3EPA
United States
Environmental Protection
Agency
Robert S. Kerr Environmental Research EPA-600/2-80-063
Laboratory April 1980
Ada OK 74820
Research and Development
A Regional
Assessment of the
Economic and
Environmental
Benefits of an
Irrigation Scheduling
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL PROTECTION TECH-
NOLOGY series. This series describes research performed to develop and dem-
onstrate instrumentation, equipment, and methodology to repair or prevent en-
vironmental degradation from point and non-point sources of pollution. This work
provides the new or improved technology required for the control and treatment
of pollution sources to meet environmental quality standards.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-60Q/2-80-063
April 1980
A REGIONAL ASSESSMENT OF THE ECONOMIC AND ENVIRONMENTAL
BENEFITS OF AN IRRIGATION SCHEBOLING SERVICE
Marshall J, English
Gerald L. Homer
Gerald T. Or lob
Joseph Erpenbeck
Michael Moehlman
Richard H. Cuenca
Daniel J. Dudelc
University of California
and
Natural Resource EconoauLcs Division
Economies, Statistics and Cooperative Service
United States Department of Agriculture
Davis, California 95616
EPA-IAS-B1-0121
Project Officer
G. Hormsby
Source Management Branch
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
ROBERT S. KERR ENVTROSMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OKLAHOMA 74820
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DISCLAIMER
This report has been reviewed by the Robert S. Kerr Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for publication.
Approval does not signify that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor does mention of
trade names or commercial products constitute endorsement or recommendation
for use.
ii
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FOREWORD
Environmental protection efforts dealing with agricultural and nonpoint
sources have received increased emphasis with the passage of the Clean Water
Act of 1977 and the subsequent implementation of the Rural Clean Water Pro-
gram. As part of this Laboratory's research on the occurrence, movement,
transformation, fate, impact, and control of environmental contaminants, data
and analytical methodologies are developed to assess the causes and possible
solutions of adverse environmental effects of irrigated agriculture.
This report addresses the need for methodology to assess the regional
economic aspects of implementing irrigation scheduling as a resource con-
servation and crop production tool. Water-use efficiency and economic
efficiency must be weighed in environmental management decisions. This re-
port should benefit environmental managers as they attempt to identify and
implement pollution control strategies relevant to western irrigated
agriculture.
William C. Galegar
Director
Robert S. Kerr Environmental
Research Laboratory
iii
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ABSTRACT
Irrigation scheduling is a technique for systematically determining the
proper date and quantity of each irrigation in individual fields. This
technique is presently being used by government agencies and private companies
in the western United States to assist farmers in planning irrigations.
This report describes a case study in which the regional environmental and
economic benefits of irrigation scheduling were assessed. The analysis in-
dicated that substantial environmental benefits could be realized through
use of the technique. However, it was also found that imperfections which
normally occur in actual irrigation scheduling operations could drastically
reduce these benefits. The economics of irrigation scheduling appeared
favorable in the particular circumstances of the case study.
This report was submitted in fulfillment of Interagency Agreement
EPA-IAG-D6-0121 by the Economics, Statistics and Cooperative Service, U.S.
Department of Agriculture under the sponsorship of the U.S. Environmental
Protection Agency. This report covers the period October 1, 1976 to
December 31, 1977, and work was completed March 31, 1979.
iv
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CONTENTS
Foreword
Abstract iv
Figures vi
Tables vill
Acknowledgements x
1. Introduction 1
2. Conclusions 4
3. Recommendations 7
4. Analytical System 8
5. Study Area and Data Base 11
Study Area 11
Data Base 11
6. Physical Analytical Subsystem. ...... 15
Soil Moisture Model 15
Irrigation Model 26
Salinity Model 39
Sediment Model . .41
Crop Production Model 48
Physical Analytical System Results 55
7. Regional Economic Model 67
Derived Demand for Resources 67
Derived Demand for Irrigation Scheduling Services 68
Regional Linear Programming Model 70
8. Regional Effects of an Irrigation Scheduling Service . 91
Potential Impacts of a Scheduling Service .... 91
Voluntary Adoption of a Scheduling Service. ... 93
Reducing Return Flows by Scheduling 102
Variable Water Costs and Scheduling 102
References 106
Appendix A 110
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FIGURES
Number Page
1 Irrigation scheduling analytical system 9
2 Location of the A and B District, Idaho 12
3 Map of the A and B Irrigation District, Idaho 14
4 Rate of drainage (J) from a 60cm and 105cm soil column
as a function of time (in days) 21
5 Rate of drainage (J) from a 60cm and 105cm soil column
as a function of soil moisture depletion 21
6 Crop coefficient curve for beans, peas, grains, sugar beets
and potatoes 24
7 Distribution of errors in timing of irrigations, Falls
Irrigation District '. 29
8 Application errors on sugar beets, Grand Valley (cm) .... 30
9 Statistical distribution of timing errors (number of days
departure from recommended irrigation date) under
imperfect scheduling regime 32
10 Statistical Distribution of errors in quantity of water
applied under the imperfect irrigation scheduling regime;
(expressed as a ratio of actual to recommended
quantities) 33
11 Histogram of 88 irrigation events on alfalfa with various
field slopes 35
12 Surface runoff for 88 irrigation events on alfalfa with
various field slopes ... 35
13 E ratio and the amount of applied water to wheat fields ... 37
14 Salinity concentration of leachate for four irrigation water
dilution levels by leaching fraction 42
vi
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Number Page
15 Total solids gained and lost during an irrigation set ... 44
16 Rate of runoff from a furrow irrigated field 46
17 Relationship of sediment concentration to rank of irrigation
event for non-forage crops in the A and B District ... 47
18 Crop production as function of ET 50
19 Soil moisture histories for two fields 60
20 Soil moisture histories for two fields 61
21 Histogram of soil moisture at time of irrigation for 350
irrigation events in bean fields 63
22 Soil moisture histories of two fields with and without the
effects of an ideal irrigation scheduling service .... 64
23 Output and scheduling effects of a rise in the cost of
scheduling 70
24 Aggregation of individual demand 71
25 A and B District linear programming model 75
26 Estimated scheduled acreage and scheduling cost, A and B
District, 1973, 1974, and 1975 95
27 Estimated water use and scheduling cost, A and B District,
1973, 1974, and 1975 98
28 Estimated deep percolation as a function of scheduling
cost, A and B District, 1973, 1974, and 1975 99
29 Estimated salt load as a function of scheduling cost, A and
B District, 1973, 1974, and 1975 100
30 Estimated average annual surface runoff and sediment load,
A and B District, 1973, 1974, and 1975 101
vii
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TABLES
Number
1 Moisture Holding Capacities (% by volume) of Five Soil
Samples Taken in Upper 150 cm of Profile in the Study
Area 16
2 Comparison of Average Consumptive Use Estimated for the A
and B District and Measured Consumptive use at Various
Sites 25
3 Soil Moisture Levels at Which Simulated Irrigations were
Scheduled 27
4 Runoff Model Coefficients and Correlation Coefficients
Resulting From Linear Regression . 34
5 Statistical Characteristics of Actual and Estimated Runoff
Data 38
6 Variability of Percolation in Furrows 40
7 Sediment Concentrations in Runoff from Non-Forage Crops by
Rank of Irrigation 48
8 Yield Indices Used in Stepwise Regression Analysis for
Yield Deficits 53
9 Yield Deficit Regression Models 54
10 Comparison of Water Use Scheduled and Unscheduled Regimes
for 204 Fields .56
11 Return Flow Quality, Scheduled and Unscheduled Regimes for
204 Fields 57
12 Estimated Concentrations of Constitutents (meq/A) in
Leachate as a Function of Leaching Fraction for Typical
Circumstances in the A and B District 57
13 Results Estimated for 10 Cases Selected from Among the 204
Cases Studies: Examples of Variability of Results .... 59
viii
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Number Page
14 Number of Irrigations, by Crop, Scheduled and Unscheduled
Regimes for 204 Fields ............. . ..... 62
15 Estimated Changes in Yields in the A and B District with
Irrigation Scheduling ................... 65
16 Definition of Low, Medium and High Water-Use (Unscheduled
Irrigation Regime) and Proportion of Irrigated Cases in
Each. Category ..... «
17 Water Application Rates, Labor Requirements and Crop Yields,
A and B District ...................... 78
\
18 Crop Yield Trend Equations for the A and B Irrigation
District .......................... 81
1.9 Average Commodity Prices A and B District: 1973-1975 ..... 82
20 Irrigation Water Costs, A and B District, 1973, 1974, and
1975 ............................ 82
21 Crop Production Costs, 1973, 1974, and 1975 A and B District . 83
22 Returns to Land, Management and Risk by Amount of Water
Application ........................ 86
23 Volume and Quality of Irrigation Return Flow Per Acre,
A and B District ...................... 89
24 Estimated Average Annual Returns to Land, Management and
Risk for Unscheduled and Scheduled Irrigation in the A
and B District, 1973, 1974, and 1975 ............ 91
25 Estimated Average Annual Irrigation Return Flows in the A
and B District, 1973, 1974, and 1975 ............ 94
26 Estimated Average Annual Irrigation Water Use and Return
Flows Alternative Scheduling Policies, A and B District . . 103
27 Estimated Average Annual Irrigation Water Use, Scheduling
Activity, Return Flows, Sediment Loss and Salt Load for
Alternative Water Costs, A and B District ......... 105
A-l Crop Acreage, Returns, Water Use and Irrigation Return
Flows Resulting from Scheduled Irrigation at Varying
Scheduling Costs ......................
A-2 Crop Acreage, Returns, Water Use and Irrigation Return
Flows Resulting from Scheduled Irrigation at Varying
Water Costs ......................... 112
ix
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ACKNOWLEDGEMENTS
This research would not have been possible without the generous assis-
tance of a number of people. The support, cooperation and understanding
of Arthur Hornsby, Project Officer, Robert S. Kerr Environmental Research
Laboratory, Ada Oklahoma was appreciated and contributed substantially to
the completion of this project.
We also wish to express our gratitude to Dr. Marvin Jensen of the
Science and Education Administration for the considerable time he devoted
to answering our questions, offering suggestions and reviewing and
critiquing our work. We are very much indebted also to the Bureau of
Reclamation which supplied the data upon which this study is founded. In
addition, a number of individuals within the Bureau made a considerable
personal effort on our behalf. These included Jerry Buchheim and
Lowell Ploss at the Denver Federal Center, and Leo Bush and Earl Corliss at
Burley, Idaho. These people, along with Joe Lord of Harza Engineering,
were most cooperative and helpful in acquainting us with the many aspects
of irrigation scheduling.
James Wright of the Science and Education Administration and
Dorell Larson and Galen McMaster of the University of Idaho contributed a
great deal to our understanding of irrigated agriculture in southern Idaho.
We also wish to thank Richard Hanks of Computerized Farming Incorporated,
John Hammond of the State of Idaho Department of Water Resources,
Gerald Tyler of the Soil Conservation Service, and Bill Hewitt, Ed Forester,
Monty McVey, Bob Hamburg, Chuck Huntley, Christy Brost and Marvin Shaffer,
all of the Bureau of Reclamation, for their help in various aspects of this
project.
We are greatly indebted to Dr. J.D. Oster of the U.S. Salinity Labora-
tory in Riverside for his considerable help with development of the
salinity model, and to Dr. J. Ian Stewart of the University of California
for assistance in the development of crop production models. Special
thanks is expressed to Deborah Ruggles for editing and typing several
drafts of this report. There were also many other people who helped us in
various ways who have not been listed here. To them also we extend this
statement of appreciation.
While all of the people mentioned above contributed in one way or
another to this research, nevertheless the interpretation, analysis and
write-up of this research were done by the authors, and any errors or over-
sights must be regarded as our responsibility.
x
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SECTION 1
INTRODUCTION
In recent years a new approach to irrigation has emerged in which a
computer is used, in combination with trained personnel working in the field,
to determine the appropriate timing and amount of each irrigation for indi-
vidual fields. The computer is used to model soil moisture conditions and
forecast the required date and amount of upcoming irrigations. The field
personnel interpret the computer outputs, periodically check soil moisture
in the fields and advise the farmer on his irrigation schedule. This
scheduling procedure is based upon principles of soil science, agronomy,
meteorology and engineering and is often referred to as scientific irriga-
tion scheduling. It was developed originally by Dr. Marvin Jensen of the
U.S. Science and Education Administration (SEA) between 1968 and 1971, was
modified and developed by the U.S. Bureau of Reclamation (USER), the U.S.
Soil Conservation Service (SCS) and others (Gear, et al.,1976; Buchheim and
Ploss, 1977) and is now being applied as a commercial service to farmers
throughout the Western United States. A comprehensive review of the
theory, application and early results of irrigation scheduling has been
written by Jensen (1975).
It is generally held that the potential benefits of an irrigation
scheduling service (ISS) may include:
a. reduced water use, with attendant reductions in drainage
problems and reduced salinity of downstream flows,
b. increased crop yields,
c. reduced production costs for water, fertilizer, and pesticides,
and
d. improved farm operating efficiencies due to the ability to plan
irrigations well ahead of time.
In practice, however, these benefits are often disputed. It has been
found, for example, that water use increased in some fields when an ISS
was used.* On the basis of some preliminary results, crop yields appear to
have increased significantly in some areas, but only slightly or not at all
*This has been attributed to farmers following recommended schedules
having shorter intervals between irrigations but not following
recommendations for reduced water use (Jerry Buchheim, pers. comm.)
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in other areas (USER, 1974; Schaack, 1975). Many farmers have discontinued
the use of scheduling services because they did not feel that they derived
a net benefit from them (Jensen, 1975). In short, the advantages and dis-
advantages of an irrigation scheduling service have not been clearly estab-
lished. There is therefore a need for comprehensive, systematic analyses
of the benefits and costs of irrigation scheduling services. In order to
objectively evaluate an irrigation scheduling service there is a need to:
a. determine who does and who does not benefit from the service,
and to what extent,
b. give all interested individuals a clearer understanding of the
benefits and costs of an ISS in order to assist them in making
a decision to utilize the program, and
c. assess the effectiveness of alternative ISS program configura-
tions under different circumstances.
In light of these questions both the Environmental Protection Agency (EPA)
and Bureau of Reclamation (USER) have pointed out the need for comprehen-
sive data collection programs in areas where scheduling services are being
utilized (Jensen, 1975; USER, 1972). Such programs are now underway at
some USER scheduling operations. Data-.are being collected from groups of
farms which are using a scheduling service and from matching groups of farms
which are not using such a service. The difference in water use and crop
yields between the two groups should represent the benefits of a scheduling
service. These comparative field studies will produce valuable information
about the overall results now being achieved.
An alternative to the comparative field studies approach of the USER
is a mathematical modeling of the scheduling process. It was this approach
that was taken in the present study. The requirements of a modeling ap-
proach are, first, that the irrigation practices of farmers not using a
scheduling service must be characterized in an empirical way; second, that
the irrigation practices of farmers who do use such a service must be
characterized; third, that the inter-relationship between these irrigation
practices and the various parameters of interest (water use, water quality,
and income) must be established. With such information at hand, the
regional totals of the parameters of interest can be estimated first for
farms not using a scheduling service, and again for the same farms based
upon use of a scheduling service. The difference in the respective totals
can be attributed to the use of the scheduling service.
The benefits of an irrigation scheduling service naturally depend upon
the quality of the service and the willingness of farmers to follow its re-
commendations. The quality of a scheduling service is strongly dependent
upon the training, experience and motivation of service personnel (Jensen
1975; Lord, 1976). The willingness of farmers to follow recommendations of
the service depends on their motivation, the degree of confidence which they
have in the service and their ability to actually implement service recom-
mendations. Other farm operations may interfere with irrigation schedules,
water deliveries may not be possible on a recommended date and other factors
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may make recommended irrigations unacceptable to a farmer. In light of these
considerations, an analysis of irrigation scheduling should consider the
consequences of imperfect scheduling. The word "imperfect" here denotes a
scheduling operation in which theoretically optimum schedules are not fol-
lowed. Imperfect operations may be due to-poor performance on the part of a
scheduling service or failure or the inability of farmers to implement re-
commended schedules.
A modeling approach will reveal which factors are most important to the
success of a scheduling operation and it permits a close examination of the
ways in which irrigation scheduling influences non-point-source pollution.
It also enables one to study the impacts of irrigation scheduling procedures
that are not actually found in current practice but may be of some future
value. Finally, the modeling approach has the advantage of speed. Rather
than waiting for many years to find out what changes will occur in regional
water use, water quality and income as a result of irrigation scheduling
under a variety of economic and environmental conditions, these changes
can be estimated quickly.
This approach is only as reliable as the models used in the analysis.
Models selected for use in the study were as sophisticated as practical
and were calibrated when possible with local field data. Conclusions drawn
from this research were based on differences between model estimates, thus
model biases would be minimized.
The specific objectives of this research were to:
a. develop a method of assessing the regional environmental and
economic benefits and costs of an irrigation scheduling service,
b. apply that method to a case study for purposes of evaluating the
method and developing some perspective on the factors which
affect the benefits and costs of a scheduling service,
c. develop some appreciation for the ultimate potential of irriga-
tion scheduling by evaluating two different scheduling services
in a real world setting, one being an imperfectly implemented
scheduling service and the other being an ideal scheduling
service.
The results of this research should be of particular interest to those
policy makers concerned with the question of whether scheduling services are
economically justified and, if so, how they can best be implemented and
financed. In addition, private companies and government agencies which pro-
vide scheduling services to farmers will gain an improved understanding of
those factors which determine the benefits to be derived from the service,
and the factors which influence the effectiveness of a scheduling service.
The study focuses on benefits and costs associated with crop yields, water
use, and irrigation return flows.
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SECTION 2
CONCLUSIONS
This discussion of conclusions is in two parts. The first five items
relate to the impacts estimated for an irrigation scheduling service oper-
ating in the A and B Irrigation District of Southern Idaho. Subsequent
items describe the techniques that were used in this analysis and the prob-
lems encountered in applying them. The conclusions which pertain to the
A and B District can be regarded as somewhat general, that is the A and B
District should be a good indicator of what to expect from other irriga-
tion districts since irrigation efficiencies are relatively high, and irriga-
tion costs are moderate. In districts where water use is particularly
inefficient, or water costs are high, the benefits attributed to irrigation
scheduling would probably be greater than those described below. In
exceptionally efficient districts, the converse would probably be true.
1. General - Although the A and B Irrigation District's average
water use is relatively efficient, there is substantial
variability in the scheduling practices of individual fanners.
Both timing and quantity of irrigation applications varied
tremendously in the fields involved in this study. An irri-
gation scheduling service operating in the district could
produce important environmental and economic benefits. Those
benefits would vary substantially from one farmer to another
and, to a lesser extent, from one crop to another.
2. Economic Benefits - Although irrigation costs in the A and B
District are not particularly high, the potential reduction
in irrigation costs due to use of an irrigation scheduling
service would pay the cost of such a service in most instances.
Improved yields are also possible; the analysis produced some
indication that yield improvements might be realized with a
scheduling service, and the returns attributed to such in-
creased yields could exceed the cost of the scheduling service.
Data problems and yield variability were so great, however,
that estimates of yield changes can only be regarded as in-
dicative rather than conclusive.
3. Environmental Benefits - Substantial reductions in total water
use and deep percolation could be brought about with the use
of an irrigation scheduling service. Somewhat less surface
runoff would also occur. These changes would result in re-
duced salinity and sediment loads in return flows. Estimated
return flow changes with irrigation scheduling in the A and B
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District included up to 77 percent reduction in deep perco-
lation, 31 percent reduction in surface runoff, 33 percent
reduction in TDS loads, and 24 percent rieduction in sediment
loads. The reduced total dissolved solids (TDS) loads would
be accompanied by a shift toward a higher sodium adsorption
ratio and lower alkalinity in return flows. The reduced
sediment load could be accompanied by corresponding reduc-
tions in pesticide and nutrient levels in return flows.
4. Imperfect Scheduling - The potential benefits of a
scheduling service can be largely nullified by deviations
from the prescribed irrigation schedule in terms of timing
and quantity of water applied. As noted earlier, such
errors could be due to imperfect knowledge on the part
of the service or to an inability or unwillingness of
farmers to implement recommended schedules. The environ-
mental benefits mentioned above would be largely offset
by such errors. Soil moisture conditions when using
scheduling could conceivably be even less favorable to crop
production than without a scheduling service. For example,
it was estimated that average season total evapotranspira-
tion could be less in a few cases when imperfect scheduling
is used than when no scheduling service is used. Since
evapotranspiration is a direct indicator of yields, it
appears possible that potential improvements in yields due
to irrigation scheduling could be offset to some extent by
imperfections in the scheduling procedures.
5. Demand - The acreage of scheduled irrigation activity was
found to be fairly sensitive to varying scheduling costs.
At zero cost, approximately 70 percent of the irrigated
cropland in the A and B District would be scheduled but a
$5.00 charge per acre ($12.36/ha) would reduce scheduling
to approximately 25 percent of the acreage. The amount of
water use was also affected by changes in scheduling costs.
At zero scheduling cost, water use would approximate 75
percent of the water use in the A and B District without
a scheduling service and approximate 95 percent when the
scheduling costs was raised to $5.00 per acre ($12.36/ha).
The amount of scheduling increased and the amount of water
use and return flows were substantially reduced as water
costs were increased. As water costs approach $20.00 per
acre foot, ($24.46/103cm3) virtually all of the district
would employ the scheduling service to reduce the amount
of water applied.
6. Analysis of Irrigation Water Use Under Field Conditions -
Two general observations can be made regarding analysis
of irrigation water use. First, the variability of field
data is substantial and it is often difficult to do much
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more than model average values and the variability of
some factors. Crop yields and surface runoff were two
factors which were found to be particularly erratic. The
scatter in the data appeared to be due to the fact that
some very unpredictable inputs had very significant ef-
fects. For example, farmers may intervene to adjust sur-
face runoff from time to time, making it difficult to predict
this quantity. Thus, probablistic modeling is likely to
be of paramount importance in modeling irrigation water use.
Second, some of the most important relationships are not
unders-tood sufficiently well to be modeled accurately under
field conditions. Notable examples are crop development
and root zone expansion.
7. Estimating Evapotranspiration - Great care must be taken in
modeling evapotranspiration since this proved to be the most
important single element of the study. Care must be taken to
use an evapotranspiration model that is appropriate for lo.cal
conditions, and to be.sure that the crop coefficients used
in estimating ET are consistent with the potential evapo-
transpiration model that is being used.
8. Modeling Soil Moisture - In order to arrive at reasonably
accurate estimates of deep percolation and leaching frac-
tions, it is necessary to use a model of soil drainage which
accounts for soil moisture conditions both above and below
nominal field capacity. In addition, a major effort should
be made to accurately estimate effective root depths. Al-
though the results of the analysis were not especially sensi-
tive to moderate errors in root depth, there is a possibility
of extremely large errors in this quantity making it one
of the more critical factors in the models.
9. Modeling Crop Production - Unexplained yield variability can
be very great. Consequently yield estimates must be cali-
brated for each field on an individual basis if unbiased
crop production models are to be developed.
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SECTION 3
RECOMMENDATIONS
1. Irrigation scheduling services should be promoted by
water quality agencies to reduce the amount of return
flows in most irrigated areas of the west.
2. Irrigation scheduling services should be recommended
to water agencies to reduce water diversions and
pumping for crop production.
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SECTION 4
ANALYTICAL SYSTEM
The analytical system is composed of the physical analytical subsystem
and a regional economic model (Figure 1). The physical analytical subsystem
estimates crop yields, irrigation water use, frequency of irrigation and
salt and sediment loads of return flows on a per acre (ha) basis. This
information is used by the regional economic model to estimate changes in
regional farm income, water use, scheduled acres (hectares) and the amount
and quality of irrigation return flows that could result from the use of a
irrigation scheduling service.
The physical analytical subsystem is composed of the soil moisture, ir-
rigation, salinity, sediment and crop production models. The soil moisture
model estimates evapotranspiration (ET) and soil moisture on a daily basis.
These estimates are used by the crop production model to estimate crop yields
and by the irrigation model to establish when subsequent irrigations are
required. The irrigation model determines irrigation timing and the amount
of water to be applied, which is used by the crop production, soil moisture
and regional economic models. The irrigation model also estimates the
amounts of runoff and deep percolation. These estimates are then used by
the sediment and salinity models.
The soil moisture model estimates daily soil moisture by computing a
water budget for the crop root zone. The extent of the root zone is deter-
mined by a submodel of root growth. Depletion of soil moisture is estimated
by submodels of evapotranspiration and deep percolation. The evapotrans-
piration submodel accounts for bare soil surface, wet soil surface and dry
soil profile conditions. Soils in the study area are deep, well drained
and sufficiently similar so no provisions were made for upward or lateral
soil water movement.
The irrigation model was used to simulate scheduling of fields and the
consequences of irrigation applications under the scheduled regimes. The
model determines the proper timing of each irrigation event on the basis of
the amount of moisture remaining in the root zone. When an irrigation is
called for, the model specifies the amount of water to be diverted, calcu-
lates losses in the distribution system and generates an estimate of sur-
face runoff. The balance of each simulated diversion is then added to the
soil water budget either to be stored in the soil profile or ultimatley to
drain beyond the root zone. In scheduling irrigations, the model follows
essentially the same decision rules used by a scheduling service presently
operating in the distirct. The model can simulate either an ideal scheduling
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Physical analytical subsystem
Crop
Production
Model
Regional Farm Income & Water Use.
Acres Scheduled & Amount & Quality
of Return Flows
ET Soil Moisture
Soil
Moisture
Model
Irrigation
&
Scheduling
Model
Irrigation Amount
Irrigation Amount &
Frequency
FIGURE 1. Irrigation scheduling analytical system.
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operation, in which each irrigation event is presumed to be in accord with
scheduling service recommendations, or an imperfect scheduling operation.
The imperfect operation is simulated by introducing random deviations from
specified dates and amounts of scheduled irrigations. The statistical char-
acteristics of the random errors generated in this model were estimated from
earlier observations of such errors by the USER in actual field operations
of scheduling services.
The salinity model predicts TDS concentrations in water percolating be-
yond the root zone on the basis of the chemical composition of applied water
and seasonal leaching fraction. Estimated total salt load in deep percola-
tion is then calculated as the product of estimated TDS concentration and
estimated volume of deep percolation.
Regression analysis was used to predict sediment concentrations in sur-
face runoff as a function of the rank* of each irrigation event and the
volume of water applied per unit of land area. Certainly many other factors
influence erosion and an attempt was made to develop a more sophisticated
model that would account for some of the more obvious factors. However,
that effort was largely unproductive. Nevertheless, this model was deemed
adequate for the purposes of this analysis, as will be explained later.
