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.

*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]: The variable is the

*j*th index value of the

*i*th sample, and are the maximum and minimum values of the

*j*th 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.

*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: and is defined as the projection component value of the sample

*i*index

*j*, and is the unit length vector in the formula.

*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

### Grade evaluation

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).

Target layer . | Standard layer . | Index layer . | Unit . | Method of index calculation . | Index attribute . | Evaluation grades and standards . | |||
---|---|---|---|---|---|---|---|---|---|

Grade I . | Grade II . | Grade III . | Grade IV . | ||||||

Water resources carrying capacity | Water resources subsystem | Modulus of water resources | 10^{4} m^{3}/km^{2} | 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 | 5 | ||

Modulus of water supply | 10^{4} m^{3}/km^{2} | Total water supply/area | Negative | 10 | 60 | 120 | 200 | ||

Sociology subsystem | Population density | p/km^{2} | 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 | 1 | ||

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 | L | 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 | 4 | 7 | 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 | m^{3}/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 | 5 | ||

Ecological environment water consumption per capita | m^{3}/p | Ecological environment water consumption/population | Positive | 50 | 25 | 10 | 5 | ||

Sewage discharge rate | % | Total amount of sewage/total amount of water consumption | Negative | 5 | 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 | m^{3}/p | Total water resources/total population | Positive | 3,000 | 2,000 | 1,000 | 500 | |

GDP water consumption every RMB10,000 | m^{3}/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 layer . | Standard layer . | Index layer . | Unit . | Method of index calculation . | Index attribute . | Evaluation grades and standards . | |||
---|---|---|---|---|---|---|---|---|---|

Grade I . | Grade II . | Grade III . | Grade IV . | ||||||

Water resources carrying capacity | Water resources subsystem | Modulus of water resources | 10^{4} m^{3}/km^{2} | 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 | 5 | ||

Modulus of water supply | 10^{4} m^{3}/km^{2} | Total water supply/area | Negative | 10 | 60 | 120 | 200 | ||

Sociology subsystem | Population density | p/km^{2} | 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 | 1 | ||

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 | L | 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 | 4 | 7 | 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 | m^{3}/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 | 5 | ||

Ecological environment water consumption per capita | m^{3}/p | Ecological environment water consumption/population | Positive | 50 | 25 | 10 | 5 | ||

Sewage discharge rate | % | Total amount of sewage/total amount of water consumption | Negative | 5 | 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 | m^{3}/p | Total water resources/total population | Positive | 3,000 | 2,000 | 1,000 | 500 | |

GDP water consumption every RMB10,000 | m^{3}/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.

Serial number . | Evaluation index . | Optimal projection direction component . | Index weight . |
---|---|---|---|

1 | Modulus of water resources | 0.2000 | 10 |

2 | Water resources utilization ratio | 0.2162 | 8 |

3 | Proportion of total water consumption | 0.1181 | 21 |

4 | Proportion of reclaimed water | 0.1579 | 15 |

5 | Modulus of water supply | 0.0577 | 26 |

6 | Population density | 0.0778 | 23 |

7 | Population growth rate | 0.0773 | 24 |

8 | Urbanization rate | 0.1555 | 16 |

9 | 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 | 3 |

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 | 7 |

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 | 4 |

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 | 9 |

20 | Forest coverage rate | 0.3220 | 2 |

21 | Ecological water consumption rate | 0.1195 | 20 |

22 | Ecological environment water consumption per capita | 0.3500 | 1 |

23 | Sewage discharge rate | 0.1795 | 11 |

24 | Exploitation rate of groundwater | 0.2485 | 6 |

25 | Water resources per capita | 0.2779 | 5 |

26 | GDP water consumption every RMB10,000 | 0.0909 | 22 |

27 | River length ratio of water quality up to standards | 0.1443 | 17 |

Serial number . | Evaluation index . | Optimal projection direction component . | Index weight . |
---|---|---|---|

1 | Modulus of water resources | 0.2000 | 10 |

2 | Water resources utilization ratio | 0.2162 | 8 |

3 | Proportion of total water consumption | 0.1181 | 21 |

4 | Proportion of reclaimed water | 0.1579 | 15 |

5 | Modulus of water supply | 0.0577 | 26 |

6 | Population density | 0.0778 | 23 |

7 | Population growth rate | 0.0773 | 24 |

8 | Urbanization rate | 0.1555 | 16 |

9 | 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 | 3 |

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 | 7 |

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 | 4 |

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 | 9 |

20 | Forest coverage rate | 0.3220 | 2 |

21 | Ecological water consumption rate | 0.1195 | 20 |

22 | Ecological environment water consumption per capita | 0.3500 | 1 |

23 | Sewage discharge rate | 0.1795 | 11 |

24 | Exploitation rate of groundwater | 0.2485 | 6 |

25 | Water resources per capita | 0.2779 | 5 |

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

*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.

A linear projection was used, so the relationship between *y* and *z* was linear, and described by the equation , *R*^{2} = 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.

