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Journal of Resources and Ecology >

2026 , Vol. 17 >Issue 2: 533 - 545

DOI: https://doi.org/10.5814/j.issn.1674-764x.2026.02.016

Ecosystem Services and Ecosystem Assessment

Ecological Resilience Prediction of the Coal Cities in China Based on a Markov-ARIMA Model—Taking Xuzhou as a Case

  • XING Qinfeng , * ,
  • XUE Weilong ,
  • WANG Beibei
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  • College of Humanities and Social Sciences, Anhui University of Science and Technology, Huainan, Anhui 232001, China
* XING Qinfeng, E-mail:

Received date: 2024-12-15

  Accepted date: 2025-06-20

  Online published: 2026-04-13

Supported by

The Social Sciences Innovation Development Research Project of Anhui Province(2022CX072)

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Abstract

This study takes the ecological resilience of coal cities as the research theme, constructs an index system including 41 constraint factors from the three dimensions of social economy, resources and the environment, and takes Xuzhou as a typical case study with data from 2002 to 2023 as the original data. The GM-Markov time series prediction model and ARIMA model are used to fit the developmental prospect of ecological resilience in 2024-2040, with the aim of accurately predicting the future development trend. The results show that Xuzhou will reach the “ideal state” of ecological resilience in 2031 at the earliest and 2032 at the latest. In that state, the case city can better coordinate the contradictory relationship between the “limitation” and “need” of ecological resilience, and realize positive development of the socio-economic, resource and environmental subsystems. Then, the understanding of this research topic is deepened and the following coping strategies are proposed based on the research results: improve the collaborative digital governance co-construction model and lay a solid foundation for ecological resilience, optimize the collaborative digital co-governance mechanism to enhance the efficiency of ecological governance, adhere to the fundamental spirit of shared development and release the dividends of ecological governance.

Key words： ecological resilience; forecast; GM-Markov model; ARIMA model

Cite this article

XING Qinfeng , XUE Weilong , WANG Beibei . Ecological Resilience Prediction of the Coal Cities in China Based on a Markov-ARIMA Model—Taking Xuzhou as a Case[J]. Journal of Resources and Ecology, 2026 , 17(2) : 533 -545 . DOI: 10.5814/j.issn.1674-764x.2026.02.016

1 Introduction

Ecological resilience refers to avoiding the retrogressive evolution of biological populations, physical structures, and service functions within a specific time and spatial scope, while also enhancing the positive development of the social economy, natural resources, and environmental conditions. This is achieved by reconciling the contradictory relationship between natural security constraints and human development needs, on the premise that the ecological environment remains undamaged and ecological potential is not impaired. The prediction of ecological resilience in coal cities involves using econometric models to fit the developmental trends of the social economy, coal resources, and environmental conditions. Its purpose is to facilitate the harmonious coexistence between humans and nature, as well as among humans, and to improve the intervention effect of event regulation.
The idea of ecological resilience prediction has a long history both domestically and internationally. Specifically, international research on ecological resilience prediction started earlier and has established a relatively mature theoretical and methodological system. However, research findings at home and abroad are mostly concentrated in the fields of ecological disasters, ecological risks, and ecological conflicts. They focus on applying numerical techniques and measurement models to realize ecological scenario reproduction, and emphasize the dynamic simulation of ecological resilience in specific fields or at the micro level to achieve early warning prediction of its future development (Xu, 1996; Dong et al., 2007; Xu et al., 2012a; Li et al., 2017; Liu et al., 2017; DaSilva et al., 2019). First, regarding the understanding and mechanism of ecological resilience, the conceptual model was constructed, the prediction indicators were selected, and the in-depth research on regional ecological resilience prediction was conducted. In addition, by comprehensively analyzing biological populations, physical structures, and service functions within a specific spatiotemporal scope, the mechanism of ecological early warning prediction was improved to address the management issue of “ex-ante control” (Zhang et al., 2010). Furthermore, some studies have argued that artificial composite ecosystems should be taken as the research theme of ecological resilience prediction. Thus, conducting all-round and whole- process monitoring and issuing timely early warning forecasts hold important research value and guiding significance for preventing ecological risks and crises (Tao, 2013). Some authors have also proposed that future early warning prediction of ecological resilience should be organized and implemented as a public welfare social service. It is also necessary to improve the prediction mechanism, strengthen “ex-ante control”, and better respond to environmental emergencies (Guo, 2001). Second, in terms of the main research methods of ecological resilience, ecological resilience prediction has been regarded as a quantitative study of ecological problems such as resource depletion and environmental pollution. By constructing an indicator system that includes development and constraint indicators, timely prediction of the retrogressive evolution of ecological resilience and positive guidance for its positive development were strengthened (Chen and He, 1999). Moreover, studies have found that the urban land ecosystem cannot avoid the contradictory relationship between socio-economic development and natural resources and environmental conditions since it is a system with limited carrying capacity that requires timely measurement and early warning. Therefore, some scholars have suggested that dynamic prediction methods such as the BP neural network algorithm be used to measure and issue early warnings for land ecological resilience. This approach can effectively resolve ecological dilemmas and provide decision-making references for guiding the positive development of urban ecological resilience (Li and Lai, 2011). Third, concerning the index system of ecological resilience, some have held that ecological resilience prediction is an ex-ante control of ecological resilience within a certain spatiotemporal scope. This requires the construction of prediction indicators based on the status of ecological carrying capacity and regional socio-economic- resource development, which can effectively improve the governance efficiency of ex-ante control for ecological resilience (Xu et al., 2017).
Domestic and foreign research on ecological resilience prediction includes both theoretical explorations on its contemporary value, strategic impact, operational mechanism, succession law, and prediction indicators, and dynamic predictions on specific topics and specific regions. For dynamic prediction, scholars have widely used research tools such as the comprehensive index method, analytic hierarchy process, fuzzy synthesis method, neural network method, scenario analysis method, and system dynamics to conduct quantitative research on subjects like arable land and forests (Fu, 1993; Gao et al., 2015; Ke et al., 2021). Relevant research results have helped to scientifically identify factors that threaten ecological resilience and provide timely early warnings and forecasts to strengthen “ex-ante control”. However, existing studies still have several shortcomings. For example, they lack targeted research on ecological resilience prediction in coal cities (a type of resource-based city with distinct ecological characteristics), and the integration of coal resource development characteristics into prediction models and index systems is insufficient. Meanwhile, research should focus on strengthening the combination of coal city-specific ecological problems with prediction methods, optimizing the index system based on coal resource development and ecological carrying capacity, and improving the applicability and accuracy of ecological resilience prediction for coal cities.

