It is of great significance to establish a scientific and reasonable water resources carrying capacity evaluation system and evaluation method on the basis of studying the interdependence and mutual relations of water resources, society, economy and the ecological environment. This can guide water resources utilization and economic and social development planning, and promote the sustainable development of water resources and the socio-economic system. Projection pursuit technology can achieve automatic index selection and index weight confirmation. When used to assess water resources carrying capacity, the subjectivity and uncertainty of index weights can be avoided. Meanwhile, it can also be used to optimize the index system, and can improve the accuracy of evaluation results and discrimination. In this paper, the projection pursuit grade model of water resources carrying capacity is established. The evaluation criteria are determined by combining the theory with practice. Grades I to IV indicate that the water resources capacity declines gradually. This is the first study of water resources carrying capacity in four municipalities in China. The results show that the water resources carrying capacity of the four municipalities in 2012 belong to the third level, Chongqing is close to the second level and Tianjin is close to the fourth level.

INTRODUCTION

Water resources are not only basic natural resources that support the development of the social economy, but are also strategic economic resources that lead to the achievement of sustainable development of the ecological environment. Because of the rapid expansion of the urban population and the rapid development of the economy and society, and the naturally irregular distribution of water resources and irrational patterns of human use, the development and utilization of water resources has been close to or has even exceeded the carrying capacity of local water resources in many areas. This leads to water shortages and increasingly serious water pollution problems that directly impact human health and the sustainable development of the social economy. It is of important theoretical and practical significance to establish a scientific and rational evaluation system as well as evaluation methods for the carrying capacity of water resources based on studying the interdependence and the interactive relationship of water resources, society, economy and the ecological environment (Castelletti & Soncini-Sessa 2007; Nguyen et al. 2007; Simonovic & Verma 2008). This system could guide water resource use and economic and social development planning and promote the sustainable development of water resources and socio-economic systems.

Research on evaluation methods for the carrying capacity of water resources has developed from a static analysis of a single indicator to a multi-objective, dynamic comprehensive analysis. At present, the principal evaluation methods include the general trend method, the comprehensive evaluation method, the system dynamics method, the multi-objective analysis method and the principal component analysis method. The general trend method is simple and direct, but it ignores the interrelation among indexes. This method cannot comprehensively evaluate the water resources carrying capacity according to each index, nor can it reflect the water resources carrying capacity of a region (Duan et al. 2010). The index selection and index weights in comprehensive evaluation method are determined by experts' subjective experience, consequently providing potentially unstable and unreliable evaluation results (Du et al. 2011). The system dynamics method is rapid, but it has many shortcomings, such as the variables (total population, industrial output, road area and so on), complex structure and a requirement for majority data, which limits the application and development of the method (Sun et al. 2016). The difficulty with and the key feature of the multi-objective analysis method are the establishment of the objective function and the selection of the dimension reduction algorithm. As for the principal component analysis method, the method for determining the principal components is controversial and the physical meaning is also unclear. Suitable control points are difficult to choose in practice, which leads to a lack of control of the carrying capacity of the water resources (Zhang 2004).

In short, research on the comprehensive evaluation of the carrying capacity of water resources involves many factors, and the relationships among the factors are very complex. Such research is multi-factorial, non-normal and nonlinear and is related to the high-dimensional data analysis and processing required. Projection pursuit technology is a statistical method that deals with complex, multi-factorial problems that can overcome the subjectivity and uncertainty of the evaluation index selection and weight determination inherent in traditional evaluation methods to a certain extent. This type of method can yield stable and reliable results.

Projection pursuit is a new statistical method used for managing and analyzing high-dimensional data, especially non-normal and nonlinear data. It is interdisciplinary, encompassing statistics, applied mathematics and computer technology. It is not only an exploratory analysis method but also can be used for deterministic analysis. Its basic premise is to project high-dimensional data to a lower-dimensional (1 ∼ 3 dimension) subspace to find the optimal projection vector that can highlight the original high-dimensional data feature to the greatest degree. Projection pursuit is a typical exploratory data analysis method driven by the sample data (Li 2005), using a new way of thinking, i.e., ‘directly inspecting data – analyzing and simulating data – software program testing’. This type of methodology emphasizes its completely different characteristics, compared with traditional evaluation methods. It has become the most stable and practical method for solving high-dimensional, non-normal and nonlinear problems.