Serial number . | Evaluation index . | The component value of each index in the evaluation sample in the optimal projection direction . | |||
---|---|---|---|---|---|

Beijing . | Tianjin . | Shanghai . | Chongqing . | ||

1 | Modulus of water resources | 0.0083 | 0 | 0.1894 | 0.2000 |

2 | Water resources utilization ratio | 0.1289 | 0.1600 | 0 | 0.2162 |

3 | Proportion of total water consumption | 0 | 0.0671 | 0.1181 | 0.1140 |

4 | Proportion of reclaimed water | 0.1579 | 0.0368 | 0 | 0 |

5 | Modulus of water supply | 0.0529 | 0.0539 | 0 | 0.0577 |

6 | Population density | 0.0778 | 0.0168 | 0 | 0.0661 |

7 | Population growth rate | 0 | 0.0773 | 0.0486 | 0.0348 |

8 | Urbanization rate | 0.0134 | 0.0309 | 0 | 0.1555 |

9 | Engel coefficient of urban residents | 0 | 0.0415 | 0.0709 | 0.1711 |

10 | Daily water consumption per capita | 0 | 0.1621 | 0.0029 | 0.1062 |

11 | Centralized treatment rate of sewage treatment plant | 0 | 0.1005 | 0.2242 | 0.3015 |

12 | Rate of harmless treatment of living garbage | 0.1112 | 0 | 0.1265 | 0.0958 |

13 | Per capita GDP | 0.1240 | 0.1364 | 0.1178 | 0 |

14 | GDP annual growth rate | 0.2095 | 0.0524 | 0.2269 | 0 |

15 | Second industrial added value accounted for the proportion of GDP | 0.1682 | 0 | 0.0879 | 0.0206 |

16 | Industrial added value of water consumption every RMB10,000 | 0.2737 | 0.2361 | 0.2918 | 0 |

17 | Repeating utilization factor of industrial water | 0.0154 | 0.0622 | 0.0492 | 0 |

18 | Effective irrigation rate | 0.0039 | 0.0029 | 0 | 0.0001 |

19 | Grain yield of unit cultivated area | 0.2105 | 0.0501 | 0 | 0 |

20 | Forest coverage rate | 0.3220 | 0 | 0.0083 | 0.2951 |

21 | Ecological water consumption rate | 0.1195 | 0.0508 | 0 | 0.0027 |

22 | Ecological environment water consumption per capita | 0.3500 | 0.1241 | 0.0057 | 0 |

23 | Sewage discharge rate | 0.1236 | 0.1514 | 0 | 0.1795 |

24 | Exploitation rate of groundwater | 0 | 0.0529 | 0.2485 | 0.2466 |

25 | Water resources per capita | 0.0025 | 0 | 0.0159 | 0.2779 |

26 | GDP water consumption every RMB10,000 | 0.0909 | 0.0780 | 0.0225 | 0 |

27 | River length ratio of water quality up to standards | 0.0738 | 0 | 0.0637 | 0.1443 |

Optimal projection eigenvalue | 2.6379 | 1.7443 | 1.9187 | 2.6856 |

Serial number . | Evaluation index . | The component value of each index in the evaluation sample in the optimal projection direction . | |||
---|---|---|---|---|---|

Beijing . | Tianjin . | Shanghai . | Chongqing . | ||

1 | Modulus of water resources | 0.0083 | 0 | 0.1894 | 0.2000 |

2 | Water resources utilization ratio | 0.1289 | 0.1600 | 0 | 0.2162 |

3 | Proportion of total water consumption | 0 | 0.0671 | 0.1181 | 0.1140 |

4 | Proportion of reclaimed water | 0.1579 | 0.0368 | 0 | 0 |

5 | Modulus of water supply | 0.0529 | 0.0539 | 0 | 0.0577 |

6 | Population density | 0.0778 | 0.0168 | 0 | 0.0661 |

7 | Population growth rate | 0 | 0.0773 | 0.0486 | 0.0348 |

8 | Urbanization rate | 0.0134 | 0.0309 | 0 | 0.1555 |

9 | Engel coefficient of urban residents | 0 | 0.0415 | 0.0709 | 0.1711 |

10 | Daily water consumption per capita | 0 | 0.1621 | 0.0029 | 0.1062 |

11 | Centralized treatment rate of sewage treatment plant | 0 | 0.1005 | 0.2242 | 0.3015 |

12 | Rate of harmless treatment of living garbage | 0.1112 | 0 | 0.1265 | 0.0958 |

13 | Per capita GDP | 0.1240 | 0.1364 | 0.1178 | 0 |

14 | GDP annual growth rate | 0.2095 | 0.0524 | 0.2269 | 0 |

15 | Second industrial added value accounted for the proportion of GDP | 0.1682 | 0 | 0.0879 | 0.0206 |

16 | Industrial added value of water consumption every RMB10,000 | 0.2737 | 0.2361 | 0.2918 | 0 |

17 | Repeating utilization factor of industrial water | 0.0154 | 0.0622 | 0.0492 | 0 |

18 | Effective irrigation rate | 0.0039 | 0.0029 | 0 | 0.0001 |

19 | Grain yield of unit cultivated area | 0.2105 | 0.0501 | 0 | 0 |

20 | Forest coverage rate | 0.3220 | 0 | 0.0083 | 0.2951 |

21 | Ecological water consumption rate | 0.1195 | 0.0508 | 0 | 0.0027 |

22 | Ecological environment water consumption per capita | 0.3500 | 0.1241 | 0.0057 | 0 |

23 | Sewage discharge rate | 0.1236 | 0.1514 | 0 | 0.1795 |

24 | Exploitation rate of groundwater | 0 | 0.0529 | 0.2485 | 0.2466 |

25 | Water resources per capita | 0.0025 | 0 | 0.0159 | 0.2779 |

26 | GDP water consumption every RMB10,000 | 0.0909 | 0.0780 | 0.0225 | 0 |

27 | River length ratio of water quality up to standards | 0.0738 | 0 | 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.

. | Advantage Index . | Short 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 Index . | Short 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.