2 Construction of the ecological resilience prediction index system

Based on the above analysis, this study took the economy- resource-environment conceptual model as the criterion layer for constructing the ecological resilience prediction index system of coal cities, including 41 specific evaluation indicators in three dimensions: 17 evaluation indicators in the socio-economic subsystem, 10 evaluation indicators in the resource subsystem, and 14 evaluation indicators in the environmental subsystem.
(1) Socio-economic subsystem
The socio-economic subsystem is an entity composed of various social and economic factors with significant “human” characteristics in the ecosystem, which is a concentrated embodiment of the ecological resilience characterized by human-centered orientation. The ecological resilience level of the socio-economic subsystem is mainly determined by its own development. It is more strongly affected by the ecological resilience level of the resource subsystem and the environmental subsystem, and their supporting role has an important impact on the high-quality development of the socio-economic subsystem. Combined with the practical needs of ecological resilience research in coal cities, it has 17 evaluation indicators: Population density (X1), Per capital GDP (X2), Natural population growth rate (X3), GDP growth rate (X4), Urbanization rate (X5), Proportion of the output value of secondary industry in GDP (X6), Proportion of carbon industrial output value in total industrial output value (X7), Per capital fixed assets investment (X8), Engel coefficient of urban residents’ life (X9), Per capital disposable income of urban residents (X10), Proportion of output value of the tertiary industry (X11), Employment rate (X12), Proportion of educational expenditure in GDP (X13), Proportion of R&D expenditure in GDP (X14), Per capital urban road area (X15), Number of health-institution beds per 10000 people (X16) and Proportion of built-up area (X17).
In the socio-economic subsystem, society and economy are not divided into two different analysis subsystems, and both are important components of artificial ecosystems with obvious human characteristics. However, their separation cannot reflect the supporting value of ecosystem service functions. In addition, the 17 evaluation indicators of the socio-economic subsystem are basically important reference indicators for the level of urban development, which reflect the interventional intention of the ecological risks and challenges of coal cities.
(2) Resource subsystem
Resources refer to all kinds of natural material assets that have a certain value and function in meeting human needs, improving people’s quality of life and promoting social and economic development. The resource subsystem is an entity constructed by various factors that reflect the utilization value and use status of natural material assets. It is crucial for identifying ecological environmental damage and ecological potential damage, which can effectively prevent the reverse evolution of ecological resilience and support the positive development of the social economy. Combined with the practical needs of ecological resilience research in coal cities, it has 10 evaluation indicators: Energy consumption per unit GDP (X18), Electricity consumption per unit GDP (X19), Water consumption per unit GDP (X20), Gas penetration rate which refers to the number of permanent sites (X21), Per capital water resources (X22), Per capital crop sown area (X23), Per capital raw coal production (X24), Per capital coal holding (X25), Coal resource storage and production ratio (X26) and Per capital park green area (X27).
In the selection process of evaluation indicators for the subsystem of coal urban resources, in addition to paying attention to water resources, green space, cultivated land and other indicators, the mining, processing and circulation of coal resources must also be analyzed, and relevant evaluation indicators were selected.
(3) Environmental subsystem
The environment is the sum of natural and social conditions that maintain ecological resilience. The environmental subsystem is an entity constructed by various factors that reflect the natural and social conditions of ecological resilience, and it is a direct parameter for evaluating the temporal heterogeneity of ecological resilience and predicting the future development trend. The key support for the development of society and the economy is to identify the observable indicators of environmental subsystems and correctly deal with their logical relationships with the social economy and coal resources. Based on these considerations, it includes 14 evaluation indicators: Industrial sewage discharge intensity (X28), Industrial waste gas emission intensity (X29), Industrial solid waste emission intensity (X30), Regional traffic noise value (X31), Industrial wastewater discharge up to the standard rate (X32), Industrial SO2 emission intensity (X33), Industrial chemical oxygen demand emission intensity (X34), Industrial smoke (powder) dust treatment rate (X35), Proportion of days with air quality at Class II or above (X36), Comprehensive utilization rate of industrial solid waste (X37), Green coverage rate of built-up areas (X38), Subsidence area ratio (X39), Proportion of environmental protection investment in GDP (X40) and Harmless disposal rate of domestic waste (X41).
The environmental subsystem includes 14 evaluation indicators with eight observable indicators for industrial waste gas, waste water, solid waste, etc.; four for harmless treatment rate of household waste, green coverage rate of built-up areas, etc.; and two for the proportion of environmental protection investment in GDP and the proportion of subsidence area.
According to the social and economic development strategy of coal cities and the sustainable development planning of resource-based cities, the characteristic evaluation indicators were screened, and the index system including 41 constraint factors in the three dimensions of social economy, resources and the environment was constructed.

3 Study area

3.1 Features of Xuzhou

Xuzhou is located in the northwestern part of Jiangsu Province at 116°22′-118°40′E, 33°43′-34°58′N. It spans about 210 km from east to west and 140 km from north to south, with a total land area of 11765 km2, and has a resident population of about 9 million people. Xuzhou is an important comprehensive transportation hub located in the bordering areas of the four provinces of Jiangsu, Shandong, Henan, Anhui and other provinces, so it has a significant advantage in terms of strategic location. It is an important national transportation hub that has built a modern transport system of “five links and convergence”.
As the center city of the Huaihai Economic Zone, Xuzhou will complete its transformation and development as the coal city by 2020. It is the strategic pivot point of the “One Belt, One Road” Initiative, and a key development area of the National Land Planning. The Huaihe River Ecological and Economic Belt Development Plan issued by the State Council in 2018 specifies the strategic positioning of Xuzhou as the center city of the Huaihai Economic Zone in the “three belts and one area”. As an independent block in the “1+3” strategic layout of Jiangsu Province, it has also issued special guiding policies to promote the development and upgrading of the whole region.
With more than 100 years of coal resource mining history, Xuzhou is an old national industrial base and the only coal-producing area in Jiangsu province (Xu and Wang, 2021). As a regenerative coal city, the improvement of its ecological environment and ecological potential has already begun to drive the high-quality development of northern Jiangsu, further enhance its radiation-driven role in the development of the Huaihai Economic Zone, and also provide a referenceable experience for the transformation and development of other resource-exhausted cities. As a new regenerative coal city, Xuzhou is a pioneer area for the transformation and development of coal cities, basically moving past resource dependence and taking the lead in establishing a long-term mechanism for sustainable development (Yu et al., 2018), which is perfectly suited to the needs of the new era of ecological civilization construction and the development strategy of new urbanization. Therefore, Xuzhou is in the rising period of rapid urbanization, with vast space and huge potential for future development. Finally, there is great theoretical value and practical significance in exploring and revealing the essential attributes and contradictory operational laws of the ecological resilience in Xuzhou from a systemic viewpoint, in order to build a scientific and reasonable evaluation index system, to optimize the methodological system of evaluation and prediction, and to complete the strategic system of modern ecological governance.

3.2 Data sources

The relevant data for the case cities mainly came from the Statistical Yearbook and the Statistical Bulletin of National Economic and Social Development of each city, the China Statistical Yearbook, the Provincial Statistical Yearbook, the Bulletin of Provincial Environmental Conditions, the Provincial, Municipal and County Statistical Bulletin of National Economy and Development, the Statistical Yearbook of China Cities, and other sources. For the data that still could not be accessed, the method of regression fitting for similar years was used to make up for the shortages. To ensure that the data with different units of measurement reflect the vast majority of information for the original variables, this study used the extreme value method and the coefficient of variation method to standardize the collected original data (Zhu et al., 2020), which provided rich and reliable data resources for the subsequent time-series evaluation and prospect prediction.

