performance evaluation and optimization of irrigation canal systems using genetic algorithm

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ECONOMIC SIMULATION AND OPTIMIZATION OF IRRIGATION

WATER IN HUMID REGIONS

Ram N. Acharya

Certificate of Approval:

Neil R. Martin, Jr.

Professor, Agricultural

Economics and Rural Sociology

Gregorys. TraxlerAssociate Professor, Agricultural


L. Upton Hatch, Chair

Professor, Agricultural


F. PntchettDean, Graduate School

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Style manual or journal used: American Journal of Agricultural Economics

Software used: Corel Word Perfect 7.0. GAMS. Lotus Release 5. SAS 6.11 for

Windows. EPIC __________________________________________________________

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VITA

Ram N. Acharya, son of Janardan and Leelawati Acharya, was bom in a remote

village in Nepal, from where he started his journey to reach his ultimate goal- to achieve

a Ph.D. from the land o f opportunity, the United States of America. He finished his

schooling, and tried his hand at Engineering. Two years later, he decided that his career

was else where so he entered the college for business and obtained a degree. Upon

completion, he joined the working population in order to prepare himself for further

education. He then entered Tribhuvan University for his Master’s degree in Economics

and graduated as a gold medalist in the faculty. After graduation, he taught economics in

the Shaker Dev Campus and the Kirtipur Campus of Tribhuban University, Nepal. He

was, then, granted scholarship by Winrock International to pursue his academic career in

Malaysia. He completed his Master’s Degree in Natural Resources and then few months

later arrived at Auburn University, Alabama, as a doctoral student in Agricultural

Economics.

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In the resulting model, rainfall was treated as a stochastic process, which follows

its own historical pattern randomly. This capability to deal with an erratic rainfall

process distinguishes the recursive stochastic linear programming model from other

multi-period programming models. The optimization model was designed to solve a

series of irrigation decisions problem faced by a model farm, which is growing com,

cotton, and peanuts. Different irrigation decision rules were derived for dry and normal

weather conditions. Using a preference scale and the flow data of Chattahoochee river

measured at Columbus, the residual flow that could be used for crop irrigation was

calculated. The results indicated that even if the historical flow could be maintained in

the future, it would not be enough to meet the total irrigation demand in many instances.

The aggregate optimal demand for irrigation water in the Middle Chattahoochee

Sub-Basin was estimated to be 3.211 million gallons per week. The contribution of this

optimal irrigation level to net farm income would be $ 1.175 million per year for dry

years and $ 0.711 million for normal years. Thus the aggregate impact of water shortage,

measured at the optimum use level, would be higher in dry years by $ 0.464 million as

compared to normal years. Since the impact of water scarcity on net farm income is

expected to be much higher in dry years than in normal years, two separate marginal

relationships were estimated. Once the existing supply and weather conditions are

known, these marginal functions can be used to derive the impact o f reduced stream flow

on net farm income. For the Middle Chattahoochee Sub-Basin, the average impact of a

15 percent draw-down in downstream flow on net farm income was calculated to be less

than $3.10 per acre in dry years and $ 0.57 per acre in normal years.

iv

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ACKNOWLEDGMENTS

The author extends genuine appreciation to Dr. Upton Hatch , Dr. Neil R. Martin,

Jr., and Dr. Greg Traxler for their guidance throughout the graduate years. It would not

have been possible to finish this work without their support and confidence. I would also

like to thank God for all the knowledge gained and used during this four year period.

“Knowledge is light to the world and He is the creator of this light.”

Above all, I would like to express earnest appreciation to my wife, Anita and son

Ajju for their understanding and encouragement throughout the stressful years. Without

their love, sacrifices and indefinite support, the work would never have been completed.

This dissertation is dedicated to my father, Janardan Acharya, who taught me to

respect education and believe in its strength.

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TABLE OF CONTENTS

Page

LIST OF TABLES.................................................................................... ix

LIST OF FIGURES.................................................................................. xi

LIST OF MAP S........................................................................................ xiii

INTRODUCTION.................................................................................... I

Methods and Procedures............................................................... 3ACF River Basin........................................................................... 4

The Study Area............................................................................. 7

Objectives ..................................................................................... 11Rational and Significance............................................................. 12

LITERATURE REVIEW ......................................................................... 13

Introduction.................................................................................. 13

Water Scarcity and Sources....... _ ................. 14

Basinwide Water Resource Management Models....................... 15

Plant Water Relationship.............................................................. 18Irrigation Demand Studies ............................................................ 20

Yield Response to W ater .............................................................. 23

Optimal Allocation of Irrigation Water ....................................... 25

RESEARCH METHODOLOGY............................................................. 29

Conceptual Framework ................................................................ 29

Methods and Models.................................................................... 31

The EPIC Model.......................................................................... 32

Recursive Programming.............................................................. 33Recursive Stochastic Linear Programming................................ 36

Specification of the RSLP Model ________ 41

VI



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RESULTS AND DISCUSSION............................................................... 43

Simulation Results........................................................ ,.............. 44

Yield Response Functions........................................................... 45

Marginal Physical Productivity of Water .................................... 51Marginal Value of Irrigation Water.............................................. 54

Dry and Normal Weather Conditions.......................................... 54

Irrigation Decision Rules.............................................................. 57

Optimal Demand for Irrigation Water .............................. 64Aggregate Irrigation Demand....................................................... 67

Historic Flow of Chattahoochee River ........................................ 71

Impact of Water Shortage on Net Farm Income.......................... 75

WATER MANAGEMENT ISSUES........................................... 83

Land Allocation/Cropping Pattern................ 85

Adoption of Water Saving Technologies........................ 86The Impact of Reduction in Stream Flow ....................... 87

SUMMARY AND CONCLUSIONS...................................................... 93

Limitations and Recommendations............................................. 99

REFERENCES.......................................................................................... 101

APPENDIX- 1 .......................................................................................... 107



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LIST OF TABLES

1. Summary of Farming Activities by County in the Study Are a 9

2. Major Crops Grown in 1996...................... 9

3. Population Distribution by County ........................................................ 10

4. Number of Farms, Total Land in Farms, and

Average Farm Size by County and Year .............................................. 10

5. Average Crop Yield and Water Stress Lev els...................................... 46

6. Yield Response Functions for Com, Cotton and Peanut ..................... 50

7. Average Marginal Physical Productivity o f Com, Cotton, and Peanut 52

8. Marginal Value of Irrigation Water by C rops ....................................... 55

9. Ranking of Marginal Value of Irrigation Water by Crops.................... 55

10. Optimal Allocation of Irrigation Under Water Scarcity

(Supply=l acre-inch).......................................................................... 58

11. Optimal Allocation of Irrigation Under Water Scarcity

(Supply=2 acre-inch).— .............................— ................................. 58

12. Optimal Allocation o f Irrigation Under Water Scarcity

(Supply=3 acre-inch).......................................................................... 59

