An Optimal Water Strategy for China - 2013MCM, Feb. 2013

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Challenge or Opportunity?

An Optimal Water Strategy for China

Control Group 20639

COMAP Mathematical Contest in ModelingFebruary 04, 2013



Abstract

The fresh water resource is one of the most essential element of human being. As the growth of population and the trend of economic development, water management is becoming a challenge of every country in the world. In this paper, we are to propose a water strategy of 2013 for China tomeet the water need in 2025.

Firstly, we divide China into six regions to look for a macroscopic water plan. By observing the

“inputs” and “outputs”, we use a system model to analyze the change of water for a certain region.The water reserves for emergencies is considered to ensure the “stability” of the system. We defineRichness Index with water, population and GDP to describe the richness of water resource. A standardvalue of this index is defined and used to determine the standard demand of water.

In the basic model, we predict the water supply in 2025 under current policy without a new strategy,then compare it with the standard demand to get the shortage. We predict the water supply usinga binary regression of population and GDP. The result shows that Region 2 (North China) and 3(Central China) will suffer from critical shortage in 2025 under current policy, which provides aguide to our water strategy.

To fill the water shortage in 2025, we build an advanced model including four aspects: transfer andstorage, desalinization, pollution control and agricultural utilization. After analyzing respectively,we combine the four aspects together in a comprehensive optimization model, then solve it to get anoptimal water strategy for the six regions. This strategy can solve the problem of Region 2 and 3, andthe Richness Index will become more even among the six regions. The total cost of this water strategyis 2044.16 billion dollars, which is about 1.26% of the total GDP from 2013 to 2025 of China. We alsodiscuss the implication on economy, health/living condition and environment of our strategy.

The method of our model can be generalized to give a detailed strategy of each region. Our waterstrategy is based on careful analysis and performs well, but we also ignore some factors such as thechange of price. Further strategy for each region, climate changes and advertising should be theguidance of future works.



Team number 20639 Page 1 of 34

Contents

1 Introduction 3

2 Criterion of Success 5

3 Analysis and Preparations 6

3.1 System Model: Input and Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2 Define Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.3 Criterion of Richness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Basic Model: Under the Current Policy 9

4.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2 Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.3 Original Water Supply S origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.3.1 Correlation of Water, Population and GDP . . . . . . . . . . . . . . . . . . . . . 10

4.3.2 Predicting Population and GDP from 2013 to 2025 . . . . . . . . . . . . . . . . . 11

4.3.3 Get S origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.4 Standard Demand Dstand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.5 Shortage and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Advanced Model: Our Water Strategy 14

5.1 Transfer and Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.1.1 Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.1.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.1.3 Determine the Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.2 Desalinization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.2.1 Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.2.2 Production and Cost in 2025 by Desalinization . . . . . . . . . . . . . . . . . . . 16

5.3 Pollution Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.3.1 Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.3.2 Cost and Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.4 Agricultural Utilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.4.1 Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.4.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19




5.4.3 Water Saving by Improving Irrigation Mode . . . . . . . . . . . . . . . . . . . . 19

5.4.4 Calculation of Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.5 Comprehensive Model: An Optimal Strategy . . . . . . . . . . . . . . . . . . . . . . . . 20

5.5.1 Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.5.2 Optimization Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.5.3 Result: A Detailed Plan for Six Regions . . . . . . . . . . . . . . . . . . . . . . . 21

6 Evaluation of Implications 22

6.1 Economies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6.2 Physical Health and Living Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

6.3 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

7 Strengths and Weaknesses 24

8 Future Works 25

9 A Position Paper of 2025 Water Strategy 25

Appendices 28




1 Introduction

“Congratulations! China, we both reach the top 5 richest countries in fresh water resource!” saidAmerica, after a recent world water conference. “Thank you,” answered China, “but... I am stillworrying...” “Why? You have so many lakes and rivers, the supply should be quite enough!” “Well,that’s the truth,” answered China again, “but meanwhile, we are so crowded, and the irregular waterdistribution results in many troubles.”

Figure 1: China’s worry of water resource

As the conversation above between China and United States, water management is both a challengeand an opportunity for every country in the world. An undeniable trend is that growing populationand productivity call for growing demand of fresh water, and thus push more pressure on the watersupply and protection. As the biggest developing country, China is faced with water managementproblem in the next period and is planning for an effective strategy to meet the water needs of 2025.

Natural Condition

The nartural condition of China can be concluded as topography and climate[1]. The topographydescends in elevation from the west to the east, and the complex types of climate can be summarized

as “the southeastern wet, the northwestern dry”, as shown in Figure 2.




(a) Topography (b) Precipitation: “the southeastern wet, the north-western dry” (Spatial Climate Analysis Service, Ore-

gon State University, 2001)

Figure 2: Topography and precipitation of China

Water resource in China

Although the total amount is large, the water resource per Capita in China is only a quarter of theworld average level (ranking 110 among all countries). At the end of 20th century, 2/3 of the 600cities in China suffered from water shortage [2]. Except the large Chinese population, the two mainproblem is the uneven distribution in space and pollution. Almost 80 percent of the total resourcesare in the South of China [3]. In addition, the inconsistency between water resource and productivitydoes inhibit the development of economy. With more than 60% of farmland and 46% of popula-tion, the six Northern river basins contribute 44% of the national GDP, but have merely 20% of the

country’s water resource [1].

Therefore, to control the population and find a balance of water distribution should be the guide of water strategy. As a pratical reaction, China launched the South-to-North Water Transfer Project in2002, including East, Middle and West routes, to alleviate the water shortage in the north [4]. By themid-21th century, the project will reach a transfer capacity of 44.8 billion m3, bringing great help insocial and ecnomic development of the nation.

Now we are faced with the following task:

Propose a 2013 water strategy for the country, te meet the water needs of 2025. Considering storageand movement, desalinization, conservation and other aspects, we need to build a mathematical

model and make up a plan for the next 12 year’s project.

Our approach is:

1. Use a system model to analyze the change of water resource for a certain region.

2. Divide China into six regions to plan for a strategy in a macroscopic perspective.




3. Define Richness Index (considering water resource, population and GDP) as the criterion of water richness.

4. Build a basic model (under the current water policy) to predict the water shortage of eachregion in 2025.

5. To fill the shortage, we build an advanced model to analyze four main aspects: transfer andstorage, desalinization, pollution control and agricultural utilization.

6. Combine the four aspects together to build a comprehensive optimization model, then solve itto find an optimal strategy for the six regions.