4 Research model

4.1 Index independence tests

Reliability reflects test reliability, which refers to the consistency of results obtained when the same method is used to measure the same object repeatedly. SPSS 24.0 software was used for reliability analysis of the questionnaire shown in Table 1, and the Alpha reliability coefficient was 0.625, or greater than 0.6, which indicated acceptable reliability of the questionnaire scale.
Table 1 Reliability analysis of ecological resilience evaluation indicators in Xuzhou
Statistical parameter Reliability statistical results
Kronbach’s alpha 0.625
Number of terms 41
Validity refers to indicator validity, that is, the degree to which the measurement tool or means can accurately measure the thing that is being measured. Through the validity analysis (Table 2), the KMO value of the overall questionnaire data was 0.730, which is between 0.7 and 0.8, and the significance level was less than 0.001, which show that the validity of the questionnaire is good.
Table 2 Validity analysis of ecological resilience evaluation indicators in Xuzhou
Statistical parameter Validity statistical results
KMO sample appropriateness measure 0.730
Bartlett sphericity test Approximate chi-square 6017.631
Degrees of freedom 108.000
Significance <0.001
These analyses showed that the questionnaire data passed the reliability and validity tests, and has basic structural stability, so it can be further analyzed.

4.2 Index weight calculation

The entropy method was used to calculate 41 evaluation indicators of ecological resilience in Xuzhou, and the results are shown in Table 3.
Table 3 Weights of ecological resilience evaluation indicators in Xuzhou
Indicator
variable		 Unit Index property Weight
X1 people km-2 - 0.0192
X2 yuan + 0.0051
X3 ‰ - 0.1608
X4 % - 0.0090
X5 % - 0.0065
X6 % - 0.0070
X7 % - 0.0628
X8 yuan person-1 + 0.0112
X9 % - 0.0321
X10 yuan person-1 + 0.0091
X11 % + 0.0087
X12 % + 0.0087
X13 % + 0.0160
X14 % + 0.0232
X15 m2 person-1 + 0.0341
X16 beds (104 people)-1 + 0.0338
X17 % + 0.0331
X18 tons of standard coal (104 yuan)-1 - 0.0209
X19 kWh (104 yuan)-1 - 0.0380
X20 m3 (104 yuan)-1 - 0.0112
X21 % + 0.0104
X22 m3 person-1 + 0.0164
X23 ha person-1 + 0.0220
X24 t person-1 - 0.0227
X25 t person-1 + 0.0211
X26 % - 0.0246
X27 m2 person-1 + 0.0284
X28 t (104 yuan)-1 - 0.0084
X29 standard price (104 yuan)-1 - 0.0095
X30 t (108 yuan)-1 - 0.0090
X31 dB - 0.0133
X32 % + 0.0365
X33 t (109 yuan)-1 - 0.0085
X34 t (109 yuan)-1 - 0.0088
X35 % + 0.0729
X36 % + 0.0395
X37 % + 0.0075
X38 % + 0.0217
X39 % - 0.0235
X40 % + 0.0325
X41 % + 0.0125

4.3 GM-Markov model

The Grey prediction model is a type of prediction model based on Grey theory, which is a research method that uses synchronous observation methods to obtain data with strong regularity to forecast either the characteristic quantity at a certain moment in the future or the time to reach a certain characteristic quantity. This method has the advantages of simple modelling and a wide range of application, so it is widely used in ecological resilience alarm forecasting. It analyzes the heterogeneity among the physical factors of an ecosystem, identifies the contradictory relationships between natural security constraints and human development needs, predicts the developmental prospects of ecological resilience in case cities, and provides methodological references to support sustainable socio-economic development and the enhancement of human happiness and well-being, by using the corresponding differential equations to measure time-ordered data based on the original sequence. Compared with other time series models, the GM model has a more significant prediction effect for short-term time series data. Based on the classical paradigm of GM(1,1), the model constructs the first-order differential function of the predictor variables with respect to time, and achieves the linearity estimation of non-linear time series data through the method of linear accumulation, which reduces the stochasticity of the original time series and strengthens its regularity characteristics (Quan, 2020). Among many prediction methods, many scholars use the Markov model to correct the predictions of GM models, and this prediction method can effectively improve the prediction accuracy of a model (Li et al., 1998). When a stochastic process has a conditional probability distribution of future states that depends only on the current state, given the present state and all past states, a stochastic process with this property is called a Markov process.

