1. 淮阴师范学院城市与环境学院,江苏淮安 223300
2. 淮河生态经济带研究院,江苏淮安 223300

The Conceptual Model and Its Empirical Studies of Sustainable Carrying Capacity of Water Resources:A Case Study of China Mainland
ZANG Zheng1,2,*
1. School of Urban and Environmental Sciences, Huaiyin Normal University, Huai’an, Jiangsu 223300, China;
2. The Research Institute of Huaihe River Watershed Ecological Economy Belt, Huai’an, Jiangsu 223300, China;
*Corresponding author: ZANG Zheng, E-mail: zangzheng@126.com
Abstract

Based on the interactive development of new industrialization, rapid urbanization and agricultural modernization (IUAM), and from the viewpoint of interactive responses and supply-demand relationships between regional water resources carrying capacity and economic-social development, this paper puts forward the concepts and characterization methods of water resources relative intensity (WRI), water resources carrying rate (WCR) and sustainable index of water resources system (WSI). Considering the catastrophic trait of water resources carrying capacity and its contradictory relationship with WRI, a modified Catastrophe Model, which combines Catastrophe Theory and Fuzzy Mathematic Theory, was introduced to perform a multi-objective and multi-criterion comprehensive assessment of the sustainability of water resources carrying capacity (WSCC) based on benchmarking. According to these concepts and models, land WSCC for the China mainland was set as an example for empirical analysis. The results showed that at the scale of first-grade water regions, Liaohe River, Yangtze River and Pearl River regions had high WRI of domestic water, while Northwestern Rivers, Southeastern Rivers regions and Yangtze River region in some years had high WRI of eco-environment water. However, they were all in a downtrend, while the other four northern regions had low WRI in an uptrend. The agricultural WRI in Songhua River, Yellow River and Northwestern Rivers regions were relatively high and industrial WRI in Songhua River, Yangtze River and Pearl River regions were also relatively high. At the provincial scale, WSCC of urban domestic water was relatively stable, WSCC of eco-environment was obviously fluctuating, and WSCC of agriculture and industry were constantly rising. Overall, WRI in the China mainland generally decreased. The convergence of provinces with high consumption intensity of water resources and spatial spillover of WUE in high WCR provinces promotes water resources development and utilization, progressing toward doubly sustainable development. In the future, China should try to find new ideas and methods of dynamic management of regional water resources and unified management of basin water resources, building on the foundation of traditional water resources planning. Meanwhile, water resources should be considered in regional PRED (population, resources, ecology and development) systems for integrated dispatching and optimizing configuration so that the improvements of WSCC and harmonious development of water resources and regional populations, eco-environment, economy and society can be achieved.

Keyword: hydrography; multi-objective optimization; sustainability; supply-demand relationship; China mainland
1 Introduction

National or regional resources carrying capacity is the population that the nation or region can continuously sup-port with local energy, natural resources, human intelligence and technology under a living condition that agrees with its social cultural norms for a foreseeable period (UNESCO, 1985). With more and more research on sustainable development, the concept of resources carrying capacity has expanded in its overall vision and visibility in many fields including human resources, social resources and natural resources (Irmi et al., 1999; Arrow et al., 1995; Cohen, 1997). Consequently, the concepts of population carrying capacity, cultural carrying capacity, land carrying capacity and water resources carrying capacity (WRC) have emerged and they have been applied widely, enriching the approaches and methods for sustainable development research (Daily et al., 1992).

