Evaluation of water resource carrying capacity in the middle reaches of the Yangtze River Basin using the variable fuzzy-based method

The middle reaches of Yangtze River Basin (MYRB) are rich in water resources, with a large number of rivers and lakes. However, in recent years, water resources from this basin are no longer sufficient to support the region’s rapid economic development. This study established a model to evaluate the water resource carrying capacity incorporating water resources, population, and socio-economic data. The characteristic values of water resource carrying capacity were calculated using the variable fuzzy evaluation method in MYRB from 2005 to 2020. Although both population and GDP in the MYRB showed an increasing trend between 2005 and 2020, the water supply capacity increased and then decreased. The weights of each index for evaluating the water resource carrying capacity of perennial botanical gardens were as follows: degree of water resource development (0.311) > total water resources (0.24) > population density (0.156) > GDP per capita (0.097) > water resources per capita (0.077) > water supply per capita (0.064) > water resources per unit area (0.055). Furthermore, the water resource carrying capacity in the MYRB showed an increasing trend from 2005 to 2020. In 2020, the carrying capacity of water resources in Changsha, Jingmen, Xiangtan, Hengyang, Wuhan, Xiaogan, Nanyang, and Xiangyang was attributed an evaluation grade of level 3, which indicates that the development and utilization of water resources in these areas were at their saturation point.


Introduction
Water resources are essential for the sustainable development of human society (Lv et al. 2021). However, terrestrial freshwater resources that can be directly used by humans today account for only 2.53% of the total amount of all water bodies on Earth (Yan and Xu 2022). China has a large amount of freshwater, with a total of 2,800 billion m 3 (Ren et al. 2020), accounting for 6% of the global water resources, and is the fourth largest water resource country in the world after Brazil, Russia, and Canada . However, it is one of the poorest countries in the world in terms of water resources, as its per capita water resources are only 2,200 m 3 , which is 1/4 of the global average . Recently, due to rapid socioeconomic development and population growth, the demand for and use of water resources have increased, leading to scarcity of water resources and the deterioration of the water environment, which has now become a global environmental problem (Wang et al. 2021a, b).
To better understand the relationship between water resources and economic development and thereby solve the problem of inevitably destroying water resources while Responsible Editor: Marcus Schulz developing economically, scholars have conducted extensive research on issues related to water resource carrying capacity (Table 1). For example, Yang et al. (2016) evaluated the carrying capacity of water resources in the Karst region of southwest China; Feng et al. (2020) studied the water resource carrying capacity of Xi'an based on the analytical hierarchy process-fuzzy synthetic evaluation model. However, research on water resource carrying capacity has mainly focused on the design of evaluation models and research methods. Commonly, the research methods used to study water resource carrying capacity include factor analysis, principal component analysis, and neural network methods. For example,  explored water carrying capacity based on hierarchical cluster analysis; Li et al. (2021) applied the variable premise-type cloud algorithm to water resource research. The majority of these studies use different methods to establish their evaluation systems and determine the weights of water resource carrying capacity evaluation; at present, this is the main direction of research on water resource carrying capacity (Jia et al. 2018). Although the vast majority of evaluation methods treat the evaluation criteria as integrals, since the criteria of the factor indicators actually used for evaluation are intervals, this form of treatment is inadequate and cannot fully reflect the rank of the indicators ). However, due to its rigorous theory and high accuracy, the variable fuzzy pattern recognition model can comprehensively evaluate the multiple index evaluation problems in different fields (Feng et al. 2020). Although the variable fuzzy evaluation method has a relatively large calculation amount, the concept of opposite fuzzy sets can greatly reduce the calculation amount and is well applied to the evaluation of water resources carrying capacity (Ge et al. 2021).
The Yangtze River is the main river of China, providing important freshwater resources for most of the country and supporting the development of the Chinese nation (Wang et al. 2021a, b). Since 1998-2018, the total water supply of Yangtze River has increased from a low of 167.5 billion m 3 to 207.5 billion m 3 , while the total water resources have stabilized at around 10,000 billion m 3 . The middle reaches of the Yangtze River Basin (MYRB) is the most densely populated area in the Yangtze River basin, and the water environment in this region has been damaged as a result (Ren et al. 2021). This has also led the MYRB to become an area with high intensity of water resource exploitation and endless ecological and environmental problems (Zhou 2022). Therefore, there is an urgent need to assess the state of water resources in this region by establishing a model with which to evaluate its water resource carrying capacity (Meng et al. 2022).
This study evaluates the water resource carrying capacity of the middle reaches of the Yangtze River using the variable fuzzy method, which provides an effective method for such cases (Yang and Wang 2022). The main objectives of this study were (1) to reveal the socio-economic and water resource base in the MYRB; (2) to calculate the relative affiliation of each indicator; and (3) to analyze the water resource carrying capacity level in the MYRB.
The organizational framework of this study is as follows: Section 2 describes the geographical location of the MYRB and its important regional characteristics; Section 3 describes the data and methods used to describe the water resources carrying capacity of the MYRB; Section 4 is the basic characteristics of water resources carrying capacity elements and water resources carrying capacity in the MYRB; Sections 5 and 6 are the discussion and conclusion on the water resources carrying capacity of the MYRB, respectively.