7. Summarize and discuss the result of the comprehensive model.

8. Discuss the implications of our water strategy on 1) economy, 2) health and living condition, 3)environment.

9. Draw a conclusion of the strengths and weaknesses of our model, and discuss the improvementfor future works.

2 Criterion of Success

• Meet the standard water demand. A basic requirment is to fit the water needs of 2025under current degree of water usage, then we just need to predict the need of 2025 with 2013and the former data. However, a fact is that China is a water-shortage country in the world,and the country has been “hydropenia” for a long time. So besides the basic need (of currentdegree), we also consider how to promote the total level of water usage, which may reflect the“demand from the heart”. We set the standard water demand (usually higher than the current

level) and use our strategy to struggle for it.• Minimize the overall cost of the strategy. Among the methods of the water project

such as transfer, desalinization of sea water and pollution controlling, the expenditure is animportant concern. A economic plan can not only save money for the government and improveefficiency, but also help to prevent unexpected cases (such as interrupt of project due to fundingshortage).

• Enough water reserves under emergencies. To plan ahead for the possibile emergen-cies (natural disasters, project accidents) is necessary. If the supply from outer area is blocked,the local water reserves should at least provide the domestic water for a period (such as oneweek) to wait for the rescue. As the saying goes, “get ready for rainy days”.

• An even and reasonable water distribution. To solve the problem of water distribu-

tion in China is a major concern, and “reasonable” means our strategy should consider popu-lation and productivity of a region, since they reflect the demand of water.




3 Analysis and Preparations

3.1 System Model: Input and Output

For a certain region, we introduce a system model to describe the character of water resource. Theinput and output are analogies of the increase and decrease of water respectively, as follow in Fig-ure3.

Figure 3: The system model of water resource

With the system model above, we can divide all factors into two parts: input (cause increase) andoutput (cause decrease). So the behavior or change of water resource is clearly monitored. Supposea system with zero initial condition (no water at the beginning), the remaining water resource can bedescribed as: Input − Output, which may roughly be the supply minus demand. Usually, we hopeto have enough water and avoid shortage, namely:

Input− Output 0

Moreover, as for the “stability” of the system, we should consider how strong or robust the systemis under emergencies. For a water system of a certain region, whether it is stable depends on how

much water it reserves. For example, during an earthquake, a region might be isolated and the outersupply of water is blocked, the water reserves should be enough at least for domestic use for a periodof time. We define this extra water as Emergency water , denoted asε. So the expression above should

be changed as:

Input− Output ε,

Input−Output− ε 0 (3.1)

For ε, here we plan for a 7-day (a week) water reserves of domestic use (Ddaily is the daily domesticdemand of a region):

ε = 7 ·Ddaily (3.2)




3.2 Define Regions

For simplification and a more macroscopic strategy, we hope to divide the area of China into severalregions. According to the national standard of water quality in 2002, the area is divided into sixregions based on economic level, climate and precipitation [5]. The definition of six regions areshown in Table 1.

Table 1: Six regions of Chinain the analysis of water strategy

Region Name Provinces included1 Northeast Heilongjiang, Jilin, Liaoning, Inner Mongolia2 North China Beijing, Tianjin, Hebei, Shandong, Henan, Shanxi, Shaanxi, Ningxia, Gansu

3 Central China Hubei, Hunan, Jiangxi, Anhui, Jiangsu, Shanghai, Zhejiang, Fujian

4 South Guangdong, Guangxi, Hainan5 Southwest Chongqing, Sichuan, Guizhou, Yunnan6 Tibet and Sinkiang Sinkiang, Tibet, Qinghai

In the later of this paper, our strategy is mainly designed for the six regions, considering each regiona “sub-system” of the whole country. In other words, we focus our strategy on:

1. how to meet the water need of each region;

2. how the regions complement each other.

3.3 Criterion of Richness

In order to measure the richness of water for a certain region, we need to consider what factors are

related to water consumption. Here we maily use population and GDP to measure it. More people

means more water use, and GDP represents the productivity and economic development, which call

for a great water demand. We define Richness Index R to describe the richness:

R =water

population ·GDP (3.3)

where “water” stands for the actual water supply, or “input”, of a certain region. R represents theshare of per unit of population and GDP, and the higher R indicates the richer of water supply.

For year 2011, we begin to calculate R of each province of China:

The water supply, population and GDP of each province are as follow (population and GDP data

are from the website of National Bureau of Statistics of China [6], and water from the website of The Ministry of Water Resources of the People’s Republic of China [7]):

For Region 1, we have:

R =7.029×1010

134.48×952,410 = 548.80 m3/ (million people · million dollars)




Table 2: Water supply, population and GDP of six regions (2011)

Region 1 2 3 4 5 6

water supply (m3) 7.029× 1010 1.102× 1011 2.339× 1011 8.768× 1010 4.539× 1010 6.316× 1010

population (million) 134.48 401.79 422.39 160.27 190.69 30.8GDP (million dollar) 952,410 2,483,276 2,940,963 1,074,566 730,537 139,956

Table 3: Richness Index R of six regions (2011)

Region 1 2 3 4 5 6R 548.80 110.50 188.29 509.11 325.83 14,652.10

Unit: m3/ (million people · million dollars)

In the same way, we calculate R of the other 5 regions (see in Table 3).

The result is shown as a color map in Figure 4:

Figure 4: Richness of water in 2011 (represented by Richness Index )

Standard Richness Index

As we discuss above,R is a metric of richness, and it represents the level of water resources. So toimprove the water condition is equivalent to enhance the value of R, then a standard value of R isneeded. At first, we have tried to find the data of a developed country with sufficient water resources.However, after calculation we find it was not a practical idea for this 12-year plan to achieve.

Noting in Table 3 that R values of Region 2 and Region 3 (North and Central China) are significantlyless than the other 4 regions, which may be explained by the large population (61.49% of the nation)




and strong productivity (65.18% of the national GDP). To solve the main problem, we hope to set astandard value of R higher than 110.50 (Region 2) and 188.29 (Region 3), then propose an effectivestrategy till 2025 to fulfill this goal. Namely, here we define Standard Richness Index:

Rstand = 200 m3/ (million people · million dollars),

to be the guide of water strategy of 2025.

By multiplying the population and GDP in 2025, we can get the “standard water demand”. This will be discussed later in Chapter 4.4 .

4 Basic Model: Under the Current Policy

4.1 Approach

To propose a new strategy for 2025 water needs, we should first discuss what may happen if China

maintain the current water policy. However, the exsisting policies and projects are too difficult to

analyze, thus we make an assumption that under current water policy, the water supply will change

according to the previous pattern. In other words, we can predict the water supply of each region

from 2013 to 2025 by fitting the corresponding history data of population and GDP. The procedure is

concluded in Figure 5 below. Since this supply does not conclude our strategy (discussed in the next

Chapter), we define it as original supply, denoted as S origin.

Figure 5: Procedure to get the water supply of 2025 under current policy

As for the demand, we use the Standard Richness Index Rstand to calculate the standard water demand(Dstand) based on the formula below:




Dstand = Rstand · population ·GDP (4.1)

Therefore, the system should only consist of an input S origin and an output Dstand, as described below:

Figure 6: Water system of basic model

4.2 Assumption

During the period from 2013 to 2025 in China, we assume:

• The water policies and major projects (such as the South-to-North Water Transfer Project) re-main unchanged.