4.3.1 Principles of GM(1, 1) model construction

GM(1, 1) is a first-order differential function of the variable for time, which is defined as:
$\frac{\text{d}{x}^{(1)}}{\text{d}t}+a{x}^{\left(1\right)}=u$
where ${x}^{\left(1\right)}$ is the time series generated by the indicator after an accumulation; t is time; a is the development Grey number, and u is the endogenous control Grey number (Kang et al., 2022).
Step 1: Establish the GM(1, 1) model to generate the series by accumulating values one at a time.
Let the original series be defined as:
${x}^{(0)}=\left\{{x}^{(0)}(1),{x}^{(0)}(2),{x}^{(0)}(3),\cdots,{x}^{(0)}(n)\right\}$
Then, the comprehensive index of ecological safety in the case city was obtained from 2002 to 2023 as the original sequence, and a one-time accumulation was used to obtain the new time series, which can be defined as:
${X}^{1}=\left\{{x}^{1}\left(1\right),{x}^{1}\left(2\right),\cdots,{x}^{1}\left(n\right)\right\}$
Finally, the sample space is defined as:
${x}^{1}\left(k\right)={\displaystyle \sum }_{k=1}^{n}{x}^{0}\left(k\right)\text{ }\text{ }\text{ }\text{ }k=1,2,\cdots,n$
Step 2: Establish the first order linear differential equation.
This equation is defined as:
$\frac{\text{d}{X}^{1}}{\text{d}t}+a{X}^{1}=\mu $
where a is the developmental Grey number of the time series, which reflects the developmental trend of ecological safety in the case city; and µ is the endogenous control Grey number of the time series, which reflects the trend of change between the time series.
Step 3: Calculate the developmental Grey number and endogenous control Grey number of the GM(1, 1) model.
The developmental Grey number and endogenous control Grey number can be calculated by the least squares method (Xu et al., 2012b). Specifically, we first established the matrix sum and then defined the formula as:
$B=\left[\begin{array}{ccc}-\frac{1}{2}\left[{x}^{1}\left(1\right)+{x}^{1}\left(2\right)\right]& \cdots & 1\\ ⋮& \ddots & ⋮\\ -\frac{1}{2}\left[{x}^{1}\left(n-1\right)+{x}^{1}\left(n\right)\right]& \cdots & 1\end{array}\right]$
${y}_{n}=\left[\begin{array}{c}\begin{array}{c}{x}^{0}\left(1\right)\\ {x}^{0}\left(2\right)\\ {x}^{0}\left(3\right)\end{array}\\ ⋮\\ {x}^{0}\left(n\right)\end{array}\right]$
Next, the above matrix was solved by defining the formula as:
$\left[\begin{array}{c}\widehat{\alpha }\\ \widehat{\mu }\end{array}\right]={\left({B}^{\text{T}}B\right)}^{-1}{B}^{\text{T}}{Y}_{n}$
Then, by substituting it into the original equation, the $\text{GM}$evaluation model of ecological safety for the case city was generated, and defined as:
${X}^{1}\left(k+1\right)=\left({X}^{0}\left(1\right)-\frac{\widehat{\mu }}{\widehat{\alpha }}\right){e}^{-ak}+\frac{\widehat{\mu }}{\widehat{\alpha }},\text{ }\text{ }\text{ }\text{ }k=1,2,\cdots,n$
Step 4: GM(1, 1) model test
The methods for testing model accuracy include the residual test, correlation test and a posteriori difference test (Yang et al., 2016). In this study, the a posteriori difference test was adopted. The specific definition of the formula includes the following three parts.
(1) Calculate the mean square deviation of the original series, defined as:
${S}_{0}=\sqrt{\frac{{S}_{0}^{2}}{n-1}},\text{ }\text{ }{S}_{0}^{2}={\displaystyle \sum }_{i=1}^{n}{\left[{x}^{\left(0\right)}\left(i\right)-{\overline{x}}^{\left(0\right)}\right]}^{2},\text{ }\text{ }{\overline{x}}^{\left(0\right)}=\frac{1}{n}{\displaystyle \sum }_{i=1}^{n}{x}^{\left(0\right)}\left(i\right)$
(2) Calculate the mean square deviation of the residual series, defined as:
$S_{1}=\sqrt{\frac{S_{1}^{2}}{n-1}}, S_{1}^{2}=\sum_{i=1}^{n}\left[\varepsilon^{(0)}(i)-\bar{\varepsilon}^{(0)}\right]^{2}, \bar{\varepsilon}^{(0)}=\frac{1}{n} \sum_{i=1}^{n} \varepsilon^{(0)}(i)$
(3) Calculate the variance ratio, defined as:
$C=\frac{{S}_{1}}{{S}_{0}}$
Calculate the “probability of a small error”, defined as:
$P=\left\{\left|{\varepsilon }^{\left(0\right)}\left(i\right)-{\overline{\varepsilon }}^{\left(0\right)}\right|<0.6745{S}_{0}\right\}$
(4) GM(1, 1) model prediction accuracy test
The GM(1, 1) model test accuracy can be determined by the C-value and the P-value. Among them, the reference standards of these values are specified in Table 4 (Jiang et al., 2019).
Table 4 Classification of the prediction accuracy levels
Small error probability P-value Variance ratio
C-value		 Prediction accuracy level
P≥0.95 C≤0.35 Preferable
0.80≤P<0.95 0.35<C≤0.50 Eligible
0.70≤P<0.80 0.50<C≤0.65 Barely passing
P<0.70 C>0.65 Substandard
Finally, when the test passes, the model can be used to make predictions, defined as:
$\widehat{x}\begin{array}{c}{\widehat{x}}^{\left(0\right)}\left(n+1\right)={\widehat{x}}^{\left(1\right)}\left(n+1\right)-{\widehat{x}}^{\left(1\right)}\left(n\right)\\ {}^{\left(0\right)}\left(n+2\right)={\widehat{x}}^{\left(1\right)}\left(n+2\right)-{\widehat{x}}^{\left(1\right)}\left(n+1\right)\\ \cdots \cdots \end{array}$
Then, the results of Equation (14) were used as the predicted values.

4.3.2 Marlov model correction to the GM(1, 1) model

First, the Marlov model normalization was performed.
Assume that the stochastic process is generally formed into the following Markov chain, as below:
$\left\{{X}_{n}\right.,\text{ }\text{ }\left.n=0,1,2\cdots \right\}$
where, for an $ n\ge 0$, arbitrary state $ i$, and $ j,{i}_{0},{i}_{1},\cdots,{i}_{n-1}$, the Marlov model exists with probability P in the state space.
Second, the constraints on the spatial state of the M model were analyzed, as expressed in Equation 16.
$\begin{array}{l}P\left\{\left.{X}_{n+1}=j\right|{X}_{n}=i,{X}_{n-1}={i}_{n-1},\cdots,{X}_{1}={i}_{1},{X}_{0}={i}_{0}\right\}=\\ P\left\{{X}_{n+1}=j\right.|\left.{X}_{n}=i\right\}\end{array}$
where ${X}_{n}=i$ denotes the Markov process is in state $i,\text{ }\left\{0,\right.\left.1,2,\cdots \right\}$ at the moment $n$ is the state space of the process, denoted as $S$. When the past state space ${X}_{0},{X}_{1},\cdots,{X}_{n-1}$ is given for a Markov process, the conditional distribution of states ${X}_{n},{X}_{n+1}$ is uncorrelated with the past states. In addition, the conditional probability $\left.P\left\{{X}_{n+1}=j\right.\right|\left.{X}_{n}=i\right\}$ is the probability of spatial transfer at each step of the Markov chain, denoted as ${P}_{ij}$. Also, it represents the probability that state $i$ is transferred to state $j$ at the next step.
Third, the Markov model spatial matrix was constructed as shown in Equation 17.
$P=\left[\begin{array}{ccc}{P}_{00}      {P}_{01}& \cdots & {P}_{0n}\\ ⋮& \ddots & ⋮\\   {P}_{n0}      {P}_{n0}    & \cdots & {P}_{nn}\end{array}\right]$
where P means the spatial state transfer probability matrix. Furthermore, when ${P}_{ij }\ge 0,i,j\in S;\text{ }{\displaystyle \sum }_{j\in S}{P}_{ij}=1,\forall i\in S$. The Markov model can calculate the predicted values by transferring the probability matrix P, and then the spatial state is constantly transformed.
Fourth, the Markov model was corrected for relative errors.
Then, the relative error between the predicted and actual values of the GM model was calculated as:
${c}_{k}=\left.\left|{\varepsilon }_{k}\right.\right|/$${x}^{\left(0\right)}\left(k\right)\times 100\%$
where the GM model predicts a sequence of the residual ${\varepsilon }_{k}={x}^{\left(0\right)}\left(k\right)-{\widehat{x}}^{\left(0\right)}\left(k\right),\text{ }\text{ }k=1,2,\cdots,n$. The Markov model state interval ${E}_{ij}=\left[{L}_{ij},{U}_{ij}\right]$ was then divided into $n$ states based on the magnitude of the relative error of the GM model. Note that ${L}_{ij}$ and ${U}_{ij}$ denote the upper and lower bounds of the state, respectively.
The relative error of the Markov model was calculated. If $ c\left(k\right)<0.2,$ then it is considered to fulfill the general requirement; but if $c\left(k\right)<0.1,$ then it is considered to fulfill the higher requirement.
Fifth, the Markov model level deviation test was performed.
Based on $\rho \left(k\right)=1-\frac{(1-0.5\alpha)}{(1+0.5\alpha)}\lambda \left(k\right),\text{ }k=2,3,\cdots,n$, the Markov model level deviation was calculated. If $\rho \left(k\right)<0.2,$ then it is considered to meet the general requirement; but if $\rho \left(k\right)<0.1,$ then it is considered to meet the higher requirement.
Sixth, the spatial state transfer probability matrix of the M model was corrected.
The number of transfers from state Ei to state Ej after n steps is denoted as Mij, and the number of occurrences of state Ei is denoted as Mi. Let Pij=Mij/Mi, be the one-step transfer probability of data from state Ei to state Ej. In this way, a matrix P of state transfer probabilities for the M model can further be calculated.
Seventh, the Markov model prediction value was calculated. The predicted value calculated by the GM model was corrected using the Markov model state transfer probability, and the median value of the state interval was used as the corrected value of the Markov model prediction according to the relative error state interval, which was calculated as:
$\frac{{\widehat{x}}^{\left(0\right)}\left(k\right)}{1\pm 0.5({L}_{ij}+{U}_{ij})}={x}_{\left(k+1\right)}$
where a positive sign is used when the predicted value is higher than the actual value, and a negative sign is used when the predicted value is lower than the actual value. Lij and Uij denote the upper and lower bounds of the state, respectively.