METHODS

The steps of the projection pursuit technique include data preprocessing, construction of a projection index function and optimization of the function of the projection indexes and evaluation of the grade (Li et al. 2014).

Data preprocessing

Because of the difference in the transference range of each index dimension and the index value, some indexes could be amplified or narrowed. This can affect the accuracy and reliability of the evaluation results. Therefore, to eliminate dimensional effects, the original data must be preprocessed before establishing the evaluation model.

is the sample set of each index for evaluation of the grade standard, where n is the number of samples, and p is the number of indexes. Each index datum was range-normalized using the following formulas, and the normalized index values were in the range of [0, 1]: 
formula
1
 
formula
2
The variable is the jth index value of the ith sample, and are the maximum and minimum values of the jth index value, and is the index value after range normalization, and is the sample set after range normalization.

The structure of the projection index function

The projection index function is the basis for finding the best projection direction, the projection rule and classification criterion, which is followed by projection-clustering the high-dimensional data to the low-dimensional space. ‘Projection’ is defined as the observation of the sample data from different angles, to discern the best viewing angle that can reflect the data features and fully reflect data information; that is the best projection direction. Linear projection is used to project the high-dimensional data into linear space.

is the sample set for range normalization, is the projection vector for the m-dimensional unit. The projection pursuit method is to transform the p-dimensional data into a one-dimensional projection value based on the projection direction, so the projection characteristic value of can be expressed as: 
formula
3
and is defined as the projection component value of the sample i index j, and is the unit length vector in the formula.
Then, according to a one-dimensional scatter diagram for classification, and using standard deviation and local density to construct the projection index function, the projection index function can be expressed as: 
formula
4
where is the standard deviation of the projection value , and is the local density of the projection value , i.e.: 
formula
5
 
formula
6
where E(z) is the mean value of the sequence , and R is the window radius of local density, i.e., the density of the window width.

The selection of R should not only make the average number of projection points contained in the window too few to keep the sliding average deviation from becoming too large but also prevent R from increasing too rapidly with the increase in n. R can be determined empirically. Its span is , where is the distance between the samples, ; is a unit speed function with a value of 1 when , and a value of 0 when .

The optimization of the projection index function

When the sample set of each index value is given, the projection index function changes with the change of the projection direction . Different projection directions can reflect different data structural features. The optimal projection direction is the projection direction that can represent a certain structural feature of the high-dimensional data. So, the optimal projection direction must be estimated by solving the maximization problem of the projection index function, i.e.: 
formula
7
 
formula
8
The projection component value of the optimal projection direction is: 
formula
9
This is a complicated nonlinear optimization problem with as the optimization variable, which is difficult to address using the traditional optimization method. We used the accelerated genetic algorithm (RAGA), which is the simulated biological survival of the fittest and intra-group information exchange mechanism based on a genetic algorithm to solve the high-dimensional global optimization problem.

Grade evaluation

Substituting the optimal projection direction derived by RAGA into formula (3), we can obtain the projection value of each grade sample point of the evaluation grade standard. According to the values of each grade of sample points and the corresponding projection value , the projection pursuit evaluation model is established: 
formula
10

Then, the evaluating sample is range-normalized, the evaluating projection value calculated, and the projection value is substituted into the projection pursuit evaluation model , finally yielding the grade of the evaluation samples.

Case study

Four municipalities of China were chosen as the empirical analysis objects for this study: Beijing, Tianjin, Shanghai and Chongqing. From an urban development standpoint, the four municipalities directly under the central government occupy an important position in national politics, the economy, culture and in other aspects. They are also faced with different degrees of water shortage problems, which have seriously restricted their economic and social development. The results of this research are beneficial for providing direction and policy suggestions for the utilization of water resources and economic social development planning in the four municipalities. Beijing and Tianjin are the representative cities of the Haihe River Basin, and Chongqing and Shanghai are the representative cities of the upstream and downstream Yangtze River. According to their regional characteristics and water resources, Beijing and Tianjin are typical cities that experience water shortages in north China, Chongqing and Shanghai are typical cities in the coastal areas of the southwest and the east that experience water shortages. Statistical data for the four municipalities directly under the central government are relatively complete and easily obtained. Therefore, the selection of these four municipalities as the research objects is representative. The evaluation research work also has significance as a reference for other, similar cities.

