Comprehensive Evaluation of Agricultural Water Resources’ Carrying Capacity in Anhui Province Based on an Improved TOPSIS Model

Abstract

In recent years, China has made significant progress in rural revitalization and agricultural modernization. Agricultural water resources play a crucial role in promoting high-quality agriculture and ensuring the sustainable use of water resources. This study focuses on assessing the status of agricultural water resources’ carrying capacity in Anhui Province and promoting their sustainable use. The evaluation index weights were determined using the improved structural entropy weighting method under the traditional TOPSIS model. The gray weighted TOPSIS model was then constructed using the gray correlation matrix to evaluate the carrying capacity of agricultural water resources in Anhui Province. The findings indicate that the carrying capacity of agricultural water resources in Anhui Province has shown a fluctuating upward trend from 2000 to 2020. The lowest carrying capacity was observed in 2001, with a comprehensive score of 0.2647, while the highest was in 2020, with a comprehensive score of 0.7004. According to the M-K trend test, the carrying capacity of agricultural water resources in Anhui Province is expected to increase in the future. Specifically, the carrying capacity in the southern region of Anhui Province is gradually increasing, while that in the northern region is decreasing. The central cities have remained relatively stable in recent years. To ensure the sustainable use of agricultural water resources, it is recommended that Anhui Province increase the construction of agricultural water resource management and field water conservation facilities, as well as promote the construction of high-standard farmland. These measures will contribute to the high-quality development of agriculture and the coordinated spatial use of water resources.

1. Introduction

Water resources have become one of the most critical issues worldwide in the 21st century, attributed to the effects of global climate change and the continuous growth of the population [1]. China, as a nation with limited water resources, faces challenges in per capita water availability, which was only 2098.5 cubic meters in 2021, substantially below the global average. Rapid socioeconomic development amplifies the demand for water resources, leading to escalating concerns regarding water scarcity, unequal distribution, and water pollution [2].

Within this context, China, as a significant agricultural country, persists with high agricultural water consumption throughout the year. In 2021, agricultural water consumption accounted for 60% of total water consumption, reaching a staggering 364.43 billion cubic meters. The average agricultural irrigation water consumption during the period from 2012 to 2021 was 14.314 billion cubic meters, with an average agricultural water resource utilization rate of 19.1% and a coefficient of agricultural irrigation water utilization averaging at 0.53.

Concurrently, China has prioritized rural revitalization and agricultural modernization within its 14th Five-Year Plan. Recognizing the importance of agricultural water resources as a natural prerequisite for agricultural development, comprehensive studies are crucial in promoting high-quality agricultural development and ensuring the sustainable utilization of water resources [3]. Therefore, an in-depth investigation into agricultural water resources holds significant implications for achieving sustainable utilization and advancing high-quality agricultural practices.

As one of the important indicators for evaluating regional agricultural water resources, the evaluation of agricultural water resources’ carrying capacity can fully reflect the degree of development and utilization of regional water resources and the levels of agricultural development and socio-economic development, and its evaluation can, to a certain extent, provide a reference for the government in formulating relevant policies to improve the level of agricultural development and promote the sustainable use of agricultural water resources [4]. However, at present, most of the foreign research focuses on agricultural water resource treatment [5,6], and most of the domestic research focuses on water resources’ carrying capacity, which once subdivided to study the carrying capacity of agricultural water resources is not much. Various methods have been employed in the study of water resources’ carrying capacity, including the fuzzy comprehensive evaluation method [7,8,9], principal component analysis method [10,11,12], system dynamics method [13,14,15,16], multi-objective decision method [17,18], projection tracing method [19] and TOPSIS model [20,21,22,23]. These methods offer a solid theoretical basis and practical applicability, thereby establishing a methodological foundation for investigating the carrying capacity of agricultural water resources.

Among the above models, the TOPSIS model is widely used in the evaluation of water resources’ carrying capacity due to its simple principle and accurate evaluation results; so, in this paper, the TOPSIS model is selected as the method to evaluate the carrying capacity of agricultural water resources in Anhui Province [24]. However, the traditional TOPSIS method still has some shortcomings, and most of the experts and scholars mainly focus on the weight calculation method or distance calculation formula when improving it [20,21,22,23,24,25,26]. In order to make the evaluation results more accurate, this paper will improve the traditional TOPSIS method in both the weight calculation method and distance calculation formula. For the determination of index weights, there are mainly two kinds of subjective assignment methods and objective assignment methods, but both subjective assignment and objective assignment have their own advantages and disadvantages; in order to synthesize the advantages of both, this paper will combine the subjective assignment of the structural entropy weight method and the objective assignment of the entropy weight method (EWM) by adjusting coefficients and will use the gray correlation matrix instead of Euclidean distance, so as to construct a weighted gray TOPSIS model to evaluate the carrying capacity of agricultural water resources in Anhui Province, aiming to provide a scientific basis for the sustainable use of agricultural water resources and high-quality agricultural development in Anhui Province.