4.4 ARIMA prediction model

4.4.1 Principles of ARIMA model construction

The Auto Regressive Integrated Moving Average Model, known as ARIMA, is a research method that transforms a non-stationary time series into a stationary time series, and then regresses the dependent variable with its lagged value and the present value of the random error term. The ARIMA model was first proposed as a time series forecasting method by Box and Jenkins in the early 1970s, so it is also known as the Box-Jenkins model or Box-a-Jenkins method (Zhuo and Zhou, 2017). According to their differences, the characteristics of a smooth series can generally be divided into three types of dynamic forecasting models. First is the auto-regressive model (referred to as the AR model), with an auto-correlation function of the trailing-end type but a partial correlation function of the truncated-end type. Second is the moving average model (MA model for short), which has a truncated auto-correlation function but a trailing partial correlation function. Third is the auto-regressive moving average model or auto-regressive integrated moving average model (referred to as ARMA model or ARIMA model, respectively), in which the auto-correlation and partial correlation functions are trailing (Zhou et al., 2016).
The basic principle of the ARIMA model is to consider the data series of the forecast object over time as a random sequence based on the time series, then use the auto- correlation function, partial auto-correlation function and their respective correlation plots to describe the stochastic characteristics of the time series, and finally combine the past and present values of the time series to predict the developmental prospects of the research object (Hong et al., 2014).

4.4.2 ARIMA model construction

Let ${x}_{t}^{\left(i\right)}$, ${y}_{t}$ be the time series, where $i=1,2,\cdots,k$. Then, they are defined as:
$\begin{array}{l}{y}_{t}={\displaystyle \sum }_{j=0}^{\infty }{v}_{j}^{\left(1\right)}{B}^{j}{x}_{t}^{\left(1\right)}+{\displaystyle \sum }_{j=0}^{\infty }{v}_{j}^{\left(2\right)}{B}^{j}{x}_{t}^{\left(2\right)}+\cdots +\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{\displaystyle \sum }_{j=0}^{\infty }{v}_{j}^{\left(k\right)}{B}^{j}{x}_{t}^{\left(k\right)}+\left[\theta \left(B\right)/\varphi \left(B\right)\right]\times {a}_{t}\end{array}$
where ${x}_{t}^{\left(k\right)}$ refers to the input factor (intervention factor), ${y}_{t}$ refers to the output factor, ${v}_{j}^{\left(1\right)}$ is the “transmission coefficient” of policies under different lag periods, and ${B}^{j}{x}_{t}^{\left(1\right)}$ refers to the value of the lag period $j$ of the “extracted” sequence ${x}_{t}$. In this case, the transfer function is defined as:
$\begin{array}{c}\theta \left(B\right)=1-{\theta }_{1}\left(B\right)-\cdots -{\theta }_{q}{B}^{q}\\ \varphi \left(B\right)=1-{\varphi }_{1}\left(B\right)-\cdots -{\varphi }_{q}{B}^{q}\end{array}$
In addition, to reduce the number of parameters, the simplified formula of the ARIMA model was defined as:
$\begin{array}{l} {Y}_{t}=c+{\varphi }_{1}{Y}_{t-1}+{\varphi }_{2}{Y}_{t-2}+\cdots +{\varphi }_{p}{Y}_{t-p}+{\theta }_{1}{\varepsilon }_{t-1}+\\ \text{ }\text{ }\text{ }\text{ }\text{ }{\theta }_{2}{\varepsilon }_{t-2}+\cdots +{\theta }_{q}{\varepsilon }_{t-q}+{\varepsilon }_{t}\end{array}$
where ${Y}_{t}$ is the time series data of ecological safety of the case city; ${\varphi }_{1}$,${\varphi }_{2}$,...,${\varphi }_{p}$ is for the $\text{AR}$ parameter, indicating the relationship between the current data and the ecological safety index at p past time points; ${\theta }_{1}$,${\theta }_{2}$,...,${\theta }_{q}$ is for the $\text{MA}$ parameter and denotes the relationship between the current value and the past q time error terms; ${\varepsilon }_{t}$ is the error term for period t; and $c$ is the constant term.

4.4.3 Data smoothing

After the model is constructed, the time series data need to be tested and corrected for smoothness. The data are judged to be smooth by a time series scatter plot or line graph, and if the data do not meet the requirements, it is necessary to differentiate the data until it becomes smooth time series data (Zhang, 2018). At this point, the ARIMA(p, d, q) model can be formed, where p is the auto-regressive term of AR, q is the number of moving average terms of MA, and d is the number of differences made to reach the smooth series data. After the data smoothing process, we simplified the ARIMA(p, d, q) model to the ARMA(p, q) model.

4.4.4 Model ordering

At that point, the statistics of the correlation coefficients were introduced to identify the coefficient characteristics and order of the ARIMA(p, q) model and to select a suitable prediction model. We selected a forecasting model that met the requirements from three categories: the AR model, the MA model, and the ARMA or ARIMA model, since the ARIMA model can both consider the dependence on a time series and analyze the disturbance of random fluctuations in the dynamic prediction process. Considering that the comprehensive index of ecological safety in the case city showed an increasing trend and the length of the study was 22 years, the ARIMA model was chosen for modelling in this study. In the choice of methods for smooth time series data, if the auto-correlation function is a series that presents a cyclical pattern, then a seasonal product model can be chosen for fitting; but if the auto-correlation function is a series that presents a complex pattern, then a nonlinear model can be chosen for dynamic fitting. In this study, we combined the dynamic complexity characteristics of ecological resilience and data characteristics, and we chose the latter as the prediction model.

4.4.5 Model testing

The model parameters need to be diagnosed and tested, i.e., and the model parameters need to be tested for significance as well as for white noise in the residual series. If the residual series is not white noise, then the residual series must contain other components, and the auto-correlation coefficient will not be zero (Song and Hao, 2012).