WRC is one of the important components of resources carrying capacity. It is a critical indicator for measuring the relationship between development and utilization, supply and demand of national or regional water resources. Overseas WRC research has always involved water resources in regional sustainable development (Yao et al., 2002), and is characterized by less specialized research than land carrying capacity (Long et al., 2004). The uneven spatial-temporal distribution of water resources in China leads to serious problems of regional water resource shortages. In that case, Chinese scholars have completed a series of studies mainly on WRC and have made many notable achievements. Shi et al. (1992) put forward that WRC is the maximum economic scale, urban development scale and population capacity that regional water resources could bear without damage to society and the ecosystem under the existing stage of social lifestyle and scientific technology. Based on traditional multi-objective analysis and decision methods, Xu et al. (1999) studied the WRC of Heihe River basin in Gansu province by a scenario analysis method. Xia et al. (2002) illustrated the microscopic conceptualization and challenges of WRC from the view of water resources security. They then came up with the measurement and assessment methods of WRC considering both the total and its components, ecological water demand, balance index of basin water resources and others. Cheng (2002) sorted out the developmental history and evolutionary characteristics of resource carrying capacity, illustrated the application background and conditions of carrying capacity, and put forward the application framework and assessment indicator system of WRC in the Northwest of China. Wang et al. (2004) came up with the assessment indicator system and calculation process of WRC in arid regions according to the high dependence of these ecosystems on water resources in eco-environmentally fragile regions. Zuo (2005), Fang (2005), and Duan et al. (2010) respectively completed empirical studies on the concepts, theories and methods of urban or regional WRC at different time-space scales. In addition, Min et al. (2004), Liu et al.(2011), Xie et al. (2005) and Zhou et al.(2006) used Fuzzy Mathematic Theory, System Theory, Index Evaluation and PCA (Principal Component Analysis) to carry out integrated analyses of WRC in different regions.

To sum up, all of these Chinese studies on WRC have enriched the quantitative evaluation methods of sustainable development. However, because there have been few essential breakthroughs in recent years, the progress of WRC research has become slower than ever.

At present, China is in a developing period of IUAM interaction and coordination. Rapid changes of regional urban populations, land use types and water utilization efficiency (WUE) of industrial and agricultural production not only bring pressure to regional sustainable development (Li et al. 2013, Yang et al. 2014; Wang et al. 2014), but also add uncertainty to the unified management of basin water resources. Sustainable utilization of water resources in some regions is in a state of emergency (Ling et al., 2012). With the increases of water demand, traditional water resource recycling has changed from a signal natural-driving mode to a binary nature-human-driving mode (Wang et al. 2009). The change from one steady state to another in the developing process has threatened the healthy and stable development of the regional economy and society. WRC is a dynamic concept, in which the connotations of relative limits and ethical features are included. Having close relationships with water resources endowment, development and utilization methods, social choices and human values (Yao et al., 2002), WRC is essentially dynamic and nonlinear (Arrow et al., 1995; Cohen, 1997; Jin et al., 2018). Traditional water resources planning has emphasized the static assessment of WRC based on human water demand. However, the assessment method, replacing demand by supply or replacing supply by demand, might neglect the complicated relationships among different water demands (Long et al., 2004) and lack the thinking of dynamic responses between the supply and demand (Chen and Yu, 1999). Therefore, this deficiency may cause water resources planning to depart from the essence of sustainable development, and limit the function of guiding production and practice. Considering the special historical background of IUAM promotion, from the view of the coupled PRED system consisting of regional water resources, local population, eco-environment and economic-social development (Chen and Yu, 1999; Chen et al., 2000), this paper proposes the concepts and characterization methods of regional WRI (water resources relative intensity), sustainable carrying capacity of water resources (WSCC) and WSI. Considering the fuzziness, catastrophe, uncer-tainty and nonlinearity of regional water resources systems, and based on the contradictory relations among regional water demands, human demands and WSCC, a multi-objectiveand multi-criterion comprehensive assessment of the sus-tainability of WSCC for the China mainland was completed, in which a modified Catastrophe Progression Method was used by referencing Fuzzy Mathematic Theory and Catas-trophe Theory. It provides a new concept and method for dynamic assessment of regional WRC in the context of a changing environment.

2 Research methods
2.1 Concept and connotation of WSCC

2.1.1 Characterization of water demand and consumption level

From the perspective of the relationship between water re-sources and humans, water resources (R) and regional population (P), eco-environment (E) and economic development (D) restrict and promote each other to consti-tute the complex PRED system (expressed simply as “ water resources system” hereafter). Like energy consumption, water resource consumption is an important basis to supporthuman daily life, to protect the eco-environment and to maintain economic development. Therefore, referencing the concept of energy intensity, regional water resource intensity (WI) is defined as the water resource consumption per unit population, unit land acreage (characterizing eco-environment) or unit economic output (characterizing development). The formula is as follows:

$S=R/CQ\ (1)$

where S is regional WI (unit: m3/person, m3/ha-1 or m3/(104 Yuan) characterizing water consumption level of relevant sectors; R (unit: m3) stands for the supply amount of regional water resources of each sector, respectively the supply amount of domestic water, economic production water and eco-environmental water; and CQ (unit: person, ha or 104 Yuan is the real carrying capacity of regional water resources, namely the real population, land scale or economic scale supported by the regional water resources. To evaluate the consumption level of regional water resources from relative aspects, a WRI model was put forward as expressed below:

$LS=S/{{S}_{0}}\ (2)$

where LS is the regional WRI (zero dimension) that characterizes the comparison of regional WI and average consumption that is set as reference standard; and S0represents the reference standard of WI, namely the fiducial value of comparison. Because there is no unified or perfect benchmarking water efficiency (Zheng et al., 2018) the demands for residential living, economic development and eco-environmental demands at present, this study replaces it with the average water consumption of the reference areas as follows:

${{S}_{0}}={{R}_{0}}/C{{Q}_{0}}\ (3)$

where R0denotes national annual water consumption of water sector in the reference areas; and CQ0stands for the real population, land scale or economic scale supported by some sector of reference areas.

2.1.2 Concept and characterization of WSCC

In order to make WRC close to the essence of sustainable development, the concept of regional WSCC is put forward based on the PRED system. It is defined as the optimum population, land or economical scales that the supply amount of regional water resources could bear in a certain historical period, with a certain productivity and technological condition, which put sustainable water utilization and economic-social development as targets (a double sustainable standard). It can be expressed as:

$CC=R/{{S}_{0}}\ (4)$

where CC(unit: person, ha or 104 Yuan) is regional WSCC. According to the concept mentioned above, S0has the connotation of an ideal value that guarantees both sustainable utilization of water resources and economic-social development demand. As the reference standard, the WSCC in reference areas (CC0) equals its real carrying capacity, that is to say:

$C{{C}_{0}}=C{{Q}_{0}}\ (5)$

where CC0as the reference standard, is the optimal WSCC; therefore, CC0 stands for the optimal WSCC, namely the ideal value under the double sustainable standard.

2.2 Comprehensive evaluation indicators of
sustainability for water resources system

2.2.1 Quantitative characterization of the contradiction between water supply and demand

To further compare real carrying capacity with its ideal value (namely WSCC), the WCR model was established as follows:

$CR=CQ/CC\ (6)$

where CR is WCR (zero dimension). CR> 1 is called overload, representing real carrying capacity higher than the ideal value, whileCR< 1 is an under load scenario. CR=1 is called full load, denoting that real carrying capacity equals WSCC, that water resources are being fully utilized, and that the carrying capacity is in an ideal state of sustainability.

According to the above mentioned concept and connotation, under the conditions of the current stage and existing technology, the ideal situation of water supply and demand occurs when CR=1. Namely, the water supply to regional (or each part of a sector) residential living, economic productivity and eco-environment quality is ensured and the configuration and utilization of regional water resources is reasonable. CR> 1 represents cases where regional WI is low, but water supply to residential living, economic productivity and eco-environment quality cannot be guaranteed. Nevertheless, CR< 1 describes cases where water supply to residential living, economic productivity and eco-environment quality is well guaranteed, but the WI is higher than the reference standard, meaning that water resource allocation is unreasonable and the function of water resources does not work well, which ultimately leads to water resource waste. Transforming formula (1), putting it into formula (6) together with formula (4), and combining formula (2), yields a new formula as follows:

$CR\times LS=1\ (7)$

Formula (7) shows that, with a certain amount of water resource supply to a region or a sector, co-rotating changes of CR and LS are impossible. If WSCC is reduced, the WRI will increase, which would lead to an unreasonable configuration (being occupied) and inefficient utilization (being waste) of water resources. Alternatively, if WSCC rises, WRI will decrease, which may make real population, land and economic scales larger than the ideal values of regional WSCC of some sector, or have a harmful impact on the whole economic-social system function because the sector’ s water was occupied.

