Spatial difference analysis and driving factor diagnosis for regional water resources carrying capacity based on set pair analysis

Abstract

Studying regional water resources carrying capacity (WRCC) is an important way to find out and solve regional water resources problems. Analyzing the spatial difference of WRCC and diagnosing its driving factors is the basis for the implementation of the water control policy named “spatial balance”. This study selects evaluation indicators for WRCC from three aspects: water resources, social economy, and ecological environment. The weights of indicators were determined by fuzzy analytic hierarchy process based on accelerated genetic algorithm (FAHP-AGA), and an evaluation method for WRCC was constructed based on set pair analysis (SPA). On this basis, the spatial difference analysis of regional WRCC and its key driving factor diagnosis model was established, and the empirical study was carried out in Anhui Province as an example. The results show that from 2011 to 2020, the WRCC of Anhui Province was increasing, with the average increase of each city reaching more than 0.3. The spatial difference of WRCC decreased, and the Gini coefficient decreased from 0.16 to 0.08. The key driving factors leading to the spatial difference of WRCC in Anhui Province include water resources module, water consumption per 10,000 yuan of GDP, equilibrium degree of water use structure, per capita GDP, population density, percentage of forest cover, and amount of chemical fertilizer applied per unit of effective irrigated area. Compared with common WRCC evaluation models, this model improves the comparability of the evaluation results. In addition, this model can further analyze the influence of multiple factor interactions on the evaluation results based on the common single factor analysis. The driving factor diagnosis results can provide theoretical guidance for the formulation of regulation measures for regional WRCC and the implementation of the “spatial equilibrium” water control policy.

Graphical abstract

1. Introduction

Water resources are essential resources for maintaining human survival and development. Food security, energy security, and ecological security are all closely related to water resources security. However, with the development of economy and the improvement of human living standards, the demand for water resources is increasing gradually, and the contradiction between water supply and water demand is becoming increasingly prominent [1]. Water resources have become the same important strategic resource as food and oil. Therefore, it is necessary to carry out the study of regional water resources carrying capacity (WRCC) to clarify the utilization potential and limitation conditions of regional water resources, so as to provide a scientific basis for the rational allocation of water resources. The regional WRCC reflects the supporting capability of regional water resources for socio-economic development under the principle of sustainable development and the condition of maintaining the benign circular development of the ecological environment at a certain stage. It can be seen that the regional WRCC is determined by the joint action of water resources, social economy and ecological environment. Therefore, it is necessary to carry out the research of regional WRCC from the relationship among water resources, social economy, and ecological environment, so as to provide ideas for solving the contradiction between water resources and human production and life, and for realizing the coordinated development of water resources, social economy and ecological environment.

There is no international consensus on the definition of WRCC. Most international studies about WRCC are included in sustainable development research [2,3]. As a water shortage country and the most populous country in the world, many scholars in China have conducted research on WRCC since its concept was proposed in 1995. For example, Jia and Wang [4] studied the WRCC of Zhengzhou from 2010 to 2019 and pointed out that the study of WRCC is conducive to the effective treatment of the relationship between water resources, social economy, and ecological environment, and can provide guidance for the reasonable regulation of water resources; Zhou [5] pointed out that the scientific and reasonable evaluation of water resources carrying capacity is of great significance to determine the current situation of regional water resources and ensure the regional social and economic development; By simulating the WRCC of Changchun in different situations, Wang et al. [6] provides suggestions for the sustainable development of Changchun from the aspects of water resource allocation, industrial structure adjustment and ecological protection. Most studies use the method of comprehensive evaluation to measure the regional WRCC quantitatively. In terms of theoretical research, most researches focus on the construction of the index system and the methods of comprehensive evaluation. At present, the common index systems of WRCC include the index system consists of water resources subsystem, economic social subsystem, and ecological environment subsystem [7], the index system based on the DPSIR model [4], the index system based on the PSR model [8], support-pressure-regulation index system [9], the index system including four elements of water quantity, water quality, water area, and water flow [10], etc. And the common evaluation methods include fuzzy comprehensive evaluation [11], system dynamics [12], TOPSIS model [13], set pair analysis method [14], and combination evaluation method [6], etc. In terms of application research, more studies focus on the evaluation of WRCC in a specific region [10,11], and some studies further analyze the spatial and temporal evolution of WRCC on this basis [15,16]. Simple qualitative analysis or spatial autocorrelation analysis are mostly used in the spatial and temporal evolution analysis [15,16]. For example, Deng et al. [15] analyzed the spatial and temporal distribution characteristics of WRCC in Dongting Lake basin according to the evaluation results of WRCC; Wen et al. [17] calculated the global Moran's I according to the evaluation results of WRCC in Anhui Province, and drew the LISA cluster map of WRCC with GeoDa software, and the spatial evolution characteristics of WRCC in Anhui Province from 2011 to 2019 were analyzed. In terms of the identification of impact factors, the common study is to apply the obstacle degree model to identify the obstacle factors of regional WRCC, whose main purpose is to diagnose the main factors leading to poor WRCC [18]. Jin et al. [19] proposed a diagnostic method for the vulnerability index of WRCC by subtraction set pair potential. Shi [20] used the Pearson correlation coefficient method and the improved second-order main substrate analysis method to identify the key driving factors of WRCC; He et al. [21] used the geographical detector method to analyze the key driving factors of WRCC in Anhui Province.

