A Comprehensive Evaluation of Water Resource Carrying Capacity Based on the Optimized Projection Pursuit Regression Model: A Case Study from China

Abstract

The Han River Ecological Economic Belt (HREEB) has a substantial amount of water resources; however, its distribution is uneven, and issues such as seasonal and engineering water shortages are prevalent. This necessitates a thorough assessment of the current water resource situation and trends in water resource carrying capacity (WRCC) to provide scientific support for the rational allocation of water resources. This study employed the RAGA-PP model to establish a WRCC evaluation index system composed of four subsystems: water resources, economy, society, and the ecological environment. The WRCC of the 17 major cities in the HREEB was evaluated from 2008 to 2022. The differentiation method was introduced to compare the reliability of the RAGA-PP model with three evaluation methods: the entropy weight TOPSIS method, the rank sum ratio method, and the principal component analysis method. In addition, an obstacle degree model was introduced to analyze the factors influencing WRCC enhancement. The results indicated the following. (1) In the differentiation test of the four models, the RAGA-PP model was found to have the highest differentiation value, and the results showed that it was more reliable in the WRCC evaluation of HREEB. (2) WRCC in the HREEB underwent significant changes between 2008 and 2022. (3) The WRCC in Shiyan and Wuhan, which are located in the eastern part of the HREEB, were high in Hubei, low in four cities in Henan, and satisfactory in three cities in Shaanxi. (4) The carrying capacity of the subsystems of the cities in the HREEB exhibited fluctuating changes with obvious internal variations. (5) The problems in the WRCC guideline layer were consistent across all cities in the HREEB, with limited per capita water resources being the primary issue in the indicator layer. Assessing WRCC is essential for achieving sustainable water resource use and high-quality regional development.

1. Introduction

Water resources are indispensable for sustaining life, crucial for facilitating production, and fundamental for maintaining ecological balance. Since the 21st century, industrialization and modernization have become the main modes of socioeconomic development in most countries and regions, which has brought about ecological problems in terms of water resources and the water environment on a global scale. Although developed countries generally have abundant water resources, some regions still face shortages, inefficient use, and unequal distribution [1,2,3]. In contrast, developing countries suffer from the same problems as well as pollution and serious soil erosion [4]. As the world’s largest developing country, China’s water resource problem is a comprehensive and complex issue. The Han River Ecological and Economic Belt (HREEB), located at the junction of China’s northern and southern natural zones, is a key ecological protection barrier in China [5]. The environmental situation of the water resources in cities along the HREEB is a significant concern and is typically representative of broader issues. To ensure sustainable and green water use, it is necessary to assess the carrying capacity (WRCC) of major cities in the HREEB. This assessment provides an invaluable reference for developing strategies to improve water resource management and to support the construction of eastern and southern megacities.

WRCC is usually defined as the limit of the ability of the water resource system to meet the living, production, and ecological needs of human beings within a certain area under the combined effect of the natural environment and human activities [6]. This capacity encompasses not only the physical quantity of water resources (flow, quantity, quality, etc.) but also the sustainable use and management of water resources. WRCC research plays a pivotal role in the field of environmental management and sustainability. Firstly, environmental sustainability necessitates that anthropogenic activities align with the regenerative capacity of natural resources. WRCC research contributes to determining the sustainable level of water resource utilization and mitigating over-exploitation. Secondly, precise WRCC assessment provides a scientific foundation for the formulation of water resources management policies and planning. Lastly, WRCC research emphasizes the utilization of water resources while maintaining a virtuous cycle of the ecological environment, thereby contributing to ecological security and equilibrium [7].

The multivariate evaluation of WRCC mainly includes principal component analysis (PCA) [8,9], the accelerated genetic algorithm for projection pursuit (RAGA-PP) [10], rank sum ratio analysis (RSR) [11], and TOPSIS [12,13]. Both PCA and RAGA-PP methods have been used for dimensionality reduction in multivariate statistical analysis [14]. PCA aims to extract a new set of unrelated variables from the original variables and principal components that explain as much of the variability in the original data as possible [15]. The RAGA-PP method projects multidimensional data into a low-dimensional space by determining the optimal projection direction in a high-dimensional space to reveal the structural features of the data [16]. The two are slightly different in that the goal of PCA is to reduce the dimensionality of the data, whereas the goal of PP is to find the optimal projection direction. Both TOPSIS and RSR rank multiple alternatives to determine the optimal or relatively optimal solutions. The TOPSIS method (Technique for Order Preference by Similarity to Ideal Solution) ranks the solutions according to their distance by calculating the distance of each solution from the ideal and negative ideal solutions [17]. The basic idea of the RSR method is to convert the score of each program on each evaluation index into rank order and then calculate the rank sum of each program [18]. In contrast, the TOPSIS method relies on the concepts of ideal and negative ideal solutions, whereas RSR is based on the assignment of the rank order [19,20].

All four of these evaluation methods have been widely used in WRCC evaluations; however, the accuracy and reliability of the evaluation methods have rarely been studied. Therefore, to compare the reliability and accuracy of the four methods in the WRCC evaluation of HREEB, a differentiation model is introduced in this study. Differentiation is defined as the ratio of the sum of the distances between two neighboring points of the evaluation results to the distance between the first and last points and is used to compare the reliability of different evaluation models [21]. When studying the WRCC of HREEB, the use of the differentiation model can filter out the most reliable method from the four evaluation methods, thereby improving the accuracy of the WRCC evaluation of HREEB.

The remainder of this paper is structured as follows. Section 2 describes the study area, data, and assessment indicators used in this research. Section 3 outlines the four modeling approaches, including the differentiation and barrier models. Section 4 assesses the accuracy of the RAGA-PP model compared with the other three models for evaluating the WRCC in the HREEB. The WRCC of the HREEB was analyzed temporally and spatially using the RAGA-PP, and the factors impeding the increase in WRCC were identified and analyzed sequentially. Section 5 and Section 6 discuss the results and conclude the paper with a succinct summary of the research findings. A technical line diagram of the study is shown in Figure 1.

2. Study Area and Data

2.1. Study Area

The HREEB encompasses significant natural sites, including the Qinba Mountains and the Danjiangkou Reservoir [22]. The HREEB covers 16 cities (forest areas) with an area of 1.92 × 10⁵ km², including Shiyan, Xiangyang, Jingmen, Suizhou, Xiaogan, Tianmen, Qianjiang, Xiantao, Wuhan, Shennongjia Forestry Region, Luoyang, Sanmenxia, Zhumadian, Hanzhong, Ankang, and Shangluo (Figure 2). The HREEB is mostly characterized by mountainous areas, whereas to the south of Zhongxiang, it is predominantly composed of flat plains, with a significant amount of hilly terrain in the intermediate regions [23], which is a subtropical monsoon climate zone with substantial rainfall and an irregular mean annual distribution characterized by significant interannual changes.

2.2. Data Sources

The data sources for this research were categorized into four components: per capita water resources, modulus of water production, precipitation, and per capita water use in the water resources subsystem. These data are obtained from the “Hubei Water Resources Bulletin” (2008–2022), “Shaanxi Water Resources Bulletin” (2008–2022), and Henan Water Resources Bulletin (2008–2022); the data on urban population density, natural population growth rate, urbanization rate, and GDP per capita for the economic and social subsystems are collected from various sources, including the “China Urban Statistical Yearbook” (2008–2022), the “Hubei Statistical Yearbook” (2008–2022), the statistical yearbooks of related cities (2008–2022), and the “Statistical Bulletin of National Economic and Social Development” (2008–2022); and the information for the ecological environment subsystem’s indicators, such as the amount of green space in cities, the amount of wastewater discharged by factories per person, and the percentage of land and water erosion areas, came from the “Soil and Water Conservation Bulletin of Hubei Province” (2008–2022), the “Soil and Water Conservation Bulletin of Shaanxi Province” (2008–2022), the “Soil and Water Conservation Bulletin of Shaanxi Province” (2008–2022), the “Soil and Water Conservation Bulletin of Shaanxi Province” (2008–2022), and the “Soil Fitted values. They were used to replace missing data for all historical years.

2.3. Construction of the WRCC Evaluation Index System

Water resources are intimately linked to economic, social, and ecological environments, forming a complex socioeconomic system of water resources. The water resources subsystem is the most basic of the four subsystems, but the dynamics of the economic, social, and ecological subsystems have a considerable impact on WRCC. This study provides a set of WRCC evaluation index systems for four subsystems: water resources, the economy, society, and the ecological environment. These index systems are based on relevant research and consider factors such as representativeness, comprehensiveness, scientific rigor, and data availability [4,24,25]. The specific index systems are listed in

Table 1. Evaluation system for the WRCC of major cities in the HREEB.