• Under current water policy, the water supply will change according to the previous pattern.

• No abnormal change in climate geographical condition.

4.3 Original Water Supply S origin

4.3.1 Correlation of Water, Population and GDP

To take Region 1 (Northeast) as an example, the data of water (original supply S origin), populationand GDP from 1997 to 2011 are listed in Table 4:

Table 4: Water supply, population and GDP of Region 1 (1997 to 2011)

Year 1997 1998 1999 2000 2001 2002 2003

S origin(×106m3) 61,949 62,400 62,000 60,800 59,600 55,600 54,800population (million) 128.43 129.19 129.83 130.31 130.73 130.94 131.09GDP (billion dollar) 140.36 151.99 160.70 178.97 195.48 213.92 241.69

2004 2005 2006 2007 2008 2009 2010 2011

55,860 56,940 60,020 60,500 61,370 64,380 66,550 70,290131.27 131.43 132.14 132.57 132.88 133.07 134.27 134.48286.40 335.12 393.66 454.99 577.43 661.46 784.94 952.41

We make two scatterplots for the two pair of variables, and make linear regressions of them as follow:

To combine the two linear model together, we have:




(a) Population and water (S origin) (b) GDP and water (S origin)

Figure 7: Scatterplot and linear regression

S origin = β 0 + β 1 · population + β 2 ·GDP (4.2)

where β 0 = 5.31 × 1011,β 1 = −3673.78,β 0 = 0.0352;

S origin: m3, population: per person, GDP : dollor.

4.3.2 Predicting Population and GDP from 2013 to 2025

Population:

We use the data of Region 1 (1997 to 2011) to build a Logistic model of population:

population =pmax

1+( pmax/p0−1)e−r(t−1997)

where t is the year and p0 = 128.43 is the population of year 1997. The fitted curve is shown in Figure8:




Figure 8: Logistic model of population

Thus we get the formula:

population =146.02

1+(146.02/128.43−1)e−0.0312(t−1997)

So in 2025, the population of Region 1 should be:

146.021+(146.02/128.43−1)e−0.0312(2025−1997) = 138.12 million.

GDP:

We perform a linear regression to predict the GDP of Region 1:

Figure 9: Linear regression of GDP




Table 5: S origin in 2025

Region 1 2 3 4 5 6

S origin (billion m3) 76.71 106.11 267.80 94.75 52.39 69.77

The fitting result is:

GDP = p1 · year + p2

where p1 = 5.29 × 1010, p2 = −1.056 × 1014, and R2 = 0.8657.

So the GDP in 2025 is: p1 · 2025 + p2 = 1522.5 billion dollar.

4.3.3 Get S origin

Substituting eq. (4.2) with population = 138.12 million and GDP = 1522.5 billion, we have theoriginal water supply of Region 1 in 2025:

S origin = β 0 + β 1 · 138.12 × 106 + β 2 · 1522.5 × 109 = 76.71 billion m3

Similarly, we can get the original water supply S origin of the other five regions in 2025:

4.4 Standard Demand Dstand

According to eq. (4.1), we calculate the standard water demand Dstand of six regions in 2025.

Table 6: Dstand of six regions in 2025

Region 1 2 3 4 5 6Dstand (billion m3) 42.0590 344.9813 414.2402 71.5225 44.0218 1.4957

4.5 Shortage and Conclusions

Now we need to determine whether the water resource in 2025 is enough of each region, then de-termine the shortage. In the discussion Chapter 3.1 we concluded eq. (3.1) and eq. (3.2) to meet thewater needs and “stability”: Input − Output − ε 0. In this basic model, the Input and Outputare S origin and Dstand respectively; ε,the Emergency water, should be the 7-day reserves of domestic

water use:

S origin −Dstnad − ε 0 (4.3)




Calculation of ε.

According to The standard of water quantity for city’s residentialuse [5], the standard of daily domestic

water consumption of each region is listed below in Table , and we calculate the daily consumptionof each region thus get eachε:

Table 7: Domestic water consumption per day and ε

Region 1 2 3 4 5 6daily domestic water per person (L) 80 85 120 150 100 75

daily domestic water of the region (million m3) 11.05 36.36 53.08 29.90 19.60 2.60ε (7-day of the region, million m3) 77.35 254.51 371.55 209.33 137.21 18.21

To combine the data of S origin, Dstand and ε in Table 5, 6 and 7, we get the difference of them basedon eq.(4.3), which reflect the shortage of each region:

Table 8: S origin −Dstnad − ε of six regions in 2025

Region 1 2 3 4 5 6S origin −Dstnad − ε (billion m3) 34.5736 -239.126 -146.812 23.018 8.231 68.256

Conclusion:

• In Table 8 we find that in Region 2 and Region 3, the value of S origin − Dstnad − ε < 0, whichrepresents a water shortage in 2025 under current policies. In other words, if the governmentdo not make any change in water policy, by 2025 the two major regions (North and Central)would suffer from critical shortage of water.

• Therefore, our strategy is going to alleviate the shortage problem in Region 2 and Region 3.

From a nationwide perspective, one alternative method is to transfer water from other regions.

5 Advanced Model: Our Water Strategy

In the model of water strategy, we mainly discuss four aspects: transfer and storage, desalinization,pollution, and agricultural utilization.

Table 9: A conclusion of factors (inputs and outpus) of water

Factor (Inputs / Outputs) Change in water Cost

Original supply S origin +

Standard demand Dstand -Transfer (in/out) + / - +

Desalinization + +Pollution control + +

Agricultural utilization + +




Approach:

1. Analyze the four aspects respectively to get a guidance of the strategy;

2. Combine them into a global decision model and find an optimal solution to fill the shortagewhile minimizing the cost.

Basic Assumptions:

• Migration among the six regions can be ignored compared with the population growth respec-tively.

• The economic development in China would appear a steady growth, without significant fluc-tuation.

• During the period from 2013 to 2025, no serious disaster happens (such as earthquake, floodand pestilence). No war happens.

• Climate (precipitation) is stable, and topography would not change.

• The price level in China would not change greatly during the period.

5.1 Transfer and Storage

5.1.1 Assumption

1. In the cost of reservoirs (storage), we mainly consider the construction cost, while the operatingcost is much lower so we ignore it.

2. The transfer cost only depends on the volume of water being transferred, but not related to thedistance.

3. Only a “sufficient” region (except Region 2 and 3) can transfer its water to other regions.

4. All transfer-in water become storage in resrvoirs, which means we should construct at leastenough reservoirs to store the transfer-in water.

5.1.2 Notation

T i (m3) : the transfer-in water supplement of Region i (i = 1, 2,..., 6).