Study area
The MYRB is located between 108°E ~ 118°E and 25°N ~ 33°N in the middle of the Yangtze River Economic Belt in central China (Meng et al. 2020). The upstream and midstream divides of the Yangtze River are Yichang; the midstream and downstream divide is Hukou, which is 955 km long with a basin area of 680,000 km 2 and includes 54 municipal units and 293 county units. The main provinces covered are Jiangxi, Hubei, and Hunan, which also flow through small parts of Anhui, Shaanxi, Henan, and Sichuan (Peng and Deng 2020).
In 2017, the MYRB urban agglomeration had a land area of approximately 326,100 km 2 , a total population of 125 million, and a regional GDP of 7.90 trillion RMB (Wang et al. 2022a, b). The city cluster in the MYRB created 9.6% of the total economic volume, with 3.4% of the national land  (Qiu et al. 2021). Rapid economic development in recent years has led to an imbalance between water supply and demand and high levels of water pollution in the MYRB. The study area is shown in Fig. 1.

Data
MYRB land area data were obtained from the national administrative division data set released by the national administrative division query platform (available at: http:// xzqh. mca. gov. cn/ map, January, 15, 2022), including the administrative area of each municipal unit in the MYRB for a total of four periods (e.g., 2005, 2010, 2015, and 2020). The areas of 54 municipal units for a total of four years were collated and summarized for collection. Annual precipitation, surface water resources, underground water resources, storage variables, total water resources, water supply, and water demand for each province and city in the MYRB were collected and compiled. Data were obtained from the Water Resources Bulletin published by the Chinese Ministry of Water Resources (http:// www. mwr. gov. cn).
Data included the population and regional GDP of the MYRB. The population density and GDP per capita of the region were obtained by calculating the ratio of the total population and GDP in each administrative region to the area of each administrative region. Data related to population and regional GDP were obtained from the China Municipal Statistical Yearbook 2005-2020.

Water carrying capacity indices
Establishing an evaluation system and selecting reasonable and effective evaluation indices is key to the study of water resource carrying capacity Qiao et al. 2021). The selection of indicators should take all factors into consideration and reflect the state of water resources, the development and utilization of water resources, human water supply and demand, ecological and environmental water use, social development level, and economic situation of the region in a multi-level and multifaceted manner . In this study, the following seven relative evaluation indices were selected, in combination with the natural geographical features of the MYRB (i.e., Eqs. (1)-(7)): 1. Population density: ratio of total population to land area, Eq. (1): where ρ is the population density, M is the total population, and S is the area of the region.
(1) = M S where D denotes the degree of water resource development, d denotes water demand, and T denotes total water resources. 4. Water supply modulus: ratio of water demand to land area, Eq. (4): where M denotes the water supply modulus, d denotes water demand, and S denotes the area of the region. 5. Per capita water supply: ratio of total water demand to total population, Eq. (5): where‾S denotes the per capita water supply, d denotes the water demand, and M denotes the total population. 6. Water resources per capita: ratio of total water resources to total population, Eq. (6): where‾T is the amount of water resources per capita, T is the total amount of water resources, and M is the total population. 7. Water resources per unit area: ratio of water resources to land area, Eq. (7): where AT is the amount of water resources per unit area, T is the total amount of water resources, and S is the area of the region.

