IMPACTS OF SALINIZATION IN LAND: AN ARIZONA CASE Maria Irles A

IMPACTS OF SALINIZATION IN LAND: AN ARIZONA CASE Maria Irles A

ECONOMIC

IMPACTS OF SALINIZATION IN

IRRIGATED

AGRICULTURAL

LAND: AN ARIZONA CASE

STUDY by

Maria Irles

Mayorga

A

Thesis Submitted to

the

Faculty

of the

SCHOOL

OF

RENEWABLE NATURAL RESOURCES

In Partial

Fulfillment

of the

Requirements

for the

Degree

of

DOCTOR

OF

PHILOSOPHY

WITH

A MAJOR IN

WATERSHED

MANAGEMENT

In the

Graduate College

THE UNIVERSITY OF ARIZONA

1988

THE UNIVERSITY OF ARIZONA

GRADUATE COLLEGE

As members of the Final Examination Committee, we certify that we have read the dissertation prepared by

Maria

Irles

O. Mayorga entitled

Economic Impacts of

Salinization in Irrigated Agricultural Lands:

An Arizona Case Study.

and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of

Doctor of Philosophy

(

n

-r

eje./L-

Dat

Date

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0

/ 9S(

S

i

?

/11(

e

Date

Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate

College.

I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation require

/ ht.

1

,,/

Dissertation

Dir tor

'ilis

.

.sert tion COLDIrector'

STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the

University of Arizona and is deposited in the University

Library to be made available to borrowers under rules of the

Library.

Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when is his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED:

/A

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1

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a/LA:a t.A.

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M 041 onc_

3

4

ACKNOWLEDGMENTS

Special thanks are due to Dr. Peter F. Ffolliott and

Dr. Roger Fox as co-directors of my dissertation. Thanks also to the other members of my committee, Dr. Martin Fogel and Dr. Gordon Lehman, and Dr. Paul Krausman as the representant of the Graduate College. Apprecciation is extended to Dr. John Thames, Dr. Malcolm Zwolinski and Mrs. Mary

Soltero for their support during the courses.

Thanks to Dr. Keith Knapp, Celso Romanel, Dr. Timothy

Finan, Mariano Hernandez and Marcos Menezes for their help with the computer models. Thanks also goes to Dr. Thomas

Tucker and Dr. James Watson for their support in providing the data and all information necessary for my research.

To Dr. Tarquinio Prisco, Prof. Faustino A. Sobrinho,

Prof. Antonio Albuquerque, Dr. Ahmad Saeed Khan, Universidade Federal do Ceara and Coordenacao de Pessoal de Nivel Superior, deserve thanks for their support in my coming to the

University of Arizona. I would like to express my appreciation to Dr. Vicente Lopes, Dr. Maria Nascimento, Dr.

Moises S. Leao, Dr. Everaldo Porto, Hilton Gomes, Reinaldo

Gomide, Antonio Fernando Guerra, Antonio Sabino, Alzira

Duncan, Ademilde Cabral, Mrs. Dolly Murray and Dr. Burris

Duncan for their assistance.

Special gratitude is expressed to my parents, my relatives, my husband, Dario, and my sons, Fernando and Rodrigo, for their encouragement and their lovely assistance.

5

TABLE OF CONTENTS

Page

8 LIST OF ILLUSTRATIONS

LIST OF TABLES

10

12 ABSTRACT

CHAPTER

I. INTRODUCTION

III.

Objectives of this Study

Literature Review

THEORITICAL FORMULATION OF THE FRAME OF ANALYSIS 25

25 Water Availability

Water Requirement, Water Quality and

Crop Yield.

Water Requirement

.

Irrigation Efficiency

Water Quality and Crop Yield .

Total Salt Content

Sodicity Hazard

Specific Ion Toxicity Hazard

Choride and Sodium Hazard

Boron Hazard

Other Minor Constituents

Economic Theory of Production

The Factor-Product Relationship. . .

The Factor-Factor Relationship . . .

Marginal and Average Physical Product

Elasticity of Production

Isoquant

Rate of Technical Substituion.

Isocust-Line

40

40

41

42

43

43

46

47

50

50

36

37

40

40

28

28

33

35

DESCRIPTION OF THE STUDY AREA: MARICOPA

COUNTY

The Resource Base

Water Availability and Water Rights.

Water Quality for Irrigation

52

54

56

59

14

16

17

6

TABLE OF CONTENTS-Continued

IV.

Page

Land Resource

Description of the Irrigation Districts in Maricopa County

Salt River Project (SRP)

Harquahala Valley Irrigation District

(HVID)

Maricopa County Municipal Water

60

63

64

65

Convervation District #1

McMicken Irrigation District (MID). .

Queen Creek Irrigation District . . .

Roosevelt Irrigation District

66

66

67

68

Roosevelt Water Conservation District 69

Tonopah Irrigation District

70

Buckeye Water Conservation and Drainage

District

The Cotton Story

Cotton Management Practices

70

71

75

MATERIAL AND METHODS

81

The Data

Costs and Return

Net Return Over Variable Costs

Costs of Production

Cost of Pumping Groundwater . .

Operation Costs

Ownership Costs

Model for Tracing Salt Distribution in the Soil

Empirical Application of the Model .

Crop-Production Model

Economic Evaluation

Profit Function

86

86

86

Best Combination of Water Quantity and Quality in the Short-Run .

The Long-Run Optimization

97

105

Statistical Analysis

A Dynamic Programming Model

Simulation of the Dynamic Programming

105

106

88

90

91

95

95

81

85

85

85

Model 107

Description of the Constraints. . . 111

Description of a Risk Situation . . 112

Cost-Benefit Analysis 114

Calculation of Project Worth

Sensitivity Analysis

114

115

Block-Diagram Presentation: An Overview 116

TABLE OF CONTENTS-Continued

Page

V.

RESULTS OF THE ANALYSIS

REFERENCES

118

Application of

Bresler's

Model 119

Application of the Crop-Production Model.

119

Average Productivity and Marginal

Productivity

122

Best Combination Among the Inputs

.

Application of the Dynamic Programming

Model

123

125

VI.

SUMMARY AND CONCLUSIONS

APPENDIX A: SYMBOLS AND ABBREVIATIONS

APPENDIX

B:

137

143

APPENDIX C:

DATA FOR THE SOIL SALINITY RELATION AND

CROP WATER PRODUCTION FUNCTION

RESULTS OF THE QUADRATIC PRODUCTION

FUNCTION

145

148

150

8

LIST OF ILLUSTRATIONS

Figure

1.

Divisions for Relative Salt Tolerance

Ratings of Agricultural Crops

( Maas, 1984 )

2.

Total Physical Product Curve for Total Crop

Yield and Water Quantity (Hypothetical).

3 Relationship Between Total Crop Yield and

Water Quality (Hypothetical)

4.

Production Surface Relating Total Crop Yield to Water Quantity and Water Quality

5.

Classical Three-Stage Production Function and Marginal and Average Curves - Single

Factor Variable

.

6.

Solution to the Factor-Factor Decision Using

Isoquants and isocosts (Hypothetical)

7.

Map of the State of Arizona

8.

Distribution of Land in the Salt River Project

Region, Maricopa County, Arizona

9.

Salt Tolerance of Selected Crops (Bernstein,

1964)

10.

Location of University of Arizona Maricopa

Agricultural Center

11.

The Steady-State Profile of Soil Salinity. .

12.

Solution to the Factor-Product Decision Using a Total Physical Product Curve and a Break-

Even Line (Hypothetical)

Page

38

44

44

45

48

49

53

62

78

83

92

98

13.

Solution to the Best Combination Decision

Using Isoquant and Isocost (Hypothetical). . . 100

14. Solution to the Best Combination Decision

Using Iso-Salinity Curve and Isocost

(Hypothetical) 103

9

LIST OF ILLUSTRATIONS-Continued

Figure

15.

Value of Marginal Revenue Productivity .

16.

A Generalized Block-Diagram Presentation of an Input-Output System for the Dynamic

Programming Model

Page

113

117

1

0

LIST OF TABLES

Tables

Page

1.

Volume of Water in the Hydrosphere

2.

Consumptive Use of Water for Major Crops.

Mesa & Tempe, Arizona

26

30

3.

Estimated Amounts of Groundwater Potentially

Available and Actual Average Surface Water

Use by Irrigation Districts and by Source of Water, Maricopa County, Arizona

(Acre-feet) Average Amounts from 1968-1981. 57

4.

Guidelines for Interpretation of Water Quality for Irrigation

61

5.

United States Cash Receipts from Crops, 1910-1980 73

6.

Arizona Cash Receipts from Crops, 1965-1985. .

7.

Summary of the Number of Samples Collected in the

Cotton Experiment. Maricopa

8.

Cost of one Acre-Foot of Water for Different Lift and Energy Sources in Maricopa County. Arizona,

1985

74

84

87

9.

Operation Costs to Producing an Acre of Cotton with Drip Irrigation. (excluding water and nitrogen costs) in Maricopa County,1985 . .

10.

Ownership Costs to Producing an Acre of Cotton in Maricopa County. 1985

87

89

11.

Estimated Yield Response Function and Soil

Salinity Relation for Cotton

120

12.

Marginal and Average Physical Productivities for the Cotton Response Function

124

13. Marginal and Average Physical Productivities for the Soil Salinity Relation 124

14. Marginal Rate of Substitution and the Ratio of

Prices for the Yield Response Function . . . 126

11

LIST OF TABLES-Continued

Table

15.

Marginal Rate of Substitution and the Ratio of Prices for the Soil Salinity Relation .

16.

Simulation of the Optimal Decision Rule for

Cotton Irrigated with Two Different Sources of Water (good and medium Quality)

17.

Simulation of the Optimal Decision Rule for

Cotton Irrigated with Two Different Sources of Water (good and poor quality)

Page

. 126

129

130

18.

Simulation of the Optimal Decision Rule for

Cotton Irrigated with Two Different Sources of Water (medium and poor quality)

19.

Time Paths for Soil Salinity

20.

Net Present Value Analysis for Cotton in

Maricopa County, 1985 ($1.00)

21. Sensitivity Analysis of Net Present Value for Cotton in

Maricopa County, 1985 ($1.00) .

131

133

134

136

12

ABSTRACT

The dynamics of salt accumulation in the soil over time is one of major important information input needed for decision-making in regard to irrigate with saline water. As all waters contain some dissolved salts, during the irrigation these salts tend to concentrate in the soil causing depressed plant growth. Saline irrigation water, low soil permeability, inadequate drainage conditions, low rainfall and poor irrigation management all contribute to the tendency of salt accumulation in the soil. The principal salt accumulation problem of economic importance arises when non-saline soils become saline as result of irrigation.

The dynamics of salt accumulation in this study, is based on the model for tracing salt distribution in the soil affected by the quantity and quality of irrigation water, amount of nitrogen and initial soil salinity.

To verify the model for tracing salt distribution in the soil and to statistically estimate a crop-production function and soil salinity relation, agronomic data were used from field experiment conducted at the

University of Arizona, Maricopa Agricultural Center (MAC), during the 1985 growing season and that utilized cotton variety Delta Pine 61.

13

From the point of view of the response functions and salt accumulation in the soil, many assumptions were made before formulating the models. Results show that (1) no conclusions could be drawn with respect to the model of salt accumulation in the soil, (2) in the case of yield production function and soil salinity relation, the water quantity coeffient had an absolute value greater than one,

(3) water quality and nitrogen coefficients had an absolute value less than one, (4) initial soil salinity coefficient had negative value, (5) looking for the best combination amoung the variables inputs, the marginal rate of substitution was greater than the ratio of prices, (6) the time path for soil salinity converge to a steady state conditions, and (7) the profitability of cotton irrigated with drip system is sensitive to yield increases and increases in the price of cotton.

CHAPTER 1

INTRODUCTION

The importance of irrigation in the world is rapidly increasing. Although it is practised on a large scale, mainly in arid and semi-arid areas where a large proportion of the world's population resides, supplementary irrigation is becoming popular in humid regions as well (Framji, 1976).

Managers of these irrigated lands face problems in coping with salinity in irrigation water. All irrigation waters contain some dissolved constituents. Because of the presence of these constituents, the application of irrigation waters to soils may markedly alter their properties for the growth of plants. The changes in soil properties which take place upon irrigation can be either beneficial or detrimental, depending upon the composition and concentration of the dissolved constituents in the water and the original characteristics of the soil.

Sometimes, the application of water results in the eventual correction of undesirable conditions originally present in soils. However, irrigation water often has an adverse effect on soil continued use of properties and productivity. The irrigation water has necessitated the abandonment of formerly productive soils in many parts of the world. It is estimated that one third of the world irrigated agriculture is affected by salinity. West Pakistan with about

100,000 acres are going out of production per year. India with

15 million acres and Iran with 60 million acres have gone completely out of production because of salt-affected by salinity (Evans 1974, p. 153).

Theprospects for the future suggest that the problems related to salinity in arid and semi-arid regions will continue or even increase. Australia, with a recent history of irrigation, now finds problems developing due to salinity. In the U.S.S.R., the province of Uzbekistan, a major irrigated cotton-producing region suffers from soil salinization.

14

The United States has a modern irrigation history of about ,100 years. The U.S. Regional Salinity Laboratory estimates that 28% of the irrigated lands in the seventeen western states suffer depressed crop yields because of salinity. The essence of the salinity problem stems from the fact that practically all irrigation waters contain some amount of dissolved salts. During irrigation, these concentrate in the soil, unless rainfall. Saline irrigation they are salts tend to leached by water, low soil permeability, inadequate drainage conditions, low rainfall and poor

irrigation management all contribute to the tendency of salt to accumulate in soils which, in turn, adversely affects crop growth conditions and yield levels.

The principal salt problem of economic importance arises when previously non-saline soils become saline as a result of irrigation. It is, therefore, of foremost importance thatwhennewirrigationisintroduced,measures safeguarding against the possibilities of salinization be adopted from the very beginning.

Agricultural production under these conditions represents one aspect of planning in the development of a water resource. Thus, a broad systems viewpoint and longterm perspectives are absolutely essential to the rational planning of solutions to salinity problems.

Objectives of this Study

15

The overall objective of this study was to investigate the dynamics of salt accumulation in the soil over time as affected by the quantity and quality of irrigation water, amount of nitrogen and initial soil salinity. Empirical analysis of the problem is based on experimental data for cotton production in Maricopa County, Arizona. The dynamics of salt accumulation is based on the model for tracing salt distribution in the soil suggested by Bresler. .cp 6

The specific objectives were:

( 1 ) tocalculate the salt distribution in the soil profile over a number of soil layers as a result of several irrigations;

( 2 ) to calculate the best combination of water quality and quantity in the short-run and the long-run, within the options of the research;

( 3 ) to analyse the irrigation practices with the purpgse of optimizing the use of water resources of varying salinity levels; and

( 4) to conduct cost-benefit analysis fordifferent state and decision variables.

Literature Review

Dynamic programming is a mathematical technique that is applicable to many types of problems such as in physics, engineering, economics, biology, and operations research.

The dynamic programming approach uses the principleof optimality

(Belman and Kalaba, 1965) which started with Bellman in 1957.

The economic literature dealing with the use of dynamic programming for optimal scheduling of irrigation with saline water is new and limited, but there is extensive work on the physical relationships between crop yield and variable inputs such as water quantity, water quality and nitrogen. A thorough review of dynamic programming considerations necessary for assessing the effects of salinity on irrigated agriculture is presented by Dinar and

Knapp (1986), Knapp (1984);

Yaron et al. (1980); and Yaron and Olian (1973). With the aid of a linear programming model, these paperspresent an economic analysis of irrigation with saline water over a period of time.

Dinar and Knapp (1986) estimated a crop-production function for alfalfa in southern Arizona and cotton in Lost

Hills,California. The purpose of thispaperwasto relate crop yield and salt accumulation in the soil to water quantity, water salinity and initial soil salinity. They incorporated the estimated functions into the dynamic programming model to determine optimal water applications for different levels of initial soil salinities and crop and water prices. The model assumed two different sources of good and poor. Under the irrigation water, relatively optimal decision rules it is not feasible to use poor water quality.

For cotton, water quantities increase as initial soil salinity levels increase.

In the case of alfalfa,the results were unexpected. Increases in the price ofcotton and/or water do not significantly change the decision rules.