To fill the shortage of Region 2 and 3 by transferring water from other regions, we have:

T 2,3 > 0, T 1,4,5,6 < 0.

N i : the number of large-scale reservoirs needed for storage ( i = 2, 3).

A large-scale reservoir can store more than 100 million m3 of water [8] and the storage cost percubic metre is cheaper than a small-scale one. So our priority is the large-scale, thus we have:

N i = floor(T i/(100 × 106))

where floor (·) means rounding down to the nearest integer.

CT i (dollar) : the cost of transfer and storage for Region i (i = 2, 3).




5.1.3 Determine the Cost

Transfer cost: The average cost of water transfer is 0.4 dollar per cubic metre[9].

Storage cost: For a large-scale reservoir (capacity >100 million), the cost is 1.87 dollar per cubicmetre; for a small-scale one (capacity <100 million) it is 4 dollar per cubic metre [8].

Hence, for Region i in need of transfer-in water, the total cost of transfer and storage can be describeas the following formula:

Cost = 0.4 × waterin + 1.87 ×Numberlarge + 4 ×Numbersmall

Since the large-scale is our priority (cheaper), we have the total cost CT i (i = 2, 3):

CT i = 0.4 · T i + 1.87 ·N i · 100 × 106 + 4 · (T i −N i · 100 × 106) (5.1)

5.2 Desalinization

Desalinization is a flourishing industry in fresh water supply. As a country with water shortage,China has been developping relevant techniques for decades. More projects are launched in recentyears, which is both a trend and a response to China’s water policy [10]. Different from the otherthree factors, for desalinization, we assume that supports from the government is consistent withthe current trend. In the following years from 2013 to 2025, the production of water by desalinizationwill keep on growing, and we assume it fits a Logistic growth. So our task is:

• To predict the production of water by desalinization in 2025;• Then to calculate the corresponding financial cost that the government need to pay for.

5.2.1 Assumption

1. Supports to desalinization from the government is consistent with the current trend.

2. The production of water (by desalinization) fits a Logistic growth.

5.2.2 Production and Cost in 2025 by Desalinization

Production

The production by desalinization from 2000 to 2011 in China are as below[10]:

Table 10: Production by desalinization in China

Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011Production 10 19 20 30 35 70 150 150 162 270 520 575

(thousand m3 per day)




Production =2707.28

1+(2707.28/10−1)·e−0.395(year−2000)

Figure 10: Logistic fitting of production by desalinization

We use a Logistic model to fit the data above, and the results are as below:

Thus, in 2025 the production by desalinization is:

2645.97 (thousand m3 per day).

Distribution of Production

According to the research by Guoling Ruan from State Oceanic Administration, all ongoing projectsof desalinization locate in the Southeast Coast of China. Compared with the six regions we found84.7 percent of them belong to North China (Region 2) and 15.3 percent belong to Central China(Region 3) [11].

Therefore, for Region 2, the total water provided by desalinization in 2025 should be:

D2 = 2645.97 × 103 × 365 × 84.7% = 818 million (m3)

Similarly, for Region 3 we have:

D3 = 2645.97 × 103

× 365 × 15.3% = 147.7 million (m3

)

Cost

The unit cost of desalinization reduces by 4% yearly, and the current cost (2013) is 0.8 dollar/m3 [10],so we have:

Unit cost in 2025 DE = 0.8 × (1 − 4%)12 = 0.49 dollar/m3




For Region 2, the total cost on desalinization in 2025 is:

CD2 = D2 · 0.49 = 400 million dollar,

For Region 3,

CD3 = D3 · 0.49 = 72.4 million dollar.

5.3 Pollution Control

5.3.1 Assumption

1. The technology in pollution treatment is at the same level over the country.

2. We only consider industrial and domestic pollution of water.

3. Controlling polluted water is equivalent to fresh water production in the same volume.4. Among the total water consumption, 30 percent is of industrial and domestic use (70 percent

of agriculture) [12].

5.3.2 Cost and Volume

The construction cost of a wastewater plant is 145 million dollar; and the treating capacity is 183million m3 per year [13].

For Region i, the volume of polluted water being treated is S i m3, so the cost CS i should be:

,

CS i = 1.45 · ceil

S i1.83

(dollar) (5.2)

where ceil (·) means rounding down to the nearest integer. Noting that S i should be less than thetotal industrial and domestic pollution of water.

5.4 Agricultural Utilization

5.4.1 Assumption

1. Agriculture consume 70 percent of the total water consumption for each region[12].

2. The irrigation land accounts for 50% of total agricultural land [14].

3. Based on the standard of Israel in agricultural water conservation, we hope that by 2025, at best60% of irrigation land in China can reach the standard (by changing the modes of irrigation).

4. No significant change in the total area of agricultural land.

5. For simplicity, we assume all irrigation land in China use flooding irrigation as the onlymethod.




5.4.2 Notation

W 0i water consumption under current irrigation mode in Region ia% (0<a60) percentage of irrigation land under improved mode (of Israel) in Region i

△W i water saving after improving the irrigation mode in Region i

5.4.3 Water Saving by Improving Irrigation Mode

In general, the four types of irrigation methods are: trickling, micro-irrigation, moving irrigationand flooding irrigation. The irrigation mode (proportion of each method) of Israel is as follow [15]:

Table 11: Irrigatnion mode of Israel

Method trickling micro-irrigation moving irrigation flooding irrigation

Proportion 80 % 10 % 5 % 5 %Efficiency in water use 95 % 95 % 90 % 50 %

For Region i, suppose a % of the irrigation land follows the mode above of Israel, we can calculatethe water saving:

△W i = W 0i−[W 0i ·

(80%

95%+ 10%

95%+ 5%

90%+ 5%

50%

)· 50% · a% + W 0i · (1 − a%)

]

= 0.449 ·W 0i · a%(m3) (5.3)

5.4.4 Calculation of Cost

The expenditure of micro-irrigation and moving irrigation are as below [16]:

micro-irrigation moving irrigation0.2489 dollar/m3 0.1397 dollar/m3

Area of agricultural land ( Area of Cultivated Land at Year-end by Region, 2008 [17]):

Table 12: Agricultural land of six regions (×109 m3)

Region 1 2 3 4 5 6Aagriculture 2859.27 3630.38 2526.96 777.57 1874.07 502.89

So the cost of improving irrigation mode (by a %) should be:




CW i = Aagriculture · 109 · 50% · a% · (90% × 0.2489 + 5% × 0.1397)

=0.257 ·Aagriculture · 109 · △W i

W 0i

(5.4)

Meanwhile, △W i should be less than the best condition (when a% = 60%), namely:

△W i W 0i · 60% · 0.449 .

5.5 Comprehensive Model: An Optimal Strategy

5.5.1 Assumption

1. We only consider transfer between two ajacent regions.

2. Only the “sufficient” regions can transfer water to the others. Although Region 2 and 3 areajacent, they cannot transfer water to each other (because of the shortage).