Variable fuzzy evaluation method
The variable fuzzy evaluation method, based on fuzzy mathematics, is a comprehensive evaluation method with clear and systematic results ). The method transforms qualitative evaluation into quantitative evaluation, which can better solve the problems of uncertainty and difficulty of quantification, and is applicable to various nondeterministic problems . The core of the variable fuzzy method is to determine the affiliation function, which is the relationship between the evaluation value and evaluation factors (Song et al.2020). The variable fuzzy evaluation method can solve problems influenced by multiple factors (Wang et al. 2022a, b). The m indicator feature vectors of the sample to be evaluated were as follows: where x denotes the indicator value and m denotes the number of evaluation indicators.
The matrix of standard value intervals based on the c levels was: where I = 1, 2, 3…m and h = 1, 2…c (m is the number of evaluation indicators, and c is the number of levels).
The sample was evaluated using the following solution steps: 1. The range value matrix I ab for the interval of variation were constructed based on the standard value interval matrix I cd for known c levels: where i = 1, 2…m and h = 1, 2, 3…c.

Based on the analysis of the actual situation of indicator
i and the physical meaning of indicator i, matrix M with level h of indicator i was determined: where i = 1, 2…m and h = 1, 2…c. 3. The indicator weight vector was determined, Eq. (12): where w denotes the weight and m denotes the number of evaluation indicators.
4. The application formula was applied, Eq. (13): where D A (u) denotes the relative degree of difference and μ A (u) denotes the relative degree of affiliation. 5. The relative affiliation matrix was calculated (e.g., Eq. (16)). The data in matrices I ab , I cd , and M were used to calculate the relative affiliation matrix of indicator i corresponding to level h: where μ A (u) denotes the relative affiliation matrix and μ A (u) ih denotes the relative affiliation. 6. Application model, Eq. (17): The integrated relative affiliation vector of the data to level h was calculated as: where h = 1, 2…c. 7. Normalization: The integrated relative affiliation vector of level h was normalized, and the normalization condition was Eq. (19): The integrated relative affiliation vector of the samples satisfying the condition for level h was obtained: The level eigenvalue formula was used to calculate the level eigenvalue of the sample, Eq. (21).
9. According to the relevant principles of the fuzzy variable set about the transformation model and the parameters in the transformation model, we can repeat steps (12)-(21) to obtain the variation range of the sample level eigenvalue H, analyze the stability of the sample level eigenvalue, and finally determine the evaluation level of the sample, so as to improve the variation range of the eigenvalue H.
In this study, the model is transformed by transforming the distance parameter p and the model optimization criterion parameter a (i.e., this study has four models, including one nonlinear model and three linear models).

Natural socio-economic factors
This part mainly introduces the spatial characteristics and differences of natural social economic factors about water resources carrying capacity (e.g., population density, GDP per capita, total water resources, etc.) in the MYRB between 2005 and 2020. Figure 2 shows the population density in the MYRB during 2005-2020. Only the population density of Wuhan City in the MYRB was found to reach more than 1000 people/km 2 in 2005, and the population density of the entire Hubei province was higher than those of other provinces in the MYRB, with most cities having population density values in the interval [0, 400] (Fig. 2a). Compared with 2005, the population density in the region did not change significantly in 2010 (Fig. 2b). However, the population density in the MYRB in 2015 showed a tendency to accumulate in the central cities (Fig. 2c). The population of cities with an initially large number of people continued to increase, while the population density of cities with an initially low population density did not grow rapidly. In 2020, the distribution of population density in the MYRB increasingly highlighted the fact that the population density in economically developed cities was growing much faster than that in areas characterized by slow economic development (Fig. 2d). Generally, the population in the east of the MYRB increased significantly, while the population in the west change slightly from 2005 to 2020. Figure 3 displays the spatial distribution of the GDP per capita in the MYRB from 2005 to 2020. Only Wuhan City in the MYRB had a GDP per capita of more than 30,000 RMB. Yichang, Changsha, and Huangshi exceeded 20,000 RMB, while the rest of the regions had a GDP per capita of less than 10,000 RMB in 2005 (Fig. 3a). The GDP per capita in the MYRB rose, but only Tongren and Qiandongnan sustained a GDP per capita of less than 10,000 RMB in 2010 (Fig. 3b). In 2015, the MYRB achieved rapid growth in GDP per capita, with Wuhan and Changsha both exceeding RMB 100,000 (Fig. 3c). Only a few cities in Hubei and Hunan provinces did not have a GDP per capita exceeding 30,000 RMB, while the remaining cities achieved breakthroughs in their GDP per capita, exceeding 60,000 RMB (Fig. 3d). On the whole, the GDP growth in the MYRB was obvious, which also indicated that the demand for water resources in the region will increase significantly.