Knapp (1984), assuming steady-state salinity conditions for navel orange crops in two regions of California, estimated the profit-maximization of water quantity, given the choice of crop and water quality, taking into account the dynamics of salt accumulation over time. He adopted different irrigation scheduling policies, twenty soil layers and two diferrent water prices in each region. He concluded that in many cases enough water is applied to maintain maximum yields.

Economic theory as water price increases.

suggests that water quantity decline

Yaron et al. (1980) used a dynamics programming model to estimate the optimal scheduling of irrigation with water of varying salinity and soil salinity for sorghum in the semiarid area of Gilat, Israel. The results presented by these authors suggest several policy rules for decision- makers: (1)

16

frequent applications of small quantities of water are preferable to application of large quantities at extended intervals; (2) under relatively high saline conditions, an extra amount of irrigation water for leaching the soils is generally justified at the beginning of the growing season; and (3) under relatively low saline conditions, it is worthwhile to extend the irrigation over a longer period, as compared to the high salinity affected situations.

Yaron and Olian (1973) also used a dynamic programming model with Markov chains to analyze the optimal quantity of water for soil leaching of a single perennial crop. The economic significance of the model and the results which may be derived through its use are on two levels, the farm level and regional water resource development.

Extensive review of economic analysis of crop- water productions functions over a period of time, have been .pa

presented by Dinar et al. (1985); Feinerman and Yaron (1983);

Moore (1981); and Moore (1972).

Dinar et al. (1985) in a long-run economic model, estimated a crop-water production function, assuming steadystate conditions,to investigate the combined effects of salinity, irrigation non-uniformity and different drainage requirements at field scale for corn and cotton. Optimum applied water and associated profits, yield and drainage volumes were computed for each crop. Their results indicated that the type of drainage disposal system affects the optimal values of applied water, profits,yield, and drainage volumes, except for uniform water application and non-saline irrigation water. The long-run results revealed that, under saline conditions and/or different drainage disposal system, a sensitive crop such as corn is not profitable and is taken out of production.

Feinerman and Yaron (1983 ) used linear programming models, deterministic in the short-run and stochastic in the long-run, to analyze the complex relationship involved in irrigation with water of varying salinity concentrations and the optimization of their use within a framework of a single farm. The empirical application of the model is based on data for a Kibutz in southern Israel. The irrigation season was defined as one year and the farm had three water sources of different quantities and qualities. The cropping alternatives of the farm were potatoes, carrots, cotton and a mature grapefruit grove; The results provide priorities in the allocation of water of varying salinity levels and empirical estimates of the shadow prices and the rates of substitution between the limited resources.

Moore (1981) analyzed in individualfarm changes the effects

17

inthequality and quantity dimensionsofthewater supply, using a case study of the Imperial Valley of California. In this study, he concluded that declining water quality has a negative effect on yield.

Other papers, such as Feinerman et al. (1984); Feinerman et al. (1983); Boster (1976); Moore et al.

(1974); Bresler and

Yaron (1972); Yaron and Bresler (1970) and Bresler (1967), present the same relationships but in a short run framework.

Feinerman et al. (1984) estimated the effects of irrigation water salinity and uniformity of infiltrated water on average crop yield. They assumed steady-state and transient salinity conditions to investigate the economically optimal water applications and profits for corn. Economically, optimal water quantity and profits depend on water prices, salt concentration and uniformity of infiltrated water.

Feinerman et al. (1983) estimated a crop- water production function with non-uniform water infiltration.

These authors derived the effects of non- uniformity using two production functions that differ in terms of the sensitivity of yield to application of water greater than that needed to achieve maximum yield. They concluded that where crop yield is sensitive to excess water, levels of productivity and optimal water application are lower in non-uniform fields than in uniform ones. On the other hand, if crop yield is not sensitive to excess water, profits depend on the water and crop prices.

Boster (1976) applied a mathematical programming model to study the economic impacts of introducing CAP water into Pinal

County, Arizona, for use in irrigated agriculture. The techniques developed have broad application to similar water resource projects involving the conjunctive use of multiple water sources of different salinity levels. The results present an increase in salinity caused by the of CAP water.

importation

Some papers, such as

Feinerman et al. (1982); Yaron et al. (1972); and Shalhevet and Reiniger (1964), present an agronomic analysis of crop production function but do not take into account the economic effects of salinity in irrigation water.

'A few papers, such as Sampath et al. (1986); Letey et al. (1983); Kelly (1981); Ayer and Hoyt (1981); Stearns (1980);

Hexem and Heady (1978); and Maas and Hoffman (1977) relate the economic analysis of yield as a function of water quantity and non-water inputs, but they do not take into account the the effects of water quality.

Ayer and Hoyt (1981) estimated crop-production functions

18

19 and provided an economic analysis based on four of Arizona's most important crops - - - cotton, wheat, sorghum and alfalfa -

- - with the goal of helping both those who conservation policy and private consultants management services to irrigated farmers.

formulate water who offer water

Moore et al. (1974) and Ayer and Hoyt (1979), both using production functions, estimated the elasticity of demand for irrigation water. In the former study, they estimated yield as a function of water quality and supply of irrrigation water, while the second approach used only water quantity and non-water inputs in crop response.

They are identical in their results, suggesting that the pricing mechanism will have no effect in the decrease of water use.

Jurinak and Wagenet (1981) studied the interactive effects of soil fertility and salinity that are of major concerns in arid and semiarid regions. They concluded that although it was impossible to generalize the effects of salts and fertilizers on crop yield, it can be stated that in most cases moderate levels of soil salinity can be compensated by increased fertilization, so long as the salinity level is not excessively high nor the crop particularly salt-sensitive. The exact nature of crop response, however, depends greatly on crop type, fertilizer .pa form and quality, soil type, and irrigation water quality and soil salinity.

This reseaarch will be based on the dynamic programming method proposed by Dinar and Knapp (1986), Knapp (1984), Yaron et al.

(1980), and Yaron and Olian (1970).

It is a comprehensive approach which takes into account the dynamics of salt accumulation in the soil, thus permitting a closer representation of the actual field behavior.

Inthe recent past emphasis was placed on both linear programming and marginal analysis techniques, but their disadvantage is that they are static models and are are not abletorepresent changes over time.

Given today's computational resources the dynamics analysis is fast becoming the preferred approach of researches working in natural resources as well as in any other field involving time depend

14

CHAPTER 1

INTRODUCTION

The importance of irrigation in the world is rapidly increasing. Although it is practised on a large scale, mainly in arid and semi-arid areas where a large proportion of the world's population resides, supplementary irrigation is becoming popular in humid regions as well (Framji,

1976). Managers of these irrigated lands face problems in coping with salinity in irrigation water. All irrigation waters contain some dissolved constituents. Because of the presence of these constituents, the application of irrigation waters to soils may markedly alter their properties for the growth of plants. The changes in soil properties which take place upon irrigation can be either beneficial or detrimental, depending upon the composition and concentration of the dissolved constituents in the water and the original characteristics of the soil.

Sometimes, the application of water results in the eventual correction of undesirable conditions originally present in soils. However, irrigation water often has an adverse effect on soil properties and productivity. The continued use of irrigation water has necessitated the abandonment of formerly productive soils in many parts of the world. It is estimated that one third of the world irrigated agriculture is affected by salinity. West

15

Pakistan with about 100,000 acres are going out of production per year. India with 15 million acres and Iran with 60 million acres have gone completely out of production because of salt-affected by salinity (Evans 1974, p. 153).

The prospects for the future suggest that the problems related to salinity in arid and semi-arid regions will continue or even increase. Australia, with a recent history of irrigation, now finds problems developing due to salinity. In the U.S.S.R., the province of Uzbekistan, a major irrigated cotton-producing region suffers from soil salinizat ion.

The United States has a modern irrigation history of about 100 years. The U.S. Regional Salinity Laboratory estimates that 28% of the irrigated lands in the seventeen western states suffer depressed crop yields because of salinity. The essence of the salinity problem stems from the fact that practically all irrigation waters contain some amount of dissolved salts. During irrigation, these salts tend to concentrate in the soil, unless they are leached by rainfall. Saline irrigation water, low soil permeability, inadequate drainage conditions, low rainfall and poor irrigation management all contribute to the tendency of salt to accumulate in soils which, in turn, adversely affects crop growth conditions and yield levels.

16

The principal salt problem of economic importance arises when previously non-saline soils become saline as a result of irrigation. It is, therefore, of foremost importance that when new irrigation is introduced, measures safeguarding against the possibilities of salinization be adopted from the very beginning.

Agricultural production under these conditions represents one aspect of planning in the development of a water resource. Thus, a broad systems viewpoint and longterm perspectives are absolutely essential to the rational planning of solutions to salinity problems.

Objectives of this Study

The overall objective of this study was to investigate the dynamics of salt accumulation in the soil over time as affected by the quantity and quality of irrigation water, amount of nitrogen and initial soil salinity. Empirical analysis of the problem is based on experimental data for cotton production in Maricopa County, Arizona. The dynamics of salt accumulation is based on the model for tracing salt distribution in the soil suggested by Bresler.

The specific objectives were:

( 1 ) to calculate the salt distribution in the soil profile over a number of soil layers as a result of several irrigations;

17

( 2 ) to calculate the best combination of water quality and quantity in the short-run and the long-run, within the options of the research;

( 3 ) to analyse the irrigation practices with the purpose of optimizing the use of water resources of varying salinity levels; and

( 4 ) to conduct cost-benefit analysis for different state and decision variables.

Literature Review

Dynamic programming is a mathematical technique that is applicable to many types of problems such as in physics, engineering, economics, biology, and operations research.

The dynamic programming approach uses the principleof optimality (Belman and Kalaba, 1965) which started with

Bellman in 1957.

The economic literature dealing with the use of dynamic programming for optimal scheduling of irrigation with saline water is new and limited, but there is extensive work on the physical relationships between crop yield and variable inputs such as water quantity, water quality and nitrogen. A thorough review of dynamic programming considerations necessary for assessing the effects of salinity on irrigated agriculture is presented by Dinar and

Knapp (1986), Knapp (1984); Yaron et al. (1980); and

Yaron and Olian (1973). With the aid of a linear

18 programming model, these paperspresent an economic analysis of irrigation with saline water over a period of time.

Dinar and Knapp (1986) estimated a crop-production function for alfalfa in southern Arizona and cotton in Lost

Hills, California. The purpose of this paper was to relate crop yield and salt accumulation in the soil to water quantity, water salinity and initial soil salinity. They incorporated the estimated functions into the dynamic programming model to determine optimal water applications for different levels of initial soil salinities and crop and water prices. The model assumed two different sources of irrigation water, relatively good and poor.

Under the optimal decision rules it is not feasible to use poor water quality. For cotton, water quantities increase as initial soil salinity levels increase. In the case of alfalfa,the results were unexpected. Increases in the price of cotton and/or water do not significantly change the decision rules.

Knapp (1984), assuming steady-state salinity conditions for navel orange crops in two regions of California, estimated the profit-maximization of water quantity, given the choice of crop and water quality, taking into account the dynamics of salt accumulation over time. He adopted different irrigation scheduling policies, twenty soil layers and two diferrent water prices in each region. He concluded that in many cases enough water is applied to maintain maximum yields.

Economic theory

19 suggests that water quantity decline as water price increases.

Yaron et al. (1980) used a dynamics programming model to estimate the optimal scheduling of irrigation with water of varying salinity and soil salinity for sorghum in the semiarid area of

Gilat, Israel. The results presented by these authors suggest several policy rules for decisionmakers: (1) frequent applications of small quantities of water are preferable to application of large quantities at extended intervals;

(2) under relatively high saline conditions, an extra amount of irrigation water for leaching the soils is generally justified at the beginning of the growing season; and

(3) under relatively low saline conditions, it is worthwhile to extend the irrigation over a longer period, as compared to the high salinity affected situations.

Yaron and Olian (1973) also used a dynamic programming model with Markov chains to analyze the optimal quantity of water for soil leaching of a single perennial crop. The economic significance of the model and the results which may be derived through its use are on two levels, the farm level and regional water resource development.

Extensive review of economic analysis of cropwater productions functions over a period of time, have been

20 presented by Dinar et al. (1985); Feinerman and Yaron

(1983); Moore (1981); and Moore (1972).

Dinar et al. (1985) in a long-run economic model, estimated a crop-water production function, assuming steadystate conditions, to investigate the combined effects of salinity, irrigation non-uniformity and different drainage requirements at field scale for corn and cotton. Optimum applied water and associated profits, yield and drainage volumes were computed for each crop. Their results indicated that the type of drainage disposal system affects the optimal values of applied water, profits, yield, and drainage volumes, except for uniform water application and non-saline irrigation water. The long-run results revealed that, under saline conditions and/or different drainage disposal system, a sensitive crop such as corn is not profitable and is taken out of production.

Feinerman and Yaron (1983 ) used linear programming models, deterministic in the short-run and stochastic in the long-run, to analyze the complex relationship involved in irrigation with water of varying salinity concentrations and the optimization of their use within a framework of a single farm. The empirical application of the model is based on data for a Kibutz in southern Israel. The irrigation season was defined as one year and the farm had three water sources of different quantities and qualities.

The cropping alternatives of the farm were potatoes,

21 carrots, cotton and a mature grapefruit grove. The results provide priorities in the allocation of water of varying salinity levels and empirical estimates of the shadow prices and the rates of substitution between the limited resources.

Moore

(1981) analyzed in individual farm changes the effects in the quality and quantity dimensions of the water supply, using a case study of the Imperial Valley of

California. In this study, he concluded that declining water quality has a negative effect on yield.

Other papers, such as Feinerman et al. (1984);

Feinerman et al. (1983); Boster (1976); Moore et al.

(1974); Bresler and Yaron (1972); Yaron and Bresler (1970) and

Bresler (1967), present the same relationships but in a short run framework.

Feinerman et al. (1984) estimated the effects of irrigation water salinity and uniformity of infiltrated water on average crop yield. They assumed steady-state and transient salinity conditions to investigate the economically optimal water applications and profits for corn. Economically, optimal water quantity and profits depend on water prices, salt concentration and uniformity of infiltrated water.

Feinerman et al. (1983) estimated a crop- water production function with non-uniform water infiltration.

These authors derived the effects of nonuniformity using two production functions that differ in

22 terms of the sensitivity of yield to application of water greater than that needed to achieve maximum yield. They concluded that where crop yield is sensitive to excess water, productivity and optimal levels of water application are lower in non-uniform fields than in uniform ones. On the other hand, if crop yield is not sensitive to excess water, profits depend on the water and crop prices.

Boster (1976) applied a mathematical programming model to study the economic impacts of introducing CAP water into

Pinal County, Arizona, for use in irrigated agriculture.

The techniques developed have broad application to similar water resource projects involving the conjunctive use of multiple water sources of different salinity levels. The results present an increase in salinity caused by the importation of CAP water.

Some papers, such as Feinerman et al. (1982); Yaron et al. (1972); and Shalhevet and Reiniger (1964), present an agronomic analysis of crop production function but do not take into account the economic effects of salinity in irrigation water.

A few papers, such as Sampath et al. (1986); Letey et al. (1983); Kelly (1981); Ayer and Hoyt (1981); Stearns

(1980); Hexem and Heady (1978); and Maas and Hoffman (1977) relate the economic analysis of yield as a function of water quantity and non-water inputs, but they do not take into account the the effects of water quality.

23

Ayer and Hoyt (1981) estimated crop-production functions and provided an economic analysis based on four of

Arizona's most important crops - - - cotton, wheat, sorghum and alfalfa - - - with the goal of helping both those who formulate water conservation policy and private consultants who offer water management services to irrigated farmers.

Moore et al. (1974) and Ayer and Hoyt (1979), both using production functions, estimated the elasticity of demand for irrigation water. In the former study, they estimated yield as a function of water quality and supply of irrrigation water, while the second approach used only water quantity and non-water inputs in crop response. They are identical in their results, suggesting that the pricing mechanism will have no effect in the decrease of water use.

Jurinak and Wagenet (1981) studied the interactive effects of soil fertility and salinity that are of major concerns in arid and semiarid regions. They concluded that although it was impossible to generalize the effects of salts and fertilizers on crop yield, it can be stated that in most cases moderate levels of soil salinity can be compensated by increased fertilization, so long as the salinity level is not excessively high nor the crop particularly salt-sensitive. The exact nature of crop response, however, depends greatly on crop type, fertilizer

24 form and quality, soil type, and irrigation water quality and soil salinity.

