Optimal Allocation of Agricultural Water Resources ...

Optimal Allocation of Agricultural Water Resources Based on Virtual Water Subdivision in Shiyang River Basin Xiaoling Su, Jianfang Li & Vijay P. Singh

Water Resources Management An International Journal - Published for the European Water Resources Association (EWRA) ISSN 0920-4741 Volume 28 Number 8 Water Resour Manage (2014) 28:2243-2257 DOI 10.1007/s11269-014-0611-5

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Author's personal copy Water Resour Manage (2014) 28:2243–2257 DOI 10.1007/s11269-014-0611-5

Optimal Allocation of Agricultural Water Resources Based on Virtual Water Subdivision in Shiyang River Basin Xiaoling Su & Jianfang Li & Vijay P. Singh

Received: 21 October 2013 / Accepted: 30 March 2014 / Published online: 12 April 2014 # Springer Science+Business Media Dordrecht 2014

Abstract Without subdividing into blue and green virtual water, the virtual crop water is currently used in the allocation of water resources based on virtual water strategy. In order to improve agricultural water use efficiency and the proportion of green water utilization, a multi-objective optimal allocation model for agricultural water resources is developed in this study. The model is based on the subdivision of virtual water into blue and green virtual water, subject to three objectives of the maximum net benefit from agriculture, the minimum fairness difference in the utilization of water, and the maximum proportion of green water utilization. Taking Shiyang River basin as an example, agricultural water resources are optimized through regional virtual water trade in the basin. Results show that compared with the situation in the year 2007, the net benefit of agriculture, the fairness difference in the utilization of water, and the proportion of green water utilization are optimized. At the same time, the planting ratio of food crops, such as corn, reduces, while the planting ratio of cash crops, such as cotton, vegetables, and fruits, increases. Through regional virtual water strategy in the basin, with the crops of different districts having comparative advantages, the proportion of green water utilization and the blue water use efficiency are improved. The study provides a scientific basis to solve the water shortage problem in the basin. Keywords Virtual water . Blue water . Green water . Agricultural water resources optimal allocation . Shiyang River basin

X. Su (*) College of Water Resources and Architectural Engineering, Northwest A & F University, Yangling 712100, China e-mail: [email protected] J. Li Huizhou City Huayu Water Resources and Hydropower Engineering investigation Co., Ltd, Huizhou 516003, China V. P. Singh Department of Biological & Agricultural Engineering, and Zachry Department of Civil Engineering, Texas A & M University, College Station, TX 77843-2117, USA

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1 Introduction Growing population, coupled with continued socioeconomic development, is putting pressure on the globe’s scarce water resources (Mekonnen and Hoekstra 2010). Water, it is said, may become as precious as oil during this century (Qadir et al. 2003). The rational allocation of water resources is one important way to achieve regional sustainable development of water resources. The concept of virtual water was formulated in 1993 by a British scholar, Tony Allan. It refers to the quantities of water needed to produce products and services (Allan 1993). The virtual water trade is that water-poor countries or regions through trade purchase waterintensive products from water-rich countries or regions to ensure water and food security. The virtual water theory applies economic principles to the allocation of water resources in the larger regional context and challenges the traditional concept of source and saving-based water resources allocation. The virtual water trade has expanded the scope of regional resources utilization. Not only it is an important strategic choice to achieve the sustainable use of water resources but is also a powerful tool for the rational allocation of regional water resources. In this paper, virtual water is separated into green water and blue water, consistent with the global hydrological cycle. “Crop Virtual Water Content” (CVWC) forms the basis for examining the quantity of virtual water embodied in the international food trade (Yang et al. 2006). In the virtual water literature, models have been applied for estimating CVWC. CropWat is one of the most widely used models (Hoekstra and Hung 2002) and is used in the present study. The CropWat model calculates crop water requirement of different crop types. Green water refers to the water that is stored in the unsaturated zone of soil and available for evapotranspiration by crops. Falkenmark and Rockstrom (2004) defined green water as the soil water in the unsaturated zone derived from precipitation and blue water as liquid water above and below the ground (rivers, lakes, groundwater, etc.). Blue water can be further divided into renewable water sources, such as streamflow and shallow groundwater; and nonrenewable water, such as deep groundwater with little recharge (so-called fossil groundwater) and glacier melt water. The degree of green water utilization by crops is different in different growing seasons. Blue water can be used directly by other socio-economic sectors, but green water cannot. Therefore, application of virtual water should entail the subdivision into blue water and green water in the virtual water content (Ma et al. 2010). Green water is highly immobile, making it difficult to substitute for other water uses and leading to a low opportunity cost of production. For this reason, green water is primarily utilized either in rainfed agriculture or by natural vegetation (Yang et al. 2006). Both green and blue water resources are important for food production. Rain-fed agriculture uses green water only, while irrigated agriculture uses both green and blue water. Without considering green water, water use assessments are incomplete (Liu et al. 2009). Green water is an important resource for agricultural production. However, green water uses have drawn less attention (Liu and Yang 2010; Brewn et al. 2009). Blue water has a direct cost associated with it, due to infrastructure requirement as well as a high opportunity cost, since there are many potential end users of blue water resources (Yang et al. 2006; Aldaya et al. 2010; Konar et al. 2012). The question arises: How to make full use of green water for saving blue water? Currently, virtual water research focuses on virtual water content, its role in food security and water security, and virtual water trade between regions. There is a growing body of literature on the concept of virtual water and its potential contribution to water saving (Aldaya et al. 2010), its quantification (Siebert and Döll 2010 ), and the relevance of green water (soil water originating from rain) in the international commodity trade (De Fraiture et al. 2008; Allan 2006; Chapagain et al. 2006; CAWMA 2007; Aldaya et al. 2010), especially in water-short nations (Hoekstra and Hung 2002; Hoekstra 2003; Hoekstra and Chapagain 2008). Some studies have focused on plant structure

