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1. School of Civil Engineering and Hydraulic Engineering, Ningxia University, Yinchuan 750021, China; 2. Engineering Research Center of the Ministry of Education for the Modern Utilization of Modern Agricultural Water Resources in Arid Areas, Ningxia University, Yinchuan 750021, China; 3. Innovation Team of Ministry of Education for Modern Utilization of Modern Agricultural Water Resources in Arid Areas, Ningxia University, Yinchuan 750021, China

Abstract Based on water resources conditions, social development, social economy and ecological conditions, the Indicators system for sustainability assessment of water resources use (ISSAWRU) was established for Yinchuan City. Using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), the sustainable development and utilization plan of water resources was assessed for Yinchuan City during 2010-2014. In 2010-2014, there were no significant changes in the natural conditions of water resources in Yinchuan City; however, with the promulgation of national water resources related policies, Yinchuan City realized gradual increase in the water resources utilization rate, gradual improvement in the ecological environment, and gradual optimization of water resources sustainable utilization situation at the same time of ensuring rapid economic growth.

Key words Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) model, Water resources sustainable utilization, Analytic hierarchy process (AHP)

1 Introduction

The total volume of China’s water resources accounts for 6% of the world, ranking fourth in the world. The total volume is large, but the per capita volume of water resources is only 2 300 m3, which is only 1/4 of the world average, so China is one of the 13 countries with shortage of water resources. As the population continues to increase, the per capita volume of water resources will continue to decline. TheReporttotheEighteenthNationalCongressoftheCommunistPartyofChinastated that it is imperative to promote water recycling and build a water-saving society.

Sustainable water resources utilization is a rational use of water resources that meets the normal demands of people’s life, production and economic development while maintaining a virtuous cycle of ecosystems and sustainable social and economic development. The 1992 International Conference on Water Resource and Environment (WRE 1992) held in Dublin in 1992, first described the status and role of water resources in the environment and development, and clearly proposed the research on water resources systems and their sustainability[1]. Since then, extensive discussions and studies have been made on sustainable water resources utilization by scholars both at home and abroad. The assessment of sustainable use of regional water resources is a main method of sustainable use research. Based on the establishment of the Indicators System for Sustainability Assessment of Water Resources Use (ISSAWRU) and evaluation criteria, it describes the complex relationship between indicators and criteria, to realize the classification or ranking of the sustainable use of water resources in time or space, so as to provide a scientific basis for coordinating the relationship between regional water resources development and utilization and population, society, economy, and environment[2-3].

There are many methods for the assessment of sustainable water resources utilization. According to the nature and theoretical basis of the methods, the typical assessment methods can be roughly summarized as: mathematical statistics methods, such as principal components analysis (PCA)[4], factor analysis method[5]and projection pursuit method[6]; operational decision-making methods, such as analytic hierarchy process (AHP)[7], data envelopment analysis (DEA)[8], TOPSIS method; grey system method, such as gray correlation evaluation method[9], gray cluster analysis method[10]; fuzzy mathematics methods, such as fuzzy comprehensive evaluation method[11], variable fuzzy evaluation method[12], fuzzy cluster analysis method[13], machine learning methods, such as artificial neural network (ANN)[14], support vector machine (SVM)[15]; other methods, such as set pair analysis[16], matter element analysis method[17]and so on.

In view of poor water resources endowment conditions, Ningxia has launched the pilot project to build a water-saving society since 2005 and has made outstanding achievements. The economic and social development shows a relatively rapid trend, the sustainable water resources utilization has been improved and is showing an excellent trend. However, there is still a wide gap between Ningxia’s current water use level, water saving level and Ningxia’s economic and social development goals and water resources conditions, and the potential of water saving needs to be further explored. In 2015, the status of sustainable use still remains in a general state, and the task of building a water-saving society is still very arduous. Under the long-term existence of water resources restrictions, it is necessary to strengthen the work of water saving and reclaimed water utilization in Ningxia[18].