This reseaarch will be based on the dynamic programming method proposed by Dinar and Knapp (1986), Knapp (1984),

Yaron et al. (1980), and Yaron and Olian (1970). It is a comprehensive approach which takes into account the dynamics of salt accumulation in the soil, thus permitting a closer representation of the actual field behavior.

In the recent past emphasis was placed on both linear programming and marginal analysis techniques, but their disadvantage is that they are static models and are are not able to represent changes over time.

Given today's computational resources the dynamics analysis is fast becoming the preferred approach of researches working in natural resources as well as in any other field involving time dependency.

25

CHAPTER 2

THEORICAL FORMULATION OF THE FRAME OF ANALYSIS

The principal concepts of concern to this study, such as water availability, water requirements, water quality and crop yields and irrigation efficiency, along with the theoretical basis of the economic analysis are presented in this chapter.

Water Availability

The estimated total quantity of water on earth is

3

1,366 million Km , of which 97 percent is contained in oceans. Most of the remaining

3 percent, which makes up the world total supply of fresh water, is frozen in polar ice and in glaciers in various parts of the world. Only 0.64

percent of fresh water is surface and ground water

(Table

1). The most important features of this 0.64 percent of water is not its quantity, but its dynamic quality.

In its eternal cycle from the rain drop to the land, water is virtually an undiminished resource, unchanged by time. Where it was available centuries ago, it is available today, in about the same quantity, form and season, but it is different in quality ( Framji and Mahajan, 1969 ).

There is an ever growing need to control and use the world's resources of fresh water as wisely as possible so that demands made on it by the growing human population can

TABLE 1. Volume of Water in the Hydrosphere

Parts of Hydrosphre

Volume of Water

3

Km

World Oceans

Glaciers

Ground-water

Surface

TOTAL

1,327,752.0

29,505.6

8,469.2

273.2

1,366,000.0

Source: Framji and Mahajan, 1969.

Percent of

Total Volume

97.20

2.16

0.62

0.02

100.00

26

27 be met. Water quality, on the other hand, is continually deteriorating due to increased salinity and population growth. Consequently, the water supply for irrigation which is already an important problem, directly linked with food production, is becoming gradually a crucial issue for the development of many areas.

In agriculture, efficient water utilization reflects how best the water would be stored, distributed and used in crop production. The availability of water in the right quantity and at the right time is essential for good plant growth and yield. Both the amount of water as well as the time may differ for different crops. Thus, what may be true for one crop may not necessarily be so for other crops, growing even in the nearby fields.

The amount of water is of concern both in terms of shortage and excess. Problems more often arise in situations when water supply is insufficient. It is only during the rainy season or when the snow pack melts that there may be excess water. This situation can also arise when a farmer obtains water through a public distribution system. The farmer is more apt to apply excessive amounts of water for two reasons. First, farmers are usually unaware of the concept of optimal requirement and use of water by crops and usually feel that the application of water is helpful irrespective of its amount. Secondly, the

28 farmer often has no guarantee that he will receive water when the crop needs it again.

Water Requirement, Water Quality, and Crop Yield

Water Requirement

The estimation of the water requirement

(WR) of crops is one of the basic needs for crop planning on a farm and for the planning of any irrigation project. Water requirement may be defined as the quantity of water, regardless of its source, required by a crop or diversified pattern of crops in a given period of time and place for its normal growth under any given field conditions. Water is needed mainly to meet the demands of evapotranspiration (ET) and the metabolic activities of the plant, together known as consumptive use (CU). Since the water used in the metabolic activities of the plant is negligible, ET is practically considered equal to CU. The total water requirement includes the ET plus the other losses during the application of irrigation water and the quantity of water required for special operations such as land preparation, transplanting and leaching.

Erie et al.

(1982) provided graphs of daily, semimonthly, and cumulative water consumption crops by major in the Southwestern United States. Their graphs are based on the Blaney

- Criddle formula and experimental data from the averages for several years in which enough

29 water was applied to prevent plant stress and thereby maximize yield. The values of the graphs are sumarised in

Table 2.

Water Requirement can thus, be formulated as:

WR = ET or Cu + Application losses + Special needs ( 1 )

Water requirement is, therefore, a "demand." The

"supply" would consist of contributions from any of the sources of water, where the major sources are the irrigation water, effective rainfall and soil profile contribution including that from shallow water tables.

Effective rainfall indicates the proportion of total rainfall which is useful or utilizable for productive purposes. It has been interpreted differently by the workers in different disciplines. From the point of view of water requirement of crop, the Food and Agricultural

Organization of the United Nations has defined the effective rainfall "as the amount of precipitation that is useful in meeting the crop demand or the leaching requirement"

(Ayers and Westcot, 1976 p. 8). Consequently, the ineffective rainfall is that portion of the total annual or seasonal rainfall which is lost by surface run off, deep percolation beyond root zone, and the moisture remaining in the soil after the harvest of the crops that is not useful for the next crop.

30

TABLE 2. Consumptive Use

of

Water

for

Major Crops, Mesa &

Tempe, Arizona.

Month Alfafa Barley Cotton Sweet Soy- Grain Doubble

Corn Beans Sorghum Cropped

Grain

(in) (in) (in) (in) (in) (in)

Sorghum

(in)

JAN.

1st half

2nd half

FEB.

1st half

2nd half

MAR.

1st half

2nd half

APR.

1st half

2nd half

MAY

1st half

2nd half

JUN.

1st half

2nd half

JUL

1st half

2nd half

AUG.

1st half

2nd half

SEP.

1st half

2nd half

OCT.

1st half

2nd half

NOV.

1st half

2nd half

DEC.

1st half

2nd half

1.81

2.75

3.22

5.48

5.30

4.55

4.33

.59

.88

1.39

1.95

3.00

4.59

3.54 5.42

4.02

4.28

4.61

5.36

5.34

5.48

4.98

4.29

3.18

2.48

1.87

1.68

1.77

.15

.15

.33 1.95

.68 4.10

1.28 6.70

1.95 5.90

3.30

4.65

5.84

5.70

5.60

4.35

3.30

2.25

1.25

.57

.19

.30

.50

1.60

1.90

2.90

3.30

3.80

3.50

2.50

1.70

.60

3.20

5.25

6.72

4.80

2.85

1.50

.48

.08

.90

2.55

4.80

6.15

6.60

3.75

3.20

2.40

4.16

5.85

4.05

2.55

1.92

1.35

.90

.45

.48

74.30 25.00 41.20 19.60

.30

TOTAL 25.40 51.50

Source: Estimation from the

Blaney-Criddle formula for consumptive use of water by major crops in the Southwest

United States. ( Erie et al., 1982).

31

The common methods of estimating the water requirement of crops and its various components, along with the factors influencing them, are evaporation, transpiration and evapotranspiration or consumptive use.

Evaporation is the process during which a liquid changes into a gas. The process of evaporation of water in nature is one of the basic components of the hydrological cycle by which water changes to vapor through the absorption of heat energy. This is the only form of moisture transfer from land and ocean into the atmosphere.

The fundamental principle of evaporation from a free water surface was enunciated by Dalton in the year

1882.

Dalton stated that evaporation is a function of the difference or gradient in the vapor pressure of the water and the vapor pressure of the adjacent air.

Several empirical equations for estimating evaporation are based on Dalton's law, which may be written as

E=(e -e )*f (u) d where:

( 2 )

E = Evaporation es

= saturation vapor pressure at the temperature of evaporating surface in inches of mercury; ed = saturation vapor pressure at the dewpoint temperature in inches of mercury.

f (u) = a function of the horizontal wind velocity

32

Evaporation from the land surface is affected mainly by the degree of wetness of the surface, temperature of air and soil, atmospheric humidity and wind velocity.

Transpiration is the process by which water vapor leaves the living plant body and enters the atmosphere. It involves continous movement of water from the soil into the roots, through the stem and out through the leaves to the atmosphere.

Transpiration is basically an evaporation process.

However, unlike evaporation from a water surface, transpiration is modified by plant structure and stomatal behavior operating in conjunction with the physical principles governing evaporation.

Climate, soil and plant factors influence transpiration. The important climatic factors are light intensity, atmospheric vapor pressure, temperature and wind.

The soil factors are those governing the water supply to the roots, and the plant factors include the extent and efficiency of root systems in moisture absorption, leaf area, leaf arrangement and structure, and stomatal behavior.

In designating water use by crops, evaporation and transpiration are combined into one term, evapotranspiration (ET), since it is difficult to separate these two losses in cropped fields. The relative amount of direct evaporation from the land and water surfaces and transpiration depends usually on the extent of ground

33 cover. For most crops completely covering the soil surface, only a small amount of water is lost from the ground surface as evaporation (Schulz, 1980).

The principal methods for direct measurement of evapotranspiration are by lysimeter experiments and field experimental plots, soil moisture depletion studies, and the water balance method. These methods yield very reliable values of ET provided elaborate installations and precise measurements are made.

Irrigation Efficiency

Hansen et al. (1980, p. 153) defined irrigation application efficiency "as a ratio of water stored in the root zone during irrigation divided by the water delivered to the farm". The selection of an irrigation method that is efficient for applying water depends upon a number of conditions: the crop to be grown, topography, soil characteristics, availability of water, soluble-salt content of water and salinity status of the soil.

Trickle irrigation is best adapted to arid and semiarid conditions because it has the advantage of higher water application efficiency than the other irrigation systems such as furrow and sprinkler. With trickle irrigation, water can be applied efficiently to small trees and widely spaced plants where adequated water can be placed in the root zone without wetting the soil where no roots exist.

34

Saraiva Leao (1975) reviewed some studies related to trickle irrigation. Those studies reported increases in crop yield when trickle irrigation was used in place of other conventional irrigation methods.

Efficient utilization of water in irrigation can be defined and evaluated with the following two approaches: 1) the engineering and planning approach which is mainly concerned with the evaluation of the hydraulic performances at different levels in an irrigation project,and 2) agro-economic approach which is based on crop yields in relation to water used.

Enginners define efficiency in various ways. It is the net amount of water added to the root zone or used in evapotranspiration by a crop, as a fraction of the water diverted from some source. Since this efficiency term includes different forms of losses of water during conveyance and application, it will depend upon the unit of evaluation of which can be an entire project, and individual farm, or a field.

Irrigation efficiency, in economic terms, is the financial return per unit of water applied or the return on the amount of money invested in the water supply project; this will vary widely according to the economic conditions prevailing in time and space.

35

Water Quality and Crop Yield

Irrigated agriculture is dependent on an adequate water supply of usable quality, This quality is determined by the composition and concentration of the dissolved substances or solutes that are present in the water. The principal solutes are the cations calcium, magnesium and sodium, and the anions bicarbonate, sulfate and chloride. The total concentration of dissolved salts (TDS) is probably the most important single criterion of irrigation water quality.

Total concentration can be expressed in terms of parts per million (PPM) of dissolved solids or as electrical conductivity (EC) in micromhos per centimeter (EC mmho/cm)

( Ayers and Westcot, 1985 ).

There are wide differences in the TDS and composition of water used for irrigation around the world.

These differences depend on climatic zone, source of water, location along the water course, time of year, geology and irrigation development. In general, irrigation water in humid zones has a lower salt content than in arid zones, ground water is more saline than surface water, river water during the spring is less saline than in the fall, and finally, river and ground waters are less concentrated before irrigation development than after.

There are large seasonal and yearly changes in water quality as well as changes along river courses. The changes are due to human activity, rainfall dilution or geological

36 strata through which the water flows. Whatever the cause may be, it is obvious that a single water analysis is entirely insufficient. Water has to be sampled at regular intervals - - - at least seasonally - - - and at several stations along river courses.

The three basic criteria that are essential in evaluating irrigation water are total salt content, sodicity hazard, and specific ion toxicity hazard.

Total Salt Content

Total salt content is the single most important criterion for evaluating irrigation water quality. The total content may be expressed either in terms of electrical conductivity (EC), or in terms of concentration in parts per million (PPM) or milliequivalents per litter (meq./1).

The importance of total concentration is because most plants respond to the total concentration of ions in their growth (osmotic effect), rather than to any specific ion.

However, some plants are especially sensitive to some toxic ions and for them total salinity may not be a sufficient criterion for evaluating irrigation water.

A

series of studies conducted by the US Salinity

Laboratory, Bernstein (1964) and Maas (1984), indicated that, except for the very tolerant crops, most plants show

37 a progressive decline in growth and yield with increasing soil and water salinity. Tolerance of crops to salinity is expressed in terms of the eletrical conductivity of the root zone soil at which a specified reduction in crop yield is experienced. Figure 1 shows curves relating yield to salinity with categories from sensitive to tolerant.

Sodicity Hazard

Among the soluble constituents of irrigation water such as sodium, carbonate, bicarbonate, calcium, magnesium and chloride, sodium is considered the most hazardous. Water which might be considered suitable under a given salinity classification may not be suitable if sodium predominates.

The effect of sodium is two-fold. It may affect the permiability of the soil pores, and it may cause injury to crops specially sensitive to sodium such as fruit crops.

The effect of sodium depends not on its total concentration in the water but on its concentration relative to the concentration of the other cations

(calcium and magnesium). The presence of a high concentration of carbonates and bicarbonates results in an increase in the proportion of sodium, because of precipitation of calcium and magnesium carbonate upon contact with the soil.

80

60

5

5

1

10

1111111

15

11

20

1111111

EC w

15

.

I

I I

20 25 30

Ill 1 1 1 mill t

EC, = Electrical Conductivity of the Saturation

Extract (dS/m)

35

EC e

EC w

= Electrical Conductivity of the Irrigation

Water (dS/m)

EC, = 1.5 EC,„

40

UNSUITABLE

FOR CROPS

20 o o

I

SENSITIVE MODERATELY MODERATELY

SENSITIVE TOLERANT l f 1

1

1

1

5

I l I I 1 1

10

15

TOLERANT

I

20

I

1

I

25

I I I

30

I I I

35

EC e

0

I

5

10

1

1 dS/m

,

15

.

I l

20

I I

I

I

EC vi

Figure 1.

Divisions for Relative Salt Tolerance Ratings of

Agricultural Crops (

Maas, 1984 ).

38

39

Workers at the U.S. Salinity Laboratory proposed the sodium adsorption ratio (SAR) to characterize the relative sodium status of irrigation waters and soil solution

++

Na

SAR =

V

-

Ca++ +

Mg++

-I

( 3 ) where:

SAR = sodium adsorption ratio

Na

= sodium

( meq/1 )

Ca

= calcium

( meq/1 )

Mg

= magnesium

( meq/1 )

The effect of sodium on soil permeability is inversely related to the total ion concentration. The higher the concentration the smaller the effect.

On the other hand, the rate of soil sodicity is directly related to total electrolyte concentration. The higher the concentration the faster the rate. Consequently, any classification system must take into account the two factors,

SAR and total electrolyte concentration.

The most widely used scheme of classification is that proposed by the U.S. Salinity Laboratory, which is based on the

SAR of the water and the total electrolyte concentration expressed in electrical conductivity

(EC

= dS/M) units.

40

Specific Ion Toxicity Hazard

Chloride and Sodium Hazard

Sometimes the chloride hazard is confused with the salinity hazard. This happens because in some locations, water salinity is defined in terms of its NaC1 (sodium chloride) content, rather than in terms of TDS or EC.

Chloride should be considered as a hazard only for chloride sensitive crops. Since in most instance chloride appears together with sodium, the effect of the two may be confounded.

Boron Hazard

Boron is very toxic to most plants even at low concentration in the soil solution. Some irrigation waters contain boron in toxic concentrations and thus require special considerations. It is generally more difficult to leach out boron than other salts. Crops have a wide range of tolerance to boron.

Other Minor Consituents

Sodium, chloride and boron are generally the only specific toxic elements which are regularly considered in evaluating water for irrigation. Under some conditions, especially when water is polluted by industrial wastes,

41 other elements such as selenium, lithium, copper, arsenic, zinc, etc may be present in toxic concentrations.

Economic Theory of Production

The economic theory of production deals with problems of allocation and utilization of limited resources by individual firms. Firms are considered to be technical units which transform inputs into outputs.

The production process that specifies the maximum output obtainable from any combination of inputs is said to be technically efficient.

A mathematical expression that relates inputs and outputs through technical efficiency production processes is called a production function.

Equation

(4) represents a production function, f, for a production process involving one output, Y, and variable inputs Xi, . . ,Xn.

