Tingju Zhu1, Guilherme F. Marques2, Jay R. Lund3

Economic Optimization of Integrated Water Management

and Transfers under Stochastic Surface Water Supply

1International Food Policy Research Institute, Washington, DC2Universidade Federal do Rio Grande do Sul, Brazil

3Department of Civil and Environmental Engineering, University of California, Davis, CA

World Environmental & Water Resources Congress

2013, Cincinnati, OH

Sectors, Choices, and Decision-making Structure

Perennialo Citrus o Grapes o Fruit nuts

Annual

Cotton

Field crop

Truck crop

Alfalfa

Misc grain

Long-termo Toileto Dishwashero Washing

machineo Leakageo Xeriscaping

Short-term Toilet dam Dry lawn Dry shrub

Quantifying Seasonal Flow Forecasting Skill

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Model

Historical weather data

Seasonal forecasts / hindcast

Observed flow data

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Formulation of Three-stage Stochastic Programming Problem

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Subject to a set of constraints

D1: 1st stage decisions, being made only

once at the beginning of the entire planning

period, and are independent of any

particular hydrological year types.

D2: 2nd stage decisions, being made

when seasonal forecasting becomes

available.

D3: 3rd stage decisions, being made when

actual year type is known.

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Analytical Analysis of Two-Stage Water Transfer Problem -Formulation

Constraints

Objective

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Equimarginal principle (2): Marginal benefit of growing annual crop X2jk in year type j equals the value of the portion of marginal applied water that does not percolate into aquifer plus the cost to pump the rest of marginal applied water that percolates into the aquifer, in year j.

Analytical Analysis of Two-Stage Water Transfer Problem -Equimarginal principle

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For any two different year types j1 and j2, the marginal value of irrigation water minus marginal cost of groundwater pumping or recharging in year type j1 should equal that in j2

Analytical Analysis of Two-Stage Water Transfer Problem -Equimarginal principle

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Under economically optimal situation the difference between urban water shadow value and irrigation water shadow value in year type j should equal the marginal cost of water transfer.

Analytical Analysis of Two-Stage Water Transfer Problem -Equimarginal principle

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Stochastic mass conservation of groundwater aquifer

Capacity constraints: Land, water, infrastructure

Water balance in urban sector

Water balance in ag sector

Two-stage Programming Model

Objective function

Discrete probabilities of surface water availability for the normal, dry, and wet scenarios

Base –Conjunctive use plus water transfers

noWT –Conjunctive use without water transfers

NoCU –Watertransfers without conjunctive use

NWNC – No conjunctive use plus no water transfers

Inflow Scenario -

Normal

X X X X

Inflow Scenario - Dry

X X X X

Inflow Scenario -

Wet

X X X X

Hydrologic and Water Management Scenarios

-200

-150

-100

-50

0

50

100

150

200

250

300

0.0

44

0.2

64

1.2

42

4.0

22

9.6

52

18

.68

8

30

.56

4

44

.25

2

57

.93

4

69

.91

6

79

.86

2

86

.93

2

91

.89

8

95

.19

6

97

.28

2

98

.48

8

99

.22

8

99

.60

0

99

.79

2

99

.89

2

99

.93

0

99

.96

4

99

.98

2

99

.99

2

99

.99

8

Agr

icu

ltu

ral w

ate

r su

pp

ly, a

lloca

tio

n a

nd

use

(1

06

m3/y

r)

Non-exceedence frequency of hydrologic year type (%)

U-A transfer

A-U transfer

Artificial recharge

GW pumping

Surface water supply

Ag Use

Agricultural water supply and optimal pumping, recharge, transfers and use decisions in various year types

0

2000

4000

6000

8000

10000

12000

14000

16000

Base noCU noWT NWNC

Pe

ren

nia

l cro

p a

rea

(ha)

Normal Dry Wet

Perennial crop areas under various surface water availability and management scenarios

60

70

80

90

100

110

120

130

140

150

80 130 180 230 280 330Ir

riga

tio

n w

ate

r u

se (

10

6m

3)

Surface water availability (106 m3)

Base NoCU

NoWT NWNC

0

500

1000

1500

2000

2500

80 130 180 230 280 330

An

nu

al c

rop

are

a (h

a)

Surface water availability (106 m3)

Base NoCU

NoWT NWNC

Annual crop areas and water uses under normal surface water availability scenario

-40

-20

0

20

40

60

80

100

0.0

44

0.2

64

1.2

42

4.0

22

9.6

52

18

.68

8

30

.56

4

44

.25

2

57

.93

4

69

.91

6

79

.86

2

86

.93

2

91

.89

8

95

.19

6

97

.28

2

98

.48

8

99

.22

8

99

.60

0

99

.79

2

99

.89

2

99

.93

0

99

.96

4

99

.98

2

99

.99

2

99

.99

8

Urb

an w

ate

r su

pp

ly, c

on

serv

atio

n, t

ran

sfer

s an

d u

se (

10

6m

3/y

r)

Non-exceedence frequency of hydrologic year type (%)

Dry lawn

Leakage control

Toilet upgrade

A-U transfer

U-A transfer

Surface water supply

Urban water use

Urban water management decisions under normal surface water availability scenario and base case water mgt

0

10

20

30

40

50

60

70

80 130 180 230 280 330

Urb

an w

ate

r u

se (

10

6m

3)