13. Optimal Allocation o f Irrigation Under Excess Water Supply

(Supply=6 acre-inch).......................................................................... 59

14. Optimal Demand for Irrigation Water by Crop and Growth Stage.... 66

15. Total Optimal Demand for Irrigation and Rainfall by Growth Stage 66

viii



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16. Total Soil Moisture Available to the Plants at Different Growth Stages 68

17. Irrigation Demand Estimates for the Middle Chattahoochee

Sub-Basin by C rop .............................................................................. 68

18. Aggregate Irrigation Demand for the Middle Chattahoochee Sub-Basin 70

19. M&I and Irrigation Demand Projections for the ACF

Basin and the Study A re a ................................................................... 70

20. Incidence o f Water Shortage in Meeting Future M&I

and Irrigation Demand (r= 0) ............................................................... 74

21. Incidence o f Water Shortage in Meeting Future M&I

and Irrigation Demand (r= l) ............................................................... 74

22. Expected Incidence o f Water Shortage To Meet M&I

and Irrigation Demand (r=0 )............................................................... 76

23. Expected Incidence o f Water Shortage To Meet M&I

and Irrigation Demand (r = l) ............................................................... 76

24. Summary o f Results from the Optimization Model (RSLP)............... 78

25. Average Net Farm Income and Marginal Impact of Water Scarcity.. 79

26. Aggregate Net Farm Income at Various Supply Levels ..................... 79

27. Scenario: 1 Incidence of Water Shortage in Meeting FutureIrrigation Demand (r=0)...................................................................... 91

28. Scenario: 1 Incidence of Water Shortage in Meeting Future

Irrigation Demand (r= 1 )...................................................................... 91

29. Scenario: 2 Incidence o f Water Shortage in Meeting Future

Irrigation Demand (r=0 )...................................................................... 92

30. Scenario: 2 Incidence of Water Shortage in Meeting Future

Irrigation Demand (r = l) ...................................................................... 92

ix



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LIST OF FIGURES

1. The Recursive Programming M odel ............................ 35

2. Com Yield and Water Stress Levels..................................................... 46

3. Cotton Yield and Water Stress Leve ls.................................................. 47

4. Peanut Yield and Water Stress Le ve ls.................................................. 47

5. AMPP of Irrigation at Various Plant Growth Stage (com).................. 52

6. AMPP of Irrigation at Various Plant Growth Stage (cotton) ............... 53

7. AMPP of Irrigation at Various Plant Growth Stage (peanut)............... 53

8. Marginal Value of Irrigation for Normal Y ear .................................... 56

9. Marginal Value of Irrigation for Dry Years......................................... 56

10. Optimal Allocation of Irrigation in Normal Years

(Suppiy=2 acre-inch)........................................................................... 60

11. Optimal Allocation of Irrigation in Dry Years

(Supply=2 acre-inch) ........................ 60


(Supply=3 acre-inch).......................................................................... 61


(Supply=3 acre-inch).......................................................................... 61


(Supply=6 acre-inch).......................................................................... 62


(Supply=6 acre-inch).......................................................................... 62

x



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16. Optimal Allocation o f Irrigation in Normal Years

(Supply=5 acre-inch).......................................................................... 65


(Supply=5 acre-inch)........................................................................... 65

18. Irrigation & Net Farm Income in Normal Y ears................................ 77

19. Irrigation & Net Farm Income in Dry Years ...................................... 77

20. Net Farm Income in Dry and Normal Y ears....................................... 80

21. Marginal Impact of Irrigation on Farm Income................................. 80

22. Impact o f Irrigation & Weather on Farm Income (Standard Deviation) 82

23. Impact of Water Scarcity on Net Farm Incom e................................. 82



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LIST OF MAPS

1. Apalachicola-Chattahoochee-Flint River Basin..................................... 5

2. Location o f Counties Within the Study Area ......................................... 8



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INTRODUCTION

Water has always been an important factor in determining social and economic

development. Search for new sources of water supply and construction of large dams

have been the dominant water management practice in the past. As the demand for the

fixed water resource is increasing and the possibility o f developing new sources are

becoming scarce, searches for efficient management systems are being initiated.- The

conflict among water user groups in the Alabama-Coosa-Tallapoosa and Apalachicola-

Chattahoochee-Flint (ACF) river basins presents a case of such need for a change in

water sharing rules. A better understanding of temporal and spatial aspects of water

allocation issues will provide a sound starting point for negotiation to resolve water

conflicts. This study examines optimal irrigation strategies under different water scarcity

levels and plausible weather scenarios and estimates the economic impact of irrigation

shortage on net farm income.

The water flowing in a river can be put into different uses at various locations.

Uses that involve withdrawal of water from the stream such as municipal, industrial, and

irrigation reduce flow in the river. Both quantity as well as quality of water available to

downstream users is directly affected by upstream water management decisions. As

water becomes scarce, the conflict between upstream and downstream users and among

competing uses at a particular location within the watershed increases. This increase in

1



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competition among uses and users within and across the geographical location over time

makes it difficult to derive optimal allocation rules. The value of water applied to various

uses at different times and places within the river basin should be known before any

optimal allocation rules can be derived.

This difficulty in deriving an objective value of water, when applied to different

competing uses, has given rise to various alternative approaches such as “conflict

resolution” to resolve basin-wide water allocation problems. This method attempts to

resolve water allocation disputes through various processes which may include

mediation, negotiation, and bargaining (Dinar and Loehman). Basically, this approach

aims to resolve the conflict by bringing all stakeholders together, educating them about

each other’s economic interests, strengths, and weaknesses, and encouraging them to

settle the conflict through consensus (sometimes mediators are used to initiate this

process).

The role of economics in this process, whenever possible, is to provide the value

of the resource applied to its competing uses and users at different times and locations.

This information, the marginal value of resource, provides the economic basis for

deriving optimal allocation rules. Wreck et al. (hereafter referred as Comprehensive

Study) examined the impact of changes in upstream water allocation rules, in the ACT-

ACF river basins, on downstream uses by using long term planning models. The

methodology used in the above study is not capable of handling short term issues such as

drought and floods. Although it is important to know long term prospects for developing

existing resources, short term allocation issues cannot be ignored.



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Other things remaining the same, the value of a resource applied to a production

process depends on its ability to contribute in producing output and the value o f that

output in the market. Unlike in many industrial production processes, the value of

irrigation water depends on various factors including weather conditions and stages of

plant growth. For example, the marginal physical productivity o f irrigation water would

be much higher in flowering and fruit development stage than in other periods (Bruce et

al.). On the other hand, the demand for water would be relatively higher in dry period as

compared to normal weather conditions. These aspects of water demand and productivity

play an important role in short term water allocation decisions.