2.2.2 Constitution of a regional water resources system based on PRED perspective

As mentioned above, in a regional PRED system, water resources and regional population, the eco-environment and economic-social development are coupled, and constitute a water resources system with n subsystems. Because water resources support the population, land and economic development, it can be divided into three subsystems including a water resources-population subsystem (R-P), a water resources-environment subsystem (R-E) and a water resources-development subsystem (R-D). Meanwhile each subsystem is formed by m elements (or water sectors). The complicated inner mechanisms of each subsystem and each element in the subsystems causes the fuzziness and uncertainty of the regional water resources system (Lindberg et al., 1997; Buckley, 1999). In the context of IUAM interactive development, regional population, eco-environmental and economic scales dynamically change. Adjusting living, eco-environmental and production water scales according to different developing targets from microscopic viewpoints is necessary, as well as adjusting water demand according to different criteria from microscopic viewpoints. Increasing or decreasing of living, eco-environmental and production water supplies lead to responses of the regional water resources system, which influence the development of human living, eco-environment and production. Due to space limitations, only parts of this scenario are listed in Table 1.

Table 1 Contradictory scenario of regional water resource supply and demand in the context of IUAM interactive development

2.2.3 Comprehensive assessment of WSCC

To describe the sustainable stage trait of the water resources system, a comprehensive assessment model of the water resources system was proposed using the concept of fuzzy membership in Fuzzy Mathematical Theory (Min et al., 2004). The formula is as follows:

${{D}_{ij}}=|C{{R}_{ij}}-\text{1}|\ (8)$

$SI=\sum\limits_{i=1} {n}{\sum\limits_{j=1} {m}{{{W}_{ij}}\cdot U({{D}_{ij}})}}\ (9)$

where Dij (zero dimension) is the absolute distance between the condition of water supply and demand and the ideal condition of the jth water sector in the ith subsystem. A larger value indicates a larger gap to the ideal condition. SI(zero dimension) is WSI, ranging from 0 to 1. A larger value of SI denotes worse sustainability of the water resources system, meaning that there is much to do to optimize the water resources configuration and improve WUE.Wij is the normalized weight of different water sectors; and U(Dij) is the corresponding fuzzy membership.

According to formula (4), the concept of WSCC, involved in the double sustainable connotation, is a dynamic assessment indicator focusing on human demands and WSCC. Therefore, WSCC is elastic in a certain period. It is feasible to promote sustainable development of a regional water resources system through engineering technology or to make reasonable criteria. In the regional PRED system, water resource consumption is the material basis to support human living and development. A series of intervening measures or incentive policies will be used for improvement, if either human living, production and consumption cause over-consumption of water resources, or undersupplying of regional water resources reduces the residential living level, production efficiency and eco-environment quality, or an imbalanced allocation of water resources threatens regional sustainable development. Therefore, the public comprehensive judgment of the current water resources system condition is the precondition of taking adjustment and control actions. Hence, referencing relevant research results (Zuo et al., 2008; Yao et al., 2008), and the concept of warning color signals used in Meteorology and Science of Disaster, a classification standard of sustainable stages and the warning signals of regional water resources system was proposed (shown in Table 2) according to WSI. In conjunction with Table 1, this system was used to assist in the assessment of the regional water resources system.

Table 2 Assessment standard of development stage and warning states of regional water resources system
2.3 Multi-objective solution of the water resources system based on Catastrophe Theory

2.3.1 Analysis of catastrophic traits of water resources system

According to Table 1 and the abovementioned WSCC concept, in a given area or a certain inner sector, the ideal values of WI and WCR are 1. Real carrying capacity of water resources higher or lower than theoretical WSCC will lead to either overload or under load of the regional water resources system. Therefore, water resources system has the obvious catastrophic trait and bifurcation (Yao et al., 2013; Li et al., 2013; Sun et al., 2013). The system changes from one stable state to another when one or more parameters were disturbed to break through the ideal WSCC value or standard of WI by themselves or by outside forces. Finally, system structure and function will change dramatically. Therefore, Catastrophe Theory and the Catastrophe Progression Method were introduced to perform a multi-objective and multi-criteria assessment of the regional WSCC to improve its scientific basis and reliability.