2. Study Area

Anhui Province is a huge, warm-temperate and subtropical overland region with a land size of around 140,000,000 km². The “2021 Anhui Water Resources Bulletin” informs us that Anhui Province has an average annual rainfall of 1178.2 mm and average annual water resources of 73.835 billion m³, making the total water resources very adequate. However, due to regional variations in topography and climate, Anhui Province’s water resources vary by region. In general, the province’s southern and southeastern regions are relatively rich in water resources, while its northern and northwestern regions have relatively few of them. The distribution of total water resources by cities in Anhui Province in 2021 is shown in Figure 1 below. In Anhui province, the agricultural water consumption ratio was 13.623 billion m³ on average between 2000 and 2020, and it is expected to remain largely over 50% in 2021. In Bengbu, Chuzhou, Luan and Xuancheng in particular, the agricultural water use ratio is over 60%. The ratio of agricultural water use in each city of Anhui Province in 2021 is shown in Figure 2 below. Anhui Province’s annual total water use has stayed above 25 billion m³, and its annual agricultural water use has remained above 13 billion m³. The detailed use of total water consumption and agricultural water consumption in Anhui Province from 2000 to 2020 is depicted in Figure 3 below.

3. Materials and Methods

3.1. Data Sources

The data for this paper come from the 2000–2021 Anhui Statistical Yearbook, the Anhui Water Resources Bulletin and the Anhui Ecological and Environmental Conditions Bulletin.

3.2. Evaluation Index System

Considering that there is no unified evaluation index system for the evaluation of agricultural water resources’ carrying capacity, this paper selects the agricultural water resources’ carrying capacity evaluation index system in Anhui Province based on the principles of hierarchy, scientificity, locality and operability, and the selected agricultural water resources’ carrying capacity evaluation index can reflect key factors such as agricultural water consumption per unit area and water use efficiency [27]. By referring to the existing literature [4,28,29], nine evaluation indicators are selected in this paper at the three levels of water resource system, socio-economic system and agricultural water resource development and utilization system, and the indicators are selected as shown in

Table 1. Agricultural water resources’ carrying capacity evaluation index system.

Target Layer	Guideline Layer	Indicator Layer	Unit	Indicator Meaning	Characteristic
Agriculture Industry Water Resources Source Undertake Load Force A	Water system B1	Total water resources C1	108 m3	-	Positive
		Groundwater resources C2	108 m3	-	Positive
		Rainfall C3	108 m3	-	Positive
	Socio-economic system B2	Arable land area C4	hectares	-	Positive
		Food production per capita C5	Kg/person	Total food production/agricultural population	Positive
		Agricultural output per capita C6	Yuan/person	Total agricultural output value/agricultural population	Positive
	Agricultural water resource development and utilization system B3	Effective irrigated area ratio C7	%	Effective irrigated area/cultivated land area	Positive
		Agricultural water use ratio C8	%	Agricultural water consumption/total water consumption	Negative
		Single-party water agricultural output C9	Yuan/m3	Total agricultural output value/agricultural water consumption	Positive

below.

3.3. Structural Entropy Weight Method

The structural entropy weighting method is an analytical method that combines qualitative and quantitative analysis to determine the weighting of indicators, which is based on the Delphi expert survey method and the fuzzy analysis method to form a “typical ranking”; it then uses the entropy method in information theory to measure the uncertainty of the above ranking and, through the “blindness” analysis and literacy, achieves the purpose of optimizing the weights. Because of its objective science and easy operation, many experts and scholars have solved a lot of practical problems using this method [30,31,32]. However, the traditional structural entropy weight method still has some shortcomings, such as the traditional structural entropy weight method affiliation function. Expression affiliation value is located in $-1~0$ interval, which is not consistent with the nature of the affiliation function [33]. Based on this, this paper corrects the transformation form of the affiliation function and adopts the analytic form of entropy; meanwhile, in order to make the expert scoring more accurate, this paper filters the expert ranking using the Pearson correlation coefficient, and the specific improvement steps are as follows:

Step 1: Collecting expert ranking tables to form a subjective “typical ranking”

First, k experts were selected for n evaluation indicators ${\mathrm{C}}_{\mathrm{j}}$ ($\mathrm{j}=1,2,\cdots ,\mathrm{m}$) for subjective ranking, and their values are counted as ${\mathrm{a}}_{\mathrm{ij}}\left(\mathrm{i}=1,2,\cdots ,\mathrm{k};\mathrm{j}=1,2,\dots ,\mathrm{m}\right)$, constituting a typical ranking table as shown in

Table 2. Typical ranking table.

Evaluation Indicators	C1	C2	$\cdots$	Cm
Expert (1) ranking of indicators	${\mathrm{a}}_{\mathrm{i}1}$	${\mathrm{a}}_{\mathrm{i}2}$	$\dots$	${\mathrm{a}}_{\mathrm{im}}$
$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$
Expert (k) ranking of indicators	${\mathrm{a}}_{\mathrm{k}1}$	${\mathrm{a}}_{\mathrm{k}2}$	$\cdots$	${\mathrm{a}}_{\mathrm{km}}$

Note: The most important indicator is ranked as 1, the second most important indicator is ranked as 2, and so on. If experts think that two indicators are of equal importance, they can be ranked equally.

below.