The methodology, developed in this study, can be used by water use

administrators in making optimal allocation decisions under various weather conditions

and water scarcity levels. Since the value of irrigation applied at different stages of plant

growth is the economic basis for allocation decision making, availability of this

information is expected to provide impetus in resolving the existing conflict among water

user groups in the ACF river basin.

The results obtained from the farm level optimization model are extrapolated to

calculate aggregate demand for irrigation water in the Middle Chattahoochee Sub-basin.

The incidence of water scarcity is estimated using basinwide demand and supply data and

optimal water allocation rules are derived.

Methods and Procedures

A combination o f simulation, optimization, and econometric models are

developed to examine the optimal allocation o f irrigation water under two plausible



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weather scenarios, normal and dry, among three competing crops (peanut, cotton, and

com) grown in the middle Chattahoochee sub-basin. Since both timing and amount of

irrigation have important bearing on crop yield, the relationship between the amount of

irrigation water applied at various plant growth stages and crop yield must be established

for each crop before the optimal allocation of irrigation water can be determined.

The empirical estimation of such relationships requires actual experimental data,

which are not readily available. In the absence of real world data, a biophysical

simulation model, known as Erosion Productivity Impact Calculator (EPIC), is used to

simulate the relationship between various irrigation management practices and crop yield.

The relationship between the amount of soil moisture available to the plants at different

stages of plant growth and final crop yield is specified to be log linear and is estimated by

using the simulated data. The estimated parameters o f the yield response function are

used to develop a Recursive Stochastic Linear Programming (RSLP) model. Then, the

RSLP model is used to determine the optimal irrigation strategies and to estimate the

impact o f water shortage on net farm income.

ACF River Basin

The ACF basin originates in northern Georgia, covers parts of Alabama, Florida,

and Georgia and drains into the Gulf of Mexico (Map 1). The total area drained by this

basin is about 19,800 square miles. Approximately 2.636 million people were living in

this basin in 1990. On average, the daily water withdrawal rate for 1990 was

approximately 2,098 million gallons, of which nearly 86 percent was withdrawn from

surface water sources. About 17 percent of the total withdrawal was consumptively used,



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Map 1. Apalachicola-Chattahoochee-Flint River Basin

produce d with permission of the copyright owner. Further reproduction prohibited withou t permission.


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6

5 percent was exported out of the basin, and 78 percent was returned back to the system.

About 223 million gallon per day (mgd) o f municipal wastewater was generated and

discharged in the ACF basin. The sectoral distribution of surface water withdrawal was

as follows: power generation 60 percent, public supply 24 percent, self-supplied

commercial-industrial uses 12 percent, and agricultural uses 4 percent. Alabama shares

about 2,800 square miles of land area (14 percent), 0.19 million people (7 percent), and

183 million gallon/day (9 percent) o f total water withdrawn from the basin (Marella,

Fanning, and Mooty).

Droughts and floods are the two extreme cases of water supply that impose severe

costs on the economy. During February and March 1990, record flooding occurred at 74

sites, and 46 sites had peak level discharges that exceeded or equaled the 100-year

recurrence interval discharge (Pearman et ai) . The drought of 1980-81 caused a

reduction in power generation, curtailed navigation, increased water level drawdown in

recreational lakes, and imposed restrictions on lawn watering and other uses. During

mid-summer, a lowest flow on record occurred in many streams, much earlier than the

minimums that occurred during past droughts. Discharge measurements of zero flow

were observed at 694 non-recording stream locations in Alabama, Georgia, South

Carolina, and eastern Tennessee during the 1986 drought period. Out of 370 continuous-

record gauging stations, 99 stations experienced new record minimum daily flows in

1986. Moreover, 27 stations had 7-day minimum average flows and 11 stations recorded

90-day minimum flows with a recurrence interval of more than 50 years (Hale, Hopkins,

and Carter).



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Hatch et al. studied farmer’s response to droughts in the Chattahoochee-

Choctawhatchee river basins of Alabama. They observed that water is a limiting resource

for agricultural production in Alabama. They report that supplemental irrigation

increases yield, reduces yield variability, improves output quality, allows double

cropping, and helps in reducing frost damage.

The Study Area

The study area comprises the middle Chattahoochee sub-basin of ACF river basin

(Cataloging Unit Number 03130003), which includes Barbour and Russell counties of

Alabama and Chattahoochee, Muscogee, Quitman, and Stewart counties of Georgia (Map

2). In 1996, the total farmland of these six counties was 361,182 acres and the total

cropped area was 152,120 acres (Table 1). About 37 percent of the total cropped area

was irrigated.

Based on total cropped area, the major crops grown in this sub-basin were

peanuts, cotton, hay, com, and wheat (Table 2). Complete information on irrigation

status o f individual crops is not reported to avoid disclosing data of individual farms.

Based on available data, cotton was the major irrigated crop followed by peanut, com,

and hay. Wheat was not irrigated at all in the 1996 crop year.

There were 276,352 people living in the middle Chattahoochee sub-basin in 1990.

About 84 percent of the population was living in urban areas and the rest in rural areas.

Most of the people of Muscogee county lived in urban area (96.8 percent), while in

Stewart and Quitman counties, there was no urban population (Table 3).



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8

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33*

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30*

GULF OF MEXICO SO MILES

SO KILOMETERS

29*

Map 2. Location of Counties within the Study Area

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9

Table I . Summary o f Fanning Activities by County in the Study Area

Description Barbour RussellMusco

geeChatta

hoochee

Quit

manStewart Total

Total No. 421 213 44 16 24 97 815

Farm Acres 177189 112620 4870 5901 11559 49043 361182

Acres 80496 36513 2006 1677 5870 25558 152120

Crop

LandIrrigated 24654 14127 95 0 321 16850 56047

% 30.63 38.69 4.74 0.00 5.47 65.93 36.84

Source: http://govinfo.kerr.orst.edu/cgi-bin/imagemap/agga2752,138 , Table 1, 8 and

13 for respective counties.

Table 2. Major Crops Grown in 1996

Description Barbour Russell Chatta

hoochee

Quitman Stewart Total

Total 4476.00 789.00 70.00 469.00 1782.00 7586.0

Com Irrigated 492.00 307.71* 23.45* 1176.12* 1999.3

% 10.99 39.00 5.00 66.00 26.4

Total 5953.00 4823.00d

1040.00 11816.0

Cotton Irrigated 925.00 1640.00 686.40* 3251.4

% 15.54 34.00 66.00 27.5

Total 21994.0 2324.00 1390.00 5217.00 30925.0

Peanut Irrigated 993.00 906.36* 69.50* 1628.00 3596.9

% 4.51 39.00 5.00 31.21 11.6

Source: http://govinfo.kerr.orst.edu/cgi-bin/imagemap/agga2752,138, Table 13 for

respective counties. Notes a The ratio between total irrigated and total cropped area was used to estimate

the proportion of irrigated acreage because the irrigation information was not

available for these crops.d Indicates data withheld to avoid disclosing data for individual farms.


http://govinfo.kerr.orst.edu/cgi-bin/imagemap/agga2752,138http://govinfo.kerr.orst.edu/cgi-bin/imagemap/agga2752,138http://govinfo.kerr.orst.edu/cgi-bin/imagemap/agga2752,138http://govinfo.kerr.orst.edu/cgi-bin/imagemap/agga2752,138


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10

Table 3. Population Distribution by County

Description Barbour Russell Chatta

hoocheeMusco

gee

Quit

man

Stewart Total

Total 25417 46860 16934 179278 2209 5654 276352

No. 12378 30318 14614 173541 0 0 230851Urban

% 48.7 64.7 86.3 96.8 0.0 0.0 83.5

No. 13039 16542 2320 5737 2209 5654 45501Rural

% 51.3 35.3 13.7 3.2 100.0 100.0 16.5

Source: U.S. Department of Commerce, Bureau of the Census, 1990 Census of

Population and Housing, Special Tabulations.