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adjustments (Ren et al. 2009; Liang and Wang 2010). However, research on the optimal allocation of agricultural water resources, based on the subdivision of virtual water into blue water and green water, has been rarely reported. Under climate change and population growth, water demand in the future will increase. The question arises: How to meet the demand based on the available water resources at the river basin scale? The issue is then how to most efficiently allocate and use the available water. There were regional differences in crop profitability and thus net return from a unit volume of irrigation water due to variations in agro-climatic zones punctuated by production and irrigation technologies and access to water resources (Abu-Sharar et al. 2012). Hoekstra and Hung (2002) proposed three decisions about water efficiency at different levels that can be made to deal with the available water resources. The first level is the user level, where “the local water use efficiency” can be increased by creating awareness, charging prices based on full marginal cost and by stimulating water-saving technology. Second, a higher level is the country or catchment level, where choices on “water allocation efficiency” have to be made. The third is a level at which one can talk about ‘global water use efficiency.’ This paper only studies agriculture water allocation efficiency at the catchment level. The present paper subdivides the crop virtual water content (CVWC) into blue water and green water, develops a multi-objective optimization model for agricultural water resources and applies the model to the Shiyang River basin to achieve a reasonable allocation of water resources, agricultural planting structure adjustment program, and improvement of efficiency and green water basin agricultural water use ratio.

2 Data and Methods 2.1 Study Area The study area is Shiyang River basin (36°29′~39°27′N, 101°41′~104°16′E), which is located in the easternmost Hexi corridor of Gansu Province, northwest China. Shiyang River originates in the Qilian mountain and ends at the Minqin oasis, between the Tenggeli and Badanjilin deserts, with an area of 41 400 km2. It is made up of nine counties (or districts) of four cities (Fig. 1). The climate is characterized by strong solar radiation, adequate sunshine, great temperature difference between day and night, less precipitation, strong evaporation and dry air. The mean annual precipitation is 221 mm in the basin, only 116 mm in Minqin County, which is located in the lower reaches of the basin. But the mean annual evaporation from water surface is very high, for example, 2,600 mm in Minqin County. Thus water is a key factor for the economic development and sustainability of the ecosystem. The economic water use increases with the increasing population. The transformation between surface water and groundwater many times in the basin results in the repeated utilization of water resources and the over-exploitation of groundwater. Thus the result is that the utilization rate of water resources in the basin in 2000 was 172 % (Kang et al. 2008), which is the highest utilization rate of water resources among the inland river basins of China. Agriculture is the largest single user of water with 80 % of freshwater being currently used for irrigation. The competition between agricultural water use and ecological water demand gradually has resulted in eco-environmental deterioration, such as the falling of groundwater table, serious loss of vegetation, soil salinization and desertification in Mingqin basin, which have endangered local communities and threaten the sustainable development of the basin.