Step 2: Determine the valid expert scores

In order to avoid the influence of this situation on the evaluation results and to obtain valid expert scores, this paper eliminates invalid expert scores by using Pearson correlation coefficients; now assume that there exist two m-dimensional normalized feature vectors X and Y of expert score ranking, where $\mathrm{X}={\left[{\mathrm{X}}_1{\mathrm{X}}_2\cdots {\mathrm{X}}_{\mathrm{m}}\right]}^{\mathrm{T}}$, and $\mathrm{Y}={\left[{\mathrm{Y}}_1{\mathrm{Y}}_2\cdots {\mathrm{Y}}_{\mathrm{m}}\right]}^{\mathrm{T}}$, then the Pearson correlation coefficients of X and Y are formulated as follows [34]:

$${\rho }_{XY}=\frac{cov\left(X,Y\right)}{{\sigma }_X{\sigma }_Y}=\frac{E\left[\left(X-{\mu }_X\right)\left(Y-{\mu }_Y\right)\right]}{{\sigma }_X{\sigma }_Y}=\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{X}}\right)\left({\mathrm{Y}}_{\mathrm{i}}-\overline{\mathrm{Y}}\right)}{\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{X}}\right)}^2}\sqrt{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Y}}_{\mathrm{i}}-\overline{\mathrm{Y}}\right)}^2}}$$

(1)

where ${\rho }_{XY}$ is the Pearson correlation coefficient between the authoritative expert; and each expert $X_i$ and $Y_i$ are the elements of the eigenvectors X and Y, respectively; $\overline{\mathrm{X}}$, and $\overline{\mathrm{Y}}$ are the feature vectors; X and Y are the mean values of ${\rho }_{XY}$. In terms of the values of $-1~1$ between vectors and ${\rho }_{XY}$, the larger the absolute value, the higher the correlation between the scores, and the experts with too low of a correlation are eliminated accordingly.

Step 3: Blindness analysis

In order to avoid bias in the comparison of the importance of the indicators by the experts involved in the ranking, it is necessary to transform the above “typical ranking” qualitatively and quantitatively, and to define the affiliation function for the transformation of the qualitative ranking according to the principle of information theory as follows:

$$\mathrm{X}\left(\mathrm{I}\right)=-\frac{\mathrm{n}+1-\mathrm{I}}{\mathrm{n}}\ln \left(\frac{\mathrm{n}+1-\mathrm{I}}{\mathrm{n}}\right) \mathrm{I}=1,2.\cdots \mathrm{n}$$

(2)

If the equation $\mathrm{I}={\mathrm{a}}_{\mathrm{ij}},{ \mathrm{b}}_{\mathrm{ij}}=\mathrm{X}\left({\mathrm{a}}_{\mathrm{ij}}\right)$, then ${\mathrm{b}}_{\mathrm{ij}}$ is the value of the affiliation function corresponding to the ranking number I. The arithmetic mean of the array $\left\{{\mathrm{b}}_{1\mathrm{j}}, \cdots ,{ \mathrm{b}}_{\mathrm{kj}}\right\}$ is taken as ${\mathrm{b}}_{\mathrm{j}}$, and $1-{\mathrm{b}}_{\mathrm{j}}$ is the average awareness degree of k experts on the evaluation index ${\mathrm{C}}_{\mathrm{j}}$.

Let the uncertainty of k experts about the evaluation index ${\mathrm{C}}_{\mathrm{j}}$ be the awareness blindness Q:

$${\mathrm{Q}}_{\mathrm{j}}=\max \left({\mathrm{b}}_{1\mathrm{j}},{ \mathrm{b}}_{2\mathrm{j}},\cdots ,{\mathrm{b}}_{\mathrm{kj}}\right)$$

(3)

Then, k experts’ awareness of the evaluation index ${\mathrm{C}}_{\mathrm{j}}$ is the overall awareness of ${\mathrm{x}}_{\mathrm{j}}$:

$${\mathrm{x}}_{\mathrm{j}}=\left(1-{\mathrm{b}}_{\mathrm{j}}\right)\left(1-{\mathrm{Q}}_{\mathrm{j}}\right)$$

(4)

Step 4: Normalization process

$${\mathsf{\omega }}_{\mathrm{j}}^{\prime }=\frac{{\mathrm{x}}_{\mathrm{j}}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{j}}} \mathrm{j}=1, 2.\cdots ,\mathrm{n}$$

(5)

where ${\mathrm{x}}_{\mathrm{j}}$ is the evaluation index of k experts’ ${\mathrm{C}}_{\mathrm{j}}$ the overall degree of awareness, ${\mathsf{\omega }}_{\mathrm{j}}^{\prime }$ is the structural entropy weighting method weight of the jth indicator, and ${{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{m}}{\mathsf{\omega }}_{\mathrm{j}}^{\prime }=1$.

3.4. EWM

Although the abovementioned structural entropy weight method measures the uncertainty of the expert ranking and literacy through the entropy method in information theory so as to achieve the purpose of optimizing the weight of evaluation indexes, the method is mainly based on the awareness of experts does not fully take into account the information entropy contained in the original data; so, in this paper, based on the subjective assignment of the structural entropy weight method, the entropy weight method is used to calculate the objective weight of the different evaluation indexes of each evaluation object. The specific steps of the entropy method are as follows [35]:

Step 1: Construct the decision matrix

Suppose there are n evaluation objects and m evaluation indicators, forming a decision matrix $X={\left(x_{ij}\right)}_{n\times m}$:

$$X=\left[\begin{array}{cc}\begin{array}{cc}{x}_{11}& x_{12}\\ x_{21}& x_{22}\end{array}& \begin{array}{cc}\cdots & x_{1m}\\ \cdots & x_{2m}\end{array}\\ \begin{array}{cc}⋮& ⋮\\ x_{n1}& x_{n2}\end{array}& \begin{array}{cc}\ddots & ⋮\\ \cdots & x_{nm}\end{array}\end{array}\right]$$