2.3.2 Solution of indicators membership and critical value

Catastrophe Theory was established by Thom based on Bifurcation Theory, Singularity Theory and Stability Theory. It was used to study the discontinuous movement (Zheng et al., 2014). The model was established by analogy and topological transformation and assesses the singularity of the model to explain and forecast the change of the system. Here it is applied to multi-objective system evaluation and decision-making. The Catastrophe Progression Method decomposes the multi-layer targets into many levels. Then we use the catastrophe model and fuzzy mathematical model to get a multidimensional Fuzzy Membership Function. Finally, the membership functions of general targets can be obtained by quantitative calculation of the normalization formulas.

The simplified solution process is shown here. The general indicators, sustainable carrying rate of water resources system, were decomposed into three layers (target layer, criterion layer and indicator layer, shown in Table 3) to determine the catastrophe type. The discontinuous process of the system, rapidly changed from a stable configuration to another by disturbance, can be expressed by geometric figures with particular shapes (different catastrophe types have different corresponding potential functions, shown in Table 3). Then the critical point of the system was classified by the potential function and the bifurcation set was normalized to get the U(Dij) of bottom indicators as well as the catastrophe membership of the general indicator. Finally, analyzing and evaluating the characteristics of discontinuous change progress around the critical point is available (i.e., critical value obtained). More details can be obtained from the relevant reference (Zheng et al., 2014).

Table 3 Assessment indicator system of WSCC and corresponding formulas of catastrophe models

2.3.3 Indicator weight and decision-making principle

Control variables and state variables of the catastrophe model are two aspects of the contradiction. The control of the former over the latter is determined by the model. Thus, the influence of control variables on state variables is different. In the course of solution, the relative importance of each control variable needs be determined. The method of Delphi is a commonly used method. Besides, decision- making principles should be determined according to the real situation. If indicators have little connection or are independent, we should choose the non-complementary minimax principle, otherwise if indicators connect closely, the complementary principle (averaging) is suitable.

Considering that the sustainable utilization target of water resources contains both natural and social attributes, to lessen the influence of subjective weighting to the uncertainty of results, this study follows several steps to modify the weight solutions of the control variables. According to calculated values of each water resource subsystem or sector, a subjective weight was obtained by AHP and an objective weight by the entropy method. Next, the weighted average was set as the combination weight to determine the relative importance of evaluated indicators. In that case, catastrophe progression and the membership of the target layer can be obtained. This process makes the results more scientifically objective and reliable. Since these two methods are widely applied, these steps are explained in greater detail in some methods papers (Min et al., 2004; Liu et al., 2011). Besides, considering the checks and balances among human living water, eco-environment water and production water, this study chose the complementary principle.

3 Empirical analysis

Because of the uneven distribution of water resources at temporal-spatial scales, the different situations of regional population distribution, resource endowment and economy development, the contradiction between water resource supply and demand has been one of the major problems restricting water resource sustainable development and utilization in China. To embody the close relationship between water resources and regional demands an empirical analysis has been completed based on 31 provincial administration and 10 first-grade regions of water resources in China. Hong Kong, Macao, Taiwan and Diaoyu Island, and the South China Sea Islands were not included for lack of data.

Due to data availability and the reliability of evaluation results, this assessment focused on urban residential domestic water (R-P), eco-environmental water (R-E), agricultural water and industrial water (R-D1, R-D2) from 2001 to 2017 (odd years). For data sources, the supply amounts of the four types of water resources, population scales, acreage of urban green land and output values of agriculture and industry in each provincial administration came from Chinese Statistical Yearbook. The eco-environmental water of Tibet in 2005, 2007, 2009 and 2011 was calculated by linear interpolation. The supply amounts of the four types of water resources of first-grade regions were collected and calculated by referencingWater Resources Bulletin, Chinese Urban Statistical Yearbook and the national water resources division guidelines published by SAC.

Calculated by formula (1) to formula (3) and previous data, the WRI for urban residential domestic water, eco-environmental water, agricultural water and industrial water of 10 first-grade water resource regions on the China mainland are shown in Fig. 1. Fig. 1 shows that, except for the WRI of Southwestern Rivers and Huaihe River which were relatively low, the changes of WRI in other basins was irregular.