Combining the existing literature we found that the most studies focus on the determination of WRCC evaluation index system and the evaluation method of WRCC, while less attention is paid to the preprocessing method of indicator data. Most studies often utilize standardization or extreme value normalization as treatment methods for the preprocessing of indicator data [22,23]. However, the evaluation results derived from these methods may vary depending on the evaluation sample set, thus resulting in a lack of comparability between evaluation results obtained from different sample sets. Furthermore, there were few studies about the identification of driving factors leading to the spatial difference of WRCC. Most studies on the influence factor of WRCC analyze the influence degree of a single factor, lacking of the analysis of the interaction of multiple factors. Therefore, it is necessary to carry out further in-depth research on the above problems, which requires us to clarify the relationship between the index sample value and the evaluation grade, and the relationship between the driving factors and the spatial difference of the evaluation results. The set pair analysis (SPA) method can quantitatively describe the interrelationship between two sets from three aspects through the connection number. It exhibits the qualities of comprehensiveness, meticulousness, extensiveness, and conciseness in analyzing problems, and has been widely applied to system evaluation issues. Therefore, this paper intends to introduce the SPA method into the WRCC evaluation and driving factor analysis model to solve the above problems. Specifically, this study primarily aims to achieve the following two objectives: (1) Establish a spatial difference analysis model for WRCC based on the SPA method, ensuring that the spatial difference analysis results across different sample sets are comparable. (2) Develop a driving factor diagnosis model for spatial difference in WRCC using SPA, enabling quantitative analysis of the driving effects of both individual factors and their interactions.

In order to realize the above objectives, this paper firstly establishes the evaluation index system of WRCC on the basis of field investigation and literature research, determines the classification standard and weight of each index, and establishes the WRCC evaluation model based on the SPA method. Secondly, the spatial difference of WRCC is analyzed using the Gini coefficient. Finally, the quantitative relationship between the spatial difference of WRCC and its driving factors are described by connection number, and the diagnostic model of the spatial difference of WRCC is established. Moreover, the proposed models were applied in Anhui Province, China to testify its reliability, and the research findings will provide a theoretical basis for reducing the difference of WRCC among different regions and implementing the water control policy aimed at achieving “spatial balance ".

2. Methods and data

To clearly explain the research ideas of this paper, the research framework is drawn, as shown in Fig. 1. Overall, the study includes the following 6 parts: construct the evaluation system of WRCC, establish the evaluation grade criteria, calculate the weights of evaluation system, evaluate the regional WRCC, analysis the spatial difference of WRCC, diagnose the driving factors leading to the spatial difference of WRCC.

Fig. 1.

The research framework of this study.

2.1. Principles of index system construction

Regional WRCC is a comprehensive reflection of the interaction between water resources system, social economy system, and ecological environment system (Fig. 2). On the one hand, the quantity and quality of water resources directly determine the scale and potential of socio-economic development. While socio-economic development leads to a continuous increase in water demand, it also improves the efficiency of water resource utilization. On the other hand, water resources directly participate in the material cycle and energy flow in the ecological environment system, which is crucial for maintaining the basic functions of the environment and ecological balance. At the same time, the ecological environment affects the quality and quantity of water resources through self-purification, water conservation, and regulation of surface runoff. Hence, in the construction of the regional WRCC index system, we select 3 subsystems pertaining to water resources, social economy, and ecological environment respectively [5]. The water resources subsystem represents the available level of water resources, which should not only consider the original water resources conditions in the region, but also reflect its water production capacity, and the utilization of water resources. Based on the existing research [24,25], this paper selects 9 indicators from 3 aspects: water resources conditions, water resources utilization efficiency, and water resources utilization structure. The social economy subsystem describes the development level of regional society and economy. Referring to the existing research [24,25], this paper selects 7 indicators from 4 aspects of economic strength, industrial structure, social structure, and social construction. The ecological environment subsystem describes the healthy state of the regional ecological environment. Referring to the existing research [13,24,25], this paper describes it from support and pressure of ecological environment. The specific index system is shown in Appendix Table 1, and calculation methods and meanings of each indicator are shown in Appendix Table 2.

Fig. 2.

The relationship between WRCC and water resources, social economy, ecological environment.

2.2. Principles of establishing the evaluation grade criteria

Evaluation grade is a ranking division of the quantitative characterization of the evaluation objective. These divisions constitute the evaluation grade sets. In this paper, the regional WRCC is divided into 5 grades, among which grade I corresponds to the maximum WRCC and grade V corresponds to the minimum WRCC. The evaluation grade criteria are the specific regulation of the evaluation object fully meets these grades. The critical threshold of the main characteristics of the evaluation object is generally used to express the evaluation grade criteria. The critical threshold of each index was determined based on the existing research results [25], the characteristics of the research areas, and the expert opinions, as shown in Table 1.

Table 1.

Evaluation grade criteria.

Primary indicator	Grade I	Grade II	Grade III	Grade IV	Grade V
W1 (104m3/km2)	>80	[50,80]	(35,50)	[25,35]	<25
W2 (m³/person)	>2500	[1000,2500]	(700,1000)	[400,700]	<400
W3 (m³)	<200	[200,400]	(400,600)	[600,800]	>800
W4 (%)	>80	[60,80]	(40,60)	[20,40]	<20
W5 (m³)	<80	[80,110]	(110,150)	[150,200]	>200
W6 (m3)	<50	[50,100]	(100,150)	[150,200]	>200
W7 (m3/hm2)	<2000	[2000,4000]	(4000,5000)	[5000,6000]	>6000
W8	>0.7	[0.65,0.7]	(0.6,0.65)	[0.55,0.65]	>0.55
W9 (%)	<40	[40,50]	(50,60)	[60,70]	>70
S1 (104yuan)	>8	[6,8]	(4,6)	[2,4]	<2
S2 (%)	<5	[5,10]	(10,15)	[15,20]	>20
S3 (%)	>50	[40,50]	(35,40)	[30,35]	<30
S4 (person/km2)	<200	[200,400]	(400,600)	[600,800]	>800
S5 (%)	<40	[40,50]	(50,60)	[60,70]	>70
S6 (kW/km2)	>1750	[1500,1750]	(1250,1500)	[1000,1250]	<1000
S7 (%)	>90	[80,90]	(70,80)	[50,70]	<50
E1 (%)	>4	[3,4]	(2,3)	[1,2]	<1
E2 (%)	>80	[60,80]	(40,60)	[20,40]	<20
E3 (102m3/yuan)	<1	[1,2]	(2,4)	[4,6]	>6
E4 (103 kg/km2)	<60	[60,70]	(70,80)	[80,100]	>100

2.3. Weight calculation method based on the fuzzy analytic hierarchy process based on accelerated genetic algorithm (FAHP-AGA)

In this article, we adopted the FAHP-AGA method to determine the index and subsystem weights. The fuzzy analytic hierarchy process (FAHP) is an improvement of the traditional analysis hierarchy process (AHP). In the FAHP method, the fuzzy judgment matrix is established by inviting experts to compare the importance of indicators. However, the fuzzy judgment matrix given by experts is difficult to have satisfactory consistency, so it is necessary to modify the judgment matrix. Therefore, we use the accelerated genetic algorithm (AGA) for the objective function solving to obtain the modified judgment matrix. And the weight can be obtained accordingly. The specific steps can be referred to the literature [26].