Surface water availability (106 m3)

Base NoCU

NoWT NWNC

Urban water uses under normal surface water availability scenario

-30

-20

-10

0

10

20

30

88.0

97.7

107.1

116.3

125.5

134.8

144.1

153.5

162.9

172.2

181.6

191.1

200.6

210.1

219.4

228.8

238.1

247.7

256.8

266.8

276.4

285.4

294.1

304.0

314.7

Wat

er T

ran

sfer

(0

6m

3)

Surface water availability (106 m3)

(a) Normal

-40

-30

-20

-10

0

10

20

30

79.5

87.5

96.3

105.1

114.0

122.9

131.8

140.8

149.8

158.8

167.8

176.8

185.8

194.8

203.8

212.9

222.4

231.2

240.0

248.6

257.5

266.9

276.0

288.6

294.6

Wat

er T

ran

sfer

(0

6m

3)

Surface water availability (106 m3)

(b) Dry

-30

-20

-10

0

10

20

30

115.0

124.4

133.7

142.9

152.1

161.5

170.9

180.3

189.8

199.2

208.6

218.1

227.5

237.1

246.6

256.0

265.7

274.9

285.1

294.0

303.2

312.6

322.9

333.0

344.1

Wat

er

Tran

sfe

r (0

6m

3)

Surface water availability (106 m3)

(c) Wet

Water transfer from agricultural sector to urban sector (A-U) and visa verse (U-A)

-100

-50

0

50

100

150

200

88

98

10

7

11

6

12

6

13

5

14

4

15

4

16

3

17

2

18

2

19

1

20

1

21

0

21

9

22

9

23

8

24

8

25

7

26

7

27

6

28

5

29

4

30

4

31

5Wat

er q

uan

tity

(1

06

m3)

Surface water availability (106 m3)

-100

-50

0

50

100

150

200

88

98

10

7

11

6

12

6

13

5

14

4

15

4

16

3

17

2

18

2

19

1

20

1

21

0

21

9

22

9

23

8

24

8

25

7

26

7

27

6

28

5

29

4

30

4

31

5Wat

er q

uan

tity

(1

06

m3)

Surface water availability (106 m3)

Groundwater management in the base (a) and NoWT (b) water management cases, under normal surface water

scenario

(a) Base

(b) NoWT

0

200

400

600

800

1000

1200

1400

1600

80 100 120 140 160 180 200 220 240 260 280 300 320 340Mar

gin

al e

xpe

cte

d v

alu

e (

00

0$

/106

m3)

Surface water availability (106 m3)

Base

NoCU

NoWT

NWNC

0

200

400

600

800

1000

1200

1400

1600

80 100 120 140 160 180 200 220 240 260 280 300 320 340Mar

gin

al e

xpec

ted

val

ue

(00

0$

/10

6m

3)

Surface water availability (106 m3)

Base

NoCU

NoWT

NWNC

Marginal expected value of water in the agricultural district and urban area for the four management cases under

normal surface water availability scenario

(a) Agricultural (b) Urban

0

200

400

600

800

1000

1200

1400

80 100 120 140 160 180 200 220 240 260 280 300 320 340

Mar

gin

al e

xpec

ted

val

ue

(00

0$

/10

6m

3)

Surface water availability (106 m3)

(a) AgricultureNormal

Dry

Wet

0

200

400

600

800

1000

1200

1400

1600

80 100 120 140 160 180 200 220 240 260 280 300 320 340

Mar

gin

al e

xpec

ted

val

ue

(00

0$

/10

6m

3)

Surface water availability (106 m3)

(b) UrbanNormal

Dry

Wet

Marginal expected value of water in (a) the agricultural area and (b) urban center under normal, dry and wet surface

water availability scenario, base case management

Inflow Management

Agricultural benefit Urban cost System net benefit

Perennial

crops Total

Permanent

conservation Total Value

Change from base

(%)

Normal Base 142.9 142.4 -2.0 -23.4 116.7 0.0

NoCU 118.4 119.8 -2.4 -24.6 93.1 -20.2

NoWT 143.0 144.0 -2.4 -45.1 98.9 -15.2

NWNC 109.9 111.6 -2.4 -45.1 66.5 -43.0

Dry Base 137.0 136.4 -2.4 -23.3 110.3 0.0

NoCU 110.1 111.3 -2.4 -25.1 83.6 -24.2

NoWT 141.4 142.1 -3.1 -50.7 91.4 -17.1

NWNC 102.9 104.6 -3.1 -50.7 53.8 -51.2

Wet Base 144.2 145.2 -0.4 -22.1 121.6 0.0

NoCU 137.2 138.7 -2.4 -24.0 113.6 -6.5

NoWT 144.2 145.6 -2.4 -34.4 111.2 -8.5

NWNC 127.9 129.6 -2.4 -34.4 95.2 -21.7

Benefit and Cost – Three Inflow Scenarios & Three management Scenarios

Conclusions

Urban and agricultural water users have significant ability to adjust to imperfect water supply reliability through various water conservation and crop production decisions

Water transfers provide local incentives to facilitate coordinated urban and agricultural water conservation and water transfers

Conjunctive use and water transfer operations complement each other and increase flexibility in local water management facing uncertain surface water supply