(6)

Step 2: Dimensionless data processing

Positive indicators:

$$y_{ij}=\frac{x_{ij}-min\left(x_{ij}\right)}{max\left(x_{ij}\right)-min\left(x_{ij}\right)}$$

(7)

Inverse indicators:

$$y_{ij}=\frac{max\left(x_{ij}\right)-x_{ij}}{max\left(x_{ij}\right)-min\left(x_{ij}\right)}$$

(8)

Then, the normalization matrix $Y={\left(y_{ij}\right)}_{n\times m}$ is

$$Y=\left[\begin{array}{cc}\begin{array}{cc}{y}_{11}& y_{12}\\ y_{21}& y_{22}\end{array}& \begin{array}{cc}\cdots & y_{1m}\\ \cdots & y_{2m}\end{array}\\ \begin{array}{cc}⋮& ⋮\\ y_{n1}& y_{n2}\end{array}& \begin{array}{cc}\ddots & ⋮\\ \cdots & y_{nm}\end{array}\end{array}\right]$$

(9)

Step 3: Determination of indicator weights

$$\{\begin{array}{c}{e}_j=-\frac{1}{\ln n}{{\displaystyle \sum }}_{i=1}^n\frac{y_{ij}}{{\sum }_{i=1}^n{y}_{ij}}\times \ln \frac{y_{ij}}{{\sum }_{i=1}^n{y}_{ij}}\\ d_j=1-e_j\\ {\omega }_j^{”}=\frac{d_j}{{\sum }_{j=1}^m{d}_j}\end{array}$$

(10)

where $e_j$ is the entropy value of the jth indicator, and ${\mathsf{\omega }}_{\mathrm{j}}^{″}$ is the weight of the entropy method of the jth indicator.

3.5. Portfolio Weights

Let the subjective weights of the evaluation indicators obtained by the above structural entropy weighting method be denoted as ${\omega }_j^{\prime }$ and the objective weights of evaluation indicators obtained by EWM be denoted as ${\omega }_j^{”}$ The combination of the structural entropy weighting method and the evaluation index weights obtained by EWM results in the combined weights ${\omega }_j$ is [36]:

$${\omega }_j=\alpha {\omega }_j^{\prime }+\beta {\omega }_j^{”}$$

(11)

In the above equation $\alpha$ and $\mathsf{\beta }$ are the adjustment coefficients, and $\alpha +\mathsf{\beta }=1$, and $\alpha$ and $\mathsf{\beta }\ge 0$.

To reduce the difference between subjective and objective empowerment, the coefficient of variation is defined as

$$q_i={{\displaystyle \sum }}_{j=1}^m{\left(\alpha y_{ij}{\mathsf{\omega }}_{\mathrm{j}}^{\prime }-\beta y_{ij}{\mathsf{\omega }}_{\mathrm{j}}^{"}\right)}^2$$

(12)

Since the coefficient of variation $q_i$ is smaller, the smaller the difference between the evaluation index weights obtained by subjective assignment and objective assignment, the smaller the difference can be adjusted by $\alpha$, and $\mathsf{\beta }$ can indirectly reduce the difference of subjective and objective weights by adjusting the size of $\alpha$ and $\mathsf{\beta }$. The optimization model is as follows:

$$\{\begin{array}{c}{q}_i={{\displaystyle \sum }}_{j=1}^m{\left(\alpha y_{ij}{\mathsf{\omega }}_{\mathrm{j}}^{\prime }-\beta y_{ij}{\mathsf{\omega }}_{\mathrm{j}}^{"}\right)}^2\\ minQ\left(q_1,q_2,\cdots ,q_n\right)\end{array}$$

(13)

The model is essentially a single-objective optimization problem:

$$\{\begin{array}{c}minQ={{\displaystyle \sum }}_{i=1}^n{q}_i={{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^m{\left(\alpha y_{ij}{\mathsf{\omega }}_{\mathrm{j}}^{\prime }-\beta y_{ij}{\mathsf{\omega }}_{\mathrm{j}}^{"}\right)}^2\\ s.t \alpha +\mathsf{\beta }=1,\alpha ,\mathsf{\beta }\ge 0\end{array}$$

(14)

Rule:

$$\mathsf{\alpha }=\frac{{\sum }_{i=1}^n{\sum }_{j=1}^m{y}_{ij}^2{\mathsf{\omega }}_{\mathrm{j}}^{″}\left({\mathsf{\omega }}_{\mathrm{j}}^{\prime }+{\mathsf{\omega }}_{\mathrm{j}}^{″}\right)}{{\sum }_{i=1}^n{\sum }_{j=1}^m{y}_{ij}^2{\left({\mathsf{\omega }}_{\mathrm{j}}^{\prime }+{\mathsf{\omega }}_{\mathrm{j}}^{″}\right)}^2}$$

(15)

$$\mathsf{\beta }=\frac{{\sum }_{i=1}^n{\sum }_{j=1}^m{y}_{ij}^2{\mathsf{\omega }}_{\mathrm{j}}^{\prime }\left({\mathsf{\omega }}_{\mathrm{j}}^{\prime }+{\mathsf{\omega }}_{\mathrm{j}}^{″}\right)}{{\sum }_{i=1}^n{\sum }_{j=1}^m{y}_{ij}^2{\left({\mathsf{\omega }}_{\mathrm{j}}^{\prime }+{\mathsf{\omega }}_{\mathrm{j}}^{″}\right)}^2}$$

(16)

3.6. TOPSIS

TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), first proposed by C.L. Hwang and K. Yoon in 1981, is a multi-objective decision analysis method based on the idea of approximating an ideal solution [37]. The method calculates the Euclidean distance between the evaluated objective and the optimal and inferior solutions by using the information of the original data, and the closer the evaluation unit index parameters are to the positive ideal solution, the higher the comprehensive score; the closer the negative ideal solution, the lower the comprehensive score; the closer the index parameters of the evaluation unit are to the positive ideal solution, the higher the overall score; and the closer the negative ideal solution, the lower the overall score [38].