Establishment of an evaluation index system

Along with the carrying capacity of the water resources and related theoretical research results, 24 evaluation indexes were selected from the water resources, social, economic and ecological systems. Three important system parameters, the per capita water resources, water consumption per GDP (gross domestic product) 10,000 RMB and the standard river length ratio, were also chosen as comprehensive coordination indexes, which constitute the comprehensive evaluation indexes of the water resources carrying capacity (see Table 1). The grade standard values were determined by the actual index values for many cities based on the relevant research results inside and outside of the country (Xu 1993; Joardar 1998; Harris & Kennedy 1999; Zhang & Wang 2001).

Table 1

Evaluation index system and evaluation criteria of the water resources carrying capacity

Target layerStandard layerIndex layerUnitMethod of index calculationIndex attributeEvaluation grades and standards
Grade IGrade IIGrade IIIGrade IV
Water resources carrying capacity Water resources subsystem Modulus of water resources 104 m3/km2 Total water resources/total area Positive 50 35 25 10 
Water resources utilization ratio Development and utilization of water resources/total amount of water resources Negative 20 35 45 60 
Proportion of total underground water consumption Groundwater consumption/total water consumption Negative 10 25 35 50 
Proportion of recycled water Amount of reclaimed water/total water consumption Positive 40 25 15 
 Modulus of water supply 104 m3/km2 Total water supply/area Negative 10 60 120 200 
Sociology subsystem Population density p/km2 Population/area Negative 100 300 600 800 
Population growth rate ‰ (Population from the end to the beginning of the year)/annual average population × 1,000‰ Negative 0.2 0.4 0.7 
Urbanization rate Urban population/total population Negative 35 50 65 80 
Engel coefficient of urban residents Life necessities expenses/total expenses Positive 50 40 30 20 
Daily water consumption per capita Yearbook statistical data Negative 65 80 100 120 
Centralized treatment rate of sewage treatment plant Yearbook statistical data Positive 90 80 70 60 
Rate of harmless treatment of living garbage Yearbook statistical data Positive 95 85 70 55 
Economy subsystem Per capita GDP RMB10,000/p GDP/total population Positive 30,000 15,000 8,000 5,000 
GDP annual growth rate (This period GDP–last period GDP)/this period GDP Negative 12 15 
Second industrial added value accounted for the proportion of GDP Second industrial added value/GDP Negative 20 30 45 55 
Industrial added value of water consumption every RMB10,000 m3/RMB10,000 Industrial water consumption/industrial added value Negative 10 30 70 100 
Repeating utilization factor of industrial water Repeated water consumption/total industrial water Positive 85 70 50 35 
Effective irrigation rate Effective irrigation area/farmland area Positive 65 45 35 20 
Grain yield of unit cultivated area t/mu Grain yield/cultivated area Positive 0.4 0.3 0.2 0.15 
Ecological environment subsystem Forest coverage rate Total forest area Positive 50 35 25 15 
Ecological water consumption rate Ecological water/gross amount of water resources Positive 20 15 10 
Ecological environment water consumption per capita m3/p Ecological environment water consumption/population Positive 50 25 10 
Sewage discharge rate Total amount of sewage/total amount of water consumption Negative 10 25 35 
Exploitation rate of groundwater Exploitation quantity of groundwater/groundwater amount Negative 15 40 60 80 
Comprehensive coordination index Water resource per capita m3/p Total water resources/total population Positive 3,000 2,000 1,000 500 
GDP water consumption every RMB10,000 m3/RMB 10,000 Total water consumption/total GDP Negative 20 35 45 60 
River length ratio of water quality up to standards River length accounted for the proportion of director of river length when the water quality is class V and above Positive 75 65 55 45 
Target layerStandard layerIndex layerUnitMethod of index calculationIndex attributeEvaluation grades and standards
Grade IGrade IIGrade IIIGrade IV
Water resources carrying capacity Water resources subsystem Modulus of water resources 104 m3/km2 Total water resources/total area Positive 50 35 25 10 
Water resources utilization ratio Development and utilization of water resources/total amount of water resources Negative 20 35 45 60 
Proportion of total underground water consumption Groundwater consumption/total water consumption Negative 10 25 35 50 
Proportion of recycled water Amount of reclaimed water/total water consumption Positive 40 25 15 
 Modulus of water supply 104 m3/km2 Total water supply/area Negative 10 60 120 200 
Sociology subsystem Population density p/km2 Population/area Negative 100 300 600 800 
Population growth rate ‰ (Population from the end to the beginning of the year)/annual average population × 1,000‰ Negative 0.2 0.4 0.7 
Urbanization rate Urban population/total population Negative 35 50 65 80 
Engel coefficient of urban residents Life necessities expenses/total expenses Positive 50 40 30 20 
Daily water consumption per capita Yearbook statistical data Negative 65 80 100 120 
Centralized treatment rate of sewage treatment plant Yearbook statistical data Positive 90 80 70 60 
Rate of harmless treatment of living garbage Yearbook statistical data Positive 95 85 70 55 
Economy subsystem Per capita GDP RMB10,000/p GDP/total population Positive 30,000 15,000 8,000 5,000 
GDP annual growth rate (This period GDP–last period GDP)/this period GDP Negative 12 15 
Second industrial added value accounted for the proportion of GDP Second industrial added value/GDP Negative 20 30 45 55 
Industrial added value of water consumption every RMB10,000 m3/RMB10,000 Industrial water consumption/industrial added value Negative 10 30 70 100 
Repeating utilization factor of industrial water Repeated water consumption/total industrial water Positive 85 70 50 35 
Effective irrigation rate Effective irrigation area/farmland area Positive 65 45 35 20 
Grain yield of unit cultivated area t/mu Grain yield/cultivated area Positive 0.4 0.3 0.2 0.15 
Ecological environment subsystem Forest coverage rate Total forest area Positive 50 35 25 15 
Ecological water consumption rate Ecological water/gross amount of water resources Positive 20 15 10 
Ecological environment water consumption per capita m3/p Ecological environment water consumption/population Positive 50 25 10 
Sewage discharge rate Total amount of sewage/total amount of water consumption Negative 10 25 35 
Exploitation rate of groundwater Exploitation quantity of groundwater/groundwater amount Negative 15 40 60 80 
Comprehensive coordination index Water resource per capita m3/p Total water resources/total population Positive 3,000 2,000 1,000 500 
GDP water consumption every RMB10,000 m3/RMB 10,000 Total water consumption/total GDP Negative 20 35 45 60 
River length ratio of water quality up to standards River length accounted for the proportion of director of river length when the water quality is class V and above Positive 75 65 55 45 