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Fig. 1 Location of Shiyang River Basin in China

The Shiyang River basin used to be a commodity grain production base with abundant light and heat resources, but it is no longer appropriate to be a commodity grain base for the shortage of rainfall and water resources. The best way is to reduce area of crops with high water consumption in order to save water. 2.2 Data The National Meteorological Centre of China operates four weather stations at Minqin, Yongchang, Wuwei and Gulang in Shiyang River basin. Daily meteorological data of four stations were collected from China Meteorological Data Sharing Service System (http://cdc. cma.gov.cn/) for the period of January 1959–December 2008, with mean, maximum and minimum air temperatures, relative humidity and bright sunshine hours, and wind speed at 2 m height. These measured daily data were input parameters for the reference crop evapotranspiration (ET0) model. Agricultural yields data per ha were collected from the Statistical Yearbook and Economic Information Network of Gansu Province (http://www. gsei.com.cn/). Crop coefficient Kc was directly obtained from Kang et al. (2009). Agricultural price data were obtained from the Gansu prices net (http://www.gswj.gov.cn/). According to balanced diet pagoda of Chinese Dietary Guidelines (2007), as well as the actual situation in Shiyang River basin, annual minimum grain demand was determined to be 400 kg per person, of which wheat 200 kg per person, maize 100 kg per person, other grain 100 kg per person; vegetable oil 7.3 kg per person, oil yield calculated at 0.4; vegetables 292 kg per person; fruit 73 kg per person; cotton market demand was 20,810 t. For 2007 the available watershed agricultural water resources are shown in Table 1.


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Table 1 Available agricultural water resources of Shiyang River Basin in 2007 (108m3) Local available water

Water transferred out of basin

Water demand for living

Water demand for Water demand production for ecology

Available water for agriculture

15.86

0.53

0.98

1.62

12.55

1.24

2.3 Methodology The methodology consists of four parts: (1) water demand for crops, (2) virtual water content of crop and subdivision, (3) optimization model of agriculture water resources and solution, (4) virtual water flow. 2.3.1 Calculation of Crop Water Demand The crop water demand is calculated using the methodology developed by FAO (Allen et al. 1998). It is computed from the accumulated evapotranspiration (ET) over the crop-growing period as CWR ¼ 10

lgp X

ET

ð1Þ

d¼1

where CWR is the crop water demand (m3 ha−1); the factor 10 is meant to convert the water depth in millimeters into water volume per land surface area in m3 ha−1; the summation is done over the period from the day of planting (day 1) to the day of harvest (lgp stands for the length of growing period in days); ET is evapotranspiration (mm/day) and is calculated as follows: ET ¼ K c ET 0

ð2Þ

in which Kc is the crop coefficient; and ET0 is the reference crop evapotranspiration (mm/day). The only factors affecting ET0 are climatic parameters. ET0 is calculated on the basis of the FAO Penman-Monteith equation (Allen et al. 1998):

ET 0 ¼

900ðea −ed Þ T þ 273 Δ þ γ ð1 þ 0:34U 2 Þ

0:408ΔðRn −GÞ þ γ

ð3Þ

in which △ is the slope of the vapor pressure curve (kPa °C−1), Rn is the net radiation at the crop surface (MJm−2 day−1), γ is the psychrometric constant (kPa °C−1), T is the average air temperature (°C), U2 is the wind speed measured at 2 m height (m s−1), ea is the saturation vapor pressure (kPa), and ed is the actual vapor pressure (kPa). 2.3.2 Calculation of Virtual Water Content and Subdivision The virtual water content (VWC) of a crop is defined as the crop water requirements (CWR) (m3 ha−1) during a cropping period divided by the total crop yield (Y) (kg ha−1). The VWC of primary crops can be calculated according to the methodology developed by Hoekstra and Hung (2002) as follows: VWC ¼ CWR=Y

ð4Þ

When considering the economic value of water, it is necessary to subdivide the virtual water into blue water and green water. The blue and green virtual water contents are calculated as follows:


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VW C blue ¼ CW Rblue =Y ¼ 10 ET blue =Y

ð5Þ

VW C green ¼ CW Rgreen =Y ¼ 10 ET green =Y

ð6Þ

where VWCgreen and VWCblue are the green and blue water components, respectively, of VWC for a crop (m3 kg−1), CWRgreen and CWRblue are green and blue water consumptions over the crop-growing period (m3 ha−1), and ETgreen and ETblue are green and blue water evapotranspiration values over the crop growing period (mm). The minimum of crop water requirement and effective rainfall is green water consumption of crop. The blue water consumption is the difference between the crop water requirement and green water. ETgreen and ETblue during the crop-growing period can be estimated using the Food and Agriculture Organization’s CROPWAT model (FAO 2003; Hoekstra et al. 2011; Sun et al. 2013) ET green ¼ minðET; Peff Þ