For each region, we define SD = |S origin − Dstnad − ε| as the shortage in 2025 according to Table 8,namely:

SD1 SD2 SD3 SD4 SD5 SD6

34.5736 239.126 146.812 23.018 8.231 68.256

• For sufficient regions, Region 1, 4, 5, 6 can transfer water to other regions;

• Region 2 can accept water from Region 1 and 6, Region 3 can accept water from Region 4 and5.

5.5.2 Optimization Model

After analysis, we conclude the model as follow:




We solve the model using Genetic Algorithm in MATLAB, and the result is concluded in the nextsection.

5.5.3 Result: A Detailed Plan for Six Regions

We summarize our result in the following Table 13.

Table 13: A detailed plan for 2025

Region 1 2 3 4 5 6Transfer-in (million m3) 180527.88 110208.44

Desalinization (million m3) 818 147.7Wastewater plant constructed 126 172 132 156 86 115

Wastewater treated (million m3) 23012.94 31429.48 23986.87 28423.99 15716.92 20931.00

Saving in agriculture (million m3) 14461.98 20008.74 23984.02 17867.72 5434.79 13156.85

a % 59.58 % 60.00 % 28.49 % 60.00 % 33.01 % 60.00 %

Transfer-in: For Region 2, 78737.56 million m3 from Region1 and 101790.31 million m3 from Region6;

For Region 3, 33504.23 million m3 from Region 5 and 76704.20 million m3 from Region 4.




Table 14: Total cost of the strategy for 2025 (billion dollar)

Transfer and Storage Desalinization (of 2025) Pollution control Agriculture Total Cost

981.16 billion 427.4 million 83.81 billion 978.73 billion 2044.16 billion

We plot two color maps of the Richness Index (six regions) in 2025: the first under the current waterpolicy, and the second under the new water strategy.

(a) under current policy (b) Under the new water strategy

Region 1 2 3 4 5 6R (under new strategy) 200 188 200 203 201 200

standard deviation: 5.3541

Figure 11: Richness of water in 2025

Conclusion:

From Figure 11 we can see the improvement that Richness Index R distribute more evenly, withhigher values in Region 2 and 3 than before. The total cost of the strategy is about 2044.16 billiondollar.

6 Evaluation of Implications

6.1 Economies

Total Cost and GDP

From the previous analysis we can figure out the total GDP from 2013 to 2025 of China is about162684.63 billion dollar. The total cost of our water stategy is 2044.16 billion dollar, which is 1.26 %of the total GDP of this period. Meanwhile, the cost of water construction is 0.66 % of the total GDP,which is a bit lower than the best value of 0.79%~0.84% [18]. Therefore, the government can spendmore money on the practical plan.




Economic Growth and Domestic Demand

The South-to-North Water Transfer Project in China has invested 74.12 billion dollar (price of 2000)in recent years, raising the growth rate of GDP by 0.12 % yearly [19]. The investment of the waterstrategy proposed in this paper is more than 10 times, and we are eager to see its stimulation on theeconomy of China.

Empirical analysis shows that 40 % of investment will turn into consumption, which means thisstrategy may probably stimulate about 817.66 billion dollar of the domestic demand.

Employment

The water strategy can provide people with more oppotunities of employment in the projects of construction, which helps to improve the condition of employment in the country.

6.2 Physical Health and Living Conditions

Transfer Project, Moving House?

In the water transfer project, the construction of reservoirs usually compel the local people to leavetheir hometown. Because of the South-to-North Water Transfer Project, more than 0.44 million peoplehave been forced to move [20], and our water strategy will also cause this problem (or even worse).

But transfer is a major and effective way to alleviate the shortage of water, and it would keep onworking for people in need. The government should consider the arrangement for those have tomove away.

More Drinkable Water by Desalinization

Water produced by seawater desalinization can be drank directly, which alleviate the crisis of drink-able water in coastal regions. According to our prediction, in 2025 the desalinization will provide2645.97 thousand m3 of water per day in China, supplying water for 33,000 people.

Better Irrigation, More Income

With the strategy to improve the irrigation mode, the water consumption in agriculture will re-duce significantly, which saves money for the farmers. The result indicates the total saving wateris 94914.08 million m3, which saves about 9151.7 million dollar (12.3 dollar for each farmer).

Pollution Control Brings Healthy Life

Currently, China is faced with severe pollution of water: 78 % of the city reaches and 50 % of groundwater is polluted [21]. Through the optimal water strategy, more wastewater plants will providemore clean water, which is good for our health.




6.3 Environment

According to our water strategy, in 2025 the proportion of water use should be (each region re-spectively): 31.3%, 72.3%, 22.8%, 19.2%, 9.1% and 15.4%. Five of them are lower than 40%, whichindicates that these regions do not have excessive usage and this would help in environmental pro-tection. However, Region 2 (North China) reaches a risky value of 72.3% and it may cause destructionof ecosystem. So we need to pay attention to this in future improvement of the strategy.

As for the utilization rate in agriculture, the average value of six regions will reach 50.25% in 2025,which is close to our expectation (60%).

7 Strengths and Weaknesses

Strenghs:

1. We use a system model to analyze the change of water resources, which helps to better under-stand the relevant factors.

2. We consider the emergency water use and provide enough water reserves in the plan. This isimportant when dealing with unusual events.

3. In our strategy, the four aspects (transfer and storage, desalinization, pollution control and agri-culture use) are carefully discussed; a comprehensive optimization model is built to combinethem together, and we solve it to find the best strategy.

4. Our methods can be generalized to analyze the inner provinces of each region.

Weaknesses

1. We did not consider the influence of topography and river trends in water transfer. For sim-plicity, we did not take construction expenses (such as transport channels) into account.

2. Each of the six regions is relatively large, and the macroscopic analysis does not include de-tailed plan inside a region.

3. We ignore the variance of exchange rate and price, meanwhile assuming GDP to grow steadily.Actually, these factors may have great impact on the calculation of cost.

4. The data we used should be more adequate. Some statistical work of 2012 has not yet beenfinished.

5. Our strategy lacks public advertisements of saving water.




8 Future Works

• A more detailed water strategy is needed for inner provinces of each region (such as the trans-fer among provinces).

• The river orientation should be analyzed in water transfer project. The orientation of transfershould accordant with that of the river.

• Consideration of the possible variance of price from 2013 to 2025 can enhance robustness of the model.

• Climate changes should be an important concern, especially the influence of precipitation.

• Advertising work of water conservation should be concerned.

9 A Position Paper of 2025 Water Strategy

Dear Sir,

We are honored to write to you with our key findings in “the 2025 China water strategy”, a recentstudy of us. A fact is that growing population and the trend of economic development are callingfor challenges in water management and conservation of our country. As a water-shortage nation,China has been struggling for the improvement of water condition for decades. In recent years, ourgovernment has achieved in alleviating the shortage in some provinces, but the shortage still existsthrough the country.