In this study, using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and analytic hierarchy process (AHP), we established the TOPSIS model for assessment of water resources sustainable utilization and carried out a comprehensive assessment and calculation for water resources sustainable use in Yinchuan City.

2 Study methods

The TOPSIS method is to find a closest solution to the ideal solution. The basic idea is to classify the problem of comprehensive assessment into a matrix, determine the ideal solution and the negative ideal solution through matrix normalization, and then calculate the distance from the ideal solution to the negative solution and compare the closeness to the ideal solution, finally obtain the comprehensive assessment ranking. Compared with other assessment methods, TOPSIS method has no strict limitation on data distribution and sample content indicator. It is applicable to both small sample data and large system data with multiple assessment units and multiple indicators. Besides, it can be used for both horizontal comparison and vertical comparison. Flexible application and simple calculation make the results quantitative and objective, so this method has high practical value and has been widely applied in many fields of comprehensive assessment.

The indicator weights calculated by the AHP model considered the hierarchical relationship between the indicators and the relative weights, making the comprehensive assessment ranking more scientific and reasonable, and increasing the objective reference value of the assessment results.

2.1AssessmentindicatorsystemTo accurately assess the allocation of regional water resources, it is necessary to establish a scientific and reasonable assessment indicator system. When selecting indicators, it is necessary to pay attention to the comprehensiveness, representativeness, rationality and availability of indicator factors[19]. Based on this principle, we established an assessment indicator system. The highest hierarchy is the target hierarchy, reflecting the research object of the assessment indicator system; the second hierarchy is the criterion hierarchy, composed of relevant indicators reflecting the target hierarchy; the third hierarchy is the indicator hierarchy, showing the specific indicator factors of each sub-criterion hierarchy.

2.2MethodfordeterminingtheweightofassessmentindicatorsAssumed there are m assessment objects in the water resources sustainable utilization assessment system, and each assessment object hasnassessment indicators, thus forming anm×ndecision matrix:

(1)

i= 1，2，…，m;j= 1，2，…，n.

2.2.1Pretreatment of assessment indicators. The assessment indicators reflecting the objects to be assessed generally have different dimensions and orders of magnitude, and some indicators are positive indicators, that is, the bigger the better, some indicators are the reverse indicators, that is, the smaller the better. To facilitate the calculation and comparison, we conducted polarity treatment and adopted the reciprocal method to obtain the normalized matrix:

(2)

Normalized the same trend matrices:

(3)

2.2.2Determination of assessment indicator weight. In this study, we determinedthe indicator weight using the hierarchy process (AHP).

(i) We built the judgment matrix. Starting from the second hierarchy of the indicator system, we used the pairwise comparison method and 1-9 comparison scale to build the matrix, until the lowest hierarchy.

(ii) We calculated the vector and conducted the consistency test. Then, calculated the maximum eigenvalue and the corresponding eigenvector for each matrix, and carried out the consistency test, the consistency ratioCI<0.1. If it passes the test, the polarity is weight vector; if not, it is necessary to rebuild the matrix for test.

(4)

2.3AssessmentbyTOPSISmethod(i) After determining the weights of the indicators, we established an indicator weighted criterion matrix using the following formula:

(ii) We calculated the ideal solutionV+and the negative ideal solutionV-of the indicator weighted criterion assessment value using the formula (6) and formula (7).

(6)

(7)

(iii) When determining the distance from the vector of each assessment indicator to the ideal solution and the inverse ideal solution, the traditional TOPSIS model uses the Euclidean formula. However, this formula does not consider the weighted distance, so the error is large. In this study, we made an improvement and considered the weighted distance and calculated the distance using the weighted Euclidean distance formula[20]:

(8)

(9)

(iv) We calculated the relative closeness of each assessment indicator value vector to the ideal solutionV+using the formula (10).

(10)

Then, the relative closeness degree was used as the comprehensive assessment value of the object to be assessed, and each object to be assessed was ranked according to the relative closeness. The greater the relative closeness, the better; the closer the closeness, the worse.

