1、 2025, Water War Summary Water resources shortage is a new challenge that the whole world confront and its especially significant in China. This article establishes a mathematical model to solve the water resources crisis that faces China. We primarily use the Gray Model and the Linear Regression Mo
2、del to forecast total water resources and total water needs with the average error of 15% and 2%.Because of the big fluctuation of total water resources, the predi-cation model proves ineffective with significant error. Based on the average error, we work out the floor limit for the predication of t
3、otal water resources to deal with the problem. With the predication statistics, we get the water deficit and water shortage degree of each province in 2015、 2020、 2025. The results of water shortage risk assessment shows we must pay close attention to Shanghai and Ningxia which are in great water sh
4、ortage. To meet the projected water needs, we formulate four different strategies that consist of water save and conservation, movement of water resources among adjacent regions, de-salinization and water storage. Afterwards, we analyze each strategy by feasibility, water-saving and economic benefit
5、s. The application of the Analytical Hierarchy Process (AHP) gives the strategy pri-oritization of the comprehensive implications. The results shows that the best strategy is water save and conservation, the second is movement of water re-sources among adjacent regions, the third is de-salinization,
6、 and the worst strategy is water storage. Finally, this paper gives the specific solution to water shortage as well as the expenditure predication. By applying our plans, the water shortage can be reduced from 42.8 billion cubic meters to 36.8 billion cubic meters, and the costs also reduce by 45.1%
7、 in 10 years. It is obvious that our plan is effective and feasible. 2025, Water War Team: 17578 Abstract Water is an important natural resource that is used every day, not only do we humans use it just about every day, but every living thing needs it to live. Environmental problems, water waste and
8、 pollution have created many chal-lenges for water conservancy in China, causing serious problems. To meet the projected water needs of China in 2025, we establish a mathematical model to determining an effective, feasible, and cost-efficient water strategy for 2013. By using the Gray Model and the
9、Linear Regression Model, we primarily forecast the total water resources and total water needs. By comparing the average error of the two models, we choose the Gray Model for its better re-sults. With total water resources and total water needs, we obtain the water shortage degree and corresponding
10、risk assessment of different provinces and regions. To meet the projected water needs, we formulate four different strat-egies that consist of water save and conservation, movement of water re-sources among adjacent regions, de-salinization and water storage. After-wards, we analyze the four strateg
11、ies by feasibility, water-saving and eco-nomic benefits. In order to evaluate the economic, physical, and environmen-tal implications of the four strategies, we apply the Analytical Hierarchy Pro-cess (AHP) to give the comprehensive implications and strategy prioritization. Finally, we discuss the s
12、olution to water shortage in 2025 and its cost. The rel-ative low and decreasing expenditure of proves the effectiveness and feasibil-ity of our plans. The application of computer programming enables the fast process of mass data, which solves the management of water resources quickly and effectivel
13、y. The application of model is not limited in handling water resources manage-ment, it is also powerful to deal with the other management problems of sim-ilar kinds. Key Words: Water crisis; Water resources management; Gray Model; AHPTeam # 17578 3 / 49 Contents 1 Introduction . 5 2 Assumptions 6 3
14、Total Water Resources Prediction Model 6 3.1 Calculation of Total Water Resources from 2003 to 2011 6 3.2 Prediction of Total Water Resources 7 3.2.1 An Introduction to Grey Prediction Model . 7 3.2.2 An Introduction to Linear Regression Model . 9 3.2.3 Fitted Value and Predicted Value of Total Wate
15、r Resources 10 3.3 Error Analysis and Model Evaluation . 11 4 Total Water Needs Prediction Model . 13 4.1 Calculation of Total Water Needs from 2003 to 2011 13 4.2 Prediction of Total Water Needs. 14 4.3 Error Analysis and Model Evaluation . 15 5 Analyses of Water Supply and Demand . 16 5.1 Predicti
16、on of Water Supply and Demand in 2015, 2020 and 2025 . 16 5.2 Analyses of Water Supply and Demand in 2015, 2020 and 2025 . 17 5.2.1 Water Shortage Degree 17 5.2.2 Risk Assessment 18 6 Water Strategies for China . 19 6.1 Save and Conservation 19 6.1.1 Decrease in Industrial Water Needs . 19 6.1.2 Inc
17、rease in Effective Utilization Coefficient of Agricultural Water20 6.1.3 Decrease in Water Pollution 21 6.1.4 Summary 22 6.2 Movement 24 6.2.1 South-to-North Water Transfer Project 24 6.2.2 Analyses of Water Price . 24 6.2.3 Cost Estimation . 25 6.3 De-salinization . 25 6.3.1 Introduction . 25 6.3.2
18、 Cost Estimation . 25 6.3.3 Comparative Analyses between De-salinization and Movement26 6.4 Storage 27 6.5 The economic, physical, and environmental implications of the strategy 27 6.5.1 Introduction and Analysis . 27 6.5.2 The Analytic Hierarchy Process Model . 27 6.6 Analyses of Water Strategies f
19、or China . 30 7 Evaluation and Generalization . 33 Team # 17578 4 / 49 7.1 Strengths . 33 7.2 Weaknesses 33 7.3 Generalization . 33 8 References 34 A position paper to governmental leadership 36 Appendices 40 Team # 17578 5 / 49 1 Introduction As we all know, water resources are vital to human produ
20、ction and life. Many countries are now facing a shortage and pollution of freshwater , and China is not an exception. Water resources deficiency has restricted economic development and peoples life enormously. Thus, Close attention has been paid to water storage, movement, de-salinization and conser
21、vation, as well as the prevention and disposal of water pollution. China is an arid and hydropenic countries. Although the fourth country in total freshwater amount, China is one of the poorest countries in per capita water. At the end of the 20th century, a scant supply of water had occured in abou
22、t 400 cities in all the more than 600 cities of China, 100 of which are fac-ing serious water scarcity1. The facing problems of Chinas water resources are as followings: shortage and pollution of water resources, serious soil erosion, serious waste of water, and uneven distribution. Freshwater is re
23、newable resource, supplied by at-mospheric precipitation. The distribution of atmospheric precipitation in space and time is extremely uneven in China, which exacerbates the supply and demand contradiction of freshwater. Freshwater is one of the few resources that can not be imported. We can only re
24、ly on water conservation and reasonable utilization and regulation. Surface water and groundwater are both the components of freshwater. The conductivity of surface water is high, while the volume of water storage is small. Groundwater is on the contrary. Therefore, the water resources can be regula
25、ted more sufficiently and efficiently when the two combined. Moreover, the exploitation potential of deep aquifers is low, and overusing deep aquifers will lead to surface subsidence and other serious consequences. Water re-sources in the north of China are less than those in the south, so the move-
26、ment of people to water-deficient areas should be avoided. South-to-North water diversion project can relieve the shortage of water in the north, while the cost is high, so this project can only be used in extreme arid regions. In the south of China, atmospheric precipitation is sufficient, but wate
27、r needs of ag-ricultural, domestic and industrial is huge, so water shortage is caused largely by unreasonable utilization and pollution2. Team # 17578 6 / 49 2 Assumptions There will be no wars or serious natural disasters from now to the year 2025. The total water resources in our models are all a
28、vailable. Underground water will not decrease because of leaking. Risk of water shortage can be measured by water shortage degree. 3 Total Water Resources Prediction Model 3.1 Calculation of Total Water Resources from 2003 to 2011 We apply the following equation to calculate total water resources： W
29、 R Q D where W is the total water resources, R is the surface water resources, Q is the groundwater resources, and D is the transform amount of surface water and groundwater. Based on the statistic data from 2003 to 20113, we can calculate the total water resources of China and each province. See Ta
30、ble 1. Table 1. Total water resources of China and each province from 2003 to 2011(100 million cubic meters). Province 2003 2004 2005 2006 2007 2008 2009 2010 2011 China 27460.2 24129.6 28053.1 25330.1 25255.2 27434.3 24180.2 30906.4 23258.5 Beijing 18.4 21.3 23.2 22.1 23.8 34.2 21.8 23.1 26.8 Tianj
31、in 10.6 14.3 10.6 10.1 11.3 18.3 15.2 9.2 15.4 Hebei 153.1 154.2 134.6 107.3 119.8 161.0 141.2 138.9 157.2 Shanxi 134.9 92.5 84.1 88.5 103.4 87.4 85.8 91.5 124.3 Team # 17578 7 / 49 Inner Mongolia 495.6 437.6 456.2 411.3 295.9 412.1 378.1 388.5 419 Liaoning 220.0 285.7 377.2 261.4 261.7 266.0 171.0
32、606.7 294.8 Jilin 326.5 323.7 559.7 353.6 346.0 332.0 298.0 686.7 315.9 Heilongjiang 826.8 652.1 744.3 727.9 491.8 462.0 989.6 853.5 629.5 Shanghai 15.1 25.0 24.5 27.6 34.5 37.0 41.6 36.8 20.7 Jiangsu 619.1 204.0 467.0 404.4 495.7 378.0 400.3 383.5 492.4 Zhejiang 574.5 675.7 1014.4 903.6 892.1 855.2
33、 931.3 1398.6 745 Anhui 1083.0 500.7 719.3 580.5 712.5 699.3 733.1 922.8 602.3 Fujian 806.6 712.2 1401.1 1623.5 1072.9 1036.9 800.8 1652.7 774.9 Jiangxi 1362.7 1034.6 1510.1 1630.0 1113.0 1356.2 1166.9 2275.5 1037.9 Shandong 489.7 349.5 415.9 199.3 387.1 328.7 285.0 309.1 347.6 Henan 697.7 406.6 558
34、.5 321.8 465.2 371.3 328.8 534.9 328 Hubei 1234.1 926.4 934.0 639.7 1015.1 1033.9 825.3 1268.7 757.5 Hunan 1799.2 1641.3 1671.0 1770.3 1426.5 1600.0 1400.5 1906.6 1126.9 Guangdong 1458.4 1187.7 1747.5 2216.2 1581.2 2206.8 1613.7 1998.8 1471.3 Guangxi 1901.0 1604.5 1720.8 1881.1 1386.3 2282.5 1484.3
35、1823.6 1350 Hainan 291.8 171.1 307.3 227.6 283.5 419.1 480.7 479.8 484.1 Chongqing 590.7 558.8 509.8 380.3 663.0 576.9 455.9 464.3 514.6 Sichuan 2589.8 2434.2 2922.6 1865.8 2299.8 2489.9 2332.2 2575.3 2239.5 Guizhou 915.5 991.0 834.6 814.6 1054.6 1140.7 910.0 956.5 626 Yunnan 1699.4 2106.3 1846.4 17
36、11.7 2255.5 2314.5 1576.6 1941.4 1480.2 Tibet 4757.1 4665.2 4451.1 4157.1 4321.4 4560.2 4029.2 4593.0 4402.7 Shanxi 574.6 309.4 490.6 275.5 377.0 304.0 416.5 507.5 604.4 Gansu 247.2 171.9 269.6 184.6 228.7 187.5 209.0 215.2 242.2 Qinghai 634.7 606.8 876.1 569.0 661.6 658.1 895.1 741.1 733.1 Ningxia
37、12.3 9.9 8.5 10.6 10.4 9.2 8.4 9.3 8.8 Xinjiang 920.1 855.4 962.8 953.1 863.8 815.6 754.3 1113.1 885.7 3.2 Prediction of Total Water Resources We draw scatter plots according to data from Table 1, and combining sta-tistic data and analyses, we establish the grey prediction model and linear re-gressi
38、on model for predicting the total water resources 3.2.1 An Introduction to Grey Prediction Model The grey theory can deal with systems that are characterized by poor in-formation and for which information is lacking. The grey system theory is a useful method for short-term prediction. A relatively s
39、mall number is suffi-cient for prediction in the grey model, and its margin of error is less than that of other models4. Therefore, the grey prediction model is suitable to predict Team # 17578 8 / 49 the total water resources. This paper uses the first-order linear model of grey prediction, or 1,1G
40、M , to predict the total water resources. The establishment of the 1,1GM mod-el consists of five steps4: Step 1: Organize the total water resources data into a nonnegative original sequence 0X . 0 0 0 01 , 2 , , X X X X n (1) Step 2: Apply the original sequence to establish an accumulated-generation
41、 sequence 1X . 1 1 1 1120 0 01 1 11 , 2 , , , , nt t tX X X X nX t X t X t(2) Step 3: Establish the 1,1GM model. 01X t aZ t b, 2,3, ,tn , (3) 1 1 111Z t X t X t . Here, a and b are parameters to be estimated, is the horizon-tal-adjusting factor, and 01 . Because the data structure of the total water
42、 resources is not special, this study sets at a general value of 0.5. The solution of (3) can be expressed as 10 11 atbbX t X eaa (4) Step 4: Use the 1,1GM model to create a matrix and the estimates of a and b . where 00023XXYXn, 00023XXYXn, ab . Using the ordinary least-square method, the estimatio
43、n of parameters a and b is given by Team # 17578 9 / 49 1 TTa B B B Yb (5) Step 5: Make predictions through inverse accumulated-generation operation. Substitute the parameter values of a and b obtained from step 4 into equation (4) in order to obtain 1 1Xt . Series 1X is the original series 0X produ
44、ced through the one-time accumulated generation. Therefore, before the prediction begins, 1 1Xt , ob-tained through prediction, must undergo an inverse accumulat-ed-generation restoration to become 0 1Xt . The inverse generated series is 0 1 1 11X t X t X t . (6) 3.2.2 An Introduction to Linear Regr
45、ession Model Suppose a model of the form y Ax B is expected and it has been de-cided to use the m data points , , 1 , 2 , ,iix y i m, to estimate A and B . Denote the least-squares estimate of y Ax B by y ax b . Applying the least-squares criterion to this situation requires the minimization of 2 21
46、1mmi i i iiiS y f x y a x bA necessary condition for optimality is that the two partial derivatives Sa and Sb equal zero, yielding the equations 120mi i iiS y ax b xa120miiiS y ax bbThese equations can be rewritten to give 21 1 111m m mi i i ii i immiiiia x b x x ya x mb yThe preceding equations can
47、 be solved for a and b once all the values for Team # 17578 10 / 49 ix and ix are substituted into them. The solutions for the parameters a and b are easily obtained by elimination and are found to be 22i i i iiim x y x yam x x, the slope and 222i i i i iiix y x y xbm x x, the intercept Computer cod
48、es are easily written to compute these values for a and b for any collection of data points5. 3.2.3 Fitted Value and Predicted Value of Total Water Resources Applying the two models, we obtain the fitted value from 2003 to 2011(see Appendix 1) and predicted value of 2015, 2020 and 2025(see Table 2). Table 2. Predicted value of total water resources in 2015, 2020 and 2025 Model Gray Model Linear Regression Model Province 2015 2020 2025 2015 2020 2025 China 26678.9 27094.
