1、 For office use only T1 _ T2 _ T3 _ T4 _ Team Number 21185 Problem Chosen B For office use only F1 _ F2 _ F3 _ F4 _ 2013 Mathematical Contest in Modeling (MCM) Summary Sheet Summary There are mainly three water problems in China: too little water in northern and northwestern part; too much floods in
2、 southern part; and too dirty water produced by industry and agricultural pollutants. In order to address problems above and provide a thirteen-year water strategy (2013-2025) for the leadership of China, we conclude five sub-problems and its solution in our paper: 1)Prediction of the supply and dem
3、and of water in a period of thirteen years based on historical data;2) Model building of national water storage and movement strategy to solve Chinas uneven distribution of water in time and space; 3)Model designing of regional water de-salinization strategy to increase the total amount of available
4、 water;4)Model building of water conservation strategy, including regional water pollution treatment and national water-saving; 5)Long run cost-benefit analysis of four water strategies above and the discussion of the optimal combination of water strategies. In first model, we choose the most approp
5、riate Fitting Function. Using Grey Predicted Model, we can get the correlation degree between water consumption and population, industrial GDP and agriculture output. Then we successfully finger out the water demand in 2025 is 6770 hundred million m3 by using GM prediction. In our second model, we u
6、se CV (coefficient of Variation) and water supply pressure as the decision-making index and work out a water storage project list by using Goal Programming. Based on cost and benefits analysis, we build Minimum Spanning Tree to work out the optimal water transfer plan. That is, we should transfer wa
7、ter from Yangtze watershed to Yellow watershed and Hai watershed. Besides, we devise a local water transfer strategy. In the third model, we build a set of parameters to describe the degree of water purification demand of each city and successfully get the water de-salinization plant building scheme
8、. In the fifth model, we do long run cost-benefit analysis of four water strategies above. We first analyze weights of economic, physical, environmental implications by using AHP (analytic hierarchy process). Then we use Neural Network Algorithm to classify the quality of each strategy and finally g
9、et a reasonable strategy evaluation model. In the whole modeling process, we give full consideration to validity, feasibility and cost-efficiency of our model. Five Models for Chinas Water Scarcitys Contents 1 Introduction . 1 2 Nomenclatures . 2 3 Model one: Water demand and supply Forecast (2013-2
10、025) . 3 3.1 Introduction 3 3.2 Assumptions . 3 3.3 Function Fit Model . 3 3.3.1Analysis of Chinas water use . 4 3.3.2Model Testing 6 3.3.3Prediction Results and Conclusion . 6 3.4 Grey Forecasting Model . 7 3.4.1Reasons for Improvement . 7 3.4.2Correlation Degree Analysis . 8 3.4.3Thirteen-year wat
11、er forecast based on Verhulst Model. 9 3.4.4Model Solution 10 3.4.5Model Testing 10 4 Model Two: Water Storage and Movement 12 4.1 Terminology 12 4.2 Water Storage Model: Time Balancing Strategy of Water Resources 13 4.2.1Introduction . 13 4.2.2Analysis . 13 4.2.3Model Solution 14 4.2.4Conclusion 16
12、 4.3 Water Transfer Model: Spatial Balancing of Water Resources Strategy 16 4.3.1Introduction . 16 4.3.2Backgrounds and Water Movement Principles . 17 4.3.3Model Analysis . 18 4.3.4Objective Function of water transfer strategy . 21 4.3.5Model Testing 21 4.3.6National water transfer strategy 21 4.3.7
13、Conclusion 22 5 Model Three: Water De-salinization Strategy 23 5.1 Introduction 23 5.2 Terminology 23 5.3 Assumptions . 23 5.4 Model Building . 24 5.5 Model Solving 24 5.6 Analysis and Conclusion 25 6 Model Four: Water Conservation Strategy 25 6.1 Introduction 25 6.2 Water Pollution Control Model 25
14、 6.2.1 Introduction 25 6.2.2 Assumptions . 25 6.2.3 Terminology . 26 6.2.5 Model solution: 27 6.2.6 Model analysis: 28 6.3 Water-saving Model 29 6.3.1 The water consumption per unit GDP . 29 6.3.2 Analysis and Conclusion 30 7 Model Five: Impacts Evaluation Model 31 7.1 Introduction 31 7.2 The Compar
15、ison of (the actual benefit of a project) 31 7.3 Evaluation of Economic, Physical, and Environmental impacts using AHP . 31 7.4 Neural Network Evaluation Algorithm 33 7.4.1 Analysis 33 7.4.2 Conclusion . 34 8 Strengths and Weaknesses 35 8.1 Strengths 35 8.2 Weaknesses 35 9 Position paper for the Gov
16、ernmental leadership of China . 36 10 References 36 11 Appendix and Supporting Datas . 37 Team # 21185 Page 1 of 42 1 Introduction Water, the magic encounter between one hydrogen and two oxygen atoms, is vital for all kinds of life forms in the earth. The human body, myriad ecological systems and th
17、e big biosphere of our entire planet, all of these cant live without the beautiful gift from our Almighty God. However, in many parts of the world nowadays, we human are facing severe water problems. Take China for example. With more than 20 percent of worlds population but less than 7 percent of it
18、s freshwater, China is continuously facing issues associated with water. There are mainly three problems in China: too little water in northern and northwestern part of country; too much floods in southern part; and too dirty water produced by industry and agricultural pollutants. Furthermore, being
19、 a developing country, China has the responsibility to deal both the soaring water demand caused by booming economy and the increasing need to improve water consumption efficiency. In order to address problems above and provide a thirteen-year water strategy (2013-2025) for the leadership of China,
20、we conclude five sub-problems to tackle in our paper. Prediction of the supply and demand of water in a period of thirteen years (2013-2025) based on historical data Model building of national water storage and movement strategy to solve Chinas uneven distribution of water in time and space Model de
21、signing of regional water de-salinization strategy to increase the total amount of available water Model building of water conservation strategy, including regional water pollution treatment and national water-saving Long run cost-benefit analysis of four water strategies above and the discussion of
22、 the optimal combination of water strategies In the whole modeling process, we give full consideration to validity, feasibility and cost-efficiency of our model. Team # 21185 Page 2 of 42 2 Nomenclatures The fresh water demand of a region The fresh water supply of a region The total amount of water
23、resources of a region The fresh water demand of whole nation The fresh water demand of whole nation The groundwater resources of a region The surface water resources of a region The population size of a region Gross Domestic Products Real GDP per capita The water supply pressure of a region The nati
24、onal average water supply pressure The water consumption per unit GDP The capacity of a reservoir The average construction costs of a reservoir The actual benefit of a project The range of water resource in a certain period of time The number of a certain province in model two The amount of water a
25、region cant provide by itself The watershed attribute of the number i province The terrace attribute of the number i province The geographical coordinates of a regions capital city The distance between region i and j The Earth Radius The edge weights of national water transferring network The estima
26、ted water consumption in 2013 The growth rate of water consumption The desalinization cost of tons of seawater The desalinization cost of tons of seawater in 2013 The optimal time to build water purification plant The measurement of the seawaters desalination cost Demand for water-pollution control
27、degree of number k watershed The water supply pressure of a watershed The highest level of water quality The middle level of water quality The lowest level of water quality The ratio between the sum of , and water of resources to the total water resources Demand for Water-pollution Control Degree of
28、 the number j city in number k watershed Team # 21185 Page 3 of 42 Water Resources of the number city in number watershed The total COD in the citys water of the number city in number watershed COD The chemical oxygen demand The emission of COD per year of the number city in number watershed The wat
29、er consumption of a unit GDP 3 Model one: Water demand and supply Forecast (2013-2025) 3.1 Introduction In order to devise an effective water strategy, we firstly need to predict the total amount of water demanded and that should be supplied in 2013-2025. The water demand and supply forecast is the
30、preparation work for models aiming to increase water resource. That is to say, our water storage and movement, water purification, conservation strategy are all based on the forecast of water. 3.2 Assumptions Assume that Chinas population and other policies dont have sharp change in the 2013-2025 As
31、sume that China maintains a steady economic growth from 2013 to 2025 Assume that the worlds climate dont have dramatic changes from 2013 to 2025 3.3 Function Fit Model To do water forecast, we apply Function Fit Model. First, we collect ten-year water resources data (2000-2010) from China Statistica
32、l Yearbook, including total water use, Industrial water consumption, Agricultural water consumption and Live water consumption. Considering the relationship between time and Chinas total water use per year, we then build a Function Fit Model. Namely, we get the most approximate year-water-use functi
33、on by minimizing the residual sum of squares. Then, putting the time value into the estimated function, we can predict the water demand and supply in next thirteen years. Team # 21185 Page 4 of 42 3.3.1 Based on data we have got, we can draw a 1997-2010 Chinas water use table as shown below: Water c
34、onsumption 1997 1998 1999 2000 2001 2002 2003 100million m 35566 5435 5590.88 5497.59 5567.43 5497.28 5320.4 Water consumption 2004 2005 2006 2007 2008 2009 2010 100million m 3 5547.8 5632.98 5794.969 5818.67 5909.95 5965.1545 6021.99 Then, we can get a water consumption trends figure as shown below
35、: From the figure above, we can see that the average water consumption per year from 1997 to 2004 fluctuates up and down around an intermediate value of 5500. And the deviation value of 2003, which fell sharply to 532 billion cubic meters, probably results from the drought happened in 2003 spring. A
36、fter 2004, national water consumption per year rise steadily. Team # 21185 Page 5 of 42 Using the Fit Function Model to fit the data, we firstly can get the Linear and Nonlinear Fit Function as shown below: From the two linear and non-linear figures above, we conclude the Linear and Nonlinear Fit Fu
37、nction dont achieve the ideal imitative effect. Thus, aiming to exclude the climate change factor which restricts water use, in the fitting process we abandon data with sharp fluctuations during 1997-2000, and finally find the real demand of Chinas water resources. The figure above shows results of
38、three fitting methods: linear fitting, interpolant and power function fitting, and the table below shows the fitting degree of those three kinds of fitting methods. Linear fitting Power fitting Interpolant fitting Function y=59.35*x-113300 y=1.248e-066x21.1 - SSE 1.119e+005 1.086e+005 0 R-square 0.7
39、759 0.7826 1 Adjusted R-square 0.751 0.7283 - RMSE 111.5 116.5 - We can draw the conclusion that the first two fitting results are very close to each other. Team # 21185 Page 6 of 42 3.3.2 Model Testing Now, we need to test whether this Function Fitting Model is right. We find the data from “Chinas
40、sustainable development of water resources in the Strategic Studies”. The data shows that the predicted water use in 2013 is 7000-8000 one hundred million cubic meters. Then we use our own model to predict the water use in 2013. Comparing these two kinds of data, we find our water use prediction is
41、in great consistency with the data we have find in the report. That is to say, Our model is efficient to predict the probable water use in the future. 3.3.3 Prediction Results and Conclusion Using the Function Fitting Model, we successfully predict the water demand in 2025. The results show in the t
42、able below: Year Linear fitting Power fitting Interpolant fitting 2013 6166.41 6187.05 6201.94 2014 6225.76 6252.21 6264.81 2015 6285.12 6318.03 6329.02 2016 6344.47 6384.5 6394.48 2017 6403.82 6451.64 6461.13 2018 6463.18 6519.45 6528.89 2019 6522.53 6587.95 6597.69 2020 6581.89 6657.12 6667.46 202
43、1 6641.24 6726.99 6738.13 2022 6700.59 6797.56 6809.61 2023 6759.95 6868.83 6881.85 2024 6819.3 6940.81 6954.77 2025 6878.65 7013.51 7028.3 However, the confidence of the results obtained by the Function Fitting Model is not very high. We believe the reason lies in the fact that we only use data fro
44、m 2000 to 2010. And it is difficult to do a thirteen-year prediction by using ten-year data. Because of Chinas current rapid economic development, the growth of population and the speed of economic development is changeable. So we must take changes in social indicators into account to better predict
45、 water consumption. Team # 21185 Page 7 of 42 3.4 Grey Forecasting Model 3.4.1 Reasons for Improvement The result we get from Function Fit Model is not very ideal, and we believe the key reason lies in the lack of data. In other words, we only get the data from 1997 to 2010. So the fourteen-year dat
46、a is too less to forecast the thirteen-year trends of future and the exact results is based on the fact that we have get the data of past forty or fifty years. In view of current situation, we devise a Grey Forecasting Model to get data with higher reliability, thus successfully overcoming the weakn
47、ess of Function Fit Model. The advantage of using Grey Forecasting Model is that we can get more reliable results with lacking accessible data, which perfectly fitted with our current situation. The total amount of water use is consists of agricultural, industrial, live water consumption, and these values are respectively relevant to agricultural GDP, industrial GDP and population, whose data of recent decades can be easily found in China Statistical Yearbook. Thus, if we quantify the interdependence coefficients between each consumption and respective production and the coeffici
