Evaluation of water resource carrying capacity of two typical cities in northern China

Global climate change and human activities are increasingly affecting the regional water resource carrying capacity (WRCC). For sustainable development, an important social challenge is understanding the carrying level of regional water resources. In this study, to assess the WRCC status, we used a fuzzy comprehensive evaluation model and combined the natural and social attributes of WRCC. Moreover, from the three dimensions of support force subsystem, pressure force subsystem (PFS), and regulation force subsystem (RFS), 12 evaluation indicators were selected. Furthermore, using the fuzzy comprehensive theory and natural and social comprehensive indicators, we constructed a WRCC-level evaluation model and used it to evaluate the carrying level of two typical cities in China, Shijiazhuang and Langfang, for the 2006 – 2015 period. The results demonstrate that the regional water-carrying status of each of these cities is slightly above that of WRCC and that carrying levels show an interannual increasing trend. Note that, in both cities, the primary reason for the low regional WRCC is water shortage, while PFS improvement, supported by an interannual PFS increasing trend during the same time period, is the primary reason for carrying-level improvement for both cities in the past 10 years. For the RFS dimension, evaluation scores were in the range of 2.14 – 2.98 for Shijiazhuang and 2.12 – 2.79 for Langfang. Furthermore, the evaluation model and the indicator system demonstrated complementary functionality; thus, our results have an important academic value, particularly with reference to evaluating the WRCC. For the regional management of water resources, our study provides both the theoretical basis and data support.


INTRODUCTION
Because of climate change, processes related to the water cycle have changed considerably. The spatiotemporal distribution and the available amount of water resources have been altered, which has affected the regional water resource carrying capacity (WRCC) (Brown et al. ; Wang et al. ). The United Nations Educational, Scientific, and Cultural Organization World Water Development Report reported that, with an increase in water demand and the influence of climate change, the amount of available water resources of multiple regions will continuously decrease (UNESCO ). Because of the influences of rapid economic and social development and climate change, the imbalance between demand and supply of water resources has increased, the water environment pollution has increased, and the natural ecosystem has been incrementally damaged (Cosgrove & Rijsberman ).
Thus, for managers, investigating the WRCC has gradually become an urgent problem. In particular, under the influence of both climate change and human activity, the supply and demand of water resources in the basin is unbalanced, and natural disasters attributed to excessive water use are increasingly evident (Liu & Yang ), particularly in northern China. After the 1990s, large areas in Hebei Province, China, experienced groundwater overexploitation, which has caused disasters to occur from time to time in recent years.
The WRCC, which expands the concept of carrying capacity in the field of water resources, is a part of natural resource carrying capacity. In the late 1980s, the WRCC was proposed by Chinese researchers because of the increasingly prominent water problem. Internationally, to replace the WRCC, the concept of rationing the water supply to water demand or water availability is often used. For example, Falkenmark & Lundqvist () used the concept of water availability to mean the same as the WRCC when they examined how to deal with water security issues for policy orientation and human adaptability. Similarly, in rural areas, during a study of key environmental indicators of sustainable development, Schultink ()  Recently, many studies have focused on the concept, connotations, and evaluation of WRCC (Wei et al. ).
Currently, the WRCC is considered to have three components: the theory of scaled water resource development, water resources supporting sustainable development capacity, and water resources supply to the largest population (Zhou et al. ). To address the scaled development of water resources, the focus is on the extent of water resource development and use that can nevertheless guarantee the coordinated development of the economy, society, and ecological environment under the current and foreseeable productivity, and the scientific level via allocation of water resources (Li et al. ; Yang et al. ). The key point is to ensure that the WRCC is at the maximum capacity that can still support sustainable economic and social development based on a certain level of science while still maintaining the ecological environment. The requirement for water resources to supply the largest population is related to the regional capacity of water supply to meet population size. Accordingly, the WRCC needs to address the maximum population capacity because of the current and expected regional economic Many researchers focused on the exploitable scale of water resources or the capacity of water resources to support the economy and society; therefore, studies on WRCC should focus on its evaluation and analysis of its application.
The selection of a more effective method for scientific evaluation is a popular topic, particularly the evolution of water resource endowment because of climate change.
Many methods are being developed to evaluate the WRCC: they can be divided into empirical estimation, index system evaluation, and complex system analysis.
When searching for individual influencing factors, the empirical estimation method requires experienced researchers to estimate the regional WRCC. This type of method has a certain subjectivity because it does not consider a sufficient number of factors, e.g., based on the conditions in Israel. Walmsley et al. () reported that the water resources in the Shiyang River Basin could supply to a larger population and economic scale. To calculate the water consumption of human beings, Hoekstra & Chapagain () used water footprints, basically reflecting global water resources. To evaluate carrying capacity, the index system evaluation method uses several indices that influence the WRCC. This method's advantage is that there are no limitations on the characteristics of the study area, the application of a mathematical theory is more exten- Furthermore, by integrating multiple requirements, the final recommended scheme is obtained (Qiu et al. ). Based on an original model combined with the regional water resource change and differences in regional water use and accommodating the changing environment, we chose to study Shijiazhuang and Langfang, two typical cities in northern China. Furthermore, we aimed to analyze and evaluate the WRCC, study the contribution of water resource change to the carrying capacity under climate change, investigate the regional WRCC because of different future development modes, predict the WRCC and the degree of overload in different years, and evaluate local reasons for overload. For the regional management of water resources, our study provides both the theoretical basis and data support.