Total water resources
The first column in Fig. 4 shows the spatial distribution of total water resources in the MYRB. By comparing the total water resources in the MYRB over 4 years (2005, 2010, 2015, and 2020), the total water resources in Suizhou, Xiantao, Jingmen, Xiaogan, Tianmen, and Qianjiang in Hubei Province and Xiangtan, Zhangjiajie, and Loudi in Hunan Province were found to be below 5 billion m 3 , while the total water resources in Huaihua, Shaoyang, Yongzhou, and Chenzhou were stable above 15 billion m 3 . The total water resources in Hanzhong were more than 30 billion m 3 in most years. To sum up, the water resources in the west and south of the MYRB were significantly more abundant than those in the east and north from 2005 to 2020.

Degree of water resource development and utilization
The second column in Fig. 4 describes the extent of water resource development in the MYRB. The degree of water resources development in the MYRB was found to show an increasing then decreasing trend from 2005 to 2020, with most cities in Hubei, Hunan, and Jiangxi Province reaching 50% of water resource development in 2005, including Wuhan City and E'zhou City, which reached over 70%. However, Shangluo City, Ankang City, En'shi, and Shennongjia Forest Area had a lower degree of water resource development in 2010, below 10%. In 2010, the level of water resource development in the MYRB was roughly the same as in 2005, with no significant changes. In 2015, the percentage of water resource development in Nanyang City, Qianjiang City, Tianmen City, and Xiangtan City increased, while the level of water resource development in the remaining cities did not increase significantly. In 2020, the degree of water resource development in the MYRB decreased overall, with only E'zhou City experiencing a degree of water resource development over 50%, while development in the remaining cities remained stable between 30 and 50%. Therefore, with the development of social economy and the increase of population, the development and utilization of water resources in the MYRB increased significantly during 2005-2020.

Water supply modulus
The third column in Fig. 4 presents the water supply modulus in the MYRB. The overall performance was high in some cities in Hubei and Hunan provinces, whereas the water supply modulus in all other provinces was between 0 and 10. It is worth noting that only one city, E'zhou, was found to have a water supply modulus of 60 or more. In this study, while the population of E'zhou was found to be at a medium level, the land area was small (only 0.15 million km 2 ). As such, E'zhou had a high value of water supply modulus. Spatially, the water supply modulus of cities in the MYRB was greater in the east and lower in the west, which corresponded to the indicators of GDP per capita and population density. This is indicative of the rapid development of the eastern region of the MYRB, a high demand for water resources, and a high degree of water resource development. To sum up, the water supply modulus in the MYRB did not change significantly between 2005 and 2020.

Per capita water supply
The fourth column in Fig. 4 shows the per capita water supply in the MYRB. The trend of per capita water supply in the MYRB from 2005 to 2020 was found to increase overall, followed by a partial decrease. The cities with the highest per capita water supply in the MYRB were Zhuzhou, Changde, Xiangyang, Jingmen, and Yueyang, with a per capita water supply exceeding 500 m 3 . The per capita water supply capacity in Huaihua City, Shaoyang City, and Suizhou City was slightly lower but also exceeded 300 m 3 . Most cities in Shaanxi and Guizhou Province had a per capita water supply capacity below the average of 100 m 3 . In 2010, the per capita water supply capacity did not change much compared to 2005. However, in 2015, the per capita water supply capacity in the southern part of the MYRB surged in Changsha City, Yiyang City, and Huaihua City to the south, with the per capita water supply exceeding 500 m 3 . However, by 2020, the per capita water supply in the MYRB decreased to the levels in 2010. Therefore, the change of water supply per capita in the middle reaches of the Yangtze River is not linear, which increased first and then decreased.