Criterion Layer	Index Layer	Calculation	Attribute
Water resources subsystem	X1 water resources per capita	Total water resources/Total population	+
	X2 Modulus of water production	Total water resources/Area	+
	X3 Share of surface water resources	Surface water resources/Total water resources	+
	X4 Precipitation	Statistical data	+
	X5 Water resources utilization rate	Water supply/Total water resources	-
Social subsystem	X6 Urban population density	Total urban population/Area	-
	X7 Number of students enrolled in higher education	Statistical data	+
	X8 Urbanization rate	Urban resident population/Total resident population	+
	X9 Per capita urban domestic water use	Urban domestic water use/Total urban population	+
	X10 Natural population growth rate	Statistical data	+
Economic subsystem	X11 Total retail sales of consumer goods per capita	Total retail sales of consumer goods/Total population	+
	X12 GDP per capita	Total GDP/Total regional population	+
	X13 GDP growth rate	GDP growth/Total GDP	+
	X14 Percentage of tertiary sector	Statistical data	+
	X15 Water consumption per 10,000 GDP	Water consumption/Total GDP	-
	X16 Water consumption of 10,000 yuan of industrial added value	Industrial water use/Industrial value added	-
Ecosystem subsystem	X17 Area of urban green space	Statistical data	+
	X18 Industrial wastewater discharge per capita	Industrial wastewater emissions/Population	-
	X19 Percentage of area with soil erosion	Soil erosion area/Land area	-
	X20 Ecosystem water use rate	Ecosystem water use/Total water resources	-
	X21 Centralized urban sewage treatment rate	Statistical data	+
	X22 Sulfur dioxide emissions per capita	Sulfur dioxide emissions/Total population	-
	X23 Forest cover	Statistical data	+

.

3. Methods

3.1. RAGA-PP

3.1.1. Projection Pursuit

Projection Pursuit (PP) modeling is a multivariate data analysis method for discovering structural features and patterns in data [26]. The idea of the operation is to project high-dimensional data into a low-dimensional subspace using random or deterministic means to find the structural features of the data in that subspace [27]. The concept involves transforming intricate multi-dimensional data into a lower-dimensional or one-dimensional subset. The calculation steps are as follows.

Step 1. Normalization

Let $x \times (i,j)\{i=\mathrm{1,2},\dots ,n;j=\mathrm{1,2},\dots ,p\}$, be the sample value for each indicator, where $n$ and $p$ are the sample capacity and the number of indicators, respectively. To eliminate the scale of each indicator value, the data must be normalized.

$$x\left(i,j\right)={\displaystyle \frac{x \times \left(i,j\right)-x_{\min \left(j\right)}}{x_{\max \left(j\right){-x}_{\min \left(j\right)}}}}$$

(1)

$$x\left(i,j\right)={\displaystyle \frac{x_{\max \left(j\right)}-x \times \left(i,j\right)}{{x_{\max \left(j\right)}-x}_{\min \left(j\right)}}}$$

(2)

In the formula, $x_{\max \left(j\right)}$ and $x_{\min \left(j\right)}$ represent the maximum and minimum values of the indicator, respectively, and $x(i,j)$ represents the normalized eigenvalue sequence of the indicator.

Step 2. Set the projection function $Q\left(a\right)$

The PP model transforms p-dimensional data $x \times (i,j)\{j=\mathrm{1,2},\dots ,p\}$ into a one-dimensional projected value$z\left(i\right)$of $a=\left\{a\right(1),a(2),\dots ,a(p\left)\right\}$.

$$z\left(i\right)=\sum _{j=1}^{p}a\left(j\right)x\left(i,j\right),(i=\mathrm{1,2},\dots ,n)$$

(3)

$$Q\left(a\right)=S_z{D}_z$$

(4)

$$S_z=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{\left(z\left(i\right)-E\left(z\right)\right)}^2}{n=1}}}$$

(5)

$$D_z=\sum _{i=1}^n\sum _{j=1}^n{\left(R-r\left(i,j\right)\right)}^{\ast }u\left(R-r\left(i,j\right)\right)$$

(6)

where $a$ is the unit-length vector. $S_z$ is the standard deviation of $z\left(i\right)$,$D_z$ is the local density of the projected value $z\left(i\right)$, and $E\left(z\right)$ is the mean value of $z\left(i\right)(i=\mathrm{1,2},\dots ,n)$. $R$ is the window radius of the localized density, and $R$ is taken to be 0.1, according to previous studies [28]. $r\left(i,j\right)$ denotes the distance between samples, $r\left(i,j\right)=\left|z\left(i\right)-z\left(j\right)\right|$. $U\left(t\right)$ is a unit step function when $t\ge 0$, $u\left(t\right)$ is 1, and when $t<0$, $u\left(t\right)$ is 0.

Step 3. Set the maximum projection function

For a given set of samples, the projection indicator function $Q\left(a\right)$ varies only with the projection direction $a$.

The objective function is maximized:

$$Max:Q\left(a\right)=S_z{D}_z$$

(7)

Restrictive condition:

$$s.t.\sum _{j=1}^p{a}^2\left(j\right)=1$$

(8)

Step 4 Calculate the index

After substituting the best projection direction $a^{\ast }$ into formula (3), the projection value $z^{\ast }\left(i\right)$ of each sample point is obtained. The $z^{\ast }\left(i\right)$ value is the calculated index value of the index, which can be further analyzed according to the results of the calculation of the sample.

3.1.2. Real Coded Accelerating Genetic Algorithm (RAGA)

The RAGA is an adaptive global optimization probabilistic search technique designed to solve complex nonlinear combinatorial and multi-objective function optimization problems [29]. After building the projection tracing model, the projection objective function was optimized to compute its features using the projection tracing model via the following computational steps:

Step 1. Initial parent group

By setting the size of the parent population $n$, $n$ randomly on the interval [0, 1] to generate n groups of random numbers, where each group contains p values, groups $x\left(i,j\right)$ are introduced into Equation (9) to obtain the corresponding objective function values.

$$\left\{x\left(j,i\right)|j=\mathrm{1,2},3\dots p,i=\mathrm{1,2},3\cdot \cdot \cdot n\right\}$$

(9)

Step 2. Selection of fitness function values

A fitness function was created to determine the quality of each participant’s answers. The fitness function can be either an objective function itself or a function that has been modified to the value of the objective function. Substituting each set of values from the initial parent population into the fitness function returns the appropriate function value $f\left(i\right)$, which is inversely proportional to the fitness of the individual.

$$F\left(i\right)={\displaystyle \frac{1}{f^2\left(i\right)+0.001}},i=\mathrm{1,2},3\cdot \cdot \cdot n$$

(10)

Step 3. Choice probability

Individuals from the population were selected for reproduction based on their fitness values. Each individual’s fitness function determines their likelihood of being chosen.

$$P\left(i\right)={\displaystyle \frac{F\left(i\right)}{\sum _{i=1}^{n}F\left(i\right)}}={\displaystyle \frac{\frac{1}{f^2\left(i\right)+0.001}}{\sum _{i=1}^n\frac{1}{f^2\left(i\right)+0.001}}}$$

(11)

Step 4. Hybrid species

Using $y_1^{\prime }\left(i,j\right),y_2^{\prime }\left(i,j\right)\dots$to denote the selected parent, they are randomly paired to obtain $(y_1^{\prime }\left(i,j\right),y_2^{\prime }\left(i,j\right))$. The arithmetic crossover method is then used to obtain two offspring$X$and$Y$:

$$\left\{\begin{array}{c}X=c · y_1^{\prime }\left(i,j\right)+\left(1-c\right)\times y_2^{\prime }\left(i,j\right)\\ Y=\left(1-c\right)\times y_1^{\prime }\left(i,j\right)+c · y_2^{\prime }\left(i,j\right)\end{array}\right.$$

(12)

The second-generation group is $\left\{y_2\right(i,j\left)\right|\left(j=\mathrm{1,2},\dots ,p;i=\mathrm{1,2},\dots ,n\right)\}$.

Step 5. Variation

The mutation operator is used to change the genes of progeny individuals, thereby increasing population variety. In n-dimensional space, the direction of variation is freely chosen. Equation:

$$y_3^{\prime }\left(i,j\right),+Kd,i=\mathrm{1,2},\dots ,p$$

(13)

In this formula, the range of $K$ is (0, 1), regardless of the value of $K$, and $y_3^{\prime }\left(i,j\right)$ is always replaced with $X=y_3^{\prime }\left(i,j\right)+Kd$. This operation is repeated to obtain the third-generation population ${ y}_3^{\prime }\left(i,j\right)|\left(j=\mathrm{1,2},\dots ,p;i=\mathrm{1,2},\dots ,n\right)$.