As the saying goes, “get ready for rainy days”. At the begining of a new year 2013, we are planningfor an effective water strategy. Now we will present the core of our strategy in four parts.

Water condition under current policy

For comparison, we first tried to figure out what may happen if we maintain the current water policytill 2025. After analysis and proper assumptions, we find that in 2025 two of the six regions in China(North China and Central China) will suffer from water shortage. This confirms us that a new,effective water strategy is needed.

Water transfer plan

Region 2 (North China) and Region 3 (Central China) are in great need of transfer-in water. Accord-

ing to our calculation, an optimal plan in 2025 is:

• Region 2 transfer-in: 180527.88 million m3. 78737.56 million from Northeast region, and 101790.31million from Tibet and Sinkiang.

• Region 3 transfer-in: 110208.44 million m3. 33504.23 million from Southwest region, and 76704.20million from South region.




Desalinization plan

As for seawater desalinization, we recommand that the government should keep on supporting theprojects on desalinization as recent years. In other words, we need to increase the production bydesalinization yearly. In the result of our model, the water production by desalinization in 2025should be: 818 million m3 in North China region, and 147.7 million m3 in Central China region.

Pollution and agriculture

Pollution is a severe problem of the water condition in China. According to our calculation, weshould build 787 wastewater plant nationwide by 2025 to control the pollution.

Agricultural consumption is the main demand of water (70% of the total consumption), so it is essen-tial to do something in saving agricultural water. The key point is to improve irrigation utilizationrate of water. Our suggestion is: to take the irrigation mode of Israel as the standard, and gradually

change the irrigating mode from flooding to micro-irrigation and moving irrigation. Great effect will be seen if we keep on this strategy.

In total, the cost of this water strategy is 2044.16 billion dollars, which is about 1.26% of the total GDPfrom 2013 to 2025 of China. The result implies a good prospect of the strategy.

We hope our findings to be helpful to you. Best wishes for the water strategy of China!




References

[1] Li Yuanyuan, Water Development and Management Strategy of China,http://unpan1.un.org/intradoc/groups/public/documents/APCITY/UNPAN026604.pdf

[2] Water Resource of China, http://www.china.com.cn/node_7064072/content_19634796.htm

[3] Water resources of the People’s Republic of China,http://en.wikipedia.org/wiki/Water_resources_of_the_People’s_Republic_of_China#cite_note-FAO-1

[4] Quanfa Zhang, The South-to-North Water Transfer Project of China: Environmental Implica-tions and Monitoring Stategy, Journal of The American Water Resources Accociation, Vol. 45,No. 5, October 2009.

[5] Ministry of Construction of the People’s Republic of China, The standard of water quantity for

citys residential use, GB/T 50331-2002, http://scl.yljy.cn/index.php/iss/files/download/949[6] National Bureau of Statistics of China, http://www.stats.gov.cn/

[7] The Ministry of Water Resources of the People’s Republic of China, http://www.mwr.gov.cn/

[8] Liping Pan, Lulong Zhang, Another Large-Scale Reservoir in Shaoxing, Shaoxing Daily, March1st, 2009, http://epaper.shaoxing.com.cn/sxrb/html/2009-03/01/content_220015.htm

[9] South-to-North Water Transfer, http://baike.baidu.com/view/26518.htm

[10] Wang Sheng-hui, Zhao He-li, Development Environment and Market Prospect for the SeawaterDesalinization Industry in China, MARINE ECONOMY, Vol.2 No.3, Page 18, Jun. 2012.

[11] Guoling Ruan, The Technique and Industry of Seawater Desalinization in China,

http://wenku.baidu.com/view/8c2d3a8102d276a200292e1b.html

[12] http://www.jsgg.com.cn/Index/Display.asp?NewsID=10293

[13] http://wenku.baidu.com/view/10db2e4ef7ec4afe04a1df27.html

[14] http://www.aquasmart.cn/news/irrigation/scdt/37165_2.html

[15] Analysis of South-to-North Water Transfer Project,http://wenku.baidu.com/view/89dfbbd3240c844769eaeebe.html

[16] Micro-Irrigation Techniques, http://58.30.20.123/jpkc/ysm/doc/jc/wgjis.htm

[17] Area of Cultivated Land at Year-end by Region (2008),http://www.stats.gov.cn/tjsj/ndsj/2011/html/M1303c.xls

[18] http://money.163.com/10/1207/09/6N9T0DFE00251M00.html

[19] http://www.dss.gov.cn/Article_Print.asp?ArticleID=87786

[20] http://news.xinhuanet.com/fortune/2009-12/09/content_12618463.htm

[21] http://wenku.baidu.com/view/178271738e9951e79b8927f3




Appendices

( MATLAB Script)

1. Draw the map of China

1 global h;

2 plot(province.long,province.lat,’color’,[0 0 0]);

3 hold on;

4 plot(border.long,border.lat,’color’,[0 0 0],’linewidth’,1.5);

5 h=plot(NaN,NaN,’b-’,’linewidth’,1);

6 plot([city(2:end).long],[city(2:end).lat],’o’,’markersize’,3,...

7 ’markeredgecolor’,’b’,’markerfacecolor’,’g’);

8 plot(city(1).long,city(1).lat,’p’,’markersize’,5,...

9 ’markeredgecolor’,’r’,’markerfacecolor’,’g’);

10 axis([70 140 15 55]);

2. Logistic model

1 function f=logisticmodel(a,t)

2 f=a(1)./(1+(a(1)/128.43-1)*exp(-(t-1997)*a(2)));

3. Predict the population

1 x=1997:2011;

2 y=[12843 12919 12983 13031 13073 13094 13109 13127 13143

13214 13257 13288 13307 13427 13448];

3 y=y*10000;

4 y=y./1000000;

5 plot(x,y,’*r’);

6 a0=[800,0.001];

7 a=lsqcurvefit(’logisticmodel’,a0,x,y);

8 xi=1997:2025;

9 yi=logisticmodel(a,xi);

10 hold on

11 plot(xi,yi,’-b’)

12 a

13 legend(’history population’,’fitting population’)

14 hold off

4. Predict the original water supply S origin




1 pre_population=[138.1248643 427.7512343 442.3280157 199.3658669 196.0446796

34.6904843];

2 pre_population=pre_population.*1000000;3 pre_GDP=[1522500000000.00 4032500000000.00 4682500000000.00

1793750000000.00 1122750000000.00 215575000000.00 ];

4 pre_water=zeros(1,6);

5 one_water=[619.49 624 620 608 596 556 548 558.6 569.4 600.2 605 613.7

643.8 665.5 702.9]’;

6 one_water=one_water*100000000;