Note: ‘positive’ indicates that larger is better, and ‘negative’ indicates that smaller is better in the index attribute.

The index system and evaluation criteria for the water resources carrying capacity evaluation are shown in Table 1.

Construction and optimization of the projection index function

The projection index function was constructed using the R2013b MATLAB software, and the optimization was solved by using an accelerated genetic algorithm. First, the normalized range data were brought into the program, and then the RAGA toolbox was directly searched to solve the model using the order ‘gatool’. The results of many experiments showed that a larger population quantity yielded more stable calculation results. When the number of the population was 400, the maximum objective function with a value of 4.4589 after 51 iterations was obtained. The best projection vector was = (0.2000 0.2162 0.1181 0.1579 0.0577 0.0778 0.0773 0.1555 0.1711 0.1621 0.3015 0.1265 0.1364 0.2269 0.1682 0.2918 0.0622 0.0039 0.2105 0.3220 0.1195 0.3500 0.1795 0.2485 0.2779 0.0909 0.1443).

After the optimal projection direction vector was obtained by establishing and solving the model, each index weight of the water resources carrying capacity could be obtained according to the weight of each index in the optimal projection direction vector (as shown in Table 2). The weight of each index could be arranged according to the component of an individual index in the optical projection direction. A greater component value was linked to a greater incidence of the index of the water resources carrying capacity, allowing the key factors that affected the water resources carrying capacity of the urban water resources to be selected.