5 Results and discussion

5.1 Results and analysis

The test results of the GM model and Markov model for the city of Xuzhou were calculated and are shown in Table 5.
Table 5 Test results for the comprehensive ecological resilience index based on the GM-Markov model in Xuzhou from 2002 to 2023
Year Original value GM model predictions Markov model predictions
Residual Relative error Gradation deviation Residual Relative error Gradation deviation
2002 0.237 0.000 0.000 - 0.000 0.000 -
2003 0.307 -0.046 0.150 0.216 -0.001 0.003 0.207
2004 0.339 -0.034 0.101 0.082 -0.003 0.009 0.070
2005 0.366 -0.029 0.078 0.059 0.001 0.003 0.049
2006 0.393 -0.023 0.059 0.054 0.003 0.008 0.044
2007 0.509 0.071 0.140 0.217 0.012 0.024 0.207
2008 0.505 0.045 0.090 -0.023 -0.003 0.006 -0.035
2009 0.510 0.028 0.054 -0.006 -0.010 0.020 -0.017
2010 0.495 -0.010 0.020 -0.046 0.006 0.012 -0.058
2011 0.547 0.019 0.035 0.082 0.003 0.005 0.071
2012 0.549 -0.003 0.005 -0.012 -0.032 0.058 -0.023
2013 0.567 -0.008 0.014 0.018 0.004 0.007 0.006
2014 0.593 -0.006 0.010 0.029 -0.003 0.005 0.018
2015 0.658 0.034 0.052 0.085 0.005 0.008 0.075
2016 0.624 -0.025 0.039 -0.071 0.000 0.000 -0.083
2017 0.726 0.052 0.072 0.127 0.009 0.012 0.117
2018 0.668 -0.032 0.047 -0.103 0.001 0.001 -0.116
2019 0.714 -0.011 0.015 0.051 0.008 0.011 0.039
2020 0.774 0.022 0.028 0.063 0.001 0.001 0.053
2021 0.737 -0.042 0.056 -0.066 -0.001 0.001 -0.078
2022 0.800 -0.006 0.008 0.064 -0.008 0.010 0.054
2023 0.781 -0.003 0.012 0.042 -0.008 0.010 -0.052
In Table 5, the relative error and level of deviation of the Markov model are smaller than those of the GM(1, 1) model. The relative error of the Markov model is basically less than 0.1, but the level of deviation of the Markov model is greater than 0.1 only in 2003, 2007, 2017, and 2018, and in all other years it is less than 0.1. This shows that the Markov model has a higher prediction accuracy for the ecological resilience composite index in Xuzhou, so it can provide a reference for predicting the ecological resilience composite index in Xuzhou for the period of 2024-2040.
Furthermore, from the perspective of the annual average change in the composite index of ecological resilience in Xuzhou, the change calculated by the GM model is maintained at around 2.69%.
To intuitively analyze the accuracy of the Markov model’s improvement over the GM(1,1) model, we plotted the original values of the ecological resilience composite index in Xuzhou and the predicted values of the two models from 2002 to 2023 as a trend graph, and the results are shown in Figure 1.
Figure 1 Ecological resilience prediction results in Xuzhou from 2002 to 2023 by the GM-Markov model
In Figure 1, the Markov model predictions are closer to the original values of the ecological resilience composite index in Xuzhou than the GM model predictions in the period from 2002 to 2023.
In Figure 2, from 2002 to 2023, the predicted values of the Markov model are very close to the original values of the ecological resilience composite index in Xuzhou, so from 2024 to 2040, the predicted values of the Markov model tend to be more in line with the ecological resilience development in Xuzhou city. Furthermore, Xuzhou reached a value of 1.017 as early as 2032. At that time, the relationship between the social and economic subsystem, the resource subsystem and the environmental subsystem of the case city will have reached a harmonious state of symbiosis.
Figure 2 Ecological resilience prediction result in Xuzhou from 2002 to 2040 by the Markov model
By fitting the ARIMA model to the ecological resilience composite index in Xuzhou, we found that the optimal values of p, d, q are (0,1,1), respectively, i.e., the optimal model for ARIMA is (0,1,1), and the specifics of its model parameters are shown in Table 6. In addition, we obtained the optimal modelling formula of the ARIMA model, and the specific definition of the formula is:
${Y}_{t}=0.026-0.638{\varepsilon }_{t-1}$
Table 6 ARIMA(0,1,1) model parameters for the ecological resilience comprehensive index in Xuzhou
Term Notation Ratio Standard error Z-value P-value 95% CI
Constant term c 0.026 0.004 6.995 0 0.019-0.033
MA parameters β1 -0.638 0.251 -2.539 0.011 -1.130-0.145
AIC value: -69.218
BIC value: -66.231
In Table 6, all the statistics are greater than 0.1, i.e., the original hypothesis is rejected at the 10% level, so the ARIMA(0,1,1) model passes the white noise test and the modelling is valid. Meanwhile, the prediction results using the ARIMA model were obtained (Figure 3).
Figure 3 ARIMA model prediction values of the ecological resilience comprehensive index in Xuzhou
In Figure 3, the predicted values of the composite index of ecological resilience in Xuzhou from 2024 to 2040 improve from 0.799 to 1.24, with an average annual change of 2.3%, which is higher than the fitting criterion of the baseline scenario (2.21%). In addition, the fitting results of the ARIMA(0,1,1) model show that the predicted value of the ecological resilience index in Xuzhou is greater than 1 in 2031, so the matching relationship between the natural security constraints and the needs of human development will have reached the “ideal state” status in that year.

5.2 Discussion

The results of this study show that if the prediction index of ecological resilience in the case city evolves according to the preset or established annual average change, then the “ideal state” between “limitation” and “need” will be achieved by 2031 at the earliest and 2032 at the latest, so the fundamental improvement of ecological resilience will be realized. Therefore, to meet the growing needs of people for a better ecological environment, we should improve the effect of intervention and strengthen PR management. Spe-cifically, this is manifested in three aspects.
(1) The co-construction paradigm of complete collaborative digital therapy is necessary.
From the concept of co-construction, coal cities need to be based on the new development stage, give full play to the advantages of The Times of digital governance, break through the temporal and spatial constraints of traditional ecological management, clarify the dependency among the socio-economic, the resource and environmental subsystems, pay attention to the intervention focus of safety level, eliminate the intervention dilemma of core influencing factors, and provide solid and reliable reference materials for collaborative digital governance (Yu et al., 2024; Zeng et al., 2024). In terms of the intention of co-construction, coal cities need to use digital concepts and digital means to build a new platform for collaborative digital governance, create a new pattern of collaborative digital governance led by the Communist Party of China, which should be led by government agencies with the active participation of market players and social groups, and maintain the positive development speed of the socio-economic, resource and environmental subsystems (Zhang and Niu, 2022; Ma and Ye, 2024). In this way, the coal cities can ensure an “ideal state” of ecological resilience by 2032 at the latest.
(2) The co-governance mechanism of collaborative digital governance still has much room for improvement.
Since the reform and opening up, the mining and utilization of coal resources has played an irreplaceable role in supporting sustainable social and economic development and enhancing human happiness and well-being, but it has also led to severe ecological risks and crises, and the ecological threats and challenges are unprecedented (Shen, 2024). Therefore, the collaborative digital treatment of ecological safety in coal cities is a large-scale and complex digital treatment project (You et al., 2019). In terms of the simulation results of technological innovation and environmental protection scenarios, it will be necessary to use modern information technology and its intelligent terminals to achieve the digital transformation and intelligent development of prediction indicators, optimize the atmosphere and conditions for the collaborative participation of governance subjects and target groups, strengthen collaborative digital governance capabilities, and achieve timely and precise intervention (Chen and Gao, 2024; Guo et al., 2024). In this state, we can ensure the fundamental improvement of ecological resilience in coal cities and their subsystems by 2031 at the earliest.
(3) A shared background vision is inevitable.
“Common prosperity is the essential requirement of socialism.” In the process of the collaborative digital treatment of ecological resilience in coal cities, it will be necessary to make the cake bigger and divide the cake well, so that the target groups can participate in the monitoring and management of 41 indicators in the three dimensions of social economy, resources and environment in all aspects (Chen and Ma, 2018; Zhong and Liu, 2024). As we all know, the exploitation and utilization of coal resources is an important guarantee for the sustainable development of the social economy and overall national security. However, China is “rich in coal, poor in oil and short on gas”, so coal resources account for nearly 70% of the primary energy, and this development pattern cannot be changed for a long period of time (Li et al., 2024). In this context, it will be particularly important to use synergistic and digital advantages to break through the constraints of time and space to realize the harmonious symbiosis between man and nature as well as between people (Liu and Zhang, 2024). Therefore, coal cities need to take advantage of collaborative digital governance to achieve ecological safety, efficient governance and high-quality development, produce more and better ecological products, let target groups share the ecological dividends, and strive to achieve fundamental improvement of the ecological environment by 2035 at the latest.