However, the traditional TOPSIS has certain defects, in that the distance of the ideal solution obtained by calculating the Euclidean distance does not take into account the correlation between the evaluation units, and when the evaluation results of two evaluation units are similar, it cannot distinguish the spatial location of each evaluation and objectively reflect the state of each evaluation unit [39].

In order to make up for the above shortcomings, using the improved TOPSIS model with weighted gray correlation matrix instead of Euclidean distance for the comprehensive evaluation of agricultural water resources’ carrying capacity in Anhui Province, the similarity of the overall trend between each indicator parameter of the unit and the positive and negative ideal solutions is used as the evaluation result, which can well highlight the change pattern within the rating unit, and the specific improvement steps are as follows:

a. Calculate the optimal vector $Y^{+}$ and the inferior vector $Y^{-}$:

$$Y^{+}=\left(Y_1^{+},Y_2^{+},\cdots ,Y_m^{+}\right)=\left(max\left\{y_{11},y_{21},\cdots ,y_{n1}\right\},max\left\{y_{12},y_{22},\cdots ,y_{n2}\right\},\cdots ,max\left\{y_{1m},y_{2m},\cdots ,y_{nm}\right\}\right)$$

(17)

$$Y^{-}=\left(Y_1^{-},Y_2^{-},\cdots ,Y_m^{-}\right)=\left(min\left\{y_{11},y_{21},\cdots ,y_{n1}\right\}, min\left\{y_{12},y_{22},\cdots ,y_{n2}\right\},\cdots ,min\left\{y_{1m},y_{2m},\cdots ,y_{nm}\right\}\right)$$

(18)

b. Calculate the gray correlation coefficient between each sample and the positive and negative ideal solutions ${\delta }_{ij}^{\pm }$:

$${\delta }_{ij}^{\pm }=\frac{\underset{i}{\min }\underset{j}{\min }\left|Y_{ij}-Y_j^{\pm }\right|+\phi \underset{i}{\max }\underset{j}{\max }\left|Y_{ij}-Y_j^{\pm }\right|}{\left|Y_{ij}-Y_j^{\pm }\right|+\phi \underset{i}{\max }\underset{j}{\max }\left|Y_{ij}-Y_j^{\pm }\right|}$$

(19)

where $\phi$ is the resolution factor, generally taken as 0.5.

c. Calculate the weighted gray correlation $D_i^{+}$, $D_i^{-}$:

$$D_i^{\pm }={{\displaystyle \sum }}_{j=1}^m{\omega }_j{\delta }_{ij}^{\pm }$$

(20)

where ${\omega }_j$ are the weights of the improved structural entropy weighting method.

d. Calculate the relative closeness of the resulting optimal solution $S_i$:

$$S_i=\frac{D_i^{+}}{D_i^{+}+D_i^{-}}(\mathrm{i}=1,2,\cdots ,\mathrm{n})$$

(21)

Due to regional differences, there is no clear grade classification standard for agricultural water resources’ carrying capacity level. In order to further analyze the spatial and temporal differences of the agricultural water resources’ carrying capacity level of each city in Anhui Province from 2000 to 2020, this paper uses the standard deviation grading method [40]. In order to further analyze the spatial and temporal differences of agricultural water resources’ carrying capacity in Anhui Province from 2000 to 2020, the paper divides the agricultural water resources carrying capacity into $V_1$,$V_2$, $V_3$ and $V_4$. Four grades are used. The results of the classification are shown in

Table 3. Agricultural water resources’ carrying capacity level grading table.

Year	Grading Criteria
	V1 (0, V−S]	V2 (V−S, V]	V3 (V, V+S]	V4 (V+S, 1]
2000	(0, 0.3742]	(0.3742, 0.4272]	(0.4272, 0.4802]	(0.4802, 1]
2005	(0, 0.3787]	(0.3787, 0.4373]	(0.4373, 0.4959]	(0.4959, 1]
2010	(0, 0.4072]	(0.4072, 0.4467]	(0.4467, 0.4862]	(0.4862, 1]
2015	(0, 0.4199]	(0.4199, 0.4627]	(0.4627, 0.5055]	(0.5055, 1]
2020	(0, 0.3924]	(0.3924, 0.4414]	(0.4414, 0.4905]	(0.4905, 1]

Note: V in the table is the mean, and S is the standard deviation.

below.

4. Results and Discussion

4.1. Results of Weight Calculation

Firstly, eight experts were invited to score the importance of the agricultural water resources’ carrying capacity evaluation indexes in Anhui Province; the specific scoring situation is shown in

Table 4. Expert ranking table.