3 Case study: taking Yinchuan City as an example

The climate of Yinchuan City is temperate continental climate with little rainfall, high evaporation, the average annual precipitation is 200 nm, the average annual evaporation is 1 690 mm, so Yinchuan City belongs to the typical inland arid area. Yinchuan City is located in the arid inland area of Northwest China, and water shortage is one of the main ecological problems[21]. The per capita water resources of Yinchuan City is only 1/9 of the national per capita water resources, thus Yinchuan City is one of the top 100 severely water-scarce cities in China. In addition, with the development of industrialization and urbanization, the economic scale and population size of Yinchuan City are expanding rapidly. The water consumption for industrial water and urban living is also growing rapidly, and the water issue will become more prominent.

In 2011, No. 1 document of central government set forth the "three red lines" goal of water resources management. Ningxia Autonomous Region actively responded to this requirement and determined the red line for water resources development and utilization in 2012. By 2015, the total water withdrawal in Ningxia did not exceed the limit, the volume of water use for generating every 10 000 yuan in industrial value added dropped to 64 m3(30% lower compared with the year 2010), the agricultural irrigation water utilization factor rose to 0.48, and water quality compliance rate of functional areas of key first-level rivers and lakes was up to 70%. As an important area in the Belt and Road Initiative, there are many similarities between Ningxia and the arid countries on the Silk Road economic belt such as Arabia. Water resources are one of the important factors that constrain their development. 2015 China-Arabia Exhibition "China (Ningxia) International Water Saving Exhibition aimed to build China’s largest water-saving equipment and technology distribution center. It is an international comprehensive trading platform for communication and economic exchanges with Arab countries and western drought-stricken areas, water-saving technologies and water-saving equipment, provides broad prospects for strategic cooperation between the Arab countries along the "Belt and Road" and is an important measure for realizing the Belt and Road Initiative.

According to the development status of Yinchuan City, we established the hierarchical structure of sustainable development of water resources in Yinchuan City. The criteria hierarchy is determined according to the connotation of sustainable development, and the target is to realize coordinated development of economic, social, and ecological environment with water resources. Four criteria hierarchy is set: regional water resources condition system, social development system, social economic system, and ecological condition system, and 19 assessment indicators are set, as shown in Fig. 1.

Fig.1HierarchicalstructureofsustainabledevelopmentanduseofwaterresourcesinYinchuanCity

C6,C8,C9,C12,C17, andC18are cost indicators, andC1,C2,C3,C4,C5,C7,C10,C11,C13,C14,C15,C16, andC19are benefit indicators (Table 1).

Table1AssessmentcriteriaforthesustainableuseofwaterresourcesinYinchuanCity[22-31]

C1104 m3/km2C2108 m3C3104 m3C4108 m3C5108 m3C6108 m3C7104 m3/km2C8108 m3C9 m3/104 yuanC10 104 yuan20102.161 21.63081.782 10.7887.49396 714.1931.991 55 1049131 43620111.774 11.33866.051 20.7757.31388 802.7333.000 55 1826448 37420122.706 22.04199.741 01.2277.390979 79.3931.992 85 3815256 317.8220131.662 71.25460.198 70.7097.083108 990.8032.487 45 77642.261 68420141.694 51.27860.031 00.7256.79473 006.2522.943 56 31638.7467 012.53C11 yuanC12104 peopleC13 yuanC14C15104 m3C16ha C17104 tC18104 m3C19104 m3201017 073199.316 1610.439 121.015 7015 893.7010 523.905 311201119 48120 5727 0700.4511 527.979 15 8656 078.189 611 284.9136 817201221 901204.638 0680.4711 390.996 1655 963.1813 706.557 718201323 940208.319 3410.4814 877.557 6946 194.3513 921.9311 260201426 118212.8910 2750.4713 5968 6945 49612 95116 388

3.1Calculationofweight(i) Single hierarchical arrangement and judgment matrix consistency test (Table 2).