ð7Þ

ET blue ¼ maxð0; ET−Peff Þ

ð8Þ

where Peff is the effective rainfall over the crop-growing period (mm). 2.3.3 Optimization Model of Agriculture Water Resources The objective of water resources system optimization is to maximize benefits, minimize costs, and meet the various water demands, subject to the mass balance equation and other related constraints (Rani and Moreira 2010). Optimization models determine the values for a set of decision variables that will maximize or minimize an objective function subject to constraints (Haro et al. 2012). Because of different water demands and yields of different crops, choices for the allocation of water can be more or less ‘efficient’, depending on the value of water for alternative uses. The optimization model presented in this paper is a multi-objectives decision model. The agricultural water allocation problem is to find the optimal distribution of water between different crops and different districts under limited water resources. The planting area of crop in the district is decision variable for the model. Crops were included food crops (wheat, corn, other grain crops) and economic crops (cotton, flax, vegetables and fruits). (1) Objective function Three objectives of the maximum net benefit of irrigation water, the minimum fairness difference in the utilization of water, and the maximum proportion of green water utilization were used. The objective functions of the optimization model are multiobjectives, including economic objective, equity objective and blue water saving objective. The economic objective is the maximum irrigation benefit of water resources and was formulated as: maxf 1 ¼

m X n X i¼1

ðxic Y ic Pc −xic C ic −Ctc Pc Þ

ð9Þ

c¼1

where f1 is the total net benefit (¥) of irrigation water use, m is the number of calculated units, n is number of crop types, xic, Yic and Cic are, respectively, the irrigation area (ha),


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yield per ha (kg ha−1) and cost per ha (¥ ha−1) of crop c in calculated unit i; Ctc is the amount of food trade of crop c from exporting region to importing region (kg); and Pc is the price per kg of crop c, including the cost of planting, labor and water price. The equity objective is the minimum difference of water use per capita among units. Its definite standard deviation of water use per capita is defined as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m uX 2 u W i =Pi −W =P u W =P t i¼1 ð10Þ minf 2 ¼ m−1 W i ¼ W Di þ W I i þ W E i þ

n X

xic Y ic VW C ic

ð11Þ

c¼1

W¼

m X

ð12Þ

Wi

i¼1

where Wi is the total water use of unit i, which is the sum of domestic water use WDi, industrial water use WIi, ecological water use WEi, and irrigated agriculture water use (including blue water and green water). W is the total water use of study area. Pi is the population of unit i and P is the population of study area. The water saving objective is the maximum utilization rate of green water of crop: m X n X

maxf 3 ¼

xic Y ic VW C green ic

i¼1

c¼1 m X n X i¼1

100%

ð13Þ

xic Y ic VW C ic

c¼1

(2) Constraints An optimization problem does not end with the objective function. In the case of water resources systems, the calculation of the best value for the control variables must comply with water supply for and demand of users. Water demand for domestic, industry and ecology systems is a priority to be met. Therefore, the available irrigation water is the water available after subtracting the sum of water demand for domestic, industry and ecology: m X n X i¼1

xic Y ic VW Rblueic ≤W a −

c¼1

m X

ð W Di þ W I i þ W E i Þ

ð14Þ

i¼1

where Wa is the total water available in the basin; and WDi , WIi, and WEi are the water demands for domestic use, industry and ecology, respectively. The irrigation area of unit i would be less than the effective irrigation area Ai (ha): n X

xic ≤Ai

ð15Þ

c¼1

Agriculture product would be to meet the local demand: xic Y ic þ Ctic ≥Pi Dc

ð16Þ


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Here, Dc is minimum demand per capita for crop c (kg/per capital). (3) Model Solution The model is a multi-objective programming algorithm with nonlinear objective functions. It was solved in two steps. First, through introduction of an auxiliary function, the multi-objective decision problem was changed to a single objective optimization problem. According to the weight of each objective, the multi-objective function was reduced to a single objective function. The single objective is the weighted average of these three objectives: maxf ¼ ω1 f 1 þ ω2 f 2 þ ω3 f 3