Step 6. Iteration

The third generation of population ${ y}_3^{\prime }\left(i,j\right)|\left(j=\mathrm{1,2},\dots ,p;i=\mathrm{1,2},\dots ,n\right)$ is sorted, and the (n-k) individuals are moved to the next evolutionary iteration to establish the fitness function, hybridization, mutation, and other processes that will be repeated.

Step 7. Accelerate

The number of accelerations was set, and Steps 1–6 were repeated until the optimal projection evaluation value was obtained.

3.1.3. Natural Breakpoint Categorization (NBC)

Natural breakpoint categorization (NBC) is a univariate cluster analysis classification method proposed by the U.S. Environmental Systems Research Institute. This is a method of classification and division based on the intrinsic distributional characteristics of the data, and its basic idea is to classify similar values into the same group to minimize the internal differences within each group and maximize the numerical differences between different groups [30]. This was accomplished by separating the data into multiple categories and placing borders at points where there were significant variances in the data values.

Step 1: The total sum of squared deviations (SDHN) is computed for an array of a particular class in the classification results, and a set of results is denoted as HI, with a mean value.

$$SDHN=\sum _{i=1}^n{\left(X_i-\overline{x}\right)}^2$$

(14)

where $n$ is the number of elements in the array.

Step 2: The sum of squares of the total deviation of the class (SDFN) is calculated for the combination of each range in the classification results, and the smallest value is obtained and denoted as ${\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_{min}$. The dataset consisting of $N$ elements is divided into $q$ different classes, which in turn gives $q$ different subsets. The total deviation sum of squares for each subset ${\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_i$,${\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_j$,...,${\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_n$, and sum ${\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_1$ is computed as follows:

$${\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_1={\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_i+{\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_j+\cdot \cdot \cdot +{\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_n$$

(15)

Similarly, it is possible to divide the classification result into other cases containing different subsets and compute the values of ${\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_2,\dots ,{SDFN}_c^{k_n}$ respectively. By comparing the sum of squares of all the total deviations and selecting the smallest one as the final ${\mathrm{S}\mathrm{D}\mathrm{F}\mathrm{N}}_{min}$, the class thus obtained is the best classification, and the WRCC level is graded by the natural suspended method so that the WRCC level can be evaluated in a more intuitive way.

3.1.4. RAGA-PP WRCC Evaluation Model

In this study, a WRCC evaluation model was constructed based on the RAGA-PP by adopting an improved genetic algorithm to optimally determine the best projection of the projection tracing model. The process of constructing the RAGA-PP is illustrated in Figure 3.

3.2. Three Comparative Models

3.2.1. Rank Sum Ratio (RSR)

The RSR method comprehensively evaluates each evaluation object by transforming multiple evaluation indicators into dimensionless rank and rank ratio values [31]. According to previous studies [32], the specific steps include determining the set of alternatives, identifying the decision criteria, assigning weights to the criteria, scoring the performance of the criteria, calculating the rank sum, calculating the ratio, calculating the weighted RSR to the total score, and ranking the options. Specific formulae are not described here.

3.2.2. Entropy Weight TOPSIS

The entropy weight TOPSIS method is a commonly used multi-criteria decision-making method [33]. The entropy weight method was applied to determine the weights of each criterion, and the TOPSIS method was introduced to rank the alternatives based on these weights. Based on previous studies [34], the specific steps include determining the set of alternatives, constructing the decision matrix, standardizing the data, calculating the entropy value of the criterion, determining the weights of the criterion, calculating the weighted standardized decision matrix, calculating the relative proximity, and ranking the options. Specific formula algorithms are not described here.

3.2.3. Principal Component Analysis (PCA)

PCA is a widely used statistical method in the fields of data dimensionality reduction, feature extraction, data visualization, and data preprocessing [35]. With reference to previous studies [36], the specific steps included determining the data normalization, calculating the covariance matrix, solving the eigenvalues, selecting the principal components, downscaling, and interpreting the results. Specific formula algorithms are not described here.

3.3. Discrimination

Discrimination refers to the ability of a model to distinguish correctly between individuals or objects of different classes or states [37]. Differentiation was originally an examination concept that referred to the ability of a paper’s test questions to identify the examinee’s level of knowledge and ability. For each evaluation result, assuming there are m evaluation objects, they are ranked in descending order of their score Z. Each score is then assigned the serial number K, $1\le i\le m$. The best-evaluated coordinate value is $(Z_1,1)$, and the worst-value coordinate is $(Z_m,1)$. The differentiation formula is as follows:

$$D={\displaystyle \frac{{\displaystyle \sum _{i=1}^{m-1}}\sqrt{{\left(Z_{i+1}-Z_i\right)}^2+{\left(K_{i+1}-K_i\right)}^2}}{\sqrt{{\left(Z_m-Z_1\right)}^2+{\left(K_m-K_1\right)}^2}}}$$

(16)

In the formula $D$ ≥ 1, the larger the value of $D$, the more dispersed the two neighboring points, and the better the differentiation of the evaluation results. The better the degree of differentiation, the greater the reliability of the evaluation results, and the more stable the evaluation.

Because the results of the various evaluation methods have different ranges of extreme values, they must be standardized to be comparable. In this study, the standardized processed point value was set between 0 and m. The coordinates of the maximum value point are (m, 1), the coordinates of the minimum value point are (0, m), and the standardized value of a point in the middle is processed according to the equal proportion of the difference between the original and maximum values. The formula is

$$Z_i=m\times \left(1-{\displaystyle \frac{\left|Z_{i^{\prime }}-Z_{i^{\prime }}\right|}{Z_{1^{\prime }}-Z_{m^{\prime }}}}\right)$$

(17)

where $Z^{\prime }$ is the original indicator value and $Z_i$ is the standardized indicator value.

After standardizing the underlying data, the calculation of the degree of differentiation can be simplified as follows.

$$D={\displaystyle \frac{{\displaystyle \sum _{i=1}^{m-1}}\sqrt{{\left(Z_{i+1}-Z_i\right)}^2+1^2}}{\sqrt{(m-0{)}^2+(m-1{)}^2}}}$$

(18)

3.4. Obstacle Degree Model (ODM)

The ODM was applied to quantify the degree of obstruction that affected the improvement in the WRCC of the HREEB. The factors influencing regional WRCC enhancement were analyzed by determining the severity of the influencing factors according to the extent of the barrier [38].

Step 1: Determine the factor contribution $F_{ij}$

$$F_{ij}=z^{\ast }\left(i\right)$$

(19)

Step 2: Calculation of the deviation $I_{ij}$ for each indicator for each year

$$I_{ij}=1-X_{ij}$$

(20)

In the formula, $X_{ij}$ is the value normalized for each indicator.

Step 3: Calculation of the degree of impediment

$$Q_{ij}={\displaystyle \frac{F_j{I}_{ij}}{\sum _j{F}_j{I}_{ij}}}\times 100\%$$

(21)

4. Results

4.1. Results of the Four Evaluation Models

4.1.1. Results of the Rank Sum Ratio Method

A sample of 23 indicators from 17 cities for 2019–2022 WRCC was used, and the probit value obtained using the RSR analysis method was applied as the WRCC assessment value for each city (

Table 2. Probit values for municipalities in the HREEB, 2019–2022.

2019	Probit	2020	Probit	2021	Probit	2022	Probit
Shennongjia	7.178	Shiyan	7.154	Shiyan	7.178	Shennongjia	7.178
Wuhan	6.565	Shennongjia	6.534	Shennongjia	6.565	Wuhan	6.565
Hanzhong	6.187	Wuhan	6.150	Wuhan	6.187	Shiyan	6.187
Ankang	5.929	Xiantao	5.887	Ankang	5.929	Xiantao	5.929
Shiyan	5.722	Suizhou	5.674	Xiangyang	5.722	Tianmen	5.722
Xiantao	5.541	Ankang	5.489	Xiantao	5.541	Ankang	5.541
Qianjiang	5.377	Xiangyang	5.319	Hanzhong	5.377	Hanzhong	5.377
Xiangyang	5.223	Jingmen	5.157	Luoyang	5.223	Qianjiang	5.223
Suizhou	5.074	Hanzhong	5.000	Tianmen	5.087	Suizhou	5.074
Shangluo	4.926	Qianjiang	4.999	Suizhou	5.074	Xiangyang	4.926
Zhumadian	4.885	Luoyang	4.843	Shangluo	4.926	Nanyang	4.786
Sanmenxia	4.777	Xiaogan	4.681	Jingmen	4.777	Jingmen	4.777
Jingmen	4.623	Tianmen	4.511	Nanyang	4.623	Luoyang	4.685
Tianmen	4.459	Nanyang	4.326	Sanmenxia	4.459	Hanzhong	4.623
Luoyang	4.278	Shangluo	4.113	Zhumadian	4.433	Shangluo	4.459
Xiaogan	3.813	Sanmenxia	3.850	Qianjiang	4.278	Sanmenxia	4.278
Nanyang	3.775	Zhumadian	3.745	Xiaogan	4.071	Zhumadian	3.813

).