Table2Calculatedvaluesofeachhierarchyweightvector

Hierarchy WeightWeight vector CIRICRTest resultsA-B4.1981[0.504 8, 0.143 1, 0.063 5, 0.287 6]T0.066 00.900.073 3Consistent B1-C5[0.2, 0.2, 0.2, 0.2, 0.2]T01.120Consistent B2-C4.264 0[0.177 5, 0.535 6, 0.092 6, 0.194 3]T0.0880.900.097 8Consistent B3-C5[0.2, 0.2, 0.2, 0.2, 0.2]T01.120Consistent B4-C5.380 7[0.145 1, 0.406 7, 0.092 7, 0.059 2, 0.296 3]T0.095 21.120.085Consistent

(ii) Weights of indicators for the sustainable use of water resources in Yinchuan City (Table 3).

Table3WeightsofindicatorsforthesustainableuseofwaterresourcesinYinchuanCity

IndicatorC1C2C3C4C5C6C7C8C9C10Weight0.100 960.100 960.100 960.100 960.100 960.025 40.076 60.013 30.027 80.012 9IndicatorC11C12C13C14C15C16C17C18C19Weight0.012 090.012 900.012 900.012 900.041 70.117 00.026 70.017 00.085 2

3.2AssessmentbyTOPSISmethodCalculating by formula (5), we obtained the weighted criteria matrix:

According to formula (6) and formula (7), we calculated the ideal solution and the inverse ideal solution, respectively:

According to the formula (8) and formula (9) and the weight of each indicator, we calculated the distance from the vector of each assessment indicator vector to the ideal solution and the inverse ideal solution is calculated. The results are as follows:

Using the formula (10), we calculated the relative closeness of each assessment indicator value vector to the ideal solutionV+and the result is as follows:

Ki={0.299 2, 0.187 8, 0.581 8, 0.351 6, 0.481 6}

3.3AnalysisofassessmentresultsAccording to the relative closeness, the order of sustainable development of water resources in Yinchuan City from 2010 to 2014 is as follows: 2012 > 2014 > 2013 > 2010 > 2011.

Through specific analysis and comparison, it can be found that: (i) The sustainable development of water resources in 2012 is better than the other four years. According to the data, it can be found that the water resources conditions are the best in 2012, and the total volume of water resources is much higher than the other four years, so that the sustainable water resources development in 2012 is the best. (ii) The sustainable development of water resources in 2014 is slightly lower than that in 2012, but social development, social economy and ecological conditions are the best in five years, reflecting that Yinchuan City has made great achievements in the sustainable development of water resources. (iii) Compared with the five years data, Yinchuan City still has great potential and development space in the sustainable development of water resources. From the comparative analysis, it can be found that although Yinchuan City is located in the arid and semi-arid regions of Northwest China, due to the flow of the Yellow River, the total volume of water resources is large in the Northwest regions. With the rapid development of the economy, the total volume of water resources, especially the total volume of groundwater, has dropped significantly. In recent years, with the proposal of "three red lines" policy and the Belt and Road Initiative, the sewage treatment capacity of Yinchuan City has gradually increased, but there is still much room for growth, thus it is recommended to improve the treatment process of existing sewage treatment plants, and build larger sewage treatment plants. The concept of water use is strengthening. Although the total population is slowly increasing and the discharge of domestic sewage is decreasing year by year, it is still necessary to continuously increase the reuse rate of household water. Besides, it is recommended to implement stricter industrial wastewater discharge policies, achieve 100% treatment of industrial wastewater, and increase the scale of use of recycled water in industrial water. Since groundwater has been mined too much in the past, it is recommended to consider recharge groundwater with reclaimed water to increase groundwater level. At the same time of ensuring the quality of crop water, adding appropriate volume of reclaimed water and brackish water in the agricultural irrigation water can increase the irrigation water utilization factor, so it is recommended to incorporate reclaimed water into the water for ecological environment. In summary, it is necessary to increase the water resources sustainable use from every water consumption object.