Y = f ( X1,X2,X3, . , Xn ) ( 4 )

Specific functional forms for f (both linear and nonlinear) are used in empirical estimation of production functions. Starting with the production function as given, economic production theory assumes that firms behave in order to maximize economic efficiency, and focuses on decision made by the firm with regard to optimal levels of inputs and outputs. For a review of producion function

42 theory, see Beattie and Taylor

(1985) and Henderson and

Quandt (1971).

The Factor-Product Relationship

In this case, the technical relationship between a variable input and output is based in the short-run analysis

(short-run means time sufficiently short that is not possible change some fixed inputs such as machinery, building, water distribution system, etc.) and can be mathematically expressed as

Y

= f ( X1 : X2, . , Xn )

( 5 ) where Y denotes output,

X1 is the variable input and

X2, .

., Xn are the fixed inputs of production.

Figure

2 is a graph of the generalized crop-water production function Y

= f(W/Ciw,CSo) where Y is the yield per acre,

W

(water) is the variable factor of production, given the other inputs such as salt concentration of irrigation water

(Ciw) and initial soil salinity

(CSo) as the fixed inputs of production.

The generalized functional relationship between total crop yield and different levels of irrigation water salinity while all other inputs are held constant also may be expressed in the form of a total physical production function of the type

Y = f (Ciw/ W, CSo) where

Y is the total crop yield,

Ciw is the salinity of irrigation water

43

(variable input), W is the quantity of irrigation water and

CSo as fixed inputs. Figure 3, represents the general functional relationship between yield and salinity of irrigation water.

Factor-Factor Relationship

For the case of two-variable inputs, we denote the production function by

Y = f ( W,Ciw CSo ) ( 6 ) where Y is the quantity of output and

W (water quantity) and

Ciw

(water salinity) are the variable inputs while CSo is the fixed input. Figure

4, illustrates the total cropyield to the water quantity and water quality model with three different possible water quantities (W1,W2 and

W3) and three different levels of water salinity

(Ciwl,C1w2,Ciw3), nine possible combinations of water quantity and quality exist to give nine different levels of output.

Marginal and Average Physical Product

The marginal physical product,

MPP, of an input is the addition to total product (output) resulting from use of one more unit of the input, other resources being held at a constant level. More exactly, the marginal product is the frist derivative of output with respect to the particular input or

Total physical product

WI

Water

W

2

W

3

quantity

-p-

Figure

Z•

Relationship Between Total Crop Yield and

Water Quantity ( Hypothetical ).

44

Ciw 1 Ciw2

Ciw3

Salinity of irrigation water

Figure 3. Relationship Between Total Crop Yield and

Water Quality ( Hypothetical ).

WI

W2

W3

Water quantity

Figure 4.

Production Surface Relating Total Crop Yield to

Water Quantity and Water Quality

( Hypothetical

).

45

46

MPP = dY dXi

and the average physical productivity is

APP =

Y

X

( 7 )

( 8 )

Elasticity of Production

The elasticity of production is a measure of the percentage change in output in response to an infinitesimal percentage change in an input given that all other inputs are held constant.

The factor elasticity,

E,

for one single-variable-input production function

f(X),

is defined as

%

change in output

dY/Y dY

E =

=

%

change in input

dX/X dX

X

( 9 )

Y

If

E

is greater than one, an increase in the input level will result in a more than proportionate increase in output; for

E

less than one the proportionate increase in output is less than that of input; and for

E

equal one the proportionate increases are equal. There is a closed relationship between elasticity of production and

productivities

(average and marginal) providing the definition of the stages of production. When

E > 1, APP

is increasing,

MPP

can be increasing or decreasing, and

47

MPP > APP. This stage is defined as the irrational stage of production because the variable input Xi is being used insufficiently. When E < 1, APP is decreasing, MPP is decreasing but greater than zero; this stage is defined as rational in the use of the factor variable. When E < 0, APP is decreasing, MPP is negative and decreasing; this stage is defined as irrational because of the excess use of the variable factor.

From these definitions it can seen that, as the single input case, values for partial elasticities are related to features of the productivity functions ( Figure 5 ).

Isoquant

An isoquant or production indifference curve is a curve that combines all factor combinations which give the same output. For a given output level,

(6) becomes

Y

= f (W,Ciw CSo) ( 10 ) where Y is a parameter. The locus of all combinations of water quantity (W) and water salinity

(Ciw) which satisfy

(11) forms an isoquant. Three curves from a family of isoquants are shown in Figure 6. All the input combinations which lie on an isoquant will result in the output indicated for the curve.

Y

Figure 5. Classical Three-Stage Production Function and Marginal and Average Curves: Single

Factor Variation ( Beattie and Taylor, 1985).

48

Water Quantity

Figure 6. Solution to the Factor-Factor

Decision Using

Isoquants and Isocosts (Hypothetical).

49

50

Rate of Technical Substituion

The slope of the tangent to a point on an isoquant is the rate at which

X1 must be substituted for X2 ( or X2 for

X1) in order to maintain the corresponding output level.

The negative of the slope is defined as the rate of technical substitution (RTS): dX2

RTS = dX1

Isocost Line

An isocost line is defined as the locus of input combinations that can be purchased for a specified total cost:

TC

= Pw * W + Pciw * Ciw + FC ( 12 )

Where

Pw and Pciw are the respective prices of water quantity and water quality and FC is the cost of the fixed input. Three curves from a family of isocost are shown in Figure 6.

Profit-Function

Profit is total revenue minus total costs. Revenue is the product of yield and output prices and total costs includes payments to all resources used in the production.

51

These payments are based on the opportunity costs of the resources. A detailed description of profit function for cotton crop production is presented in the Chapter 4.

52

CHAPTER 3

DESCRIPTION OF THE STUDY AREA:

MARICOPA COUNTY, ARIZONA

The study area, Maricopa County, is located in the south central section of Arizona (Figure 7) and covers an area of 9,233 square miles, over half of which (51%) is federally owned. Only 25 percent of the land is in private ownership, and another 16 percent is accounted for by Indian reservations and 8 percent is state owned. Maricopa County is characterized by broad, featureless valleys between north-south2 oriented mountain ranges. Elevations range from

750 to 1,350 feet in the valleys and from 900 to 3,700 feet in the mountains. The general landforms in the area are valley plains, streams channels, flood plains, and low terraces, alluvial fans, and mountains and low hills (Soil

Survey of Maricopa County).

Maricopa County includes 19 incorporated cities and towns. The largest city is Phoenix, which is the ninth largest city in the United States and one of the fastest growing cities in the sunbelt. The total population of the county in

1985 was 1,830,927. It has experienced tremendous population growth during the past

35 years, increasing by

452 percent while the State has increased 320 percent and the country 42 percent. In spite of its large urban

Mohave

Coconino

HaveJo

4••••••11.11.

n

MMINIMPI

Apache

53

Figure

7. Map of the State of Arizona.

N4e r"am

- -

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54

Maricopa County is the most important agricultural county in the state.

In 1985 the county had a cash receipt from agricultural marketing of 636,3 million dollars that correspond to 42 percent of the state. The second place was Yuma with 21 percent ( Arizona Agricultural

Statistics, 1986 ).

The Resource Base

The physical resource base of soil, climate and water upon which the county's agriculture depends are the basic physical inputs for an economic analysis of this area.

The soils of the county as mapped by soil survey in the period 1958-72 are composed of two general classes of material, alluvium and hard bedrock. Most of the soils are derived from alluvium, which, in turn, is derived from a variety of sources and from geologic materials of several different ages. Soils in the center of the intermountain valleys are generally very mixed and are derived from both local and distant sources. Most of the soil material has been transported into these areas by major streams, such as the Gila, Salt, Agua Fria, and

Hassayampa Rivers. Smaller amounts of sediment are derived locally from tributaries of these streams that originate in the mountains nearby. The soils are generally suited to irrigated agriculture (Soil Survey of Maricopa County,

1977).

55

The climate of the area is characterized by long, hot summers and short, mild winters; low annual rainfall; low relative humidity; high evaporation; and a high percentage of days with sunshine. The annual precipitation averages about 8 inches. There are two separate precipitation seasons. The first occurs from

November to March, when the area is subject to occasional storms from the Pacific Ocean. Winter precipitation is greatest when the middle latitude storm track is unusually far south, so that storms enter Arizona directly from the West or Southwest after picking up considerable moisture from the Pacific Ocean.

The second precipitation season occurs from

July to September when the area experiences wide-spread thunderstorm activity associated with moist air moving into Arizona from the south and southeast. These thunderstorms result in heavy amounts of precipitation during short periods of time.

Temperatures are normally high in the summer months from early June until mid September. The afternoon maximum temperature commonly exceeds 100 F.

According to records kept at the Phoenix Airport, about

83 days per year have maximum temperature of 100 F or higher. Winter temperatures usually do not exceed

65 to 70 F.

56

Water Availability and Water Rights

Irrigation water for Maricopa County comes from ground water (public and private wells) and surface water

(Salt and Verde Rivers). The Central Arizona Project (CAP) will import 1.2 million acre feet of water per year from

Lake Havasu on the Colorado River. CAP water will flow into the Phoenix area after being lifted about 600 feet; then part of it will be lifted and additional 1,300 feet to

Casa Grande and Tucson (Table 3).

Thiele, (1965) presented an analysis of groundwater supply in Maricopa County and specifically the Phoenix

Metropolitan Area beyond the year 2020. The groundwater storage reserve to 1,000 feet depth was roughly 100 million acre feet, with 54 percent located in the Phoenix Basin and

46 percent in the Mesa Basin, forming two independent groundwater units. The accumulative depletion during the period 1963-2020 will be 61,8 million acre feet, causing an average groundwater depletion of more than 1.0 million acre feet per year. Groundwater conservation and a continuous reduction in groundwater withdraws are necessary for the state to achieve the balance of withdraws.

To counter larger overdrafts the 1980 Groundwater

Management Act prohibits the expansion of irrigated acreage and will restrict pumping, over time, in four Active

Management Areas (AMA) of the state (Arizona Water

Commission). These are geographical areas of the state in

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58 which intensive groundwater management will be required to bring water consumption and replishment into balance. The

1980 Groundwater Management Act placed water rights and water management functions under the jurisdiction of the newly created Department of Water Resources (DWR).

Within the AMA's, the law requires 45 year water conservation and management programs, and it establishes several ways of obtaining the right to use groundwater. The

45 year management effort is divided into five periods, and a management plan is to be developed for each period.

During the first management period, 1980-1990, and for each subsequent period, the

DWR must develop a groundwater management plan consistent with guidelines set out in the

Act. The guidelines mandate a conservation program for each type of groundwater use. After the year 2026, the state may initiate a program to purchase and retire groundwater permits, if such a program is necessary to meet the longterm management goal.

To achieve agricultural water conservation, the act established water duties. Based on historical cropping patterns, each farm is to be assigned a maximum allowable water use based on the consumptive needs of the crop and assuming use of certain conservation practices.

During each management period, water duties are to be readjusted to reflect increasing levels of conservation as necessary to assist in the management goal.

59

Lierman (1983) studied the changes for agriculture in the Phoenix Active Management Area resulting from the implementation of policies of the 1980 Arizona Groundwater

Management Act such as pump tax and water duty, which were designed to regulate the use of groundwater. He found that a water duty is more effective in curbing groundwater use then the proposed pump tax. Investment in more water conserving technologies is also important, but substantial amounts of capital are necessary to begin this investment.

Water Quality for Irrigation

The CAP water is expected, (in many instances) to be of better quality than the existing sources of groundwater in the county. The deliverable CAP water is assumed to be similar to water quality of the Colorado River at Parker

Dam. Studies by the Bureau of Reclamation have shown that the average salinity of the Colorado River below the Parker

Dam from the period of October 1963 to September of 1976 was

732 mg/l.

The metropolitan Phoenix area, lying within the boundaries of the Salt River Project (SRP), has an average total dissolved salts (TDS) of less than 500 mg/1 and is supplemented as needed with more saline groundwater.

Ayers (1977) summarized water quality criteria for irrigation in Maricopa County. These criteria are based on problems with salinity, permeability, toxicity and other

60 factors. Permeability problems are normally associated with irrigation water of very low salt content or a high sodium content relative to calcium and magnesium. Boron, chloride and sodium can exert a direct toxic effect on certain sensitive crops. Table 4 contain water quality guidelines of importance in Maricopa County.

Land Resources

The total land devoted to farming in Maricopa County is decreasing. Within the central part of the county there has been a constant absorption of agricultural land by urban development. In the Salt River Project the amount of land in urban use has increased at an average rate of 10 percent per year since 1977 (Figure 8). Consequently cultivated land is being retired from agriculture use at a similar rate.

The development of new irrigated acreage has been restrainted in Maricopa County by the Arizona Groundwater

Management Act of 1980. A major premise of the groundwater code is that within AMA's, only land with a history of legal irrigation between 1975 and 1980 may be irrigated in the future. Irrigation is defined by the law as the application of water to two or more acres of land for the purpose of growing crops for human or animal consumption or sale.

Exception to the irrigation restrictions are permitted only

61

TABLE 4. Guidelines for Interpretation of Water Quality for Irrigation in Maricopa County.

Constituents

Salinity (EC dS/m)

Chloride (mg/L)

Boron (mg/L

Ammonia - N and Nitrate for sensitive crops

< 750

< 140

< .5

<5

Source: Ayers (1979).

None

Extent of the problem

Moderate Severe

750 - 3,000

140 - 350

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> 20

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2‘10

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80

40

19

'

77

19'78

1979

19'85

I.

2000

(f

985 e4 2000'projectcd)

Figure 8. Distribution of Land in the Salt River

Project Region,

Maricopa

County, Arizona.

62

63 if it can be documented that substantial capital was invested prior to the passage of the law, and in some cases if new acreage is located near the CAP delivery system.

As land uses have changed in the urbanizing areas of

Maricopa County, some farmers have moved from those areas of high water cost to locations with lower land and water prices such as Yuma and Final County. Further water development for irrigation on Indian lands along the

Colorado River and on Indian lands to be served by the CAP will encourage agricultural expansion in those areas.

Description of the Irrigation Districts in Maricopa County

.

Nineteen major organized irrigation within the Maricopa County.

These districts organized lie districts encompass 463,089 acres of agricultural land (Census of Agriculture, 1982). From this total only 9 districts were described in this study, since they are important cotton producing areas.

All irrigation districts have applied for CAP water for irrigation purposes with the exception of the Buckeye

Conservation and Drainage District.

Water

As required by the master repayment contract for the CAP, the water would be used only for agricultural purposes on eligible land and would replace pumped groundwater on an acre-foot per acre-foot basis.

64

Each irrigation district included in this study is briefly described according to the CAP Environmental Impact

Statement. This section draws from that study.

Salt River Project (SRP)

The Salt River Valley Water Users' Association was incorporated February 9, 1903, for the benefit of 4,800 landowners who pledged their lands as collateral for the loan from the Federal Government to build the reclamation project. The SRP Agricultural Improvement and Power

District was created in 1937, primarily to refinance debts incurred for construction of facilities built during the

1920's. The SRP will divert its CAP water allocation from

Reach

12 to the Granite Reef Aqueduct and use its own existing canal system to distribute the water to project lands.

A total of 151,800 acres of land with a history of irrigation was classified within the district of which

151,608 acres were arable and irrigable. A large percentage of the Project's lands have been subdivided for urban usage.

The district, based on present projected population growth rates, is expected to become completely urbanized by the end of the century. The present crop distribution for the project in small grains (12%), alfalfa hay (27%), silage

(9%), cotton (46%), vegetables (6%), and fruits, including

citrus (3%). cropped.

65

About 50 percent of the land is double

Harquahala Valley Irrigation District (LIVID)

Harquahala Valley Irrigation District (LIVID) is located in Maricopa County, about 35 miles west of Buckeye. The

District was organized in 1964 to permit unified action in the application for Central Arizona Project water and in the solution of common problems such as flood hazard. The

District has neither physical assets nor a consolidated system. Much of the private distribution system is lined.

Harquahala will receive its CAP water allocation from a gravity flow delivery canal which will divert water from Reach 4 of the Granite Reef Aqueduct. At its nearest point, the District is located about 2 miles from the

Granite Reef Aqueduct.

A total of 38,350 acres of land with a history of irrigation was classified within the District of which 37,619 acres were arable and irrigable. The encroaching urbanization of the metropolitan areas has not affected this District due to its distance from

Phoenix. The District remains agricultural with cotton being the principal crop and accounting for about 64 percent of the irrigated crop land. Wheat comprises about 33 percent and double cropped lettuce about

66

7 percent. Other crops are safflower, fruit, vegetables, and alfalfa.