The crop production or yield model was based in part on known relation-
ships between water use and yields. Yields are adversely affected when
either too little or too much water is applied to a crop, and these adverse
effects are related to the stage of growth of the crop. A model was devel-
oped that would take these principals into account. The model was founded
upon a yield-evapotranspiration relationship since the link between these
parameters is well established. A stepwise regression procedure was then
used to identify other water-related factors which might be useful in pre-
dicting yields such as the total water applied and the soil moisture at
critical stages of growth.
Crop yield, water use and return flow coefficients for each crop were
derived by the physical analytical subsystem under scheduled and unscheduled
irrigation operations. These data, crop production costs and commodity
prices were used in formulating the regional economic model to determine
the amount of water use and type of irrigation system that maximizes
regional net farm income. Subsequent runs of the economic model were made
to estimate the changes in incomes, water use, scheduled acres (hectares)
and return flows that result from varying scheduling costs, water costs and
environmental policies. The present research did not deal with specific dol-
lar values associated with changes in water quality, but did yield consider-
able insight into the relationships between irrigation scheduling and the
quality of irrigation return flows.
*Rank refers to the number of event, e.g., the first, second or
third event for a given field in a given season would have a
rank of one, two or three,respectively.
10
-------
SECTION 5
STUDY AREA AND DATA BASE
STUDY AREA
The analysis was a case study involving the A and B Irrigation District,
a 76,800 acre (31,104 hectare) district located on the Snake River near
Burley in southern Idaho (Figure 2). An irrigation scheduling service
has been in use there for ten years. Earlier study indicated that utiliza-
tion of that service may increase local yields of some crops (USER, 1974).
As far -as the environmental consequences of irrigation in the area are con-
cerned, there is little problem with salinity in return flows but sediment
from erosion is a major problem. The principal reasons for choosing the A
and B District were, first, that the area is relatively homogeneous in
physical characteristics which simplified the analysis, and second, that a
great deal of necessary data and other research have already been compiled
by various agencies in the area.
The district is supplied with water pumped both from the Snake River
and from wells, with a lift of approximately 200 feet (61 meters) in
either case.
One important characteristic of farmers in the A and B District is that
even without the benefit of an irrigation scheduling service their irriga-
tion operations are relatively efficient for surface irrigation systems in
southern Idaho. It was estimated in this study that distribution system
losses were approximately 10 percent of water delivered to the farm while
surface runoff and deep percolation account for 39 percent of water applied
to the fields. During the ten year period from 1958 to 1968, A and B
District deliveries averaged'3.18 acre feet (3.92 x 10^ cm^) per acre which
was considerably less than the 4.1 and 5.09 acre feet per acre (5.06 x 10^
and 6.28 x 103 Cm^) in two adjacent districts.
DATA BASE
The analytical procedure developed for this project required both field
data and simulation modeling. This work was made easier by the fact that
the study area has been the scene of extensive research pertaining to irri-
gated agriculture. The results of that research were incorporated into the
simulation models arid analytical procedures of the present study. The
shaded area in Figure 3, designated roman numeral I, encompases six farms
(approximately 600 acres) which participated in a USER study of irrigation
water use between 1964 and 1968 (USER, 1971). An exhaustive data collection
11
-------
A & B Irrigation District
FIGURE 2. Location of the A and B District, Idaho.
12
-------
program was conducted in each field (maximum number of fields in any one year
was 47; number varied from year to year) during each of those years. The data
included climatic variables, soil conditions and agronomic and irrigation
practices.
Climatic data included daily temperature, humidity, wind, rainfall and
solar radiation. Soil moisture and salinity at the beginning of the season
were also recorded. The dates of all cultivation, planting and harvesting
were recorded along with crop acreages, amounts of fertilizer and pesticide
use, and crop yields, losses and quality. Irrigation data included irriga-
tion water quality, amount of distribution system losses, irrigation methods
used, field length, slope, row spacing, dates of irrigation, time per set,
rate of delivery, labor requirement, infiltration rate, rate of advance
and surface runoff. (For a description of this subarea, an outline of USER
research methods and a summary of the data, see Use of Water on Federal
Irrigation Projects, USER, 1971.) These data were collected for 204 cases,
each case representing one of the fields during one growing season. This
data set is referred to in the present report as the six-farm study.
The areas designated by roman numeral II in Figure 3 represent 4,340
acres (1,756 hectares) encompassing 40 farms, which participated in an
earlier interagency study (1958-1963) similar to the six-farm study (Tyler,
et al., 1964). The goal of the earlier study was the evaluation of irriga-
tion water use and efficiencies. Data collected on these 40 farms included
water deliveries, runoff, weather data and crop yields. However, the data
collection effort during the 40-fann study was neither as comprehensive nor
as complete as that of the six-farm study.
Another important resource available to the present study was the USDA-
SEA Snake River Conservation Research Center, located at Kimberly, Idaho,
40 miles (64 km) west of the A and B District. The soil moisture and evapo-
transpiration (ET) models used in this project were developed in large part
by researchers at that facility who have been working with the same crops,
soil and climate as are found in the A and B District.
The University of Idaho maintains experiment stations at Kimberly and at
Aberdeen, 80 miles (129 km) east of the A and B District. Research at these
stations and comments and suggestions from University of Idaho researchers
located there and elsewhere in Idaho also provided a great.deal of needed
information, on the subjects of farm practices, crop production and erosion.
In addition to the data collected during the six-farm study, the USER
offices in Burley, Idaho (adjacent to the A and B District), Boise, Idaho,
and Denver, Colorado, also provided insight and detailed information con-
cerning scheduling procedures, the performance of the USER scheduling ser-
vice and irrigation practices and other habits of farmers in and around
the A and B District.
13.
-------
FIGURE 3. Map of the A and B Irrigation District, Idaho.
-------
SECTION 6
PHYSICAL ANALYTICAL SUBSYSTEMS
The environmental and economic impacts that would occur on all farms in
the region were inferred from results observed on the 46 farms which partic-
ipated in the studies described above. The analysis took place in two.
phases. In the first phase, data collected from the sample farms were used
to establish relationships between irrigation practices, crop yields, and
the amount and quality of return flows. Also, the irrigation practices of
farmers in the region were studied and characterized for each crop. The
information and relationships developed in the first phase were then combined
to establish coefficients for a regional economic linear programming model
used in the second phase. The linear programming model determined optimum
water use and utilization of a scheduling service under three different irri-
gation regimes and a variety of scheduling and water costs.
The three irrigation regimes differed in how the irrigation water was
managed. The three regimes are unscheduled, ideal scheduling, and imperfect
scheduling. Under the unscheduled regime farmers are assumed to be irriga-
ting using their own judgment of crop water needs. An ideal scheduling
regime is presumed to have perfect knowledge of soil moisture conditions
in every field at all times and, furthermore, each farmer is presumed to ir-
rigate his fields precisely when advised'to do so, using exactly the rec-
ommended amount of water. The imperfect scheduling regime assumes that
errors occur in both the timing and amount of irrigations, which is currently
the rule rather than the exception in irrigation scheduling operations.
SOIL MOISTURE MODEL
The soil moisture model estimates evapotranspiration (ET) and soil
moisture for each crop by calculating soil moisture budgets for the active
root zone and a lower zone into which the root system will eventually move.
Soil Moisture Holding Capacities
On the basis of field data from several sources, the moisture holding
capacities of soils in the study area were assumed to be:
15
-------
1. 37 percent by volume* on the day following a thorough
irrigation;
2. 30.7 percent by volume at the limit of gravity drainage;
and
3. 10 percent by volume at the limit of extraction for
evapotranspiration (15 bars tension assumed).
The soil was assumed homogeneous with respect to these capacities
throughout the study area. However, this assumption is only an approxima-
tion, the validity of which may be judged by the variability in gravimetric
analyses of five soil samples taken from different sites in the study area.
These are presented in Table 1. The values shown are composite values of
samples taken at a depth of from 10 to 150 cm. The standard deviation of
the soil moisture content at one-third bar tension is 6 percent of the mean.
TABLE 1. MOISTURE HOLDING CAPACITIES (% BY VOLUME) OF FIVE
SOIL SAMPLES TAKEN IN THE UPPER 150 CM OF SOIL
PROFILE IN THE STUDY AREA
Sample Number
Mean ± Std. Dev.
Moisture content,
1/3 bar
27.32 28.56 32.26 29.47 28.98* 29.32 + 1.83
Moisture content, 8.74 9.32 9.83 8.06 8.32* 8.85 + 0.72
15 bar
Bulk density,
gm/ cm
1.38 1.40 1.41 1.39
1.40 + 0.01
*Mean value of bulk density used to compute values.
The model computes the soil moisture budgets as follows. When water is
applied at the soil surface it is added to the moisture budget of the cur-
rent root zone until the limit of capacity (37%) is reached. Any additional
water infiltrating the soil will be added to the budget of the lower portion
of the root zone. When the limit of capacity of the lower root zone is
reached additional water is assumed to percolate beyond the maximum root
zone. When the soil moisture is between 10 percent and 30.7 percent, de-
pletion will take place only through evapotranspiration. When the moisture
level is between 30.7 percent and 37 percent, depletion taking place by both
evapotranspiration and percolation processes is simulated by the model.
*Throughout this report, where soil moisture is expressed as a
percent it refers to percent by volume.
16
-------
Estimates of percolation and soil moisture content can be significantly
affected by large errors in the value of the maximum moisture holding capac-
ity used in the soil moisture model. In fact, a dominant impression to come
from this study has been the importance of properly modeling soil moisture
at levels above nominal field capacity. Otherwise, substantial errors in
computation of leaching fractions and soil moisture budgets may result. The
model therefore estimates both ET and percolation simultaneously at soil
moisture levels above field capacity.
Root Zone Depth
The estimation of evapotranspiration and percolation also depend
on the size of the active root zone. The active zone increases with the
growth of the crop. Jensen developed a root zone model that relates root
zone size to the crop growth stage (M. E. Jensen, personal communication,
1979). The equations of this model are:
L(t) = (Z - 15) • k (t) +15 t < full cover date (1)
m co —
L(t) = Z t > full cover date (2)
m
where
L(t) = root zone depth at time t, in centimeters (cm),
Z = maximum root zone depth for the given crop,
m
k (t) = crop coefficient used in the evapotranspiration
equation (to be discussed below)
This model has been used by the USER in its Irrigation Management Services
(IMS) program.
The following are assumed effective maximum root zones used for the
various crops (Z ). They were derived from Doorenbos and Pruitt (1975),
Hagan et al., (1?67) and Hansen (1972).
Crop Maximum Root Zone in Cm
Alfalfa 213
Barley 91
Beans 61
Peas 91
Potatoes 61
Wheat 91
Sugar Beets 76
The values shown are not absolute maximum root zones. Rather, they are
estimates of the depths from which most of the water will be drawn by the
17
-------
crops tinder normal circumstances. Under stress conditions, these crops might
tap water from greater depths. For example, sugar beet roots may extract
water down to 180 cm (M. E. Jensen, personal communication, 1979; University
of California, 1976) and beans in some circumstances may reach depths of
from 183 to 274 cm (from field studies, University of California at Davis,
Summer 1977; Juan Tosso, personal communication).
Deeper root zones, had they been used in the model, would have resulted
in fewer irrigations and greater pre-season soil moisture availability.
Under these circumstances, the evaluation of irrigation scheduling would have
been more favorable. The shallower root zones are deliberately selected to
avoid biases that would attribute unattainable benefits to scheduling.
Equally important, these shallower root zones are consistent with the some-
what conservative estimates of root zones which scheduling services generally
use in selecting allowable soil moisture depletions between irrigations.
There remains a question of whether actual effective root zones might
be shallower than the values used. This possibility was suggested because
local soils are underlain by a moderately cemented layer between approxi-
mately 46 and 91 cm. below the surface which might be a barrier to root
development.
Kohl and Kolar (1976) found that alfalfa grown in this soil was able to
penetrate the cemented layer and develop an extensive root system below it.
However, there was no assurance that this would be true of other shallower
rooted crops. A bean field in the A and B District was studied by the
authors during the summer of 1977. Twenty-five neutron probes were installed
throughout a section of the field and soil water extraction by the crop was
measured to a depth of 91 cm. A fungus which occurs in this area (Fuserium
root rot) commonly attacks the tap root of beans, sometimes destroying it
within 15 cm. of the surface (McMaster, et al., 1965), so this crop could
be expected to have more difficulty penetrating the cemented layer to a
significant extent than would other crops. However, it was found that soil
water extraction in the upper 91 cm. accounted for less than half of the
consumptive use estimated by a locally calibrated Penman ET model. The
bean crop was obviously growing well and not suffering significant stress.
It was concluded that in spite of the problems presented by this soil, the
root zones used in the study are reasonable.
The degree of uncertainty of root depths is very great, as may be il-
lustrated by the following ranges of published root depths (Doorenbos and
Pruitt, 1975; Hagan et al., 1967; Hansen, 1972; Nielsen et al., 1973; M. E.
Jensen, Personal Communication, 1976).
18
-------
Maximum Root Zone Depth in Cm
Alfalfa
Beans
Sugar Beets
Grains
90
45
60
60
to
to
to
to
360
900
120
120
It appears that large errors in estimation of root development may be dif-
ficult to avoid and therefore this must be regarded as one of the critical
factors in the model. Root depths used in the analysis were conservative
estimates, i.e., probably shallower than is actually the case. This would
lead to conservative estimates of any benefits that might result from the
use of scheduling.
A sensitivity analysis was conducted to assess the significance of
errors in root depth estimates. Percolation was found to be sensitive to
root depths, while consumptive use was found to be rather insensitive. For
example, in the ten representative fields used in the sensitivity analysis,
a 20 percent increase in root depths caused a 10 percent decrease in per-
colation and a 1.0 percent increase in ET under the unscheduled irrigation
regime.
Soil Drainage Submodel
The rate of percolation is computed by the following function of soil
moisture and root zone depth:
J = BQ(L) +
(6o - 6) + B2(L) • (6o - 9)'
(3)
B3(L)
- 6)-
in which B±(L) = £
k=o
(4)
where
J
L
8
B±(L)
aik
= rate of drainage, in cm per day, from the root zone,
= depth of the root zone, in cm,
= maximum soil moisture (37% by volume)
= current soil moisture, expressed as percent by volume
= a coefficient dependent upon depth L, in cm
= coefficients used in calculating B..
In deriving these equations, polynomial regressions were used to fit a family
of soil moisture drainage curves generated by a theoretical model calibrated
with experimental data for Portneuf silt-loam soil in Kimberly, Idaho. The
soil drainage model estimates drainage rate from a soil profile of depth L
and moisture content 8. If hydraulic conductivity is taken to be an ex-
ponential function of soil water content of the form:
19
-------
k(9) = K exp [a(9 - 9Q)]
where
K = conductivity under conditions of steady state infiltration
rate,
9 = soil moisture content under conditions of steady state
infiltration rate,
a = a constant,
tthen flux and soil moisture can be estimated as the following functions of
time (Nielsen, et al., 1973):
K
o
- aK t
9 = 9 - i In (1 + -r5-) (6)
o a L
in which
J = flow rate through the bottom of the soil profile,
L = depth of soil profile
t = time (with t = 0 at 6Q)
Soil drainage rates were measured by Jensen (personal communication,
1976) at a single site, for Portneuf silt loam soil at depths of 60 cm and
105 cm as indicated by the solid lines in Figure 4. These data were used to
calibrate equation 5 for a and K . The dashed lines in Figure 4 represent
the resulting calculated drainage rates. Equations 5 and 6 were then used
to generate paired values of J and soil moisture depletion (8 - 6) for
values of t and for L ranging from 10 cm to 2 m. The result was a family
of curves, each relating J to (6 - 6) for a specific value of L, as
illustrated by the example curves for 60 and 105 cm in Figure 5. A polynomial
regression function of the form:
J = B + B (9 - 9) + B (9 - 9)2 + B (9 - 9)3 (7)
L *"L L L
was derived for each of these curves. The coefficients B. are unique for
L
each depth L. The set of B. coefficients for each i were then used with a
XL
second polynominal regression to derive an equation for B as a function of
L: i
B.(L) = a + a. L + a. L2 + a. L3 (8)
1 ^ 11 X2 13
20
-------
1.5
ra
•o
x.
u
1.0
0.5
Measured *
Model estimate
6 78 9 10
DAYS AFTER IRRIGATING
11
12
13 14
FIGURE 4. Rate of drainage (J) from a 60 cm and 105 cm soil column as a function of time
(in days). * Based on Jensen, 1976, personal communication.
Model estimate
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
SOIL MOISTURE DEPLETION (percent by volume)
FIGURE 5. Rate of drainage (J) from a 60cm and
105cm soil column as a function of soil moisture
depletion.
21
-------
Soils in the study area are very deep and well drained and there is no water
table close to the surface. Therefore, no provisions for upward movement
of groundwater were included in the model.
Evapotranspiration Submodel
Calculation of evapotranspiration follows methods proposed by Jensen,
et al., (1969). The potential rate (PET) is computed by the Penman
equation with a modified wind function. Actual ET is then:
ET = k • PET (9)
c
in which
k = k • K + K ,
c co a s
k = crop coefficient (a time dependent coefficient),
k = Jln(M. + l)/£n(10)
a A
M = percent available moisture remaining at the time of the
estimate,
K = (0.9 - k • K ) ' 0.8 on first day after water is applied
s co a
=(0.9-k * K ) '0.5 on second day after water is applied
CO ci
= (0.9 - k • K ) • 0.3 on third day after water is applied
co a
= 0 at all other times
K is an adjustment term for low soil moisture conditions, and K adjusts for
a s
wet soil surface conditions. The parameter k is usually defined, somewhat
ambigously, as the ratio of the actual ET rate to the potential rate for a re-
ference crop under well watered conditions. The ambiguity in the definition
of k arises from the meaning of potential rate and the determination of the
actual rates from which the crop coefficients were derived. PET may be either
the evapotration rate as measured for a reference crop in a lysimeter or the
rate calculated by one of the several available models (e.g., Penman or Jensen-
Raise) . The actual ET rates used to derive k may or may not include
evaporation from wet soil surfaces during the period immediately following
an irrigation or rainfall. For this study k was defined as the ratio of
co
actual ET, for a well watered crop under dry soil surface conditions, to the
potential rate for alfalfa calculated by the Penman equation with a modified
wind function and with the vapor saturation deficit calculated as the daily
mean of the maximum and minimum deficits. Several requisite crop curves
consistent with this definition have been developed at the Snake River Con-
servation Research Center, 64 km west of the study area. For other published
crop curves, it was necessary to make adjustments to account for the methods
by which they were derived. In making these adjustments the investigators
22
-------
were assisted by suggestions from Dr. Marvin Jensen and related research by
R.D. Burman (Jensen, 1973). The crop coefficient curves used in the study are
presented in Figure 6. The curves presented for sugar beets, grains, peas
and beans were developed by McMaster (1976), Ruffing, et al., (1974),
Ruffing and Jensen (1976) and Wright and Jensen (1976), respectively. The
crop coefficient for potatoes is essentially a compilation of information
from local experts and is not from published sources. Using recorded dates
for planting, full cover and harvest, the daily crop coefficients k were
calculated for the entire season for each field. Soil moisture was measured
once in each of the 204 cases, early in the season, by the USER. Soil
moisture conditions were initialized for the day on which that measurement
took place and soil moisture was calculated daily from that point on.
Initially a crop coefficient of 0.1 was used for bare soil evaporation.
This resulted in evident errors in estimates of soil moisture, so an empiri-
cal soil evaporation model suggested by Jensen (1977) was used for the bare
soil case:
— n
E = 8.0 e mm/day (10)
in which t is the number of days since the last irrigation or rainfall. The
cumulative evaporation calculated by this equation may not exceed the amount
of water applied and the daily rate may not go below 1 mm/day. This model
was used until the day on which the crop was assumed to have completely
emerged. The following emergence dates were selected after consultation
with irrigators and irrigation advisory services in the area.
Crop Time of Emergence in Days
Barley 10
Beans 10
Peas 10
Potatoes 10
Sugar Beets 30
Wheat 10
The soil moisture model was of central importance to this research since
this model generated estimates of soil moisture, evapo transpiration and deep
percolation. These values were used not only directly in the analysis, but
also as inputs to the other models. An evaluation of the sensitivity of
model outputs to various input parameters was conducted using data from ten
representative fields. As might be expected, it was found that evapotrans-
piration estimates were of critical importance. However, the ET submodel
was developed from the Penman equation and calibrated locally by Wright and
Jensen (1972) . Furthermore, several of the crop curves as well as the ET
adjustment equations were developed by Wright and Jensen under essentially
the same conditions of soil, climate and crop varieties. It is therefore
reasonable to expect a high degree of accuracy in the ET estimates used in
the study.
23
-------
N)
JS.
O BEANS
• POTATOES
D SUGAR BEETS
• GRAINS
A PEAS
10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100
PLANTING TO EFFECTIVE COVER (PERCENT) DAYS AFTER EFFECTIVE COVER
FIGURE 6. Crop coefficient curve for beans, peas, grains, sugar beets and potatoes.
-------
The accuracy of model estimates of evapotranspiration may be judged by
comparing the average season total evapotranspiration, as estimated by the
model for each of the crops, with total evapotranspiration observed for these
same crops under controlled experimental conditions (Table 2). The majority
of the experiments were done at Kimberly, Idaho, and therefore involved the
same climate and soil type as found in the A and B District.
TABLE 2. COMPARISON OF AVERAGE CONSUMPTIVE USE ESTIMATED FOR THE
A AND B DISTRICT AND MEASURED CONSUMPTIVE
USE AT VARIOUS SITES
Average of
Model Estimates Average of Hectares
of ET, Measurement ET, in Production
Crop A and B District Various Locations Absolute Error* in 1977
(cm) (cm) (cm)
Alfalfa
Barley
Beans
Potatoes
Wheat
Beets
Peas
87.1
43.2
39.6
51.3
43.7
63.0
Q /
35.6-
91.7^
?/
43.2-'
3/
50. 0^'
LI
59.4-'
45. 1-
6/
61.7-'
11
34.0^-'
-4.6
0
-10.4
-8.1
-2.0
+1.3
+1.8
16039
14965
5860
5443
9567
12026
1675
*A and B District 1975, Weighted Average Error -3.4%.
_!/ Measured at Kimberly, Idaho.
2f Estimated by D.T. Westermann from field research at Kimberly, Idaho.
3/ Measured at Kimberly, Idaho, 1973, 1974 (J. Wright,' .personal communication)
_4/ Measured at Kimberly, Idaho, 1972 (J. Wright, .personal communication)
51 Average of values measures at sites in S. Alberta (16.3 in., 18.2 in.)
and S. Dakota (19.4 in.).**
j6/ Measured at Kimberly, Idaho.
TJ Measured at site in South Alberta.**
j8/ Average of values from fields in which alfalfa was not grown simultane-
ously.
**"Consumptive Use of Water and Irrigation Water Requirements," Irrigation
and Drainage Division, Jensen, 1973 (ASCE).
Based on the 1975 cropping pattern for the entire district the model
predictions show a weighted average error of -3.8 percent. This slight
underestimation may be due in part to the fact that researchers referenced
in Table 2 were generally careful to keep their crops well watered, whereas
some of the farmers in the A and B District were occasionally observed to
let their fields become drier than would -be advised. It was concluded that
evapotranspiration estimates generated by the soil moisture model are very
nearly unbiased, which increases confidence in estimates of changes in
25
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water use and deep percolation that would occur due to irrigation
scheduling.
IRRIGATION MODEL
The amount and timing of irrigations for each crop is estimated by the
irrigation model. This information is used by the production (yield), soil
moisture, and regional economic models.
The irrigation model was used to simulate scheduling of fields and the
consequences of irrigation applications under the scheduled regimes. The
model determines the proper timing of each irrigation event on the basis
of the amount of moisture remaining in the root zone. When an irrigation is
called for, it specifies the amount of water to be diverted, calculates
losses in the distribution system and generates an estimate of surface run-
off. The balance of each simulated diversion is then added to the soil
water budget either to be stored in the soil profile or ultimately to drain
beyond the root zone. In scheduling irrigations the model follows essen-
tially the same decision rules used by a scheduling service presently op-
erating in the district.
Water Application Submodel
A critical soil moisture level was selected for each of the stages of
growth for each crop (Table 3). Whenever soil moisture reached the
critical level an irrigation was called for. The amount of water to be
applied was calculated by the equation.
(W - W)
WD = -If (ID
in which
W = nominal field capacity in the root zone, in inches,
r L
W = present soil moisture content, in inches,
E = overall efficiency of irrigation, including all losses,
runoff and percolation,
W = amount of water to be diverted, in inches.
The choice of values for W and E could significantly affect the results
FC
achieved by a scheduling service (and therefore the estimates produced in
this study). The local USER scheduling service uses an efficiency of 65
percent for surface irrigation systems in the study area, based on calcula-
tions of attainable efficiencies. However, USER personnel felt that 60
percent was more realistic for the efficiencies actually achievable in the
area. The lower estimate of efficiency results in a more conservative evalu-
ation of the potential benefits of irrigation scheduling. The value of field
capacity, W , was taken to be 33.5 percent moisture by volume, which was
I* (_•
the moisture level that was usually calculated by the soil moisture model
26
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TABLE 3. SOIL MOISTURE LEVELS AT WHICH SIMULATED
IRRIGATIONS WERE SCHEDULED
Critical Soil Moisture Level
Crop (% by volume)
Alfalfa 20
Barley, Wheat 18
20
16
Beans 18
20
Peas 20
21
20
Potatoes 23
22
Sugar Beets 20
21
Dates
All season
Until 80% cover
Until 20 days after
full cover
Until end of season
Until 80% cover
Until end of season
Until 80% cover
Until 10 days after
full cover
Until end of season
Until full cover
Until end of season
Until 75% cover
Until end of season
after two or three days of drainage following a thorough irrigation. Note
that W is not equivalent to the limit of gravity drainage (30.7 percent).
JbC
Rather it is the soil moisture level which would probably be selected as the
field capacity by a scheduling service. Equation 11 was used to determine
the need for irrigations under both the ideal and imperfect scheduled re-
gimes. However, under the imperfect regime random errors in the actual timing
and amount of each irrigation were then introduced. The submodel that was
used to simulate these errors consisted of two random error generators,
which simulated random deviations from the specified quantity of water to
be applied and random numbers of days difference between recommended and
actual irrigation dates. The statistical parameters used for the random
error generators were based upon data collected by the USER from two other
locations in which irrigation scheduling is being practiced. One site was
the Falls Irrigation District, located approximately 80 km east of the
A and B District, near American Falls, Idaho. The other site was the Grand
Valley, near Grand Junction, Colorado. In the Falls District the USBR col-
lected data on timing errors in scheduled fields for several different crops
(USBR, 1974). The Grand Valley data consisted of observed errors in quanti-
ties applied to sugar beet crops by furrow irrigation (Brost, 1977). Sea-
sonal ET in the Falls District is slightly lower than in the A and B District.