Evaluation Indicators	C1	C2	C3	C4	C5	C6	C7	C8	C9
Expert 1	4	3	1	6	9	7	5	2	8
Expert 2	3	1	1	2	6	5	4	3	5
Expert 3	2	2	2	1	7	6	3	5	4
Expert 4	1	2	2	3	6	7	4	5	5
Expert 5	2	2	1	4	6	5	1	2	3
Expert 6	4	5	3	9	8	7	2	1	6
Expert 7	5	4	4	2	7	7	3	1	6
Expert 8	3	2	1	5	8	7	5	4	6

below. In order to determine the effective expert scoring, this paper was based on formula (1) Pearson correlation coefficient, referencing the most authoritative Expert 1 scoring, and finally selected six experts’ scoring as the effective scoring; it was then calculated by formula (2)–formula (5) evaluation index structure entropy weighting method. The selected situation and the weight calculation results are shown in

Table 5. List of typical ranking structure of evaluation indexes calculated using entropy weight method.

Evaluation Indicators	Expert Ranking						bj	Qj	xj	ωj′
	Expert 1	Expert 2	Expert 5	Expert 6	Expert 7	Expert 8
C1	4	3	2	4	5	3	0.2570	0.3631	0.4732	0.1044
C2	3	1	2	5	4	2	0.1851	0.3265	0.5488	0.1211
C3	1	1	1	3	4	1	0.0859	0.3198	0.6218	0.1372
C4	6	2	4	9	2	5	0.2636	0.3604	0.4710	0.1039
C5	9	6	6	8	7	8	0.2856	0.3342	0.4756	0.1049
C6	7	5	5	7	7	7	0.3482	0.3662	0.4131	0.0911
C7	5	4	1	2	3	5	0.2275	0.3466	0.5048	0.1113
C8	2	3	2	1	1	4	0.1368	0.2938	0.6096	0.1345
C9	8	5	3	6	6	6	0.3428	0.3678	0.4155	0.0916

below, and the Pearson correlation coefficient graph of expert scoring is shown in Figure 4 below.

In order to make up for the shortage of subjective weighting of the structural entropy weighting method, the objective weights of each evaluation index were calculated from Equations (6)–(10), and then the weights of the structural entropy weighting method and the EWM weights were combined according to Equations (11)–(16); the final combined weights are shown in

Table 6. Agricultural water resources’ carrying capacity evaluation index weights.

Guideline Layer	Guideline Layer Weights	Indicator Layer	Structural Entropy Weighting Method Weights	EWM Weights	Combination Weights
Water systems B1	0.3333	Total water resources C1	0.1044	0.0975	0.1012
		Groundwater Resources C2	0.1211	0.0743	0.0993
		Rainfall C3	0.1372	0.0661	0.1041
Socio-economic system B2	0.3333	Arable land area C4	0.1039	0.2839	0.1876
		Food production per capita C5	0.1049	0.0946	0.1001
		Agricultural output per capita C6	0.0911	0.1352	0.1117
Agricultural water resources development and utilization system B3	0.3334	Effective irrigated area ratio C7	0.1113	0.1075	0.1096
		Agricultural water use ratio C8	0.1345	0.0424	0.0916
		Single-party water agricultural output C9	0.0916	0.0985	0.0948

below. From Table 6, we can see that the evaluation indexes with relatively high weights are arable land area, agricultural output value per capita, effective irrigation area ratio and rainfall. In the agricultural production activities, the larger the effective irrigation area, the better the water-saving effect and the higher the corresponding agricultural water resources’ carrying capacity; from the 2021 Anhui Water Resources Bulletin, we know that the actual irrigated area of arable land in the province is 3,745,286.67 ha, and the effective irrigation area ratio is maintained at about 80% all year round, but the fluctuation range has been relatively large in recent years. Meanwhile, due to the influence of the monsoon climate, climate change in Anhui Province is diverse, rainfall varies greatly within the year and natural disasters such as droughts and floods are frequent, which has a significant impact on the sustainable development of agricultural water resources in Anhui Province. As a large agricultural province, the area of arable land in Anhui Province is the basis of agricultural production, and its area is directly related to the amount of water used for agricultural irrigation. Currently, China is vigorously promoting the high-quality development of agriculture, and the increase in agricultural output value per capita plays a key role in promoting the improvement of water use efficiency, which in turn promotes the improvement of the carrying capacity of agricultural water resources and the high-quality development of agriculture. For the above reasons, in order to make the evaluation results more objective and accurate and closer to the actual agricultural water resources in Anhui Province, the weighting values of arable land area, per capita agricultural output value, effective irrigation area ratio and rainfall index should be increased in the evaluation of the agricultural water resources’ carrying capacity in Anhui Province.

4.2. Carrying Capacity Evaluation Results

The values of the agricultural water resources’ carrying capacity evaluation indexes in Anhui Province from 2000 to 2020 are shown in

Table 7. Agricultural water resources’ carrying capacity evaluation index values for Anhui Province from 2000 to 2020.