2.4. Evaluation method for WRCC based on set pair analysis (SPA)

Assuming that the sample data can be denoted as {x_ijk |i = 1,2, …,m; j = 1,2, …,l; k = 1,2, …,n_j} and its evaluation criteria as {s_gjk |g = 0,1, …,5; j = 1,2, …,l; k = 1,2, …,n_j}, where x_ijk is the value of the evaluation index k in the evaluation sample i subsystem j; s_gjk is the threshold of the grade criteria of the evaluation index k in the subsystem j; m is the number of samples; l is the number of subsystems; n_j is the number of indicators in the subsystem j. The evaluation method for WRCC based on SPA can be divided into the following 3 steps:

Step 1

Single-index evaluation. Single-index evaluation is a quantitative description of the degree that the evaluation index sample value x_ijk meets the evaluation grade standard. Combine the evaluation index value and grade criteria into a pair, and the connection number between sample x_ijk and grade criteria can be obtained refer to Eq. (10), (11), (12) in the literature [27]

$$u_{ijk}=a_{ijk}+b_{1ijk}{I}_1+b_{2ijk}{I}_2+b_{3ijk}{I}_3+c_{ijk}J$$ (1)

where a_ijk is the similar degree of u_ijk; b_1ijk, b_2ijk, b_3ijk are the different degrees of u_ijk; c_ijk is the opposite degree of u_ijk; a_ijk, b_1ijk, b_2ijk, b_3ijk, c_ijk reflects the relative degree of x_ijk belonging to grade I ∼ V, all ranging from 0 to 1 and a_ijk + b_1ijk + b_2ijk + b_3ijk + c_ijk = 1; I₁, I₂, I₃ is the difference coefficient; J is the opposition coefficient.

Then, combined with the weight of index k in subsystem j, the connection number u_ij of sample i subsystem j can be obtained by weighting [27,28].

$$u_{ij}=\sum _{k=1}^{n_j}{w}_{jk}{a}_{ijk}+\sum _{k=1}^{n_j}{w}_{jk}{b}_{1ijk}{I}_1+\sum _{k=1}^{n_j}{w}_{jk}{b}_{2ijk}{I}_2+\sum _{k=1}^{n_j}{w}_{jk}{b}_{3ijk}{I}_3+\sum _{k=1}^{n_j}{w}_{jk}{c}_{ijk}J=a_{ij}+b_{1ij}{I}_1+b_{2ij}{I}_2+b_{3ij}{I}_3+c_{ij}J$$ (2)

where w_jk is the weight of index k in subsystem j; a_ij is the similar degree of u_ij; b_1ij, b_2ij, b_3ij are the different degrees of u_ij; c_ij is the opposite degree of u_ij; I₁, I₂, I₃ is the difference coefficient; J is the opposition coefficient.

Similarly, the connection number u_i for sample i can be obtained [27,28].

$$u_i=\sum _{j=1}^3{w}_j{a}_{ij}+\sum _{j=1}^3{w}_j{b}_{1ij}{I}_1+\sum _{j=1}^3{w}_j{b}_{2ijk}{I}_2+\sum _{j=1}^3{w}_j{b}_{3ij}{I}_3+\sum _{j=1}^3{w}_j{c}_{ij}J=a_i+b_{1i}{I}_1+b_{2i}{I}_2+b_{3i}{I}_3+c_{i}J$$ (3)

where w_j is the weight of subsystem j; a_i is the similar degree of u_i; b_1i, b_2i, b_3i are the different degrees of u_i; c_i is the opposite degree of u_i; I₁, I₂, I₃ is the difference coefficient; J is the opposition coefficient.

Step 2

Calculation of the evaluation value for sample. Subtraction set pair potential (SSPP) is an adjoint function of the connection number proposed by Jin et al. [19]. The SSPP of connection number u_i can be calculated by Eq. (4) [27,28].

$$y_i=\left(a_i-c_i\right)\left(1+b_{1i}+b_{2i}+b_{3i}\right)+0.5\left(b_{1i}-b_{3i}\right)\left(b_{1i}+b_{2i}+b_{3i}\right)$$ (4)

where y_i is the SSPP of connection number u_i, y_i ∈ [-1,1]. When y_i equals 1, the WRCC of sample i is the best. Conversely, when y_i equals −1, the WRCC of sample i is the worst. To be consistent with previous studies, the SSPP is linearly transformed so that the values range between 0 and 1.

$$Y_i=0.5y_i+0.5$$ (5)

where Y_i is the evaluation result for sample i.

Similarly, the single-index evaluation result of the sample value X_ijk can be calculated according to Eq. (1) and Eq. (6) [27,28]. The evaluation results of subsystem j in sample i can be calculated according to Eq. (2) and Eq. (7).

$$X_{ijk}=0.5\left[\left(a_{ijk}-c_{ijk}\right)\left(1+b_{1ijk}+b_{2ijk}+b_{3ijk}\right)+0.5\left(b_{1ijk}-b_{3ijk}\right)\left(b_{1ijk}+b_{2ijk}+b_{3ijk}\right)\right]+0.5$$ (6)

$$Y_{ij}=0.5\left[\left(a_{ij}-c_{ij}\right)\left(1+b_{1ij}+b_{2ij}+b_{3ij}\right)+0.5\left(b_{1ij}-b_{3ij}\right)\left(b_{1ij}+b_{2ij}+b_{3ij}\right)\right]+0.5$$ (7)

where X_ijk is the single-index evaluation result of x_ijk; Y_ij is the evaluation results of subsystem j in sample i.