Total water supply
The fifth column in Fig. 4 presents the spatial distribution of the total water supply in the MYRB. From 2005 to 2020, the water supply in the MYRB showed a stable trend in general, except for E'zhou, where the water supply doubled from 600 million m 3 to 1.2 billion m 3 . However, the water supply in other cities remained stable at the corresponding values. The spatial distribution of water supply volume coincided with the distribution of per capita water supply volume, which was greater in the north and lower in the south.

Water resources per capita
The last column in Fig. 4 shows the per capita water resources in the MYRB. From 2005 to 2020, the overall spatial and temporal distribution of water resources per capita in the MYRB stayed relatively stable. However, the water resources per capita in the eastern part of the MYRB increased, while the water resources per capita in the southwestern part of the Yangtze River increased then decreased. In the central region, per capita water resources were not high relative to the large population.

Relative affiliation of major indicators
After analyzing the main natural, social, and economic factors, we need to determine the weight of each factor and the relative affiliation, so as to provide basic data for comprehensive evaluation in different scenarios.

Determination of indicator weights
To evaluate the water resource carrying capacity in the MYRB, the analytic hierarchy process (AHP) decision analysis method was used to determine the weights of each indicator. The importance ranking consistency theorem was applied to obtain the weights of each indicator of water resource carrying capacity, as shown in Table 2. The ranking of each indicator according to importance was as follows: degree of water resource development (0.311) > total water resources (0.24) > population density (0.156) > GDP per capita (0.097) > water resources per capita (0.077) > water supply per capita (0.064) > water resources per unit area (0.055). The degree of water resource development had the greatest weight, which indicated the importance of this factor in the water resource carrying capacity of a region, followed by the total amount of water resources, while the amount of water resources per unit area and the amount of water supply per capita had less influence on the degree of water resource development.

Relative affiliation of major indicators in 2005
The first column in Fig. 5 describes the relative affiliation of the major indicators (e.g., the degree of water resource development, total water resources, and population density) in 2005. The relative affiliation value of the degree of water resource development was highest in 2005, ranging from 0.55 to 0.99, while the relative affiliation values of total water resources and population density were lower than those of the degree of water resource development, with values of [0.35, 0.8] and [0.31, 0.6], respectively. The relative affiliation values of the degree of water resource development, total water resources, and population density decreased in order, indicating that the influence level of these three indicators on the water resource carrying capacity in the MYRB decreased in that order. This is consistent with the weighting order derived from the AHP decision analysis.

Relative affiliation of major indicators in 2010
The second column in Fig. 5 shows the relative affiliation of some indicators in the MYRB for 2010. The relative affiliation values of the degree of water resource development, total water resources, and population density in 2010 were found to be [0.61, 0.95], [0.51, 0.8], and [0.21, 0.51]. Comparing the relative affiliation values of these three indicators in 2005, the relative affiliation value of the degree of water resource development was found to decrease, while the relative affiliation value of total water resources did not change significantly. By contrast, the relative affiliation value of population density increased, while the overall ranking did not change. These results indicate that the influence of population factors on water resource carrying capacity increased.

Relative affiliation of major indicators in 2015
The third column in Fig. 5 shows the relative affiliations of some indicators for 2015. Increased economic levels, as well as factors such as population and GDP, were found to increase the carrying capacity of water resources. The relative affiliation of some indicators in the MYRB in 2015 was generally not very different from that in 2005 and 2010. However, the intervals of relative affiliation values of all three indicators expanded, with the highest relative affiliation value of 0.99 and the lowest 0.52 for the degree of water resource development. The highest and lowest relative affiliation values of total water resources were 0.8 and 0.4, respectively. The interval of the relative affiliation value of population density also increased, and the relative affiliation value of population density in some areas reached 0.6, while the value in some areas was as low as 0.2. This indicates that the influence level of each indicator on water resource carrying capacity changed with economic development.

Relative affiliation of major indicators in 2020
The fourth column in Fig. 5 shows the relative affiliation map of some indicators for 2020. The relative affiliation value intervals for the degree of water resource development, total water resources, and population density increased compared to 2015.