 Figure Option Fig. 1 Comparison of water resources relative intensity for first-grade water resource regions in China mainlandNote: T1 to T9 stand for 2001, 2003, 2005, 2007, 2009, 2011, 2013, 2015, 2017 respectively.

For domestic WRI, the LS values of Songhua River and Southeastern Rivers regions were close to 1, which indicates that the WRI of residential domestic water is roughly the same as the national average. City close-set areas, including the Liaohe River, Yangtze River and Pearl River basins, have higher LSvalues demonstrating that water resources in these regions have made big contributions to supporting urban residents’ living. Low values of LS appear in the Yellow River, Huaihe River, Northwestern Rivers and Southwestern Rivers basins, which denote that compared with the national average, per capita domestic water consumption in these regions was lower. These regional differences might have emerged from local eating habits, life style, water abundance and allocation.

For eco-environmental WRI, the LS of Pearl River and Southwestern Rivers regions were low. LS of the other four northern regions, except for Northwest Rivers region, were also low but have been on the rise; and the WRI of Northwest Rivers, Southeast Rivers and Yangtze River regions were high in some years. In particular, LS of eco-environmental water in the Northwest Rivers region was obviously high. The eco-environment cannot be improved without the contribution of water resources, but unrealistic targets of eco-environment protection complicate reasonable utilization strategies for regional water resources (Lu, 2009). Therefore, the north, which is relatively short on water resources, should consider regional realities to make scientifically-sound ecological planning and adjust measures to local conditions to develop public green policies.

For agricultural WRI, Songhua River, Yellow River and Northwestern Rivers regions were at high intensity. Specifically, LS of Northwestern Rivers region was higher than the national average. LS of Yellow River was high as well, where it was influenced by climate, planting construction of crops and other factors. Songhua River region is an important commodity grain base. Although the amount of water resources in this region is not small, the uneven distribution of water resources diminishes from east to west and north to south, and leads to heavy agricultural WRI. Compared to the national situation, agricultural WRI levels were not high in other regions. However, considering the primary status of agriculture, there is plenty of remaining WI to ensure national food security.

For industrial WRI, a heavy load intensity was found in Songhua River, Yangtze River and Pearl River regions. This might be because Yangtze River and Pearl River regions have large industrial scales and abundant water resources, and Songhua River has a large proportion of the heavy industry and many water-consuming enterprises. In contrast, LS of Northwest Rivers and Southwest Rivers regions were low considering their small industrial scales. Five regions in the north and Southeast Rivers region had lower intensity for the improvement of industrial WUE or the optimization of the industrial distribution that was caused by water resource shortages, and is worthy of further research.

3.2 Analysis of WSCC in each provincial administration

According to formulas (3) and (4), the WSCC for residential domestic water, eco-environmental water, agricultural water and industrial water in the provincial administrations of the China mainland were calculated and are shown in Fig. 2a to Fig. 2d.

 Figure Option Fig. 2 Changing trends of WSCC for Provinces in China mainlandNote: P01 to P31 respectively stand for Beijing, Tianjing, Hebei, Shanxi, Inner Mongolia, Liaoning, Jilin, Heilongjiang, Shanghai, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Shandong, Henan, Hubei, Hunan, Guangdong, Guangxi, Hainan, Chongqing, Sichuan, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang; T1 to T9 respectively stand for 2001, 2003, 2005, 2007, 2009, 2011, 2013, 2015, 2017.

Fig. 2a shows that the change of urban residential domestic WSCC was relatively gradual, which is noteworthy since China’ s urban population has expanded constantly and rapid urbanization has a stable impact on urban residential domestic water use because the priority was given to residential domestic water. Combining detailed calculation results, we show that WSCC of Beijing, Tianjin, Fujian, Hainan, Chongqing, Shaanxi, Qinghai and Ningxia remained stable; WSCC of Liaoning, Hunan and Guizhou had a small downward trend while those of other provinces fluctuated in a narrow range; the lowest values existed in Tibet, Qinghai and Ningxia, which reflects their underpopulation and low-level urbanization; and Guangdong had the highest WSCC for urban residential domestic water (over 160 million people all the years) which conformed to its first-large population status and highest level of urbanization.