Step 3

Determination of the evaluation grade. The classification standard of WRCC can be obtained by taking x_ijk = s_gjk (g = 0, 1, …, 5) into Eqs. (1), (2), (3), (4), (5): when Y_i ∈ [0,0.06), the WRCC belongs to Grade V; when Y_i ∈ [0.06, 0.38), the WRCC belongs to Grade IV; when Y_i ∈ [0.38, 0.63], the WRCC belongs to Grade III; when Y_i∈ (0.63, 0.94], the WRCC belongs to Grade II; when Y_i∈(0.94,1], the WRCC belongs to Grade I. Grade I corresponds to the best WRCC while Grade V corresponds to the worst WRCC.

2.5. Evaluation method of the spatial difference of WRCC based on Gini coefficient

This paper uses a simple Gini coefficient calculation method [29] to quantitatively evaluate the spatial difference of WRCC in the study area:

$$G=1-\frac{1}{m}\left(2{\sum }_{i=1}^{m-1}{z}_i+1\right)$$ (8)

$$z_i={\sum }_{k=1}^i{Z}_k/{\sum }_{i=1}^m{Y}_i$$ (9)

where G refers to the Gini coefficient; Z_k (k = 1, 2, …, m) is the new sequence of Y_i (i = 1, 2, …, m) ranked from small to large; m is the number of subregions within the region. The larger the Gini coefficient G is, the greater the spatial difference in WRCC within the region.

2.6. Driving factor diagnosis based on set pair similarity analysis

Wang et al. [30] pointed out that if an independent variable has an significant influence on a dependent variable, the spatial distribution of the independent variable should be similar to the dependent variable. Based on this fundamental hypothesis, this paper proposed a driving factor diagnosis method based on set pair similarity analysis, which combines evaluation results and evaluation indicators into a pair and performs a diagnostic analysis of driving factors by measuring the similarity between the two. It can be seen from Section 2.4 that the evaluation results of WRCC are weighted by the evaluation results of three subsystems. Therefore, when analyzing the key driving factors, the diagnosis is also carried out separately by subsystem. Specifically, it includes the following five steps:

Step 1

Discretization of the independent and dependent variables. In this paper, the results of the single-index evaluation are taken as the independent variable, and the evaluation results of the subsystem are taken as the dependent variable. If the evaluation result of the subsystem j is Y_j = {Y_ji| j = 1, 2, …, l; i = 1, 2, …, m}, The single-index evaluation result of the sample i index k is X_jk = {X_jki |j = 1, 2, …, l; k = 1, 2, …, n_j; i = 1 2, …, m}, where n_j is the number of evaluation index in subsystem j and m is the number of samples. Divide Y_j and X_jk into three discrete categories with Eq. (10) and Eq. (11) [31].

$$Y_{ji}^{\prime }=\{\begin{array}{cc}1& Y_{ji}\le {\bar{Y}}_j-k_1{s}_j\\ 2& {\bar{Y}}_j-k_1{s}_j\le Y_{ji}\le {\bar{Y}}_j+k_2{s}_j\\ 3& Y_{ji}\ge {\bar{Y}}_j+k_2{s}_j\end{array}$$ (10)

$$X_{jki}^{\prime }=\{\begin{array}{cc}1& X_{jki}\le {\bar{X}}_{jk}-k_1{s}_{jk}\\ 2& {\bar{X}}_{jk}-k_1{s}_{jk}\le X_{jki}\le {\bar{X}}_{jk}+k_2{s}_{jk}\\ 3& X_{jki}\ge {\bar{X}}_{jk}+k_2{s}_{jk}\end{array}$$ (11)

where Y'_ji is the discrete results of Y_ji; X'_jki is the discrete results of X_jki; ${\bar{Y}}_j$ is the mean of and Y_j, ${\bar{Y}}_j=\frac{1}{m}\sum _{i=1}^m{Y}_{ji}$; ${\bar{X}}_{jk}$ is the mean value of X_ji, ${\bar{X}}_{jk}=\frac{1}{m}\sum _{i=1}^m{X}_{jki}$;s_j is the standard deviation of Y_j, $s_j={\left[\sum _{i=1}^m{\left(Y_{ji}-{\bar{Y}}_j\right)}^2/\left(m-1\right)\right]}^{0.5}$; s_jk is the standard deviation of X_ji, $s_{jk}={\left[\sum _{i=1}^m{\left(X_{jki}-{\bar{X}}_{jk}\right)}^2/\left(m-1\right)\right]}^{0.5}$; k₁ and k₂ are the empirical coefficients, in this article, k₁ = k₂ = 0.44 [31].

Step 2

Establish the connection number between the independent and dependent variables. The evaluation results of subsystem j and the evaluation results of index k in subsystem j are combined into a pair H(Y_j, X_jk). For sample i, if |Y'_ji-X'_jki| = 0, the evaluation result of subsystem j and index k in subsystem j are considered to be in the same state; correspondingly, if |Y'_ji-X'_jki| = 1, then the two are considered to be in a different state; If |Y'_ji-X'_jki| = 2, then the two are considered to be in a opposite state. Count the number of the same state, different state, and opposite state and denote them as S_jk, F_jk, and P_jk respectively. Then, the connection number of H(Y_j, X_jk) can be constructed [32].

$$u_{Y_j-X_{jk}}=\frac{S_{jk}}{m}+\frac{F_{jk}}{m}I+\frac{P_{jk}}{m}J=a_{jk}+b_{jk}I+c_{jk}J$$ (12)

where S_jk, F_jk,and P_jk are the number of the same state, different state, and opposite state in m samples, and S_jk + F_jk + P_jk = m; a_jk、b_jk and c_jk are the proportions of the same, different, and opposite states to the total sample size m, respectively, and a_jk + b_jk + c_jk = 1; I is the difference coefficient; J is the opposition coefficient. The larger the a_jk is, the more samples are in the same state.