Table 4. Number of Farms, Total Land in Farms, and Average Farm Size by County

Description Barbour Russell

Chatta

hoochee

Musco

gee

Quit

manStewart Total

1992 421 213 16 44 24 97 815

Number

of Farm1987 498 276 13 49 25 99 960

1982 587 314 18 49 34 111 1113

Total1992 177189 112620 5901 4870 11559 49043 361182

Area 1987 207906 143568 4268 5304 17655 47913 426614

(acres)1982 222066 141048 5086 11879 23354 67679 471112

Average1992 421 529 369 111 482 506 2418

Farm 1987 417 520 328 108 706 484 2563

Size1982 378 449 283 242 687 610 2649

Source: Agriculture Census - Table 1 County Summary Highlights

(http ://go vinfo.kerr.orst.edu/cgi-bin/ag-list701 -005.ale).

eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission.


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The trend o f the total number of farms, farm acreage, and the average farm size

for the period 1982 to 1992 is reported in Table 4. The total number of farms in this area

consistently decreased for all counties. The total farm acreage has decreased, except for

Chattahoochee county.

The average farm size, however, has moved in both directions. In the case of

Barbour, Russell, and Chattahoochee counties, average farm size is increasing. The

average farm size o f Muscogee and Steward counties decreased substantially in 1987

from its 1982 level and then increased again in 1992. While in the case of Quitman

County, the total area under farm, the number o f farms, and the average farm size are

decreasing over time.

Objectives

This study will attempt to develop optimal irrigation strategies for three

competing crops grown in middle Chattahoochee sub-basin and estimate the marginal

value of supplemental water applied to these crops at different crop growth stages and

weather conditions. In particular, it attempts to fulfill the following objectives:

• simulate various irrigation management practices and associated crop yield for

com, cotton, and peanuts grown in the Middle Chattahoochee Sub-Basin using

EPIC,

• estimate the functional relationship between irrigation water applied at various

growth stages and final crop yield,

• determine optimal irrigation strategies at various levels of water shortages and

growth stages for each crop, and



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• derive policy conclusions that are helpful in addressing basin-wide water

management issues.

Rationale and Significance

During recent droughts in the Southeast U.S., conflict over the allocation o f water

became more contentious. Political and legal conflict is currently proceeding between the

U.S. Army Corps of Engineers and the states of Georgia, Florida and Alabama. Data on

demand and supply o f water are being collected and analyzed for eventual inclusion in a

basin-wide management model under an institutional framework yet to be determined. In

this respect, information on the optimal irrigation strategies and marginal value of water

applied at various stages of crop growth and weather conditions would be helpful in

making basinwide water allocation decisions. This marginal relationship can also be used

to calculate the total value of irrigation water and compare it with other competing uses

under different supply scenarios.



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LITERATURE REVIEW

Introduction

As the twenty-first century approaches, supply of enough water of required

quality to satisfy growing demand is becoming a major challenge for many communities.

The demand for water is increasing over time but the possibility of developing new

sources is becoming more scarce. The cause o f this problem can partly be attributed to

the faulty management approach adopted in the past. Search for new sources of water

supply and construction o f large dams have been the dominant strategy rather than

making better use of existing resources (Winpenny).

Water flowing in a river system is characterized by serial technical externality,

which means that upstream users can affect downstream users but downstream users

cannot impact those upstream (Brooks et al.). Both quantity as well as quality of stream

flow is mainly determined by upstream uses. For example, municipal and irrigation uses

involve withdrawal of water from the stream, which affects both water quality and stream

flow. On the other hand, recreation, hydro-power generation, and navigation are non

consumptive in-stream uses, which may not reduce the flow of water in the river but can

change the quality o f water.

The major uses of water in the middle Chattahoochee sub-basin have been

classified as municipal and industrial, hydro-power generation, recreation, and irrigation

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(Comprehensive Study). Among these uses, whenever a serious shortfall in water supply

is encountered, the municipal and industrial water demand receives first priority. Then,

the remaining water can be allocated among other competing uses based on marginal

conditions.

Water Scarcity and Sources

Water comes from two sources: surface water and groundwater. Surface water

consists of water from rivers, lakes, ponds, and reservoirs that is stored or flows on the

earth's surface. Ground water comes from the bodies o f water stored beneath the earth

known as aquifers. Unlike surface water, ground water is a finite as well as a renewable

resource. It is a finite depletable resource, when the rate of withdrawal exceeds the

natural rate of recharge. For the US as a whole, an annual withdrawal of 400 trillion

gallons is considered to be a renewable resource, while a rate of withdrawal higher than

this amount makes it a finite depletable resource (Council on Environmental Quality).

Irrigation is the largest single user of groundwater resource in the nation, which

accounts for more than 70 percent of the total groundwater use. Use of groundwater is

increasing by double the rate of increase of surface water. About a half million wells are

drilled each year (Henderson et al.). In some regions, groundwater overdraft is

accompanied by increased aquifer salinity. The contamination of groundwater will also

affect the quality o f surface water because they are closely related. About 30 percent of

the stream flow in the US is supplied by ground water (Saliba). Thus, unrestricted

pumping from the aquifer could reduce the stream flow. In particular, the effect of



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excessive withdrawal of groundwater would be chaotic during the growing season when

the stream flow is lower than average.

The consequences of drawdown in stream flow could be serious when it is

accompanied by a severe drought. On the other hand, heavy rainfall may result in

flooding and damage crops. As discussed before, the ACF basin experienced a record

flooding at 74 sites, and 46 sites had peak level discharges that exceeded or equaled the

100-year recurrence interval discharge in 1990 (Pearman et al.).

A severe drought was observed in 1980, which caused a reduction in power

generation, curtailed navigation, increased water level drawdown in recreational lakes,

and imposed restrictions on lawn watering and other uses. A lowest record flow was

experienced in many streams (Hale, Hopkins, and Carter).