Water resource carrying capacity of each region in the MYRB in multiple scenarios
Combining the membership degree and variable fuzzy set, we then evaluated the water resources carrying capacity of the MYRB from 2005 to 2020. According to the calculations of the level characteristic values in the interval [0, 3], the evaluation level of water resource carrying capacity was divided into three levels: (1) when the level characteristic values were in the interval [0, 1], the evaluation level of water resource carrying capacity was considered to be at level 1; (2) when the level characteristic values were in the interval [1, 2], the evaluation level of water resource carrying capacity was considered to be at level 2; (3) when the level characteristic values were in the interval [2, 3], the evaluation level of water resource carrying capacity was considered to be at level 3. The smaller the calculation result, the more undeveloped the water resources in the area, indicating that the water resources in the area had a large carrying capacity, and the calculation result was closer to 3, indicating that the water resources in the area were in poor conditions. In turn, this indicates that the carrying capacity of water resources is close to its saturation value, at which point further development and utilization is small. This leads to water shortages and hinders the development of the social economy, for which the corresponding countermeasures should be taken. The classification basis of evaluation grade of water resources carrying capacity is shown in Table 3.

Water resource carrying capacity in the scenario with parameter α1 and p = 1
Under the conditions of α = 1 and p = 1, most areas of water resource carrying capacity in the MYRB were as shown in the first row of Fig. 6. All of them were level 2, which indicates that the water resource carrying capacity in the MYRB was in good condition. The cities with evaluation results of level 3 were Wuhan, E'zhou, Xianmen, Qianjiang, Xiantao, and Xiangyang. The water resource carrying capacities of these cities were close to saturation. From 2005 to 2020, the water resource carrying capacity of many provinces and cities in the southwestern part of the region changed from level 1 to level 2, and only the Shennongjia Forest Area and En'shi Tujia autonomous Prefecture were found to be at level 1.

Water resource carrying capacity in the scenario with parameters α = 1 and p = 2
The evaluation results of water resource carrying capacity in the MYRB under the conditions of α = 1 and p = 2 are shown in the second row of Fig. 6. According to the evaluation results, Ankang and Shangluo were at level 1 in 2005, while Nanyang, Xiangyang, Wuhan, E'zhou, Xianmen, Qianjiang, Xiantao, Xiangtan, and Hengyang were at level 3. In 2020, only the Shennongjia Forest Area and En'shi Tujia autonomous Prefecture were found at level 1.

Water resource carrying capacity in the scenario with parameter α = 2 and p = 1
The evaluation results of the water resource carrying capacity in the MYRB under the conditions of α = 2 and p = 1 are shown in the third row of Fig. 6. Under this scenario, the cities with evaluation results of level 1 in 2005 were Ankang, Shennongjia Forest Region, En'shi Tujia autonomous Prefecture, Zhangjiajie City, Xiangxi, and Tongren City. The cities with level 3 evaluation results were Luoyang, Nanyang, Xiangyang, Xiaogan, Wuhan, E'zhou, Xianmen, Qianjiang, Xiantao, Xiangtan, and Hengyang. The remaining cities were all at level 2. The evaluation results for 2020 under this scenario were the same as those for the parameters α = 1 and p = 1 and α = 1 and p = 2.

Water resource carrying capacity in the scenario with parameter α = 2 and p = 2
The evaluation results of the water resource carrying capacity of the MYRB under the conditions of α = 2 and p = 2 are shown in the fourth row of Fig. 6. The changes in the water resource carrying capacity in the MYRB from 2005 to 2020 were roughly the same as before. However, in 2020, except for the Shennongjia forest area, all other regions in the MYRB were found at level 2 or above. That The degree of water resources development is low and has great potential for development Low level Level 2 1.00-2.00 The degree of water resources development has a certain scale, still has a certain degree of development potential Intermediate Level 3 2.00-3.00 The degree of water resources development has the characteristics of saturation stage; the development potential is small Saturation level is, under such conditions, the water resource carrying capacity of the middle reaches of the Yangtze River was average.