Table 2

Best projection vector and index weight of the water resources carrying capacity

Serial numberEvaluation indexOptimal projection direction componentIndex weight
Modulus of water resources 0.2000 10 
Water resources utilization ratio 0.2162 
Proportion of total water consumption 0.1181 21 
Proportion of reclaimed water 0.1579 15 
Modulus of water supply 0.0577 26 
Population density 0.0778 23 
Population growth rate 0.0773 24 
Urbanization rate 0.1555 16 
Engel coefficient of urban residents 0.1711 12 
10 Daily water consumption per capita 0.1621 14 
11 Centralized treatment rate of sewage treatment plant 0.3015 
12 Rate of harmless treatment of living garbage 0.1265 19 
13 Per capita GDP 0.1364 18 
14 GDP annual growth rate 0.2269 
15 Second industrial added value accounted for the proportion of GDP 0.1682 13 
16 Industrial added value of water consumption every RMB10,000 0.2918 
17 Repeating utilization factor of industrial water 0.0622 25 
18 Effective irrigation rate 0.0039 27 
19 Grain yield of unit cultivated area 0.2105 
20 Forest coverage rate 0.3220 
21 Ecological water consumption rate 0.1195 20 
22 Ecological environment water consumption per capita 0.3500 
23 Sewage discharge rate 0.1795 11 
24 Exploitation rate of groundwater 0.2485 
25 Water resources per capita 0.2779 
26 GDP water consumption every RMB10,000 0.0909 22 
27 River length ratio of water quality up to standards 0.1443 17 
Serial numberEvaluation indexOptimal projection direction componentIndex weight
Modulus of water resources 0.2000 10 
Water resources utilization ratio 0.2162 
Proportion of total water consumption 0.1181 21 
Proportion of reclaimed water 0.1579 15 
Modulus of water supply 0.0577 26 
Population density 0.0778 23 
Population growth rate 0.0773 24 
Urbanization rate 0.1555 16 
Engel coefficient of urban residents 0.1711 12 
10 Daily water consumption per capita 0.1621 14 
11 Centralized treatment rate of sewage treatment plant 0.3015 
12 Rate of harmless treatment of living garbage 0.1265 19 
13 Per capita GDP 0.1364 18 
14 GDP annual growth rate 0.2269 
15 Second industrial added value accounted for the proportion of GDP 0.1682 13 
16 Industrial added value of water consumption every RMB10,000 0.2918 
17 Repeating utilization factor of industrial water 0.0622 25 
18 Effective irrigation rate 0.0039 27 
19 Grain yield of unit cultivated area 0.2105 
20 Forest coverage rate 0.3220 
21 Ecological water consumption rate 0.1195 20 
22 Ecological environment water consumption per capita 0.3500 
23 Sewage discharge rate 0.1795 11 
24 Exploitation rate of groundwater 0.2485 
25 Water resources per capita 0.2779 
26 GDP water consumption every RMB10,000 0.0909 22 
27 River length ratio of water quality up to standards 0.1443 17 

Deciding the evaluation grade

Substituting the optimal projection direction vector into Equation (3) allows the projection eigenvalue vector of the standard sample to be obtained. Figure 1 shows the relationship between the projection characteristic value and the water resources carrying capacity corresponding with the grade standard sample, with the water resources carrying capacity grade (y) as the ordinate and the grade-corresponding projection characteristic values as the abscissa. A projection pursuit grade evaluation model for the water resources carrying capacity could be established according to the variability derived from the figure.
Figure 1

Fitting map of projection eigenvalue and water resources carrying capacity grade value.

Figure 1

Fitting map of projection eigenvalue and water resources carrying capacity grade value.

A linear projection was used, so the relationship between y and z was linear, and described by the equation , R2 = 0.998, indicating a very good linear relationship. Figure 1 shows that the projection function value z = 4.6542 was the boundary between grades I and II, z = 2.9919 was the boundary between grades II and III, and z = 1.3671 was the boundary between grades III and IV.

According to Equation (3), we obtained the projection eigenvalue of the water resources carrying capacity grade evaluation model of the four municipalities (Beijing, Tianjin, Shanghai and Chongqing), which were 2.6379, 1.7443, 1.9187 and 2.6856, respectively. When these values were substituted into Equation (10), the corresponding grades of the water resources carrying capacity were 2.25, 2.83, 2.71 and 2.22, respectively. Figure 1 shows that the water resources carrying capacity of the four municipalities in 2014 were all in the third level. The order of the water resources carrying capacity from highest to lowest was Chongqing > Beijing > Shanghai > Tianjin. The value for Chongqing was close to grade II while that for Tianjin was close to grade IV.

The ‘advantage index’ and the ‘short board index’

The projection component value of the sample index in the optimal projection direction could be obtained by using Equation (9), as shown in Table 3. Because the projection component value of each index in the optimal projection direction represents the contribution to the water resources carrying capacity of the region, and a greater component value indicates a greater contribution, sorting each index according to the contribution of the water resources carrying capacity from the largest to the smallest clearly reveals the degree of the impact of each index in different regions.

