar research results, which relies on expert experience and is highly subjective (Andersen et al., 2011; Ventura et al., 2018). Standard deviation classification (Papathoma-Köhle et al., 2019) and the equal space method (Saedpanah and Amanollahi, 2019) are also applied to grade the EES evaluation results. However, these methods oversimplify the interaction between the EES influencing factors. In this study, the unsafe status of EES in mining areas can be directly identified using the method developed, which avoids anthropogenic interference and makes the results more reliable. The method developed introduces the catastrophe theory and PPM into the assessment of EES in mining areas. By identifying the spatial mutation points of natural and anthropogenic influencing factors in the mining area in some time period, the EES assessment formula is obtained and the spatial distribution mapping of EES in mining areas during this period is revealed. Meanwhile, the data of different periods are introduced into the method developed to reveal the EES spatial distribution mapping of long time series. The method developed integrates the advantages of describing the shift of a process from a gradual and quantitative status to a sudden and qualitative status of catastrophe theory, and the advantages of robustness, anti-interference, and high precision of PPM, which make the determination of index weight more objective (Sepulveda et al., 2017; Tang et al., 2018). So, the method developed is particularly suitable for EES process evaluation with a long time series.

Although the results of the EES evaluation showed high accuracy, it can still be improved in the following aspects. First, the resolution of the indicator data used is inconsistent. For example, data based on the interpretation of high-resolution RS data are more accurate, while data based on statistical yearbooks are mostly county-based, resulting in lower accuracy (Yang and Hendra, 2018). Second, some indicators (i.e. mine development and environmental protection policies) are difficult to quantify and, therefore, were not included in the evaluation index system (Olander et al., 2018), which may affect the accuracy of EES assessment. In addition, the spatial interpolation method was used to allocate the meteorological station data of temperature and precipitation to the pixel scale. This approach assumes that the closer the spatial location, the more likely the features are to be similar. Using the known point data to estimate the unknown point data may affect the accuracy of EES assessment (Bartier and Keller, 1996).

Overall, the evaluation method developed is effective for the multi-index comprehensive evaluation of EES in mining areas. Moreover, this method is also applicable to other types of mining areas or regions of high-intensity human activity (e.g. hydropower, agriculture, and animal husbandry). It should be noted that when establishing an evaluation system, the specific indicators for different human activity types should be fully considered.

2 Causes of the EES spatio-temporal process

2.1 Unsafe status

The unsafe status region was mainly distributed in Xiqu County and Hongge Township in Yanbian County, two of the eight major iron mineral resource development concentration areas in China, and six major coal fields in Sichuan (Guo et al., 2013; Wei et al., 2014). Large mines with the unsafe status mainly included Zhujiabaobao-lanjian iron mine, Huashan coal mine, and Hongge iron mine. Excessive exploitation of mineral resources and neglect of EGE protection were the dominant factors that led to an unsafe EGE. The main reason for the increase in unsafe status was that the demand for coal and steel was relatively large from 2009 to 2013 in China (Zhang et al., 2014; Zhao, 2019) (Figure 12(a)). However, after 2013, coal and steel consumption decreased with the structural transformation of energy consumption in China (Liao, 2017). Thus, a large number of middle and small mining enterprises had been shut down. Therefore, the EGE in the unsafe status areas improved from 2013 to 2018. In addition, the Chinese government has strengthened supervision over the implementation of environmental rehabilitation projects in mines since 2009. RS monitoring results showed that the mine ecological restoration area in the study area increased by 631.78 ha from 2009 to 2018, which explains the decrease in unsafe status areas (Figure 12b).

2.2 Warning status

The warning status included severe warning status and mild warning status. First, the severe warning status regions mainly included the Huashan coal mine area, Panzhihua iron mine area, and Hongge iron mine area, which were also the core areas of economic development and the most densely populated area. EGE stress caused by mining is an important factor affecting EES (Enaruvbe and Atafo, 2019). The increase in severe warning status areas from 2009 to 2014 was due to the increase in mining activity intensity. Parts of medium and small mines were closed following the restructuring of the industry from 2014 to 2018, so severe warning status in this region was effectively avoided (Figure 12(c)). However, according to the yearbook and RS monitoring (People’s Government of Panzhihua Municipal, 2018), its built-up area increased from 60.65km² in 2009 to the current 81.05km². The expansion of urban construction land had a negative impact on EES (Lu et al., 2018) (Figure 11(d)). Second, the mild warning status regions were mainly located on both sides of the Anning River valley and Jinsha River valley, which had extensive agricultural activities, with sloping farmland as the main cultivated land. Dry-hot and serious soil erosion are important factors affecting EES (Choubin et al., 2019). The mild warning status shifted mainly towards the relative safety status (Figure 12(e), (f)), in which the implementation of ecological projects such as returning farmland to forest played an important role (Wang et al., 2020).

Figure 12.

EES variation process of typical mines in the study area. Parts (e)–(f) has been defined in the legend.

2.3 Safe status

The safe status included both good safety status and relative safety status, mainly distributed in the northwest and northeast of the study area. During the study period, the area of this status increased. Low population density and less human disturbance provided an important guarantee for EES in this area (Hayashi et al., 2019).

V Conclusion

In this study, the EES evaluation method for mining areas was developed based on catastrophe theory and the PPM, with the support of RS and GIS. EES assessment in the Panxi area was carried out. The main conclusions are as follows:

Based on catastrophe theory and the PPM, the developed method is feasible for EES evaluation in mining areas.

The EES evaluation method solves the problem of contingency and human disturbance in the classification of evaluation results, improves the objectivity of index weight determination, and completes the objective evaluation of the EES spatio-temporal process. RS and GIS combined with catastrophe theory and PPM have a significant effect on the evaluation of EES, which further promotes the study of EES in mining areas. Further improvements in index data acquisition and quantitative expression are necessary.

The EES in the study area is mainly in the good safety status and the relative safety status, followed by mild warning status and severe warning status, and the area of unsafe status is the least prominent. Mining exploitation, urban expansion, and soil erosion are the main factors affecting the EES. During the study period, the EES in the study area continued to deteriorate from 2009 to 2013 and improved to a certain extent after 2013.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article:This study was supported by National Science Foundation of China (Grant No. 41302282, 41374002), and Science and Technology Program of Sichuan Province (Grant No. 20ZDYF1142).

ORCID iD

Xiaofei Sun

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