Based upon USBR estimates of ET in both locations, the difference appears to
be on the order of lO percent. Therefore, the errors simulated by the model
would tend to be conservative. The Grand Valley data could not be used
directly because there was no assurance that circumstances there were similar
to the A and B District. However, the Grand Valley data were used to estab-
lish the general shape of the statistical distribution used for the A and
B District.
27
-------
The raw data from these sites are summarized in Figures 7 and 8. Errors
in timing were found to range approximately between plus ten and minus ten
days for three categories of crops, although the shape of the distributions
differ within those limits. (An error on the plus side indicates that an
irrigation took place after the recommended date.) Additional data from
alfalfa fields were available, but were insufficient for presentation in this
graphical form. However, mean and standard deviation of errors for alfalfa
was +3.0 days and 6.37 days, respectively.
Application errors in the Grand Valley show a pronounced bias on the
positive side, indicating that farmers used considerably more water than was
recommended (Figure 8). The expected error in applications was +7.50 cm
and the standard deviation was 8.20 cm. The data presented in Figure 8 do
not include two extreme valued errors that were observed (+58.2 cm and
+66.0 cm). The forms of the statistical distributions of simulated errors
for the A and B District were taken from these data.
The distribution of timing errors used in simulation of imperfect sched-
uling was a composite of the distributions observed for the various crops
in the Falls district. The same composite distribution was used for all
crops. This approximation was deemed acceptable for purposes of estimating
regional average water use, deep percolation, runoff and associated water
quality parameters. On the other hand, this approximation could lead to
biased estimates of crop yields (as well as crop quality in the case of po-
tatoes) since yields of different crops would be affected differently by
timing errors in irrigation scheduling. However, no estimates of yields were
made for the imperfect scheduling regime.
The statistical errors in quantity applied were assumed to have the same
shape of distribution as the Grand Valley data, but the parameters of the dis-
tribution were estimated from A and B District data. The errors observed in
the Grand Valley were normalized by dividing them by the average error (7.50
cm). The resulting normalized distribution was then used to simulate errors
in the A and B District. Random errors were generated using the normalized
distribution, then multiplied by the expected error for the A and B District.
A USER study (1974) of irrigation scheduling in the A and B District es-
timated that water use on scheduled fields in 1972, actually increased
slightly, by a weighted average of 2 percent. From our own initial analysis
of 204 cases (to be discussed below), it was estimated that average historical
water use was 32.3 percent greater than the ideal quantity. The expected
error for any single irrigation was therefore arbitrarily set at 35 percent
of the recommended amount. Note, however that this will lead to a conser-
vative estimate of the effects of error in quantity applied. Insofar as
scheduling reduces the total number of irrigations, the final estimate of
water use under the imperfect regime would still be less than under the
unscheduled regime.
The computational procedure for generating errors in quantity applied
can be represented by the following equation:
QA = Qx (1.0 + 0.35 (1 + RQ)) (12)
28
-------
20
10
n
GRAINS
fin ~
I
30
-10
10
DAYS IN ERROR
20
10
O
S
g
O
u.
O
DC
111
CD
3
3
Z
SUGAR BEETS
r-n
i n
-10
10
DAYS IN ERROR
20
30
20
10
POTATOES
-10
0 10
DAYS IN ERROR
20
30
FIGURE 7. Distribution of errors in timing of irrigations, Falls Irrigation
District.
29
-------
15 r
OJ
o
CO
§10
CC
UU
CO
CO
O
CC
tu
00
-38.1
J_
-25.4
-12.7 0 12.7
ERROR IN APPLICATION, (CM.)
25.4
38.1
FIGURE 8. Application errors on sugar beets, Grand Valley (cm.).
-------
in which
Q = actual application (cm)
A
Q = ideal application (cm)
RQ = normalized error in application (cm/cm)
The statistical distributions of errors in timing and normalized errors in
quantity (RQ) used in the model are shown in Figures 9 and 10.
The possibility of correlation between errors in timing and errors in
quantity was considered, but Grand Valley data indicated that this might be
of little consequence. The Grand Valley data included errors in timing as
well as quantity and the coefficient of correlation between these two types
of error was 0.11. Consequently, this correlation was not simulated by the
irrigation model.
Runoff Submodel
The runoff submodel was developed empirically using data from 1,050 ir-
rigation events that were monitored by the USER. Runoff was assumed to be
determined by: (1) the small scale physical characteristics of the fields,
including furrow shape and roughness, vegetative resistance and infiltra-
tion rate, (2) the large scale features of slope and length of run, (3) the
rate and amount of water application, and (4) the techniques and skills of
individual farmers. The slope, length of run, rate of application and
amount of water applied were known quantities. The small scale physical
features and the farmer's skill were unknown quantities, so it was desired
to use some indirect indicator for each of them. The indicators considered
were time (starting at planting data and scaled to season length), type of
crop and antecedent soil moisture conditions. Time was regarded as a pos-
sible index of the influence of vegetative cover and any other time variant
factors such as furrow conditions. Crop type was also assumed to reflect
vegetative cover, as well as many factors associated with a particular type
of crop, such as furrow shape and roughness or rates of application. Ante-
cedent soil moisture condition was assumed to be at least somewhat indicative
of average infiltration rate. Total water applied per unit of land area was
regarded as a rough indicator of the rate of application since virtually all
farmers used the same set times (24 hours). In summary then, the factors
considered for the runoff model were crop type, rate of application, quantity
of water applied, slope, length of run, antecedent moisture conditions and
time (scaled to crop development).
These factors were combined in a stepwise linear regression model. A
non-linear least squares fit was also tried. In addition, each factor was
plotted individually against runoff to develop a visual impression of the
data and to detect,any obvious non-linear relationships. Finally, histo-
grams of each factor were plotted to get a better perspective on the sig-
nificance of the various factors.
31
-------
.30
.20
o
z
LU
w °
M HI
DC
U.
.10
-10
-5
10
15
NUMBER OF DAYS
FIGURE 9. Statistical distribution of timing errors (number of days departure from recommended
Irrigation Date) Under Imperfect Scheduling Regime.
-------
.20 r
.15
u>
UJ
O
3
O
111
cc
u.
.05
0.5
1.0
1.5
2.0
2.5
RATIO OF SIMULATED IRRIGATION TO RECOMMENDED IRRIGATION
FIGURE 10. Statistical distribution of errors in quantity of water applied
under the imperfect irrigation scheduling regime; (expressed as a ratio of
actual to recommended quantities).
-------
It was found that crop type and the quantity of water applied were
closely correlated with runoff. Rate of application was of equal importance
with quantity applied; i.e., either of these factors was suitable for use in
the regression. Antecedent moisture conditions also appeared to affect run-
off to a minor extent. Slope, length of run and time, were found to be un-
usable as predictors. That is not to say that they are unimportant, but
in the stepwise regression they produced results that were either unreason-
able or insignificant. Upon examination of the plots and the histograms it
was found that the statistical distributions of the slope and length of run
may have been too uneven to permit their use in a regression model. For
example, the regression procedure assigned a negative coefficient to slope,
indicating runoff would decrease with increasing slope (Figures 11 and 12).
From the histogram in Figure 11, it is seen that a disproportionate number of
fields had low slopes. Because of the inherent fluctuations in runoff, a
large sample set will have a greater range of scatter than a small sample.
Probably because of this, the highest runoff values at the lowest slope
were greater than those at the highest slope, as indicated by Figure 12.
This would explain the negative regression coefficient.
A linear regression equation was recalculated for each crop using water
applied and total available storage capacity in the root zone (Table 4). As
indicated by the R values, the predictive ability of these regression equa-
tions was low. Consequently, they could not be expected to reproduce the wide
range of observed runoff events. For these reasons it was decided that a
statistical runoff model was needed. Such a model would not recreate the
runoff from any single irrigation, but it could recreate the statistical
distribution of a large number of events. A high degree of variability in
runoff might be expected to produce different average sediment and TDS loads
in return flows than would result from a narrower range of variability.
Because the simulated runoff were to be used to estimate TDS and sediment
loads in return flows it was important that the variability of the runoff
be accurately simulated.
TABLE 4. RUNOFF MODEL COEFFICIENTS AND CORRELATION
COEFFICIENTS RESULTING FROM LINEAR REGRESSION
Crop
Alfalfa '
Beans
Peas
Potatoes
Sugar Beets
Barley
Spring Wheat
Winter Wheat
Wheat and Barley
ao
-2.781
0.129
0.335
-0.494
-0.236
-0.322
-0.440
-0.023
0.081
al
0.202
0.125
0.121
0.194
0.131
0.234
0.206
0.087
0.090
Number of R2
2 3 Observations
0.140
0.011
0
0.027
0.131
0.012
0.025
0.006
0.013
1.0
1.0
1.5
1.5
1.0
2.0
2.0
1.0
2.0
88
313
157
143
123
58
55
49
41
0.39
0.20
0.15
0.46
0.39
0.41
0.31
0.36
0.32
34
-------
60
50
tu
u
u. 3°
O
oc
m 20
a
§10
1.0
2.0
SLOPE (%)
3.0
4.0
FIGURE 11. Histogram of 88 irrigation events on alfalfa with
various field slopes.
40
30
o
- ~.
O 20
z
oc
10
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
1
1.0
2.0
SLOPE (»/;)
3.0
4.0
FIGURE 12. Surface runoff for 88 irrigation events on alfalfa
with various field slopes.
35
-------
Normalized errors were calculated for each irrigation event by the
equation:
R
Ei =
Y
in which
E.
cl .
i
= normalized error in runoff prediction for the ith event,
= actual runoff from ith irrigation event,
= runoff predicted by the regression model for the ith event.
For each crop the statistical distributions of these normalized errors were
determined. In simulating irrigation events these distributions were used
to generate random deviations from the runoffs predicted by the regression
equations. That is, for each simulated irrigation the runoff was estimated
by:
.
(1 +
E.)
(14)
where
R.
V
= simulated runoff for the jth event,
+ E
Bisj
B2(Q
j
a, B , B_ = regression coefficients,
S .
Q.
E.
J
1 , _
= antecedent available capacity in the root zone at the
time of the jth simulated irrigation event,
= quantity of water diverted for the jth simulated
irrigation event,
= Minimum application for runoff to occur,
= the random error term.
The reason for using the normalized error to characterize the random compon-
ent, rather than the absolute error, was that the magnitude of the error will
depend upon the amount of water diverted. The normalized errors were found
to be fairly evenly distributed over the full range of values of diversions,
as illustrated for wheat fields by Figure 13.
Under a scheduling regime, the timing and amount of water applied will
change. The change in timing implies a change in the antecedent moisture
conditions. The model that was formulated accounts for these factors ex-
plicitly in the regression equation. All other determinants of runoff for
each crop are assumed to be accounted for by the random component and
36
-------
iJ.O
1.0
0
p
< 0
oc
UJ
- 1.0
- 2.0
o
o
o °o
o
O 80
o
oo°oo°
o
I ° I I I I «
10 ° 20 0 30 40 50 60
0 ° 0° o
0 °
O 0
0 ,00 0 ° 0
o ^>o o o
o
APPLIED WATER (CM.)
FIGURE 13. E ratio and the amount of water applied to wheat fields.
-------
therefore, in this model, are implicitly assumed to be unaffected by
scheduling. Obviously a model that combines a statistical component with a
linear function of just water applied and antecedent moisture conditions can-
not be considered a reliable predictive model for field use. Nevertheless,
the investigators feel that it is adequate for estimating the regional change
in runoff that would ensue from the use of a scheduling service. The larga
number of irrigations used to calibrate the model (1050) should insure that
the statistical characteristics of the runoff will also be reproduced by the
model.
To test the predictive ability of the runoff model, the original set of
1050 runoff events were estimated. The mean and standard deviations of the
estimated runoff events for all cropswere reasonably close to the actual
events (Table 5). The errors indicated in Table 5 were judged to be
TABLE 5. STATISTICAL CHARACTERISTICS OF ACTUAL
AND ESTIMATED RUNOFF DATA
Actual Runoff Data
(cm)
Estimated Runoff Data
(cm)
Crop
Alfalfa, pasture
Small Grains
Beans
Peas
Potatoes
Sugar Beets
All Crops
Mean
6.4
2.9
2.3
3.0
2.6
3.3
3.1
Std. Deviation
6.0
2.4
1.7
2.4
2.2
2.5
1.20
Mean
6.5
3.0
2.2
2.7
2.8
3.2
3.0
Std. Deviation
7.4
2.3
1.6
1.9
2.2
2.2
3.3
acceptable for the purposes of this analysis.
Spatial Variability of Applications
One other important assumption which was made in the irrigation model
was that applied water was distributed uniformly over the fields. However,
since furrow irrigation was the predominant method it must be recognized
that, in fact, infiltration of water would be rather variable and this could
cause errors in estimates of percolation. To evaluate the significance of
the assumption of uniform applications, a test case was analyzed. The
characteristics of the test were the following:
(a) A 3-foot (91.4 cm) root zone was assumed, roughly the same as
the root zone used for most crops in the study.
(b) The soil moisture prior to irrigation was set at each of five
different levels; 20 percent (by volume), 22.5 percent, 25
percent, 26 percent, 27.5 percent.
38
-------
(c) Two example irrigations were run, one in which it took
8 hours for the stream to reach the end of the furrow
and one in which it took 12 hours. (All study fields
had slopes of 1.0 percent or more). Set time was as-
sumed to be 24 hours.
(d) Since consumptive use rates affect total percolation,
two rates were considered: one at mid-season (high
rate) and one at end of season (low rate).
Twenty combinations were therefore considered. For each combination the drain-
age following an irrigation was computed in two ways. First, the field was
divided into four segments representing the first 36 percent of the run, the
next 28 percent of the run, the next 21 percent of the run, and the last 15
percent of the run (these were assumed arbitrarily to be the distances travel-
ed by the stream in the first, second, third and fourth quarters of the total
advance time). Water intake for each segment was determined from a cumulative
infiltration curve prepared by USBR from studies in these fields. A typical
curve was used (USBR, 1971, pages 90-92). The resulting soil moisture level
for each segment was determined and total drainage, from time of irrigation
until cessation of gravity drainage, was calculated. The area-weighted average
drainage was then computed for the entire length of run.
The second way was to compute total drainage without regard for spatial
variability, as was done in the model. Drainage estimates by these two
methods were compared (Table 6). In summary, the assumption of uniform
distribution resulted in overall estimates of percolation that were 1.3
percent low for the 8-hour case and 5.5 percent low for the 12-hour case.
These figures represent average of errors weighted by volume of percolation.
Large percentage errors occurred in a few cases, but were associated with
small total' percolation, hence their significance was negligible. For the
1.0 to 2.0 percent slopes common in the study area the 8-hour case is con-
sidered typical. It therefore seems likely that the order of magnitude of
error should be well below 5 percent.
Distribution System Losses
Distribution system losses simulated by the irrigation model included
percolation from head ditches and non-beneficial consumptive, use. Losses
measured by the USBR were used to develop a simple linear relationship be-
tween distribution losses and the amount of water diverted. Non-beneficial
consumptive use was estimated as a linear function of evapotranspiration
rates using a simple formula calibrated by the USBR for each farm during
each year of the 1964-68 water use study (USBR, 1971).
SALINITY MODEL
The salinity model predicts TDS concentrations in water percolating be-
yond the root zone on the basis of the chemical composition of applied water
and seasonal leaching fraction. Estimated total salt load in deep percola-
tion is then calculated as the product of estimated TDS concentration and
39
-------
TABLE 6. VARIABILITY OF PERCOLATION IN FURROWS
Drainage in Centimeters
For Each Segment
Time to
end of
furrow
8 hours
8 hours
8 hours
8 hours
8 hours
8 hours
8 hours
8 hours
8 hours
8 hours
12 hours
12 hours
12 hours
12 hours
12 hours
12 hours
12 hours
12 hours
12 hours
12 hours
ET
Rate
High
High
High
High
High
Low
Low
Low
Low
Low
High
High
High
High
High
Low
Low
Low
Low
Low
Initial
Soil
Moisture
20%
22.5%
25%
26%
27.5%
20%
22.5%
25%
26%
27.5%
20%
22.5%
25%
26%
27.5%
20%
22.5%
25%
26%
27.5%
36%
0
.91
2.41
3.73
5.10
0
.46
1.30
2.15
3.53
0
.23
1.14
1.88
3.25
0
.74
2.11
3.45
4.83
28%
0
.74
1.91
3.05
4.55
0
.20
1.02
1.68
2.98
0
.13
.84
1.32
2.61
0
.51
1.68
2.41
4.19
21%
0
.46
1.63
2.31
4.09
0
.01
.79
1.27
2.52
0
0
.36
.69
1.42
0
0
.94
1.40
2.54
15%
0
.05
1.04
1.68
3.3
0
0
.46
.84
1.78
0
0
.15
.41
.91
0
0
.61
.99
1.80
Segment Overall
Field
Weighted
Average
0
.64
1.91
2.95
4.47
0
.25
.99
1.64
2.90
0
.12
.74
1.16
2.34
0
.41
1.52
2.36
3.71
Field
Average
0
.74
1.91
3.05
4.47
0
.20
1.02
1.68
2.90
0
.08
.69
1.09
2.25
0
.28
1.40
2.03
3.82
% Error
0
12.3%
-0.3
-3.8
0
0
+21%
-2.5
-2.4
0
0
-34.8%
-7.8%
-1.4
-3.9
0
-31.3
-7.9
-14.4
+2.9
-------
estimated volume of deep percolation.
The salinity model used in this study was developed at the U.S. Salinity
Lab (Rhoades, et al., 1974). That model predicts specific ion concentra-
tions in the leachate based upon chemistry of. applied water, leaching frac-
tion and soil characteristics.
The chemistry of irrigation water used in the A and B District was found
to be fairly constant. However, in some seasons during the five years of the
USER study, there was an appreciable amount of rainfall. It was assumed that
rainfall occurring during the growing season would dilute the total applied
water proportionately. That dilution was as much as 30 percent in some
cases. The salinity lab model was therefore used to estimate salinity of
leachate at four different levels of dilution of applied water, 0, 10 percent,
20 percent and 30 percent.
Four curves were derived by regression on discrete data points generated
by the model (Figure 14). Each curve represents one of the four levels of
dilution. These regression models were incorporated into the case study and
seasonal leaching fraction was computed for each field. Total rainfall and
applied water were used to determine the level of dilution of applied water.
The TDS concentrations associated with the calculated leaching fraction were
calculated for each field by interpolating between the appropriate curves.
Salinity of surface runoff was assumed to be the same as that of applied
water, since USER field data showed no appreciable difference between the
two.
The salinity model was not locally calibrated and could not be expected
to precisely predict salt loading from any single field in any one year,
since significant data errors are inevitable and the model bias is not
known. Nevertheless, for purposes of predicting changes in regional average
salt loading, the model is considered adequate because random errors will
tend to cancel out and model biases will be mitigated by virtue of the fact
that the analysis is concerned with differences in model predictions under
differing irrigation regimes.
In the case of the A and B District, reductions in regional TDS loads
in return flows would be accompanied by a decrease in calcium concentrations
relative to sodium, which would increase sodium adsorption ratios of return
flows. At the same time, alkalinity would be reduced.
SEDIMENT MODEL
Sediment loading was regarded as an indicator of nitrogen, phosphorous
and pesticide concentrations in return flows, since these factors are direct-
ly linked to erosion rates (Carter and Bondurant, 1976). The sediment model
predicts sediment concentrations in surface runoff on the basis of the rank*
*The rank of an irrigation refers to its order in a sequence of irri-
gations in one particular field, e.g., the first, second, third, etc.
41
-------
10,000
5,000
-------
of each irrigation event and the volume of water applied per unit of land
area. Sediment loads in surface runoff are extremely variable and difficult
to predict. Nevertheless it was possible to estimate sediment loads in the
case study using a simple model calibrated with USER measurements of sediment
concentrations in surface runoff. Although it cannot be claimed to be an
accurate predictor of sediment loads in return flows from any single irriga-
tion event, the model can be expected to produce a reasonably accurate es-
timate of aggregate sediment loads from the A and B District under different
scheduling regimes.*
The rate of sediment loss from a furrow irrigated field can be expected
to be initially high at the beginning of an irrigation, then decline rapidly
during the irrigation until it approaches a steady state (Figure 15). Total
sediment loss for... an irrigation will generally be higher with the first irri-
gation of the season and decline with subsequent irrigations (Hagan, et al.,
1967, p. 957). However, cultivation of fields can cause high total sediment
losses later in the season (Busch, et al., 1975).
Sediment data collected in the A and B District by the USER were used
for development of the model. The data consisted of grab samples of runoff
from each of the fields at various times during the,season. A single sample
was taken for each irrigation; that is, there were no multiple samples from
any single irrigation. With this data limitation in mind the model was for-
mulated on the basis of the following postulates:
(1) Each sample must be considered a single random sample from
a statistical distribution of sediment concentrations that
would look similar to the curve shown in Figure 15. The
statistical distribution coincides with the distribution
of concentrations with time.
(2) The shape of the curve typified by Figure 15 will change
with each irrigation, as ground surface conditions and
crop development proceed. In general it may be supposed
that there is a representative curve for first irrigations,
another representative curve for second irrigations, etc.
(3) The time integral of these representative curves can be
estimated, as an approximation, from the average concen-
tration of all those samples taken during first irriga-
tions, all those taken during second irrigations, and so
on.
*Note that it was assumed that only irrigation schedules would change.
The changes in irrigation techniques that might result in con-
junction with irrigation scheduling were not considered.
43
-------
cc
D
O
CO
Q
UJ
o
z
UJ
Q.
CO
D
CO
O
120
100
O
5 80
CO
O
60
40
20
Total suspended solids applied
Total suspended solids lost
, n
— '
0 4 8 12 16 20 24
HOURS FROM BEGINNING OF IRRIGATION SET
FIGURE 15. Total suspended solids gained and lost
during an irrigation set (after Busch,
et a/. 1972).
-------
(4) Forage crops are generally not tilled and have essentially
full cover early in the season so it may be assumed that
sediment losses from such crops are constant and relatively
low during the season.
(5) The average total sediment load from an irrigation will
be the product of the average concentration and the total
volume of runoff.
The fifth postulate would be true if the rate of runoff were constant
during an irrigation. This will not actually be the case,however. Run-
off rate will increase very rapidly at first and then continue to increase
slightly during the remainder of the time water is applied, as illustrated
by Figure 16. This has the affect of causing the product of the average
concentration and the volume of runoff to slightly overestimate total sedi-
ment loads in runoff.* Since field data on the time distribution of surface
runoff for each individual field were unavailable, a constant correction
factor was applied to the average estimated by the method described above.
The correction factor was determined by analysis of the hydraulics of flow
in typical fields in the area. The factor used was 0.75.
USER field data on average sediment concentrations were assembled and
the ranking of each irrigation was determined. The average concentration
for each rank was then determined (Table 7). From these averages, the
following regression model was derived:
S = 1832 if0'3374 (15)
3
in which
S = average sediment concentration, in mg/&,
3.
R = rank of irrigation
This regression function is displayed in Figure 17.
The 0.75 correction factor was determined by first developing typical
curves for the time distribution of concentrations and the time distribution
of runoff. The data from all rank 2 irrigations were used to estimate the
distribution of concentrations. The distribution of runoff rates was es-
timated by selecting typical field characteristics and using a typical ap-
plication rate, time of set and furrow intake rates for the A and B District.
The typical values chosen were based on data reported by the USER (1971).
*As an example, the sediment load for the case illustrated in
Figures 15 and 16 would be overestimated by 26 percent by the
method indicated in steps 1 through 5.
45
-------
QC
D
O
o
z
LL
LL
O
z
LU
O
<
LL
CC
D
CO
0.40
0.30
0.20
0.10
r
_r
j
r
r
i
4 8 12 16 20
HOURS FROM BEGINNING OF IRRIGATION SET
24
FIGURE 16. Rate of runoff from a furrow irrigated field
(after Busch et a/. 1972).
-------
2000 _
1500
1000
O
h-
<
tr
i-
5
O
O
O
UJ
z
2 500
c/>
CONCENTRATION =
1832 RANK~°'3374 mg/l
j_
j_
4 5
RANK
8
FIGURE 17. Relationship of sediment concentration to rank of
irrigation event for non-forage crops in the A and B District.
-------
TABLE 7. SEDIMENT CONCENTRATIONS IN RUNOFF FROM
NON-FORAGE CROPS BY RANK OF IRRIGATION
Number of Average Sediment
Average Sediment Irrigations Load Estimated by
Rank of Irrigation Concentration (mg/&) Sampled Regression (mg/&)
1
2
3
4
5
6 and above
1,847
1,611
1,134
1,049
796
1,243
34
26
24
14
11
15
1,832
1,450
1,264
1,147
1,064
1,008
The model thus derived, while very simple, can be expected to predict
regional average sediment loads fairly well. To more accurately predict
sediment loads of individual irrigations it would be necessary to examine many
additional relevant factors, such as furrow shape, rate of application, soil
roughness, slope, stage of crop growth, etc. Initially, these and other
factors were considered in the analysis. An attempt was made to incorporate
them into the model, but with no notable success. The simpler model pre-
sented above is adequate for examining the question of interest: what would
be the A and B District sediment load under the 1975 existing irrigation
practice, and what would the regional load have been if total water use and
irrigation frequency had been altered by irrigation scheduling? Since the
sediment loads estimated by this model are based on local data and reflect
the influence of quantity of runoff and frequency of irrigations (through
rank of irrigations) the model will be adequate for estimation of the change
in sediment loads in the A and B District as scheduling procedures change,
i.e., as quantity and frequency of irrigations change.
For forage crops, a simpler model was used. It was assumed that sedi-
ment concentrations would not change during the season. Based on USER data,
an average concentration of 343 mg/2. was estimated for forage crops.
CROP PRODUCTION MODEL
The crop production or yield model estimated crop yield per acre based on
the information provided from the soil moisture and irrigation model. It
is generally recognized that poor irrigation practices can reduce crop yields
in several ways. If too little water is applied, overall crop growth is re-
duced and losses due to certain hazards such as weeds or frost may be in-
creased. At certain critical times, fruit development may be greatly impair-
ed or, if too much water is applied, yield reductions may result from poor
soil aeration, excessive vegetative growth at the expense of fruit yield,
or difficulties with harvesting due to lodging of grains.
48
-------
The crop production model conceived for this project had three com-
ponents. The first was a submodel for estimating the potential yield based
upon seasonal evapotranspiration. The second was a linear regression model
which predicted yield deficit that would be attributable to poor timing of
applications or excessive water use. The third was a coefficient of adjust-
ment intended to account for unexplained variations in yields. The overall
model may therefore be represented by the following equation.