ð17Þ

where ω1, ω2, ω3 are the weights of economic objective, equity objective and water saving objective, respectively. The fuzzy two-element comparison method (Chen 1994) was applied to determine the weights of the three objectives. Second, the single objective optimization model was solved by using the pattern search algorithm from Matlab R2009b toolbox. A pattern search (PS) method is a direct search method. It handles optimization problems with nonlinear, linear, and bounding constraints. The advantage of so doing is that the calculation does not require objective functions to be differentiable or continuous. So the solution is more effective and has an efficient global search capability, easy to implement on a computer, and is reliable. There are two approaches to call the pattern search tool under the environment of Matlab. One is graphical user interface (GUI), and the other is call function of the pattern search in the program. In this paper the GUI is used to solve the optimization model. The main parameters are set as follows: Initial decision variables x0 =0; and initial mesh size is set as 1.0 by default. The algorithm stops if the mesh size becomes smaller than Mesh tolerance (TolMesh) value 1e-6 by default, or stops if the number of iterations reaches Max iteration (MaxIter) value 1,000.

2.3.4 Virtual Water Flows Virtual water flows between regions were calculated by multiplying commodity trade flows by their associated virtual water contents (Hoekstra and Chapagain 2007): VW F c ¼ Ctc VW C c

ð18Þ

in which VWFc denotes the virtual water flow (m3 year−1) from exporting region to importing region as a result of trade in commodity c; Ctc the commodity trade (kg year−1) from the exporting to the importing region; and VWCc the virtual water content (m3 kg−1) of the commodity, which was defined as the volume of water required to produce the commodity in the exporting region.

3 Results and Discussions 3.1 Virtual Water Content and Composition of Major Agricultural Products in Shiyang River Basin The average values of VWC, blue and green VWC, and rate of green VWC of major crops of sub-districts in Shiyang River basin during 2003–2007 are shown in Table 2. The major crops are wheat, corn, other grains (mainly barley, beans, potatoes, etc.), cotton, flax, and vegetables.


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Table 2 Virtual water content and composition of major agricultural products in Shiyang River basin VWC Value unit Unit VWCblue VWCgreen Rate of (m3/kg) (m3/kg) yield (m3/kg) VWCgreen VWCblue (Kg/ha) (%) (¥/m3)

Crop

Subdistrict

ET (mm)

Peff (mm)

Wheat

Liangzhou

525.3

45.4

6,564

0.80

0.73

0.07

8.6

2.60

Minqin

612.1

24.2

7,129

0.86

0.82

0.03

4.0

2.30

Gulang

538.9

139.8

2,844

1.90

1.41

0.49

25.6

1.34

Tianzhu Jinchuan

435.3 612.1

221.7 24.1

3,488 5,950

1.25 1.03

0.62 0.99

0.63 0.04

50.2 4.0

3.05 1.92 2.85

Corn

Other food crop

Cotton Flax

Vegetable (pepper)

Fruit (apple)