Fuzzy comprehensive evaluation model
The WRCC scheme is affected by multiple indices. Although each index is known to exert mutual influence, the degree is unclear and thus cannot be quantitatively expressed.
the characteristic value of each index of scheme j. Moreover, X is the scheme set of WRCC; x ij is the value of index i of the scheme j; and the interval range of single index i of the scheme set is determined as where I ij is the optimal interval of index i in scheme j, and the upper and lower limits of the optimal interval are the extreme values of index i in the scheme set or the interval range of the internationally recognized index is considered. Based on the evolution of the relative difference degree of variable sets, the optimal interval I ij is divided into c level, and the interval matrix of index eigenvalues of c level is given by  (1), , the point k ih with the corresponding level h membership degree of 1.
where k ih is the point with the subordination degree of h level corresponding to index i in the optimal interval, and c is the index evaluation level; other variables are defined above. From Equation (1) and matrix I, to obtain matrix , if the eigenvalue of the scheme set index x ij is in the interval between two adjacent levels h and (h þ 1) of matrix K, the relative membership degree of x ij to level h is then calculated as follows: where μ ij (u j ) is the relative membership degree of index i of scheme j to level h and other variables are defined above.
Note that the relative membership degree of x ij is 0 when it is less than h and greater than (h þ 1). Similarly, the relative membership matrix μ h (u ij ) of each index of u i is obtained, and the comprehensive relative membership vector of each scheme to level h is then calculated as follows: where V h (u j ) is the relative membership degree of each index of scheme j to level h; w i is the weight of index i; and w 1 þ The characteristic value in the corresponding level of scheme j is derived as follows: where v 0 h (u j ) is the normalized vector (v h (u j )). In this study, to form the evaluation system, we established the primary indicators affecting the WRCC. Because of certain complicated influence indicators, many factors are involved, and we used multivariate membership functions for judgment. Thus, we based the building of the evaluation indicator system on previous studies and the fuzzy mathematical theory.

Evaluation indicators for WRCC
The traditional concept of WRCC emphasized that water resources could afford the freshwater requirements of human activities, which should not affect the laws of nature; however, because of the development of various WRCC theories, the WRCC concept embraces a wider understanding such as allowance for maintaining the original natural state of the water cycle and the effect of climate change and human activities. Note that climate change affects the amount of water resources available regionally and determines the primitive carrying capacity of regional water resources (Zhang et al. ). Both water use and its efficiency are directly related to the level of regional economic and social development. Therefore, the primary point for evaluating the regional WRCC is to ensure that water use does not alter the natural water cycle and that the capacity of limited water resources can afford social uses of water (Chi et al. ; Zhang et al. ). In particular, the WRCC must first ensure that water resources are available and that water use is efficient.
Second, the water resources should be sufficient to meet the requirements of human activities. Third, the management of water resources should be efficient in ensuring the normal waterbody function. Finally, water-based ecosystems should be considered a limited resource to meet human requirements. Based on the current description of WRCC, the concept of force subsystems is fundamental to its evaluation. For determining the regional WRCC, water resource is a critical element, but both water abundance and use must be considered. In particular, in densely populated areas, such as Shijiazhuang and Langfang, the social service function of water resources is quite competitive; therefore, water use is considered to be the utilization level of water resources. Furthermore, both regional population and economic scale are considered. For studying water management, all known or possible factors should be considered because the regional WRCC is limited. The study of WRCC indicators helps realize socially and ecologically sustainable development of water resources. Therefore, we established a water-carrying capacity evaluation indicator system with three dimensions, i.e., the support, pressure, and regulation force subsystems (SFS, PFS, and RFS), and four indicators for each criterion layer (Tables 1 and 2).
As demonstrated by the selected evaluation indicators, three dimensions can truly reflect the overall WRCC. Furthermore, the weight of the selected indicators is an important part of the evaluation system and is the basis for establishing the mathematical evaluation model. Between the evaluation system and factual data, the indicator weight of the comprehensive evaluation is in quantitative agreement. In this study, we used prior-published research results and experts' comprehensive analyses, as shown in that water use has little influence on the natural water cycle, and water resources can support both optimal social and ecological development of a region. Furthermore, the capable of carrying level indicates that the water use agrees with the natural water cycle, as coordinated development is maintained between them. The moderate-carrying level indicates that the natural water cycle has been affected by the water use and has exerted certain influence on the ecological environment of the region; however, the extent of influence is controllable. The slight over-carrying level indicates that the influence of water use has already threatened the natural water cycle, and the WRCC has reached an alert state. The severe over-carrying level indicates that the regional water resource demand has considerably exceeded the carrying range of the natural water cycle because of actual water use, and the natural water cycle has entered a vicious circle. The flowchart of this method can be seen in Figure 1.

