&EPA
United States
Environmental Protection
Agency
Robert S. Kerr Environmental Research EPA-600/2-79-149
Laboratory August 1979
Ada OK 74820
Research and Development
Potential Effects of
Irrigation
Practices on Crop
Yields in Grand
Valley
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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-
vironments 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-600/2-79-149
August 1979
POTENTIAL EFFECTS OF IRRIGATION PRACTICES
ON CROP YIELDS IN GRAND VALLEY
by
Gaylord V. Skogerboe
J.W. Hugh Barrett
Berry J. Treat
David B. McWhorter
Agricultural and Chemical Engineering Department
Colorado State University
Fort Collins, Colorado 80523
Grant No. S-800687
Project Officer
James P. Law, Jr.
Source Management Branch
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
ROBERT S. KERR ENVIRONMENTAL 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 commerical products constitute endorsement or
recommendation of use.
11
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FOREWORD
The Environmental Protection Agency was established to
coordinate administration of the major Federal programs designed
to protect the quality of our environment.
An important part of the Agency's effort involves the
search for information about environmental problems, management
techniques and new technologies through which optimum use of the
Nation's land and water resources can be assured and the threat
pollution poses to the welfare of the American people can be
minimized.
EPA's Office of Research and Development conducts this
search through a nationwide network of research facilities.
As one of these facilities, the Robert S. Kerr Environmental
Research Laboratory is responsible for the management of programs
to: (a) investigate the nature, transport, fate and management
of pollutants in groundwater; (b) develop and demonstrate methods
for treating wastewaters with soil and other natural systems;
(c) develop and demonstrate pollution control technologies for
irrigation return flows; (d) develop and demonstrate pollution
control technologies for animal production wastes; (e) develop
and demonstrate technologies to prevent, control or abate pollu-
tion from the petroleum refining and petrochemical industries;
and (f) develop and demonstrate technologies to manage pollution
resulting from combinations of industrial wastewaters or
industrial/municipal wastewaters .
This report contributes to the knowledge essential if the
EPA is to meet the requirements of environmental laws that it
establish and enforce pollution control standards which are
reasonable, cost effective and provide adequate protection for
the American public.
C,.
William C. Galegar
Director
Robert S. Kerr Environmental
Research Laboratory
111
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PREFACE
This report is the second in a series of two reports
resulting from U.S. Environmental Protection Agency Grant No.
S-800687, "Irrigation Practices, Return Flow Salinity and Crop
Yields." This report focuses upon the impact of various irri-
gation practices in determining crop yields, with particular
emphasis on corn and wheat. The first report, "Irrigation
Practices and Return Flow Salinity in Grand Valley" focuses
upon the prediction of subsurface irrigation return flow salinity.
These reports have been used as input to another research project
conducted in Grand Valley and largely funded by the U.S. Environ-
mental Protection Agency under Grant No. S-802985, "Implementa-
tion of Agricultural Salinity Control Technology in Grand Valley."
Three reports have been produced under Grant No. S-802985.
The first report, "Implementation of Agricultural Salinity Con-
trol Technology in Grand Valley," describes the design, construc-
tion and operation of a variety of salinity control technologies
implemented on farmers' fields. The second report, "Evaluation
of Irrigation Methods for Salinity Control in Grand Valley," is
concerned with the evaluation of furrow, border, sprinkler and
trickle irrigation as individual salinity control alternatives.
The third report of this series, "'Best Management Practices'
for Salinity Control in Grand Valley," develops the methodology
for determining the cost-effectiveness of individual salinity
control measures, as well as a complete package of salinity
control measures that should be implemented in the Grand Valley.
IV
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ABSTRACT
An analysis has been undertaken to determine the
economically optimal seasonal depth of irrigation water to apply
under conditions of both limited and plentiful water supply.
The objective was to determine if general guidelines having
practical utility could be postulated for all water supply
situations. An extensive range of literature pertaining to the
relationship between crop yield and the amount of water applied
has been reviewed and differences suggested by various authors
have been resolved. In addition, 32 plots of corn and 10 plots
of wheat were grown under different irrigation regimes in the
Grand Valley of Colorado to supplement the results of other
researchers and to provide further insight into the effects of
stress at different stages of plant growth.
There is an economically optimal depth of seasonal
irrigation water to apply which is not particularly sensitive
to irrigation efficiency or to the price of the inputs or the
returns. The methodology shows how the correct depth of appli-
cation could theoretically be obtained with more precision, but
the conclusion is drawn that such precision is unrealistic. The
answer is given within the bounds of the accuracy of application
for the given irrigation method. The results are extended to
conditions where irrigation provides only a supplementary portion
of the crop water supply, and to include a range of crops within
the enterprise. In addition, management practices which allow
the most effective use of the available water supply are
discussed.
The results of the field experiments on corn and wheat show
that irrigation can be terminated sooner than is the common
practice in Grand Valley, which will result in benefits to
farmers in increased crop yields and to downstream water users
because of reduced saline return flows reaching the Colorado
River.
This report was submitted in fulfillment of Grant No.
S-800687 by Colorado State University under the sponsorship of
the U.S. Environmental Protection Agency. This report covers
the period of February 18, 1974 to June 17, 1977, and was
completed as of August 31, 1978.
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CONTENTS
Foreword .........................