5.3 Countermeasures

To effectively address the ecological challenges in coal cities, targeted countermeasures are essential. The following strategies, focusing on governance models, mechanisms, and shared development, will work in synergy to boost ecological resilience and achieve long-term goals.
(1) Improve the collaborative digital governance co-cons truction model and lay a solid foundation for ecological resilience
Coal cities need to base themselves on the new stage of development, take digital governance as the core handle, and break through the temporal and spatial limitations of traditional ecological management. They must clarify the interdependent relationship among the three subsystems of social economy, resources and environment, focus on the key points of ecological security level intervention, break through the intervention predicament of core influencing factors, and provide reliable references for collaborative digital governance. Relying on digital concepts and technologies, a brand-new collaborative governance platform must be built to establish a co-construction pattern characterized by “Party leadership, government dominance, and active participation of the market and social forces”, to ensure the healthy developmental rhythm of the three subsystems. By integrating the data resources of 41 indicators from 2002 to 2023, a dynamic monitoring and data sharing mechanism will be established to ensure information exchange and coordinated actions among all entities in the construction of ecological resilience, which will lay a solid foundation for achieving the “ideal state” of ecological resilience by 2032.
(2) Optimize the collaborative digital co-governance mechanism to enhance the efficiency of ecological governance
In response to the ecological risks brought about by the development of coal resources, modern information technology and intelligent terminals should be used for support to promote the digital transformation and intelligent development of ecological resilience prediction indicators. The coal cities need to optimize the atmosphere and conditions for the collaborative participation of governance subjects and target groups, enhance their ability to carry out precise intervention, and promptly identify ecological risks in technological innovation and environmental protection scenario simulation. They also should improve the multi-subject co-governance responsibility system, clarify the responsibilities of the government, enterprises and social organizations in ecological monitoring, risk early warning and emergency responses, and establish a cross-regional and cross-departmental collaborative and interactive mechanism. By combining the prediction results of the GM-Markov and ARIMA models, the co-governance strategy can be dynamically adjusted. For the key nodes of ecological resilience development from 2024 to 2040, differentiated governance plans must be formulated to ensure that the fundamental improvement of ecological resilience is achieved as early as 2031.
(3) Adhere to the fundamental vision of shared development and release the dividends of ecological governance
Centering on the goal of common prosperity, the target groups should be fully involved in the monitoring and management of the 41 indicators in the three dimensions of social economy, resources and environment, and their right to know and participate in the construction of ecological resilience should be guaranteed. Based on China’s energy pattern of “abundant coal, scarce oil and limited gas”, by relying on the advantages of collaborative digital governance, we will break through the limitations of time and space to promote harmonious coexistence between humans and nature as well as among people. We can accelerate the realization of ecological product value, combine the improvement of ecological resilience with the enhancement of people’s livelihoods, and allow the public to share the ecological dividends through the development of eco-tourism, green industries, and other enterprises. We need to establish a mechanism for sharing and evaluating the achievements of ecological governance, regularly disclose the predictions and construction results of ecological resilience from 2024 to 2040, and ensure that the fundamental improvement of the ecological environment is achieved by 2035 at the latest, so that the achievements of ecological governance in coal cities can benefit all the people.

6 Conclusions

This study focused on the ecological resilience of Chinese coal cities, with Xuzhou (a representative coal city) as the test case. It constructed a multi-dimensional evaluation index system encompassing 41 indicators across three dimensions. Using 2002-2023 data, the GM-Markov and ARIMA models were applied to predict Xuzhou’s ecological resilience from 2024 to 2040. The results show that the GM-Markov model has higher accuracy (relative errors mostly <0.1) than the single GM model, and the optimized ARIMA (0,1,1) model passes the white noise test. Both models confirm that Xuzhou’s ecological resilience will reach the “ideal state” (realizing the harmonious coexistence of the socio-economic, resource, and environmental subsystems) by 2031 at the earliest and 2032 at the latest. To achieve this, this study proposes a strategy of improving the co-construction paradigm of collaborative digital governance, optimizing its co-governance mechanism, and upholding the shared development orientation.
Furthermore, this study only took Xuzhou as a case, so the representation of coal cities in different regions or development stages is lacking, which limits the universality of the conclusions. In addition, the GM-Markov and ARIMA models rely on historical data while ignoring sudden factors and subsystem interactions, thereby reducing long-term prediction accuracy. Future studies should expand the case scope to include coal cities in diverse regions/stages for comparative analysis, optimize the index system by adding renewable energy and biodiversity indicators, integrate system dynamics into the models to simulate subsystem interactions, and refine the “ideal state” evaluation standards to enhance the research applicability and guidance.

References

Publishing order | Descend order by publishing year | Descend order by cited within
[1]
Chen G J, He J F. 1999. Discussion on theories and methods of ecological environment prediction. Chongqing Environmental Science, (4): 8-11. (in Chinese)

[2]
Chen X Y, Gao X H. 2024. Collaborative governance: The theoretical foundation of the Yangtze River Delta ecological environmental governance and mechanism innovation. Journal of Soochou University (Philosophy and Social Sciences Edition), (6): 31-41. (in Chinese)

[3]
Chen Y Y, Ma Y L. 2018. Economic logic of realizing the value of ecological products: Based on the perspective of the triangular steady—state relationship of ecological civilization. Ecological Economy, 40(11): 205-211. (in Chinese)

[4]
DaSilva G F P, Pegetti A L, Piacesi M T, et al. 2019. Dynamic modelling of an prediction system for natural disasters for natural disasters. Systems Research and Behavioral Science, 37(2): 292-314.