Step 3

Single factor analysis. The partial positive term in the semi-partial subtraction set pair potential [33] is used to measure the similarity between the subsystem and the index.

$$h_k^j=a_{jk}+b_{jk}{a}_{jk}/\left(a_{jk}+b_{jk}\right)$$ (13)

where $h_k^j$ represents the degree of similarity between the evaluation results of index k and the evaluation results of subsystem j. The greater the $h_k^j$ is, the higher the similarity between the evaluation results of index k and the evaluation results of subsystem j, which indicates the index has a greater influence on the spatial differences in WRCC.

Step 4

Factor interaction analysis. Factor interaction analysis can identify the interaction of different indices on the evaluation results. In other words, it can evaluate whether the interactive factor will enhance or weaken the impact of the single factor on the evaluation results. Through Eq. (14), the evaluation result of two index interaction is constructed. For the index k and index l of sample i, the evaluation result after their interaction is

$$X_{k-l}^i=\frac{w_k}{w_k+w_l}{X}_{ki}+\frac{w_l}{w_k+w_l}{X}_{li}$$ (14)

where w_k and w_l are the weights of index k and l, respectively. Repeat steps 1 to 3 to calculate the similarity of the interactive factor and the evaluation result. And the interactive type of the two factors can be determined by Eq. (15). For convenience, the symbol "∩" is used to indicate the interaction between two factors.

$$\{\begin{array}{cc}\text{weakened}\text{type}& h_{k-l}^j<\min \left(h_k^j,h_l^j\right)\\ \text{homogenized}\text{type}& \min \left(h_k^j,h_l^j\right)\le h_{k-l}^j<\max \left(h_k^j,h_l^j\right)\\ \text{enhanced}\text{type}& h_{k-l}^j\ge \max \left(h_k^j,h_l^j\right)\end{array}$$ (15)

where $h_{k-l}^j$ is the degree of similarity between the evaluation result of interactive factor k∩l and the evaluation results of the subsystem j, $h_{k-l}^j$ ∈[0, 1]. Larger $h_{k-l}^j$ indicates the greater influence of this interaction index on the evaluation results.

Step 5

Key driving factor diagnosis. Combining the results of the single factor analysis and the factor interaction analysis, factor whose similarity with evaluation results was always greater than 0.9 is considered as a key driving factor.

2.7. Study area and data sources

Anhui Province straddles the north-south dividing line of China, resulting in significant differences in geography and climate between its northern and southern regions. The water resources in Anhui Province show the distribution characteristics of more in the south and less in the north. On the contrary, the population density of Anhui Province shows the overall distribution characteristics of more in the north and less in the south. This leads to the large spatial difference of per capita water resources in Anhui Province. According to the classification standard of the Swedish hydrologist Falkenmark [34], the water resources supply and demand situation of the 16 cities in Anhui Province can be divided into 4 categories. Accordingly, it can be inferred that there is a large spatial difference in WRCC among the 16 cities in Anhui Province. Therefore, Anhui Province was selected as the empirical research area.

The data used in this article mainly includes basic data on water resources, social economy, and ecological environment of 16 cities in Anhui Province from 2011 to 2020. The data set contains 20 indicators data of 16 cities every year. The research data are mainly calculated according to the basic data in the Statistical Yearbook of Anhui Province (2011–2021) and the Water Resources Bulletin of Anhui Province (2010–2020), and some missing data are supplemented by linear interpolation.

3. Results

3.1. Calculation of weight for indexes and subsystems by AGA-FAHP

According to the method described in section 2.3, the weights of the three subsystems are calculated as 0.4, 0.3, and 0.3. The weight vector for water resources subsystem is w₁ = [0.101, 0.128, 0.101, 0.074, 0.127, 0.093, 0.127, 0.137, 0.112]. The weight vector for social economy subsystem is w₂ = [0.317, 0.100, 0.150, 0.138, 0.113, 0.082, 0.101]. The weight vector for ecological environment subsystem is w₃ = [0.175, 0.325, 0.200, 0.300].

3.2. Evaluation of WRCC from city scale, 2011–2020

According to the method described in section 2.4, the evaluation results of WRCC for 16 cities in Anhui Province from 2011 to 2020 were calculated, as shown in Fig. 3. As can be seen from Fig. 3, during 2011–2020, the WRCC of 16 cities in Anhui Province generally showed an upward trend, with an average increase of more than 0.3 over the 10 years. Among them, Bozhou, Chuzhou, and Lu'an had increases exceeding 0.4, while Huaibei, Ma'anshan, Wuhu, and Tongling had increases of less than 0.3. Through analysis of the raw data, it was found that the increase in WRCC in Bozhou, Chuzhou, and Lu'an was mainly attributed to the significant improvement in water use efficiency. In contrast, the slower growth in Ma'anshan, Wuhu, and Tongling was related to insufficient attention to ecological and environmental protection. As for Huaibei, its modest increase was primarily due to the fact that although there were improvements in various indicators during the period from 2011 to 2020, the range of change was relatively small.

Fig. 3.

Evaluation results of WRCC in Anhui Province, 2011–2020.

According to the classification standard of WRCC described in Section 2.4, the WRCC grade of 16 cities in Anhui province is divided, as shown in Fig. 4. Compared with 2011, the WRCC of 16 cities in Anhui province in 2020 has improved significantly, from most of the original in Grade IV in 2011 to most in Grade II in 2020. Among them, Bozhou, Suzhou, Fuyang, Chuzhou, Lu'an, Anqing, Xuancheng have been upgraded 2 grades; Tongling has been always in Grade III, and the rest of the cities have been upgraded 1 grade.

Fig. 4.

Evaluation grade of WRCC of 16 cities in Anhui Province from 2011 to 2020.