At 694 non-recording stream locations of Alabama, Georgia, South Carolina, and

eastern Tennessee, a discharge measurement of zero flow was observed during the 1986

drought period. While in 99 continuous-record gauging station, out of 370, new record

minimum daily flows were observed. Moreover, seven-day minimum average flows

were observed in 27 stations and 11 stations recorded ninety-day minimum flows with a

recurrence interval of more than 50 years (Hale, Hopkins, and Carter).

Basinwide Water Resource Management Models

Since water flowing in a river system is subject to serial technical externalities, a

water allocation scheme that ignores this spatial relationship between upstream and

downstream users and uses is not capable of putting water to its optimal use. To

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address this issue of basinwide water management, many studies have used a

combination of simulation and multiobjective programming models.

The Comprehensive Study, “Basin-wide Management o f Water in the Alabama-

Coosa-Tallapoosa and Apalachicola-Chattahoochee-Flint River Basins” has developed a

simulation model, “Shared Vision Model”, to help decision makers in determining

optimal allocation rules. The data used in this study come from other demand forecast

studies and future supply estimates. Future demand estimates were made for municipal

and industrial (M&I), navigation, agriculture, electric power, recreation, water quality,

and environment by sources. Most agricultural withdrawal of water in the ACF basin

comes from groundwater. As there is a close relationship between the amount of water

withdrawn from an aquifer and the stream flow, this relationship should be quantified

before any effective demand and supply analysis can be started. The Comprehensive

Study used correlation coefficients to quantify this relationship (Wreck et al.).

The Shared Vision Model is expected to provide a broader view on basin-wide

water management issues to different water user groups and policy makers and help them

in resolving the existing conflict on water allocation. This model, however, is not

capable of addressing short term water allocation issues for two reasons. First, it is based

on monthly time step in estimating demand and supply scenarios, which might be very

long for many uses. For example, irrigation decisions, in most cases, can effectively be

made on weekly basis depending on weather condition and soil moisture content. On the

other hand, an hourly decision making might be more appropriate for hydro-power

generation.



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Second, the methods used in estimating the value of water are not capable of

capturing short-term effects o f water scarcity. For example, in case of com production,

the impact of drought would be much higher during tasseling period which lasts less than

a month (ACES Circular ANR-165). On the other hand, a long drought of two to three

weeks might be enough to destroy crop production, if supplemental irrigation is not

applied.

Multiobjective programming models have also been used by many researchers to

determine the optimal allocation of resources at a watershed level. Chang et al. used

compromise programming techniques and multiobjective simplex method to examine the

impact o f various land use patterns on water quality in Tweng-Wen reservoir watershed

system o f Taiwan. Other uses of multiobjective programming models include watershed

management (Goicoechea and Duckstein), regional development, environmental quality

control, and industrial land use (Van and Nijkamp; Das and Haimes), constrained

optimization of limited resources (Glover and Martinson), impact o f land use pattern on

groundwater richarge rate (Ridgley and Giambelluca), and correlation between land use

pattern and lake alteration (Leon and Marini).

As the “Shared Vision Model”, these multiobjective programming studies are

more tuned to long-term resource planning and examine the watershed management

problem in general rather than addressing the short-term water allocation issues. While

the present study focuses on the short-term water allocation problems faced by an

individual production unit and relates them with the basinwide resource management

issues.



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Plant Water Relationship

Water is an essential element of any plant life support system. Plant roots absorb

water from the soil. On the average, a large tree uses 100 to 150 liters of water on a hot

sunny day (Kramer and Kozlowski).

The soil texture, which is determined by the relative percentage of sand, silt, and

clay, affects the water retention capacity of soil, and thus the amount o f water available

for plant use. However, not all moisture contained in the soil is available for plant use.

Plants can effectively absorb water from the soil when the level of moisture contained in

the soil is within the domain o f the permanent wilting point and the field capacity of the

soil (Heady and Hexem).

The permanent wilting point is defined as the level of soil moisture at which the

leaves o f the plants become permanently wilted. While the field capacity is defined as

the amount o f water a soil can hold against the gravity when allowed to drain freely

(Heady and Hexem). A plant can easily absorb water from the soil with moisture at its

field capacity. As plants absorb water, soil moisture content decreases; whereas, soil

tension (the force at which soil particles hold water) increases. This increase in soil

tension makes it difficult for plants to extract water from the soil. At the permanent

wilting point, soil moisture content becomes very low, resulting in lower amount of water

absorbed than the amount lost due to transpiration. Therefore, it is necessary to apply

supplemental water so that a desired level of crop yield can be obtained (Heady and

Hexem).



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Factors such as deep percolation, stages of plant growth and coverage of soil by

the plant, leaf glossiness, geographical location, planting season, and temporary weather

fluctuation affect the total consumptive use of water. Moreover, irrigation can be used as

a means to control soil salinity, to cool plants during hot periods, and to reduce frost

damage during cold periods (James). Part of this water need is supplied through

precipitation. However, the amount o f precipitation is erratic and not sufficient for most

crops. The difference between optimal water level and the water available through

precipitation gives the demand for supplemental water.

Although the daily water requirement of a plant depends on various factors

including locality, plant type, soil conditions, and weather conditions, the impact of a

water shortage on crop yield at some critical stages o f plant growth can be particularly

serious. For example, the daily water requirement of a peanut plant increases with its age

up to 80 days and then starts to decline (Stansell et al.; Rochester et al.). While, in the

case of com, the daily water requirement reaches its peak during the period 50 to 100

days after planting. Moreover, as the amount of soil moisture (water) available to the

plants decreases from its field capacity, the demand for supplemental irrigation increases

until it reaches to the permanent wilting point.

The actual impact o f shortage in soil moisture on crop yield depends primarily on

the stage of plant growth. Field experiments conducted by the experiment stations

indicated that the impact of drought on com at the tasseling period would be much more

serious than at any other period of plant growth (ACES Circular ANR-165 and ANR-531;

Bryant et al.). Moreover, crops may also differ in their ability to withstand droughts.



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Irrigation Demand Studies

The demand for irrigation arises because it enables cultivation in dry soils and

increases productivity. The demand for irrigation water, as the demand for other farm

inputs, is determined by the optimizing behavior of the farmers. A rational farmer will

use irrigation, as long as the marginal benefit o f irrigation water is higher than the cost of

irrigation. Since the marginal productivity o f water decreases as the application of water

increases, keeping all other factors constant, the profit maximizing level of water will be

lower than the yield maximizing level, unless the water is a free good.

As the price of water increases, in the short run, a rational farmer may respond by

reducing the amount of irrigation. Such reduction in irrigation will stress the plants and

reduce crop yield. As water becomes more scarce and costly, adoption o f more efficient

irrigation systems or investment in more efficient irrigation technology may become a

more attractive strategy than allowing increased plant stress. For example, use of drip

irrigation in Arizona made it possible to double the cotton yield by using only half of the

amount of water used in conventional method (furrow irrigation systems).