4.1.2. Results of the Entropy Weight TOPSIS Method

The weights obtained from the entropy weight TOPSIS method were applied as the WRCC evaluation values for each municipality using 23 indicators from 17 municipalities in the 2019–2022 HREEB as a sample (

Table 3. Weights of the municipalities in the HREEB, 2019–2022.

2019	Weights	2020	Weights	2021	Weights	2022	Weights
Shennongjia	0.1353	Shennongjia	0.1347	Shennongjia	0.1432	Shennongjia	0.1285
Wuhan	0.0914	Wuhan	0.0948	Wuhan	0.0976	Wuhan	0.0951
Hanzhong	0.0773	Xiantao	0.0703	Xiantao	0.0642	Xiantao	0.0653
Ankang	0.0705	Shiyan	0.0583	Shiyan	0.0598	Tianmen	0.0602
Xiantao	0.0647	Zhumadian	0.0574	Ankang	0.0562	Hanzhong	0.0572
Shiyan	0.0571	Ankang	0.052	Luoyang	0.0538	Ankang	0.0567
Shangluo	0.0545	Suizhou	0.0518	Nanyang	0.0536	Shiyan	0.0566
Qianjiang	0.0536	Tianmen	0.0508	Shangluo	0.0534	Shangluo	0.0536
Suizhou	0.0489	Qianjiang	0.0504	Hanzhong	0.0524	Nanyang	0.0514
Tianmen	0.0481	Xiangyang	0.0503	Zhumadian	0.0511	Luoyang	0.0513
Xiangyang	0.0473	Shangluo	0.05	Xiangyang	0.0503	Zhumadian	0.0513
Sanmenxia	0.0446	Hanzhong	0.0489	Sanmenxia	0.0489	Sanmenxia	0.0499
Zhumadian	0.0441	Nanyang	0.0485	Suizhou	0.0479	Qianjiang	0.0492
Nanyang	0.0422	Luoyang	0.0484	Qianjiang	0.0473	Suizhou	0.049
Luoyang	0.0421	Sanmenxia	0.0474	Tianmen	0.0454	Xiangyang	0.0466
Jingmen	0.042	Jingmen	0.0459	Jingmen	0.0421	Jingmen	0.0431
Xiaogan	0.0363	Xiaogan	0.0402	Xiaogan	0.0328	Xiaogan	0.0348

).

4.1.3. Results of Principal Component Analysis

A sample of 23 indicators from 17 cities in the 2019–2022 HREEB was used, and the composite scores obtained via principal component analysis were used as the WRCC rating values for each city (

Table 4. Combined score of the WRCC for municipalities in the HREEB, 2019–2022.

2019	Scores	2020	Scores	2021	Scores	2022	Scores
Shennongjia	1.483	Wuhan	1.454	Wuhan	1.362	Wuhan	1.292
Hanzhong	0.379	Shennongjia	0.469	Qianjiang	0.370	Tianmen	0.598
Wuhan	0.337	Xiaogan	0.215	Tianmen	0.348	Qianjiang	0.275
Ankang	0.306	Xiangyang	0.116	Xiaogan	0.256	Luoyang	0.180
Shiyan	0.242	Shangluo	0.103	Jingmen	0.244	Xiaogan	0.167
Shangluo	0.171	Shiyan	0.010	Xiangyang	0.206	Jingmen	0.084
Luoyang	−0.061	Xiantao	−0.030	Luoyang	0.182	Nanyang	0.056
Nanyang	−0.094	Luoyang	−0.055	Nanyang	0.131	Xiangyang	0.026
Zhumadian	−0.095	Qianjiang	−0.066	Xiantao	0.026	Shiyan	0.021
Sanmenxia	−0.100	Tianmen	−0.082	Suizhou	−0.116	Shangluo	0.002
Suizhou	−0.155	Suizhou	−0.144	Shiyan	−0.169	Suizhou	−0.079
Xiaogan	−0.166	Nanyang	−0.200	Hanzhong	−0.190	Shennongjia	−0.117
Tianmen	−0.171	Hanzhong	−0.217	Shangluo	−0.224	Sanmenxia	−0.249
Xiantao	−0.175	Ankang	−0.225	Shennongjia	−0.338	Xiantao	−0.278
Jingmen	−0.250	Jingmen	−0.325	Sanmenxia	−0.401	Ankang	−0.401
Xiangyang	−0.299	Sanmenxia	−0.429	Ankang	−0.417	Hanzhong	−0.459
Qianjiang	−0.421	Zhumadian	−0.446	Zhumadian	−0.471	Zhumadian	−0.522

).

4.1.4. Results of the RAGA-PP Calculations

The projected eigenvalues obtained from RAGA-PP were used as the WRCC assessment values for each city, using 23 indicators from 17 cities in the HREEB from 2019 to 2022 as samples (

Table 5. Projected eigenvalues of the municipalities in the HREEB, 2019–2022.

2019	Eigenvalues	2020	Eigenvalues	2021	Eigenvalues	2022	Eigenvalues
Shennongjia	3.1564	Wuhan	3.1458	Shennongjia	3.3821	Shennongjia	3.6287
Wuhan	2.8231	Shennongjia	3.013	Wuhan	3.2296	Wuhan	2.6868
Hanzhong	2.5346	Shiyan	2.2639	Shiyan	2.6885	Shiyan	2.5848
Ankang	2.4822	Xiantao	1.9664	Ankang	2.2908	Xiantao	2.3927
Shiyan	2.4002	Xiangyang	1.8712	Hanzhong	2.1405	Ankang	2.3887
Xiantao	2.4002	Suizhou	1.8683	Xiantao	2.128	Hanzhong	2.3089
Qianjiang	2.0107	Qianjiang	1.8525	Xiangyang	2.121	Suizhou	2.2934
Suizhou	1.9181	Ankang	1.8251	Luoyang	1.8769	Qianjiang	2.2568
Jingmen	1.8219	Xiaogan	1.6183	Suizhou	1.8765	Jingmen	1.9313
Xiangyang	1.8215	Jingmen	1.6183	Shangluo	1.8759	Zhumadian	1.9237
Xiaogan	1.8215	Tianmen	1.6183	Nanyang	1.78569	Tianmen	1.9233
Tianmen	1.8215	Hanzhong	1.6183	Jingmen	1.6877	Shangluo	1.9233
Shangluo	1.8215	Shangluo	1.6183	Xiaogan	1.6875	Xiangyang	1.9232
Sanmenxia	1.5469	Luoyang	1.6183	Qianjiang	1.6875	Sanmenxia	1.9231
Zhumadian	1.3615	Zhumadian	1.6183	Sanmenxia	1.6875	Xiaogan	1.9229
Luoyang	1.3611	Sanmenxia	1.6174	Zhumadian	1.6875	Nanyang	1.914583
Nanyang	1.355423	Nanyang	1.612568	Tianmen	1.1582	Luoyang	1.668

).

4.2. Comparative Analysis of Model Reliability

To show the evaluation effect of each model more clearly, we carried out four statistical analyses, namely, evaluation index weight allocation, model differentiation, sensitivity analysis, and computational complexity analysis, and obtained the corresponding results, as shown in

Table 6. Statistical analysis table.

Model	Discrimination (D)	Weight Allocation Uniformity	Data Sensitivity	Computational Complexity
RAGA-PP	1.234	High	Low	Medium
Entropy TOPSIS	1.120	Medium	Medium-High	Low
RSR	1.095	Low	High	Low
PCA	1.114	Medium	Medium	Medium

.

The assignment of evaluation indicator weights is an analysis of the differences in the determination of weights across the models and the impact of these weights on the WRCC’s final assessment results. The degree of differentiation is an important indicator of the stability of different evaluation methods and can be used to assess the reliability of a particular evaluation method [39]. The differentiation of the models was calculated and compared to assess their effectiveness in differentiating between the different levels of carrying capacity. We assessed the WRCC of 17 major cities in the HREEB from 2008 to 2022 and calculated the discrimination of each method. Discrimination was measured by the ratio of the distances between adjacent points in the model results; the larger the value, the stronger the ability of the model to differentiate.