3.3. Spatial difference analysis of WRCC in Anhui Province, 2011–2020

According to the classification standard of WRCC in section 2.4, the grade distribution map of WRCC in Anhui Province is drawn (Fig. 5a). As can be seen from Fig. 5a, there are obvious spatial differences in WRCC of 16 cities in Anhui Province, and the overall spatial distribution rule is high in the south and low in the north. To further quantitatively evaluate the spatial difference of WRCC in Anhui Province over time, the Gini coefficient was calculated, as shown in Fig. 5b. As can be seen from the figure, from 2011 to 2020, the Gini coefficient of WRCC in Anhui Province showed a downward trend in the fluctuation, indicating that the spatial difference of Anhui Province showed a trend of decreasing, and the spatial equilibrium of WRCC was improved.

Fig. 5.

The spatial difference of WRCC in Anhui Province, 2011–2020.

3.4. Diagnosis of driving factors for the WRCC of Anhui Province

3.4.1. Single factor analysis

According to the method described in section 2.6, the similarity of the index to each subsystem is calculated separately, and the factors with greater similarity are listed in Table 2.

Table 2.

Single factor diagnostic results.

subsystem	sort	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
water resources	1	W5	W8	W5	W8	W8	W8	W8	W8	W8	W8
		0.938	0.938	0.902	0.938	0.921	0.938	0.984	0.871	0.871	0.671
	2	W8	W5	W8	W5	W5	W5	W5	W5	W3	W3
		0.809	0.871	0.902	0.871	0.9	0.902	0.835	0.833	0.788	0.600
	3	W7	W6	W6	W3	W3	W6	W3	W3	W5	W5
		0.763	0.736	0.804	0.809	0.714	0.714	0.788	0.788	0.714	0.577
	4	W6	W3	W3	W6	W6	W3	W6	W9	W9	W9
		0.733	0.733	0.75	0.714	0.656	0.671	0.703	0.714	0.692	0.577
social economy	1	S7	S7	S7	S7	S1	S7	S1	S1	S1	S1
		0.871	0.921	0.938	0.859	0.938	0.871	0.938	0.859	0.902	0.938
	2	S2	S2	S2	S2	S2	S2	S2	S2	S2	S2
		0.714	0.804	0.835	0.835	0.938	0.833	0.833	0.833	0.833	0.833
	3	S1	S1	S1	S1	S7	S1	S4	S7	S7	S7
		0.684	0.750	0.809	0.809	0.75	0.809	0.692	0.763	0.736	0.736
ecological environment	1	E2	E2	E2	E2	E2	E4	E2	E2	E4	E4
		0.833	0.859	0.788	0.859	0.871	0.902	0.900	0.900	0.921	0.900
	2	E4	E1	E1	E4	E4	E2	E4	E4	E2	E2
		0.809	0.804	0.736	0.859	0.809	0.871	0.871	0.871	0.809	0.809

Fig. 6, Fig. 7, Fig. 8 display the analysis results of the driving factors for three subsystems. Here, the value in the diagonal position represents the effect level of a single factor on the spatial difference, while the remaining values indicate the effect level on the spatial difference after the pairwise interaction of the factors.

Fig. 6.

Factor interaction detection results of water resources subsystem.

Fig. 7.

Factor interaction detection results of social economy subsystem.

Fig. 8.

Factor interaction detection results of ecological environment subsystem.

For the water resource subsystem (Fig. 6), it can be found that the similarity of W₁∩W₈ has always been at a high level. Comparing the results of single factor analysis and interactive factor analysis for the water resources subsystem, it was found that sometimes the interactive type of W₁∩W₈ is the enhanced type and sometimes the homogenized type. This indicates that the influence of W₁∩W₈ on the evaluation results is not necessarily great than that of a single factor. However, there were no factors with a similarity consistently greater than 0.9 from 2011 to 2020, whether single or interactive factors. Therefore, W₅, ranked second in similarity in the single factor analysis, was attempted to conduct a multi factor interaction analysis with W₁ and W₈. The analysis showed that from 2011 to 2020, the similarity between W₁∩W₅∩W₈ and the evaluation results of the water resources subsystem was always greater than 0.9. Therefore, water resource modulus, water consumption per 10,000 yuan of GDP, and equilibrium degree of water use structure were selected as key driving factors for the water resource subsystem, respectively characterizing regional water resource endowment, water use efficiency, and water use structure.

For the social economy subsystem (Fig. 7), the impact of interaction between S₁ and other indicators in the social economy subsystem is at a high level, and the impact tends to increase over time. Comparing the results of single factor analysis and interactive factor analysis, it is found that the interactive factor of S₁∩S₄ was always enhanced, and its influence on the evaluation results of the social economy subsystem was greater than any single factor. Besides, the similarity of S₁∩S₄ was always greater than 0.9 from 2011 to 2020. Therefore, the per capita GDP, and population density were selected as key driving factors of the social economy subsystem, characterizing the region's economic strength and demographic pressures, respectively.

For the ecological environment subsystem (Fig. 8), the impact of single indicator E₂ and E₄ on the evaluation results is already at a high level. Comparing the results of single factor analysis and interactive factor analysis, it is found that the interaction factor E₂∩E₄ is always greater than any single effect, which is always greater than 0.9 in 2011–2020. Therefore, the percentage of forest cover and the amount of chemical fertilizer applied per unit of effective irrigation area were selected as the key driving factor of ecological environment subsystem to characterize the ecological environment background value and the carrying pressure due to the ecological environment pollution, respectively.

4. Discussion

4.1. Causes analysis for the reduction of spatial difference of WRCC

According to the identification results of driving factors, W₁∩W₅∩W₈, S₁∩S₄, E₂∩E₄ are the main factors affecting the spatial difference of WRCC in Anhui Province. Further analysis of the original data of these indicators shows that the decrease of the water use efficiency gap is the main reason for the decrease of the spatial difference of WRCC in Anhui Province. According to the analysis of Section 3.2, it can be seen that the main reason for the large increase of WRCC in Bozhou, Chuzhou and Lu'an is the rapid improvement of water use efficiency. It can be inferred that the rapid improvement of WRCC in Bozhou, Chuzhou and Lu'an has contributed to the reduction of the spatial difference of WRCC in Anhui Province.