Yongchang

490.8

70.5

6,321

0.78

0.67

0.11

14.5

Liangzhou

525.6

98.7

10,329

0.51

0.41

0.10

18.8

3.14

Minqin

588.4

62.5

9,237

0.65

0.58

0.07

10.4

2.24

Gulang

491.8

213.5

6,588

0.75

0.43

0.32

42.5

3.00

Jinchuan

588.4

62.5

6,669

0.90

0.80

0.09

10.5

1.62

Yongchang

489.9

127.7

8,822

0.56

0.42

0.14

25.8

3.13

Liangzhou Minqin

525.6 612.1

45.4 24.2

6,355 6,872

0.83 0.89

0.76 0.86

0.07 0.04

8.5 3.9

2.64 2.34

Gulang

538.9

139.8

3,002

1.83

1.37

0.46

24.9

1.46

Tianzhu

435.3

221.7

2,882

1.52

0.74

0.78

51.5

2.72

Jinchuan

612.1

24.2

6,410

0.96

0.92

0.04

3.9

2.18

Yongchang

490.8

70.5

7,303

0.67

0.58

0.10

14.4

3.48

Minqin

359.8

71.0

1,502

2.40

1.92

0.48

19.9

6.77

Jinchuan

362.5

71.3

2,149

1.98

1.56

0.42

21.4

8.36

Liangzhou Minqin

492.3 562.6

82.3 53.3

2,488 5,881

1.99 1.05

1.65 0.96

0.33 0.09

16.8 9.0

3.15 5.44

Gulang

461.0

173.7

2,363

2.02

1.22

0.80

39.6

4.27

Tianzhu

355.5

198.0

1,574

2.26

1.00

1.26

55.9

5.21

Jinchuan

562.6

53.3

3,446

1.78

1.61

0.17

9.5

3.23

Yongchang

458.5

112.5

2,381

2.09

1.60

0.50

23.7

3.26

Liangzhou

564.4

65.3

47,840

0.12

0.10

0.01

11.5

24.86

Minqin

641.3

39.7

24,066

0.28

0.26

0.02

5.8

9.88

Gulang Tianzhu

529.0 402.0

120.0 172.7

28,572 14,472

0.19 0.28

0.14 0.16

0.04 0.12

23.0 42.9

18.16 16.39

Jinchuan

641.3

39.7

53,740

0.13

0.13

0.01

6.1

20.59

Yongchang

523.5

88.4

57,636

0.09

0.08

0.02

16.8

34.33

Liangzhou

346.4

92.0

4,577

0.76

0.56

0.20

26.4

5.37

Minqin

395.8

56.2

3,978

1.08

0.92

0.16

14.5

3.26

Gulang

324

6,761

0.63

0.22

0.40

64.4

13.43

193

Jinchuan

395.8

56.2

4,265

0.97

0.83

0.14

14.5

3.63

Yongchang

323.3

117.1

3,906

0.86

0.55

0.31

35.9

5.42

All value is the average during 2003–2007

It is clear from Table 2 that VWC of the same crop differed strongly between districts (or counties) because of the differences in water demand during the growth period (ET) and unit yield of crop. With the lowest yield and higher ET, the VWC of wheat in Gulang County is


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twice more than it is in Yongchang, Liangzhou and Minqin County. For corn, VWC is the greatest in Jinchuan County, and least in Liangzhou District. Cotton is the crop with the highest VWC, while vegetable is the crop with the lowest VWC. The rate of VWCgreen is the percentage of VWCgreen in VWC. It varies greatly in different districts and crops because of variations of VWC and effective precipitation, and variations of agro-climatic zones. The fruit crop in Gulang is the crop with the highest rate of VWCgreen as 64.4 %. Flax, wheat and other food crops in Tianzhu are the crops with higher rates of green VWC, more than 50 %. Because of the lowest precipitation in Minqin and Jinchuan, crops with lower rates of VWC are other food crops, wheat, vegetables and flax in Minqin and Jinchuan, as lower than 10 %. Table 2 also shows the value unit blue VWC vary enormously in different districts and crops. The value of unit blue VWC of vegetable is the highest amongst all crop types and is the lowest for the food crop type. These data were the inputs for optimal allocation model of agricultural water resources. 3.2 Cropping Pattern Because of the shortage of water resources, the Shiyang River basin will not be a commodity grain production base. The food self-sufficiency rate at the basin scale is given as 100 % in the optimization model, not 146 % of the present. This means that all food is produced in the basin, but districts with water-shortage and higher VWCblue within the basin will have less food self-sufficiency than 100 %, and districts with water-rich and lower VWCblue will have higher food self-sufficiency than 100 %. The districts with the shortage of food would be satisfied through virtual water trade of agricultural products among the administrative districts within the basin. However, in order to protect regional food security, at least 50 % of food demands of the districts need to be met by self production. The places suitable for the growth of exact grain or crop can be identified by consideration of water available for agriculture and three objectives of maximum net benefit of agriculture and proportion of green water utilization, and minimum fairness difference in the utilization of water. Table 3 shows crop areas of districts after optimization. It indicates that Liangzhou and Gulang are the places suitable for the growth of wheat. Corn is suitable for planting in Gulang and Yongchang. Cotton and Flax are suitable in Minqin. Vegetable is suitable in Liangzhou ang Yongchang, while fruit is suitable in Gulang and Minqin. Figure 2 compares actual crop areas with optimal value in Shiyang River basin in 2007. Except for wheat that slightly increased in area in order to satisfy the constraints of need for wheat, the corn and other food crop area reduced. The sum of food crop areas reduced too due to reduced food self-sufficiency rate at the basin scale from the present 146 to 100 %. The area of cultivation of cash crops, such as cotton, vegetable and fruit, increased, while flax cultivation area decreased, due to a large amount of blue water consumption and lower value unit VWCblue. 3.3 Virtual Water Trade Among Districts Within the Basin The food production in individual districts indicates regional virtual water trade. Table 4 shows that the three districts or counties of Liangzhou District, Gulang County and Yongchang County constitute the region for food output, and Minqin County, Jinchuan District and Tianzhu County constitute the region for food input. Through virtual water trade, it can save blue water used in producing food crops, and produce more cash crops with a higher economic value. The efficient use of blue water in the total basin is improved.