Year	Total Water Resources/Billion Cubic Meters	Amount of Underground Water Resources/Billion Cubic Meters	Average Rainfall/mm	Arable Land Area/ha	Food Production per Capita (kg/Person)	Per capita Agricultural Output (yuan/Person)	Effective Irrigated Area Ratio/%	Agricultural Water Use Ratio/%	Agricultural Production Value per Square Meter of Water (yuan/m3)
2000	644.21	188.74	1129.6	4,229,551	1234.77	3372.98	75.60	65.00	5.88
2001	474.27	132.63	876.2	4,218,689	1265.65	3482.49	76.53	64.81	4.95
2002	824.69	205.47	1266.0	4,177,761	1431.53	3688.20	78.12	58.09	5.86
2003	1083.01	252.34	1460.9	4,084,727	1190.37	3321.10	80.43	48.51	6.99
2004	500.65	151.97	998.0	4,108,856	1528.39	4691.71	80.40	55.34	7.26
2005	719.25	195.41	1208.3	4,092,451	1474.43	4632.04	81.39	52.17	7.54
2006	580.50	159.12	1069.0	4,116,941	1643.17	5201.37	81.30	53.47	7.00
2007	712.46	181.84	1174.3	4,144,171	1769.47	6428.04	82.54	49.21	9.23
2008	699.24	178.09	1146.0	4,144,981	1897.90	7519.69	83.32	54.50	8.25
2009	733.10	185.43	1194.0	4,171,222	1960.33	8236.23	83.53	55.30	7.99
2010	939.05	197.81	1308.9	4,181,295	2023.98	9706.29	84.18	54.61	9.25
2011	602.08	143.48	1064.4	4,184,323	2100.13	10,986.63	84.78	55.09	10.11
2012	700.98	159.22	1173.8	4,184,235	2243.74	12,186.80	85.68	51.55	12.01
2013	585.59	144.54	1023.4	4,188,104	2319.71	13,553.49	102.80	52.06	12.43
2014	778.48	178.91	1278.5	5,876,410	2448.10	14,528.01	73.71	49.56	15.03
2015	914.12	193.71	1362.8	5,876,640	2545.41	14,964.65	74.88	51.82	13.91
2016	1245.17	219.26	1612.7	5,873,000	2481.59	15,518.32	75.56	51.91	14.16
2017	784.90	200.95	1255.0	5,866,760	2557.95	16,494.37	76.77	51.42	15.01
2018	835.78	203.67	1314.7	5,885,950	2939.38	16,530.95	77.10	50.69	15.56
2019	539.87	144.85	935.8	5,550,000	2972.14	17,341.60	82.54	49.53	17.20
2020	1280.41	228.60	1665.6	5,890,000	3037.50	19,085.71	78.25	48.67	19.34

below, based on the above-mentioned weighting of each evaluation index. Through the grey weighted TOPSIS model, according to the Formulas (17)–(21), we can obtain the comprehensive score of agricultural water resources’ carrying capacity in Anhui Province; the specific score is shown in Figure 5 below. The lowest agricultural water resources’ carrying capacity was in 2001, with a score of 0.2647. The total water resources in that year were 47.427 billion m³, which were lower than the average water resources in the study period of 29.610 billion m³; however, the agricultural water consumption in that year was 13.901 billion m³, higher than the average agricultural water consumption of 278 million m³, which to a certain extent impacted the agricultural water resources’ carrying capacity in Anhui Province. The year of the highest agricultural water resources’ carrying capacity in Anhui Province is 2020; the total water resources in that year is the highest during the study period, and the agricultural output value per square meter of water, per capita agricultural output value and per capita grain yield in that year are significantly higher than the average level. These indicators greatly improve the agricultural water resources’ carrying capacity. Meanwhile, the prediction curve of the index in Figure 5 below shows that the agricultural water resources’ carrying capacity in Anhui Province shows an increasing trend. For further analysis, the M-K trend test on the comprehensive score of water resources’ carrying capacity in Anhui Province shows that the M-K test statistic Z = 2.2648 > 1.96, which passes the significance test with a 95% confidence level. Figure 6 below shows the M-K mutation test curve of the comprehensive score of the water resources’ carrying capacity in Anhui Province, and it can be seen from Figure 6 that the UF statistic stays above 0 after 2003, and exceeds the critical value of 1.96 after 2010. There is also a significant increase at the significance level of a = 5%, which indicates that the comprehensive score of the water resources’ carrying capacity in Anhui Province has an obvious rising trend, and the future agricultural water resources’ carrying capacity in Anhui Province is more likely to tend to a higher level in the future; however, it is still necessary to pay attention to the sustainable use of agricultural water resources, increase the construction of agricultural water resource management and field water conservation facilities, actively promote the construction of high-standard farmland and vigorously promote the high-quality development of agriculture.

To verify the adaptability of the improved TOPSIS model, the composite index method [41], the principal component analysis method [29] and the fuzzy comprehensive evaluation method [7] were selected. The scoring of the standardized matrix of Equation (9) with the traditional TOPSIS method is calculated, and the results are sorted to obtain the results shown in

Table 8. Calculation results of agricultural water resources’ carrying capacity in Anhui Province.