4.2. Rationality analysis of the evaluation results

The results in section 3.2 show that during 2011–2020, the WRCC in Anhui Province generally increased, which is consistent with the results of literature [21]. Additionally, during 2011–2020, Huainan has always been the city with the worst WRCC in Anhui Province, while Huangshan is the city with the highest WRCC. This is in line with the actual situation of Anhui Province: Huainan is rich in coal resources, and related industries such as mining and thermal power generation will consume a large amount of water resources and damage the ecological environment. While Huangshan is located in the southernmost part of Anhui Province, with abundant water resources, developed tertiary industry and low water demand. It follows that the evaluation results of WRCC obtained in this paper are reasonable and credible.

4.3. Rationality analysis of the diagnosis results

From Table 2, it can be seen that the factors that have a significant impact on the spatial difference of WRCC in Anhui Province are W₈, W₅, W₃, W₆, S₁, S₂, S₇, E₂, and E₄. This result is partially consistent with the key driving factors for spatial differentiation of WRCC in Anhui Province [21], such as water consumption per 10,000 yuan of value-added by industry, per capita GDP, rate of tap water penetration in rural area, indicating that the calculation results in this paper have a certain degree of credibility. However, due to different selected indicator systems and calculation methods, it is difficult to obtain completely consistent results. In addition, there is no indicator of ecological environment in the main impact factors obtained in literature [21], while WRCC reflects the relationship between water resources, social economy and ecological environment. It can be seen that the results obtained in this paper have higher credibility.

Additionally, He et al. [21] used geographical detector to analyze the spatial difference driving factors of WRCC in Anhui province from 2011 to 2020. The results showed that the interaction between per capita GDP and most indicators reached more than 0.9 in 2020, which is similar to the results of this paper. This reflects the credibility of the diagnosis results of this paper in another aspect. Moreover, compared to the geographical detector method, the diagnostic method proposed in this paper is computationally simpler.

Table 2 shows that the similarity between the index and the water resource subsystem evaluation results gradually decreases over time. Taking the water consumption per 10,000 yuan of GDP as an example, from 2011 to 2020, the similarity ranking of water consumption per 10,000 yuan of GDP gradually decreased from first to third, and the similarity also decreased from the maximum of 0.938 to 0.577. Analyzing the data of water consumption per 10,000 yuan of GDP in various cities in Anhui Province over the past ten years (Fig. 9), it was found that from 2011 to 2020, the water consumption per 10,000 yuan of GDP in Anhui Province showed a significant downward trend, and the regional differences were significantly reduced. Therefore, the impact of the water consumption per 10,000 yuan of GDP on the spatial differences in water resources is gradually decreasing. Similarly, the similarity of S₁ in the social economy subsystem significantly increases over time, indicating a gradual increase in the impact of per capita GDP on spatial differences in social economy. It can be inferred that the per capita GDP differences among cities in Anhui Province further increased from 2011 to 2020, which is consistent with the actual situation in Anhui Province (Fig. 10). Therefore, it can be seen that the diagnosis results of this paper are consistent with the actual situation, which also shows the credibility of the diagnosis results.

Fig. 9.

Changes in water consumption per 10,000 yuan of GDP from 2011 to 2020.

Fig. 10.

Changes in per capita GDP from 2011 to 2020.

4.4. Comparability analysis of the results

To illustrate the advantages of the method in this paper in terms of the comparability of results, a comparison is made between the calculation results of this paper and those obtained through a commonly used method [22]. Using the sample sets of 2011–2018 and 2011–2020 respectively, the WRCC of 16 cities in Anhui Province in 2018 was calculated. The WRCC of Hefei calculated by the two methods is shown in Fig. 11. As can be seen from the figure, for the same sample point, when it belongs to different sample sets, the result calculated by method 1 differs, while the result obtained by method 2 remains the same. This is because the preprocessing method (extreme value normalization) adopted in method 1 yields a relative result that varies with the changes in the maximum and minimum values within the sample set. In contrast, results obtained by method 2 only depends on the sample value and grade threshold, and will not change with the sample set. Clearly, the results calculated by the method in this paper exhibit better comparability.

Fig. 11.

Comparison of the results between the two methods.

Note: Method 1 refers to the method in Ref. [22], which is a commonly used method. Method 2 refers to the method in section 2.4 of this paper. Sample set 1 refers to the data from 2011 to 2018. Sample set to refers to the data from 2011 to 2020.

In addition, by comparing the evaluation results of the two methods, it can be found that the change trend of WRCC calculated by method 2 is basically the same as that of method 1, but the change range is larger. It can be seen that the sensitivity of method 2 is higher and the results are more differentiated. What's more, the evaluation result of WRCC in 2019 obtained by method 2 was significantly lower than that in 2018 and 2020, while the WRCC of method 1 showed a trend of steady increase from 2018 to 2020. Actually, the total water resources in Hefei were only 2.15 million m³ in 2019, significantly less than 8.95 billion m³ in 2020 and 5.43 billion m³ in 2018. Obviously, the calculation results of method 2 are more in line with the reality and have higher credibility.

4.5. Countermeasures analysis

It is worth noting that the factors (W₁ and W₂) characterizing water resource endowments have always been considered to have a significant relationship with the spatial differences in water resources. But their performance is not prominent when conducting single factor analysis. However, when interacting with other factors, the interactive factors often have a high similarity with the subsystem evaluation results. Besides, the influence of a single factor on the water resources subsystem decreases with time. This shows that the key driving factors of the water resource subsystem tend to be diversified, and a single factor cannot dominate the spatial differences change in the whole water resource subsystem. This may be related to the fact that with the advancement of science and technology and the change of industrial structure in recent years, the influence of water use efficiency and water structure on WRCC has gradually increased. Therefore, in order to reduce the spatial difference of water resources subsystems, it is not only necessary to coordinate the amount of available water resources in different regions through water transfer projects (such as Yangtze River to Huaihe River Diversion Project), but also to improve the efficiency of water use and improve the structure of water use individually.

