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