optimal spatial dynamic management

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