Sensitivity analysis involves making small changes to the input data and observing the changes in the model’s output to assess its sensitivity to data variations [40]. We changed the indicator data by ±5% and found that the output results of the RAGA-PP model changed by less than 3%, indicating good stability. Under the same data changes, the output results of the Entropy Weight TOPSIS model changed by 5–10%, indicating a higher sensitivity to data changes. These two methods also showed higher sensitivity to data changes, with output results changing by 8–15%.

In terms of model advantages, the RAGA-PP model can effectively handle high-dimensional data, reveal the structural characteristics of the data by optimizing the projection direction, and is suitable for complex water resource assessment. RAGA-PP is more stable and accurate, as shown in the sensitivity analysis, and is insensitive to minor data changes, ensuring the stability and accuracy of the assessment results. Although the computational complexity is moderate, the application of the accelerated genetic algorithm enables RAGA-PP to quickly find the optimal solution and improve computational efficiency. The other models have limitations. Although the entropy weight TOPSIS has a certain degree of objectivity in weight allocation, it is more sensitive to data changes, which may lead to unstable assessment results. Although RSR is simple to compute, it exhibits low differentiation and stability when dealing with complex high-dimensional data. PCA may lose important information in the dimensionality reduction process, which affects the accuracy of the assessment.

Based on the above analysis, the RAGA-PP model has shown excellent performance in terms of discrimination, stability, accuracy, and computational efficiency, particularly in handling complex water resource carrying capacity assessments. The advantages of this method are evident. The RAGA-PP model is capable of handling high-dimensional nonlinear problems and can be optimized multiple times through an accelerated genetic algorithm, allowing for a more scientific analysis of WRCC levels with strong stability and accuracy.

4.3. Analysis of Temporal and Spatial Changes in the WRCC

4.3.1. WRCC Time Series Analysis

In this study, RAGA-PP was implemented using the MATLAB R2022b software. According to prior research [41], in the process of accelerated genetic calculation, the initial population size of the parent is 400, crossover probability PC = 0.8, mutation probability PM = 0.8, number of excellences is 10, and number of accelerations is 20. Between 2008 and 2022, 23 indicators from 17 cities in HREEB were used as samples. The genetic-based projection tracing model’s best projection direction was used as the weight for each indicator to determine the projection value and, finally, the evaluation value of each city’s WRCC, as shown in Figure 4. Using the NBC described above and in conjunction with previous studies, WRCC was classified into five categories: I (not carrying), II (weakly not carrying), III (weakly carrying), IV (carrying), and V (ideal state).

Figure 4 shows that the aggregate WRCC of cities in the HREEB remained steady between 2008 and 2022. In 2008, the ideal projected eigenvalues of cities in the HREEB ranged from 1.0804 to 3.3341, with Luoyang having the lowest and Shennongjia having the highest values. The WRCC in Sanmenxia is less than half that of the Shennongjia forest area and is classified as Type I non-Carrying. Luoyang and Sanmenxia are similar in the I non-Carrying interval, while Shangluo, Zhumadian, and Nanyang are in the II weak non-Carrying interval, with significant differences in the WRCC across cities. In 2012, HREEB had a range of projected eigenvalues between 1.4702 and 3.4646. Zhumadian had the lowest eigenvalue, whereas Shennongjia had the highest. Additionally, the WRCC of Zhumadian Reservoir was less than half that of Shennongjia Reservoir. In that year, except for Zhumadian, Xiaogan, Jingmen, and Tianmen, whose WRCC declined, and Nanyang, Shennongjia, Qianjiang, and Xiangyang, whose WRCC remained at the weak-carrying level of III, the WRCC levels of the remaining six cities increased. In 2016, the range of the best projected eigenvalues for the cities in the HREEB was [1.4496, 2.9155], with Xiangyang, Sanmenxia, and Zhumadian having the lowest values, and Shennongjia having the highest. Sanmenxia’s WRCC remained within the I non-Carrying interval, while Xiangyang City, Xiaogan, Tianmen, Shangluo, and Zhumadian’s WRCC were reduced to the I non-Carrying interval. Xiantao and Qianjiang were elevated to the III weak carrying interval, and Wuhan and Shennongjia’s WRCC were in the V ideal state interval. In 2020, the range of the best anticipated eigenvalues of the cities in HREEB was [1.310215, 3.1458], with Nanyang having the lowest and Wuhan having the highest. That year, Wuhan and Shennongjia had water resource carrying capacity ratings in the V ideal state interval, whereas Xiangyang, Xiantao, Qianjiang, Suizhou, and Ankang were in the III weak-carrying interval, with the remaining eight cities in the II weak-carrying interval. In 2022, the optimal projected eigenvalues of the cities in the HREEB will range from 1.125476 to 3.6287, with Shennongjia having the highest and Nanyang having the lowest. The WRCC in Shiyan and Wuhan had an IV-level capability for carrying intervals, while Xiantao, Qianjiang, and Suizhou had a weak III-level capability for carrying intervals. The remaining eight cities had a weak capability level II and were unable to carry intervals. In summary, the WRCC of cities in the HREEB region from 2008 to 2022 indicates an overall shifting tendency in the time series, and the difference between the cities is narrowing, with Sanmenxia being relatively poor and Shennongjia excelling.

4.3.2. Analysis of the Spatial Evolution of the WRCC

Using the NBC described above, ArcGIS 10.4 software was used to spatially visualize the water resource carrying capacity levels of each city in the HREEB and to analyze the distribution and change characteristics of the WRCC of each city in the temporal and spatial dimensions (Figure 5).

Spatially, the WRCC of the ten cities in the Hubei section of the HREEB as a whole shows a basic pattern of excellent WRCC in the east and west and poor WRCC in the middle. The WRCC of the three cities in the Shaanxi section is generally favorable, at levels III and IV, and the WRCC of the four cities in the Henan section is relatively poor.

The HREEB of the city’s Hubei sector has great spatial heterogeneity, with Shennongjia and Wuhan having the highest WRCC levels, which is essentially within the optimum state interval. In Shiyan and Xiantao, the WRCC primarily relies on the primary capacity; similarly, in Suizhou, Xiangyang, Qianjiang, and other municipalities, the WRCC primarily relies on the major weak capacity. The three cities with the lowest WRCC were Xiaogan, Jingmen, and Tianmen, all of which were in a weak noncarrying state. The terrain of western Hubei Province is dominated by mountains at middle and high altitudes, with high forest coverage, average annual precipitation of more than 1100 mm, abundant water resources, low population density, and less ecological damage caused by socioeconomic activities, which strengthens WRCC [42]. The water resources in the central part of the Hubei section of the HREEB were relatively limited compared with those in the rest of the province.

Although Luoyang outperformed the other three cities in the Henan sector, the WRCC in the Henan region was generally poor. In addition to the high urban population and water stress, there is limited rainfall and regional surface water resources in the Henan region. Furthermore, the socioeconomic sector and water resources are not well linked [43]. The key factors contributing to the overall excellent conditions of the three cities in the Shaanxi sector of the HREEB are the abundance of water resources and adequate precipitation. In 2016, the per capita water consumption in Hanzhong in the Han River basin reached 476.7 m³·person⁻¹, which was twice as high as the provincial per capita water consumption of CNY 10,000 of GDP water consumption, which was as high as 142.0 m³·million yuan⁻¹, three times greater than the provincial average, and the per capita water consumption in the basin, water consumption of CNY 10,000 of GDP, and the acreage water consumption of irrigated farmland were all greater than average.

4.4. Analysis of the Carrying Capacity of Subsystems in the HREEB

4.4.1. Analysis of the Carrying Capacity of Water Resource Subsystems

To capture the water resources subsystem carrying capacity (WRSCC) of the HREEB from 2008 to 2022, the RAGA-PP was applied to calculate the WRSCC of each city and classify it using the NBC. ArcGIS was employed to visualize the spatial representation and study the distribution and change in the WRSCC in time series and space in each city, as shown in Figure 6. I (not carrying), II (weakly not carrying), III (weakly carrying), IV (carrying), and V (ideal state).