Caswell and Zilberman reported that the cost of technology is an important factor

affecting growers’ decisions to adopt new water saving techniques. In particular, they

found that a) sprinkler as well as drip irrigation technologies are beneficial for tree crops

like almond and pistachios, b) ground water users are most likely to adopt new

technologies than the surface water users, c) locational factors have differential impact on

the adoption o f new technologies, and d) water pricing policies can be used to induce

farmers to adopt new water saving technologies.

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A farmer can respond in many ways to water cost increases. Depending on

factors such as output price, cost of inputs, soil type, risk, slope, salinity, and climate, he

may shift to a more drought resistant crop, change crop mix, practice crop rotation.

Bryant et al. proposed a methodology to provide decision rules to allocate irrigation

water optimally among the competing crops. They report that under certain conditions,

permanent or temporary abandonment o f low-valued crops to irrigate high-valued crops,

would be the best strategy to deal with the short-term water scarcity problems.

The empirical irrigation demand estimates are limited in various ways. Firstly,

unlike other marketable commodities, reliable data on price and quantity demanded of

irrigation water are not readily available. As a result, various indirect valuation methods

have been used in estimating the demand for irrigation water. Secondly, the value of

water depends on various factors such as crop variety, plant growth stage, soil fertility,

crop, weather, price o f the output and many other biological, environmental, and

geographical factors. Such variability in water values makes it difficult to measure the

value of irrigation water and to compare results from different studies.

Analytical tools such as water response functions, farm crop budgets, linear

programming, quadratic programming, dynamic programming, profit functions, and

many other direct and indirect market valuation methods have been used in estimating the

demand for irrigation water. Moreover, the value of water reflects various measures such

as marginal or average value, individual or mixed crop value, short-run or long-run value,

on-farm or in-stream value.



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Lacewell et al. estimated water value for Texas High Plains based on crop budgets

for 1974. Their estimates of net water value or in-stream value ranges between $15 to

$87 per acre-foot. Willitt et al. (cited in Gibbons) estimated average water values based

on crop budgets o f 1971-74 period for different crops grown in four counties of Arizona

and found it to range between $-7 to $67. Beattie found an in-use marginal value of

water to be $44 acre-foot for the northern and central Ogallala and $20 for the southern

area.

The value of water across various uses is often used as an economic justification

for the regional transfer of water resources. Robert et al. estimated the value of irrigation

water for northern and southern regions of Arkansas. The value o f water applied in rice,

soybean, and cotton production was estimated for loamy and clay soils by region.

Among these three crops, rice grown in clay soil o f northern region produced the highest

value of water. On the average, the value of water for the state was found to be $2.90 per

acre-foot at 1975 prices. This difference in water value was used as a justification for

regional water transfers.

Gibbons used a production function approach to estimate the value of irrigation

water. The marginal value of water at ten percent reduction from the yield maximizing

output level was estimated to range between $36 and $54 per acre-foot for low ($0.51)

and high ($0.76) crop price per pound o f cotton grown in Arizona at 1975 and 1980 crop

prices. Using different efficiency levels o f irrigation, he derived value of water to range

between $61 to $94 per acre-foot for low and high efficiency irrigation.

■- - - - —- _ ___

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Cotton and grain sorghum growers of seven western counties of the High Plains

of Texas experienced a relatively fixed cost of pumping during 1957-72 period and a

sharp increase during 1973-80. Nieswiadomy examined the response of cotton growers

under two scenarios of constant and increasing extraction costs o f groundwater. He

reported that as the cost of pumping increased, farmers were more responsive to changes

in the price of a relatively less water-intensive crop (cotton) than to a change in the price

of a water-intensive crop (grain sorghum). A profit function approach was used to derive

an indirect water demand function. The results of the study showed that pumpage

regulation was not beneficial in Texas High Plains. A sensitivity analysis was performed

to test the Gisser-Sanchez rule. The Gisser-Sanchez rule was found to be useful in

determining the divergence in the time paths of water uses and the percentage difference

in profits but not in determining the difference in nominal profit.

Most o f these studies have estimated the value of water used to irrigate a

particular crop irrespective of irrigation timing, except for Bryant et al. The present

study, however, attempts to estimate the value of a fixed but a continuous flow of water

which is available for crop irrigation at some critical plant growth stage. Depending upon

weather condition, the water available for crop irrigation may or may not be used at a

particular irrigation decision period. However, water not used in a particular decision

period cannot be saved for the future.

Yield Response to Water

The water-yield relationship can be derived by observing the response o f output

as the use of irrigation water increases, keeping other things constant. However,



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empirical estimation o f such water production functions is limited because it is difficult to

obtain reliable data on output associated with different levels of water. Therefore, various

indirect ways of measuring water response functions are used.

Heady and Hexem used various experimental data to estimate water response

functions for different crops. Using a quadratic water response function, they obtained

the following yield-water-fertilizer relationship for com:

Yield = - 10586 + 688.4 W,* + 36.4 N ,* * -10.0 W,2* - 0.08 N,2** + 0.41 W,N,*

R2 = 0.93, F = 100.32

where Y, N, and W denote com yield, nitrogen, and amount of irrigation water,

respectively and **,* denote significant at one and five percent level, respectively.

For this yield response function, the optimal level of nitrogen and irrigation water

will be 347 pounds o f nitrogen and 41.4 acre-inch of water per acre, respectively. This

optimal combination of nitrogen and irrigation water yield 9,985 pounds of com per acre

of land. This procedure can be used to estimate the functional relationship between total

irrigation water and yield. Crop yield is not only a function of the total amount of

irrigation applied but also a function of timing o f irrigation.

Various crop-growth simulation models have been used to estimate water-yield

response functions. Using these simulated water-yield response functions, the optimal

allocation of irrigation water across a growing season is determined (Musser and Tew;

Boggess and Ritchie; Swaney et al.). Many other studies have used water-response

functions in dynamic programming models to find optimal irrigation scheduling.

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analyzed irrigation scheduling using dynamic programming models and found that

irrigation scheduling might produce higher outputs with less irrigation water.

A numerical simulation model, known as Agricultural Field Scale Irrigation

Requirements Simulation (AFSIRS), has been used to estimate irrigation requirements for .

Florida crops, soils, irrigation systems, growing seasons, climate conditions and irrigation

management practices. AFSIRS provides gross as well as net irrigation requirements for

various plant stress levels.

The relationship between the demand for supplemental irrigation and the age of

plant has been found to be nonlinear. For example, the daily water requirements of a

peanut plant increases with its age up to 80 days and then starts to decline (Stansell et al.;

Rochester et al.). In this case, quantity as well as timing of irrigation is important in

determining the value o f supplemental water.