Y = Y • (1 - D) • C (16)
A p u
in which
Y = final estimate of yield,
A
Y = potential yield based upon seasonal evapotranspiration,
D = yield deficit, expressed as a decimal fraction of
potential yield, which would be predicted on the
basis of excessive water use or mistimed applications,
C = a coefficient which adjusts for unexplained variations
in yield.
Potential Yield Submodel
Potential yield (Y ) was predicted based on a crop production model
developed by Stewart, et al. (1973). Inherent in the model is the assump-
tion that there exists a maximum attainable yield for any given cultural
practices and circumstances of climate and soil (YM) and that there exists
some maximum beneficial evapotranspiration (ET) associated with Y . The
1. M M
Y 1 is considered to be a linear func-
—
YM)
tion of the ratio of actual ET to the yield maximizing evapotranspiration
ET
A
In Figure 18, 0' represents the upper limit of the function. At 0'
FT
.
the maximum yield is achieved (100% of Y ) when the maximum beneficial ET
(100% of ET ) is reached. If the actual season total evapotranspiration
(ET ) is less than ET the yield will fall below 100 percent of Y . In that
AM
case the relationship between the ratio
, and the ratio/ET
Y
M
by a straight line through 0* having a slope
The coefficient 8 is defined by the equation,
Y
a _ - (% reduction in yield below M)
o - (% reduction in ET below ETJ
M
49
is represented
-------
1.0
1.0
ET,
M
FIGURE 18. General nature of the crop
production function of Stewart and Hagan
(1969).
3 is therefore referred to as the yield reduction ratio.
Values of
3 have been derived experimentally by Stewart and Hagan (1969) for several
crops. When not available from field experiments, the value of B may be
estimated from other water use-yield data, under some circumstances.
The algorithm for estimating potential yield is therefore defined by
the equation:
M
ET.
- l - 3 ll -
ET,
(18)
Ml
For each crop in the case study it was therefore necessary to determine the
maximum expected yield (¥„), the associated yield-maximizing ET (ETW) and
M M
the coefficient 8 , for use in these equations.
Initially, plots of yield vs. ET for each crop in the 204 historical
cases were made. From these plots a maximum yield and associated maximum
ET were selected. Y was not necessarily the highest yield recorded in the
historical cases. Rather, it was selected to represent a "good" yield
50
-------
relative to the majority of recorded yields. The slopes of the yield func-
tions, represented by the 3 coefficients, were determined from several
sources.
The value of 8 used for beans was the average of coefficients deter-
mined experimentally by Stewart, et al. (1973, 1976) for three varieties.
It was assumed that water use and ET are equivalent when water use is very
low and the water is carefully applied. The 3 value for sugar beets was
derived from field data presented by Larsen and Johnston (1955) in which
these conditions were met. The 3 value for wheat was based on a yield-
o
water use model developed from experimental data by Whittlesey and Colyar
(1968) in which, again, these conditions were met. The coefficient for
barley was assumed to be the same as that for wheat, and the coefficient for
peas was assumed the same as that for beans. These assumptions, while es-
sentially arbitrary, were based upon a subjective evaluation of data pre-
sented for a wide range of-crops by Downey (1972). The models, derived as
described above, were rewritten as linear equations for yield as a function
of seasonal ET as follows.
Crop Potential Yield (English Units)
Spring Wheat 7.59 • ET - 27.23 (bu./ac.)
Winter Wheat 9.38 • ET - 37.5 (bu/ac.)
Barley and Mixed 8.46 • ET - 25.38 (bu/ac.)
Grains
Potatoes 42.86 * ET - 514.3 (cwt/ac.)
Sugar Beets 1.5 ' ET - 12.0 (tons/ac.)
Beans 5.0 ' ET - 45.0 (cwt/ac.)
Peas 3.54 ' ET - 3.54 (cwt/ac.)
Alfalfa yields were predicted by a simpler model. Stewart and Hagan
(1969) have presented data illustrating a clear linear relationship between
alfalfa yields and ET. Therefore alfalfa yield predictions for this study
were made by simply multiplying historical yields from each field by the
ratio of predicted ET to historical ET.
Stewart and Hagan (1969) have stated that the general model described
above can be used to predict crop yields under a wide range of circumstances.
However, a few cautionary comments are in order. First, a crop grown under
very adverse conditions may experience tissue damage, even while satisfying
evapotranspiration demands. The crop may then respond differently to eva-
potranspiration than would be the case under normal growing conditions. The
coefficient $ is only intended to be used under normal growing conditions.
Secondly, 3 may have a unique value for each variety of a crop. Finally,
Equation 18 is only valid if crop stresses are distributed evenly throughout
51
-------
the season. If severely unbalanced stresses occur, yield will fall below
the potential yield indicated by the straight line emanating from 0' in
Figure 18. Where such unbalanced stresses occur, Stewart and Hagan have pro-
posed a model in which B is determined by the relative degree of stress at
each of three growth periods during the season.
Yield Deficit Submodel
The model described above predicts yield as a function of moisture
stress. Yield deficits may be caused by a host of other factors. The state
of the art of crop production modeling has not yet advanced to -the point
where complete models formulated from first principles can account for all
such factors. Therefore a purely empirical regression model was developed
for the present study which might explain some departures from predicted
yields. The general procedure was as follows:
a) Recorded crop yields for each field were adjusted to
account for losses due to hazards specifically noted by
the USER and unrelated to water use (e.g., losses due
to frost or hail). (Where such hazard losses were noted
by the USER an estimate of the percentage of loss was
made and published with the USER data set.) The ad-
justed yield was therefore:
, ,. . , . , , Measured yield ,.._,.
Adjusted yield = =—: „ < v , (19)
1 (Estimated % Loss,
V 100 )
This adjusted yield therefore represents an estimate of the
yield that would have been realized in the absence of the
hazards noted.
b) Using the Stewart-Hagan model for potential yield described
earlier, an estimated potential yield was calculated for
each field. The difference between the adjusted yield and
the estimated potential yield was then regarded as a yield
deficit for each of the 204 fields.
c) A value for eight different indices of water use and soil
moisture conditions (Table 8) were computed for the season
as a whole, and for specific growth stages during the season,
for each field. As an example, ET deficits for the vege-
tative, pollination and maturation stages of growing sea-
son, and for the whole season, were computed.
d) A stepwise regression procedure was employed for each
crop to select appropriate variables from among the
indices described in (c).
52
-------
TABLE 8. YIELD INDICES USED IN STEPWISE REGRESSION
ANALYSIS FOR YIELD DEFICITS
Variable
No. Name
Variable Description
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
ETDEF ET Deficit (attainable ET minus actual ET)
MSMT Average soil moisture tension
MSMP Average soil moisture percentage
IRR Quantity of water applied
ARET Integral of the quantity (% soil moisture - 30.7)
for those days when soil moisture was higher
than the limit of gravity drainage (30.7% by
volume).
ADEPT Integral of the quantity (CRIT - soil moisture
tension) for those days when soil moisture was
lower than 50% available soil moisture, where
CRIT represents tension at 50% available soil
moisture.
ERAIN Net rainfall
NIRR Number of irrigations
The variables, coefficients and correlation coefficients used in the
stepwise regression models for yield deficits for each crop are shown in
Table 9. Note that a positive coefficient indicates a positive contribution
to yield deficit, and a negative coefficient indicates a "negative" contri-
bution to deficit.
A third component (C ) was included in the crop production model to ac-
count for unexplalnable yield variations. It was assumed that this compon-
ent would be constant for any given field under all of the three irrigation
regimes. Thus if C was observed to have a certain value for a given field
under the unscheduled regime it was assumed that the same yield adjustment
would be necessary for yield predictions associated with the scheduled
regimes. That is, if
Y = the recorded yield for a given field,
and
Then
Y = predicted yield under the unscheduled regime,
u
C =Yo
u -
(20)
u
53
-------
TABLE 9. YIELD DEFICIT REGRESSION MODELS
Crop
Equation
Correlation
Coefficient
(R)
Beans
(cwt/ac.)
Barley and
Mixed (bu/ac.)
Y » 113.538-64.269 MSMT (0) + 0.4839 ADEPT (10) 0.79
-6.345 ETDEF (1)* -2.5788 MSMP (0)
Y = 29.77283 + 10.6246 ETDEF (0) - 22.533 MSMT (0) 0.62
+ 0.70193 IRR (0)
Peas
(cwt/ac.)
Y = 26.995 - 3.88426 ERAIN (0) - 0.2033 ARET (0) 0.67
+ 0.50025 IRR (0)
Potatoes
(cwt/ac.)
Wheat
(bu/ac.)
Y = 229.657 - 6.74792 MSMP (1)* + 0.73037
ADEP (3)*
0.71
= 12.288 + 10.0982 NIRR (0) + 9.3249 ETDEF (0) 0.77
Sugar Beets Y = 52.6843 + 0.08352 ARET (0) - 2.22109 MSMP (0)
(tons/ac.) - 2.26122 ETDEF (0)
Winter Wheat
(bu/ac.)
0.83
= -43.765 + 26.741 NIRR (2)* + 28.758 NIRR (1)* 0.84
*Note: a variable name followed by a subscript in parentheses represents
the value of the variable calculated for a particular period;
0 = full season, 1 = vegetative period, 2 = pollination/fruit
set, 3 = maturation.
The various periods established for each of the crops are summarized
below:
Period 1 for beans: planting to full cover minus 15 days
Period 1 for potatoes: planting to 20 days after emergence
Period 3 for potatoes: full cover to harvest
Period 1 for winter wheat: planting to full cover minus 15 days
Period 2 for winter wheat: full cover minus 15 days to full cover
plus 15 days
The value of C thus determined was then used for estimating yields for that
field under any irrigation regime. Thus in effect, the models were cali-
brated separately for each field.
Given the state of the art of crop production modeling it is not pos-
sible to have a great deal of confidence in the predictions made by these
models. In the particular circumstances of this study the inaccuracies are
54
-------
probably greater still because the original yield data were evidently lumped
for each farm. That is, if wheat were grown in two different fields of a
farm the yields recorded were the average of the two, even though in many
cases the fields were irrigated quite differently and perhaps planted at
different dates and fertilized at different rates. Nevertheless, by in-
cluding C it is felt that model biases would be largely nullified and pre-
dictions should have a degree of accuracy suitable for purposes of this study.
PHYSICAL ANALYTICAL SYSTEM RESULTS
The initial analysis of 204 fields produced interesting insights into
the impacts which irrigation scheduling can have on water and return flows
and it also put the historical irrigation practices of the study area into
better perspective. It should be borne in mind, when viewing the initial
results, that farmers in the A and B District are regarded as efficient in
their use of water. Average annual diversions per irrigated acre are sub-
stantially lower in this district than in neighboring districts. However,
the potential for beneficial changes in water use in this district is still
great.
Water Use and Return Flows
Diversions and disposition of water, as well as average soil moisture
levels were estimated for the 204 cases of the six-farm study for the un-
scheduled and scheduled irrigation regimes (Table 10). A significant in-
crease in water use efficiency was estimated with the use of irrigation
scheduling. Total diversions decreased by an estimated 24 percent for the
ideal scheduling case and 8 percent for the imperfect scheduling case. The
largest part of the water savings was due to reduced deep percolation.
Delivery system losses and surface runoff decreased in rough proportion to
the total diversions. A small reduction in surface runoff and a reduction
in the amount of water left in the root zone after harvest accounted for the
remaining change in diversions. The most dramatic changes were in deep
percolation which was reduced by 78 percent under the ideal regime and 17
percent under the imperfect regime. Overall, if efficiency is defined as the
ratio of evapotranspiration to total diversions, the estimated efficiencies
under the unscheduled, ideal scheduled and imperfect scheduled regimes were
56 percent, 76 percent, and 60 percent^ respectively.
Evapotranspiration increased slightly under ideal scheduling and de-
creased slightly under imperfect scheduling. While this seems anomalous it
is in fact quite reasonable. Under ideal scheduling no serious soil mois-
ture deficits occurred whereas under imperfect scheduling such deficits did
occur from time to time. When such a deficit occurred the soil moisture
model reduced evapotranspiration to compensate for low soil moisture. Also,
under imperfect scheduling, soil moisture deficits were occasionally fol-
lowed by an irrigation application which was not sufficient to fill the soil
profile. Thus the crop would not attain.the full potential evapotranspira-
tion rate even after the irrigation, and cumulative ET would 'fall behind
that calculated for the ideal regime. On the other hand, farmers operating
55
-------
TABLE 10. COMPARISON OF WATER USE FOR SCHEDULED AND
UNSCHEDULED REGIMES IN 204 FIELDS
Water Use (cm)
Unscheduled
Cases
Diversions
Transmission Losses and
Phreatophytic Losses
Rain
Runoff
Percolation
Evapo transpiration
Average Soil Moisture
(% by Volume)
(cm)
(cm)
(cm)
(cm)
(cm)
(cm)
(cm)
84.15
9.35
7.47
14.43
20.19
7.24
25.82
Scheduled
Ideal
63.60
7.44
7.47
11.28
4.47
48.03
26.55
Cases
Imperfect
77.83
8,56
7.47
13.26
16.76
46.81
25.77
without irrigation scheduling were generally applying more water than the
imperfectly scheduled farms and also were irrigating more frequently. For
that reason the unscheduled farmers rarely failed to completely refill the
soil profile and therefore evapotranspiration almost always began at the full
potential rate following each irrigation.
Average soil moisture is seen to be slightly higher for the ideal
scheduled regime and slightly lower for the imperfectly scheduled regime
than for the unscheduled regime. The reasons for this were the same as those
mentioned above regarding evapotranspiration.
TDS concentrations in leachate were observed to increase under the
scheduled regimes, as would be expected from the reduced leaching fractions
anticipated under those regimes, but the total salt load was reduced because
of the substantial reductions in total percolation (Table 11). Reductions
in total sediment loads were due primarily to reduced frequencies of irri-
gation events. As discussed earlier, the irrigation events that would be
eliminated under scheduled regimes would be the last ranked, i.e., those
in which the sediment concentrations would be lowest. Thus the reduction
in sediment loading is not proportionally as great as the reduction in
irrigation frequency.
In addition to reducing total salinity and sediment loads in return
flows, use of irrigation scheduling would affect various other water quality
parameters. The general nature of these effects can be imputed from antici-
pated changes in salinity and sediment loads. In the case of the A and B
District, reductions in regional TDS loads and return flow would have been
accompanied by an increase in sodium concentrations relative to calcium,
which would increase sodium adsorption ratios in return flows. At the same
56
-------
TABLE 11. RETURN FLOW QUALITY, SCHEDULED AND
UNSCHEDULED REGIMES FOR 204 FIELDS
Total TDS in Deep
Percolation, kg/ha
Total Sediment Load
in Surface Runoff,
kg/ha
Unscheduled
Ideal
Schedule
1446
12935
834
8720
Imperfect
Schedule
1350
11141
time, alkalinity would have been increased. Chemical compositions of leach-
ate in the A and B District are a function of leaching fraction (Table 12).
These estimates were based upon the model developed by Rhoades, et al.
(197ft). To put Table 12 in proper perspective, regional average leaching
fractions, as calculated from Table 9 would be 0.30 for the unscheduled
regime and 0.09 for the ideal scheduled regime.
TABLE 12. ESTIMATED CONCENTRATIONS OF CONSTITUTENTS (meq/fc) IN
LEACHATE AS A FUNCTION OF LEACHING FRACTION FOR
TYPICAL CIRCUMSTANCES* IN THE A AND -B DISTRICT
Constituent
Ca
Mg
Na
K
Cl
co3
HC03
S°4
Alkalinity
SAR
.02
1.08
58.50
38.50
4.50
23.50
3.54
33.04
42.50
36.58
7.05
.04
1.80
29.25
19.25
2.25
11.75
1.18
18.38
21.25
19.55
4.89
.06
2.46
19.50
12.83
1.50
7.83
0.76
13.54
14.17
14.30
3.87
Leaching Fraction
.03 .10 .20
2
14
9
1
5
0
11
10
11
3
.99
.63
.62
.12
.88
.61
.26
.62
.87
.24
3
11
7
0
4
0
9
8
10
2
.41
.70
.70
.90
.70
.55
.96
.50
.51
.80
4.48
5.85
3.85
0.45
2.35
0.46
7.58
4.25
8.03
1.69
.30
4.91
3.90
2.57
0.30
1.57
0.44
6.85
2.83
7.28
1.22
.40
5.14
2.92
1.92
0.22
1.18
0.43
6.49
2.13
6.92
0.96
.50
5.28
2.34
1.54
0.18
0.94
0.42
6.28
1.70
6.70
0.79
*(a) Chemistry of applied water in meq/Jl: Ca = 2.34, Mg = 1.17, Na = 0.77,
K = 0.09, C03 = 0.12, HCO = 2.88, Cl = 0.47, S04 = 0.85
(b) Soil is calcareous; assume saturation with CaCO,..
57
-------
Sediment load may be regarded as an indicator of nitrogen, phosphorous
and pesticide concentrations in return flows. Thus the substantial reduc-
tions in sediment load anticipated with irrigation scheduling would indicate
that nutrients and toxic substances might also be reduced in return flows
by significant amounts. The links between these factors and sediment con-
centrations have been clearly established by other research conducted in
southern Idaho. Busch, et al. (1975) have shown that concentrations of
nitrogen and phosphorous derivatives of fertilizers are clearly linked to
concentrations of sediments in surface runoff. Carter and Bondourant (1976)
concluded from a review of related literature that biocides in surface runoff
are generally adsorbed on sediments, and that control of biocides in return
flows can be accomplished by controlling sediment loads.
The environmental benefits discussed above were found to vary widely
from one farmer to another and from one crop to another. This variability
is illustrated by Table 13, in which the values of several parameters es-
timated for ten of the cases studied are summarized. Although the use of
irrigation secheduling would have reduced the environmental impact of irri-
gation in most cases, it is interesting to note that in a few cases the
reverse would have been true.
Imperfect scheduling resulted in fewer irrigation events than did ideal
scheduling because a +35 percent bias in water applied under the imperfect
regime resulted in higher post-irrigation soil moisture levels (Table 14).
While much of that additional applied water was lost to deep percolation
during subsequent days, nevertheless it also was used to some extent to
satisfy evapotranspiration demand, thus postponing the next irrigation event
for a day or two in many cases.
Seasonal patterns of water use and soil moisture in individual fields
were often quite erratic. Four soil moisture histories were selected to
illustrate this variation (Figures 19-20). These four histories illustrate
some fairly typical patterns of irrigation timing by A and B District
farmers. The pattern represented in field B, Figure 19, was commonly ob-
served for several of the farms and crops. That is, the first irrigation
was delayed until soil moisture was quite low, then succeeding irrigations
were done at relatively high moisture levels. A tendency to allow alfalfa
to mine water is fairly common with alfalfa because of the deep and well
developed root system (Field A, Figure 20), Field A in Figure 19 and Field
B in Figure 20 illustrate highly erratic irrigation schedules observed in
many cases.
The models used in this analysis could be expected to predict regional
values of the various quantities with sufficient accuracy. However,
accurate estimates of specific values under any single set of circumstances
are not within model capabilities. This raises a question about the validity
of the estimated historical soil moisture plots presented in Figures 19 and
20. In the opinion of local experts, these plots do present a fair picture
of local irrigation practices. In most of these cases the farmers applied
considerably more water than was needed at each irrigation. Thus the soil
moisture level was often reinitialized at the maximum holding capacity of
the soil moisture. If the model were seriously biased, estimated soil
58
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TABLE 13. RESULTS ESTIMATED FOR 10 CASES SELECTED FROM AMONG THE 204 CASES STUDIES:
EXAMPLES OF VARIABILITY OF RESULTS
Farm
Crops
Total Diversions (cm)*
Unscheduled
Ideal Scheduled
Number of Irrigations
Unscheduled
Ideal Scheduled
Total Runoff (cm)
Unscheduled
Ideal Scheduled
Total Percolation (cm)
Unscheduled
Ideal Scheduled
Total Leachate TDS
(metric tons/ha)
Unscheduled
Ideal Scheduled
Total Runoff Sediment
(metric tons/ha)
Unscheduled
Ideal Scheduled
1 2
Alfalfa Alfalfa
62.2
98.3
3
2
11.2
22.9
0
4.3
0.0
0.897
0.269
0.555
225
98
7
2
77
22
86
3
3
0
2
0
.6
.8
.0
.9
.6
.6
.542
.829
.51
.555
3
Beans
39.1
60.5
1
4
11.9
6.9
23.0
8.4
0.941
0.740
1.61
.706
456
Beans Potatoes Potatoes
104.9
53.8
8
4
37.3
9.9
30.0
2.8
1.547
0.628
3.40
1.01
211.3
66.3
8
7
39.4
9.9
92.7
4.3
3.788
0.628
3.85
1.06
145.5
57.7
8
6
23.4
6.9
60.2
2.3
2.533
0.538
2.51
6.55
7
Wheat
71.1
48.3
4
2
10.7
3.6
21.3
7.4
1.255
0.717
1.18
0.471
8
Wheat
9
Sugar
Beets
49.8 165.1
37.8
2
2
4.8
4.6
6.4
6.6
0.650
0.583
0.589
0.555
74.7
6
5
20.8
13.5
23.4
5.1
1.412
0.762
1.85
1.58
10
Sugar
Beets
123.4
89.7
6
6
21.1
18.5
3.8
5.3
0.65
0.672
1.93
1.82
*Centimeters equivalent depth of application.
-------
40 r-
30
UJ
-------
40 i-
30
FIELD CAPACITY
o
£
UJ
= 10
O
PWP
MAY
JUNE
JULY AUGUST
FIELD A
SEPTEMBER OCTOBER
SOIL MOISTURE HISTORY, FARM 1, FIELD 3, 1964
40 r
30
o
cc
1U
= 10
PWP
PLANT
i
MAY
JUNE
JULY AUGUST
FIELD B
SEPTEMBER OCTOBER
FIGURE 20. Soil moisture histories for two fields.
61
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moisture levels would be either consistently high or consistently low, but
not usually high and low under the same circumstances, in fact, however, it
was common to see simultaneously very high and very low estimated soil
moisture levels within similar fields in a single season.
TABLE 14. NUMBER OF IRRIGATIONS, BY CROP, SCHEDULED
AND UNSCHEDULED REGIMES FOR 204 FIELDS
Alfalfa
Barley
Beans
Clover
Pasture
Peas
Potatoes
Wheat
Beets
Wheat & Barley
Winter Wheat
Winter Wheat
& Barley
TOTALS
Unscheduled
88
58
313
4
16
157
143
55
123
41
49
3
1,050
Ideal
Schedule
54
40
212
8
32
86
148
35
110
31
28
2
786
Imperfect
Schedule
52
39
177
6
27
85
123
34
100
31
26
2
702
The estimated soil moisture content just prior to an irrigation was
often found to vary from quite high to quite low. Figure 21 is a histo-
gram of soil moisture just prior to irrigation for 350 irrigation events in
53 bean fields. If properly timed, irrigation events would have been taking
place at a soil moisture level of about 21 percent, but in fact they were
almost equally likely to take place at any moisture level between the per-
manent wilting point and the maximum holding capacity of the soil. Eight
percent of these irrigations were done when the estimated soil moisture was
near the permanent wilting point and another 9 percent were done at about
the time when gravity drainage from preceding irrigations ceased. These
observations about unscheduled, i.e., historical, irrigation practices must
be qualified by the remark that they are based upon model estimates of soil
moisture. Only one soil moisture measurement was taken in each case, early
in the growing season.
Figure 22 graphically illustrates the changes that could have been
brought about by a scheduling service in two fields. In both fields the
62
-------
\~
UJ
u.
O
cc
UJ
CO
s
D
z
35
30
25
20
15
10
I-
z
5
Q.
O
Z
10
iiiiii
iilll
.•.•. . .'J.'.L .'.•. . . .•.•.•>.•.'. ..'.•.•.. .•••2^J.
15
20
25
30
SOIL MOISTURE (% BY VOLUME)
O
<
Q.
<
O
35
40
FIGURE 21. Histogram of soil moisture at time of irrigation
for 350 irrigation events in bean fields.
63
-------
40
UJ
I 30
oo
20
O
E
i-
o
10
APRIL
SCHEDULED
UNSCHEDULED
CROP: BARLEY
MAY JUNE
FIELD A
JULY
£
UJ
h-
O
I
O
E
40
30
20
JUNE
SCHEDULED
UNSCHEDULED
CROP: POTATOES
JULY
FIELD B
AUGUST
SEPTEMBER
FIGURE 22. Soil moisture histories of two fields with and without the effects
of an ideal irrigation scheduling service.
64
-------
farmers irrigated more frequently and applied far more water than was nec-
essary. Thus, a substantial reduction in drainage and a small reduction in
runoff were possible. The barley field also had a very uneven soil moisture
history. By scheduling that field the average soil moisture would have
changed very little, but much more consistent-moisture conditions would have
resulted.
Crop Production
Changes in crop yields due to irrigation scheduling were of -particular
interest in this analysis, since farmers' willingness to use a scheduling
service will be largely determined by prospects of improved yields. Two
approaches to estimating yields for the scheduled regimes vis-a-vis the
unscheduled regime were taken. In the first approach a semi-empirical crop
production model was developed and calibrated for each crop with data from
the 204 cases of the six-farm study. The second approach was to use a set
of estimated yield changes published by the USER that were derived from a
recent study (Table 15, USER, 1972). Both yield estimates were used
in the analysis as alternative scenarios. In one scenario (based on model
estimates), modest yield increases were estimated, while in the alternative
scenario (based on USER estimates) considerably larger increases were
generally anticipated.
TABLE 15. ESTIMATED CHANGES IN YIELDS IN THE A AND B
DISTRICT WITH IRRIGATION SCHEDULING
EPA/USDA Estimates USER*
Crop for 204 Cases Estimates
Small Grains +6.2% +24.0%
Beans -2.6% +12.0%
Peas -4.8% +31.0%
Potatoes +29.3% +22.0%
Sugar Beets +15.1% +12.0%
Alfalfa +5.9% +13.0%
*Source: USER, 1974
The estimated yield changes from the model developed for this analysis
should be regarded as indicative of potential changes rather than as con-
clusive estimates of changes. These numbers represent the estimated cumu-
lative effects of a number of changes in root zone environment which would
occur as a result of irrigation scheduling.
65
-------
The alternative set of yields estimate (USER) were derived from a study
of scheduled fields in the A and B District which was conducted between 1969
and 1971 by the USER. Measured yields from a group of farms utilizing the
scheduling service were compared with district average yields. Yield dif-
ferentials were adjusted to account for differences in management ability.
The changes in Table 15 refer only to yield changes estimated by these
two approaches. However, it is to be expected that irrigation scheduling
will also affect crop quality. The qualities of most of the crops in this
analysis are affected by soil moisture in various ways. This is especially
true of potatoes, for which quality is very adversely affected by stress
at critical times. Furthermore, in the case of potatoes, the income re-
ceived from a crop is more dependent on quality than on total yield.
66
-------
SECTION 7
REGIONAL ECONOMIC MODEL
A scheduling service can be made available to farmers either by a pri-
vate company or a public agency. The public agency may choose to offer such
a service for many reasons, such as to promote more efficient water use in
order to increase the size of a service area from a fixed supply of water,
or to reduce irrigation return flows. The purpose of this analysis is to
project the amount of irrigation activity that would be scheduled by simula-
ting the economic conditions that would exist if a private company or
public agency provided the service. This section contains the theoretical
basis for projecting the demand for a scheduling service, the empirical model
and the results.
DERIVED DEMAND FOR RESOURCES
The profit maximizing combination of production and resource use for
the farmer can be derived by first defining the production function as:
Q = f(Xr X2, ..., Xj} ..., Xn) (21)
where Q is an output and X. are resources. The production function repre-
sents the technological process by which the maximum amount of Q can be pro-
duced from the specified units of resources. It is assumed that all alter-
native combinations of imputs to maximize the production of Q are identified
in the production function.
The objective of the firm is to maximize profits from the sale of the
outputs they produce. The firm will maximize profits by producing a given
level of output (Q*) at a minimum of cost. This can be represented by:
C = P.X- + P.X0 + ••• + P.X. + ... + P X (22)
12/2 jj nn
where C represents the total cost of producing Q*and P. are prices for re-
sources X. The production function (21) can be rewritten to represent the
physically efficient set of resources to produce a given level of output as:
f(X]_, X2 ••• Xn) - Q* - 0 (23)
and if multiplied by the artificial variable A, the Lagrangian expression
representing a constrained minimization problem can be formed.
67
-------
L = P,X_, P0X0 + ••• + P X + A[f(XnX , ... X ) - Q*J (24)
11/2 nn I/ n
L is minimized by setting each partial derivative equal to zero.
i
3X= P2 + X "3X
(25)
This system of n + 1 simultaneous equations can be solved for the optimal
values of input, variables X, - X and the value of the Lagrangian variab
1 n
X. The marginal condition for optimal use of any resource is:
(26)
which states that the value of the marginal product of X. must equal the
price of the resource. The value of A is the output price and the partial
derivative represents the marginal physical product of resource X .
The demand for resources is determined by solving Equation 25 for X..
the implicit demand function can be expressed as:
X.j = f(P , P±, X, K)* (27)
where the amount of X. used in the production process depends on the price
of resource j, the price of substitutable resource, the value of the output
and the amount of fixed resources (R) .
DERIVED DEMAND FOR IRRIGATION SCHEDULING SERVICES
The demand function for a scheduling service will relate the number of
acres (hectares) scheduled to varying prices. Farmers will decide whether or
not to schedule fields on the basis of anticipated effects on total returns
*For more detail see Heady and Tweeten (1963).
68
-------
and total costs. If a larger number of scheduled acres (hectares) adds more
to gross returns than to costs, increasing irrigation scheduling will in-
crease net returns. A farmer should schedule that number of acres (hectares)
such that the last acre (hectare) scheduled contributes equally to gross
receipts and costs if he is to maximize net returns.
The value of marginal product (VHP) of irrigation scheduling is the in-
cremental increase in net market value of crop production as the farmer in-
creases the scheduled land area by one acre (hectare) . This value changes
as the absolute number of acres (hectares) scheduled increases. On any given
farm, irrigation scheduling applied to a given crop and soil type may in-
crease net returns either through increased yields or decreased irrigation
costs. However, as subsequent acres (hectares) are scheduled the increases
in net returns become smaller because increases in crop yields are smaller or
water savings are less. To maximize net returns, the number of acres
scheduled should be increased to the level at which the VHP of the last acre
(hectare) is equal to the cost of scheduling that acre. This can be written
as :
VMP = P (28)
s s
where P is the cost of scheduling per acre (hectare) . The demand curve for
S
scheduling depicts the number of acres (hectares) scheduled as the cost (P )
varies assuming the condition for profit maximization is met.
In the case of irrigated agriculture, as the price of one variable re-
source changes the amount of other variable resources will also change as
the farmer attempts to find the least cost combination of resources and to
maximize net returns. Irrigation water (w) , irrigation labor (1) , and
scheduling are substitutes for each other within a specified range of use.
For example, an increase in the price of irrigation water provides an incen-
tive for farmers to use either more labor or a scheduling service to save
water. Ideally farmers should employ levels of all these variable resources
such that the value of marginal product equals price for each. Therefore,
the profit maximizing conditions are:
VMP = P
s '
(29)
VMP = P
w w
The effect of changes in the cost of scheduling, P , upon the number of
S
acres (hectares) scheduled is graphically illustrated in Figure 23. The
slope of the line WS represents the price ratio of water and scheduling. The
line WS also represents those quantities of water and scheduling that can be
purchased by a fixed capital expenditure. If the cost of scheduling in-
creases, the line will shift to WS' to reflect the new price ratio and the
new amounts of water and scheduling that the same level of expenditures will
purchase.
69
-------
w
5 wi
t-
< w
0 81 8 S1 S
SCHEDULING
FIGURE 23. Output and substitution
effects of a rise in the cost of scheduling.
The quantity of production is represented in Figure 23 by the isoquants
Q and Q*. A single isoquant reflects one level of output and isoquants fur-
ther from the origin represent greater levels of production. Therefore the
optimum level of production using the amount of water and scheduling re-
presented by the input-price line WS is isoquant Q where WS and Q are
tangent. The optimal amount of scheduling use is Os and the optimal amount
of water use is Ow. If the cost of scheduling rises, the input-price line
shifts to MS* and production decreases from A to B. The optimum level of
water arid scheduling use is Ow^- and Os^. Therefore the change in scheduling
use due to the cost change is a decrease from s to s^ while water use in-
creased from w to w^.
The regional demand for a scheduling service can be derived by summing
horizontally each farmers demand for a scheduling service. In other words,
the amount of scheduled acres (hectares) at each cost is the sum of all
acres (hectares) scheduled by each farmer at that cost. Graph A in Figure
24 represents the demand for scheduling of a typical farmer as previously
determined and graph B represents the summation of all farmers in the region
for the scheduling service.
REGIONAL LINEAR PROGRAMMING MODEL
Linear programming (LP) is an analytical method that can derive the
optimal cropping pattern, irrigation water use, labor use and scheduling
service given a set of input-output coefficients, prices and costs. In the
previous discussion a number of assumptions were made. First, the production
function, i.e., the relationship between resource use and output, is assumed
70
-------
^ 12.50 r
0)
s
tj
<1>
0>
a.
0
(31)
where A is an m x n matrix of resource use coefficients and B is a m dimen-
sional column vector or resources available.
For every linear programming model that exists, a dual problem can be
formulated. The dual of this problem is:
71
-------
Minimize f(u) = US' (32)
where U is a m dimensional row vector representing the inputed value of the
firms resources represented by the m dimensional column vector B. The
solution is subject to:
A'U > C1
(33)
U >_ 0
where A1 is a n x m matrix of resource use coefficients and C is a n dimen-
sional column vector of net revenues. The constraints of the dual state
that the input costs of producing each output cannot be less than the value
of the product. Therefore the value of a resource, such as an irrigation
scheduling service, can be estimated for any level of service available.
The specific linear programming model used to analyze irrigation schedu-
ling in the A and B District maximized returns to land, management and risk
subject to the usual constraints and some specific resource constraints.
Specifically:
Maximize Z = £-C.0X.fl+-£P.S-WF- W F - W.F (34)
.= £ J^ J* .! J J 3 J -1 * ^
- W F - RL - DI
where:
Z is returns to land, management and risk.
C.j is the cost of 'producing one acre (.4 ha) of crop j
using water application rate H (cost excludes irriga-
tion water, labor and scheduling).
X.p is acreage (hectares) of crop j produced using water
application rate i.
P. is market price of crop j per unit of yield.
S. is amount of crop sold.
W is cost of the first 3 acre-feet (3.67 x 103 cm3)
of water per acre (.4 ha).
F is the acreage (hectares) of irrigated crops.
W is the cost of the fourth acre-foot/acre (4.93 x 103
cm3/.4 ha) of water applied.
F_ is the number of acres (.4 ha) on which four acre-foot/
acre (4.93 x 103 cm3/.4 ha) of water is applied.
W. is the cost of the fifth acre-foot/acre (6.17 x 103
A o
cmJ/.4 ha) of water applied.
F, is the number of acres (.4 ha) on which a five acre-
foot/acre (6.17 x 103 cm3/.4 ha) of water is applied.
Wj. is the cost of more than five acre-foot/acre
(6.17 x 103 cm3/.4 ha) of water applied.
72
-------
F is the number of acres on which greater than five acre-
foot/acre (6.17 x 103 cm3/.4 ha) of water is applied.
R is the cost of irrigation labor per hour.
L is the total irrigation labor used.
D is the cost of irrigation scheduling per acre (.4 ha).
I is the irrigated acreage (hectares) scheduled.
The objective function is subject to the following constraints:
EX.. < A (35)
jSL ^ ~
where A is the total acreage (hectares) of land in the District.
where y.0 is crop j yield per acre (.4 ha) when water application is £,
J^
Z X.0 - F < 0 (37)
jA J* ~
represents the total irrigated acreage (hectares) in the District.
Z a3 X - F < 0 (38)
j£ j£ ^ 3
•
where a.0 is the crop water requirement in excess of 3 acre-feet/acre
J~ o o
(3.67 x 103 cm3/. 4 ha) (1 if in excess of 4 acre-feet/acre (4.93 x 10 cm /
,4ha)) for crop j and water application £,
.J aj£ Xj£ - F4 1 ° (39)
J*-
where a.p is the crop water requirement in excess of 4 acre-feet/acre
(4.93 x 103 cm3/. 4 ha) (1 if in excess of 5 acre-feet/acre (6.17 x 103
cm3/.4 ha)) for crop j and water application £,
.1 al V - F5 1 ° (40)
where a.0 is the crop water requirement in excess of 5 acre-feet/acre
•} 3
(6.17 x 10 cm /.4 ha) for crop j and water application £,,
Z aj£ X.£ < E (41)
J *
where a . , is the total water requirement for crop j at water application
3^
rate H and E is the total District water supply,
73
-------
E g.pX.. - L < 0 (42)
j£ ^ j£
where g.fl is the irrigation labor requirement for one acre (.4 ha) of crop
3^
at water application rate £,
E X.0 < Z. for all j (43)
jA 3 J
where Z. is a crop acreage (hectare) limit that reflects historical crop
acreage,
E r X > 0 (44)
where r.0 is the surface runoff from one acre (.4 ha) of crop j at water
J ^
application rate A,
where p.0 is the deep percolation from one acre (.4 ha) of crop j at water
3^
application rate £,
.1 w - ° (46)
where d.0 is the sediment loss from one acre (.4 ha) of crop j at water
J*-
application rate £,
£ Vjt i ° (47)
where s.» is the salinity loss from one acre (.4 ha) of crop j at water
3*-
application rate i, and,
EX. - I <_ 0 (48)
j 3
represents the total acres (hectares) of scheduled irrigation.
The linear programming model for the A and B Irrigation District is pre-
sented in matrix form in Figure 25. This matrix illustrates the model
structure and assists in describing how the analysis was conducted. The
derived demand for a resource can be empirically estimated by parametrically
varying the cost of scheduling through the possible range and observing the
optimal number of acres being scheduled. This procedure provides the nec-
essary information to construct a static-normative demand function (Moore
74
-------
ACTIVITIES
Maximize C =
Row Name
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Land
Commodity
Yield
Irrigated
Acres
WATER:
Third AF/A
Fourth AF/A
>Four AF/A
Supply
Irrigation
Labor
Cropping
Pattern
Surface
Runoff
Deep
Percolation
Sediment
Salinity
Scheduling
. RHS
Acres
0
0
0
0
0
AF/Year
0
Acres
0
0
0
0
0
Type
>
>
>
>
>
>
>
>
>
<
<
i
<
>
CROP PRODUCTION
Water Application Rate
Low | Medium
High
Scheduled
-Cost of Production Per Acre
1
•y
1
a3
a«
a*
a
g
i
r
p
d
s
1.
1
•y
i
a3
a4
a*
a
9
1
r
p
d
s
2.
1
•y
i
a*
a"
as
a
9
1
r
P
d
s
3.
1
-y
1
a3
a<
a*
a
9
1
r
P
d
s
1
4.
COMMODITY
SELLING
Price per
Unit of Yield
1
5.
IRRIGATED
ACRES
-Cost
per acre
-1
6.
WATER SUPPLY
• Third
AF/Acre
• Cost for
Third AF
-1
7.
Fourth
AF/Acre
•Cost tor
Fourth AF
• 1
8.
>Four
AF/Acre
•Cost for
>4 AF
-1
9.
IRRIGATION
LABOR
-Wage
Rate
• 1
10.
IRRIGATION
SCHEDULING
-Scheduling
Cost
-1
11.
•vl
L/l
FIGURE 25. A and B District linear programming model.
-------
and Hedges). The same demand function could be constructed by parametrically
varying the level of scheduling services and observing the value of the dual
activity or value of the resource related to the constraint. In addition,
the LP model provides estimates of the amount of and quality of return flows,
irrigation water use and irrigation labor that are essential for a complete
evaluation of a scheduling program.
The LP model was optimized for three configurations. The first solu-
tion was constrained to unscheduled operations to estimate the level of
returns to producers, resource use and irrigation return flows assuming a
scheduling service did not exist. This pollution served as a basis to which
other solutions could be compared. The second model configuration required
all water applications, to be determined by a scheduling service. The dif-
ference between the solutions derived in the first and second model config-
urations served as a estimate of the potential change that could be possible
from a scheduling service.
The third configuration was not restricted to the scheduled or non-
scheduled water applications. Therefore, the optimal solution represented
the level of scheduling that would probably exist if the service were
offered on a profit or nonprofit basis. The cost of the scheduling service
and the cost of water were parameterized in the third model configuration
to determine the effect on the amount of scheduled acres.
Input Data
The analysis of USER data produced a combined set of both real and es-
timated data which related water use to crop yields and irrigation return
flows. These data were used, together with price and cost data, to derive
the regional coefficients required for the linear programming model. The
procedures for deriving water application rates, labor requirement, crop
yields, crop prices, production costs and returns to land, management and
risk are described in the following sections.
Water Application Rates—
Three levels of irrigation water application were defined as low,
medium and high on the basis of observed water use by crop in 443 unscheduled
field operations in the A and B District. The 443 cases were from the 6
farm study (204 cases) and the 40 farm study (239 cases) and included cor-
responding crop yields. Table 16 contains the specific water application
rate and the proportion of cases in each rate. As an example, the range
between 25 and 35 inches (63.5 and 88.9 cm) of applied water was defined
as medium water use for barley. Less than 25 inches (63.5 cm) and more
than 35 inches (88.9 cm) were defined as low and high water use, respectively.
Irrigation Labor—
The average irrigation labor per acre (.4 ha) per set and the average
number of irrigation sets for each crop were estimated from the six-farm
study and were used to compute the average total irrigation labor per acre
(.4 ha) by crop for each water application rate (Table 17). Substantial
labor savings could be realized by using a scheduling service for most crops.
76
-------
Labor requirements could be reduced for peas by 46 percent, alfalfa 44
percent, wheat 41 percent and beans 39 percent.
TABLE 16. DEFINITION OF LOW, MEDIUM AND HIGH WATER-USE (UNSCHEDULED
IRRIGATION REGIME) AND PROPORTION OF IRRIGATED CASES IN EACH CATEGORY
Crop
Alfalfa
Barley
Beans
Peas
Potatoes
Sugar Beets
Wheat
Low
acre- inch/year
0 - 35.1
(0.243)**
0 - 25.03
(0.541)
0 - 25.0
(.0.255)
0 - 27.0
(0.452)
0 - 30.0
(0.115)
0 - 40.1
(0.346)
0 - 25.0
(0.544)
Medium
or 1.028 ha-cm/year*
35.1 - 50.0
(0.457)
25.04 - 35.0
(0.360)
25.0 - 37.0
(0.568)
27.0 - 42.0
(0.474)
20.0 - 45.0
(0.499)
40.1 - 50.0
(0.414)
25.0 - 35.0
(0.364)
High
> 50
(0..300)
> 35.0
(0.099)
> 37.0
(0.177)
> 42.0
(0.074)
> 45.0
(0.386)
> 50.0
(0.240)
> 35.0
(0.092)
*Acre-inches/year = 1.028 ha-cm/year. Therefore 35.1 acre-inches/
year = 36.1 ha-cm/year.
**Numbers in parenthesis represent the proportion of fields of a
crop that were irrigated with the respective amount of water.
Crop Yields—
Crop yields observed on the 443 water use cases were used to estimate
yields for each crop for each level of unscheduled water use. Crop yields
had to be adjusted to reflect technologic changes that have caused gradual
increases in crop yields. Trend lines were derived using regression analysis
on the 443 average yields for the years 1958 through 1975.' The equations
of these trend lines for barley, potatoes, wheat and alfalfa were estimated
and used to adjust yield predictions to more accurately reflect yields in
the years 1973, 1974 and 1975, the years for which the case study analysis
was done (Table 18). Additionally, average yields from the six-farm study
were found to be significantly higher than district average yields for the
same years. Therefore, yields derived from the six-farm study had to be
adjusted to represent aggregate district yields. Alternative crop yields
for the ideal scheduling regime, one based upon the USER estimates of yield
increases and the other based upon the EPA/USDA estimates (Table 18).
Fertilization rates were not significantly different for the three water
application rates.
77
-------
oo
TABLE 17. WATER APPLICATION
Crop
Water
Application
Water
Range
Applications
Average
RATES, LABOR REQUIREMENTS
Average
Number of
Sets
Acre-in/year or
Alfalfa
low
med ium
high
scheduled
(ideal)
scheduled
(imperfect)
Barley
low
medium
high
scheduled
(ideal)
scheduled
(imperfect)
Beans
low
med ium
high
scheduled
(ideal)
scheduled
(imperfect)
1.028
0-35
35-40
>50
0-25
25-35
>35
0-25
25-37
>37
ha-cm/year
28.52
42.62
64.24
42.00
50.76
20.5
28.1
39.6
17.76
24.96
21.85
30.95
46.54
19.44
30.24
3.6
4.2
4.4
2.45
2.36
3.7
3.8
5.7
2.73
2.77
6.2
6.8
6.5
4.93
4.12
Labor
AND CROP
Total
Requirement Irrigation
Per Set Labor
Hours/Acre or
hours/
.365
.379
.381
.376
.376
.361
.372
.371
.367
.367
.343
.35
.364
.35
.35
.4 ha*
1.31
1.59
1.68
.92
.89
1.34
1.41
2.11
1.0
1.02
2.13
2.38
2.37
1.73
1.44
YIELDS, A & B DISTRICT
Yields
Scheduled
Unscheduled EPA/USDA
Tons /Acre or
.907 Metric Tons/.
4.56
4.25
5.2
4.87
Bushels or 63.33 kg/. 4
87.58
90.98
86.88
90.48
cwt./acre or 45.36 kg/
19.3
18.6
19.3
20.27
USER
4 ha
5.01
ha
98.74
.4 ha
23.28
Continued —
-------
TABLE 17
.—CONTINUED
Crop
Water
Application
Water
Range
Applications
Average
Average
Number of
Sets
Acre-in/year or
"Po 3 C
r eas
low
medium
high
scheduled
(ideal)
scheduled
(imperfect)
Potatoes
low
medium
high
scheduled
(ideal)
scheduled
(imperfect)
Sugar Beets
low
medium
high
scheduled
(ideal)
scheduled
(imperfect)
1.028
0-27
27-42
>42
0-30
30-45
>45
0-40
40-50
>50
ha-cm/year
19.76
34.37
46.43
17.28
23.16
27.07
37.6
51.64
24.12
30.72
35.63
45.13
57.22
27.36
32.88
4.4
4.6
6.1
2.53
2.50
6.5
7.5
7.6
7.4
6.15
7.4
7.6
5.9
5.84
5.26
Labor
Requirement
Per Set
Total
Irrigation
Labor
Yields
Unscheduled
Scheduled
EPA/USDA USER
Hours/acre or
hours/
.348
.36
.35
.354
.354
.342
.344
.357
.345
.345
.351
.347
.381
.355
.355
.4 ha*
1.53
1.66
2.14
.9
.89
2.22
2.58
2.71
2.55
2.12
2.6
2.64
2.25
2.07
1.87
cwt./Acre or
19.92
25.62
24.42
Tons/Acre or
224.60
235.1
212.1
Tons /Acre or
Acre
17.99
17.19
17.49
45.26 kg/. 4 ha
22.7 26.66
45.36 kg/. 4 ha
244.2 261.09
.907 Metric Tons/
18.21 19.84
Continued —
-------
TABLE 17.—CONTINUED
Crop
Water
Application
Wheat
low
medium
high
scheduled
(ideal)
scheduled
(imperfect)
Water Applications
Range Average
Acre-in/year or
•1.028 ha-cm/year
0-25 22.2
25-35 30.02
>35 50.21
17.28
28.44
Average
Number of
Sets
3.1
4.1
8.0
2.5
2.43
Labor Total
Requirement Irrigation
Per Set Labor
Hours /Acre or
hours/. 4 ha*
.364 1.13
.358 1.47
.35 2.8
.36 .9
.36 .87
Unscheduled
Bushel/Acre.
85.2
J9.4
85.9
Yields
Scheduled
EPA/USDA
or 66.67 kg/.
86.66
USER
4 ha
96.64
00
o
*To convert labor requirement in hours per acre to hours per hectare, multiply the hours/
acre x 2.471.
-------
TABLE 18. CROP YIELD TREND EQUATIONS FOR
THE A AND B IRRIGATION DISTRICT
Crop Trend Equation
Alfalfa y* = 2.67 + .029
(3.06) + (2.24)t
Barley y = -32.4 + 1.68t
(-1.72) (5.94)
Potatoes y = 79.5 + 2.03t
(1.18) (2.01)
Spring Wheat y = -36.0 + 1.65t
(-1.23) (3.73)
*y = yield and t = year
tNumber in parenthesis are t values where
_ regression coefficient
standard error of the regression coefficient
Crop Prices and Production Costs—
Crop prices used in the analysis were district average .prices paid to
farmers in the A and B District during the years 1973 through 1975 (Table
19). Water costs were based upon actual District costs during those same
years (Table 20). Production costs per acre (.4 ha) for alfalfa, barley,
potatoes, sugar beets, and spring wheat were based on variable preharvest
costs taken from budgets derived by Kuntz, 1976 (Table 21). Harvest costs
were adjusted proportionally for the differences between the yield per acre
(.4 ha) used in the budget and the yield per acre (.4 ha) adjusted for
trend. The production costs for dry beans and dry edible peas were derived
from costs supplied by the University of Idaho's Cooperative Extension
Service. Wage rates for irrigators were $3.04/hour, $3.50/hour, and $3.82/
hour in 1973, 1974, and 1975, respectively. A substantial increase in pro-
duction costs were experienced between 1973 and 1975 (Table 21). Increase
in alfalfa production costs for example were 23 percent for medium water
applications from 1973 to 1975. The percentage increase in costs, resulting
from general cost increases in all factors of production, except irrigation
water costs, were very similar for most other crops grown in the A and B
District. Production costs are also estimated for a scheduling service as-
suming the crop yields that the USER obtained from their studies.
Returns to Land, Management and Risk by Amount of Water Application
Gross returns -were calculated from crop yields and commodity prices by
water application for 1973, 1974 and 1975 (Table 22). Returns to land,
management and risk were estimated by subtracting the production costs
listed in Table 21. The returns are so defined because the payments for
land use and production management and explicit consideration for the effects
81
-------
TABLE 19. AVERAGE COMMODITY PRICES
A & B DISTRICT: 1973-1975
Alfalfa ($/ton or .907 metric tons)
Barley ($/bu or 63.33 kg)
Beans ($/cwt or 45.36 kg)
Peas ($/cwt or 45.36 kg)
Potatoes ($/cwt or 45.36 kg)
Sugar Beets ($/ton or .907 metric tons)
Wheat ($/bu or 66.67 kg)
1973
45.00
2.28
23.00
5.50
3.55
17.35
4.50
1974
40.00
3.00
24.50
17.00
4.10
31.50
4.10
1975
45.00
2.21
15.75
14.50
3.15
25.70
3.00
TABLE 20. IRRIGATION WATER COSTS, A & B
DISTRICT. 1973, 1974, and 1975
Water Delivered
First 3 acre-feet
(3.67 x 1()3 cm3/.4 ha)
Fourth acre-foot
(4.93 x 103 cm3/. 4 ha)
Fifth acre-foot
(6.17 x 103 cm3/. 4 ha)
Subsequent deliveries
per acre-foot
(1.233 x 103 cm3/. 4 ha)
1973
9.25
3.22
4.77
6.44
Cost
1974
$
10.00
3.45
5.55
6.94
1975
10.00
3.69
5.90
7.38
Source: A & B Irrigation District, Unpublished records.
of risk are not included in the estimation of production costs. Therefore
the returns listed in Table 21 are not "profits" to the farmer but rather
income that will cover costs not listed explicitly in the budget. Land
costs were not accounted for since a wide variation exists depending on
whether the farmer rents, leases, owns, or inherits the property. Management
costs were not included because most farmers in the A and B Irrigation
District were owner-operators and no universally accepted method exists to
separate and evaluate the management effort.
Irrigation Return Flows—
Estimates of surface runoff, deep percolation, sediment loss and TDS
were derived for the three unscheduled water application levels and the ideal
and the imperfect scheduling regimes from the data and physical models
82
-------
TABLE 21. CROP PRODUCTION COSTS. 1973,1974, AND 1975. A AND B DISTRICT
oo
Crop
Water
Application
Alfalfa
low
medium
high
scheduled**
scheduled***
imperfect
schedule
Barley
low
medium
high
scheduled**
scheduled***
imperfect
schedule
Beans
low
medium
high
scheduled**
scheduled***
imperfect
schedule
Variable
1973
64.18
60.82
71.15
67.56
69.08
57.47
58.27
57.34
58.15
60.70
70.33
69.89
70.33
70.92
72.78
1974
73.99
70.11
82.02
77.88
79.63
66.25
67.17
66.10
67.03
69.25
81.07
80.57
81.07
81.76
83.90
Costs
1975
80.68
76.45
89.43
84.92
86.83
72.24
73.24
72.07
73.09
75.51
88.40
87.85
88.40
80.15
91.48
Irrigation
Labor Costs*
1973
3.98
4.83
5.11
2.79
2.79
2.71
4.07
4.29
6.41
3.04
3.04
3.10
6.48
7.24
7.20
5.26
5.26
4.38
1974
dollars
4.59
5.57
5.88
3.22
3.22
3.12
4.69
4.94
7.39
3.50
3.50
3.57
7.46
8.33
8.30
6.06
6.06
5.04
1975
per
5.00
6.07
6.42
3.51
3.51
3.40
5.12
5.39
8.06
3.82
3.82
3.90
8.14
9.09
9.05
6.61
6.61
5.50
Water Costs
1973
acre or
9.25
11.03
19.67
10.86
10.86
13.57
9.25
9.25
10.22
9.25
9.25
9.25
9.25
9.25
12.08
9.25
9.25
9.25
1974
.4 ha
10.00
11.90
21.62
11.73
11.73
14.73
10.00
10.00
11.04
10.00
10.00
10.00
10.00
10.00
13.03
10.00
10.00
10.00
1975
10.00
12.04
22.38
11.84
11.84
15.05
10.00
10.00
11.11
10.00
10.00
10.00
10.00
10.00
13.24
10.00
10.00
10.00
Total
Production Costs
1973
77.41
76.68
95.93
81.21
82.73
70.79
71.81
73.97
70.44
72.36
86.06
86.38
89.61
85.43
87.29
1974
88.58
87.58
109.52
92.83
94.58
80.94
82.11
84.53
80.53
82.75
98.53
98.90
102.40
97.82
99.96
1975
95.68
95.56
118.23
100.27
102.18
87.36
88.63
92.24
86.91
89.33
106.54
106.94
110.69
96.76
108.09
continued
-------
TABLE 21.—CONTINUED
00
Crop
Water
Application
Peas
low
med ium
high
scheduled**
scheduled***
imperfect
schedule
Potatoes
low
medium
high
scheduled**
scheduled***
imperfect
schedule
Sugar Beets
low
medium
high
scheduled**
scheduled***
imperfect
schedule
Variable
1973
64.89
68.41
67.67
66.60
69.06
202.11
203.80
203.54
205.27
207.99
187.25
185.02
185.86
187.86
192.37
1974
74.80
78.87
78.01
76.77
79.61
232.99
234.94
230.64
236.63
239.76
215.86
213.29
214.26
216.56
221.76
Costs
1975
81.56
86.00
85.06
83.71
86.80
254.04
256,17
251.48
258.01
261.44
235.37
232.56
233.62
236.13
241.80
Irrigation
Labor Costs*
1973
4.65
5.05
6.51
2.74
2.74
2.71
6.75
7.84
8.24
7.75
7.75
6.44
7.90
8.03
6.84
6.29
6.29
5.68
1974
dollars
5.36
5.81
7.49
3.15
3.15
3.12
7.77
9.03
9.49
8.93
8.93
7.42
9.10
9.24
7.88
7.26
7.26
6.55
1975
Water Costs
1973
per acre or .
5.84
6.34
8.17
3.44
3.44
3.40
8.48
9.86
10.35
9.74
9.74
8.10
9.93
10.08
8.59
7.91
7.91
7.14
9.25
9.25
12.05
9.25
9.25
9.25
9.25
9.68
13.92
9.25
9.25
9.25
9.25
11.70
16.13
9.25
9.25
9.25
1974
4 ha
10.00
10.00
13.00
10.00
10.00
10.00
10.00
10.46
15.13
10.00
10.00
10.00
10.00
12.63
17.71
10.00
10.00
10.00
1975
10.00
10.00
13.21
10.00
10.00
10.00
10.00
11.11
15.48
10.00
10.00
10.00
10.00
12.81
18.22
10.00
10.00
10.00
Total
Production Costs
1973
78.79
82.71
86.23
78.59
81.05
218.11
221.32
225.70
222.27
224.99
204.40
204.75
208.83
203.40
207.91
1974
90.16
94.68
98.50
89.92
92.76
250.76
254.43
255.26
255.56
258.69
234.96
235.16
239.85
233.82
239.02
1975
97.40
102.34
106.44
97.15
100 . 24
272.52
277.14
277.31
277.75
281.18
255.30
255.45
260.43
254.04
259.71
Continued
-------
TABLE 21.—CONTINUED
Crop
Water
Application
Wheat
low
medium
high
scheduled**
scheduled***
imperfect
schedule
Variable Costs
1973
49.87
50.87
50.04
50.22
52.60
1974
57.49
58.64
57.68
57.89
60.64
1975
62.68
63.94
62.89
63.12
66.12
Irrigation
Labor Costs*
1973
3.44
4.67
8.51
2.73
2.73
2.64
1974
3.96
5.15
9.80
3.15
3.15
3.05
1975
4.32
5.62
10.50
3.44
3.44
3.32
Water Costs
1973
9.25
9.25
13.35
9.25
9.25
9.25
1974
10.00
10.00
14.47
10.00
10.00
10.00
1975
10.00
10.00
14.48
10.00
10.00
10.00
Total
Production Costs
1973
62.56
64.79
71.90
62.20
64.58
1974
71.45
73.79
81.95
71.04
73.79
1975
77.00
79.76
88.37
76.56
79.56
oo
Ul
*Waj?e rates per hour: 1973, $3.04; 1974, $3.50; 1975, $3.82.
**Production costs based on yields estimated in this study.
***Production costs based on yields estimated by USER.
Source: Kuntz, 1976.(unpublished data).
-------
Co
a\
TABLE 22.
RETURNS
TO LAND, MANAGEMENT
AND RISK BY
AMOUNT OF
WATER APPLICATION
Crop
Water
Application Rate
Alfalfa
low
medium
high
scheduled*
scheduled**
Barley
low
medium
high
scheduled*
scheduled**
Beans
low
medium
high
scheduled*
scheduled**
Peas
low
medium
high
scheduled*
scheduled**
1973
205.20
191.25
234.00
219.15
225.45
199.68
207.43
198.09
206.29
225.13
443.90
427.80
443.90
466.21
535.44
109.56
140.91
134.31
124.85
146.63
Gross Returns
1974
182.40
170.00
208.00
194.80
200.40
262.74
272.94
260.64
271.44
296.22
472.85
455.70
472.85
496.62
570.36
338.64
435.54
415.14
385.90
453.22
1975
Dollars /Acre
205.20
191.25
234.00
219.15
225.45
193.55
201.07
192.00
199.96
218.22
303.98
292.95
303.97
319.25
366.66
288.84
371.49
354.09
329.15
386.57
Returns
1973
or .4 ha
127.79
114.57
138.07
137.94
142.72
128.89
135.62
124.12
135.85
152.77
357.84
341.42
354.29
380.78
448.15
30.77
58.20
48.08
46.26
65.58
to Land, Management
1974
93.82
82.84
94.48
101.97
105.82
181.80
190.83
176.11
190.91
213.47
374.32
356.80
370.45
389.80
470.40
248.48
340.86
316.64
295.98
360.46
and Risk
1975
109.52
96.69
115.77
118.88
123.27
106.19
112.44
99.76
113.05
128.89
197.44
186.01
193.28
224.49
258.57
191.44
269.15
247.65
232.00
286.33
Continued —
-------
TABLE 22.—CONTINUED
Crop
Water
Application Rate
Potatoes
low
medium
high
scheduled*
scheduled**
Sugar Beets
low
medium
high
scheduled*
scheduled**
Wheat
low
medium
high
scheduled*
scheduled**
1973
797.33
834.61
752.96
866.91
926.87
312.13
298.25
303.45
315.94
344.22
383.40
402.30
386.55
389.97
434.88
Gross Returns
1974
920.86
963.91
869.61
1,001.22
1,070.47
566.69
541.49
550.94
573.62
624.96
349.32
366.54
352.19
355.31
396.22
1975
Dollars/Acre
707.49
740.57
668.12
769.23
822.34
462.34
441.78
449.49
468.00
509.89
255.60
268.20
257.70
259.98
289.92
Returns to
1973
or .4 ha
579.22
613.29
527.26
644.64
701.88
107.73
93.50
94.62
112.54
136.31
320.84
337.51
314.65
327.77
370.30
Land, Management
1974
670.10
709.48
614.35
745.66
811.78
331.73
306.33
311.09
339.80
385.94
277.87
292.75
270.24
284.27
322.43
and Risk
1975
434.97
463.43
390.81
491.48
541.16
207.04
186.38
189.06
213.96
250.18
178.60
188.64
169.33
183.42
210 . 36
*Gross returns based on yields estimated in this study.
**Gross returns based on yields estimated by USER.
-------
discussed earlier (Table 23). For almost all crops grown in the A and B
District, the amount of return flows would be reduced and the quality im-
proved by using a scheduling service when compared to the three water ap-
plication rates. However, a significant difference exists in the estimates
of return flows for an ideal or imperfect scheduling regime. The schedule
that did not have application errors reduced some return flow parameters
even below those levels achieved under low water application rates. In the
case of barley, peas and potatoes all parameters were reduced below this
level while for beans and sugar beets three parameters were so effected. In
the cases where application errors were introduced, the amount and quality
of return flows were similar to those that resulted from medium water ap-
plication rates. TDS and deep percolation were reduced on sugar beets below
the levels resulting from low application rates with both scheduling regimes.
Return flows from alfalfa were substantially higher from scheduled applica-
tions than from unscheduled applications. Typical unscheduled operations
tend to under-irrigate alfalfa and therefore substantially reduce return
flows.
Historical Cropping Patterns—
The cropping pattern established in the LP model was constrained to
those acreages that existed in 1973, 197A, and 1975 in order to focus the
analysis on the effects of a scheduling service. If the solution were not
constrained, all of the land would be allocated to the most profitable crop
making the results unrealistic. Farmers within an area do not plant the
most profitable crop in a region for a number of reasons.
First, the element of risk in growing, harvesting and selling a crop
plays an important role in the selection of a cropping pattern. To spread
the risk, farmers will plant a mixture of crops that are not subject to the
same price fluctuations, weather, insect infestations or diseases., Second,
decisions on cropping pattern are also made on projected prices rather than
current prices and all farmers use various sources of information to deter-
mine future profitability. Therefore, it is not uncommon to see varying
cropping patterns all based on projected profitability. Third, crop rota-
tions need to be established and continued to maintain the long run soil
productivity and to minimize disease and pest damage. Fourth, farmers
possess and exhibit preferences for growing specific types of crops. These
tendencies may be the result of agronomic expertise, possessing a unique
equipment complement or long term marketing arrangements to provide a
supply of a particular commodity. Fifth, some crops are contracted and
therefore subject to processor capacity and company policy. In the A and
B District, sugar beets, potatoes, beans and peas were contracted.
Substantial indepth research on the extent farmers are motivated by
factors other than price-cost considerations is required before the appro-
priate constraints can be placed on the LP solution. Therefore the solu-
tion was constrained to the 1973, 1974 and 1975 cropping pattern so that
the analysis could be focused on the optimal use of water and a scheduling
service.
88
-------
TABLE 23. VOLUME AND QUALITY OF IRRIGATION RETURN FLOW PER ACRE, A & B DISTRICT
00
VO
Crop
Water
Application Surface Runoff
Alfalfa
low
medium
high
scheduled (ideal)
scheduled
(imperfect)
Barley
low
medium
high
scheduled (ideal)
scheduled
(imperfect)
Beans
low
medium
high
scheduled (ideal)
scheduled
(imperfect)
Peas
low
medium
high
scheduled (ideal)
scheduled
(imperfect)
Acre-in/Acre or 1
5.22
6.29
14.35
11.00
9.72
2.45
4.35
9.85
1.86
3.33
4.67
6.96
8.92
4.09
4.17
2.86
5.11
10.22
2.26
3.59
Deep Percolation
.03 ha-cm/ha
0.00
3.27
13.68
2.22
12.57
2.64
6.05
14.62
2.49
7.48
2.24
6.86
16.24
.96
4.92
5.78
12.39
15.11
1.87
6.80
Sediment Loss
Total
Dissolved Solids
Tons/Acre or .907 Metric Tons/. 4 ha
.247
.402
.528
.314
.357
.422
.718
1.750
.311
.566
.522
.731
1.214
.645
.696
.491
.788
1.655
.397
.634
.086
.534
1.039
.608
1.080
.387
.535
.894
.350
.594
.311
.565
.929
.260
.484
.490
.805
.996
.342
.533
Continued—
-------
TABLE 23.—CONTINUED
Crop
Water
Application Surface Runoff
Potatoes
low
medium
high
scheduled (ideal)
scheduled
(imperfect)
Sugar Beets
low
medium
high
scheduled (ideal)
scheduled
(imperfect)
Wheat
low
medium
high
scheduled (ideal)
scheduled
Acre-in/Acre or
4.12
6.71
11.62
3.60
5.78
5.90
10.29
10.77
5.32
6.25
2.15
5.89
17.65
2.84
4.47
Deep Percolation
1.03 ha-cm/ha
5.28
11.06
23.67
1.59
6.69
6.93
10.77
22.10
2.42
6.63
2.17
9.31
8.56
1.70
5.16
Sediment Loss
Total
Dissolved Solids
Tons/Acre or .907 Metric Tons/. 4 ha
.537
.884
1.475
.507
.807
.722
1.268
1.464
.808
.942
.462
1.036
3.049
.496
.786
.563
.834
1.454
.408
.652
.716
.830
1.555
.496
.704
.395
.737
.599
.328
.499
(imperfect)
-------
SECTION 8
REGIONAL EFFECTS OF AN IRRIGATION SCHEDULING SERVICE
Two basic questions regarding the economic viability were analyzed
using the regional economic model. The first was to project the economic
costs and changes in the amount and quality of return flows if all of the
irrigation in the A and B District were required to be scheduled. The
second was to determine the degree of voluntary adoption by farmers at
varying scheduling and water costs.
POTENTIAL IMPACTS OF A SCHEDULING SERVICE
The basic economic and return flow information were estimated for each
irrigation regime requiring that all fields be scheduled free of charge
(Table 24). Crop yield coefficients for scheduling were based on the more
conservative yield estimates developed in this study. The figures presented
in Table 24 are three year averages (1973-75). Values by year are presented
in Appendix Table A-l.
TABLE 24. ESTIMATED AVERAGE ANNUAL RETURNS TO LAND, MANAGEMENT
AND RISK FOR UNSCHEDULED AND SCHEDULED IRRIGATION
IN THE A AND B DISTRICT. 1973, 1974 AND 1975*
Average Annual
Variable
Returns to Land,
Units
$1,000
Unscheduled
Irrigation
13.33
Scheduled Irrigation
Ideal Imperfect
14.41
Management & Risk
Irrigation Water:
Use AF 195.53 143.37 184.00
(1,233 cm3)
Cost $1,000 740.00 665.80 730.48
Irrigation Labor:
Use
Cost
1,000
(Hours)
$1,000
120.57
416.53
86.47
298.72
72.10
249.08
*Average irrigated acreage 65,133 (26,359 ha).
91
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Changes in Financial Returns
The average annual returns to land, management and risk were increased
by 1.08 million dollars, or $16.58 per irrigated acre (.4 ha) by requiring
a scheduling service that does not have implementation errors. Since the
cost of most scheduling services do not exceed $5.00 per acre (.4 ha) ad-
ditional returns would appear to exceed the additional cost. However, these
results do not account for the inherent element of risk either in yields or
prices. Over the long-run, these may tend to even out and the results re-
ported here may approximate the expected results but no attempt was made to
quantify the statistical distribution of yields and prices. The use of con-
servative yield estimates in the LP model, however, may underestimate the
expected benefits of an "ideal" scheduling service.
The increased annual returns to land, management and risk are attribu-
table not only to increased yields, but also to substantial reductions in
irrigation costs. To illustrate the relative importance of reduced costs
and improved yields in evaluating the scheduling service, the results from
the LP were compiled on a per acre (.4 ha) basis as follows.
Component Change Dollars Per Acre
(.4 ha)
Increased Value of Yields 13.63
Reduced Irrigation Labor Cost 1.81
Reduced Water Cost 1.14
Net Change in Annual Returns 16.58
The value of increased yields accounted for approximately 82 percent of the
total increase in annual returns. This value is net of the increased har-
vest cost of $1.44 per acre (.4 ha).
The average annual reduction in water and labor costs were $2.95 per
acre (.4 ha). The savings in these irrigation costs are almost as much as
the cost of a scheduling service. Water costs were reduced only by 10.0 per-
cent whereas total water use was reduced by 26.7 percent under the ideal
scheduling regime. This disparity is due to the water pricing schedule of
the A and B District which stipulates a fixed rate for the first three feet
of water use. Since district water use was reduced from 197,000 acre-feet
(an average of 3.05 acre feet per acre or 1.233 x 10^ cm3/.4 ha) to 144,000
acre-feet (an average of 2.23 acre feet per acre or 2.75 x 10^ cm3/.4 ha)
the reduction in water use would not reduce irrigation costs proportionately.
A comparison of weighted average* water costs for unscheduled fields and
average costs for scheduled fields indicates that the average crop water cost
for the scheduled regime was equal to the minimum cost set by the irrigation
district with the exception of alfalfa. Irrigation costs would have been
reduced more if water cost were directly proportional to water use.
^Weighted by the water-use patterns of district farmers as shown
earlier in Table 13.
92
-------
The estimated impacts on irrigation costs of an imperfect scheduling
regime are also included in Table 24 but no estimate was made on returns to
land, risk and management. As explained in the description of the produc-
tion submodel, yield predictions resulting from the imperfect scheduling
case were not possible without a more sophisticated approach. Therefore
the LP was run with the yield estimates that were used for the ideal schedu-
ling service based on the assumption that the error would probably not affect
yields substantially but would result in additional irrigation costs. If
this assumption were true, the following cost and yield changes would result.
Component Change Dollars Per Acre
(.4 ha)
Increased Value of Yields 13.63
Reduced Irrigation Labor Cost .15
Reduced Water Cost 2.56
Net Change in Annual Returns 16.34
The aggregate results from the LP indicated that farmers would irrigate
as many times as they would without a scheduling system but they would apply
substantially less water. These regional or aggregate results are heavily
influenced by the changes that occur in irrigating alfalfa. This will be
explained in the next section on return flows.
Changes in Return Flows
The estimated annual environmental consequences of the ideal scheduling
service included substantial reductions in return flows particularly deep
percolation (Table 25). The estimated sediment reduction was 37.5 percent
which would also indicate reductions in fertilizers and pesticides in return
flows. This would suggest that rates of application of these materials may
be reduced under a scheduling regime.
Surface runoff and sediment load were estimated to decrease by 23 and
28 percent respectively under the imperfect scheduling regime but deep per-
colation and salt load were not affected to a great degree. The usual error
in the imperfect regime is for farmers to irrigate less but apply more water
per irrigation. When compared to the ideal regime, surface runoff and
erosion reductions are about the same because of fewer irrigations but the
larger application per set increases the deep percolation and salt load.
VOLUNTARY ADOPTION OF A SCHEDULING SERVICE
The foregoing analysis indicated that the district as a whole would
profit from universal irrigation scheduling. However, it was also observed
earlier (see Table 17) that in some situations a farmer might be better off
not to use a scheduling service for some crops, but instead to adopt one of
the three levels of unscheduled water use because it would be more profitable.
As an exmaple, the highest profit for alfalfa growers in 1973 was realized
with high water use and no scheduling, rather than with scheduling. The
most profitable strategy would depend upon the cost of water and scheduling
93
-------
TABLE 25. ESTIMATED AVERAGE ANNUAL IRRIGATION RETURN FLOWS
IN THE A AND B DISTRICT, 1973, 1974. AND 1975
Average Annual Unscheduled Scheduled Irrigation
Variable Units Irrigation Ideal Imperfect
Surface Runoff:
Amount 1,000 AF 42.26 29.28 32.50
(1,233,000 cm )
Sediment Load 1,000 Tons 36.37 27.73 26.10
(907 Metric Tons)
Deep Percolation:
Amount 1,000 AF 48.73 11.27 44.00
(1,233,000 cm-3)
Salt Load 1,000 Tons 42.70 28.53 43.20
(907 Metric Tons)
and the value of the scheduling yield differential. Therefore the analysis
was repeated allowing the LP to select the optimum irrigation regime for
each crop given a set of water and scheduling costs.
The voluntary adoption of a scheduling service would also depend on the
relationship between the per hectare cost of providing the service and the
total acreage being scheduled by the firm. The cost characteristics of the
scheduling industry were not invested in this study but if sufficient
economies of size existed, requiring farmers to participate would lower the
per hectare cost. A policy of compensating farmers to participate would also
be more socially desirable if per unit costs decreased as the size of
operation increased.
Variable Scheduling Costs
The cost of scheduling was parametrically varied in the LP model from
zero to $5.00 to estimate average annual changes in the number of acres
(.4 ha) scheduled and the amount of return flows.*
Demand for a Scheduling Service—
The cost of scheduling affected the number of acres (ha) scheduled dif-
ferently in each year (Figure 26). However, the composite results from the
three year analysis indicates that an increase in the price of scheduling
from zero to $5.00 would reduce the number of scheduled acres (ha) from
approximately 45,000 acres (18,212 ha) to 20,000 acres (8,094 ha). This
relationship would be important to a private company in the scheduling busi-
ness. The general relationship of price to scheduled acres can be captured
by estimating the elasticity of demand as follows:
*A11 results of the parametric analysis are presented in Appendix A.
94
-------
5.00
4.00
jj
x
•a-
W
cc
O
< 3.00
C3
z
_J
0
|jj! 2.00
u.
O
K-
co
O
0 1.00
0 00
I I
I
I
I
I
I
1
1
L_
~
—
_
i i
10 20
I
i
I ^
=|— I
-
I
i
30 4
107?
107/1
1975
L
~! I i
0 50 60 70
SCHEDULED ACREAGE, (1,000 ACRES,(404.7 HA))
FIGURE 26. Estimated scheduled acreage and scheduling cost, A&B District, 1973, 1974 & 1975.
-------
T = % Change in Scheduled Acres ,,„,
D ~ % Change in Cost ( '
This measures the sensitivity of scheduled acres (ha) to cost for specific
ranges of the demand functions.
The demand function was estimated from the corner solution values il-
lustrated in Figure 26. The elasticities were estimated from the demand
function for various scheduling costs. These values are as follows:
Scheduling Cost
($/Acre or .4 ha) Elasticity of Demand
$1.00 -.059
2.00 -.125
3.00 -.286
4.00 -.502
5.00 -.800
At $3.00 or less, the effect of price on the amount of scheduled acres is
negligible but as the cost approaches $5.00, the percent change in sched-
uled acres is almost as great as the percent change in cost. Therefore,
if the scheduling service were supplied in the A and B District at current
market cost, about 38 percent of the total irrigated acres would be
scheduled.
The effect of varying scheduling costs would not effect regional returns
to a great extent (Table A-l.). The average annual returns for 1973, 74
and 75 without a scheduling service was $13.3 million or $203.36 per acre
(.4 ha). The average annual returns were increased relative to the un-
scheduled regime by a zero cost scheduling service to $14.52 million or
$222.92. An increase in the cost to $5.00 would decrease average annual
returns to $221.44 per acre (.4 ha).
Irrigation Water Use—
Applied irrigation water that does not infiltrate the soil or remain in
the root zone will pick up salts and sediment and carry them to ground water
aquifexs" or surface streams. Reducing return flows depends on applying the
right amount of water at the right time. Surface runoff will result if
water in excess of the soils absorbtion ability is applied. This requires
careful monitoring of the amount applied during any one irrigation. On
the other hand, deep percolation will result if water is absorbed in excess
of the soils water holding capacity. A certain amount of deep percolation
is required during the season to leach salts from the root zone. This can
usually be achieved applying water in excess of the water holding capacity.
Controlling deep percolation depends on irrigating when the root zone is
sufficiently dry to hold the amount of water infiltrated. Usually the total
amount of water applied in a season in a given district is indicative of the
amount of return flows.
96
-------
As reported earlier, the estimated annual water use in the A and B Dis-
trict without a scheduling service was about 195)500 acre feet (241,051 x 103
cm3) and about 120,000 acre feet (147,960 x 103 cm3) if a scheduling system
was imposed. This represents about 3.00 and 1.84 acre feet (3.67 x 103 and
2.27 x 103 cm3) per crop acre (.4 ha) per year. The 1.84 acre feet (2.27 x
103 cm3) per year application is sufficient for crop ET supplemented by
normal rainfall but not sufficient for leaching salts beyond the root zone.
In the case of a voluntary scheduling service charging $5.00 per acre (.4 ha),
the estimated average annual water use was about 178,200 acre feet (219,721
x 103 cm3). This amount was reduced to about 146,300 acre feet (180,388 x
103 cm3) if the service was offered at no charge (Figure 27).
Scheduling Cost and Return Flows—
Irrigation return flows, however, are significantly effected by changes
in scheduling costs. At zero cost, average annual deep percolation was esti-
mated at 25,000 acre feet and increased to 37,600 acre feet (30,825 x 103
and 46,361 x 103 cm3) as a result of a $5.00 scheduling cost (Figure 28).
The sensitivity of deep percolation to scheduling costs was estimated by
calculating the percent change in deep percolation resulting from a percent
change in scheduling cost.
Scheduling Cost % Change in Deep Percolation
$ Per Acre (.4 ha) % Change in Scheduling Cost
1 .048
2 .087
3 .166
4 .231
5 .285
These results indicate that deep percolation is not as sensitive to schedu-
ling costs as the amount of irrigation scheduling was. However, the level
of cost is important if the amount of deep percolation is an environmental
concern or the resulting water table presents drainage problems for other
fanners.
The amount of salts in the deep percolation is effected even less by
scheduling costs than was the amount of deep percolation. This occurs be-
cause the bulk of the salts are leached from the root zone by the first
amount of water to pass through the root zone and subsequent leaching will
pick up proportionally fewer salts. The estimated average salt load at
zero scheduling cost is about 36,000 tons (32.659 metric tons) annually and
increases to about 43,000 tons (39,010 metric tons) at a cost of $5.00
(Figure 29). This is a 18 percent increase in salt load as compared to a
50 percent increase in deep percolation from the same cost change.
The average increase in the amount of runoff and sediment load from
varying scheduling costs was similar to the change that occured in salt
load (Figure 3.0). Runoff ranged from about 34,400 to 39,700 acre feet
(42,415 x 103 to 48,950 x 103 cm3) (15.4 percent) and sediment increased from
29,200 to 34,000 tons (26,490 to 30,845 metric tons) (16.4 percent) as
"heduling costs were increased from zero to $5.00.
97
-------
VO
00
Ill
cc
O
O
z
O
u.
O
I-
V)
O
5.00
4.00
3.00
2.00
1.00
0.00
II
r
I
rr
___J
I
._J
r
J
J
i
1973
1974
1975
40 80 120 160 200 240
IRRIGATION WATER USE (1,000 ACRE-FEET (1233 x 103 cm3)
FIGURE 27. Estimated water use and scheduling cost, A&B District, 1973, 1974 & 1975.
280
-------
VO
5.00
4 • 00
X
UJ
-------
O
O
5.0U
,-, 4.00
I
<»
UJ
CC
0
< 3.00
z
a
^ 2.00
O
in
LL
O
1-
00
O
0
1.00
0.00
r— •
!
I
i
f^T
I
I
I
I
|
1
|
I
1
1
i
1"
1
1
1
i
i
rj
I I
i r_i
i i i 1 1 i
10 20 30 40
.
r-P
1
1
1
1
1
1
J
1 1
50 60 7
SALT LOAD, (1,000 TONS (907 METRIC TONS))
FIGURE 29. Estimated salt load as a function of scheduling cost, A&B District, 1973, 1974 & 1975.
-------
5.00
4.00
<
X
UJ
oc
o
3.00
Q
UJ
r
o
u.
o
V)
O
O
2.00
1.00
0.00
10
20
RUNOFF
SEDIMENT
30
40
50
60
70
RUNOFF AND SEDIMENT LOAD, (1,000 ACRE-FEET OR TONS (1233 x 103 cm3 or 907 METRIC TONS))
FIGURE 30. Estimated average annual surface runoff and sediment load, A&B District, 1973, 1974 & 1975.
-------
REDUCING RETURN FLOWS BY SCHEDULING
Irrigation scheduling could be an effective tool in managing return
flows because the program objective is to keep the soil moisture higher than
the permanent wilting point and below field capacity with a minimum number
of irrigations. This results in a minimum of return flows without reducing
acreage or yields. The main problem of course is the ability of each farmer
to implement each scheduling order with sufficient precision. As described
earlier, errors in timing and application amounts can negate most of the
crop yield or return flow benefits.
To summarize the effects of the scheduling program, water use and re-
turn flows resulting from the various scheduling policies in the A and B
District were compared with the results with no scheduling service (Table
26). The results from the regional economic model indicate that scheduling
and the degree to which it is implemented has a dramatic effect on reducing
return flows. Water use was estimated at 195,530 acre feet (241,088 x 103
cm3) without scheduling and 143,370 acre feet (176,775 x 103 cm3) with re-
quired scheduling. Water use varied between these amounts for voluntary
scheduling with costs ranging from zero to $5.00.
The scheduling cost proved to be a significant factor in determining
the aggregate amount of irrigation that will be scheduled. This is probably
true in the A and B District case for one principal reason. First, the irri-
gation practices normally applied in the District are reasonably efficient
and increasing the charge for the scheduling service will make it less
profitable than normal irrigation practices.
The estimated 26.7 percent reduction in water use as a result of a re-
quired scheduling service reduced the estimated deep percolation by 76.9.
percent, salt load by 33.7 percent, surface runoff by 30.7 and sediment load
by 37.5 percent. Similarly, a voluntary scheduling service had proportional
effects on return flows. Although the estimated return flows seem to vary
substantially from scheduling, this analysis could underestimate the true
yield and return flow benefits in the irrigated west. Many irrigation dis-
tricts hold water rights in excess of ET and percolation requirements and
do not charge farmers on the basis of water use. This promotes inefficient
water use and opportunities for large amounts of return flows to be
generated. An imposed scheduling service in these areas would have a sub-
stantial effect on return flows and bypass the more complex legal and insti-
tutional questions involved with price and water allocations.
The cost of reducing salt and sediment loads were not calculated as the
cost of scheduling was not estimated. However, for costs from $0.00 to
$5.00 per acre returns to land, management and risk increased from the no
scheduling case.
VARIABLE WATER COSTS AND SCHEDULING
The theoretical economic model formulated earlier suggests that variable
water costs should have an effect on the amount of irrigation scheduling and
102
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TABLE 26. ESTIMATED AVERAGE ANNUAL IRRIGATION WATER USE AND RETURN FLOWS
ALTERNATIVE SCHEDULING POLICIES. A AND B DISTRICT
o
CO
Scheduling
Policy
Required
Voluntary
1!
II
"
II
II
Unscheduled
Cost
($/Acre)
($.4/ha)
0.00
0.00
1.00
2.00
3.00
4.00
5.00
Water Deep
Use Percolation
(1,000 AF)
(1,233 x 103
143.37
146.30
152.67
159.04
165.41
171.78
178.15
195.53
cm3)
11.27
25.08
28.83
30.09
32.59
35.09
37.60
48.73
Salt
Load
(1,000 Tons)
(907 Metric Tons)
28.53
36.20
27.53
38.86
40.19
41.52
42.84
42.70
Surface
Runoff
(1,000 AF1
(1,233 x 10J cm3)
29.28
34.42
35.48
36.53
37.59
38.65
39.71
42.26
Sediment
Load
(1,000 Tons)
(907 Metric Tons)
22.73
29.23
30.19
31.15
32.11
33.07
34.03
36.37
-------
the generation of return flows. If farmers are profit maximizers and are
aware of irrigation alternatives and relationships, increasing water costs
will result in less water being applied as more water saving practices and
technologies are utilized. The results from the regional economic model did
confirm this relationship. The cost of water was varied from $3.00, which
approximates the current cost, to $20.00 per acre foot (1.233 x 103 cm3) to
determine water use, level of scheduling adoption and return flows (Table 27).
Estimated annual water use decreased from 195,000 acre feet (240,435 x 103
cm ) under the present schedule to 134,670 acre feet (166,048 x 103 cm3)
(31 percent) at a $20.00 cost. The decreased water use was primarily the
result of the scheduling alternatives available for each crop. At $20.00,
most of the District acreage is scheduled.
Return flows were reduced accordingly. Deep percolation was estimated
at 11,440 acres (4,630 ha) if the water cost was $20.00 per acre foot (1.233
x 10 cm ). This represents a 76.5 percent reduction and compares to the re-
sults obtained for the required scheduling policy. Surface runoff was also re-
duced by amounts similar to those achieved under a mandatory scheduling policy.
In summary, changing water costs could effect the amount of irrigation
scheduling in a district. Sufficient water savings are realized by sched-
uling to justify the service on purely economic criteria if water costs are
sufficiently high. However, water prices in the west are traditionally much
lower than the $20.00 per acre foot (1.233 x 103 cm3) hypothesized in this
analysis. Water prices are usually established by water agencies to allocate
diversion and distribution costs to individual water customers without con-
sidering the value of water in alternative uses or the social costs of return
flows. The present price structure, based primarily on diversion costs, will
generally result in more diversions, greater agricultural production, in-
creased net farm incomes and larger return flows in a specific area than
would occur under higher water prices. Markets for the transfer of water
rights and use would establish an opportunity cost of water. However,
markets for water do not generally exist.
The objectives of Section 208 of Public Law 92-500 are to decrease the
externalities of nonpoint sources of pollution by requiring the specifica-
tion of methods to control runoff from agricultural and silvicultural lands.
These controls will be a set of "best management practices" (BMP) applied
to achieve the water quality goals of PL 92-500. The BMP being considered
by the agencies conducting Section 208 analysis are specific soil and water-
use management techniques and physical treatment structures. Charging water
prices to achieve different use patterns and/or environmental results have
not been considered. The agency concern with identifying the physical pol-
lution effects of changing irrigation practices and ignoring the possibili-
ties of economic incentives is understandable. Many of the agencies do not
favor pricing policies as pollution control alternatives because they are
politically undesirable and the income and equity effects are unknown. How-
ever, adjusting irrigation water costs to account for the social costs im-
posed by return flow disposal has been suggested before (Horner and English,
1976). Results from this studv indicate that sufficient correlation exists
between return flows and water use to price irrigation water to achieve
desired environmental results.
104
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TABLE 27. ESTIMATED AVERAGE ANNUAL IRRIGATION WATER USE, SCHEDULING
ACTIVITY, RETURN FLOWS, SEDIMENT LOSS AND SALT LOAD FOR
ALTERNATIVE WATER COSTS, A AND B DISTRICT*
Water
Cost
($/AF)
($/1.233 x 103 cmj)
Present Schedule
3.00
5.00
10.00
15.00
20.00
Acres
Scheduled**
(1,000 Acres)
i (404.7 ha)
Not Scheduled
54.45
55.37
57.66
59.96
62.23
Water
Use
a 9
> ^
195.30
162.30
159.05
150.92
142.80
134.67
Deep
Percolation
(1,000 AF)
33 x 103 cm3)-
48.73
19.47
18.53
16.17
13.81
11.44
Surface
Runoff
42.27
32.56
31.61
29.21
26.82
24.42
Sediment
Loss
Salt
Load
(1,000 Tons)
(907.2 Metric Tons)
36.37
25.36
25.03
24 . 21
23.39
22.56
42.70
20.97
29.90
27.22
24.54
21.85
*Scheduling is provided at zero cost.
**Alfalfa acreage would be irrigated under the scheduling regime at low water cost but revert
to a low water application rate at higher cost (Table Appendix A-2). This is not reflected
in these average data. These relationships were estimated by regression analysis using values
of the corner solutions and cannot be compared to values reported in Table 25.
-------
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USDA, Corvallis, OR. (Unpublished).
Larson, W. E., and W. B. Johnston. 1955. The Effect of Soil Moisture Level
on the Yield, Consumptive Use of Water and Root Development by Sugar
Beets. In: Proceedings of Science Society, Society of America.
19:275-279.
Lord, J. P. 1976. Harza Agricultural Services, Fresno, CA. Personal
Communication.
McMaster, G. 1976. k Curve for Sugar Beets. University of Idaho, Moscow,
ID. Personal Communication.
McMaster, G. M., M. J. Le Baron, G. L. Corey, L. R. Hawthorn. 1965. "The
Influence of Soil Moisture on Snap Bean Seed Production," Idaho Agri-
cultural Experiment Station, Bulletin 435, 20 pp.
Moore, C. V., and T. R. Hedges. 1963. "A Method for Estimating the Demand
for Irrigation Water," Agricultural Economics Research, XV, 4, October,
pp. 131-135.
107
-------
Nielsen, D. R., J. W. Biggar, and K. T. Erh. 1973. "Spatial Variability of
Field Measured Soil Water Properties," Hilgardia, 42:215-260.
Rhoades, J. D., J. D. Oster, R. D. Ingralson, J. M. Tucker, and M. Clark.
1974. "Minimizing the Salt Burdens of Irrigation Drainage Waters,"
Journal of Environmental Quality, 3:311-316.
Ruffing, B. J., M. E. Jensen, and D. T. Westermann. 1974. "Irrigation and
Nitrogen Management for Moravian Barley in Southern Idaho." Contribution
from the Western Region, Agricultural Research Service, USDA, University
of Idaho, Research and Extension Center, Current Information Series
No. 365, Kimberley, ID. 3 pp.
Ruffing, B. J., and M. E. Jensen. 1976. "Irrigating Peas on Portneuf Silt
Loam Soil," Unpublished manuscript provided by B. J. Puffing, USDA-ARS,
Snake River Conservation Research Center, Kimberly, ID. 11 pp.
Schaack, J. M. 1975. "Are You Water Wise?" In: Irrigation and Drainage
in an Age of Competition for Resources, ASCE, Logan, UT, August 13-15.
pp. 451-455.
Stewart, J. I., and R. M. Hagan. 1969. "Development of Evapotranspiration-
Crop Yield Functions for Managing Limited Water Supplies, Seventh
Congress, International Commission on Irrigation and Drainage, Mexico
City, 25 pp.
Stewart, J. I., R. M. Hagan, W. 0. Pruitt, and W. A. Hall. 1973. "Water
Production Functions and Irrigation Programming for Greater Economy
in Project and Irrigation System Design and for Increased Efficiency
in Water Use," University of California, March. Final Report 14-06-D-
7229, USDI, USER E&R Center, Denver, CO. 161 pp.
Stewart, J. I., R. M. Hagan, and W. 0. Pruitt. 1976. "Water Production
Functions and Predicted Irrigation Programs for Principal Crops as
Required for Water Resources Planning and Increased Water Use
Efficiency," University of California, Department of Land, Air, and
Water Resources, July. Technical Completion Report 14-06-D-7329,
USDI, USER, E&R Center, Denver, CO. 81 pp.
Tyler, C. L., G. L. Corey, and L. R. Swarner. 1964. "Evaluating Water Use
on a New Irrigation Project," Agricultural Experiment Station, Depart-
ment of Agricultural Engineering, University of Idaho, Research
Bulletin No. 62, December. 24 pp.
University of California. 1976. "Sugar Beet Irrigation." Division of
Agricultural Science Leaflet 2396. May. 2 pp.
U.S. Bureau of Reclamation. 1958-1971. Annual Reports of the Minidoka
Project, A and B Irrigation District, Minidoka Irrigation District,
and Burley Irrigation District.
108
-------
U. S. Bureau of Reclamation. 1971. "Use of Water on Federal Irrigation
Projects, Minidoka Project, Northside Pumping Division, Unit A, Idaho
Summary Report," USER Region I, Boise, ID. 154 pp.
U.S. Bureau of Reclamation. 1972. "Colorado River Water Quality Improvement
Program, USER, Denver, CO. 88 pp.
U.S. Bureau of Reclamation. 1974. "Irrigation Management Services Program,
Minidoka Project, Irrigation Data 1972." Annual Report. USER Pacific
Northwest Region, Boise, ID. 52 pp.
Whittlesey, N. K., and L. J. Colyar. 1968. "Decision Making Under Weather
Uncertainty in the Summer Fallow Annual Cropping Area of Eastern
Washington," Technical Bulletin No. 58, Washington Agricultural
Experiment Station. 24 pp.
Wright, J. L. and M. E. Jensen. 1972. "Peak Water Requirements of Crops in
Southern Idaho," Journal of the Irrigation and Drainage Division, ASCE,
98:193-201.
Wright, J. L., and M. E. Jensen. 1974. "New Crop Coefficients for
Computerized Irrigation Scheduling for Potatoes," USDA-ARS, Western
Region Snake River Conservation Research and Extension Center,
Kimberly, ID. 7 pp.
Wright, J. L. and M. E. Jensen. 1976. "Development and Evaluation of
Evapotranspiration Models for Irrigation Scheduling," ASAE Paper
No. 76-2063, June. 15 pp.
109
-------
APPENDIX A
TABLE A-l. CROP ACREAGE. RETURNS. WATER USE AND IRRIGATION RETURN FLOUS RESULTING FROM SCHEDULED IRRIGATION AT VARYING SCHEDULING COSTS
Year Policy
1973
1974
No Scheduling
Scheduling Cost:
SO. 00 /A
Scheduling Cost:
$0.25/A
Scheduling Cost:
S5.00/A
Scheduling Cost:
$0.00 /A
Scheduling Cost:
54.00/A
Scheduling Cost:
$4.75/A
Scheduling
Required
No Scheduling
Scheduling Cost:
SO.OO/A
Scheduling Cost:
$0.25/A
Total
Crop
Acres
(1,000
(404.
64.5
64.5
64.5
64.5
64.5
64.5
64.5
64.5
65.3
65.3
65.3
No. of
Sched-
uled
Acres
Acres)
7 ha)
0.0
40.4
22.3
10.6
64.5
63.5
44.5
64.5
0.0
50.0
37.3
Returns
To Land
Mgtnt.
& Risk
Percent
Change
From
No
Sched-
uling
Irri-
gation
Water
Used
(Millions)
12.14
13.24
13.23
13.13
14.69
14.45
14.40
13.18
16.61
17.96
17.95
2.6
2.6
1.8
13.9
12.0
11.6
2.2
2.7
2.6
198.3
172.7
185.7
192. S
122.3
123.4
169.0
122.3
197.0
133.4
142.5
Percent
Change
From
No
Sched-
uling
Surface
Runoff
Percent
Change
From
No
Sched-
uling
Deep
Perco-
lation
Percent
Change
From
No
Sched-
uling
(1,000 Acre Feet)
(1,233 x 103 cm3)
-12.9
-6.4
-2.9
-38.4
-37.8
-14.8
-38.4
-32.3
-27.7
42.8
36.58
40.33
40.90
29.98
30.23
35.53
29.98
13.0
33.16
35.79
-14.0
-5.2
-3.8
-29.5
-28.9
-16.5
-29.5
-22.9
-16.8
47.8
33.33
38.53
43.02
11.53
12.41
30.54
11.53
50.4
21.25
25.01
-34.0
-19.4
-10.0
-75. 9/
-74.0
-36.1
-75.9
-57.9
-50.4
Sedi-
ment
Loss
Percent
Change
From
No
Sched-
uling
Total
Dis-
solved
Solids
Percent
Change
From
No
Sched-
uling
(1,000 Tons)
(907.2 Metric Tons)
35.3
27.2
32.8
32.0
22.2
22.5
25.6
22.2
36.2
28.3
32.2
-17.8
-1.2
-3.5
-33.0
-32.0
-22.9
-33.0
-20.9
-10.1
42.7
39.3
42.7
45.3
29.0
29.5
37.6
29.0
41.9
34.6
37.0
-17.8
-10.8
-5.3
-39.4
-38.4
-21.3
-39.4
-29.7
-24.9
Labor
Use
(1,000
Hours)
120.7
104.8
112.2
118.5
87.2
88.0
102.4
87.2
118.3
92.6
97.8
Continued—
-------
TABLE A-l.--CONTINUED
Year Policy
Total
Crop
Acres
No. of
Sched-
uled
Acres
Returns
To Land
Mgmt.
& Risk
(1,000 Acres)
(404.7 ha)
1974 Scheduling Cost:
$3.75/A
Scheduling Cost:
$0.00/A
Scheduling Cost:
$5.00/A
Scheduling
Required
1975 No Scheduling
Scheduling Cose
SO. 00 /A
Scheduling Cost:
S0.75/A
Scheduling Cost:
?3.25/A
Scheduling Cost:
SO.OO/A
Scheduling Cost:
S5.00/A
Scheduling
Required
65.3
65.3
65.3
65.3
65.6
65.6
65.6
65.6
65.6
65.6
65.6
19.0
65.3
65.3
65.3
0.0
54.3
39.4
23.4
65.6
65.6
65.6
17
19
19
17
11
12
12
12
13
13
12
Percent
Change
From
No
Sched-
uling
Irri-
gation
Water
Used
($)
(Millions)
.82
.86
.54
.74
.23
.35
.31
.22
.85
.52
.30
1.9
13.2
11.7
1.4
3.2
2.8
2.1
15.7
12.9
2.3
186.3
119.2
119.2
119.2
191.3
129.0
139.8
178.3
118.6
118.6
118.6
Percent
Change
From
No
Sched-
uling
Surface
Runoff
Percent
Change
From
No
Sched-
uling
Deep
Perco-
lation
Percent
Change
From
No
Sched-
uling
(1,000 Acre Feet)
(1,233 x 103 cm3)
-5
-39
-39
-39
-32
-26
-6
-38
-38
-38
.4
.5
.5
.5
.5
.9
.8
.0
.0
.0
40.
29.
29.
29.
41.
31.
34.
38.
28.
28.
28.
90
30
30
30
3
39
48
98
57
57
57
-4.9
-31.9
-31.9
-31.9
-23.9
-16.4
-5.5
-30.8
-30.8
-30.8
42.48
10.98
10.98
10.98
48.0
18.84
23.28
38.60
11.30
11.30
11.30
-15.8
-78.2
-78.2
-78.2
-60.8
-51.5
-19.7
-76.5
-76.5
-76.5
Sedi-
ment
Loss
Percent
Change
From
No
Sched-
uling
Total
Dis-
solved
Solids
Percent
Change
From
No
Sched-
uling
(1,000 Tons) —-
(907.2 Metric Tons)
35.2
22.4
22.4
22.4
37.6
27.9
32.5
35.0
23.6
23.6
23.6
-1
-37
-37
-37
-21
-8
-1
-33
-33
-33
.9
.6
.6
.6
.2
.3
.1
.5
.5
.5
44.9
28.2
28.2
28.2
43.5
33.1
35.9
42.8
28.4
28.4
28.4
-8.
-42.
-42.
-42.
-31.
-25.
-11.
-40.
-40.
-40.
,9
p 7
.7
.7
,1
3
,0
,9
.9
.9
Labor
Use
(1,000-
Hours)
112.7
83.5
83.5
83/5
122.7
95.5
101.6
113.8
88.7
88.7
88.7
-------
TABLE A-2. CROP ACREAGE, RETURNS, WATER USE AND IRRIGATION RETURN FLOWS RESULTING FROM SCHEDULED IRRIGATION AT VARYING WATER COSTS
Year Policy
1973
1974
No Scheduling
Water Cost:
S3.00/AF
Water Cost:
S4.00/AF
Water Cost:
$10.00/AF
Water Cost:
$11.00/AF
Water Cost:
S3.00/AF
Water Cost:
S15.00/AF
No Scheduling
Water Cost:
S3.00/AF
Water Cost:
59.00/AF
Total
Crop
Acres
(1,000
(404.
64.5
64.5
64.5
64.5
64.5
64.5
64.5
65.3
65.3
65.3
No. of
Sched-
uled
Acres
Acres)
7 ha)
0
40
59
63
45
64
45
0
50
44
.0
.4
.4
.5
.5*
.5
.5
.0
.0
.8
Returns
To Land
Mgmt.
i, Risk
Percent
Change
From Irri-
No gat ion
Sched- Water
uling Used
\ •ft
(Millions)
12.
13.
13.
12.
12.
14.
31.
16.
18.
18.
14
42
26
34
22
89
15
61
16
0
4.0
2.8
-4.3
-5.3
15.4
1.9
3.8
+2.9
198
207
152
148
124
146
124
197
160
125
.3
.2
.5
.2
.7
.7
.7
.0
.1
.0
Percent
Change
From
No
Sched-
uling
(
-12
-35
-37
-47
-38
-47
-32
-47
Surface
Runoff
1,000 Acre Fe<
1.233 x 103 ci
.9
.9
.8
.6
.4
.6
.3
.1
42.5
40.3
31.3
30.2
20.8
30.0
20.8
43.0
33.2
21.0
Percent
Change
From
No
Sched-
uling
a )
-14
-26
-28
-51
-29
-51
-22
-51
Deep
Perco-
lation
Percent
Change
From
No
Sched-
uling
Sedi-
ment
Loss
Percent
Change
From
No
Sched-r'
uling
Total
Dis-
solved
Solids
Percent
Change
From
No
Sched-
uling
(907.2 Metric Tons)
.0
.5
.9
.0
.5
.0
.9
.1
47.8
33.2
15.0
12.4
8.0
11.5
8.0
50.4
21.3
9.6
-30
-68
-74
-83
-75
-83
-57
-81
.6
.5
.0
.2
.9
.2
.9
.0
35.3
27.2
24.2
22.5
21.3
22.2
21.3
36.2
28.4
22.1
-;7
-27
-32
-35
-33
-35
-20
-38
8
0
0
9
0
9
9
3
42.7
39.3
31.1
29.5
19.1
28.9
19.1
41.9
34.6
19.7
-17
-34
-38
-60
-39
-60
-29
-59
.8
.9
.4
.1
.4
.1
.7
.9
Labor
Use
(1,000
Hours)
120.7
104.8
90.4
88.0
124.7
87.3
94.6
118.3
160.1
92.3
Continued—
*18,985 acres of alfalfa went from scheduled to low H-0 app. and 1,006 acres of peas from medium H-0 app. to scheduled.
-------
TABLE A-2.—CONTINUED
Year Policy
1974
1975
Water Cose:
$32.00/AF
Water Cost:
$3.00/AF
Water Cost:
$12.00/AF
No Scheduling
Water Cost:
S3.00/AF
Water Cost:
S5.00/AF
Water Cost:
$11.00/AF
Water Cost:
S27.00/AF
Water Cost:
$3.00/AF
Water Cost:
S15.00/AF
Total
Crop
Acres
(1,000
(104.
65.3
65.3
65.3
65.6
65.6
65.6
65.6
65.6
65.6
65.6
No. of
Sched-
uled
Acres
Acres)
7 ha)
47.0
65.3
47.0
0.0
54.3
63.9
47.9
49.5
65.6
49.5
Returns
To Land
Mgmt.
i Risk
i
Percent
Change
From Irri-
No gat ion
Sched- Water
uling Used
(Millions)
17
20
18
11
12
12
11
9
14
12
9
13
85
23
57
27
42
41
13
45
+2.3
15.0
7.8
5.0
2.5
-4.6
-21.3
18.0
4.0
121.8
143.0
121.8
191.3
154.8
144.7
126.1
123.7
142.3
123.7
Percent
Change
From
No
Sched-
uling
(
-48
-39
-48
-32
-36
-45
-46
-38
-46
Surface
Runoff
1,000 Acre Fe
1,233 x 103 cr
.5
.5
.5
.5
.9
.0
.1
.0
.1
20
29
20
41
31
29
21
20
28
20
.5
.3
.5
.3
.4
.0
.2
.8
.6
.8
Percent
Change
From
No
Sched-
uling
V
"3>
-52
-31
-52
-23
-29
-48
-49
-30
-49
Deep
Perco-
lation
Percent
Change
From
No
Sched-
uling
Sedi
ment
Loss
Percent
Change
From
No
Sched-
uling
Total
Dis-
solved
Solids
Percent
Change
From
No
Sched-
uling
(907.2 Metric Tons)
.4
9
4
9
8
5
5
8
5
7.6
11.0
7.6
48.0
18.8
12.8
9.8
8.3
11.3
8.3
-84.9
-78.2
-84.9
-60.8
-73.4
-79.6
-82.6
-76.5
-82.6
21.5
22.4
21.4
37.6
27.9
24.0
23.2
22.7
23.6
22.7
-40.1
-37.6
-40.1
-21.2
-32.1
-34.4
-35.8
-31.4
-35.8
18.7
28.3
18.7
43.5
33.1
29.2
20.8
20.0
28.4
20.0
-62.
-42.
-62.
-31.
-39.
-56.
-58.
-40.
-58.
1
7
1
1
3
7
3
9
3
Labor
Use
(1,000
Hours)
90.6
83.5
121.8
122.7
95.5
90.0
96.3
95.0
142.3
123.7
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/2-80-063
3. RECIPIENT'S ACCESSIOONO.
4. TITLE AND SUBTITLE
A REGIONAL ASSESSMENT OF THE ECONOMIC AND ENVIRONMENTAL
BENEFITS OF AN IRRIGATION SCHEDULING SERVICE
5. REPORT DATE
April 1980 issuing date
6. PERFORMING ORGANIZATION CODE
7.AUTHOR(S)
Marshall J. English, Gerald L. Horner, Gerald T. Orlob,
Joseph Erpenbeck, Michael Moehlman, Richard H. Cuenca,
T Hn^oL-
8. PERFORMING ORGANIZATION REPORT NO.
9."PE"FtFO"R~M"fN~G"ORGANIMATION NAME AND ADDRESS
University of California and
Natural Resource Economics Division
Economics, Statistics and Cooperative Service
United States Department of Agriculture
California QS616
10. PROGRAM ELEMENT NO.
1BB770
11. CONTRACT/GRANT NO.
EPA-IAG-D6-0121
12. SPONSORING AGENCY NAME AND ADDRESS
Robert S. Kerr Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Ada, Oklahoma 74820
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/15
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Irrigation scheduling is a technique for systematically determining the proper
date and quantity of each irrigation in individual fields. This technique is pre-
sently being used by government agencies and private companies in the western United
States to assist farmers in planning irrigations. This report describes a case study
in which the regional environmental and economic benefits of irrigation scheduling
were assessed. The analysis indicated that substantial environmental benefits could
be realized through use of the technique. However, it was also found that imper-
fections which normally occur in actual irrigation scheduling operations could
drastically reduce these benefits. The economics of irrigation scheduling appeared
favorable in the particular circumstances of the case study.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Irrigation
Irrigated Land
Evapotranspiration
Irrigation Scheduling
Economic Model
Drainage
Irrigation return flow
Water-use efficiency
Regional analysis
Salinity
Sediments
Percolation
Benefit analysis
02/A, C, D
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
124
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
114
6 US COVCflNMEHT WMTIKG OfFlCE: 1960-657-146/5654
-------
A REGIONAL ASSESSMENT OF THE ECONOMIC AND ENVIRONMENTAL
BENEFITS OF AN IRRIGATION SCHEDULING SERVICE
EPA-600/2-80-063
April, 1980
ERRATA
Computational errors were discovered in. the original
text. Rather than changing each individual number,
corrected versions of Section 8 and Appendix A are
included. Please place them in the report.