DOI

[5]
Dong W, Zhang X H, Su D, et al. 2007. Progress of ecological resilience prediction. Environmental Science and Technology, 30(12): 97-99. (in Chinese)

DOI

[6]
Fu B J. 1993. Principles and methods of regional ecological environment prediction. Chinese Journal of Applied Ecology, 4(4): 436-439. (in Chinese)

[7]
Gao Y, Cao M, Qiu H, et al. 2015. Research on ecological resilience prediction in Yulin City. Chinese Arid Zone Resources and Environment, 29(9): 57-62. (in Chinese)

[8]
Guo Z W. 2001. Construction of national ecological resilience prediction system and maintenance system—Countermeasures in the face of serious ecological crisis. Science and Technology Herald, (1): 54-56. (in Chinese)

[9]
Guo Z Y, Xu X, Jin C H, et al. 2024. Weak link identification and countermeasures of ecological and environmental governance in China based on knowledge graph. Research of Environmental Sciences, 5(8): 1858-1866. (in Chinese)

[10]
Hong S L, Zhuang Y H, Fang K. 2014. Data mining technology and engineering practice. Beijing, China: Machinery Industry Press. (in Chinese)

[11]
Jiang Y, LI X, Zhuo J W. 2019. MATLAB time series method and practice. Beijing, China: Electronic Industry Press. (in Chinese)

[12]
Kang H Q, Fu X G, Wang L, et al. 2022. Predictive analysis of forest carbon sink contribution in Jiangxi under different management levels. Southern Forestry Science, 50(6): 45-49. (in Chinese)

[13]
Ke X L, Wang C X, Guo H X, et al. 2021. Prediction study on ecological resilience of Yangtze River Economic Belt based on system dynamics. Resources and Environment of the Yangtze River, 30(12): 2905-2914. (in Chinese)

[14]
Li J L, Pu R L, Gong H B, et al. 2017. Evolution characteristics of landscape ecological risk patterns in coastal zones in Zhejiang Province, China. Sustainability, 9(4): 1-18.

DOI

[15]
Li M Y, Lai X J. 2011. Evaluation of urban land ecological resilience based on BP neural network method—Taking Guangzhou City as an example. Economic Geography, 31(2): 289-293. (in Chinese)

[16]
Li X W, Guan Z L, Chen J Y. 1998. Economic data analysis and forecasting. Beijing, China: China Railway Press. (in Chinese)

[17]
Li Y, Fang R, Han H L, et al. 2024. Study on Industrial transformation and upgrading effect of new energy development from the perspective of regional heterogeneity of coal resources. China Coal, 50(8): 34-42. (in Chinese)

[18]
Liu C C, Zhang M. 2024. The historical generation, realistic basis and development trend of harmonious coexistence between man and Nature in response to global ecological crisis. Qinghai Social Science, (2): 43-51. (in Chinese)

[19]
Liu M, Wei J H, Wang G Q, et al. 2017. Water resources stress assessment and risk prediction: A case of Hebei Province, China. Ecological Indicators, (73): 358-368.

[20]
Ma J N, Ye C. 2024. Evolution of Chinese modern view of ecological civilization path. Journal of Henan University (Social Science Edition), (6): 1-6, 152. (in Chinese)

[21]
Quan J T. 2020. Research on the evaluation of regional land resources carrying capacity—Taking Henan Province as an example. Zhengzhou, China: Henan University. (in Chinese)

[22]
Shen M H. 2024. Deepen reform of the eco-logical civilization system, introduced the background, framework, and safeguard mechanism. Journal of Management Studies, 40(5): 16-20, 157. (in Chinese)

[23]
Song T S, Hao K N. 2012. Econometric modelling methods and applications using statistical applications as an analytical tool. Chengdu, China: Southwest Jiaotong University Press. (in Chinese)

[24]
Tao X Y. 2013. Prediction evaluation of urban ecological resilience based on fuzzy element theory. Resource Development and Market, 29(8): 814-817. (in Chinese)

[25]
Xu H, Bai H T, Wang H Z, et al. 2012a. Research on technical methods of planning environmental impact assessment. Beijing, China: Science Press. (in Chinese)

[26]
Xu J H, Wang S D. 2021. Spatial extraction and spatial-temporal analysis of vegetation cover in mining cities—A case of Xuzhou City. Grassland and Turf, (3): 91-98. (in Chinese)

[27]
Xu M, Zhu X, Liu C L. 2012b. Dynamic prediction of land ecological resilience in Hunan Province based on RBF. Acta Geographica Sinica, 67(10): 1371-1382. (in Chinese)

[28]
Xu W H, Yang Y Y, Zhang L, et al. 2017. Prediction assessment method and case study of regional ecological carrying capacity. Advances in Earth Science, 36(3): 306-312. (in Chinese)

[29]
Xu X G. 1996. Assessment and prediction of ecological environment in the Yellow River Delta. Acta Ecologica Sinica, 16(5): 460-468. (in Chinese)

[30]
Yang L, Ji L J, Kang F X, et al. 2016. Application of Grey model in karst groundwater quality prediction. Environmental Monitoring Management and Technology, (3): 20-24. (in Chinese)

[31]
You W J, Cao Y R, Jiang X T, et al. 2019. Ecological environment monitoring system with data governance. Journal of Zhejiang University of Technology, 52(6): 633-640. (in Chinese)

[32]
Yu J H, Li J M, Zhang W Z. 2018. Identification and comprehensive type division of resource cities in China. Acta Geographica Sinica, 73(4): 677-687. (in Chinese)

[33]
Yu Z L, Ma L L, Wang Y Y. 2024. China energy governance of “area” all the way to build national carbon intensity. Asia-pacific Economic Review, (6): 14-30. (in Chinese)

[34]
Zeng X T, Zhang X Y, Zhang S Q, et al. 2024. Ecological belt and horizon, reducing the pollution of carbon reduction synergies Beijing-Tianjin- Hebei region research. Research of Environmental Sciences, 5(7): 1458-1469. (in Chinese)

[35]
Zhang G F. 2018. Comparative study of stochastic model and exponential smoothing model in data prediction. Wireless Interconnection Technology, 15(17): 112-113, 132. (in Chinese)

[36]
Zhang Q, Niu Z J. 2022. Modernization of urban social governance: Connotation logic and advancing path. Journal of Southwest Minzu University (Humanities and Social Sciences Edition), 43(8): 80-86. (in Chinese)

[37]
Zhang Q, Xue H F, Zhang M J, et al. 2010. Prediction model and application of regional ecological security based on topological analysis—Taking Shaanxi Province as an example. Acta Ecologica Sinica, 30(16): 4277-4286. (in Chinese)

[38]
Zhong Q L, Liu H. 2024. Ecological civilization can assign a common prosperity theory logic, intrinsic mechanism and cooperative path. Journal of Shandong Social Science, (3): 106-113. (in Chinese)

[39]
Zhou Y, Zhuo J W, Bian Y Q. 2016. Big data mining system methodology and case analysis. Beijing, China: Machinery Industry Press. (in Chinese)

[40]
Zhu X Q, Huang Z H, Zhang T C, et al. 2020. Characteristics of spatio-temporal coupling between land development intensity and ecological carrying capacity of resource cities and driving factors—Taking Maanshan City as an example. Soil and Water Conservation Research, (4): 317-326, 335. (in Chinese)

[41]
Zhuo J W, Zhou Y. 2017. Quantitative investment:MATLAB data mining technology and practice. Beijing, China: Publishing House of Electronics Industry. (in Chinese)

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