Maricopa County Municipal Water Conservation District # 1

The District is located about 22 miles northwest of Phoenix in Maricopa County. The District is bounded on the east by McMicken Irrigation District and Luke

Air Force Base; on the south by I-10 and the Roosevelt

Irrigation District; and on the west by the White

Tank Mountains. Waddell Dam, which forms Lake Pleasant, is located about 15 miles north of the District on the

Agua Fria River.

The MCMWCD # 1 will divert its CAP water allocation from the Granite Reef Aqueduct by means of an existing canal which crosses the CAP canal.

A total of 30,903 acres of land within the District are arable and qualify for CAP water. Urbanization is expected to reduce the irrigated acreage of this District in the future.

Principal crops are cotton (57%), citrus (8%), grapes (3%), lettuce (6%), roses (1%), small grains (3%), potatoes (7%) and other (13%).

McMicken Irrigation District (MID)

McMicken Irrigation District is located approximately

15 miles northwest of Phoenix. Development in the area first began in the early 1900's and was accomplished by

67 individual landowners who drilled their own wells. All ditches and wells are privately owned.

The McMicken Irrigation District would probably receive its CAP water allocation in conjunction with MCMWCD

# 1 by means of the Beardsley Canal. The water will be diverted from reach 9 of the Granite Reef Aqueduct.

A total of 39,964 acres of land with a history of irrigation was classified within the district of which

39,818 acres were arable and irrigable. Due to the location of the McMicken Irrigation District, urbanization is expected to reduce the agricultural acreage of this district significantly in the future. The crop distribution for the district lands is cotton (60%), small grains (5%), vegetables

(18%), citrus (12%), and grapes (1%).

Queen Creek Irrigation District

(QCID)

Queen Creek Irrigation District is located in southeastern Maricopa County about

12 miles southeast of Mesa. It was originally organized to obtain electrical power to operate pumps which it continues to do through contract with the Salt

River Project.

QCID will receive its CAP water allocation from 2 turnouts on the Salt-Gila Aqueduct (SGA). Water will be diverted from both Reach 2 and Reach 3 to delivery systems to be built.

68

A total of 13,675 acres of land with a history of irrigation was classified within the district of which

13,269 acres were arable and irrigable.

Urbanization is encroaching on the district and agricultural land is being subdivided into mini-farms at an increasing rate. Cotton is the predominant crop with 69 percent of the land planted to that crop. Other crops are milo (11%), wheat (27%) and potatoes, alfalfa, grapes, and citrus.

Roosevelt Irrigation District (RID)

Roosevelt Irrigation District lies to the west of

Phoenix and to the north of and adjacent to the Buckeye

Irrigation District. Water is obtained entirely from groundwater supplies. The water is delivered from district owned wells by the district owned canal system to farms.

The RID would likely receive its CAP water allocation from the Granite Reef Aqueduct via existing canal systems of Maricopa County Municipal Water Conservation

District # 1 and the Salt River Project.

A total of 34,777 acres of land with a history of irrigation was classified within the district of which

34,759 acres were arable and irrigable.

The eastern boundary of the district is only

16 miles west of the central business district of

Phoenix and urbanization of portions of the district is

69 expected in the future. Cotton is the predominant crop with about 65 percent of the district acreage planted to that crop. Other major crops and the percentage of acreage are small grains (14%), alfalfa hay (16%), sugar beets (6%), and vegetable and fruits (1%).

Roosevelt Water Conservation District (RWCD)

Roosevelt Water Conservation District is located on the southwestern boundary of the Salt River Project in Maricopa

County and extend from a diversion point northeast of Mesa to the Gila River Indian Reservation southeast of Chandler.

The

RWCD would likely receive its CAP water allocation from Reach 12 of the Granite Reef Aqueduct via the Salt River Project canals to existing RWCD canal systems.

A total of

39,001 acres of land with a history of irrigation was classified within the district of which

36,615 acres were arable and irrigable.

Due to the close proximity of the district to the communities of Apache Junction and Mesa, urbanization of district lands are expected to increase in the future.

Cotton is the predominant crop in the district with 38 percent, sugar beets (1%), vegetables (3%), citrus (17%), corn silage (7%), small grains (6%), and double cropped (28%).

70

Tonopah Irrigation District

(TID)

Tonopah Irrigation District (TID), located approximately

40 miles west of Phoenix, was formed in

1977 to apply for CAP water. The Tonopah Irrigation District owns none of the existing supply or distribution facilities.

The Tonopah Irrigation District would likely take its CAP water allocation from Reach 6 of the Granite Reef

Aqueduct where a turnout would be constructed.

A total of

8,669 acres of land with a history of irrigation was classified within the district of which

8,518 acres were arable and irrigable. The district is not expected to be influenced by the expansion of urban areas in the near future. The principal crop is cotton with

60 percent of the land in that crop.

Additional major crops are wheat

(10%), alfalfa

(25%), and small grains

(10%).

Buckeye Water Conservation and Drainage District

(BWCDD)

Buckeye Water Conservation and Drainage District located west of Phoenix was legally formed in

1922, although water rights to water from the Gila River were acquired in

1885.

Water is delivered to district farms through district owned canals.

BWCD is not a current applicant to receive CAP water for irrigation purposes.

71

Water is delivered by the district to a gross farmed area of approximately 18,000 acres each year.

Principal crops in the District are alfalfa, cotton, barley, wheat and sorghum.

The Cotton Story

The cultivation of cotton has evolved on the continents of Asia, North and South America, Europe and Africa, but it was from India that domestic cotton was carried first to

Europe and finally to North America. From 1500 BC to 1500

AD, India was considered the center of the cotton industry and is therefore called the "motherland of cotton".

It is not known how the primitive cotton culture spread from India. Some think it may have developed independently in Egypt at a very early date. The earliest reference of cotton used for cloth in Africa is around 500 B.C. Cotton made its first appearance in England in the late 12th

Century. It was used for candle wicks, embroidery yarns, as well as clothing. It became important in 1699 with the establishment of the East India Company.

Cotton has been growing in America since ancient times, but it was not until 1621 that the white man made the first planting in Virginia. This was the short staple variety, which had little commercial value because of the difficulty in separating the seeds from the lint. In 1793,

Eli Whitney solved this problem with the invention of the

72 cotton gin, a process of cleaning harvested cotton, removing seed, and balling the fiber (Jefferies et al.).

The first long staple cotton was adapted to only a small area along the Atlantic coast from the Santee River to the St. Johns. In 1791, Georgia and South Carolina together produced about 2.0 million pounds of which about a 10% was exported. By

.

1800 the use of cotton had increased so rapidly that market demand exceeded the supply. In the United

States, cotton constituted one of the major sources of farm income from all crops, with a participation of 30 percent in

1910 (Table 5). Irrigated cotton is an important crop in

Arizona, California, New Mexico, Oklahoma and Texas. These states produce 60 percent of all U.S. cotton and in the case of Arizona, cotton is the predominant crop (Table 6) and yields the highest productivity of the country with 1,301 lbs/acre in 1986 (Arizona Agricultural Statistics Service,

1987).

Cotton seed is a by product of cotton and until recently was considered almost worthless. Some farmers used the seed for cattle feed or plowed it under as fertilizer. The large bulk of seeds not used for these purposes was burned, dumped, or otherwise destroyd.

Breakdown of the seed into its usable products occurs at the oil mill. The oil mill starts the chain of processes by separating the seed into the meat, hull, and linter or short fiber trimmed from the seed coat. From the cottonseed

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74

75 hulls, a cattle feed and some minor chemical products are made; from the linters a host of fiber products and a lot of other products such as cellulose, plastics, paper, and industrial chemicals are made. From the seed kernel comes the oil and a high protein residue of great value to the livestock industry. The oil is the most important product of the seed, and around its refining and processing into usable forms cluster a large number of food industries.

Cotton is the most important source of vegetable oil in

United States. Seed from one bale of cotton will produce about

140 pounds of high grade oil. Cottonseed oil is not usually

traded internationally because it is a bulky commodity which make transportation relatively expensive

(Yearbook of Agriculture,

1985).

Cotton Management Practices

Cotton is a "subtropical crop". It is grown with full or supplemental irrigation, or totally on rainfall, on a variety of soil types ranging from heavy clays to light sandy barns. These soils must be more or less adequately drained and thus permit cotton roots to penetrate to a depth of about 1.5 meters or more. Cotton is grown in areas which differ widely in latitude, altitude, rainfall, temperature and length of growing season. The critical factor which limits cotton growing is the range in which the mean air temperature varies during the growing season. For

76 o optimum growth an average season temperature of 21 C is needed. The length of the growing season thus varies between 140 to 240 days depending on the temperature and latitude (Framji and Mahajan, 1973).

Although the cotton plant can tolerate a wide range of precipitation (75 to 2,500 mm) during the growing period, the adequate distribution of rainfall at its different stages of growth is the most important controlling factor in its production. Heavy rains injure the young seedlings as well as the fully grown plant. During the vegetative growth period, moderate rainfall with maximum sunshine is considered the best.

Most Arizona cotton growers pre-irrigate their cotton fields prior to planting. Rainfall is not considered when making decisions on cotton production management. One of the biggest decisions that the growers have to make in the early part of the cotton season is when to apply the first irrigation. In many cases growers irrigate too early.

Often young seedlings emerge when the weather is cold and windy, and thrips and other early season insects make for a shabby looking cotton stand. This premature irrigation normally lowers soil temperature and increases seedling disease. Young cotton seedlings will only grow when the temperature is favorable and no amount of water or fertilizer can make them grow if the temperature is not adequate (Stedman, 1986).

77

The nutritional needs of cotton are more complex than any other major crop. Cotton produces reproductive and vegetative growth simultaneously over a relatively long period of time and requires a continuous supply of nutrients to sustain its morphological development.

It is important that cotton has an adequate and balanced supply of mineral nutrients during the approximately 60 day period from planting to first flower.

Soil is the basic reservoir of plant nutrients and fertilizer should be applied only as needed to supplement the soil supply. Thus, nitrogen soil tests have limited utility unless the soil profile, cropping sequence, and seasonal effects are known. Of all fertilizer elements for cotton, nitrogen is needed in the greatest quantities. It takes about 140 pounds of nitrogen for two bales (960 pounds) of cotton and proportionately more for higher yields

(Maples, 1986).

Cotton can produce acceptable yields at much greater soil salinity than others crops. Maas and Hoffman (1977).

published a list of the relative salt tolerance of agricultural crops. This list provides two essential parameters sufficient for expressing salt tolerance. In the specific case of cotton, the maximum allowable salinity without yield reduction is 7.7 EC and yield decreases 5.2

percent per unit increase in salinity beyond the threshold.

In Figure 9, some crops have a specific shape of curve

I00

90 t'80

-a

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4 6 8 10 12 14

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16

EC

e

in millimhos per centimetre at

25°

Celsius

1

18

Figure 9. Salt Tolerance of Selected Crops (Bernstein,

1964).

76

79 representing the relationship between relative yield and salinity measured by EC.

Cotton diseases can begin to affect young plants from the moment the planted seed first absorbs moisture from the soil. Seed and soil-borne pathogenic fungi and bacteria, may attack seed from the inside and outside causing rot. The extent and intensity of pathogen attack is governed by forces that in some cases can be controlled or modified by judicious management.

One of the most beneficial but difficult, long term management decisions to be made concerns crop rotation or which crops should be grown in sequence. In this decision there is a conflict between economists and what might be considered good husbandry of the soil. Good crop rotation involves, in addition to other benefits, growing crops in sequences that result in reduced populations or activities of pathogenic microorganisms and increases in the beneficial ones. In general, small grains, corn or sorghum preceding cotton lead to less disease problems than, for example, alfalfa, sugar beets or continuous cotton.

Another way to manipulate the complex of beneficial and pathogenic microorganisms is through the uses of short term green manure crops such as small grains or legumes or, where available, animal manures (Garber, 1986).

This chapter dealt with the cotton crop the Maricopa

County. It introduced a brief review on the resource base

(climate,

80 soil, and water) and a description of its irrigation districts.

Maricopa County itself in 1985 contributed with 42% of cash receipts from agricultural marketing in the state of Arizona.

Given the economic importance of the cotton crop for

Arizona and the controls imposed in the utilization of groundwater ("Groundwater Management Act", 1980) for its production, a continuing search for new techniques to improve profits is of utmost significance. In Chapter 4 a detailed explanation of the methodoly adopted will be discussed.

81

CHAPTER 4

MATERIAL AND METHODS

This chapter discusses the derivation of the data and the methods necessary for the dynamic programming model. The first section is a discussion of those data necessary to define salt accumulation in the soil and the yield response function for cotton. The second section develops the theory of the model for tracing salt distribution over a number of soil layers as a result of several irrigations. The crop-production function and soil salinity relation that are incorporated in the the dynamic programming model with the goal of economic decision making are discussed in the third section. The statistical analysis of the estimated regression functions is presented in the fourth section.

The fifth section discusses the theory of dynamic programming for optimal irrigation water decisions in regard to state variables and decision variables. The last section discusses the theoretical basis for the cost-benefit analysis.

The Data

To verify the model for tracing salt distribution in the soil and to statisticaly estimate crop-production functions and soil salinity relations, agronomic data were obtained from field experiments conducted during the 1985 growing season that utilized the cotton variety Delta Pine

82

61. The experiment was conducted at the University of

Arizona, Maricopa Agricultural Center (MAC), located three miles north of the Casa Grande/Maricopa highway (Figure 10).

The purpose of the pilot study was to obtain data concerning the concentration and distribution patterns of chloride and nitrate using burned trickle irrigation and furrow irrigation.

The cotton was planted on April 12, 1985, on a soil classified as Casa Grande sandy loam, of the fine-loamy, mixed, hyperthermic Typic Natragids family (Nava Leon).

Under the burned trickle irrigation system, two water levels, 0.6 and 1.0 CU, were used in a randomized complete block design. Three sets of soil samples were taken on June

6, August 1 and October 12, and electrical conductivity and others variables like chloride and nitrate concentrations were determined from the 1:5 soil extract

(Table 7). Soil samples were taken at: 5, 20, 35, 50 cm distances measured horizontally from the drip line. At every horizontal distances, soil samples were taken at five depths: 0 - 5 cm, 5 - 20 cm, 20 - 35 cm, 35 - 50 cm and 50

- 65 cm. Each set of samples was repeated at 0, 7.5 and 15 cm from the emitter, along the drip line.

Nitrogen was injected following a six-week schedule which varied with the growth stage of the plant. The source of nitrogen was solution 32 (32 - 0 - 0) in the frist two applications and N - pHURIC ( 28 - 0 - 0 - 9 ) in

Phoenix

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Figure 10, Location of University of Arizona Maricopa Agricultural

Center.

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84

85 the following four applications. The fertilizer injection schedule started on June 10 during the presquared growth stage and termined on July 15 while the plants were flowering.

Costs and Returns

Net Return Over Variable Costs

Economic analysis of the impact of water management and water use policies requires data on the net returns over variable costs for each production activity. A production activity in the model is one acre of cotton that was grown using groundwater. Net returns above variable costs is the difference between gross income and the variable costs other than the variable cost of water and nitrogen. Gross income is the product of yield and output price. The output price assumed in this study is 65c per pound for cotton lint This price was determined from the 1985 Arizona Field Crop

Budgets for Maricopa County (Hathorn, Jr. and Farr).

Costs of Production

Hathorn, Jr. and Farr (1985), present a basic crop budget for Maricopa County as a genaral guide to the cost of producing cotton, and it can be used for any soil type and farm size. The budget was designed to help farmers in

86 making decisions on crop financing, machinery management and ownership, planning crop operations, and future expansion of the operating unit's capital. Costs in the budget are divided into cost of pumping groundwater, operations costs and ownership costs.

Cost of Pumping Groundwater

The price of water for most Maricopa County farmers is the variable cost of pumping groundwater. This cost varies with pumping lift and sources of energy, and as the depth of water varies throughout the county. Pumping lifts are divided into four categories: 310, 495, 545 and 600 foot lift. Prices of pumped water are summarized in

Table 8.

Operation Costs

Operation costs for cotton include all costs of land preparation, planting, fertilization, weed and insect control, up to and through harvesting except the costs of irrigation water and nitrogen. A summary of these costs is presented in Table 9.