7 two_water=[1163.39 1102.5 1130 1110.5 1091 1095 967.5 920.3

1032.6 1083.1 1043.4 1061.3 1075.7 1080.2 1102.5]’;

8 two_water=two_water*100000000;

9 three_water=[2065.12 1946.5 2007 2027 2047 1988 1950.5 1993.6

2114.2 2180.3 2216.8 2257.1 2290.4 2302.7 2339]’;

10 three_water=three_water*100000000;

11 four_water=[834.09 837 840 839.5 839 851 840 862.3 873.6 878.9 879.9

881.2 876.8 883.5 876.8]’;12 four_water=four_water*100000000;

13 five_water=[376.83 390 410 411.5 413 422 411 413.2 426.7 430 338 455.4

442.5 450.5 453.9]’;

14 five_water=five_water*100000000;

15 six_water=[506.2 536 584 583.5 583 575 603 599.7 616.6 622 626.9

641.3 636.2 639.5 631.6]’;

16 six_water=six_water*100000000;

17 one_population=[12843 12919 12983 13031 13073 13094 13109 13127

13143 13214 13257 13288 13307 13427 13448]’;

18 one_population=one_population*10000;

19 two_population=[36481 36750 37008 37488 37751 37993 38215 38470

38325 38575 38786 39125 39433 39950 40179]’;

20 two_population=two_population*10000;

21 three_population=[38937 39185 39416 39854 40107 40296 40614 4086540153 40387 40664 40915 41142 42028 42239]’;

22 three_population=three_population*10000;

23 four_population=[12427 12571 12745 13918 13367 13484 13622 14011

14682 14859 15062 15214 15358 15920 16027]’;

24 four_population=four_population*10000;

25 five_population=[19172 19355 19527 19232 19823 19950 20076 20166

19190 19217 19219 19313 19413 19010 19069]’;

26 five_population=five_population*10000;

27 six_population=[2462 2502 2540 2705 2662 2701 2738 2776

2830 2879 2931 2972 3006 3049 3080]’;

28 six_population=six_population*10000;

29 one_GDP=[8739.95 9464.64 10006.86 11144.26 12172.35 13320.81

15050.16 17833.86 20867.62 24513.17 28332 35956.6 41189 48878

59306.57]’;30 one_GDP=one_GDP*100000000./6.2270;

31 two_GDP=[21531.98 23202.35 24599.77 27440.84 30337.08 33651.4

39080.41 48284.07 59692.21 69937.17 80374 100324.4 109452.49

130338 154633.59]’;

32 two_GDP=two_GDP*100000000./6.2270;




33 three_GDP=[28507.52 30778.87 32704.22 36099.8 39575.67 43854.67

49977.18 59991.23 68931.92 80737.88 91515 114889.27 126859.04

152434 183133.75]’;

34 three_GDP=three_GDP*100000000./6.2270;

35 four_GDP=[9740.57 10261.08 10888.81 12230.85 13424.86 14829.22

16881.44 20150.22 26668.18 31823.42 36370 44333.58

48903.79 56978 66913.23]’;

36 four_GDP=four_GDP*100000000./6.2270;

37 five_GDP=[7107.42 7645.3 7958.92 8548.21 9331.14 10263.78 11509.52

13757.38 15764.2 18470.19 20398 26654.4 30733.3 37064 45490.6]’;

38 five_GDP=five_GDP*100000000./6.2270;

39 six_GDP=[1329.17 1428.01 1512.25 1745.41 1925.16 2100.81 2449.75 2868.73

3473.6 3994.25 4337 5555.41 5715 6798 8715.09]’;

40 six_GDP=six_GDP*100000000./6.2270;

41

42 t=1997:2011;

43 plot(one_population,one_water,’*’)

44 xlabel(’population’);

45 ylabel(’water used’);

46 figure

47 plot(one_GDP,one_water,’*’);

48 xlabel(’GDP’);


50

51 X1=[ones(15,1) one_population one_GDP];

52 b1=regress(one_water,X1);

53 figure

54 y=b1(1)+b1(2)*one_population+b1(3)*one_GDP;

55 plot(t,y,’*’,t,one_water,’+’)

56 pre_water(1)=b1(1)+b1(2)*pre_population(1)+b1(3)*pre_GDP(1);

57 legend(’history water used’,’fitted water used’);

58 figure

59 plot(two_population,two_water,’*’)



62 figure

63 plot(two_GDP,two_water,’*’);



66 X2=[ones(15,1) two_population two_GDP];

67 b2=regress(two_water,X2);

68 figure

69 y=b2(1)+b2(2)*two_population+b2(3)*two_GDP;

70 plot(t,y,’*’,t,two_water,’+’)

71 pre_water(2)=b2(1)+b2(2)*

pre_population(2)+b2(3)*

pre_GDP(2);


73 figure

74 plot(three_population,three_water,’*’)



77 figure

78 plot(three_GDP,three_water,’*’);






81 X3=[ones(15,1) three_population three_GDP];

82 b3=regress(three_water,X3);

83 figure

84 y=b3(1)+b3(2)*three_population+b3(3)*three_GDP;

85 plot(t,y,’*’,t,three_water,’+’)



88 figure

89 plot(four_population,four_water,’*’)



92 figure

93 plot(four_GDP,four_water,’*’);



96 X4=[ones(15,1) four_population four_GDP];

97 b4=regress(four_water,X4);

98 figure

99 y=b4(1)+b4(2)*four_population+b4(3)*four_GDP;

100 plot(t,y,’*’,t,four_water,’+’)



103 figure

104 plot(five_population,five_water,’*’)



107 figure

108 plot(five_GDP,five_water,’*’);



111 X5=[ones(15,1) five_population five_GDP];

112 b5=regress(five_water,X5);

113 figure

114 y=b5(1)+b5(2)*five_population+b5(3)*five_GDP;

115 plot(t,y,’*’,t,five_water,’+’)



118 figure

119 plot(six_population,six_water,’*’)



122 figure

123 plot(six_GDP,six_water,’*

’);



126 X6=[ones(15,1) six_population six_GDP];

127 b6=regress(six_water,X6);

128 figure

129 y=b6(1)+b6(2)*six_population+b6(3)*six_GDP;

130 plot(t,y,’*’,t,six_water,’+’)






133 pre_water

5. Data of water, population and GDP

1 % d at a o f w at er , p o pu la t io n a nd G DP

2 one_water=[619.49 624 620 608 596 556 548 558.6 569.4 600.2 605 613.7

643.8 665.5 702.9];

3 one_water=one_water*100000000;

4 two_water=[1163.39 1102.5 1130 1110.5 1091 1095 967.5 920.3

1032.6 1083.1 1043.4 1061.3 1075.7 1080.2 1102.5];

5 two_water=two_water*100000000;