Year	Traditional TOPSIS	Sort by	Composite Index Method	Sort by	Principal Component Analysis Method	Sort by	Fuzzy Integrated Evaluation Method	Sort by	Improved TOPSIS	Sort by
2000	0.1836	20	0.1324	20	0.3202	12	0.4411	19	0.3096	20
2001	0.0467	21	0.0308	21	0.0084	21	0.3881	21	0.2647	21
2002	0.2894	17	0.2422	17	0.4024	9	0.5004	17	0.3611	17
2003	0.4309	9	0.3832	11	0.5528	7	0.5865	9	0.4369	11
2004	0.2061	19	0.1600	19	0.0283	20	0.4273	20	0.3246	19
2005	0.3155	15	0.2694	16	0.2555	15	0.5068	16	0.3763	16
2006	0.2519	18	0.2081	18	0.0881	19	0.4553	18	0.3489	18
2007	0.3549	12	0.3188	12	0.2221	16	0.5434	12	0.4090	12
2008	0.3149	16	0.2922	15	0.2678	14	0.5185	14	0.3900	14
2009	0.3334	13	0.3146	13	0.3360	10	0.5353	13	0.4011	13
2010	0.4091	10	0.3954	9	0.5092	8	0.5876	8	0.4402	9
2011	0.3234	14	0.2946	14	0.1822	17	0.5087	15	0.3896	15
2012	0.4057	11	0.3863	10	0.2933	13	0.5688	10	0.4372	10
2013	0.4434	8	0.4184	8	0.1456	18	0.5459	11	0.4573	8
2014	0.5837	6	0.6156	6	0.6098	6	0.6624	6	0.5611	6
2015	0.6146	5	0.6488	5	0.7541	4	0.6837	5	0.5767	5
2016	0.6837	2	0.7484	2	1.0428	2	0.7108	2	0.6271	2
2017	0.6156	4	0.6515	4	0.6948	5	0.6882	4	0.5817	4
2018	0.6493	3	0.6999	3	0.7658	3	0.7063	3	0.6078	3
2019	0.5477	7	0.5743	7	0.3349	11	0.6318	7	0.5377	7
2020	0.7637	1	0.8870	1	1.1719	1	0.7791	1	0.7004	1

below. The results of all five evaluation models show that the agricultural water resources’ carrying capacity in Anhui Province is the lowest in 2001 and the highest in 2020, which indicates the effectiveness of the improved TOPSIS model in evaluating the agricultural water resources’ carrying capacity in Anhui Province. Compared with the traditional TOPSIS model, the improved TOPSIS model has the same ranking in most years, but the bearing capacity ranking is improved in the three years of 2003, 2005 and 2011, and the ranking decreases in the three years of 2008, 2010 and 2012, with the difference in ranking mainly occurring before 2012. Comparing with the ranking of comprehensive index method, the principal component analysis method and fuzzy comprehensive evaluation method provide the following results: 2005 and 2012, except for the ranking of principal component analysis method, the ranking of other evaluation methods are the same as the ranking of the improved TOPSIS model. For 2008, the improved TOPSIS model rankings are consistent with the rankings of all evaluation methods except the integrated index method. For 2010, the ranking of the principal component analysis and the fuzzy integrated evaluation method are the same, and the ranking of the integrated index method is the same as that of the improved TOPSIS model, which is two and one lower than the ranking of traditional TOPSIS model, respectively. The improved TOPSIS model is more accurate and reliable than the other four evaluation models and obtains better results in the evaluation of agricultural water resources’ carrying capacity, which is suitable for the evaluation of agricultural water resources’ carrying capacity in Anhui Province.

The following Figure 7 shows the agricultural water resources’ carrying capacity level of each city in Anhui Province. From Figure 7, we can see that the overall level of the agricultural water resources’ carrying capacity of each city in Anhui Province is good; refer to the above Table 3 agricultural water resources’ carrying capacity level zoning table. The agricultural water resources’ carrying capacity of each city in Anhui Province is mostly located in $V_2$. The bearing capacity of the agricultural water resources in the south of Anhui Province is gradually increasing; the bearing capacity of agricultural water resources in the north is decreasing; the central cities have been relatively stable in recent years; and the bearing capacity level is mostly in $V_2$ and $V_3$. In the future, Anhui Province should pay attention to the coordinated spatial utilization of water resources to promote the sustainable development of agricultural water resources.

5. Conclusions

• Specifically, this paper utilizes an improved structural entropy weight method based on the traditional TOPSIS model to determine the weight of each evaluation index. This approach effectively addresses the issue of subjective and objective bias, resulting in weights that better reflect the actual situation in Anhui Province. Moreover, by employing weighted gray correlation instead of Euclidean distance, the paper successfully overcomes the challenge of distinguishing evaluation results that are close to each other. The enhanced TOPSIS model demonstrates strong adaptability in evaluating the carrying capacity of agricultural water resources in Anhui Province. The obtained evaluation results can serve as a valuable reference for formulating policies for the sustainable development of agricultural water resources in the region.
• Notably, the overall carrying capacity of agricultural water resources in Anhui Province exhibits a fluctuating upward trend. Specifically, the lowest carrying capacity was observed in 2001 with a comprehensive score of 0.2647, while the highest carrying capacity occurred in 2020 with a comprehensive score of 0.7004. Furthermore, the M-K trend test indicates a potential future increase in the carrying capacity of agricultural water resources in Anhui Province, suggesting that Anhui Province is likely to experience greater carrying capacity.
• Looking ahead, Anhui Province should prioritize the sustainable use of agricultural water resources and the coordinated utilization of water resources in different areas. The government can play a crucial role by formulating relevant policies to address these issues. It is essential to enhance agricultural water resource management and promote the construction of water-saving facilities in agricultural fields. Additionally, real-time monitoring of water usage in agriculture should be implemented to ensure efficient and responsible water practices. Moreover, active efforts should be made to foster the development of high-standard farmland and promote high-quality agriculture. These measures will contribute to the sustainable development of agricultural water resources in Anhui Province.