According to Figure 6, the WRSCC of each city in the Han River ecological and economic belt shows fluctuating changes in the time series from 2008 to 2022. In 2008, the water resources subsystem index in the HREEB ranged from [0.148 to 0.362], with the lowest in Luoyang and the highest in Jingmen; the water resources subsystem of Luoyang was less than half of that of Jingmen. Ankang, Hanzhong, Shennongjia, and five cities in central Hubei Province, WRSCC in IV or V, four cities in Henan Province, WRSCC poor, and I or II can be seen in the HREEB across the municipalities of WRSCC with a larger gap. In 2012, the WRSCC index in the HREEB ranged from [0.124 to 0.449], with Suizhou being the lowest and Shennongjia being the highest, whereas that of Suizhou was less than 1/3 of that of Shennongjia. The carrying capacity of the central city in the Hubei section and that of Nanyang and Luoyang in the Henan section were worse and were in the range of I or II. In the Henan section, the results for Sanmenxia and Nanyang were better than those of previous years at III. In 2016, the WRSCC in the HREEB ranged from [0.121 to 0.411], with Sanmenxia being the lowest and Shennongjia being the highest, while the WRSCC of Sanmenxia was less than 1/3 of that of Shennongjia. The four cities in the Henan section and Xiangyang had a poorer carrying capacity of I or II, and the eastern part of the Hubei section and Shennongjia had a better carrying capacity of IV or V. In 2022, the WRSCC in the HREEB ranges from [0.145, 0.541], with Luoyang at the lowest, Shennongjia at the highest, and the carrying capacity levels of the three cities in the Shaanxi section, Shiyan, and Shennongjia in the western part of the Hubei section are still relatively good, all at IV or V. Henan 4 cities and Xiangyang carrying capacity level are poor. The carrying capacity of the cities in the eastern part of the Hubei section declined and was in III.

4.4.2. Carrying Capacity Analysis of Social Subsystems

To study the carrying capacity of the water resource subsystems in the HREEB from 2008 to 2022, the RAGA-PP model was applied to calculate the social subsystem carrying capacity (SUCC) in each city. ArcGIS was used to visualize the results of the evaluation, and the distribution and change characteristics of SUCC in the time series and spatial dimensions were investigated for each city (Figure 7).

Figure 7 shows that the SUCC of the cities in the HREEB in the time series from 2008 to 2022 fluctuated and changed overall, and the carrying capacity of the social subsystems further enhanced water resources in the HREEB. In 2008, the social subsystem indices of the cities in the HREEB ranged from [0.131 to 0.257], with Xiantao having the lowest and Shennongjia the highest. The SUCC of the four cities in the Henan section and the cities in the central part of the Hubei section were poor at level I. The SUCC of the three cities in the Shaanxi section, the western part of the Hubei section, and the city of Wuhan are better, all of which are IV or V. In 2012, the SUCC of the cities in the HREEB ranged from [0.158, 0.504], with the lowest in Tianmen city and the highest in Shennongjia, and the SUCC of Tianmen city was less than 1/3 of that of Shennongjia city. Except for Tianmen City and Qianjiang City, the SUCC of the other cities were all at Level III or above. Shennongjia and Xiantao had the best SUCC, reaching Level V. In 2016, the SUCC of cities in the HREEB ranged from [0.166 to 0.451], with Jingmen having the lowest and Shennongjia having the highest. Tianmen and Qianjiang showed an overall increase in SUCC level of III. The SUCC in the three cities of Shaanxi, Shiyan, Shennongjia, and Wuhan reached IV or V. Jingmen and Xiaogan had poor levels of SUCC: only I. In 2022, the SUCC of municipalities in the HREEB will range from [0.165 to 0.361], with Jingmen being the lowest and Shennongjia being the highest. Overall, the SUCC of each city improved, and the SUCC of Tianmen and Qianjiang remained poor only at level I. The SUCC of Hanzhong declined from Level V to Level III, and the remaining two cities in Shaanxi had better SUCC, all of which were Level IV or V.

To summarize, the SUCC of cities in the HREEB fluctuated during the period–2008–2022. The SUCC levels of the three cities in the Shaanxi section, the western part of the Henan section, the western part of the Hubei section, and the eastern part of the Han River are high, while the SUCC levels of Xiaogan and Jingmen are poor.

4.4.3. Carrying Capacity Analysis of Economic Subsystems

To obtain a detailed understanding of the economic subsystem carrying capacity (ESCC) of each city in the HREEB from 2008 to 2022, the RAGA-PP model was used to calculate the ESCC of each city, and ArcGIS was used to express the evaluation results in a spatial visualization to analyze more intuitively the distribution and change characteristics of the SUCC of each city in the time series and spatial dimensions, as shown in Figure 8.

In 2008, the range of ESCC indices of cities in the BREEB was [0.152 and 0.228], with Shennongjia having the lowest and Luoyang having the highest, and there was little difference in the range of ESCC indices of cities. The economic subsystems of Wuhan and Luoyang are at high levels at levels V and IV, respectively, while those of Hanzhong, Shangluo, and Zhumadian are at low levels at level I. The ESCC of Wuhan and Luoyang were at high levels, at levels V and IV, respectively. In 2012, the ESCC of cities in the Han River Ecological Economic Zone ranged from [0.146 to 0.475], with the lowest in Xiaogan and the highest in Wuhan; the ESCC of Xiaogan was less than 1/2 of that of Wuhan. The ESCC of the four cities in Henan and Wuhan was higher, reaching levels V and IV, respectively. The ESCC of the three cities in Shaanxi was basically the same as that of 2008, reaching level III, while the ESCC of Tianmen and Xiaogan was poorer at only level I. The ESCC of the four cities in Henan and Wuhan was higher, reaching levels V and IV, respectively. In 2016, the ESCC of cities in HREEB ranged from [0.193 to 0.563], with Xiaogan having the lowest and Wuhan having the highest. The ESCC of Hanzhong, Shangluo, and Ankang decreased to stages I and II, respectively. Wuhan, Luoyang, and Sanmenxia had better ESCC, reaching grades V and IV. Among the cities in the central part of the Hubei section, Xiaogan and Tianmen had poorer ESCC, whereas Qianjiang and Tianmen had better ESCC. In 2022, the ESCC carrying capacity of the cities in the HREEB will range from [0.183 to 0.394], with that of Hanzhong being the lowest and that of Wuhan still being the highest. The ESCC scores of the three cities in Shaanxi decreased from III and IV to I and II. The ESCC in Sanmenxia, Luoyang, Shiyan, and Wuhan improved, reaching V. The ESCC of the central cities in the Hubei section increased, while that of Xiaogan and Tianmen increased from I to II, and that of Qianjiang and Xiantao increased from II to IV.

To summarize, the ESCC of each city in the HREEB fluctuated from 2008 to 2022. The ESCC of Wuhan, Sanmenxia, and Luoyang were high, the ESCC levels of Xiaogan and Jingmen were increased, and the ESCC of Hanzhong was poor.

4.4.4. Carrying Capacity Analysis of Ecosystem Subsystems

To understand in detail the ecological environment carrying capacity (EECC) of each city in the HREEB from 2008 to 2022, the RAGA-PP model was used to calculate the carrying capacity of the EECC of each city, and ArcGIS was used to express the spatial visualization of the evaluation results to analyze the distribution and characteristics of the changes in the carrying capacity of the EECC of each city in both the time series and spatial dimensions, as shown in Figure 9.

In 2008, the range of EECC indices of the cities in the HREEB was [0.17, 0.263], with Shennongjia having the highest EECC indices and Sanmenxia having the lowest, and the range of EECC indices varied little among the cities. Shiyan, Suizhou, and the eastern part of the Hubei section have higher levels of urban ecosystem subsystems at levels V and IV, respectively, while Sanmenxia and Luoyang are poorer at level I. The ecosystems of Shiyan, Suizhou, and the eastern part of the Hubei section had higher levels at levels V and IV, respectively. In 2012, the EECC of the cities in the HREEB region ranged from [0.133 to 0.357]; Shennongjia was still the lowest, Sanmenxia was the lowest, and the carrying capacity of the Sanmenxia subsystem was less than 1/2 of that of Shennongjia. The EECC of Wuhan and Shennongjia were better, and both were at Level V. The three cities in the Shaanxi section and the western cities in the Hubei section improved to levels III and IV. The EECC of the three cities in the Shaanxi section and the western cities in the Hubei section increased to levels III and IV, and the EECC of Sanmenxia was the worst at level I only. In 2016, the EECC of the cities in HREEB ranged from [0.155 to 0.453], with Xiaogan being the lowest and Wuhan being the highest, and the subsystem carrying capacity of Xiaogan was less than 1/2 of that of Wuhan. The subsystem carrying capacities of Wuhan, the two cities of Shaanxi, and the western part of the Hubei section were better, with levels IV and V. The EECC of Hanzhong and the western part of the Hubei section were greater than that of Wuhan, and the EECC of the western part of the Hubei section was greater. The EECC of Hanzhong decreased by one grade after 2012 and that of Nanyang improved by one grade. In 2022, the EECC of each city in the HREEB ranges from [0.264 to 0.385], with Luoyang having the lowest EECC and Shennongjia having the highest. There is little difference in the range of the EECC indices of each city. Compared with those in 2016, the EECC in Wuhan, Jingmen, and Shangluo decreased by one rank, and that in Hanzhong increased by one rank. Sanmenxia’s EECC remained poor at level I.