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Table 3 Optimized planting areas of crops in different districts in Shiyang River basin in 2007 (103ha) District name Food crop Wheat Corn

Cash crop Other food crop Sum

Cotton Flax

Total Vegetable Fruit

Sum

Liangzhou

48.89

4.68

8.83

62.4

0.00

1.61

46.11

3.89

51.61

114.02

Minqin

0.00

5.04

8.97

14.01

27.65

3.59

1.87

4.23

37.34

51.35

Gulang

30.56

8.95

5.41

44.92

0.00

1.64

0.00

8.85

10.49

55.41

Tianzhu

3.07

0.00

0.40

3.47

0.00

0.20

0.84

0.00

1.04

4.52

Jinchuan

3.30

1.60

1.87

6.77

0.00

1.61

1.72

1.39

4.72

11.49

Yongchang

0.00

5.38

9.26

14.64

0.00

1.90

29.31

4.06

35.27

49.91

Basin total Crop rate of basin (%)

85.83 29.9

25.66 34.74 9.0 12.1

146.23 27.65 51 9.6

10.57 79.85 3.7 27.9

22.41 140.48 286.70 7.8 49 100.0

Optimal results of interregional grain trade and virtual water trade in the Shiyang River basin are shown in Table 4. A particular district may export a kind of grain, and import another kind of grain. Because of different values of VWCblue of different grain crops, the state of grain export or import was inconsistent with export or import of virtual water. For example, Liangzhou District, Gulang County and Yongchang County are export districts of food, but the export districts of virtual water are Liangzhou, Tianzhu and Yongchang districts. The total water saving due to grain trade among districts of the basin is 2267.4×104 m3. In Table 3 Lianzhou district with large planting areas of food crops are overlapped with the district where the planting areas of cash crops are also large, but in Table 6 the proportion of the area of food crops and cash crops shows a decrease from present value 68:32 to optimize value 55:45. Table 5 shows the optimal results of agricultural trade and virtual water in Shiyang River basin. For grain trade, except that Jinchuan is a net import district, other districts have different types of import or export crops: Liangzhou and Tianzhu districts import corn and other food crops, export wheat; Minqin and Yongchang Counties import wheat and export corn and other food crops; Gulang county imports other food crops and exports wheat and corn. Combined with Table 2, we find that exporting districts have a higher rate of green water use or value of VWCblue. For example, Liangzhou, Tianzhu and Gulang export wheat, because Tianzhu and Liangzhou have a higher value unit blue VWC, and Gulang has a higher rate of green water

crop area/103ha

100 80 60 40 20 0 wheat

corn

other food

cotton

flax

vegetable

crop type actual crop area

optimal crop area

Fig. 2 Comparison of actual crops areas of Shiyang River basin with optimal value in 2007

fruit


X. Su et al.

Table 4 Optimal results of Grain trade and virtual water among different districts in Shiyang River basin in 2007 District

Local food product/t

Blue water use/108m3

Import food/t

Local food product per capita/kg

Food per capita after virtual water trade/kg

Virtual water of grain trade/104m3 −4066.2

Liangzhou

5.68

433,773

−35,853

436

400

Minqin

2.02

109,706

10,294

366

400

1152.4

Gulang

1.96

161,266

−3,986

410

400

1272.4

Tianzhu Jinchuan

0.10 0.63

11,737 42,580

2,703 42,580

325 200

400 400

−29.8 3949.4

2.10

118,658

−15,738

461

400

−10.8

12.49

877,720

0

400

400

2267.4

Yongchang Total

In column of “virtual water of grain trade”, with “−” means export, the other means import

use, although the lowest value unit blue VWC. Flax and fruit can meet the need of the basin. Cotton and Vegetable are exported to other basins. The total virtual water of agriculture trade is 332.41 million m3, which is 21 % of the total available water in the basin. It indicates that through virtual water strategy at the basin scale, the comparative advantages of administrative crop can be taken into account and higher basin water use efficiency can be achieved. 3.4 Comparison of Objective Values Between Present and Optimal Allocations Comparison of objective values between present and optimal allocations in 2007 (see Table 6) shows that under the constraints of limited blue water, the net benefit for irrigation increased by 3.849 billion Yuan, mainly due to the reduction in the proportion of food crops and increase in the proportion of cash crops. The crop area proportion between food and cash crops reduced from 59:41 to 51:49. The value of VWCblue improved from 3.44 ¥ / m3 to 6.54 ¥ / m3. The difference in water use per capita among administrative districts was smaller, from the present actual value of 0.184 to the optimal value 0.163, which means more equitable in water resources allocation. The rate of VWCgreen in the total basin improved from the present actual value of 16.6 % to the optimal value of 17.9 %. Except for Liangzhou District and Tianzhu County, the rate of VWCgreen in other districts increased. It indicates that through regional virtual water trade within the basin with the crops of different districts having comparative advantages, the water use efficiency is improved. Table 5 Optimal results of agriculture trade and virtual water in Shiyang River basin in 2007 District