Table 3

The component value of each index in the evaluation sample of four municipalities in the optimal projection direction

Serial numberEvaluation indexThe component value of each index in the evaluation sample in the optimal projection direction
BeijingTianjinShanghaiChongqing
Modulus of water resources 0.0083 0.1894 0.2000 
Water resources utilization ratio 0.1289 0.1600 0.2162 
Proportion of total water consumption 0.0671 0.1181 0.1140 
Proportion of reclaimed water 0.1579 0.0368 
Modulus of water supply 0.0529 0.0539 0.0577 
Population density 0.0778 0.0168 0.0661 
Population growth rate 0.0773 0.0486 0.0348 
Urbanization rate 0.0134 0.0309 0.1555 
Engel coefficient of urban residents 0.0415 0.0709 0.1711 
10 Daily water consumption per capita 0.1621 0.0029 0.1062 
11 Centralized treatment rate of sewage treatment plant 0.1005 0.2242 0.3015 
12 Rate of harmless treatment of living garbage 0.1112 0.1265 0.0958 
13 Per capita GDP 0.1240 0.1364 0.1178 
14 GDP annual growth rate 0.2095 0.0524 0.2269 
15 Second industrial added value accounted for the proportion of GDP 0.1682 0.0879 0.0206 
16 Industrial added value of water consumption every RMB10,000 0.2737 0.2361 0.2918 
17 Repeating utilization factor of industrial water 0.0154 0.0622 0.0492 
18 Effective irrigation rate 0.0039 0.0029 0.0001 
19 Grain yield of unit cultivated area 0.2105 0.0501 
20 Forest coverage rate 0.3220 0.0083 0.2951 
21 Ecological water consumption rate 0.1195 0.0508 0.0027 
22 Ecological environment water consumption per capita 0.3500 0.1241 0.0057 
23 Sewage discharge rate 0.1236 0.1514 0.1795 
24 Exploitation rate of groundwater 0.0529 0.2485 0.2466 
25 Water resources per capita 0.0025 0.0159 0.2779 
26 GDP water consumption every RMB10,000 0.0909 0.0780 0.0225 
27 River length ratio of water quality up to standards 0.0738 0.0637 0.1443 
 Optimal projection eigenvalue  2.6379 1.7443 1.9187 2.6856 
Serial numberEvaluation indexThe component value of each index in the evaluation sample in the optimal projection direction
BeijingTianjinShanghaiChongqing
Modulus of water resources 0.0083 0.1894 0.2000 
Water resources utilization ratio 0.1289 0.1600 0.2162 
Proportion of total water consumption 0.0671 0.1181 0.1140 
Proportion of reclaimed water 0.1579 0.0368 
Modulus of water supply 0.0529 0.0539 0.0577 
Population density 0.0778 0.0168 0.0661 
Population growth rate 0.0773 0.0486 0.0348 
Urbanization rate 0.0134 0.0309 0.1555 
Engel coefficient of urban residents 0.0415 0.0709 0.1711 
10 Daily water consumption per capita 0.1621 0.0029 0.1062 
11 Centralized treatment rate of sewage treatment plant 0.1005 0.2242 0.3015 
12 Rate of harmless treatment of living garbage 0.1112 0.1265 0.0958 
13 Per capita GDP 0.1240 0.1364 0.1178 
14 GDP annual growth rate 0.2095 0.0524 0.2269 
15 Second industrial added value accounted for the proportion of GDP 0.1682 0.0879 0.0206 
16 Industrial added value of water consumption every RMB10,000 0.2737 0.2361 0.2918 
17 Repeating utilization factor of industrial water 0.0154 0.0622 0.0492 
18 Effective irrigation rate 0.0039 0.0029 0.0001 
19 Grain yield of unit cultivated area 0.2105 0.0501 
20 Forest coverage rate 0.3220 0.0083 0.2951 
21 Ecological water consumption rate 0.1195 0.0508 0.0027 
22 Ecological environment water consumption per capita 0.3500 0.1241 0.0057 
23 Sewage discharge rate 0.1236 0.1514 0.1795 
24 Exploitation rate of groundwater 0.0529 0.2485 0.2466 
25 Water resources per capita 0.0025 0.0159 0.2779 
26 GDP water consumption every RMB10,000 0.0909 0.0780 0.0225 
27 River length ratio of water quality up to standards 0.0738 0.0637 0.1443 
 Optimal projection eigenvalue  2.6379 1.7443 1.9187 2.6856 

Note: The size of each component value represents the contribution of each index to the water resources carrying capacity of the region; ‘0’ does not represent no contribution, it indicates that this index is the worst in all of the sample data.