Discussion
In this study, the degree of water resource development was found to increase from 2005 to 2020 in the MYRB. In line with these findings, Yi et al. (2020) previously noted an increased burden and consumption of water resources in the MYRB, and Yi et al. (2020) attributed this situation to an increased population and rapid economic development. The spatial distribution pattern of water resource exploration in the MYRB is high in central regions and low at more peripheral regions ). This which is consistent with the finding that the degree of water resource exploration in Hubei-Hunan Province is relatively high, reaching 40% in most cities. The analysis of population density and total water resources indicates that areas with a high population density have faster rates of economic development and higher GDP per capita, but lower total water resources, resulting in higher water resource development in areas with high population density (Wang et al. 2018). By contrast, although cities with low population densities do not develop as fast, they have higher total water resources, resulting in low water resource development in these cities (Sun et al. 2022). This leads to a situation of high water resource development in central regions and low development in the more peripheral regions.
By studying the water resource carrying capacity of the MYRB, its regional characteristic values were found to have increased since 2005, indicating an increase in the exploitation of water resources. Similarly, Zhang and Dong (2021) noted that the water-carrying capacity of the region is also rising rapidly as a result of rapid economic development. In this study, GDP per capita in the MYRB was found to have doubled in recent years, which is in line with China's rapid economic development. In addition, Ge et al. (2021); Wei et al. (2021) found that the economy of the MYRB grew rapidly with a stable total amount of water resources. However, social development is partly constrained by water resources at the current level of technology (Deng et al. 2021). However, the increasing exploitation of water resources highlights the need to exercise water use through rational and scientific methods.
The analysis of the characteristic values of water resource carrying capacity in the MYRB (e.g., En'shi and Shennongjia at level 1, Wuhan, Changsha, Nanyang, and Xiaogan at level 3 and the remainder at level 2) provided similar findings to those reported by Wei et al. (2021) using the Topsi-Aism model. Integrating the socio-economic development level and water resource base of MYRB indicated that while the economic level of the primary areas was not outstanding, their total water resources were highly abundant. Furthermore, the economic level of secondary cities was found to be good, with intermediate levels of total water resources. In turn, while the economic level of tertiary cities was outstanding, the total water resources of these cities were not sufficient to continue to support the sustainable development of the cities, in line with the findings reported by Zhou et al. (2022).

Conclusion
This study evaluated the water resources of the MYRB. The statistical data of the MYRB was calculated and analyzed for four years (i.e., 2005, 2010, 2015, and 2020). As a result, index characteristic values and an index standard value matrix of the water resource carrying capacity of the MYRB were obtained.
The main findings of this work are summarized as follows: (1) From 2005 to 2020, the population density, total water resources, and per capita water resources of MYRB did not change significantly; the water supply mode, water supply, and per capita water supply remained relatively stable, and the per capita GDP was significantly improved.
(2) The degree of water resource development, total water resources, and GDP per capita were found to be the indicators with the greatest influence on the water resource carrying capacity over time.
(3) From 2005 to 2020, the water resource carrying capacity the MYRB showed an increasing trend overall. In 2005, cities in the MYRB with water resource carrying capacity at levels 1, 2, and 3 accounted for 11.1%, 72.2%, and 16.7%, respectively. In 2010, The proportions of the cities in the MYRB with water resource carrying capacity at levels 1, 2, and 3 were 7.4%, 70.4%, and 22.2%, respectively. However, those almost accounted for 5.6%, 68.5%, and 25.9%, respectively, in 2015. In 2020, those proportions were 3.7%, 68.5%, and 27.8%, respectively. However, if the study can be carried out at the county level, the results will more accurately reflect the differences in water resources carrying capacity among regions.
was written by Yangjiale, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Data availability This research use land area data from the national administrative divisions query platform released by the national administrative data set (http:// xzqh. mca. gov. cn/ map). Data on water resources come from China's Ministry of Water Resources (http:// www. mwr. gov. cn). Social and economic data are from provincial statistical yearbooks. We would like to express our heartfelt thanks to all data supporters and websites. The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations
Ethical approval There were no studies involving human or animal subjects in this study.

Consent to participate
Informed consent was obtained from all individual participants included in the study.

Consent for publication
The authors acknowledge that all authors and participants in this study have given their informed consent to the publication of all figures in this article.

Competing interests
The authors declare no competing interests.