The EECC dynamics of cities in the HREEB varied. Wuhan and the western part of the Hubei section exhibited high EECC levels, similar to those of the three cities in the Shaanxi section. Sanmenxia and Luoyang had lower EECC.

4.5. Barrier Factor Analysis of WRCC

4.5.1. Analysis of the Obstacle Factors in the Guideline Layer of WRCC

The OBM was used to calculate the barrier degree of the water resource subsystems, social subsystems, economic subsystems, and ecological subsystems of the water resource carrying capacity of each city in the HREEB during the period 2008–2022. Four years were chosen at random to represent 2008, 2012, 2016, and 2022 (Figure 10).

As depicted in Figure 9, among the 17 cities in 2008, Xiantao, Hanzhong, Ankang, and Nanyang were subjected to greater socioeconomic subsystem impediments, with Nanyang experiencing the most pronounced constraints (35.98%). Moreover, the WRCC of the next 16 cities was the most hampered by the water resources subsystem, with Wuhan encountering the most evident constraint (38.899%). The biological environment subsystem was the second highest barrier layer of the WRCC for each municipality, with Shennongjia experiencing the most visible degree of restriction, reaching 31.42%. In comparison, the social subsystem obstacles were relatively low. In 2012, the levels of obstacles to water resources and social, economic, and ecological subsystems were relatively balanced among the cities. Hanzhong, Ankang, and Shennongjia experienced greater obstacles to the economic subsystem, with Shennongjia encountering the most apparent constraints, accounting for 32.45% of the total. Nanyang was the most constrained in the water resource subsystem (37.93%). Wuhan was clearly confined to the social subsystem, whereas Sanmenxia was severely constrained by the degree of the ecological subsystem barrier. In 2016, the number of impediments in the water resources subsystem was more evenly distributed among the municipalities, with Wuhan and Sanmenxia having slightly greater impediments. Wuhan was the most restrictive of the social subsystems, whereas Xiaogan, Tianmen, Hanzhong, and Shennongjia were restricted by more than 30% among the economic subsystems, although the ecological subsystems were significantly less restricted. In 2022, Shennongjia had a low degree of obstacles in the water resources subsystem, at 19.52%. The social subsystem did not change significantly between the cities, with Nanyang experiencing the highest level of restriction at 24.9%. Hanzhong had the most restrictions in the economic subsystem, whereas San-Menxia and Shennongjia had over 30% restrictions in the ecological environment.

4.5.2. Analysis of Obstacle Factors in the Indicator Layer of WRCC

The barrier degree of each indicator was determined using data from 2008 to 2022. The results indicate that the fluctuation in the barrier degree values of the barrier factors in the 17 cities and municipalities in the Han River ecological and economic areas was not significant from year to year. Therefore, the barrier degree was assessed and evaluated using the data from 2022, as shown in

Table 7. Main obstacles to the WRCC of cities in the HREEB in 2020.

City	Obstacle 1	Obstacle 2	Obstacle 3	Obstacle 4	Obstacle 5	Obstacle 6	Obstacle 7
Wuhan	X1	X6	X10	X14	X11	X22	X23
	0.0815	0.0556	0.0551	0.0564	0.0546	0.0649	0.0527
Xiang yang	X1	X3	X9	X14	X13	X11	X22
	0.0761	0.0486	0.0495	0.0597	0.0516	0.0581	0.0595
Shi yan	X1	X3	X14	X10	X13	X11	X22
	0.0759	0.0494	0.0608	0.0491	0.0530	0.0589	0.0607
Xiao gan	X1	X3	X14	X10	X13	X11	X22
	0.0759	0.0494	0.0608	0.0491	0.0530	0.0589	0.0607
Jing men	X1	X3	X14	X9	X13	X11	X22
	0.0736	0.0475	0.0584	0.0521	0.0503	0.0576	0.0652
Xian tao	X1	X3	X14	X9	X13	X11	X22
	0.0788	0.0509	0.0625	0.0532	0.0560	0.0633	0.0593
Tian men	X1	X5	X6	X14	X11	X22	X23
	0.0754	0.0514	0.0555	0.0608	0.0588	0.0560	0.0513
Qian jiang	X1	X5	X6	X14	X11	X20	X22
	0.0760	0.0507	0.0555	0.0607	0.0595	0.0518	0.0567
Sui zhou	X1	X3	X14	X10	X13	X11	X22
	0.0765	0.0481	0.0625	0.0478	0.0508	0.0607	0.0571
Shen Nongjia	X3	X14	X11	X13	X11	X16	X22
	0.0566	0.0626	0.0504	0.0567	0.0607	0.0541	0.0703
Han zhong	X1	X3	X14	X13	X11	X16	X22
	0.0688	0.0493	0.0638	0.0521	0.0620	0.0511	0.0635
An kang	X1	X3	X14	X13	X14	X16	X22
	0.0730	0.0492	0.0632	0.0524	0.0615	0.0487	0.0594
Shang luo	X1	X3	X14	X11	X13	X11	X22
	0.0738	0.0477	0.0605	0.0480	0.0552	0.0588	0.0820
Luo yang	X1	X6	X14	X10	X11	X19	X22
	0.0761	0.0492	0.0564	0.0533	0.0550	0.0568	0.0699
San Menxia	X1	X14	X10	X13	X11	X19	X22
	0.0763	0.0610	0.0492	0.0503	0.0591	0.0516	0.0809
Zhu Madian	X1	X3	X6	X14	X13	X11	X22
	0.0783	0.0547	0.0512	0.0614	0.0507	0.0597	0.0580
Nan yang	X1	X3	X14	X13	X11	X16	X22
	0.2739	0.3377	0.3605	0.4087	0.3134	0.2640	0.2824

.

As shown in Table 7, among the key factors impeding WRCC in the 17 cities and municipalities in the HREEB, X1, X3, X11, X13, X14, and X22 are the most frequently mentioned. The combined weights of the indicators and the degree of obstacles calculated, X1, X3, X7, X11, X14, and X22, which are all in the top ranking, are the indicators of primary concern for improving WRCC. X1 (water resources per capita) is a direct reflection of the number of resources available in the region, and the highest degree of obstruction of this indicator indicates inefficient use of water resources in the HREEB, poor water resources management, backward water-saving technology, or serious waste of water resources. The high handicap of water resources per capita and unequal distribution of water resources can also lead to this result [44]. The percentage of X3 (surface water resources) reflects the distribution of water resources, which reflects the sustainability of water resources, and is the second most important factor affecting the WRCC of the HREEB. A high barrier to surface water resources indicates that the surface water in the area is seriously polluted, resulting in a reduction in the amount of surface water available for use. A high barrier to surface water resources may also mean that water resources in the region are unevenly distributed over time and space. For example, according to data related to water resources in Wuhan (as a representative city within the Han River ecological and economic zone), the total multi-year average water resources amounted to 47.251 × 10⁸ m³, of which 3.706 × 10⁸ m³ and 11.014 × 10⁸ m³ were surface water resources and underground water resources, respectively [45]. This indicates that despite the impressive total volume, surface water resources are relatively limited and fluctuate significantly from year to year and season to season. When experiencing a dry year or a dry season, a significant decrease in the amount of surface water resources will directly affect regional WRCC. X14 (proportion of tertiary industry) reflects the degree of optimization of the regional economic structure. A high degree of obstacle in the tertiary sector indicates a low level of industrial structure. In HREEB, despite rapid economic development in recent years, the overall level of industrial structure is still low. Traditional agriculture and industry occupy a large proportion, while the development of the service industry (tertiary industry) lags behind. This industrial structure makes the utilization of water resources inefficient, which in turn affects overall WRCC. In some cities in HREEB, agriculture and industry have high water demand, and some industries are highly water-consuming and polluting. If the proportion of tertiary industries is low, economic growth is more dependent on such high water-consuming industries, which is not conducive to the conservation and efficient use of water resources [46]. X22 (sulfur dioxide emissions per capita) reflects the degree of atmospheric pollution caused by regional industrial activities. The high barrier level of this indicator of sulfur dioxide emissions per capita is a direct reflection of the environmental protection challenges faced by HREEB cities, where increased emissions can lead to deterioration of air quality and the formation of environmental problems, such as acid rain, which in turn has an indirect impact on water resources. High per capita sulfur dioxide emissions may mean that the industrial structure in the region is dominated by high-emission, high-pollution industries, which will only increase the carrying pressure on water resources and may also cause long-term cumulative damage to the regional ecological environment.