Ownership Costs

Ownership costs are for those items which do not vary as crop pattern or crop acreage changes on a farm within a

87

TABLE 8. Cost of one Acre-Foot of Water for Different

Lift and Energy Sources in Maricopa County,

Arizona, 1985 ( $/Acre-foot ).

Lift

Electric

Energy Source

Nat. Gas

Diesel

Average

310 foot

495 foot

545 foot

600 foot

42.97

72.27

82.32

90.74

49.49

82.97

94.30

105.01

Source: Hathorn, Jr. and Farr, 1985.

49.54

81.04

92.78

103.26

47.33

78.76

89.80

99.67

TABLE 9. Operation Costs to Produce an Acre of Cotton with Drip

Irrigation (excluding water and nitrogen costs) in Maricopa County,

Arizona, 1985.

Items

Cost Contents

Machinery

Materials

Depreciation, Interest,

Taxes,

Insurance

Housing and

Herbicide, Insecticide defoliant, seed and other

Labor

Service

TOTAL

Source: Hathorn, Jr. and Farr, 1985.

Amount

(dollars)

238.89

224.89

41.62

209.34

709.74

88 relatively short planning period. Depreciation of machinery and buildings, taxes, interest on farm capital, management and bookkeeping, and other charges are summarized in

Table 10.

Model for Tracing Salt Distribution in the Soil

Since all irrigation waters contain a certain quantity of soluble salts, some changes will always occur in both the chemical and physical properties of soils upon the introduction of irrigation.

A model for tracing salt distribution over a number of sucessive irrigations, suggested by Bresler (1967) and applied by many reseachers (Feinerman et al., 1984;

Knapp, 1984; Shalhevet and Reiniger, 1964; Yaron and

Bresler, 1970; Yaron and Olian, 1973; Yaron, 1973) has proved to be useful in empirical studies intended to simulate and economically evaluate the above process. The model is essentially a reformulation of the law of mass conservation; it states that the amount of salt added by water applied to the soil layer, minus the amount leached out and the amount absorbed by the plants, is equal to the net increment (positive or negative) of salt in the soil layer.

89

TABLE 10. Ownership Costs to Producing an Acre of

Cotton in Maricopa County, 1985.

Items

Cost

Contents

Machinery

General Farm

Managment

Taxes and Inter.

Manag. Services

Depreciation and Interest

Water Distri. Dep., Inter., Taxes and

Insurance

TOTAL

Source: Hathorn, Jr. and Farr, 1985.

Amount

(dollars)

98.89

245.18

14.00

102.75

60.00

521.03

90

Empirical Application of the Model

In this study, a long-run model will be used that refers to the effects of salt accumulation in the soil profile over time. It comprises a succession of short-run processes, the initial conditions of which are affected by salt accumulation in previous periods irrigation over a single season taking into account the resulting terminal conditions due to each alternative and the effects in succeeding periods (Yaron and Olian, 1973).

On the basis of the above conditions, the model for tracing salt distribution over a number of soil layers as a result of several irrigations is drawn from the Bresler model and can be represented by the following system of linear equations: i

WjCwj-(Wj-I: Ek,j)

*

*

CSi,j-1 + CSi,j i * * *

=1) (CSk,j-CSk,j-1)Vi (13) k=1 2 k=1 where:

Wj = depth of j-th irrigation water applied ( cm );

Cwj = salt concentration in the j-th irrigation water

(dS/m);

Ei,j = the moisture use from the i-th layer in the period preceeding the j-th irrigation (cm);

CSi,j = salt concentration of the soil solution in the ith layer after the j-th irrigation (dS/m);

CSi,j-1 = initial average salt concentration in the soil solution at moisture content (dS/m);

91

Vi

= represents the amount of water contained

in the relevant ith soil layer at moisture content e

( cm

).

i = is the index of the soil layer (i = 1, 2,

3, .

. .,m) j = is the index of irrigation applied (j = 1, 2,

3, . .,n)

The above system consists of in x n linear independent equations in m x n unknowns, the unknowns

* being

Cij and, accordingly, the system is solvable by routine methods. Solving for CSi,j, we get

CSi,j =

2Wj*Ciwj - CSi,j-1 ( Wj -

27

Ek,j - 2Vi

K=1

Wj -Z Ek,j + 2Vi

K=1

(14)

Typical salt distributions in irrigated soil profiles, expressed as the the electrical conductivity of the saturation extract, are shown in Figure

11.

As the leaching fraction increases, salt accumulation in the lower soil profile decreases (

Bohn, McNeal and O'Connor,

1983 ).

Crop-Production Model

There is a growing need for improved knowledge of water response functions. Numerous studies have dealt with developing theories showing either yield as a function of

\

\

1.0

o o

EC dS/m

5

Fi

0

% \\

%

10

I

15

I

20

)

N\

n

\

N

%,•• n

*........

%N.

• 111,

...,....

0.13

\

\

\

\

• \

\

\

\

\

\

\

X

NO.25

.'.2.10

0.06

.

.

N.

\

\

1

I

I

1

1 I

1

Figure 11.

The

Steady-State

Profile of

(

Bohn et al.

, 1983 ).

Soil Salinity

92

93 gross water quantity or yield as a function of water quantity and water quality simultaneously. Detailed discussions can be found in

Hexen and Heady

(1978); Boster and Martin

(1979); Boster and Martin

(1977); Ayer and

Hoyt (1979); Boster (1976); Stearns (1980); and Kelly

(1981).

state

A crop-water production function, assuming steadyconditions that quantity and quality of irrigation water are constant from one year to the next and that precipitation is negligible, but taking into account the dynamics of salt accumulation over time, will be investigated in order to combine effects of yield, water quantity, water quality, nitrogen and initial soil salinity.

The most general relation that can represent the water production function for cotton is:

Y

= f( W, Ciw, N, CSo / K ) (15) where

Y

= crop yield per unit area of land

(kg/ha);

W = quantity of water of standard quality applied per unit area of land during the growing season

( cm

);

Ciw = is the salt concentration of the irrigation water expressed by the electrical conductivity

(EC) of the water

(dS/m);

N = quantity of nitrogen applied

(kg/ha);

CSo = initial salt concentration in the soil

(dS/m);

K = designating all other be constant.

factors, assumed to

94

As the salt concentration of the soil solution is a function of other variables, which can be expressed as:

CSt+1 = g(

W, Ciw, CSo / Z ) (18) where:

CSt+1 = salt concentration in the soil at the end of irrigation season

(dS/m);

W =

Quantity of water of standard quality applied per unit area of land during the growing season (cm);

Ciw = salt concentration of the irrigation water applied

( dS/m );

CSo = index of initial soil salinity;

Z = is the vector of all the constant factors influencing soil salinity;

In the context of irrigation with saline water, physical efficiency often refers to the allocation over time of a given quantity and quality of water so as to achieve a minimal amount of salt accumulation.

study.

Two different functional forms were used in the this

These are quadratic and power function

(Cobb-Douglas). For a review of production function literature see Beattie and Taylor

(1985);

Doll and

Orazen

(1978) and

Intrillator (1978)

From the point of view of the response functions and salt distribution in the soil, many assumptions are made before formulating the models. In the case of the production function and holding other variables constant, we expect

9 5 yield to increase as water quantity increases, decrease as initial soil salinity levels increase, decrease as the salt concentration of the irrigation water increases, and increase with an increase in nitrogen. Likewise, we expect ending soil salinity levels to decrease as water application levels increase, increase as initial soil salinity levels increase, and increase as the salt concentration of the irrigation water increases.

Economic Evaluation

The economic analysis of this study centers on profit maximization from crop-production functions for cotton. The maximization is constrained by the availability of resources such as land and water. The economic analysis is explored by means of the familiar constrained profit maximization model of the firm; this means that the firm is the entire collection of farms within a particular region. The analysis is a dynamic analysis in the sense that the maximization of profits in many years is considered.

Profit-Function

In this section, we created a simple model that demonstrates the short-run of the economically optimal combination of water quantity, water quality in irrigation and the amount of nitrogen.

96

Thus, we can represent the profit function of the each irrigation district as

NR = PyY - PqW - PcCiw - PnN - FC (17) where

NR = net return above all variable production costs except the cost of water and nitrogen for cotton;

Py = price of output

(5/kg);

Pq = cost per water unit of standard salinity;

Pc

= cost of deviating the salt concentration of one water unit by one ppm from the standard salinity;

Pn =

Price of nitrogen

( $/kg)

FC = fixed cost of production

Y,

W, Ciw and

N are, as previously explained, determinations of the optimal water quantity-salinity.

If we assume that the farmer is a profit maximizer, then, given the production functions for cotton at time t, he will go on applying inputs up to that point at which the marginal revenue of an input becomes equal to its unit price assuming the inputs are divisible. Thus, the quantities of inputs chosen by the farmer are such that their respective marginal revenue productivities at that level will equal to their respective prices.

The marginal revenue for profit maximization is

Y

PY

) = Pw

(18)

Py (

Py (

Y

) =

Pc

Ciw

Y

) = Pn

97

(19)

(20)

Solving this system simultaneously, we have the quantity of each W, Ciw and N that will maximize profits relative to fixed resources. Figure 12 is the graph of a generalized Total Physical Production (TPP) function

Y = f(W / CSo, Xl, X2, Xn ), where water was chosen as variable input of production only for the purposes of explanation. Point A reprents the maximum technical efficiency per acre obtainable from the variable input water. With the price of the input water and the price of output known, the firm's break-even line (BEL) can be computed.

The BEL is expressed as

Py.Y = Pw.W (21) where

Py is the price of output and

Pw is the price of input water. The slope of the BEL is given by the inverse ratio of prices

(

Figure

12 ).

Best Combination of Water Quantity and Quality in Short-Run

Let us consider the combinations of only two variable factors of production, water quantity

(W) and water quality ( Ciw ) which give the same level of output

Y2

Y1

1

Water Quantity

W

2

Figure

12.

Solution to the Factor-Product Decision Using

Physical Product Curve and a Break-Even Line a Total

(Hypothetical).

Break-LA/en

Line

Total

Physical Product

98

99

(isoquant) denoted by YY, and drawn on a graph in two dimensions (Figure 13). The axes being the quantity of water applied in irrigation (W), and the ordinate we are measuring the salinity of irrigation water (Ciw). For a given output level, ( 6 ) becomes

Y = f ( W, Ciw/ N, CSo, K ) (22) where all variables were defined before. Analysis of the estimated isoquant curve provides information on the marginal rate of substitution ( MRS ) of water quantity for water quality at a predetermined level of Yi. The marginal rate of 'substitution is useful in determining the crops sensitive to saline irrigation water. Since these two factors (W and Ciw) are independent of each other and the other variables in the yield function, we can calculate the

MRS between water quantity and water quality from the marginal productivities using the relation a

Y /C)C

MRScw - (23) a Y /Z04

Analysis of the estimated isocost curve ( defined in

Chapter II ) provides information on the total variable cost of water quantity and water quality.

MRScw > Pw / Pc

(24)

Y

Ciw

*

w*

Water Quantity

Figure 13. Solution to the Best Combination Decision Using Isoquant and

Isocost (Hypothetical).

100

101

The least cost quantity - quality combination is represented graphically in Figure 13 with the YY curve representing the isoquant at the Y level, the line segment

BD representing the isocost of the quantity and quality of water, and the point 01 is the optimal combination where the

MRS is equal to the price ratio

MRScw = Pw / Pc (25)

Clearly, if

MRScw >

Pw

Pc

(26) at any point on the isoquant and isocost curves, it means that an increase in water quantity and a decrease in water salinity is necessery to achieve the optimal combination. A move in the opposite diretion is justified if the inequality in (26) is reserved

MRScw <

Pw

Pc

(27)

In both cases, the decision-maker has to increase or decrease the amounts of variable inputs in order to achieve the least cost combination since the prices of these inputs are fixed.

The same analysis of the best combination can be used for the case of control of soil salinity by regulating the quantity and/or quality of the water applied.

102

For a given soil solution level, ( 6 ) becomes

CSt+1 = g ( W, Ciw / CSo, Z )

(28)

All these variables were previously defined. Analysis of the estimated isoquant curve provides information on the marginal rate of substitution

( MRS ) of water quantity for water quality at a predetermined level of soil salinity

( CSt+1 ) using the relation

MRSCW =

CSt+1 / Cw

CSt+1 / W

(29)

Next, let us consider those combinations of water quantity (W) and quality (Ciw) which yield the same soil salinity at the end of the irrigation season, denoted by

CSt+1. This model is drawn on a graph in two dimensions with the axes being water quantity and the salinity of water

(Figure 14). Available information regarding the process of salt accumulation and leaching suggest that the point of o minimun Ciw represents the case in which the cumulative amount of water applied (W) is equal to the amount extracted by the plants in the root zone. On the left of the minimum point (A), only salt accumulation takes place and salinity control due to water quantity and quality substitution is irrelevant. Control of soil salinity by the application of excess water for leaching is only possible therefore within the domain lying to the right of the minimum point.

CS

(t+1)

CS

(t+1)

C

*

C iw

A

W

*

W o

Water Quantity

Figure 14. Solution to the Best Combination Decision Using Iso-Salinity

Curve and Isocost (Hypothetical).

103

104

If we asume that X is a standard salinity of irrigation water (dS/m) and Pw is the cost per unit of

3 water of standard salinity ($/m ), and Pc is the cost of deviating the salt concentration of one water unit by one dS/m from the

3 standard salinity ( $/m /dS/m), the following analysis is possible: for

Ciw > X, this imply that Pw is adjusted downwards, i.e., the quality of water is less than the standard salinity. For Ciw < X, it is adjusted upwards, this mean the quality of water is better than the standard salinity. Such an adjustment can be thought of as premium received or paid by the water user, respectively, according to the quality of water.

Then, the least cost combination of water quantity and quality is obtained when the iso-salinity curve (CSt+1) is tangent to iso-cost curve (BB), this is, the marginal rate of substituition of water quality for quantity be equal to the ratio of the cost per water unit adjusted for quality to the cost of varying the concentration of the given quantity of water by one dS/m.

MRScw= Pw / Pc (30)

Clearly, if

MRScw > Pw / Pc or

MRScw < Pw / Pc

(31)

(32)

105 at any point on the iso-salinity curve, it pays to simultaneously increase water quantity and decrease water quality in the case of inequality (31), or move in the opposite direction if the inequality in (32) is presented.

The LongLkun Optimization

The "long-run" model deals with the effects of salt accumulation over time in the soil profile. It takes into account a sucession of short-run periods, the initial conditions of which are affected by salt accumulation in previous periods, that is, according to alternative decisions: The irrigation decision over a single period may affect the terminal conditions, and their effects on succeeding periods (Yaron and Olian, 1973).

The basic concept of "long-run" problems may be viewed as comprising the following subsystems: (1) a subsystem which relates the decision variables, such as irrigation methods, time and depth of water applied, and quality of irrigation water, to the state variables, that are available to decision makers such as the variation in soil moisture and salinity; and (2) a subsystem which relates the state variables to the target variables, quantity and quality of water.

Statistical Analysis

Ordinary least square regression analysis was used to estimate the quadratic and power production functions.

106

This statistical technique estimates the intercept and slope of a line from observations of the levels of an independent variable associated levels of the dependent variable.

The coefficient of determination, R, and t-statistics are used to show the statistical reliability of the estimated regression line.

A Dynamic Programming Model

This section will deal with a dynamic programming approach for optimal scheduling of irrigation with water of different levels of salinity. This model was presented by

Yaron, Bielorai and Harpinist (1980).

The dynamic programming approach involves the optimization of a multistage decision process. That is, it basically divides given problem into stages or subproblems and then solves the subproblems sequentially until the initial problem is finally solved.

The characteristics of the dynamic programming model are: (1) the problem must be suitable for division into stages, that is a point at which a decision is to be made;

(2) at each stage the system can be in one of a number of possible states; (3) at each stage the decision made will result in a transformation from the present state in the present stage to another state in the next stage: and (4) is the principal of optimality set forth by Hellman; "An optimal policy (set of decisions) has the property that

107 whatever the initial state and decisions are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision " (Bellman and

Kalaba, 1965, p. 35).

Simulation of Dynamic Programming Model

Simulation is one technique available for solving problems. It involves the constrution of a model of the problem on which the decision-makers experiment and test alternative courses of action. This technique provides insights into the problem and places us in a better position from which to seek a solution. According to Poole and

Szymankiewicz (1977, p.4), "Simulation is a trial and error approach which allows us to describe a problem and gain understanding of the factors involved, by asking questions and observing the answers."