RESULTS AND DISCUSSION
Based on prior methods and our index evaluation system, we established two series of application schemes for  (Table 5). Subsequently, the current values of all evaluation indicators for Shijiazhuang and Langfang were obtained from water-resource bulletins, various investigations, and measurements. In a recent period of 10 years, based on the water resources, water supply, and water-use statistics of these two typical cities (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015), the above calculations were performed for each year. Figures 3 and 4 show detailed water-use and other relevant information for Shijiazhuang and Langfang. Because of the obtained eigenvalues for each scheme level, we determined that the better schemes were associated with larger levels. We could then compute a specific numeric value within the status assessment yield using which we could improve our understanding of the connection between the level degree and the three dimensions (SFS, PFS, and RFS).  Carrying scores 5 4-5 3 -4 2 -3 1 -2    scarcity that originated from the unique regional climate.
Both the lower guarantee rates of ecologically sustainable water supply and excessive groundwater exploitation were the primary reasons that led to the assessment of water ecology as inadequate. Furthermore, the actual situation revealed that the poor quality of natural rivers is a common problem for both cities and demonstrated the gap that had to be closed to attain the best level from the    the balance between water demand and supply, which is the primary approach to govern the use of water resources. For both cities, the calculations involving RFS reveal considerable differences in relation to regional industries. Thus, to optimize the management of water resources, it is necessary to foster and strengthen interregional exchanges and cooperation.

Discussion
During 2006-2015, the overall status of WRCC in Shijiazhuang and Langfang is that of slight over-carrying. Note that, in both cities, the scarcity of water resources has been the primary impetus for achieving higher carrying levels. Furthermore, to enhance regional water-resource-carrying levels, improvements in water quality and quantity have been essential approaches. The higher water-use efficiency in Shijiazhuang (compared to Langfang) is the primary reason for better performance in the carrying evaluation.
Interbasin water transfer might meet the land uneven distribution of water resources; however, because of the development of the regional economy, industry restructuring must match the regional WRCC to ensure compatibility between development and water resources. Furthermore, for selected cities in northern China, the health status of the regional water ecology should not be ignored. To date, in both Shijiazhuang and Langfang, the overexploitation of groundwater is the most significant challenge for enhancing the regional WRCC. To improve the carrying level for the two cities, the groundwater exploitation should be rational, and the requirement for ecologically sustainable water use must be met. In this study, we determined that the improvement of available water quantity and the efficiency of its use are the primary ways to enhance the regional WRCC level. Considering the limitations of objective conditions, regionally sustainable development must ensure the efficient use within the carrying capacity. Considering major regional differences between the two cities, local governments should Using a combination of the two methods, we established an indicator-based formation and evaluation system to assess the carrying status of the regional WRCC.

CONCLUSION
In this study, the methods used were comprehensive and practical evaluation while addressing several dimensions of regional WRCC. For evaluating carrying levels of a recent 10-year period, their application in the cities of Shijiazhuanag and Langfang is shown to be effective. Because of theoretical development using the fuzzy evaluation model, we managed to quantify the relationship between limited water resources and water use. By allocating evaluation indicators and assigning relative weights, the existing problems could be diagnosed when these methods were applied for evaluating the regional WRCC for different areas. The results of evaluation methods used demonstrated that the status of regional water-carrying capacity for Shijiazhuang and Langfang is slight over-carrying, and the carrying levels showed an interannual increasing trend.
Based on the derived values of indicator performance, we determined that, for both cities, limited water resources may be the primary reason for the low regional WRCC. In the recent 10-year period of 2006-2015, the improvement in the PFS dimension is the primary reason for carryinglevel improvement for both cities, within which an interannual increasing trend was seen. For the RFS dimension, evaluation scores were in the range of 2.14-2.98 for Shijiazhuang and 2.12-2.79 for Langfang. Moreover, the continuing trend of increasing RFS can improve the regional WRCC. Overall, we provided a regional development strategy by the evaluation of the two cities. A simulation of regional WRCC demonstrating how to meet the water shortage in relation to the regional population could assist in forming a sustainable regional development strategy; however, the evaluation process is complicated. Furthermore, in this study, the methods that we used have certain limitations related to the compilation of various data, regional policies, and social challenges. For the evaluation process, the thresholds of selected indicators should realistically reflect all dimensions or characteristics of regional water supply and demand.