Optimal Allocation o f Irrigation Water

The future supply of surface water is not significantly affected by current

consumption. For surface water, allocational efficiency requires a balance among the

competing users and an allowance for periodic fluctuation. In the case of ground water, if

the withdrawal rate exceeds the natural recharge rate current use affects future

availability. Therefore, an efficient allocation of groundwater delineates a distinct set of

problems.

First, since present consumption affects future availability of groundwater, it

gives rise to a marginal user cost or opportunity cost. Second, the marginal extraction or

pumping cost would rise over time as the water level in the aquifer declines. Third,



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groundwater pumping will stop when the aquifer dries, or the marginal extraction cost

becomes higher than the marginal benefit, or the marginal extraction cost becomes higher

than the cost o f obtaining water from alternative sources. Finally, groundwater might be

over-utilized because it exhibits several common property features.

Factors such as the possibility o f private bargaining solutions, hydrological

conductivity of the aquifer, and Gisser-Sanchez rule; however, may mitigate the problem

of common property exploitation. As argued by Beattie, groundwater in the High Plains

is not seriously subject to depletion by actions o f neighboring pumpers because of limited

lateral movement of aquifer. The Gisser-Sanchez rule states that if the natural recharge

rate and the slope of the demand curve for groundwater are small relative to the area of

the aquifer times storativity, and the groundwater rights are exclusively assigned, then the

welfare loss due to the inter-temporal misallocation of pumping effort is negligible

(Gisser and Sanchez).

Following Burt and Stauber, Bryant et al. (1993) defined crop output as a function

of soil moisture condition at various plant growth stages and used a dynamic optimization

procedure to allocate predetermined number of irrigations between com and sorghum.

Although the numerical optimization procedure, which is used to solve the dynamic

programming models, is ensured to attain global optimum, it becomes unmanageable

when a large number of state and decision variables is involved. In dynamic

programming literature, this problem is known as the “curse of dimensionality” (Bellman

and Dreyfus).

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For this reason, many studies have used linear programming models to determine

the optimal allocation of irrigation water. For example, Bemado et al. and Hardin and

Lacewell used linear programming models to allocate a fixed amount o f irrigation water

available to a farm. Yaron and Dinar used a dynamic programming model to select

optimal irrigation strategies and a linear programming model to determine the optimal

number o f acres to be allocated to each crop. The main limitation of these studies is that

they did not recognize the stochastic nature of plants’ need for supplemental water. The

rainfall and the amount of irrigation water applied are the only two sources o f soil

moisture. Among these two sources, rainfall is a random process, which makes the

demand for irrigation water stochastic. This erratic nature of irrigation demand can be

modeled in linear programming framework by using a recursive stochastic linear

programming (RSLP) procedure.

Day (1963) defined recursive programming as a sequential programming problem

where the parameters o f the current model are functionally related with the solution of

previous models in the sequence. In this process of sequential optimization, current

decisions are made based on past, present, and expected information. The current choices

are irreversibly constrained by past decisions and all future options are determined by

choices made in the past and present decision periods. Applications of RSLP type

models include crop analysis (Kolajo), farm planning (Smith), aquacultural investment

decisions (Tai), peanut policy (Lamb), and peanut production (Curtis).

Kolajo and Smith focused on the strategic nature of decision making under

uncertainty. They introduced stochastic elements in the model by incorporating a series



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of specific historical observations in which expectations were not equal to actual

outcomes for crop prices and yields. Tai, Lamb, and Curtis used probability distribution

functions simulated by biophysical simulation and historical data for yield and price,

respectively. A series of multiple draws were taken from the distribution functions and

optimal values associated with each combinations of yield and prices were estimated.

Since these models were designed to address the multiple year decision problems, the

strategic rather than stochastic characteristic was specified in the RSLP model description

and nomenclature.

This study examines the irrigation decision problem of a model farm faced with a

fixed but continuous flow of water. In this case, both irrigation decisions and irrigation

impacts are highly dependent on rainfall, which is a purely stochastic process. Therefore,

the RSLP modeling framework was adapted from previous studies and used to evaluate

weekly water allocation decisions. Both strategic, as well as, stochastic elements were

present in models used by Kolajo, Smith, Tai, Lamb, and Curtis. The present study,

however, mainly focuses on the stochastic nature of rainfall and reduces the strategic

nature o f sequential decision making to irrigation weeks within a s ingle year.

Accordingly, the present study retains the RSLP identity, but it represents recursive

stochastic linear programming as opposed to recursive strategic linear programming.



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RESEARCH METHODOLOGY

Conceptual Framework

Water flowing in a stream can be put into different uses at various locations. Uses

such as municipal and irrigation water involve withdrawal of water from the stream,

which reduces stream flow. Other uses such as recreation, hydro-power generation, and

navigation are non-consumptive in-stream uses, which may not reduce the flow of water

in the river. Therefore, a basin-wide water allocation model should be flexible enough to

accommodate these features of water uses.

Surface water is a replenishable but depletable resource. An efficient allocation of

this scarce resource would result when the marginal net benefit is equalized for all uses.

Moreover, most sources of surface water have seasonal patterns. They are also observed

to go through various cycles of year-to-year fluctuations. Therefore, a mechanism should

be devised to deal with such seasonal and annual fluctuations in stream flows so that the

cost of abnormal supplies can be minimized (Tietenberg).

Both surface and groundwater sources are being used to supply irrigation water in

the ACF river basin. As discussed in preceding chapter, the conditions required for

optimal allocation o f groundwater are different from those required for surface water

allocation. However, studies have shown that ground and surface waters are closely

related (Saliba). Generally, ground and surface waters are assumed to be perfectly

29

■ - - - - ______ _



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correlated below the fall line. While above this line, the degree of correlation is expected

to be less than perfect. Since the fall line crosses the ACF basin, correlation coefficients

ranging from zero to one have been used by previous studies to examine the impact of

ground water withdrawal on downstream flow (Wreck et al.). Thus, while addressing

basin-wide water allocation issues, the relationship between ground and surface water

should be taken into account.

Crop plants absorb water from the soil moisture available in the root zone. As

plants withdraw water, soil moisture content decreases. On the other hand, a decrease in

moisture content increases soil tension, the force at which soil particles hold water. This

increase in soil tension makes it difficult for plants to extract water from the soil. At

permanent wilting point, the amount of water absorbed by plants from the soil becomes

less than the amount required for plant survival, and eventually plants die. Whereas at

field capacity, which is defined as the amount of water a soil can hold against gravity

when allowed to drain freely, plants can easily absorb water from the soil. Thus, for

optimal crop yield soil moisture condition must be maintained in between permanent

wilting point and field capacity. Rainfall and irrigation are the only two external sources

of soil moisture. In humid regions, such as the Middle Chattahoochee Sub-Basin,

supplemental irrigation is applied, whenever rainfall is not enough to maintain the desired

level of soil moisture.