Spatial analysis revealed that among the barriers to WRCC in the ten towns in the Hubei area of the HREEB, X11, X14, and X22 were considered. Except for Shennongjia, the remaining nine cities had an obstruction factor of X1. The obstacles to WRCC in the three cities in the Shaanxi section were basically the same: X1, X3, X11, X13, X14, and X22. The hurdles to the WRCC in the four cities in the Henan sector were essentially the same, and X3 was one of the primary WRCC impediments in Zhumadian and Nanyang. Cities in the HREEB should be devoted to promoting ecological civilization. Cities in central Hubei and Henan, where WRCC is low, should change their industrial structure and choose the path of green and innovative growth.

5. Discussion

WRCC is a significant scientific activity with wide-ranging implications for the sustainable use and management of water resources. In terms of both theory and practical application, research on WRCC has not yet resulted in a unified scientific theoretical system or practical guidance, and there are some disparities and inadequacies in the definition and connotation of WRCC, the system of evaluation indices, and the evaluation methods. WRCC is closely related to human well-being, ecosystem health, and economic development and represents an essential step toward sustainable water resource management. Through this evaluation, we were able to better comprehend and address the challenges facing water resources and establish a solid foundation for future water security.

This paper provides an overview of the process of evaluating WRCC, carefully summarizes and analyzes the problems of the research, and proposes a universally applicable WRCC evaluation index system by combining the research on the definition, connotation, and related theories of WRCC. Considering that the study system is a water-resources-economic-social-ecological environment composite system, which itself has openness and uncertainty, and that traditional evaluation methods have many problems, such as difficulty in determining the weights and strong subjectivity, this study used the projection tracing technique for the evaluation of the WRCC combined with genetic algorithms, constructed the RAGA-PP model, and used it for empirical research on the WRCC status of the HREEB. A differentiation model was introduced to compare the accuracy of the RAGA-PP model with that of the other three models, and it was found that the RAGA-PP model had the highest accuracy in the evaluation of WRCC in the HREEB. From the comparison, it can be seen that the RAGA-PP model is more advantageous for evaluating WRCC. The RAGA-PP better solves the high-dimensional nonlinear problem in the traditional water resources evaluation method, can determine the structure and characteristics of the data itself, eliminates the interference of the remaining irrelevant variables to the greatest extent possible, and seeks the optimal solution by accelerated genetics many times to analyze the level of the WRCC in a more scientific way, with strong stability and accuracy. This study provides a new methodological contribution to the evaluation of WRCC in the basin, overcoming the many problems of traditional evaluation methods, such as the difficulty in determining weights and strong subjectivity. This study proposes specific policy recommendations based on empirical analyses to provide new guidance for basin water resource management practices and enhance the scientificity and effectiveness of policies. From 2008 to 2022, the WRCC of the major HREEB cities fluctuated, and the overall WRCC increased in 2015, with small spatial differences. In 2020, WRCC decreased, particularly in urban areas along the middle reaches of the HREEB, which corresponds with the results of previous studies [47].

In summary, the WRCC of the ten cities in the Hubei section of the HREEB as a whole shows a basic pattern of superiority in the east and west and poor in the middle, while the three cities in the Shaanxi section are in favor of the overall WRCC, and the four cities in the Henan section have a relatively poor WRCC. The results of the WRCC study can inform the development of future water management policies or sustainable practices in the region. First, WRCC accounting for HREEB provides a benchmark for policymakers to assess the current state of water resources and possible future trends. Based on the results of the WRCC study, water resource management policies, such as water allocation, water abstraction permits, water conservation measures, and water quality protection, can be formulated or adjusted. Policies should aim to optimize the allocation of water resources and ensure their rational use while protecting them from over-exploitation and pollution [48]. Finally, the research results can guide the implementation of sustainable water resource practices, such as rainwater harvesting, wastewater recycling and reuse, and eco-agriculture. It can help increase the efficiency of water use, reduce the pressure on natural resources, and promote the sustainable use of water resources [49].

Conducting HREEB WRCC research is inextricably linked to broader research areas, policy contexts, and practical applications. HREEB’s WRCC research of HREEB is closely linked to the UN Sustainable Development Goals (SDGs) for clean water and sanitation (SDG 6), contributing to the global goal of sustainable development. HREEB’s WRCC research contributes to the formulation and implementation of water environmental protection policies and supports the formulation of regional development strategies [50,51]. At the same time, HREEB is an important agricultural area, and WRCC studies can help optimize the allocation and management of irrigation water resources and improve agricultural water use efficiency. With accelerated urbanization and increasing demand for urban water supply, this study will help in the sustainable supply and management of urban water resources. The WRCC study in the HREEB can be compared with studies in other river basins in the international arena, which will help in the exploration of global water security issues and provide Chinese experience and cases for global water resources management.

Because of the authors’ constraints in terms of research, expertise, experience, and data availability, the study in this publication contains some flaws that should be addressed in future research.

(1)

Because of government department adjustments and time constraints, certain evaluation indicators were not obtained. These include the area of soil and water erosion control in the ecological subsystem, the rate of compliance with water quality standards in water functional zones, and the proportion of river and lake cross sections meeting functional zone categories. These omissions have an impact on the evaluation results.

(2)

This study can be expanded to explore the scale of research. However, it does not make any predictions or assessments of future carrying capacity dynamics based on WRCC results. These results can be combined with regional development planning to analyze and predict the future evolution of WRCC in subsequent studies.

(3)

Temporal and spatial limitations exist in the data. The data span 2008 to 2022, which limits the analysis of recent trends and may not capture long-term historical patterns. We plan to expand the dataset to include more years of data in future studies in order to provide a broader perspective. Despite the diversity of HREEB, our study may not fully capture subtle regional differences. Future studies could include more granular spatial analyses to better understand local differences. Relying on government and organizational reports for data may present potential limitations owing to possible reporting inconsistencies or biases. We are seeking to work with local authorities and research organizations to obtain more detailed ground-based data.

(4)

In future research on WRCC, it is possible to focus on the evaluation and prediction problems of deep learning in WRCC, using multiple methods and multidisciplinary cross-fertilization to comprehensively understand and solve water resource problems. Big data technology allows the processing and analysis of large amounts of water resource data, and future research could use big data analysis and artificial intelligence algorithms to improve the accuracy and efficiency of WRCC evaluation. Future research could also focus on the study of the linkage between WRCC and energy and food security by analyzing the role of water resources in securing energy production (e.g., hydropower, coal chemical industry) and food production, as well as the inter-constraints between them, to provide strategies for integrated security and safety.

6. Conclusions

In this study, the RAGA-PP was applied to comprehensively assess the WRCC of 17 cities and municipalities in the HREEB for the period 2008–2022 to analyze the spatiotemporal changes in the WRCC and to introduce the OBM to analyze the factors affecting the improvement of the WRCC. The conclusions of this study are as follows:

(1)

Using discriminant analysis, the accuracy of RAGA-PP was compared with that of the entropy-weighted TOPSIS method, RSR, and PCA, and it was found that the RAGA-PP model was more accurate in the WRCC evaluation of the HREEB.

(2)

The WRCC of cities in the HREEB from 2008 to 2022 exhibited an overall shifting tendency in the time series, and the difference between the cities narrowed, with Sanmenxia being relatively low and Shennongjia being the best.

(3)

The WRCC of the ten cities in the Hubei section of the HREEB as a whole shows a basic pattern of superiority in the east and west and poor in the central region, while the three cities in the Shaanxi section are overall superior, and the four cities in the Henan section have a relatively low WRCC.

(4)

The subsystem carrying capacity of each city in the HREEB fluctuated during the period–2008–2022, with obvious internal differences. Overall, the subsystem carrying capacity levels of the three cities in the Shaanxi section, western part of the Henan section, western part of the Hubei section, and eastern part of the HREEB are higher, while the subsystems of Xiaogan and Jingmen in the central part of the HREEB have poorer carrying capacity levels.

(5)

When analyzing the barriers to WRCC at the guideline level, the water resources, social, economic, and ecological subsystems of the cities in the HREEB were more evenly balanced, with the economic and ecological subsystems being slightly more balanced than the other two subsystems.

(6)

When analyzing the obstacles to the WRCC at the indicator level, the indicators with the highest frequency of occurrence among the key factors were the X1, X3, X14, X11, X13, and X22 sulfur dioxide emissions per capita. The most significant constraint was the amount of water per capita.