Fig. 2b shows that WSCC for eco-environment water was fluctuating within a broad range and provincial eco-environment water supply was unsteady, which indicate that urban green land water was easy to obtain by other business and local government decisions. For instance, municipal construction during the urbanization process made acreage of urban green land and the water guarantee of green land catastrophic and uncertain (Guo et al., 2013). The theoretical upper limit of WSCC for eco-environment in Xinjiang was the highest, and was over 300 thousand hectare except for during the last stage. The arid climate leads to high WI for eco-environment. Otherwise, WSCC for eco-environment in Jiangsu and Zhejiang were also high, which suggests the water consumption by eco-environment was relatively high and the water supply for urban gardening and public green land was well-guaranteed.

It is clear from Fig. 2c and Fig.2d that WSCC for agriculture and industry had obvious uptrends, which indicates that the water guarantee for agricultural and industrial production was continuously increasing. In recent years, the WSCC for agriculture in Xinjiang, Heilongjiang and Jiangsu were higher while Beijing, Tianjin and Shanghai had lower values. This kind of distribution indicates that the agricultural water guarantee has close concerns with its production conditions and land resource endowments. Therefore, the generalization of water-saving irrigation and improvement of agricultural WUE will be two of the important indicators of agricultural modernization. The high WSCC of industrial water in Guangdong, Jiangsu and Hubei manifests their large scales of industrial development. While guaranteeing industrial production water, ensuring the improvement of industrial WUE will become one of the problems these regions have to actively face during their new-type industrialization processes. The low WSCC for industrial water in Hainan, Tibet, Qinghai and Ningxia are ascribed to small industrial scales, while in Beijing and Tianjin they are low because non water-intensive industries and less water-intensive industries comprise the majority of their industrial structures.

3.3 Analysis of the comprehensive assessment of the land water resources system for China

WCR of the China mainland was calculated by formula (6) and related data, and it was normalized according to the smaller-better principle. The subjective weight vector of subsystems R-P, R-E and R-D calculated by AHP was w1= [0.600, 0.200, 0.200] Tand the objective weight vector calculated by the entropy method was w2= [0.241, 0.250, 0.509] T. So the combination weight was W= [0.421, 0.225, 0.354] T; the Catastrophe membership degree of the general indicator and 3 subsystems was calculated according to catastrophe model, the fold, the cusp and the swallowtail, as shown in Table 3. The WSI for each province from 2001 to 2017 was calculated by formulas (8) and (9). The normalized average of indicators was divided into 5 sections with intervals of 0.2. Combining catastrophe model and combination weight, the critical value (1‒4) of each interval value was obtained. According to the criteria in Table 2, the development stage and warning state of the water resources system in each province was evaluated comprehensively.

With a certain water resource supply, regional WSCC is a multi-objective function of economic-social development scale, water utilization structure, water resources management level and policies (Lu, 2009). According to the abovementioned definition and formula (10), the value of SI is the weighted distance between the real situation and the ideal situation of the regional water resources system. The assessment results indicate the integrated condition of regional water resources. From Table 4 and Fig. 3, we can see that in the initial stage there were 16 provinces on the China mainland in a stage of quasi-sustainable development (yellow warning), 7 in a stage of pseudo-sustainable development (orange warning) and 7 in a stage of weak-sustainable development (blue warning). As for the spatial distribution, provinces with corresponding warning grades were dispersed (Fig. 3a). In the last stage, with the positive changes of Xinjiang province (non-sustainable development, red warning), the number of provinces in the other 4 development stages change the same. The numbers of provinces in orange, yellow, blue and green warning states are, respectively, 7, 8, 9 and 7. As for the spatial distribution, the provinces with corresponding warning grades were concentrated.

Fig. 3 shows that in the initial stage the WRI in each province were high, showing a distribution of high agricultural and eco-environmental WRI in middle-western China and high industrial WRI in eastern China. There are large differences of water sectors among provinces. According to the former definition, LS > 1 denotes that its WRI was higher than the national average and WCR was relatively lower. Conversely, LS< 1 denotes that WRI was lower and WSCC was higher. Therefore, with the interregional dispatch and inner configuration adjustment of water resources, in last stage WRI for the China mainland generally declined. The convergence of provinces with high consumption intensities of water resources and spatial spillover of WUE in high WCR provinces promote water resource development and utilization, ultimately developing toward double sustainable development.