Simulation analysis will be used to describe alternative irrigation decisions in regard to quantity and quality of irrigation water and the quantity of nitrogen at any time of the year.

If we assume a planning horizon of N stages or years, with a single year being a basic unit in the sequence, then a dynamic programming model can be formulated. The following elements comprise the model:

(1)

(n) will denote state i at the beginning of year n, at the termination of the growing season of the previous

108 year; (2) di will denote k-th decision (k = 1, 2, ..,k) taken at state i at the beginning of any year; (3) fi is the immediate net return in any year n derived from decision k at state i; and (4) NRi(n) is the maximal excepted profit of the accumulative net return at state i in year n (Yaron,

1973).

Models of different type, presicion and complexity can be used to simulate the efficient combination of quantity and quality of irrigation water and the quantity of nitrogen applied to various crops in accordance with the desired salinity distribution within the soil profile. To evaluate this efficient combination, dynamic programming and computer simulation will be used. The objective function is the maximization of profit. The set of decision variables (time and depth of water applied, method of irrigation, quality of irrigation water, and quantity of nitrogen) and restrictions ( quantity and quality of water be predetermined) are the other components in the formulation of a linear program in order to achieve the desired objective.

The optimization problem is formulated as

Oo

1

Max NR to

:

A (l+r)t

{ Py * Y(t) - ( Pw * Wj(t)

+ Pn * N(t) )) (33)

109

Subject to:

Constraint

Constraint

Constraint

Constraint

Constraint

Constraint

Constraint

Constraint

1:

2:

3:

4:

5:

6:

7:

8:

Y

(t)

= f( W

, Ciw , N , CSo

(t) (t) (t)

(t)

/ K )

CS

(t+1)

= g(W ,Ciw ,CSo

(t) (t) (t)

/ Z )

Water

* X - TOTGW = 0

1

Water

* X - TOTMW = 0

2

Water

* X - TOTPW = 0

3

Area planted with cotton

<

Land for crops

Total Water

=

Water

+ Water

+

Water

1 2 3

C1.W1 + C2.W2 + C3.W3

Concj =

Total Water

Wj >

ET Constraint

9:

Where

NR = is the net returns above all variable costs of water and nitrogen for cotton grown with water source j; r = is the interest rate; t = number of years;

Py = is the market price of cotton

($/kg);

Y

= quantity of cotton produced in year t

(kg/ha);

Pw = price of the irrigation water ($/cm);

W = is the quantity of irrigation water from source j, in year t ( cm);

110

Pn =

price of nitrogen

($/kg);

N =

is the quantity of nitrogen

(kg/ha);

Ciw =

is the salt concentration of irrigation water from source

j (dS/m);

CSo =

is initial soil salinity in year

t (dS/m);

CS(t+1)=

is salt accumulation in the soil in the year

t+1 (dS/M);

K =

designating all other factors, assumed to be constant in the crop-production function;

Z =

is the vector of all the constant factors influencing soil salinity;

Waterl =

is an acre-feet of good water applied to each acre of cotton in year

t;

TOTGW =

slack variable

=

total water of good quality used in year

t;

Water2 =

acre-feet of water of median quality used in year

t;

TOTMW =

slack variable

=

total water of median quality used in year

t:

Water3 =

quantity of water of poor quality used for irrigation in year

t:

TOTPW =

slack variable

=

total water of poor quality available in year

t;

Concj =

is the salt concentration of irrigation water from source

j;

ET

=

is a parameter representing annual

evapotransporation

from the root zone;

J =

source of water

1 =

good water

2 =

medium water quality

3 =

poor quality water

111

Description of the Constraints

Constraint 1 is a crop-production function for cotton taking into account the water quantity, water quality, nitrogen and salt accumulation in the soil.

Constraint

2 is a soil-salinity relation as a function of water quantity, water quality and initial soil salinity.

Constraint

3 means that the total annual water of good quality used to irrigate cotton times the area planted with cotton, can not be greater than the total water of good quality available in year t.

Constraint

4 means that the quantity of water of median quality used to irrigate cotton times the area planted with cotton can not be greater than the total water of median quality available in year t.

Constraint

5 means that the total water of poor quality used to irrigate cotton times the area planted with cotton can not exceed the quantity of water of poor quality available in year t.

Constraint 6 means that the number of hectares planted with cotton must be lower or equal the total land available for crops.

Constraint 7 means that total water used to irrigate cotton is equal to water of good quality plus water of median quality plus water of poor quality.

Constraint 8 means that water concentration is equal the average concentration of different water sources.

112

Constraint 9 represents an implicit assumption that yield decreases are caused by soil salinity and not by moisture stressing.

The Description of a Risk Situation

Simulation analysis will be used again to decrease the farm risk and uncertainty with regard to the quantity and quality of water supplies and the quantity of nitrogen.

Even though a farmer is promised a certain quantity of water, he is always uncertain about the marginal productivities / aXij), since they differ according to the quantity and quality of water supplied. The farmer can be either a pessimist or a risk lover. If he belongs to the first category, which is the case for most subsistence farmers, then he will have the ratio of marginal revenue productivities of inputs to their respective prices greater than unity ( MRP > 1). From these results, we can conclude that the farmer is a risk averter since he is using less water than the efficient amount.

On the other hand, if the ratio of marginal revenue productivities will be less than the unit (MRP < 1 ), we can conclude that there is no overuse of input by farmers, but rather the failure of the water system in delivering the expected level of water ( Sampath et al., 1986). This situation can be seen in Figure 15.

1

MRP

;

Water Quantity

Figure 15. Value of Marginal Revenue

Productivity

( Hypothetical

).

113

114

If W < W , this implies that the ratio of marginal revenue productivities will be greater than unit (MRP > 1), and is in the range of farmer risk aversion. If we have the reverse situation (W > W ), this implies that the ratio of marginal revenue productivities will be less than unit ( MRP<1 ) and is in the range of failure of the water delivery system.

Cost:: Benefit Analysis

To complete the economic analysis, all costs and benefits are quantified in dollars over a planning horizon of

N years and discounted to arrive at their present value.

Cost-benefit analysis should reveal the full extent of all private and social cost and benefits with respect to their impacts on national income and the distribution of that income among the various sectors of the population in the present and future.

Calculation of Project Worth

The three principal value measures utilized in costbenefit analysis are: ( 1 ) Net Present Value, ( 2 )

Internal Rate of Return; and

( 3 ) Cost-benefit Ratio.

The Net

Present Value measure provides net dollar amounts expected from the investment at the selected discount rate. The formula for the calculation of

NPV is :

NPV=

Bt - Ct

( 1 r )t

where:

NPV =

Net Present Value

B =

benefit of year

t

C =

cost of

t r =

discount rate

t =

time, from year

1

to

n

115

(34)

The Internal Rate of Return is defined as the rate of discount which makes the present value of a stream of income less its cost equal to zero; that is, the

IRR

is the discount rate,

r,

such that:

IRR :

Bo

-

Co

= 0

(35)

The Cost-Benefit Ratio is used to compare economic benefits with costs where both are reduced to dollar values and discounted to a

commom

point in time.

Sensitivity Analysis

Because there is always uncertainty about the future, it is necessary for decision-makers to test the sensitivity of the analysis to dominant cost factors, which have the most significant impact on the total net present value

(PV) and cost-benefit ratio, and make assumptions in order to portray a complete picture of the future.

116

Decision-makers are rarely sure about their decision and the degree of uncertainty generally increases with the time interval between the decision and the occurence. At that time, when the decision-makers have only subjective notions about the future state variables, they must make the alternative decision what to do with the salt concentration in the soil profile. Then, in the following period of time, they must determine their farm management strategy, that is, these target variables will be conditional upon both the initial alternative decisions and the intervening state variables.

Block-Diagram Presentation: An Overview

A generalized block-diagram presentation of an inputoutput system for the dynamic programming model can be viewed as comprising the following major subsystems: (1) objectives and goals; (2) the input-output mechanism ( cropproduction function for cotton and soil salinity relation);

(3) decision variables (water quantity, water quality and amount of nitrogen); (4) state variable (initial soil salinity); (5) exogenous factors or uncontrolled inputs

(weather, price levels and state world economy); (6) target variable or outputs ( quantity and quality of yield, and quantity of salt accumulation in the soil); and (7) evaluation of outputs (Figure 16).

117

Decision

Variables,

-

Objectives and

Goals

Salt Accumulation Model,

Crop-Production Function and

Soil Salinity Relation ynamic Programming

Model

[

Exogenous

Factors

[ State

Variable

Target Variables or

Outputs

Evaluation of the

- - — - — — - - - --- Target Variables

Figure 16. A Generalized Block-Diagram Presentation of an

Input-Output System for the Dynamic Programming

Model.

118

CHAPTER 5

RESULTS OF THE ANALYSES

The overall objective of this study, as stated in

Chapter I, was to investigate the dynamics of salt accumulation in the soil over time as affected by the quantity and quality of irrigation water, amount of nitrogen and initial soil salinity. Empirical analysis of the problem is based on experimental data for cotton production in

Maricopa County, Arizona. The dynamics of salt accumulation is based on the model for tracing salt distribution in the soil suggested by Bresler. Bresler's model is reviewed in the first section of this chapter. Econometric estimates of crop production function are requered for the analyses.

Regression results with their respective coefficients of

-2 multiple determination (R ), the adjusted coefficient of

2 multiple determination (R ), the F value and the degrees of freedom (DF) are presented in the second section. The economic results of the yield response function and the soil salinity relation for cotton, for the best combination of the variable inputs under several alternative management strategies, are discussed in the third section. Simulations of the dynamic programming model are discussed in the fuorth section. And in the last section the results of the cost-benefit analysis are discussed.

119

Appliication of Bresler's Model

No conclusions could be drawn with respect to Bresler's model because there was not any correspondence between the observed average salt concentration in the soil profile and that calculated according to the model. The deviations between these two results apparently occurred because

Bresler's soil salinity model requires knowledge of consumptive use. Consumptive use data under drip irrigation are not yet well specified. For example, Erie et al. (1982) indicate seasonal consumptive use of 41.2 inches on cotton near Mesa, Arizona. On the other hand, on-farm experiments with drip system have produced high cotton yields with 31-35 inches of applied irrigation water. Second, during the experiment a week of cold weather with soil temperature below 50 F resulted in poor stand establisment (Tucker et al., 1986). Third, because drip irrigation on cotton is a new technology and most of the information about it is tentative, weakness in the statistical analyses is expected

(Wilson et al., 1984).

Application of Crop-Production Function

The logarithmic equations for both ralations, i.e., yield response function and salt accumulation in the soil, gave a better fit than the quadratic equations. Regression results are reported in Table 11 with their statistical

2 analyses. The yield response function presented an R value

0

r.

1

1

1

1

1

1

1

LL

.r..1

CL

OD

0 tn up

-..

Ci

En

C

,... rn rr C-1

-

r

,

UD r

,

N

N.

T

-

--.

CD

N

CD

0 • •

0

111

C.)

-

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m

Cr' rt rr; .--..

* ri

^

4

0

N1 r

,

CD

CD

IN

CD

....4 ..-1 0

s .

,-; ,,,,

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Cn

C i /r

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r‘L

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. ,.;.,,

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2:

Cr

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Cf

.-.1

-1-

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,

17: ..--.. rn r, p...

.e.

-sf ..4.

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... rin

Er,

'.Of.- To)

• t1 Nt

C1

CI

CD

N1

CD

7t

^

4

ii, 0 C)

CD

0

• . m.-, i.._,

1-3. ..,.... ,...,•

0 r-i

+

ii

D-

CP

0

,-; rn

.e-2 r, N1

CD

• • •

-i-

H p,

,A

+

4-

1

.....,

(21

Ci cr,

0

.---, :----,

1

-

I

CI

7 up "- CD

Cri

. .

.

,

...e

LA

1

N1 n'i r7

Nt 0e

,

Nt

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r:

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Cr'

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e",

rn

71"

7t

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01%

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1 f

1

120

121

2 of .86 and the log soil salinity relation an R value of

.68. This means that 86 percent of the yield variation is explained by water quantity, water quality, quantity of nitrogen and initial soil salinity, and that 68 percent of the accumulation of the soil salinity is explained by water quantity, water quality and initial soil salinity.

The empirical results have implications for economic analysis. In the case of the yield production function, the water quantity coefficient has an absolute value greater than one. This has two implications; first, it has increasing marginal productivity with respect to water quantity; second, in the case of Cobb Douglas production functions the coefficients of regression are the coefficients of elasticity of production. In the case of water quantity, the function has an elasticity of production greater than one. This means, if the quantity of water increases 10 percent it results in an increase more than proportional, 11 percent, in the production of cotton.

Water quality and nitrogen have an absolute value less than one. This implies decreasing marginal productivity with respect to these variables and elasticity of prodution less than proportional. The initial soil salinity variable has a negative regression coefficient which also impies decreasing marginal productivity and elasticity of production less than zero. This means an increase of 10

122 percent in the initial soil salinity, will decrease cotton production by

3.32 percent.

Nitrogen with a very low elasticity has little significance in the production function response. This implies that nitrogem does not contribute to increase production; on the contrary, it contributes only to decrease the profit of cotton.

In the case of soil salinity relations, the water quality coefficient has an absolute value greater than one.

This implies increasing marginal productivity with respect to this input. Water quantity and initial soil salinity have negative values which imply decreasing marginal productivity.

Average Productivities and Marginal Productivities

Table 12 presents the productivities, average and marginal, for the yield response function. The marginal productivities of the factors of production were estimated for the specific case of the Cobb-Douglas production function through the partial elasticities of production and average productivity, that is, MPPxi = bi * APPxi.

The marginal productivity of water quantity is greater than the average productivity. This means a shortage of water is being applied and the use of this variable input is in the first stage of production (Figure

5). Water quality and nitrogen presents average productivity greater than

123 marginal productivity, which implies rational use of these inputs. Initial soil salinity has a marginal productivity less than zero, which implies excess of this variable input and operation in the irrational stage of production.

Table 13 presents the productivities, average and marginal, for soil salinity function. In this case water quantity and initial soil salinity have negative marginal productivities, which imply excess of these factors of production. Water quality presents marginal productivity greather than average productivity which means that a rational level of salts was contained in the irrigation water.

Best Combination of the Factors of Production

The Marginal Rate of Substitution (MRS) is a technical concept which indicates the possibility of substitution of one input for other. With the introduction of prices it is possible to determine the best combination of the factors of production. In the case of the yield response function, the marginal rate of substitution and the ratio of prices are presented for the water quantity, water quality and nitrogen variables.

In the substitution of water quality for water quantity, that MRS is greater than the ratio of price

(table 14). This means that to obtain the optimum combination the decision-maker has to decrease the MRS

124

TABLE 12. Marginal and Average Physical Productivities for the Cotton Response Function

Inputs

Water Quantity (W)

Water Quality (C ) iw

Nitrogen (N)

Initial Soil

Salinity

(CSO)

MPP

15.62

1,813.05

.005

-16.01

APP

14.16

3,580.35

9.21

48.20

TABLE

13. Marginal and Average Physical Productivities for the Soil Salinity Relation

Inputs

Water Quantity (W)

Water Quality (Ciw)

Initial Soil

Salinity (CSO)

MPP

-.80

103.17

-.0113

APP

.87

73.77

.91

125 through an increase of water quantity and decrease in the quality of the water for irrigation. In the substitution of water quantity for nitrogen, the MRS is again greater than the ratio of prices. This implies that the farmer has to incrase the quantity of water and decrease the amount of nitrogen in order to achieve the best combination.

In the case of the soil salinty relation, the results of Marginal Rate for Substitution (MRS) and ratio of prices are presented in Table 15. In the substitution of water quality for water quantity the marginal rate of substitution is greater than the ratio of prices, this means at water quantity must be increased and the quality of water must decrease.

Application of the Dynamic Programming Model

The results of the dynamic programming model for the state variables and decision variables are presented in this section.

