optimal spatial dynamic management
DESCRIPTION
69th SWCS International Annual Conference July 27-30, 2014 Lombard, ILTRANSCRIPT
Optimal Spatial‐Dynamic Management of Groundwater Conservation and Surface Water Quality with On‐Farm Reservoirs
Kent Kovacs, Eric Wailes, Grant West, Jennie Popp, Kuatbay Bektemirov
69th SWCS International Annual ConferenceJuly 27‐30, 2014Lombard, Illinois
Irrigation storage reservoir
Pumping plant
Irrigation pipeline
Surface drain
Tail-water recovery structure
1.Irrigation reservoir2.Pumping Plant3.Irrigation Pipeline4.Irrigation Land
Leveling5.Embankment6.Surface Drainage 7.Surface Drainage8.Water Flow Control9.Tail-water
Recovery Structure
IntroductionAre groundwater conservation and water quality objectives compatible when using on-farm reservoirs?
IntroductionAre groundwater conservation and water quality objectives compatible when using on-farm reservoirs?
Spatial-dynamic model to determine:• acreage of crops (rice, soybeans, cotton, and corn)• size of reservoirs to maximize profit subject to water
and land availability• condition of the aquifer and runoff pollutants
(nitrogen, phosphorous, and sediment)
1.Craighead2.Poinsett3.Cross4.St. Francis5.Lee6.Phillips7.Desha8.Arkansas9.Monroe10.Prairie11.Woodruff
Counties
Watersheds1.L’Anguille2.Big3.Lower White
Study area 1
11
2
3
4
5
6
7
8
910
12
3
Aquifer thickness, 2012
Sediment export, 2012
P export, 2012
Tons0 - 11 - 22 - 44 - 88 - 21
Feet20 - 4343 - 5959 - 6969 - 7777 - 87
Tons0 - 1313 - 3131 - 6262 - 124124 - 343
19.9 tons2.0 tons66.8 ft.
Land Transition Equations
1
( ) ( 1) ( ) ( ) ( ) ( ), for rice, cotton
( ) ( 1) ( )
ij ij ij ij ij ij
ni i ijj
L t L t FR t DS t C t IS t j
R t R t FR t
Cropland state variablesLij (t) = amount of land in cell i in crop jRi (t) = amount of land in reservoirs
Cropland management variables
FRij (t) = new reservoirsDSij (t) = new non-irrigated soyISij (t) = new irrigated soyCij (t) = new corn
Spatial-Dynamics of Irrigation
1
1
( ) ( ) ( )
(0) ( )( )
(0)
nj ij i ij
i ic pi i n
ijj
w d L t G W t RW t
AQ AQ tG C t c c dp
L
Water state variables:
AQi (t) = amount of groundwater (acre-ft) stored in aquifer
Water management variables:GWi (t) = water from the groundRWi (t) = water from the reservoirGCi (t) = cost of an acre-ft of groundwater
Water demand Water availability
Spatial-Dynamics of Water Quality
1
1 1
( ) ( 1) ( )
( ) ( ) ( )
ni i ij ijj
n nij ij ij ij ijj j
X t X t pc C t
pr FR t ps IS t DS t
Xi (t) = pollutants sediment, phosphorus or nitrogen
pcij = difference in the per-acre pollutant export when a crop type j in cell i switches to corn (soybean, reservoir)
Farm Net Benefits Objective
1 1 1
max : ( ) ( ) ( ) ( ) ( )T m n
r rwt j ij j ij ij i i i
t i jpr y ca L t c FR t c RW t GC t GW t
Subject to: constraints of farmland and water use.
Profit w/o water costs
Reservoir construction cost
Reservoir water pumping cost
Ground water pumping cost
Results
Farmland use by crop
0
50
100
150
200
250
300
350
400
450
500
550
600
650
2012 2022 2042
Crop
land
,Tho
usan
d Ac
res
Year
Rice
Irrigated corn
Irrigated cotton
Irrigated soybeans
Non‐irrigated soybeans
Rice
Irrigated corn
Irrigated cotton
Irrigated soybeans
Non‐irrigated soybeans
With reservoir
Without reservoir
Groundwater use and aquifer level
0%10%20%30%40%50%60%70%80%90%
100%
Annual groundwater use Aquifer
2012
Percentage
2042 Without reservoirs
2042 With reservoirs
Pollutant exports
0
10
20
30
40
50
60
70
0
0.5
1
1.5
2
2.5
3
3.5
4
2012 2022 2042
Thou
sand
Metric
Ton
s
Thou
sand
Metric
Ton
s
AnnualphosphorusexportsAnnualphosphorusexportsAnnualnitrogenexportsAnnualnitrogenexportsAnnualsedimentexportsAnnualsedimentexports
With reservoir Without reservoir
2012, 2022, and 2042 farm profits
Farm profits 2012Without
reservoirsWith
reservoirs2022 2042 2022 2042
Annual farm net returns (millions in 2012$)
111 136 119 150 146
30yr PV farm net return (millions in 2012$)
-- 2,616 2,959
Low end of the policies
0
1
2
3
4
5
6
Groundwater conservationcost ($/acre‐foot)
Sediment conservation cost($/kg Sediment)
$
Cost sharereservoirconstructioncostsSubsidizereservoirpumpingcostsTax ongroundwateruse
Totalmaximumannual load
1
2
12
High end of the policies
0
1
2
3
4
5
6
7
8
Groundwater conservationcost ($/acre‐foot)
Sediment conservation cost($/kg Sediment)
$
Cost sharereservoirconstructioncostsSubsidizereservoirpumpingcostsTax ongroundwateruse
Totalmaximumannual load
1
2
1
2
Reservoir distribution, % acreage in reservoir
With Reservoir, 2042 Sediment export, % of
2012
78.1%7.1%
Percent0 - 55 - 1010 - 1515 - 2020 - 26
Percent0 - 5050 - 100100 - 140140 - 180180 - 204
Conclusions
Use of reservoirs: farm profits rise 13% aquifer levels increase 33% decrease of 30% for phosphorus and sediment
Policy to cost-effectively achieve both conservation goals Subsidize reservoir pumping costs Reservoir construction cost-share