Table 4 Comprehensive assessment results of water resources for the China mainland

 Figure Option Fig. 3 Grade distribution of comprehensive evaluation of water resources system for the China mainland

4 Conclusions and discussion

As one of the important concepts for sustainability, WSCC quantitatively measures the development and utilization, supply and demand relationship of national or regional water resources. It is not only an abstract definition, but also one of the multidimensional and specific evaluation indicator systems for measuring human welfare and regional sustainable development. From the view of contradiction between regional water supply and demand, this paper puts forward a model for measuring regional WSCC dynamic response. Through empirical analysis of China’ s land WSCC, we arrived at several conclusions.

During the period of investigation, WI of the Southwestern Rivers and Huaihe River regions were relatively low. There is no apparent rule for WI in other basins. Relevant regions should pay attention to the conflict between regional water supply and demand, involve water resources in the unified management of regional PRED systems, and determine scientifically binding targets of population and economic development scale to explore a feasible way of achieving ecological civilization.

During the period of investigation, the carrying capacity of urban domestic water for the China mainland was relatively stable, the carrying capacity of eco-environment water was fluctuating, and the carrying capacity of agricultural and industrial water was continuously rising. Each region should optimize regional configuration plans based on reality, reasonably develop and utilize water resources, and solve the conflicts between water supply and demand among different industries gradually.

During the period of investigation, the PLE water contradiction of the China mainland underwent a stage of constant pressure and a stage of easement. Sustainable utilization of water resources in each province shows complex regional differentiation. Relevant departments should constantly promote the construction of water-saving irrigation and inter-basin water transfer projects in the main grain producing areas and ecologically fragile regions, ensure coordination of the water supply of major economic zones and urban agglomerations, enhance water supplies of urban and rural areas, and strengthen emergency response abilities.

In the future, relevant departments in China should explore new concepts and new methods of pluralistic water resource management, such as dynamic management of regional water resources and unified administration of cross-basin water resources, building on the foundation of traditional water resource planning. At the same time, it is necessary to make reasonable water resource planning decisions based on water resource security to promote the harmonious development of water resources along with the regional population, the eco-environment, economy and society.

National and regional water resources are limited. The conflicts of water resources supply-demand among different regions, different sectors, different parts of the basins and human production, human living and eco-environment are complex (Zuo et al., 2014). Otherwise, considering the availability of data and reliability of results, this paper microscopically examined temporal-spatial changes of sustainable WSCC of first-grade water regions and provincial administrations for the China mainland from the aspects of urban residential domestic water, eco-environmental water, agricultural water and industrial water. By comparison with relevant references, this analysis found that former results are consistent with the situation of China mainland water resources development and utilization. These results are highly visualized and reliable. Compared with the WSCC studies based on background analysis, conventional tendency method, fuzzy comprehensive evaluation, PCA and entropy evaluation, from the point of compound relationships that coupled water resources and regional populations, eco-environment and economic development, this study has some differences. We defined the concept of regional WI and WRI, WSCC and WCR, which combined absoluteness and relativity, qualifying and quantifying, and dynamic and static states. Considering the fuzziness, catastrophe and nonlinearity of water resource systems, this study introduced multi-objective and multi-criterion decision and planning methods so that the evaluation embodied the combination of subjective and objective, linear and non-linear, economic development and ecological civilization. Besides, based on the concept and characterization method of WSI, a classification standard of sustainable development stages and warning states was employed to assist the evaluation. It was highly operable and provided concepts and methods to relevant departments to improve WUE and resolve the conflicts between resources supply and demand of basins on the basis of regional rural-urban population structure, eco-environment endowment and industrial distribution (The Xinhua News Agency, 2014). At the same time, in future research, we should include more empirical analysis and further study on extension of the temporal scale, detailed evaluation indicators, definition and description of catastrophic points of WSCC and water resources systems to improve the scientific basis, reliability and universal applicability.

The authors have declared that no competing interests exist.

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