The index that showed the largest contribution to the water resources carrying capacity was defined as the ‘advantage index’, whose weight was larger and level was higher. It defined the factor that it was most necessary to emphasize or control. The index that had a larger weight but a smaller contribution was defined as a ‘short board index’, and it represented an obstacle that hindered the improvement of the water resources carrying capacity in the region and that must be regulated. Changes in the values of indexes with small weights made little difference to the water resources carrying capacity and were not the focus of our research. The ‘advantage index’ and ‘short-board index’, which affected the water resources carrying capacity of the municipalities directly under the central government (as shown in Table 4), were selected.

Table 4

‘Advantage index’ and ‘short board index’ that affected the water resources carrying capacity of the municipalities directly under the central government

 Advantage IndexShort Board Index
Beijing GDP annual growth rate
Industrial added value of water consumption every RMB10,000
Grain yield of unit cultivated area
Forest coverage rate
Ecological environment water consumption per capita 
Modulus of water resources
Water resources utilization ratio
Centralized treatment rate of sewage treatment plant
Exploitation rate of groundwater
Water resources per capita 
Tianjin Water resources utilization ratio
Ecological environment water consumption per capita 
Modulus of water resources
Centralized treatment rate of sewage treatment plant
GDP annual growth rate
Forest coverage rate
Water resources per capita
Exploitation rate of groundwater 
Shanghai Modulus of water resources
Centralized treatment rate of sewage treatment plant
GDP annual growth rate
Industrial added value of water consumption every RMB10,000
Exploitation rate of groundwater
Water resources per capita 
Water resources utilization ratio
Grain yield of unit cultivated area
Forest coverage rate
Water resources per capita
Ecological environment water consumption per capita 
Chongqing Modulus of water resources
Water resources utilization ratio
Centralized treatment rate of sewage treatment plant
Forest coverage rate
Water resources per capita
Exploitation rate of groundwater 
Ecological environment water consumption per capita
Industrial added value of water consumption every RMB10,000
GDP annual growth rate
Grain yield of unit cultivated area 
 Advantage IndexShort Board Index
Beijing GDP annual growth rate
Industrial added value of water consumption every RMB10,000
Grain yield of unit cultivated area
Forest coverage rate
Ecological environment water consumption per capita 
Modulus of water resources
Water resources utilization ratio
Centralized treatment rate of sewage treatment plant
Exploitation rate of groundwater
Water resources per capita 
Tianjin Water resources utilization ratio
Ecological environment water consumption per capita 
Modulus of water resources
Centralized treatment rate of sewage treatment plant
GDP annual growth rate
Forest coverage rate
Water resources per capita
Exploitation rate of groundwater 
Shanghai Modulus of water resources
Centralized treatment rate of sewage treatment plant
GDP annual growth rate
Industrial added value of water consumption every RMB10,000
Exploitation rate of groundwater
Water resources per capita 
Water resources utilization ratio
Grain yield of unit cultivated area
Forest coverage rate
Water resources per capita
Ecological environment water consumption per capita 
Chongqing Modulus of water resources
Water resources utilization ratio
Centralized treatment rate of sewage treatment plant
Forest coverage rate
Water resources per capita
Exploitation rate of groundwater 
Ecological environment water consumption per capita
Industrial added value of water consumption every RMB10,000
GDP annual growth rate
Grain yield of unit cultivated area 

CONCLUSION

We used the projection pursuit technique to evaluate the water resources carrying capacity and constructed a projection pursuit grade evaluation model and used the model in an empirical study of four municipalities directly under the central government to evaluate the water resources carrying capacity of the four municipalities in 2012. The results showed that the key factors affecting the water resources carrying capacity included the ecological environment water consumption per capita, the forest coverage rate, the centralized rate of the sewage treatment plant, the industrial added value of water consumption every RMB10,000 and the water resources per capita. The water resources carrying capacity of the four municipalities in 2012 all fell into the third level, but Shanghai was close to the second level, and Tianjin was close to the fourth level. According to the projection component value of the sample index in the optimal projection direction, we filtered out the ‘advantage indexes’ and the ‘short board indexes’, which could indicate the direction for the best water resource utilization and social development plan for the municipalities.

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