On the contrary, for the social economy subsystem, the influence of per capita GDP (S₁) representing the economic strength increased with time, and gradually became the dominant driving factor affecting the spatial differences of its subsystem. This may be due to that with the development of social economy, the industrial structure is gradually reasonable, and the infrastructure construction is constantly improved. As the spatial differences caused by industrial structure and infrastructure gradually decrease, the economic differences between regions have become the dominant factors leading to their spatial differentiation. Therefore, how narrow the economic gap between regions has become the primary problem of reducing the spatial differences of social economy subsystems.

For the ecological environment system, except for the ecological water consumption rate (E₁), the influence of other indicators on the spatial difference of ecological environment subsystem are all at a high level. This may be related to the imbalance of ecological environment pressure caused by the different distribution of industrial structure in different cities, which requires the areas with poor ecological environment subsystem evaluation results to pay more attention to ecological environment protection while developing the economy, especially to the control of industrial wastewater discharge and agricultural fertilizer application, so as to achieve the purpose of reducing both point source pollution and non-point source pollution.

5. Conclusions and recommendations

5.1. Conclusions

This study presents a method for evaluating spatial differences of regional WRCC and diagnosing its key driving factors. The main reasons for the spatial difference of WRCC in Anhui Province have been identified. Compared with previous studies, this method further quantifies the microscopic uncertainty between evaluation samples and evaluation criteria, and addresses the issue that the evaluation results of commonly used single-index evaluation methods tend to vary with changes in evaluation sample set. This improves the comparability of the evaluation results. In addition, the driving factors diagnosis method proposed in this paper can further analyze the influence of multiple factor interactions on the evaluation results based on the common single factor analysis, and its diagnostic results are reasonable and credible. Compared with the commonly used geographical detector method, the method proposed in this paper has the advantage of computational simplicity. The driving factor identification results can provide theoretical guidance for formulating the regulation measures of regional WRCC and improving the spatial equilibrium of WRCC.

The application results of this method in Anhui province show that there are obvious spatial differences in WRCC of Anhui Province. In 2011, there were 10 cities in Anhui Province with the WRCC in grade IV, while the other 6 cities were in grade III; In 2020, there were 4 cities in Anhui Province with the WRCC in grade III, while the other 12 cities were in grade II. From 2011 to 2020, the average increase of WRCC in all cities reached more than 0.3, and the Gini coefficient decreased from 0.16 in 2011 to 0.08 in 2020. In general, from 2011 to 2020, the WRCC of Anhui Province showed an obvious increasing trend, while the calculation result of Gini coefficient shows that the spatial difference of WRCC was in a decreasing trend. The main driving factors causing the spatial difference of water resources carrying capacity in Anhui province include water resource module, water consumption per 10,000 yuan GDP, equilibrium degree of water use structure, per capita GDP, population density, percentage of forest cover and the amount of fertilizer applied per unit of effective irrigated area.

In short, this work can provide a research basis for regional WRCC prediction and a scientific basis for the regulation of regional WRCC. The research methods and ideas are general and can be extended to other aspects, such as driving factors diagnosis for land-use change or ecosystem evolution. However, this paper only identifies the main driving factors leading to the spatial difference of WRCC in Anhui Province. The obstacle factors of each city should be further studied if the specific and targeted regulation plans are needed. Additionally, in the method proposed in this paper, the simple method of mean and standard deviation combined with the empirical coefficients was used to discretize the independent and dependent variables, which is somewhat subjective. How to reasonably discretize the independent and dependent variables is still worth further exploration.

5.2. Recommendations

Based on the above research, the following recommendations are put forward to further reduce the spatial difference of WRCC in Anhui Province and improve its spatial equilibrium degree.

• (1)Coordinate the amount of available water resources in different regions through water diversion projects, and increase the amount of available water resources by increasing the utilization of unconventional water sources such as rainwater and reclaimed water.
• (2)In agricultural production, the water-use efficiency can be improved by promoting water-saving irrigation methods such as sprinkler irrigation and drip irrigation. In industrial production, the water-use efficiency can be improved by improving the reuse rate of water, improving production technology and reducing production water consumption. In daily life, the water-use efficiency can be improved by strengthening water-saving publicity and promoting water-saving appliances. By improving water-use efficiency, the purpose of reducing water consumption and adjusting water use structure can be further achieved.
• (3)We should promote regional cooperation through policy guidance, so as to realize resource sharing and complementary advantages, and promote the balance of regional economic development. Especially for Bozhou, Suzhou, Fuyang and Lu'an, which have relatively backward economic development, the government should intensify its support to these regions, encouraging them to explore and harness their distinctive cultural, historical, and natural assets, so as to achieve rapid and sustainable development economy
• (4)For Huainan, Tongling, and Ma'anshan, it is necessary to increase investment in improving production processes. By developing industrial wastewater recycling and reuse technologies as well as clean production technologies, the discharge of industrial wastewater can be reduced, so as to reduce the pressure of ecological environment.
• (5)Increase scientific guidance for agricultural planting. By guiding farmers to fertilize reasonably, appropriately adopting crop rotation and intercropping methods, and encouraging the use of organic fertilizers as a substitute for chemical fertilizers, the amount of chemical fertilizer use can be reduced, thus minimizing non-point source pollution and reducing the pressure on the ecological environment system.

Data availability statement

Data will be made available on request.

Ethics approval and consent to participate

Not applicable.

CRediT authorship contribution statement

Rongxing Zhou: Methodology, Formal analysis, Writing – original draft. Juliang Jin: Methodology. Yuliang Zhou: Data curation. Yi Cui: Writing – review & editing. Chengguo Wu: Data curation. Yuliang Zhang: Writing – review & editing. Ping Zhou: Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix. ASupplementary data

The following is the Supplementary data to this article: