2016美赛E题参考答案

Team # 52766

Team Control Number

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52766

Problem Chosen

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E

2016MCM/ICM

Summary Sheet

In order to predict the water scarcity and optimize the configuration reasonably, we analyze the situation of water scarcity by establishing a mathematical model, and propose the feasible suggestions on optimization. All the work is based on the sufficient data we collect.

Firstly, the local situation of water scarcity is estimated by introducing the water lacking rate index. Secondly, the local water consumption is predicted from personal living, industry, agriculture and ecology. Meanwhile, the local water consumption is predicted through establishing a compound model which based on an improved Logistic Model and the statistical regression analysis. Thirdly, the Gray Prediction Metabolism Model is used for predicting the amount of local water supply. At last, we comprehensively analyze the experimental results, and predict the ability of water supply in this local area.

To verify the availability of the model, we choose the North China as the object of study. We conclude that this area is seriously scarce before 2010 on the basis of mass data. The water scarcity will steadily remit and reach balance in 2025. This is due to China has finished the South-to-North Water Diversion and the North China gains large water resources from outside. The results call inside with the truth, so the model is reliable.

Then we try to optimize the water supplying and demanding structure in the North China, so that it can realize the internal self-sufficiency. We use analytic

hierarchy process (AHP) to assess the four schemes of water storage, water transfer, wastewater treatment and desalination from four aspects of timeliness, sustainability, economic, environmental benefits, so a more scientific water supplying system is developed. Finally, by means of adjusting the industrial structure, optimizing the mode of agricultural irrigation and improving the water conservation awareness of citizens, we propose a water resources allocation model to optimize the water supply system in the North China. In this way, the water scarcity in the North China can be solved five years ahead of the original schedule.

Key words

Water scarcity; water lacking rate index;improved Logistic Model;Gray Prediction Metabolism Model; statistical regression; analytic hierarchy process (AHP)

Team # 52766

Contents

1 INTRODUCTION & BACKGROUNDS ..................................................................................................... 1 2 PROBLEM ANALYSIS ........................................................................................................................... 1 2.1 Problem Restatement .................................................................................................................. 1 2.2 Problem solving.......................................................................................................................... 2 3 ASSUMPTIONS .................................................................................................................................... 2 4 NOTATIONS ......................................................................................................................................... 3 5 BASIC MODEL ..................................................................................................................................... 3 5.1 Model of the water consumption ................................................................................................ 3

5.1.1 Compound population Model based on Logistic Model ..................................................................... 4 5.1.2 Model of Industrial water consumption............................................................................................... 5 5.1.3 Model of total water consumption of a region..................................................................................... 6

5.2 Model of the Gray Metabolism Model GM (1, 1) ....................................................................... 6

5.2.1 Principle of common Gray GM (1, 1) Model ...................................................................................... 6 5.2.2 Principle of Gray Metabolism Model GM (1, 1)[2] .............................................................................. 8 5.2.3 Accuracy testing .................................................................................................................................. 8

5.3 Model of water supply capacity of a region ............................................................................... 9 5.4 Strengths & Weakness .............................................................................................................. 10 6 CHOOSE A REGION TO ANALYZE ........................................................................................................ 10 6.1 Brief introduction ..................................................................................................................... 10 6.2 Physical scarcity: ..................................................................................................................... 11 6.3 Economical scarcity: ................................................................................................................ 12 7 PREDICTION MODEL FOR THE NORTH CHINA .................................................................................... 12 7.1 Model of water consumption in North China. .......................................................................... 12 7.2 Water supply model in the North China ................................................................................... 17 7.3 The comprehensive evaluation to the future water resources in the North China .................... 18 7.4 Strengths and Weaknesses ........................................................................................................ 21 8 OPTIMIZATION OF WATER RESOURCES ALLOCATION ......................................................................... 21 8.1 Optimization of water supply allocation .................................................................................. 21

8.1.1 Construct the model of hierarchical structure .................................................................................... 21 8.1.2 Construction of comparison matrix of target-criterion layer. ............................................................ 22 8.1.3 Construction of comparison matrix criterion - target layer................................................................ 23 8.1.4 Total sorts of hierarchy and consistency check ................................................................................. 27 8.1.5 Interpretation of result ....................................................................................................................... 28

8.2Optimization of water consumption allocation ......................................................................... 29

8.2.1 Construction of water resources allocation model ............................................................................. 30 8.2.2 Main constraint equations ................................................................................................................. 30 8.2.3 Model Solution .................................................................................................................................. 32

CONCLUSIONS ..................................................................................................................................... 34 FURTHER DISCUSSIONS ........................................................................................................................ 34 REFERENCE ......................................................................................................................................... 34 APPENDIX ........................................................................................................................................... 35

Team # 52766

StrategyofConquering Thirst

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1 Introduction & Backgrounds

An effective plan of solving the water scarcity problem is crucial to human society. According to the United Nations, today more than one billion people lack access to safe, clean drinking water, and just 10 countries share 60 percent of the world’s natural, renewable water resources; what’s more, water use has been growing at twice the rate of population over the last century. A model of water scarcity of the world shows the serious situation. (See Figure 1)

Figure 1: the map of the world’s water scarcity

At the same time, our societal and economic growth is largely driven by the productive use of water. Actually, the world tripled its water use in the last 50 years alone. Our world population is increasing, yet we still share one water resource – and it’s limited. If we’re going to meet the agricultural, industrial and residential needs of this growing world, we must use our water in effective, efficient ways.

2 Problem Analysis

2.1 Problem Restatement

Develop a model that provides a measure of the ability that a region cab provide clean water to meet the needs of its population. Doing all this work with considering the dynamic nature of the factors that affect both supply and demand.

Pick one country or region where water is either heavily or moderately overloaded. Explain why and how water is scarce in that region.

Show what the water situation will be in 15 years, and predict how this situation impact the lives of citizens of this region. Design an intervention plan taking all the drivers of water scarcity into account according to the situation, to help with the water scarcity and optimizing the model.

Estimate the optimized model and predict the results.

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2.2Problem solving

We address the problem of optimizing water use of a region through analyzing the water situation, which provides a measure of the ability of a region to provide clean water to meet the needs of its population. The model consists of two big modules: water supply and water consumption. Water supply module is mainly composed of surface water and groundwater, the degree of environmental governance, storage capacity, precipitation, etc. Water module is mainly composed of personal living water, agricultural water, industrial water and ecological water use, etc.Finally we compare the model of water supply with the model of water consumption, then take a certain evaluation index to measure the region's water supply capacity.

Next, since the region of North China (include Beijing, Tianjin, Hebei, Shanxi, Inner Mongolia) meets the requirement of being heavily or moderately overloaded on using water, we choose the North China as the researching region. We explain the social and environmental reasons of the scarcity from physical and economical sides, to dissect what facts impact the water scarcity.

Then we make quantitative and qualitative analysis of the water supply and consumption in this region, to get what the characteristics of the situation in 15 years.

At last, according to the fourth and fifth question, we optimize the model from improving water supply and reducing water consumption, to solve the problem of water shortage. We consider about improving the water supply by the construction of reservoirs, water diversion works, water desalination, wastewater treatment, and political, economic and social considerations. On the other side, we reduce the water consumption from raising awareness about saving water and improving agricultural irrigation methods, adjusting the structure of industrial water, improving ecological aspects to consider autonomy ability. Then under the optimization of water supply and water consumption we set up a water allocation optimization model, which is used for exploitation and utilization planning of water resources, meanwhile predict the situation of water resources using in the future.

3 Assumptions

☆Ignore the impacts of the extreme disasters.

☆Ignore the impacts of the migration of population.

☆Ignore the administration cost in late period of water diversion project

☆Ignore the effects of the other polluting factors in the wastewater when consider about the polluted degree.

☆Ignore the transportation cost of the water supply when consider about the sea water desalination.

☆we assume that the gross of the population N(t) is large enough.

☆We assume that there is no big revolution in the configuration of water supply.

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?(t)?x?(k)??x?(0)(i) x(1)(1)i?1t?1?(1)(t?1)?x?(1)(t?1)?x?(1)(t),(t?0,1,2,...). ?(t?1)??x?(0)(i), we getxSincex(1)i?1t?15.2.2 Principle of Gray Metabolism Model GM (1, 1)[2]

After making a gray prediction and getting the latest information，it adds this

information into the original data series and wipes off the oldest information at the same time.Then, using the new one as original series, it repeats the above step 1.1 to set up GM（1,1） Model，so on and so forth, until the fulfillment of all the prediction objectives, and that is the Gray Metabolism Model we wanted。

5.2.3 Accuracy testing

Relative error and posterior difference ratio C are two most commonly used way to test the model, and its basic process is following:

?(0) is the series simulated by GM Model and?is residual x(0) is original series，x?(0)(t), the relative error sequence isp?1??, sequence。Within it is ?(t)?x(0)(t)?xand thus the total water resource amount in t?1 year??(?1,?2,...,?n) could be obtained. Hereinto we have?t?|?(t)x0(k)|, and ?t is the simulated relative error of the

1npoint, and????kis the average relative error.p?1??is defined as the

nt?1prediction accuracy, which is displayed in percentage.

S1??(?i??)2n?1(0),????i n(0)?(x(0)(t)?x)2?x(0)(k)S2?，x?

n?1nC?S1 S2Where S1is the mean variance of residual；S2 is the mean variance of original series;Cis the posterior difference ratio.

Here is a reference table attached that illustrates the model accuracy

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classification in details:

Table 2: The accuracy of the model

Accuracyof model Relative error/% Averagerelative accuracy (p, %) First class Second class Third class 1 5 10 Value of C ?95 80?p?95 70?p?80 ?0.35 0.35?C?0.5 0.5?C?0.65 ?70 ?0.65 disqualification 20 Thus, the method of predicting water resource amount in one place and checking the accuracy could be gained.

5.3Model of water supply capacity of a region

We define water scarcity F(t) as:

2?????at0at2?F?t??Y?t??W?N0?exp???bt0????exp?bt???B?t??C?t??D?t?22??????

In order to estimate the situation of the region[3], we lead in variable water lacking rate u:

u?F(t)*100%E(t)

For measuring the degree of water lacking in this region, we set 4th level

evaluation on the basis of water shortage rateuthe standard see table 3:

Table 3: The classificatory standard

Scarce situation Sufficient Light Middle Heavy shortage rate <5 5~10 10~20 >20 Main problems Achieves the balance between supply and demand of water resources Normal years in balance, but in the average year, the water supply may occur. Not only in design level year of water shortage occurs, also in normal times Water supply gap is extremely serious. Wading activities are severely restricted

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5.4 Strengths & Weakness

Strengths

☆It overcomes the traditional method on the forecasting water supply, facing the problems of the shortage of samples, difficult implementation and high requirement.

☆In the prediction process, we can weed out the old data and add new data constantly, maintaining the higher prediction precision.

☆It makes up the situation of Logistic population grows negatively. ☆The model is fit for many areas.

☆the models of industry, agriculture, ecological water consumption are concluded from the change rules, are sufficient in scientific nature.

Weakness

☆Without considering the uncertainty of social development, the model not always reflects the future water resources condition.

☆The model can only be used over a period of time for prediction. It is limited for extreme conditions.

☆ the models of the subsystem may not form a linear relationship in various countries, unless the situation is close to China.

6Choose a regionto analyze

In addition to the model, we also choose the region of North China to analyze.

6.1 Brief introduction

The North China is an important part of the Great Plains in the east of China，which located at north latitude 32°～40°and in the east longitude 114°～121°. North China's border is very large.The border of north is the south of Yan Mountains. The southern border is on the north side of the Dabie Mountains .The western boundary in Taihang to the Funiu Mountain Adjacent to the East is the Bohai Sea and the Yellow Sea, also with a total area of 300 thousand square kilometers. Plain has too much advantage such as flat terrain, many rivers, convenient transportation and advanced economy. From ancient times to the present, North China is the center of China in the economy, politics and culture area. And also, Beijing, the capital of China, is in its northern part.（see Figure 2）

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Figure 2: the region in red curve is the chosen area.

North China is one of the most water-lacking area of the nation, with only 6% gross、11% per capita of theaverage level. Why it is scarce in water, and how? We conclude the reasons from the physical and economic aspects, including social and environmental objects.

6.2 Physical scarcity:

The amounts of the water resources is poor. The region is alluvial plain, and lacked of rivers and lakes. What’s more, the vegetation coverage is not enough, the rain fall flows away with the solid. Thus the water conservation is poor. For many years, Water resources per capita average volume is 335 cubic meters, reaches nearly 15% of the national per capita.

Water resources are uneven distributed of time and space. Annually, it mainly performs in the event of a wet year and dry year phenomenon; within one year, mainly in summer and autumn, the precipitation and water resources quantity is more, while less rainfall in winter and spring. The uneven distribution of water resources in space mainly reflect that the water resources quantity change with zonal and surface evaporation is uneven distribution.

This region belongs to monsoon climate of medium latitudes, the rainfall is comparatively scarce.

These above are environmental causes.

The huge population and giant consumptions. The plain population accounts for about 20% of the total population, with only 6% gross、15% per capita of theaverage level.

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The urbanization and developing economics increase the demand of water in unit area. And this obviously stress the water supplying.

These above are social causes.

6.3Economical scarcity:

Serious pollution and waste, wastewater treatment rate is low. Industrial development and popularization of various kinds of agricultural chemicals leads to serious pollution. Set an example Deterioration of water quality is an important fact of water shortage in north China. Such as the Yong ding River upstream of the Guan Ting reservoir in Beijing, because of the serious pollution of water upstream reservoir has lost the function of water supply, adding to the water shortage situation in Beijing. What’s more, sewage treatment capacity in the region is not different, Beijing and Tianjin municipal wastewater treatment rate is higher, while other urban wastewater treatment rate is low.

Human activities. On the one hand, the development and utilization of water resources, and on the other hand, is characterized by the influence of land use. Due to the shortage of water resources and they have to excessive exploitation of groundwater. The region exploit 54.78% of the amount of the groundwater in China. Urbanization caused rainfall infiltration to groundwater recharge, and expanding agricultural irrigation area, increase the water evaporation consumption. The quantity of surface water and groundwater in the natural system greatly reduced—this forms a vicious circle in obtaining water.

7 Prediction model for the North China

According to the model of task 1 and the data statistics, which used to express water supply in North China, in task 2. Respectively. The model of water consumption and water supply were calculated.

7.1Model of water consumption in North China.

Table 4:the total population from 2008 to 2014 in the North

China[4](unit：thousand)

Sequence 1 2 3 4 5 6

Year 2008 2009 2010 2011 2012 2013 Population 133470 135490 140290 142080 143810 145500 Increase 2020 4800 1790 1730 1690 Growth rate per annum 0.015134487 0.035426969 0.012759284 0.012176239 0.011751617

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7 2014 147010 1510 0.010378007

Figure 3: annual average growth rate scattered points

From Figure 3 one can seethat the average population growth rate is linear with time, it also verifies the average population growth rate is linear with time in the task 1. But in 2010 there was anoutlier point, which may be related to the policy, economic and social.We could exclude the point without affecting the overall trend of population.

By the task 1, we know the average annual growth rate model P?t??at?b(t?1,2?.14)，which means when t equals 1, it represents year 2008.According to the census of North China, we could be derived from the population average annual growth rate of P ?t?.

Using the software Matlab，we geta??0.000734,b?0.017604. Therefore the average annual growth rate of population is:P?t???0.000734t?0.017604The approximate coefficient is 0.9729 which close to 1. Model fits well.

The fitting results are shown in Figure 4.

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Figure 4: Annual average growth rate of population

The fitting results could give us the fact that the annual average growth rate of population

Presented a negative correlation with time, on the other hand, the growth of the population in North China will be more slower, even there is zero growth at some time. This has a great relationship with the long-term family planning in China.

Put a??0.000734,b?0.017604into the complex model (4), we get the model of population growth in the North China.

2??????0.000734t0?0.000734t2?N(t)?N0?exp???0.017604t0????exp?0.017604t??22?????? Choose the initial conditionN(17)?147010, therefore

??0.000734t2?N(t)?147010?exp(1.043)?exp?0.017604t??2??

Sincea??0.000734?0,b?0.017604?0, we obtain the max value of N(t)b?24. This represents that the population of the North China will reach azero growth in 2032. Using the software Matlab to draw the curve of the population growth of the North China. See Figure 5:

whent??

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Figure 5:The curve of the population growth in the North China

According to the Figure 5, the data will reach zero growth in 2032 and turn to run downward. At the same time, the current growth rate of population is decreasing. After analyzing the in-depth causes, the conclusion has been drawn in two aspects. Culture is the first cause. With the development of scientific and educational standard, people receive a lengthened education which results in the postponing of average marriage age. More attention will be paid to the development of all qualities one should have and the next generation as well. Lowering the growth rate and uplifting educational quality. Raising only one child rather than raising too many with the limited money. These are why the population growth did not see effective and profound change when China lifted the restriction on one-child policy in 2014. The disconcerted population construction of northern China is another cause such as the aging population. According to the statistics, the old over 60 years take up 9.5 percent of the population in northern China which leads to the increasing of the local death rate, another cause affecting the natural increasing of population.

According to the average volume-36.5 cubic meters[5]-of water using in northern China, we can get the water using model:

??0.000734t2?A(t)?5.3659?exp(1.043)?exp?0.017604t??2??

A(t)unit: billion cubic meter

According to the analysis of the model in task one with the data of Table 5, we

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can get industrial water using model through Matlab programming

B(t)?0.1199t?4.4068

The approximate coefficient is 0.9735 which close to 1, Model fits well. The agricultural water using model

C(t)?0.1681t?19.8899

The approximate coefficient is 0.9522which close to 1, Model fits well. The ecological water using model

D(t)?0.1642t?0.585

The approximate coefficient is 0.9648 which close to 1, Model fits well.

The statistics of the water usage in northern China from 2008 to 2014 are displayed in diagram 1

The industrial, agricultural and ecological water usages are displayed,see Figure 6:

Table 5:the water usage in the North China from 2008 to 2014

Unit: billion cubic meter

year 2008 2009 2010 2011 2012 2013 2014 industry 4.77 4.38 4.56 5.11 5.02 5.12 5.25 usage agriculture ecology 20.05 0.78 20.25 0.87 20.37 1.07 20.57 1.26 20.73 1.41 20.90 1.57 21.06 1.73

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Figure 6:industrial, agricultural and ecological water usage

According to Figure 6, the agricultural water usage is on the rise much more than industrial and ecological water usage. Also, the growth rate is extremely high in accordance with the demand of agricultural production. The development of science and technology improves the output of agriculture and increase the demand of water as well. The low growth rate of industrial and ecological water usage comes from the intensive efforts put in environmental protection. The control on industrial sewage lowers the demand of water in this sector. The rise of the proportion of ecological water usage explains that the government in the North China put increasing emphasis on ecological water-supplying project. This is of great significance in improving local environment.

We can get the water consumption model in the North China from population, industrial, agricultural and ecological water using models.

??0.000734t2?E(t)?5.3659?exp(1.043)?exp?0.017604t???0.4522t?24.88172??

7.2Water supplymodel in the North China

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We can get the annual water resources in the North China in table 6:

Table 6:annual water resources in the North China

Unit: million cubic meter

Year 2008 2009 2010 2011 2012 Watersupply 30.93 30.89 31.52 32.93 33.86 We substitute the figure into the established model: 2013 34.97 2014 36.11 x(1)(t)?938.5654e0.032225*t?907.5965

x(1)(0)?30.93,withpreciseness analysis,we cangetp?100%?95%,

C?0.1758?0.35. This is a superior model and applicable. We can get the available

volume of water to supply from 2014 to 2030 in the North China as follows:

Figure 7:industrial, agricultural and ecological water usage

According to the Figure 7, the volume of water to supply is on the rise from 2008. The water supplying capacity is strengthening. Looking into the records, China started the water distribution project from south to north partly. The project was accomplished in 2014 and the water supplying capacity is extremely enhanced. Thus, the water distribution project is of great realistic significance to solving the problem of water shortage in the North China.

7.3 The comprehensive evaluation to the future

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water resources in the North China

With the establishment of the water supplying model in northern China, we draw the variation

u?F(t)?E(t), F(t) the water usage, E(t)Z the water F(t)supplying. The water demand-supply relation in northern China from 2008 to 2030 is

as follows:

Figure 8:the demand-supply relation in northern China

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Figure 9:the demand-supply relation in northern China

From the above two figures, we can see that rate of water shortage in the North China began to decline in 2010, expected to get rid of the status quo of water shortage in 2022, will reach equilibrium of supply and demand of water relations in 2025since 2008, the region raises the water demand and water supply steadily, but the speed of the water supply Y(t) is greater than the speed of E(t). And in 2025 about water supply, Y(t) is greater than E (t), the water deficit in F (t) becomes negative for the first time, and the gap between water supply and water consumption is increasing, water shortage situation in the region has been effectively improved.

Since 2008, because of China's macroeconomic regulation and control in two aspects of water and water supply. In terms of water consumption, the main policy is to reduce the rate of population growth, develop the efficient environmental protection enterprises, which makes the industrial water rate is reduced. to effectively control the rate of industrial water in north China, increasing the ecological environment water into making the region ecological environment improvement; In respect of water supply, as the south-north water diversion project fully completed, greatly increasing the ability of water supply in north China. According to this form of development bottom go to, the North China will get rid of the status quo of water shortage in 10 years.

As an economic superpower, China has large stretches, uneven distribution of water resources, which can reduce the water demands by limiting population growth rate, industrial water. And we can also solve the problem of water shortage in the North China through the establishment of large-scale water conservancy projects,

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massive south-to-north water transfer project. However the other lacking countries may not have those advantages. We care only about a region of supply and demand of water capacity, but also establish the effectiveness evaluation model of the economic measures to solve the problem of water shortage and then put forward the optimized configuration of water resources in this region, in order to solve the problem of water shortage.

7.4 Strengths and Weaknesses

Strengths

☆We use analytic hierarchy process (AHP), combining with analyzing the actual situation in North China. It greatly improves the accuracy of the model parameters and the applicant ability, leads to a good quantitative ultimate goal.

☆Strong in prediction.

Weaknesses

☆Themodel is lack of quantitative data, and unbalanced-sufficient qualitative data, lead to poor credibility.

☆Kind of ideal. It is not fit for some backward countries for the requirement of high populace's cultivation.

8Optimization resourcesAllocation

of water

8.1Optimization of water supplyallocation

We can take a variety of methods to optimize the distribution of water in a region, improve the ability of the area's water supply. Due to the actual situation that each district is different, each of the optimal methods of timeliness, sustainability, economic and environmental benefits has its emphasis, so we must consider the actual situation of local water resources and water resources development characteristics locally when making concrete measures. The main consideration includes the timeliness, sustainability, economic and environmental benefits, in order to establish a configuration of water supply system in conformity with the local actual situation to solve the water shortage problem.

8.1.1 Construct the model of hierarchical structure

Traditionally we have water engineering, water diversion engineering methods to improve the ability of water supply in a region. With the development of science and technology, there appears emerging technologies such as desalination, sewage treatment. In order to raise the weights of the four methods in solving water supply gap, based on the practice area, we adopt the analytic hierarchy process (AHP) [6]to

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evaluating the reservoir engineering, water engineering, sewage treatment and seawater desalination through the timeliness, sustainable, economic and environmental benefits. The established hierarchy map is shown in the Figure 10:

General Optimization of water supply objectiveA Criterion EconomicTimeliness SustainabiliEnvironmental layer C ty Scheme Sewage Water Reservoir Desalination layer P treatmentdiversion engineerin Figure 10:the hierarchy map

8.1.2Construction target-criterion layer.

of comparison matrix of

Taking advantages of the 1-9 scaling methods, we construct the judgment matrix

as shown inTable 7:

Table 7:comparing scale explanation

scale 1 3 meaning Compare two elements, share the same importance Compare two elements, the former a little more important than the latter Two elements, the former is obviously more 5 important than the latter Two elements, the former is strongly more important 7 than the latter Compare two elements, the former is extremely 9 important than the latter 2,4,6,8 The judgment of intermediate value Two elements, the latter is more important than the Reciprocal former We make a comprehensive analysis in the North China. As an existing developed industrial and agricultural area in the North China, with a large population, and short

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W?? 0.1579,0.1196,0.4088,0.3137?

TCI??ciCIi?0.0354

i?14Hereinto,CR?CI?0.0393?0.10passes the consistency check. RI8.1.5 Interpretation of result

It can be concluded that in North China the weight of each processing scheme is shown in:

Figure 11:Optimization scheme of water supply in North China

The results obtained from the analytic hierarchy process can be seen that wastewater treatment and seawater desalination is main measures of adjusting water supply structure in North China .It has a great environment influence and offset the huge potential of the gap, at the same time, as long as the management system is reasonable, sewage treatment and sea water desalination plant are able to achieve sustainable development, and in the early stage about large-scale economic investment,the later will bring a huge cost advantages. So, if the North China wants to get rid of the plight of water shortage and developing healthily, must be in the future, Changing itself to rely heavily on water storage projects and Water supply allocation of water diversion project of the south to North Water Transfer Project, at the same time, set up a serious of water systems such as wastewater treatment and seawater desalination technology.

The water storage project in North China could be used for the agricultural production and resource development provide a good guarantee. At the same time,it

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led to the development of tourism the breeding and other emerging industries. It also provide a large number of energy shortage of electricity and water. Meanwhile, we take into account that the reservoir is poor and high cost characteristics, through analysis the fact that water storage projects accounted for 15.8% of the total water supply is the best. This will not only solve part of the water problem also use the reservoir water, power generation regulating ecology, developing agriculture and so on.

Through water diversion project in North China, it could make use of the existing conditions to reduce the cost of obtaining water resources. Due to the input of the past few years, China's south to North Water Diversion Project has been fully started, so water diversion project is undoubtedly the current the cheapest and effective way to get water. In the short term, less cost can be used to obtain more water resources

But we take into account the question, which influents sustainable development in the North China region and water resources reserves in the south area, thought water diversion project for a long time, economic efficiency is not as well as the sea water desalination and wastewater treatment, We believe that the North China region in the future can be gradually reduced on the dependence of water project. Accounted for 11.96% of the appropriate.

As a large industrial area in North China, the problem of urban pollution is serious, through the establishment of sewage treatment plant, It can provide a lot of water to solve the problem of pollution in the city, at the same time, sewage treatment can also improve the quality of urban environment,residents to further reduce the cost of Medicine, At present, the environmental pollution is more serious in North China. So for the North China, wastewater treatment has great potential. Also it has the very big necessity.

After analysis, the North China should be invested in sewage treatment in the vast majority of the energy. Development of sewage treatment is both measures of environmental protection and economic benefits.

Due to technical constraints in North China, Seawater desalination initial investment is relatively high, however, in the process of sea water desalination, we can get a lot of fresh water resources. There are a lot of salt and other chemicals, and be able to form a circular economy industry. At the same time, it can also reduce the potential environmental pollution and improve economic performance. It is important that the North China region is facing the sea. The cost of access to the sea is low, however, taking into account the cost of the short term. Seawater can provide 31.4% of the water gap in North China in the future. This can meet the future water supply and the protection of the environment, and can be guaranteed to be in the range of acceptable

8.2Optimization of waterconsumptionallocation

Water allocation optimization of water resources, which should be combined with the water supply configuration optimization and from the water consumption of

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the population,

Agricultural water consumption, industrial water consumption and ecological water consumption are comprehensively considered. Using the model, which based on water resources allocation , to optimize allocation.[7]

8.2.1 Construction of water resources allocation model

All kinds of physical elements in water resources system (Reservoir engineering, water diversion project, seawater desalination project, sewage treatment project, water resources calculation unit, river channel intersection point, etc) Generalized as nodes, through the connection between the nodes, water source system generalization network.

Water balance simulation model of water resources system is composed of basic physical elements, Physical element measurement data, the relationship between the physical elements and the system coordination criteria, solution to the problem, o the basis of the physical elements, the five parts of the state are formed.

8.2.2 Main constraint equations

1.Equation of balance of surface water capacity of the reservoir

ttXRSVit?XRSVi?1?PRSFi?is?i,d?i??XCSI???isi,d?i??iisi,d?i??XCSAi???

?is?i,d?i???isi,d?i?XCSEi???io?i,d?i???ioi,d?i?XCSOi??2. Reservoir limit

XRSVti?XRDVti?PRSUtiXRSVti?XRDVti?PRSLitHereinto,

?PRSU1itPRSU??i?PRSU2t

itPRSL1?VRSVti?1?VRDVti?1?PRSU2itVRSVti?1?VRDVti?1?PRSU2itPRSLit?PRSL1it

Type 2 denotes the limit of the level. That is when the reservoir on flood control capacity is out of the limit, Limit for flood control storage capacity limit, otherwise still with maximum capacity for ceiling.

2. Flow capacity constraints of the River channel:

3. Minimum flow requirements of the River channel:

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4. Water balance equation of the Water consumption by Unit population:

XCSOti?XCDOti?PCSLitPZWItj?XZSF1tj?is?u?j?,j??isu?j?,j?XCSIt??ld?u?j?,j??idu?j?,j?XCDIt??XZGItj?XZTItj?XZMItj5.Water balance equation of the Ecological water unit:

lsu?j?,j?PZWEtj?XZSF3tj??XCSEt??ld?u?j?,j?ldu?j?,j?XCDEt?

??lo?u?j?,j????XCTLEt?1lou?j?,j?lou?j?,j??XCSOE??XZGEtj?XZTEtj?XZMEtj??t,j

6.Calculation of Agricultural water use efficiency

7.Calculation of industrial water use efficiency

AZBAt?PZBC1?PZBC2?AZWAtjjjjPZBC3jAZBItj?PZBC4j?AZWItjPZBC4j?Hereinto,

(10)

1Qj

8.Calculation of wastewater discharge amount

9.Calculation of the discharge of wastewater reuse

XZTIt?XZTAtj?XZTStj??PZWItj?XZMItj??PZTC1j?PZTC2j?PZTC3jXZTPtj?XZW1tj?PZTC1j??1?PZTC2j??t,j

While:

XZTItj?PZTC4??XZTIt?XZTAtj?XZTStj?XZTLtj?XZTAtj?PZTC5??XZTIt?XZTAtj?XZTStj?XZTLtj?XZTStj?PZTC6??XZTIt?XZTAtj?XZTStj?XZTLtj?

10.Equation of the Groundwater water balance

jjjjjjXZGVtj?XZGVt?1?PZGDt???PZPWt???XZWAt??j?ls?u?j?,j??XCSAt??1lsu?j?,j??l0?u?j?,j???XCSDt?1ldu?j?,j??lg?u?j?,j???XZGOt?1lgu?j?,j???XZGItj?XZGAtj??lg?t,d?j????XZGOt?1lgj,d?j??jj??j??XZGVt?1?XZGVt?

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11. Limit of Groundwater mining

1XZDItj?XZGAtj?PZGUj?PZGCj12

8.2.3 Model Solution

In this paper, we based on the established model and the past method, combined

with the adaptive scheduling method of the reservoir, propose an adaptive reverse calculation method. Combined the weight among with reservoir engineering, water diversion project, water desalination, sewage treatment, and adjustment of industrial structure and methods of water-saving, we determine the results based on the local water resources carrying capacity.

The model using GAMS language as establishing water resources system configuration model and its se basic programming language, plans every level year in simulation process of Water resources allocation model, calculating all the 2008 - July 2014 older series, for years as the calculating time, each computing time configuration process is consistent. Figure 1 for the long series calculation flow chart

Figure 12:Long series calculation flow map

Using GAMS programming can get the water supply and water conditions. See table 10

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Table 10:Data comparison

year 2008 2009 2010 2011 2012 2013 2014 Water consumption industrial 4.07 3.6 3.88 4.2 4.3 4.42 4.5 Water agricultural ecological supply 18.15 18.45 18.2 18.6 18.66 18.7 18.89 0.68 0.75 0.9 1.15 1.3 1.48 1.63 33.88 34.11 34.62 35.99 36.96 38.11 39.21 According to China's water resources for water supply and water consumption data and water resources allocation model of data comparison, it can be seen through the construction of reservoirs, water diversion, water desalination, wastewater treatment methods such as water supply has obvious improvement. By raising people's consciousness of water saving, adjusting industrial structure, optimizing the irrigation method and other methods, we have significant lower water consumption. So by raising water reduce water consumption or reduce water consumption can increase speed to solve the water shortage in the future, which has obvious effects. The model of water allocation of water resources of planning water supply, water in the North China can be very good to alleviate water crisis.

454035302520151050IndustryIndustry'AgricultureAgriculture'EcologyEcology'OutputOutput'20084.774.0720.0518.150.780.6830.9333.8820094.383.620.2518.450.870.7530.8934.1120104.563.8820.3718.21.070.931.5234.6220115.114.220.5718.61.261.1532.9335.9920125.024.320.7318.661.411.333.8636.9620135.124.4220.918.71.571.4834.9738.1120145.254.521.0618.891.731.6336.1139.21 Figure 13:Actual water supply and water consumption and water

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resources allocation model the data table

In the same way, we can predict that water crisis will ease in 2020 through the water allocation of water resources model. Compared with task 1, the result will be five years ahead. Through the prediction of the model, if we can constantly improve the reservoir, sea water desalination technology, wastewater reuse, the adjustment of industrial structure and the citizens' consciousness of water-saving in the future, then the solution will come ahead of schedule.

Conclusions

We give a brief introduction about our work in this part, and conclude as follows: ☆The model of water supply capacity is not only a simple estimate for the North China, but also suitable for other areas.

☆The Grey Metabolism GM model with the known objective characteristics can predict the characteristics of the future at some point. Through the metabolism of grey, this article predicts system for water supply in the next 15 years, the calculation is simple, easy to operate.

☆Analytic hierarchy process (AHP) starts from the actual situation of the North China, analyzing various factors that are accounted for in the area. By contrast, normalizing the regularization matrix, and then, we give the weight of each index, and finally calculated the optimal decision scheme.

Further discussions

We simplify some problems because of the limited time, and in the next step we plan to finish some further work:

☆If we divide the world into developed countries, developing countries and underdeveloped countries, adopting the same method，we can improve the precision of the model which is used for the whole world.

☆It can also be extended to other known partial information, which is small in the prediction of other information.

☆Analytic hierarchy process (AHP) can be applied to all areas of decision problems.

Reference

[1] Kefeng Duan. China's population prediction model based on a composite model [D]. Lanzhou university institute of mathematics and statistics, 2012.20. [2] Songqian Huang, Weiming Wang, Cong Zeng, Shuang Hao, Xiaojuan Cao .Based on the grey metabolism GM (1, 1) model of China's annual production of aquatic products[J].Chinese Agriculutural Science Bulletin, 2012(28):126-131. [3]Beijing Municipal Statistics Bureau.The Beijing statistics yearbook2009[EB/OL].[2016].http://www.bjstats.gov.cn/nj/main/2009-tjnj/index.htm.

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[4] The national bureau of statistics,http://www.stats.gov.cn/，2015.07. [5] China's ministry of water resources.Water China[EB/OL].[2016].http://www.mwr.gov.cn/zwzc/hygb/szygb/.

Resources

of

[6] Jian'e Chang, Taili Jiang.Analytic hierarchy process (ahp) to determine weights of research[J].Journal of wuhan university of technology, 2007.29(1). [7] Jinghai,Lli.Based on the rules of water resources allocation model[D].The China institute of water resources and hydropower research:The China institute of water resources and hydropower research, 2005.03.

[8] Huiling He.Study on the Water Use and Water[D].Tsinghua University, 2010.05.

[9] Chonghui Fu, Wenjun Wang, Xuchun Zeng.China's population fertility change and the influence factors, based on the analysis of the sixth census[J].South China Population, 2014.02.

[10] Shunjiu Wang, Yu Hou, Xinli Zhang, Jing Ding.Progress in the study of Chinese water resources optimal allocation and prospect[J].Water Resources Development Research, 2002.09.

[11] Yong Zhao,YuanSheng Pei.The urban water shortage[J].Advances in Water Science, 2006.5.3(7):389-394.

[12] zhengtao shi, xinyou liu, overwhelmed with. Urban water security evaluation index system research [j]. Journal of urban problems. 2008.155 (6), 30-34. [13] Xu shen. water supply security multi-index evaluation method research [D]. China institute of water resources and hydropower research, 2013.06.

[14] Xinmin xie, Haiqing,Zhang, Mingwan Yin,the sustainable utilization of water resources evaluation and planning theory and practice” , the Yellow River water conservancy press, 2003.

Appendix

We mainly enumerate the programs of the software Matlab. The gray forecast metabolism: function gmcal=gm1(x) sizexd2 = size(x,2); k=0; for y1=x k=k+1; if k>1

x1(k)=x1(k-1)+x(k);

z1(k-1)=-0.5*(x1(k)+x1(k-1));

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yn1(k-1)=x(k); else

x1(k)=x(k); end end

%x1,z1,k,yn1 sizez1=size(z1,2); %size(yn1); z2 = z1';

z3 = ones(1,sizez1)'; YN = yn1'; %YN B=[z2 z3];

au0=inv(B'*B)*B'*YN; au = au0'; %B,au0,au afor = au(1); ufor = au(2); ua = au(2)./au(1); afor,ufor

constant1 = x(1)-ua; afor1 = -afor; x1t1 = 'x1(t+1)'; estr = 'exp'; tstr = 't'; leftbra = '('; rightbra = ')';

%constant1,afor1,x1t1,estr,tstr,leftbra,rightbra

strcat(x1t1,'=',num2str(constant1),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(ua),rightbra)

%***************************************************** k2 = 0; for y2 = x1

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k2 = k2 + 1; if k2 > k else

ze1(k2) = exp(-(k2-1)*afor); end end %ze1

sizeze1 = size(ze1,2); z4 = ones(1,sizeze1)'; G=[ze1' z4]; X1 = x1';

au20=inv(G'*G)*(G'*X1); au2 = au20'; %z4,X1,G,au20 Aval = au2(1); Bval = au2(2); %Aval,Bval

strcat(x1t1,'=',num2str(Aval),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(Bval),rightbra)

%

nfinal = sizexd2-1 + 1; %nfinal = sizexd2 - 1 + 1; for k3=1:nfinal

x3fcast(k3) = constant1*exp(afor1*k3)+ua; end %x3fcast

for k31=nfinal:-1:0 if k31>1

x31fcast(k31+1) = x3fcast(k31)-x3fcast(k31-1); else if k31>0

x31fcast(k31+1) = x3fcast(k31)-x(1); else

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