-------
SECTION 8
REGIONAL EFFECTS OF AN IRRIGATION SCHEDULING SERVICE
Two basic questions regarding the economic viability were analyzed
using the regional economic model. The first was to project the economic
costs and changes in the amount and quality of return flows if all of the
irrigation in the A and B District were required to be scheduled. The
second was to determine the degree of voluntary adoption by farmers at
varying scheduling and water costs.
POTENTIAL IMPACTS OF A SCHEDULING SERVICE
The basic economic and return flow information were estimated for
each irrigation regime requiring that all fields be scheduled free of
charge (Table 24). Crop yield coefficients for scheduling were based
on the more conservative yield estimates developed in this study. The
figures presented in Table 24 are three year averages (1973-75). Values
by year are presented in Appendix Table A-l.
TABLE 24. ESTIMATED AVERAGE ANNUAL RETURNS TO LAND, MANAGEMENT
AND RISK FOR UNSCHEDULED AND SCHEDULED IRRIGATION
IN THE A AND B DISTRICT FOR 1973, 1974 AND 1975*
Average Annual Unscheduled Scheduled Irrigation
Variable Units Irrigation Ideal Imperfect
Returns to Land, $1,000,000 14.118 14.390 14.337
Management & Risk
Irrigation Water:
Use 1,000 AF 216.87 144.01 183.60
(1,233,000 m3)
Cost $ 1,000 841.01 665.77 718.32
Irrigation Labor:
Use
Cost
1,000 hrs
.$ 1,000
120.54
416.47
86.48
298.76
86.48
298.76
*Average irrigated acreage 65,133 (26,359 ha).
91
-------
Changes in Financial Returns
The average annual returns to land, management and risk were increased
by $272,000, or $4.18 per irrigated acre (0.4 ha) by requiring a scheduling
service that does not have implementation errors. However, these results
do not account for the inherent element of risk either in yields or prices.
Over the long-run, these may tend to even out and the results reported here
may approximate the expected results but no attempt was made to quantify
the statistical distribution of yields and prices. The use of conserva-
tive yield estimates in the LP model, however, may underestimate the
expected benefits of an "ideal" scheduling service.
The increased annual returns to land, management and risk are
attributable not only to increased yields, but also to substantial
reductions in irrigation costs. To illustrate the relative importance of
reduced costs and improved yields in evaluating the scheduling service,
the results from the LP were compiled on a per acre (0.4 ha) basis as
follows.
Component Change Dollars Per Acre
(0.4 ha)
Increased Value of Production -0.32
Reduced Irrigation Labor Cost 1.81
Reduced Water Cost 2.69
Net Change in Annual Returns 4,18
The average annual reduction in water and labor costs were $4.50 per
acre (0.4 ha). The savings in these irrigation costs are almost as much as
the cost of a scheduling service. Water costs were reduced only by 20.8
percent, whereas total water use was reduced by 33.6 percent under the
ideal scheduling regime. This disparity is due to the water pricing
schedule of the A and B District which stipulates a fixed rate for the
first three feet of water use. Since district water use was reduced from
216,870 acre feet (an average of 3.33 acre feet per acre or 4.10 x 10^
m-Vo.4 ha) to 144,010 acre feet (an average of 2.21 acre feet per acre
or 2.72 x 10-^ nrVo.4 ha) the reduction in water use would not reduce ir-
rigation costs proportionately. A comparison of weighted average* water
costs for unscheduled fields and average costs for scheduled fields in-
dicates that the average crop water cost for the scheduled regime was
equal to the minimum cost set by the Irrigation District with the ex-
ception of alfalfa. Irrigation costs would have been reduced more if
water cost were directly proportional to water use.
*Weighted by the water-use patterns of district farmers as shown
earlier in Table 13.
92
-------
The estimated impacts on irrigation costs of an imperfect scheduling
regime are also included in Table 24. As explained in the description of
the production submodel, yield predictions resulting from the imperfect
scheduling case were not possible without a more sophisticated approach.
Therefore the LP was run with the yield estimates that were used for the
ideal scheduling service based on the assumption that the error would
probably not affect yields substantially but would result in additional
irrigation costs. If this assumption were true, the following cost and
yield changes would result.
Component Change Dollars Per Acre
(0.4 ha)
Increased Value of Production -0.33
Reduced Irrigation Labor Cost 1.81
Reduced Water Cost 1.88
Net Change in Annual Returns 3.36
These regional or aggregate results are heavily influenced by the
changes that occur in irrigating alfalfa. This will be explained in the
next section on return flows.
Changes in Return Flows
The estimated annual environmental consequences of the ideal scheduling
service included substantial reductions in return flows, particularly deep
percolation (Table 25). The estimated sediment reduction was 34.7 percent
which would also indicate reductions in fertilizers and pesticides in return
flows. This would suggest that rates of application of these materials may
be reduced under a scheduling regime.
Surface runoff and sediment load were estimated to decrease by 23.1
and 11.1 percent respectively under the imperfect scheduling regime but deep
percolation and salt load were not affected to a great degree. The usual
error in the imperfect regime is for farmers to irrigate less but apply more
water per irrigation. When compared to the ideal regime, surface runoff
and erosion reductions are about the same because of fewer irrigations but
the larger application per set increases the deep percolation and salt load.
VOLUNTARY ADOPTION OF A SCHEDULING SERVICE
The foregoing analysis indicated that the district as a whole would
profit from universal irrigation scheduling. However, it was also observed
earlier (see Table 17) that in some situations a farmer might be better off
not to use a scheduling service for some crops, but instead to adopt one of
the three levels of unscheduled water use because it would be more profit-
able. As an example, the highest profit for alfalfa growers in 1973 was
realized with high water use and no scheduling, rather than with scheduling.
The most profitable strategy would depend upon the cost of water and scheduling
and the value of the scheduling yield differential. Therefore the analysis
was repeated allowing the LP to select the optimum irrigation regime for
each crop given a set of water scheduling costs.
93
-------
TABLE 25. ESTIMATED AVERAGE ANNUAL IRRIGATION RETURN FLOWS
IN THE A AND B DISTRICT FOR 1973, 1974, AND 1975
Average Annual
Variable
Units
Unscheduled
Irrigation
Scheduled Irrigation
Ideal Imperfect
Surface Runoff:
Amount 1,000 AF 42.26 29.28 32.50
(1,233,000 m3)
Sediment Load 1,000 Tons 46.38 30.27 41.22
(907 Metric Tons)
Deep Percolation:
Amount 1,000 AF 48.75 11.27 44.04
(1,233,000 m3)
Salt Load 1,000 Tons 48.38 28.54 47.26
(907 Metric Tons)
The voluntary adoption of a scheduling service would also depend on the
relationship between the per acre cost of providing the service and the
total acreage being scheduled by the firm. The cost characteristics of the
scheduling industry were not investigated in this study but if sufficient
economies of size existed, requiring farmers to participate would lower the
per acre cost. A policy of compensating farmers to participate would also
be more socially desirable if per unit costs decreased as the size of
operation increased.
Variable Scheduling Costs
The cost of scheduling was parametrically varied in the LP model from
zero to $5.00 to estimate average annual changes in the number of acres
(0.4 ha) scheduled and the amount of return flows.*
Demand for a Scheduling Service—
The cost of scheduling affected the number of acres (ha) scheduled dif-
ferently in each year. However, the composite results from the three
year analysis indicates that an increase in the price of scheduling
from zero to $5.00 would reduce the number of scheduled acres (ha) from
48,231 acres (19,519 ha) to 21,552 acres (8,722 ha). This relationship
would be important to a private company in the scheduling business. The
general relationship of price to scheduled acres can be captured by esti-
mating the elasticity of demand as follows:
*A11 results of the parametric analysis are presented in
Appendix A.
94
-------
ED _ %Change in Scheduled Acres (48)
% Change in Cost
This measures the sensitivity of scheduled acres (ha) to cost for specific
ranges of the demand functions.
The demand function was estimated from the values illustrated
in Figure 26. The elasticities were estimated from the demand
function for various scheduling costs. These values are as follows:
Scheduling Cost
($/Acre or 0.4 ha) Elasticity of Demand
$1.00 -0.122
2.00 -0.280
3.00 -0.489
4.00 -0.778
5.00 -1.208
At less than $3.00, the effect of price on the amount of scheduled acres is
negligible but as the cost approaches $5.00, the percent change in sched-
uled acres is greater than the percent change in cost. Therefore, if the
scheduling service were supplied in the A and B District at current market
cost, about 33 percent of the total irrigated acres would be scheduled.
The effect of varying scheduling costs would not affect regional returns
to a great extent (Table A-l). The average annual returns for 1973, 74 and
75 without a scheduling service were $14.118 million or $216.76 per acre
(0.4 ha). The average annual returns were increased relative to the un-
scheduled regime by a zero cost scheduling service to $14.52 million or
$222.92. An increase in the cost to $5.00 would decrease average annual
returns to $221.95 per acre (0.4 ha).
Irrigation Water Use—
Applied irrigation water that does not infiltrate the soil or remain in
the root zone will pick up salts and sediment and carry them to ground water
aquifers or surface streams. Reducing return flows depends on applying the
right amount of water at the right time. Surface runoff will result if
water in excess of the soils absorption ability is applied. This requires
careful monitoring of the amount applied during any one irrigation. On
the other hand, deep percolation will result if water is absorbed in excess
of the soil's water holding capacity. A certain amount of deep percolation
is required during the season to leach salts from the root zone. This can
usually be achieved by applying water in excess of the water holding capacity.
Controlling deep percolation depends on irrigating when the root zone is
sufficiently dry to hold the amount of water infiltrated. Usually the total
amount of water applied in a season in a given district is indicative of the
amount of return flows.
As reported earlier, the estimated annual water use in the A and B
District without a scheduling service was 216,865 acre feet (267,395 x 103
m3) and 144,813 acre feet (177,567 x 103 m3) if a scheduling system was
95
-------
5.00
4.00
3.00
2.00
01
t-l
O
oo
c
•H
.-H
3
T3
01
O
CO
Uj
O
4J 1.00
w
o
0.00
L.
I
l
I
10 20 30 40 50
Scheduled Acreage, (1,000 Acres, (404.7 ha))
60
70
Figure 26. Estimated Average Scheduled Acreage and Scheduling Cost,
A & B District for 1973, 1974 and 1975.
-------
imposed. This represents about 3.33 and 2.21 acre feet (4.11 x 103 m3 and
2.73 x 103 m3) per crop acre (0.4 ha) per year. In the case of a voluntary
scheduling service charging $5.00 per acre (0.4 ha), the estimated average
annual water use was 205,078 acre feet (252,861 x 103 m3). This
amount was reduced to 167,711 acre feet (206,788 x 103 m3) if the
service was offered at no charge (Figure 27).
Scheduling Cost and Return Flows—
Irrigation return flows, however, are significantly affected by changes
in scheduling costs. At zero cost, average annual deep percolation was
estimated at 24,418 acre feet and increased to 41,364 acre feet (30,107
x 103 m3 and 51,002 x 103 m3) as a result of a $5.00 scheduling cost (Figure
28). The sensitivity of deep percolation to scheduling costs was esti-
mated by calculating the percent change in deep percolation resulting from
a percent change in scheduling cost.
Scheduling Cost % Change in Deep Percolation
($/Acre or 0.4 ha) % Change in Scheduling Cost
1 0.105
2 0.190
3 0.260
4 0^319
5 0.369
These results indicate that deep percolation is not as sensitive to scheduling
costs as the amount of irrigation scheduling was. However, the level of
cost is important if the amount of deep percolation is an environmental
concern or the resulting water table presents drainage problems for other
farmers.
The amount of salts in the deep percolation is effected even less by
scheduling costs than was the amount of deep percolation. This occurs be-
cause the bulk of the salts are leached from the root zone by the first
amount of water to pass through the root zone and subsequent leaching will
pick up proportionally fewer salts. The estimated average salt load at zero
scheduling cost is 35,682 tons (32,364 metric tons) annually and increases
to 44,309 tons (40,188 tons) at a cost of $5.00 (Figure 29). This is a 24
percent increase in salt load as compared to a 69.4 percent increase in
deep percolation from the same cost change.
The average increase in the amount of runoff and sediment load from
varying scheduling costs was similar to the change that occured in salt
load (Figure 30). Runoff ranged from 33,709 to 40,258 acre feet
(41,563 to 49,638 x 103 m3) (19.4 percent) and sediment increased
from 37,087 to 45,394 tons (33,638 to 41,172 metric tons) (22.4 percent) as
scheduling costs were increased from zero to $5.00.
97
-------
5.00
4.00
00
0)
M
U
60
d
3
73
Q)
O
C/3
4-1
O
O
U
2.00
i.oo
0.00
40
80
120
160
200
240
2W
Irrigation Water Use (1,000 Acre-Feet (1233 x 103 m3))
Figure 27. Estimated Average Water Use and Scheduling Cost,
A & B District for 1973, 1974 and 1975.
-------
5.00 __
J
4.00 -
r~
r
co a.wi
w
o
•»»•
*
00
c
3 2.00
3
Q)
X
(J
O
% 1.00
o
o
0.00
•
J
I
.J
L ill I I I I
10
20
30
40
SO
60
70
3 3
Deep. Percolation (1,000 Acre-Feet (1233 x 10 m ))
Figure 28. Estimated Average Deep Percolation as a Function of Scheduling Cost,
A & B District for 1973, 1974 and 1975.
-------
3.W
4.00
03
•C
8 3.00
0)
o
i-1 — .
o
o — •
j? 2.00
•H
i — 1
P
-d
0)
o
to
° 1.00
4-1
(0
o
o
O.QO
J
1
1
-
_
r1
. . . rJ. . . .
10 20 30 40 SO 60
Salt Load, (1,000 Tons (907 Metric Tons))
Figure 29. Estimated Average Salt Load as a Function of Scheduling Cost,
A & B District for 1973, 1974 and 1975.
70
-------
n)
.c
_.. Sediment
50
60
70
3 3
Runoff and Sediment Load, (1,000 Acre-Feet or Tons (1233 x 10 m or 907 Metric Tons))
Figure 30. Estimated Average Annual Surface Runoff and Sediment Load,
A & B District for 1973, 1974 and 1975
-------
REDUCING RETURN FLOWS BY SCHEDULING
Irrigation scheduling could be an effective tool in managing return flows
because the program objective is to keep the soil moisture higher than the
permanent wilting point and below field capacity with a minimum number of
irrigations. This results in a minimum of return flows without reducing
acreage or yields. The main problem of course is the ability of each
farmer to implement each scheduling order with sufficient precision. As
described earlier, errors in timing and application amounts can negate most
of the crop yield or return flow benefits.
To summarize the effects of the scheduling program, water use and re-
turn flows resulting from the various scheduling policies in the A and B
District were compared with the results with no scheduling service (Table
26). The results from the regional economic model indicate that scheduling
and the degree to which it is implemented has a dramatic effect on reducing
return flows. Water use was estimated at 216,865 acre feet (267,395 x
103 m3) without scheduling and 144,013 acre feet (177,568 x 103 m3) with
required scheduling. Water use varied between these amounts for voluntary
scheduling with costs ranging from zero to $5.00.
Scheduling cost proved to be a significant factor in determining
the aggregate amount of irrigation that will be scheduled. This is probably
true in the A and B District case for one principal reason. The
irrigation practices normally applied in the District are reasonably ef-
ficient and increasing the charge for the scheduling service will make it
less profitable than normal irrigation practices.
The estimated 33.6'percent reduction in water use as a result of a
required scheduling service reduced the estimated deep percolation by 76.9
percent, salt load by 41.0 percent, surface runoff by 30.7 and sediment
load by 34.7 percent. Similarly, a voluntary scheduling service had
proportional effects on return flows. Although the estimated return flows
seem to vary substantially from scheduling, this analysis could under-
estimate the true yield and return flow benefits in the irrigated west.
Many irrigation districts hold water rights in excess of ET and percolation
requirements and do not charge farmers on the basis of water use. This
promotes inefficient water use and opportunities for large amounts of
return flows to be generated. An imposed scheduling service in these areas
would have a substantial effect on return flows and bypass the more complex
legal and institutional questions involved with price and water allocations.
The cost of reducing salt and sediment loads were not calculated as
the cost of scheduling was not estimated. However, for costs from $0.00
to $5.00, per acre returns to land, management and risk increased from the
no scheduling case.
VARIABLE WATER COSTS AND SCHEDULING
The theoretical economic model formulated earlier suggests that
variable water costs should have an effect on the amount of irrigation
scheduling and the generation of return flows. If farmers are profit
102
-------
TABLE 26. ESTIMATED AVERAGE ANNUAL IRRIGATION WATER USE AND RETURN FLOWS
ALTERNATIVE SCHEDULING POLICIES, A AND B DISTRICT
Scheduling
Policy
Required
Voluntary
»
Unscheduled
Cost
(?/Acre)
(S/0.4 ha)
0.00
0.00
5.00
Water
Use
(1,000
(1,233
144.013
167.711
205.078
216.865
Deep
Percolation
AF) (1
x 103 m3) (907
11.270
24.418
41.364
48.754
Salt
Load
,000 Tons)
Metric Tons)
28.541
35.682
44.309
48.375
Surface
Runoff
(1,000 AF)
(1,233 x 103 m3)
29.283
33.709
40.258
42.262
Sediment
Load
(1,000 Tons)
(907 Metric Tons)
30.269
37.087
45.394
46.381
-------
maximizers and are aware of irrigation alternatives and relationships, in-
creasing water costs will result in less water being applied as more water
saving practices and technologies are utilized. The results from the
regional economic model did confirm this relationship. The cost of water was
varied from $3.00, which approximates the current cost, to §10.00 per
acre foot (1.233 x 103 m3) to determine water use, level of scheduling
adoption and return flows (Table 27). Estimated annual water use decreased
from 216,865 acre feet (267,395 x 103 m3) under the present schedule to
135,635 acre feet (167,238 x 103 m3) (37.5 percent) at a $10.00 cost.
The decreased water use was primarily the result of the scheduling alter-
natives available for each crop. At $10.00, 77 percent of the District
acreage is scheduled.
Return flows were reduced accordingly. Deep percolation was es-
timated at 12,076 acre feet (14,890 x 103 m3) when the water cost was $10.00
per acre foot (1.233 x 103 m3). This represents a 75.2 percent reduc-
tion and compares to the results obtained for the required scheduling
policy. Surface runoff was also reduced by amounts similar to those
achieved under a mandatory scheduling policy.
In summary, changing water costs could affect the amount of irrigation
scheduling in a district. Sufficient water savings are realized by sched-
uling to justify the service on purely economic criteria if water costs
are sufficiently high. However, water prices in the west are traditionally
much lower than the $10.00 per acre foot (1.233 x 103 m3) hypothesized
in this analysis. Water prices are usually established by water agencies
to allocate diversion and distribution costs to individual water customers
without considering the value of water in alternative uses or the social
costs of return flows. The present price structure, based primarily on
diversion costs, will generally result in more diversions, greater agricul-
tural production, increased net farm incomes and larger return flows in a
specific area than would occur under higher water prices. Markets for the
transfer of water rights and use would establish an opportunity cost of
water. However, markets for water do not generally exist.
The objectives of Section 208 of Public Law 92-500 are to decrease the
levels of nonpoint sources of pollution by requiring the specifi-
cation of methods to control externalities from agricultural and silvicultural
operations. These controls will be a set of "best management practices" (BMP)
applied to achieve the water quality goals of PL 92-500. The BMP being
considered by the agencies conducting Section 208 analysis are specific
soil and water use management techniques and physical treatement struc-
tures. Charging water prices to achieve different use patterns and/or
environmental results have not been considered. The agency's concern with
identifying the physical pollution effects of changing irrigation prac-
tices and ignoring the possibilities of economic incentives is under-
standable. Many of the agencies do not favor pricing policies as pol-
lution control alternatives because they are politically undesirable and
the income and equity effects are unknown. However, adjusting irrigation
water costs to account for the social costs imposed by return flow disposal
has been suggested before (Horner and English, 1976). Results from this
study indicate that sufficient correlation exists between return flows and
water use to price irrigation water to achieve desired environmental
results.
104
-------
TABLE 27. ESTIMATED AVERAGE ANNUAL IRRIGATION WATER USE, SCHEDULING
ACTIVITY. RETURN FLOWS, SEDIMENT LOSS AND SALT LOAD FOR
ALTERNATIVE WATER COSTS, A AND B DISTRICT*
O
l-n
Water
Cost
(S/AF)
($/1.233 x 103 m3)
Present Schedule
3.00
5.00
10.00
Acres
Scheduled**
(1,000 Acres)
Not Scheduled
34.912
55.874
50.164
Water
Use
216.865
191.327
154.533
135.634
Deep
Percolation
(1,000 AF)
48.754
36.827
17.830
12.076
Surface
Runoff
42.262
37.390
31.618
24.647
Sediment
Loss
Salt
Load
(1,000 Tons)
(907.2 Metric Ton)
46.381
40.243
34.717
30.854
48.375
41.413
32.448
24.128
*Scheduling is provided at zero cost.
**Alfalfa acreage would be irrigated under the scheduling regime at low water cost but revert to a low water
application rate at higher cost (Table Appendix A-2).
-------
APPENDIX A
TABLE A-l. CROP ACREAGE, RETURNS, WATER USE AND IRRIGATION RETURN FLOWS
RESULTING FROM SCHEDULED IRRIGATION AT VARYING SCHEDULING COSTS
Year
1973
1974
1975
Policy
No Scheduling
Scheduling Cost:
$0.00/A
Scheduling Cost:
$5.00/A
Scheduling
Required
No Scheduling
Scheduling Cost:
$0.00/A
Scheduling Cost:
$5.00/A
Scheduling
Required
No Scheduling
Scheduling Cost:
$0.00/A
Scheduling Cost:
$5.00/A
Scheduling
Required
Total
Crop
Acres
(1,000
(404.
64.507
64.507
64.507
64.507
65.314
65.314
65.314
65.314
65.575
65.575
65.575
65.575
No. of
Sched-
uled
Acres
Acres)
7 ha)
0.0
40.375
10.358
64.507
0.0
49.987
19.018
65.314
0.0
54.333
23.329
65.575
Returns
To Land
Mgmt.
& Risk
Irri-
gation
Water
Used
(Millions)
12.898
13.242
13.181
13.184
17.488
17.957
17.892
17.745
11.967
12.353
12.294
12.241
219.026
188.232
212.013
146.720
218.135
160.056
205.353
142.994
213.435
154.846
197.868
142.326
Surface
Runoff
(1,000
(1,233
42.533
36.574
40.900
29.982
43.003
33.161
40.898
29.303
41.251
31.393
38.976
28.563
Deep
Perco-
lation
Acre Feet)
x 103 m3)
47.786
33.165
43.015
11.525
50.439
21.249
42.482
10.980
48.037
18.840
38.596
11.304
Sedi-
ment
Loss
(1,000
(907 Metric
44.280
36.323
42.647
29.630
47.762
37.760
46.833
29.821
47.174
37.178
46.701
31.357
Total
Dis-
solved
Solids
Tons)
Tons)
47.840
39.327
45.298
28.984
49.241
34.620
44.850
28.229
48.043
33.098
42.779
28.410
Labor
Use
(1,000
hours)
120.677
104.781
118.521
87.226
118.257
92.619
111.720
83.452
122.683
95.476
113.801
88.750
-------
TABLE A-2. CROP ACREAGE, RETURNS, WATER USE AND IRRIGATION RETURN FLOWS
RESULTING FROM SCHEDULED IRRIGATION AT VARYING WATER COSTS
Year
1973
1974
1975
Policy
No Scheduling
Water Cost:
S3.00/AF
Water Cost:
S5.00/AF
Water Cost:
S10.00/AF
No Scheduling
Water Cost:
$3.00/AF
Water Cost:
$5.00/AF
Water Cost:
$10.00/AF
No Scheduling
Water Cost:
$3.00/AF
Water Cost:
$5.00/AF
Water Cost:
$10.00/AF
Total
Crop
Acres
(1,000
(404
64.507
64.507
64.507
64.507
65.314
65.314
65.314
65.314
65.575
65.575
65.575
65.575
No. of
Sched-
uled
Acres
Acres)
.7 ha)
0.0
40.373
59.358
63.501
0.0
26.068
44.365
39.130
0.0
38.294
63.900
47.861
Returns
To Land
Mgmt.
& Risk
Irri-
gation
Water
Used
(Millions)
12.898
14.038
13.868
13.826
17.488
18.558
18.441
18.149
11.967
13.158
12.989
12.809
219.026
188.232
152.540
148.148
218.135
200.751
166.353
132.014
213.435
184.999
144.705
126.741
Surface
Runoff
— (1,000
(1,233
42.533
36.574
31.274
30.221
43.003
39.726
34.618
22.485
41.251
35.870
28.961
21.236
Deep
Perco-
lation
Acre Feet)
x 103 m3)
47.786
33.165
15.034
12.407
50.439
43.159
25.685
14.017
48,037
34.157
12.772
9.805
Sedi-
ment
Loss
(1,000
(907 Metric
44.280
36.323
32.260
30.023
47.762
43.795
39.880
31.601
47.174
40.610
32.012
30.937
Total
Dis-
solved
Solids
Tons)
Tons)
47.840
39.327
31.144
29.450
49.241
44.901
37.015
22.122
48.043
40.011
29.185
20.813
Labor
Use
(1,000
hours)
120.677
104.781
90.353
87.991
118.257
106.693
92.788
92.478
122.683
107.666
90.023
96.278
-------
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
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detach, or copy this cover, and return to the address in the
upper left-hand corner
EPA-600/2-80-063
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