Wheat (t) Corn (t)

Other food (t)

Cotton (t) Flax (t)

Vegitable (t) Fluit (t)

Virtual water of agriculture trade (104m3)

39,299

0

−2,085,219

−20,509

Liangzhou

−123,987 48,835

Minqin Gulang

59,999 −7,069

−16,613 −33,092 −39,389 −19,643 22,726 0

Tianzhu

−3,263

3,610

2,356

0

357

−939

2,635

Jinchuan

22,864

10,479

9,237

0

−3,221

−633

10,194

4,265

Yongchang 51,455

−26,667 −40,526 0

−2,595

−1,608,188

−1,294

−12,676

Basin total

0

0

−3,529,607

0

−33,241

0

0

−39,389

With “−” means export, the other means import

14,234

−12,002 50,557 3,227 114,814

53,942

1,028 −6,135 −66,505 1,823 −9

Optimal

Present actual

81.67

39.05

4.55

2.64 0.02

1.96

33.45

Liangzhou

Minqin

Gulang Tianzhu

Jinchuan

Yongchang

10.99

Yongchang

Basin

0.03

2.42

Jinchuan

5.57 1.45

Minqin Gulang

Tianzhu

43.18

22.73

Liangzhou

Net benefit of irrigation (108¥)

Basin

District name

2.10

0.63

1.96 0.10

2.02

5.68

12.49

2.08

0.63

0.10

2.30 2.11

5.35

12.56

Blue water consumption for irrigation (108m3)

/

/

/ /

/

/

0.163

/

/

/

/ /

/

0.184

Objective value for equitable

1,076

815

836 791

1,096

777

870

1,057

824

794

1,124 819

759

861

Water use per capita (m3/ person)

19.1

7.0

36.0 49.3

12.8

10.8

17.9

16.8

6.7

50.2

10.0 29.5

13.0

16.6

Rate of green water use (%)

115

50

103 81

91

109

100

289

53

69

122 101

157

146

Food selfsufficiency rate (%)

Table 6 Comparison of objective values between present and optimal allocation of agricultural water in Shiyang River basin in 2007

29:71

59:41

81:19 77:23

27:73

55:45

51:49

82:18

62:38

68:32

37:63 84:16

68:32

59:41

Crop area proportion between food and cash crop

15.92

3.10

1.35 0.20

2.25

6.87

6.54

5.29

3.85

0.31

2.42 0.69

4.25

3.44

Net benefit unit blue water (¥/m3)

Author's personal copy

Optimal Allocation of Agricultural Water Resources 2255


X. Su et al.

Our analysis indicates that virtual water trade is an important way to solve the water shortage problem at the basin scale. The Shiyang River basin is a region with water shortage and higher utilization rate of water resources. To solve the issue of increased water shortage in the future, the virtual water trade needs to be implemented at the national scale. That means it needs virtual water trade by importing food from other basins with abundant water. Our results show that water management can be improved if cropping patterns were decided on the basis of maximizing net benefit of agriculture and proportion of green water utilization, and minimizing fairness difference in the utilization of water.

4 Conclusions In this paper, based on VWC consistent with crop, a multi-objective model of water resources optimal allocation is developed at the basin scale. An auxiliary function and the pattern search algorithm are applied to solve model equations. Our results confirm that the higher blue water use efficiency and equitable water use at the basin scale can be achieved by virtual water subdivision and trade. The places suitable for the growth of exact grain or crop can be identified. Food trade and virtual trade among districts within the basin can be obtained. The results provide a scientific basis to solve the water shortage problem in the basin. Virtual water strategy is an approach to solve regional water shortages and to achieve efficient use of water resources in an effective way. But regions importing food have a great dependence on the regions exporting food. It may cause a regional food security question. The food trade or virtual water trade among districts needs government to balance between the economic efficiency in the total basin and equitable water use among districts in the basin. Further study will focus on the management of virtual water trade. Acknowledgments We are grateful for the grant support from the National Natural Science Fund in China (51279166) and scientific innovation key project of fundamental research funds for the central university (QN201168).

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