In this study a long-run approach to the economic results of water quantity, water quality, nitrogen and initial soil salinity was described. The period studied was five years and the emphasis of the study was on the methodology. Empirical estimates for one selected area and one crop were presented. The model can accommodate other situations such as different farm sizes and different system

126

TABLE 14. Marginal Rate of Substitution and the Ratio of Prices for the Yield Response Funtion

Ratio of Prices Inputs water quality

(Ciw) vs water quantity

(W) water quantity vs nitrogen (N)

(W)

MRS

116.07

3,323.40

1.20

2.44

TABLE 15. Marginal Rate of Substitution and the Ratio of Prices for the Soil Salinity Relation

Inputs

Water Quality

(Ciw) vs

Water Quantity

(N)

MRS

128.96

Ratio of Prices

1.20

127 of irrigation. It can accommodate other decision variables such as quality of the leaching water, timing of irrigation and intervals between sucessive irrigations, and other state variables like soil moisture. This methodology can be applied with minor modifications to the analysis of regional situations where acreage and/or water quantity and quality are constraints, in situations where there are no constraints, and in stochastic analysis where rainfall and temperature are take into account.

The estimated crop response function and soil salinity relation were incorporated into the dynamic programming analysis with the goal of economic decision model. The dynamic programming model involves the optimization of a multistage decisions process. That is, it basically divides a given problem into stages or subproblems and then solves the subproblems sequentially until the initial problem is finally solved. The model assumes one acre of cotton which can be irrigated with three different sources of water

(good, medium and poor quality). The state variable was initial soil salinity with alternatives of 1, 2, . . , 10 dS/m, and the decision variables were water quantity with depth alternatives of 104, 114, 124 and 134 cm, water quality with alternatives of 2, 4 and 6 dS/m, and nitrogen that entered in the model as an exogeneous variable and constant throughout the growing season. In each run, we

128 considered different levels of nitrogen, namely 1, 56, 75,

113, 225, and 337 kg/ha. Crop rotation was not considered in this model and cotton was grown on the same plot through the five years of the analysis.

The results of the dynamic programming model are presented in tables

16, 17 and 18. The results show that the optimal policy for a decision-maker allocates a given quantity of water and

56 lbs/acre of nitrogen for various initial soil salinity levels and over an irrigation season.

In Table 16 an optimal decision rule for cotton is simulated with two different sources of water, good (W1) and medium quality (W2), and an average salt concentration of irrigation water of 2.59 dS/m. The results in this table show low values of yield and profit per acre for cotton, and they decrease as initial soil salinity levels increase.

In Table 17 an optimum decision rule for cotton is simulated with two different sources of water, good water

(W1) and poor water (W3), and an average salt concentration of the irrigation water of 3.19 dS/m. These results are better than those presented in Table

16, but they still low.

Table

18 contains another kind of simulation for optimum decision rule in which cotton can be grown using two different sources of water, medium quality (W2) and poor water (W3), and an average of salt concentration in the irrigation water of 4.59 dS/m. These are the best results found in the analysis.

129

Table

16. Simulation of the Optimal Decision Rule for Cotton Irrigated with two Different

Sources of Water (good and medium water quality).

CSo

Ciw

(dS/m)

(dS/m)

W1

(cm)

6.00

7.00

8.00

9.00

10.00

1.00

2.00

3.00

4.00

5.00

2.59

2.59

2.59

2.59

2.59

2.59

2.59

2.59

2.59

2.59

Nitrogen

= 56 kg/ha

94.68

94.68

94.68

94.68

94.68

94.68

94.68

94.68

94.68

94.68

W2

(cm)

40.0

40.0

40.0

40.0

40.0

40.0

40.0

40.0

40.0

40.0

Yield

(Kg/ha)

605.47

480.97

420.38

382.08

352.79

333.94

317.28

303.52

291.87

281.84

Profit

(dollars)

587.34

408.93

322.10

267.22

225.25

198.23

174.36

154.64

137.95

123.58

Where,

CSo = initial soil salinity;

Ciw = concentration of the irrigation water;

W1 = good water quality;

W2 = medium water quality.

130

Table

17. Simulation of the Optimal Decision Rule for Cotton Irrigated with two Different

Sources of Water ( good and poor water quality).

Nitrogen = 56 Kg/ha

6.00

7.00

8.00

9.00

10.00

1.00

2.00

3.00

4.00

5.00

CSo

(dS/m)

Ciw

(dS/m)

W1

(cm)

3.19

3.19

3.19

3.19

3.19

3.19

3.19

3.19

3.19

3.19

94.68

94.68

94.68

94.68

94.68

94.68

94.68

94.68

94.68

94.68

W3

(cm)

40.0

40.0

40.0

40.0

40.0

40.0

40.0

40.0

40.0

40.0

Yield

(Kg/ha)

672.10

533.91

466.65

424.13

393.84

370.70

352.20

336.92

323.99

312.86

Profit

(dollars)

694.82

496.79

400.41

339.48

296.07

262.91

236.40

214.50

195.97

180.03

Where,

CSo = initial soil salinity;

Ciw = concentration of the irrigation water;

W1 = good water quality;

W3 = poor water quality.

Table 18. Simulation of the Optimal Decision Rule for Cotton Irrigated with two Different

Sources of Water ( medium and poor water quality).

6

7

8

9

3

4

1

2

5

10

CSo

Ciw

(dS/m) (dS/m)

Nitrogen = 56 kg/ha

W2

(cm)

W3

(cm)

Yield

Profit

(kg/ha) (dollars)

4.59

4.59

4.59

4.59

4.59

4.59

4.59

4.59

4.59

4.59

94.68

94.68

94.68

94.68

94.68

94.58

94.58

94.58

94.58

94.58

40.00

40.00

40.00

40.00

40.00

40.00

40.00

40.00

40.00

40.00

808.70

642.42

561.49

510.33

473.88

446.04

423.78

405.40

389.84

376.44

976.72

738.45

622.48

549.16

496.93

457.04

425.14

398.80

376.50

357.30

Where,

CSo = initial soil salinity;

Ciw = concentration of irrigation water;

W2 = medium water quality;

W3 = poor water quality.

132

I can conclude that the best results in terms of yield and profit per acre are obtained when we used water of less quality, i.e., the mixture of medium and poor water quality.

In all simulations, a steady-state solution for salt accumulation in the soil was found for each initial soil salinity (Table 19). This means that does not matter what will be the value of the state variable it will achieve the steady-state value. A steady-state solution to a dynamic optimization problem, according to Dinar and Knapp (1986, p.

64), is defined "as the value for the state variable

(soil salinity in this case) which, once achieved, will be maintained forever under the optimal policy."

The Net Present Value for the alternative that the research was using the medium and poor water quality and the initial soil salinity of 1 dS/m is present in Table 20.

The negative result for profits in the first year of our empirical analysis and in the case of negative returns to land and management can be explained by high production costs and depressed market prices.

Sensitivity analysis with respect to crop and inputs prices (water and nitrogen) was analyzed. The profibility of cotton irrigated with drip system is sensitive to yield increase, price of variable inputs, and in the interest rate. The sensitive analysis with respect to increase in yield by 20 percent and in the price of cotton by 20 percent

TABLE 19. Time Paths for Soil Salinity

5

6

3

4

7

8

9

10

1

2

Initial Soil

Salinity

1

0.184

0.182

0.181

0.180

0.180

0.179

0.179

0.179

0.178

0.178

2

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

Year

3

0.188

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

4

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

5

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

0.187

133

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135 changed the result of the net present value. The data used in this performance are presented in table 21. In this case, the results changed from - $ 5,842.00 to -$ 1,650.00.

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137

CHAPTER

6

SUMMARY AND CONCLUSIONS

Recently, greater attention is being given to water allocation over a long periods of time for irrigation and salt-leaching purposes. Use of irrigation is rapidly increasing around the world and managers of these irrigated areas are facing problems coping with salinity. Irrigated agriculture is dependent on an adequate water supply of usable quality. If the water is not of good quality, it can markedly alter the growth of the plants through salt accumulation in the soil. The principal salt problem of economic importance arises when previously non-saline soils become saline as a result of irrigation.

The objective of this study was to provide econometric estimates of a crop water response function for cotton and soil salinity accumulation in relation to water quantity, water quality, nitrogen, and initial soil salinity. This approach leads to better management of salinity in the soil because salt accumulation is a dynamic process over several irrigation seasons.

To verify the model for tracing salt distribution in the soil and to statistically estimate a crop production function and soil salinity relation, agronomic data were used from field experiments during the 1985 growing season and that utilized cotton variety Delta Pine 61. The

138 experiment was conducted at the University of Arizona,

Maricopa Agricultural Center ( MAC ). The purpose of the

1985 pilot study was to obtain data concerning the concentration and distribution patterns of chloride and nitrate using burned trickle irrigation and furrow irrigation.

The cotton was planted on April 12, 1985 on a soil classified as Casa Grande sandy loam, of fine-loamy, mixed, hyperthermic Typic Natragids family ( Nava Leon ). Under the buried trickle irrigation system, two water levels, 0.6

and 1.0 CU, were used in a randomized complete block design.

Soil samples were taken and electrical conductivity, chloride and nitrate concentrations were determined from the

1:5 soil extract.

The yield response functions and soil relations were estimated for cotton. salinity

Two different functional forms were used in the analysis, the Cobb-Douglas

( power function ) and the quadratic function. The case of

Cobb-Douglas equation, it is the most used in empirical analysis of production functions. Some assumptions were made before formulating the models. In the case of the production function, while holding other variables constant yield was expected to increase as water quantity increases, decrease as initial soil salinity levels increase, decrease as salt concentration of the irigation water increases, and increase as the increase of nitrogen.

Likewise, was

139 expected ending soil salinity levels to decrease as water application levels incease, increase as initial soil salinity levels increase, and increase as the salt concentration of irrigation water increases.

The estimated crop response function and soil salinity relation were incorporated in the dynamic programming model with the goal of economic decision making. The dynamic programming model involves the optimization of a multistage decision process. That is, it basically divides a given problem into stages or subproblems and then solves the subproblems sequentially until the initial problem is finally solved. The model assumed one acre of cotton can be irrigated with three different sources of water

(good, medium and poor water quality). The state variable was initial soil salinity and the decision variables were water quantity, water quality and nitrogen which entered in the analysis as an exogeneous variable. A five year planning horizon years was assumed.

The Cobb-Douglas production function gave the best

2 results and had an R value of .86 for the yield response function and .68 for the soil salinity relation. This means that 86 percent of yield is explained by water quantity, water quality, quantity of nitrogen and initial soil salinity, and that 68 percent of the salt accumulation in the soil is explained by water quantity, water quality and initial soil salinity. Specific results are:

140

1 ) In the case of crop response function, the water quantity coefficient had an absolute value greater than one.

This means that yield increases more than proportional to the increase in water quantity;

2 ) The water quality coefficient had an absolute value less than one but greater than zero. This means that yield increases when the salt concentration of the irrigation water increases;

3 ) The nitrogen coefficient had an absolute value less than one and greater than zero. This coefficient was very small indicating that additional units of this input will not significantly increase the output. One reason is because of high initial soil NO N.

3

According to Tucker et al. (1986), yield was increased by nitrogen applications of

50 lbs/acre;

4 ) The coefficient for initial soil salinity had a negative value which implies negative marginal productivity or excess salt in the soil;

5 ) In the case of soil salinity relations, the water quality coefficient had an absolute value greater than one.

This implies increasing marginal productivity with respect this input. Water quantity and initial soil salinity had negative coefficient which imply decreasing marginal productivity;

6 ) Concernning the best combination amoung the variable inputs, that marginal rate of substitution of water

141 quality for water quantity was greater than the ratio of prices. This means that the optimum combination is obtained by increasing the water quantity and decrease the quality of irrigation water. In the substitution of water quantity for the quantity of nitrogen, the marginal ratio of substitution also was greater than the ratio of prices.

This implies that the decision maker has to increase the quantity water until obtain the optimum point.

The estimated crop response function and soil salinity relation were incorporated in the simulation of the dynamic programming model with the goals of economic decision analysis.

The results of the dynamic programming model in terms of yield and profit per acre of cotton were very low, but the reasonable results were got when we used water of less quality, i. e., the mixture of medium and poor quality.

Time paths of soil salinity was found for different initial soil salinities. In each case the time path converge to a steady-state conditions.

The Net Present Value was calculated using the alternative of medium and poor water quality. Negative results was obtained for the returns to land and management and that can be explained by high production costs and depressed market prices. The profitability of cotton irrigated with drip system is sensitive to yield increases and increase in the price of cotton.

142

Suggested Research

The methodology used in this study represents a new approach to optimizing water resource decision making, but further research is needed to evaluate it throughly.

The following topics are suggested for future research.

1 ) A first step would be to improve the model of salt accumulation in which all variables must be defined before the field experiment be installed;

2 ) Estimate crop yield variations according to individual irrigation technologies, such as drip, sprinkler and furrow irigation;

3 ) Estimate aggregate regional production functions taking into account different soil types, farm sizes, irrigation districts, and different crops;

4 ) Estimate the regional optimal acreage to plant with an irrigated crop with the objective to restraint the production;

5 ) Study what is the best policy in terms of water conservation through the analysis of effects on quantity of water demanded when price is increased.

These recommendations should improve the results of the dynamic programming and Bresler's models and provide good results for decision makers in the county.

APPENDIX

A

SYMBOLS

AND

ABBREVIATIONS

143

cm

CU

EC centimeter consumptive use

- electrical conductivity of the 1:5 ( wt:vol ) soil extract

- evapotranspiration

ET

- liters ppm - parts per million

144

APPENDIX

B

DATA FOR THE SOIL SALINITY RELATION AND CROP WATER

PRODUCTION FUNCTION

145

TABLE B-1. Data for the Salt Accumulation in the Soil.

146

CS(t+1)

(dS/m)

Water

(cm)

ET

(cm)

V

(cm)

Ciw

(dS/m)

CSO

(dS/m)

42.07

28.43

14.20

46.57

34.97

27.01

24.21

17.00

19.40

12.85

17.30

25.53

25.53

25.53

23.43

23.43

37.76

37.76

23.74

23.74

39.43

29.43

3.47

3.47

3.47

22.40

22.40

22.40

22.40

30.16

30.16

30.16

30.16

2.17

1.87

1.71

1.04

1.04

2.11

1.89

1.48

1.60

1.92

1.62

.49

.41

.22

.38

.38

.50

.39

.27

.30

.26

.30

18.80

19.60

21.70

42.07

28.43

42.07

28.43

46.57

34.97

27.01

24.21

Where

CS(t41) = salt concentration in the soil;

W = depth of irrigation water;

ET

= evapotranspiration;

V = is the amount of water contained in the relevant soil layer at moisture content

Ciw = salt concentration of the irrigation water

CSO = initial soil salinity

TABLE B-2. Data for the Analysis of Regression.

Yield

(Kg/ha)

906.00

1083.00

771.00

1063.00

929.00

929.00

1162.00

894.00

1008.00

1036.00

890.00

1020.00

1071.00

1004.00

1225.00

1076.00

1047.00

992.00

1374.00

1475.00

1721.00

1437.00

1335.00

1571.00

1449.00

1575.00

1654.00

1654.00

1508.00

1705.00

1295.00

1638.00

1409.00

1650.00

1701.00

1654.00

Water

(Cm)

Cis+

(dS/11)

102.5

102.5

102.5

102.5

102.5

102.5

72.5

72.5

72.5

72.5

72.5

72.5

102.5

102.5

102.5

102.5

102.5

102.5

102.5

102.5

102.5

102.5

102.5

102.

72.5

72.5

72.5

72.5

72.5

72.5

72.5

72.5

72.5

72.5

72.5

72.5

.42

.42

.42

.42

.99

.39

.39

.39

.39

.22

.22

.22

.22

.22

.22

.42

.42

.39

.22

.22

.22

.22

.22

.22

.38

.32

.32

.32

.32

.32

.32

.38

.38

.38

.38

.38

Nitrogen

(Kg/ha)

113.00

225.00

337.00

1.00

56.00

75.00

113.00

225.00

337.00

1.00

56.00

75.00

113.00

225.00

337.00

75.00

113.00

225.00

337.00

1.00

56.00

75.00

1.00

56.00

75.00

113.00

225.00

337.00

1.00

56.00

113.00

225.00

337.00

1.00

56.00

75.00

CSo

(dS/m)

42.07

42.07

28.43

28.43

28.43

28.43

28.43

28.43

14.20

14.20

14.20

14.20

14.20

14.20

42.07

42.07

42.07

42.07

42.07

42.07

28.43

28.43

28.43

28.43

28.43

28.43

14.20

14.20

14.20

14.20

14.20

14.20

42.07

42.07

42.07

42.07

147

APPENDIX

C

RESULTS OF THE QUADRATIC PRODUCTION FUNCTION

148

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