Factors such as locality, plant type, growth stage, soil conditions, weather

conditions, etc. determine the actual demand for irrigation. Other things remaining the

same, the stage of plant growth and the amount o f soil moisture available to the plant in



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its root zone are the main factors that determine the value of irrigation water. Various

empirical studies have shown that the daily water requirements of crop plants increases

initially, reaches the peak, and then starts to decline. Moreover, the actual impact of

shortage in soil moisture on crop yield depends primarily on the stage o f plant growth

(Stansell et al; Bruce et al.; Rochester et al.).

Methods and Models

Although it is difficult to measure the actual demand, various attempts have been

made to quantify the requirements for irrigation water. Marella, Fanning, and Mooty

measured the demand for irrigation in the ACF basin by multiplying the number of

irrigated acres per crop type by a constant rate of application. In a study "ACT/ACF

River Basins Comprehensive Study: Agricultural Water Demand" conducted by USDA-

SCS in 1994, the Blaney-Criddle method was used to measure consumptive use of water

by plants. Assuming that the amount of water used by crops during their normal growing

season is closely related with mean monthly temperatures and daylight hours, Blaney and

Criddle developed coefficients that can be used to estimate consumptive use of water in

areas for which climatological data are available.

Heady and Hexem provide various functional relationships between irrigation

water and crop yield and estimated demand for irrigation water. Their procedure can be

used to estimate the functional relationship between irrigation water and yield. In most

cases, however, the empirical data required to estimate yield response functions are not

readily available. Moreover, crop yield is not only a function of the amount of irrigation



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but also a function o f the timing of irrigation. In this case, Heady and Hexem procedure

is not of much help.

The biophysical simulation models have also been used to examine the impact of

various irrigation management practices on crop yield (Swaney et al .; Musser and Tew;

Lynne et al.; Boggess and Ritchie). A combination of simulation and optimization

models have been used by others to find optimal irrigation scheduling. For example,

Zavaleta, Lacewell, and Taylor; Harris and Mapp; Yaron and Dinar, McGuckin et al.; and

Bryant et al. used dynamic programming models to analyzed irrigation scheduling and

observed that higher crop yield could be obtained through irrigation scheduling.

The relationship between the demand for supplemental irrigation and the age of

plant has been found to be nonlinear. In other words, the daily water requirements o f a

plant increases with its age up to certain growth stage and then starts to decline (Stansell

et al.; Bruce et al.; Rochester et al.; and Bryant et al.). In this case, quantity as well as

timing of irrigation is important in determining the value of supplemental water. Though

the estimation procedures discussed above enable us to quantify irrigation requirements

for optimal growth o f plants, none of them provide an appropriate methodology

demanded by the present study.

The EPIC Model

The EPIC model, which was originally developed to examine the impact o f tillage

practices on soil erosion, can be used to simulate the impact of various water

management practices on yield under different biophysical environments (Williams et



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al.). This model is capable of generating daily weather and other biophysical parameters

required to estimate water response functions for major competing crops.

Bryant et al. (1992) used the EPIC model to simulate yield response o f com to

soil water in the southern Texas High Plains. They used actual experimental data to

validate the simulation results and found that simulated yield explained up to 86 percent

of the variation in actual yield. Cabelguennne, Jones, and Williams used field data from

Toulouse, France, to calibrate the simulated results and concluded that EPIC can be used

to determine the optimal irrigation strategies.

Recursive Programming

In a classical-neoclassical theoretical framework, an economic agent is assumed to

behave rationally. Rationality implies that an agent is always capable of making the best

choice among available alternatives. In other words, given the level of resource

endowment, goals, and environment faced by the agent, his actions can be represented as

a solution to an optimization problem. This characterization of the economic man

imposes a strong restriction on his behavior. However, Simon observed that, by nature,

humans are not optimizing agents. At best, they are locally optimizing because resources

available to them, in terms of computational power, memory, etc., are limited. This

boundedness in each individual’s resource endowment may result in imperfect behavior,

which gives rise to bounded rather than perfect rationality (Good; Simon; Doyle; Russell

and Wefald; Zilberstein).

An agent’s expectations may not be realized because perception and cognition are

not perfect. Moreover, due to bounded rationality, agents are likely to make inconsistent



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decisions. Day (1983) observed that individuals are imperfect decision makers. He also

maintained that even if the external environment remains unchanged, agents consistently

attempt to improve their status by enhancing decisions. Inconsistent decisions that are

based on faulty anticipation are likely to lead to regrets rather than satisfaction. In this

case, conventional optimization procedures that are based on the assumption of rationality

are not entirely adequate.

Day (1983) contended that these facts of reality should be modeled as a dynamic

adaptive process, where the agent responds to its own internal conditions and to the

changes in the external environment. In this dynamic system, actions taken by an agent

affect both external environment, as well as, his own internal conditions. Thus, both

agents and environment receive feedback from each other. In this sense, the economy is

assumed to be composed of interactive adaptive processes.

Day (1978) proposed a recursive programming procedure to model the dynamic

behavior o f boundedly rational agents, who interact with system through feedback

mechanisms. In this procedure, a dynamic multi-period decision problem is broken down

into a series of recursively connected local optimization problems. The solution o f each

individual optimization problem satisfies certain “optimality properties”. “The sequence

as a whole need not and in general will not” satisfy the principle of optimality (Day, p.

10).

Day (1978) defined recursive programming as a dynamic system, which is

composed of three elements known as data (6,), optimization (Tj), and feedback (&,). He

named these components “operators”. The data operator, 6„ specifies the relationship

~ - ____



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between the parameters of objective function and the resource constraints. The

optimization component, ¥ t, defines the kinship among choice variables associated with

objective function, resource constraints, and other parameters. While the feedback

mechanism, 5)„ determines how the arguments of succeeding stages (Pt+I), such as state

(St+I), data (6t+1), and optimal decision variables (Yt+l), are functionally related with then-

respective counterparts in current period (P,). Day (1978) used the following diagram to

demonstrate the interaction among these three components o f recursive programming

\

Initial Ofm prate / ^ . Optimizingcond itions (S,) w * Datum O p tim iz e Vector

and e x og e no u s * " C M ------------ -------------

var iables (e,) ^ ”

Feedback

(&t)

Figure 1. The Recursive Programming Model.Source: Day, 1978.

In this recursive programming framework, first of all, the data set required for

optimization is generated from the existing initial conditions and then the optimization

problem is solved. Since both the optimal solution obtained in the first stage, as well as,



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other external factors affect the information transferring to the next stage, the data set is

regenerated by incorporating information from the last stage (feedback).

The information contained in Diagram 1 can also be utilized to compare and

contrast recursive programming methods with other dynamic models such as dynamic

programming and optimal control theory. Given the feedback mechanism (


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determining optimal allocation of irrigation water. In terms of diagram 1, the current

RSLP model differs from recursive programming in two ways. First, the RSLP model

accounts for stochastic nature of

performance evaluation and optimization of irrigation canal systems using genetic algorithm

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