6 three_water=[2065.12 1946.5 2007 2027 2047 1988 1950.5 1993.6

2114.2 2180.3 2216.8 2257.1 2290.4 2302.7 2339];7 three_water=three_water*100000000;

8 four_water=[834.09 837 840 839.5 839 851 840 862.3 873.6 878.9 879.9

881.2 876.8 883.5 876.8];

9 four_water=four_water*100000000;

10 five_water=[376.83 390 410 411.5 413 422 411 413.2 426.7 430 338 455.4

442.5 450.5 453.9];

11 five_water=five_water*100000000;

12 six_water=[506.2 536 584 583.5 583 575 603 599.7 616.6 622 626.9

641.3 636.2 639.5 631.6];

13 six_water=six_water*100000000;

14 one_population=[12843 12919 12983 13031 13073 13094 13109 13127

13143 13214 13257 13288 13307 13427 13448];

15 one_population=one_population*10000;

16 two_population=[36481 36750 37008 37488 37751 37993 38215 3847038325 38575 38786 39125 39433 39950 40179];

17 two_population=two_population*10000;

18 three_population=[38937 39185 39416 39854 40107 40296 40614 40865

40153 40387 40664 40915 41142 42028 42239];

19 three_population=three_population*10000;

20 four_population=[12427 12571 12745 13918 13367 13484 13622 14011

14682 14859 15062 15214 15358 15920 16027];

21 four_population=four_population*10000;

22 five_population=[19172 19355 19527 19232 19823 19950 20076 20166

19190 19217 19219 19313 19413 19010 19069];

23 five_population=five_population*10000;

24 six_population=[2462 2502 2540 2705 2662 2701 2738 2776

2830 2879 2931 2972 3006 3049 3080];

25 six_population=six_population*10000;26 one_GDP=[8739.95 9464.64 10006.86 11144.26 12172.35 13320.81

15050.16 17833.86 20867.62 24513.17 28332 35956.6 41189 48878

59306.57];

27 one_GDP=one_GDP*100000000./6.2270;

28 two_GDP=[21531.98 23202.35 24599.77 27440.84 30337.08 33651.4

39080.41 48284.07 59692.21 69937.17 80374 100324.4 109452.49

130338 154633.59];




29 two_GDP=two_GDP*100000000./6.2270;

30 three_GDP=[28507.52 30778.87 32704.22 36099.8 39575.67 43854.67

49977.18 59991.23 68931.92 80737.88 91515 114889.27 126859.04

152434 183133.75];

31 three_GDP=three_GDP*100000000./6.2270;

32 four_GDP=[9740.57 10261.08 10888.81 12230.85 13424.86 14829.22

16881.44 20150.22 26668.18 31823.42 36370 44333.58

48903.79 56978 66913.23];

33 four_GDP=four_GDP*100000000./6.2270;

34 five_GDP=[7107.42 7645.3 7958.92 8548.21 9331.14 10263.78 11509.52

13757.38 15764.2 18470.19 20398 26654.4 30733.3 37064 45490.6];

35 five_GDP=five_GDP*100000000./6.2270;

36 six_GDP=[1329.17 1428.01 1512.25 1745.41 1925.16 2100.81 2449.75 2868.73

3473.6 3994.25 4337 5555.41 5715 6798 8715.09];

37 six_GDP=six_GDP*100000000./6.2270;

38 t=1997:2011;

6. Solution of the optimization model

1 function f=fun(x)

2 f1=(2.5*(x(4)+x(5)+x(6)+x(7)-x(1)-x(8))*1000000+11.62*floor((x(4)+x(5)+x(6)+x

(7)-x(1)-x(8))/100)*100000000+24.99*((x(4)+x(5)+x(6)+x(7)-x(1)-x(8))*1000000-

floor((x(4)+x(5)+x(6)+x(7)-x(1)-x(8))/100000000)*100000000))/6.227;

3 f2=0.256*2526.96*1000000000*x(2)*1000000/(267800000000*0.7);

4 f3=1.45*100000000*ceil(x(3)*1000000/(1.83*100000000));

5 f4=0.256*1874.07*1000000000*x(4)*1000000/(52390000000*0.7);

6 f5=1.45*100000000*ceil(x(5)*1000000/(1.83*100000000));

7 f6=0.256*777.57*1000000000*x(6)*1000000/(94750000000*0.7);

8

f7=1.45*100000000*ceil(x(7)*1000000/(1.83*100000000));9 f=f1+f2+f3+f4+f5+f6+f7;

10

11 A=[1 -1 -1 -1 -1 -1 -1 1];

12 b=-115410;

13 lb=[0 0 0 0 0 0 0 0]’;

14 ub=[10 50502 80340 9879.7 15717 17868 28425 10]’;

15 options=gaoptimset(’PopulationSize’,100,’EliteCount’,10,’CrossoverFraction’

,0.75,’Generation’,500,’StallGenLimit’,500,’TolFun’,1e-100,’PlotFcns’,{

@gaplotbestf,@gaplot-bestindiv});

16 [x_best,fval]=ga(@fun,8,A,b,[],[],lb,ub,[],options)

1 function f=fun1(x)

2 f1=(2.5*(x(4)+x(5)+x(6)+x(7)-x(1)-x(8))*1000000+11.62*floor((x(4)+x(5)+x(6)+x

(7)-x(1)-x(8))/100)*100000000+24.99*((x(4)+x(5)+x(6)+x(7)-x(1)-x(8))*1000000-floor((x(4)+x(5)+x(6)+x(7)-x(1)-x(8))/100000000)*100000000))/6.227;

3 f2=0.256*3630.38*1000000000*x(2)*1000000/(106110000000*0.7);

4 f3=1.45*100000000*ceil(x(3)*1000000/(1.83*100000000));

5 f4=0.256*2859.27*1000000000*x(4)*1000000/(76710000000*0.7);

6 f5=1.45*100000000*ceil(x(5)*1000000/(1.83*100000000));

7 f6=0.256*502.89*1000000000*x(6)*1000000/(69770000000*0.7);

8 f7=1.45*100000000*ceil(x(7)*1000000/(1.83*100000000));




9 f=f1+f2+f3+f4+f5+f6+f7;

10

11 A=[1 -1 -1 -1 -1 -1 -1 1];

12 b=-135480;

13 lb=[0 0 0 0 0 0 0 0]’;

14 ub=[10 20010 31833 14466 23013 13157 20931 10]’;

15 options=gaoptimset(’PopulationSize’,100,’EliteCount’,10,’CrossoverFraction’

,0.75,’Generation’,500,’StallGenLimit’,500,’TolFun’,1e-100,’PlotFcns’,{

@gaplotbestf,@gaplot-bestindiv});

16 [x_best,fval]=ga(@fun1,8,A,b,[],[],lb,ub,[],options)

An Optimal Water Strategy for China - 2013MCM, Feb. 2013

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