Preface .......................... iv
Abstract ......................... v
Figures ... ....................... vin
Tables .......................... xi
Acknowledgments ...................... xiii
1. Introduction ................... 1
2. Conclusions .............. ..... 6
3. Recommendations ................. 12
4. Crop Response to Irrigation Regime ........ 14
5. Experimental Design ............... 41
6. Field Operations ................. 56
7. Evapotranspiration ................ 63
8. Crop Yields and Water Use ............ 73
9. Fertilizer Use Efficiency ............ 104
10. Impact of Crop Production Functions Upon
Allocation and Use of Irrigated Water ..... 114
11. Impact of Crop Production Functions Upon
Water Management Practices ........... 148
References ................. « ......
Appendices .......... .............. 163
VI1
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FIGURES
Number Page
1 Yield versus transpiration of plants grown in
containers with soil at different moisture
contents 17
2 Relation of cumulative dry matter yield of grain
sorghum to evapotranspiration and transpiration . 20
3 Relation of dry matter and grain yield of corn
to seasonal evapotranspiration . 22
4 Schematic of the experimental layout adopted by
the Consortium for International Development ... 23
5 Corn dry matter yields from several irrigation
timing treatments, related to seasonal evapo-
transpiration depths, Fort Collins, 1974 24
6 Relationship of soil-water depletion in the 0 to
120 cm depth to relative yield 27
7 Relations between the Y versus ET and Y versus Irr
functions, both set within Y versus FWS functional
context which acknowledges and quantifies contri-
butions of stored water and rainfall during
season 31
8 Variation in relative growth with available mois-
ture depletion for sandy, loam and clay soils . . 33
9 Location map of the project area 42
10 Map of the Matchett Farm fields used for the study
area 43
11 Location of plots in Field I 45
12 Location of plots in Field II 46
13 Location of plots in Field III 47
14 Plot cross-section with drain details 48
Vlll
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Number Page
15 Depth to shale bedrock from ground surface, in
meters 50
16 Irrigation treatments for corn 52
17 Watering of corn plots using gated pipe 58
18 Measurement of water applied to the plots using a
V-notch weir 58
19 Measurement of surface runoff from the plots using
a Cutthroat flume 59
20 Measurement of soil moisture using a neutron meter . 59
21 Harvesting corn for dry matter yield 60
22 Weighing corn samples for dry matter yield 60
23 Combine used for harvesting corn grain samples ... 62
24 Combine used for harvesting wheat samples 62
25 Computed and measured water use 66
26 Variation of crop coefficient with time •• "70
27 Variation of grain yield of corn with seasonal
evapotranspiration 74
28 Variation of dry matter yield of corn with seasonal
evapotranspiration 75
29 Grain yield in relation to the percent nitrogen in
the corn leaves 79
30 Variation in corn crop resulting from different
irrigation regimes 83
31 Difference in plant development between well-
watered corn plot and stressed plot 83
32 Corn grain yield versus ET: average for each
treatment 84
33 Corn dry matter yield versus ET: average for each
treatment 85
34 The effects of irrigation treatments on grain yield. 89
IX
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Number Page
35 The effects of irrigation treatments on dry matter
yield 94
36 Relationship between dry matter yield and grain
yield for corn 96
37 Water use efficiency of corn: dry matter versus
grain 97
38 Relationship between grain yield and ET and between
grain yield and crop water supply, for corn . . 100
39 Relationship between dry matter yield and ET and
between dry matter yield and crop water supply,
for corn 101
40 Variation of grain yield of wheat with seasonal
evapotranspiration 102
41 Determining optimal depth of irrigation water to
apply where water is plentiful 132
42 Influence of production function slope on optimal
depth of irrigation application 135
43 Production functions for corn at different irriga-
tion application efficiencies 139
44 Variation in returns and costs with depth of irri-
gation water applied 140
45 Determining the optimal depth of irrigation water
to apply to each crop in a multiple crop
enterprise 146
E-l Corn grain yield versus ET: Replication I .... 174
E-2 Corn grain yield versus ET: Replication II ... 175
E-3 Corn grain yield versus ET: Replication III . . . 176
E-4 Corn grain yield versus ET: Replication IV ... 177
E-5 Corn dry matter yield versus ET: Replication I . 178
E-6 Corn dry matter yield versus ET: Replication II . 179
E-7 Corn dry matter yield versus ET: Replication III. 180
E-8 Corn dry matter yield versus ET: Replication IV . 181
x
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TABLES
Number Page
1 Fertilizer Added to Field II, 1976 54
2 Comparison of Potential Evapotranspiration Esti-
mates and Evaporation Data 67
3 Computation of ET for Well-Watered Corn Crop .... 71
4 Soil Analysis from Which Fertilizer Recommendations
were Based 77
5 Analysis of Variance of Percent Total Nitrogen in
Corn Leaves 78
6 pH and the Electrical Conductivity of Composite
Soil Samples from Experimental Plots 80
7 An Analysis of Variance of the Electrical Conducti-
vity for Composite Soil Samples Taken from the
Various Irrigation Treatments 82
8 The Effect of Irrigation Treatment on the Yield
of Grain 87
9 Analysis of Variance for Yield of Grain 88
10 The Effect of Irrigation Treatment on Total Dry
Matter Yield 92
11 Analysis of Variance for Yield of Dry Matter .... 93
12 Efficiency of Irrigation Water Applied and of Total
Measured Water Use in Terms of Yield Per Unit
of Water 98
13 Leachate Volumes Collected in Vacuum Extractors
from Plots 22 and 23 During 1976 106
14 Nitrate Concentration in Leachate for Plots 22 and
23 107
XI
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Number Page
15 Total NO3 in Leachate from Plots 22 and 23 .... 108
16 Nitrate Distribution in Plots 22 and 23 in Fall
of 1976 .................... 109
17 Percent Nitrogen in Leaves of Corn Plants .... 110
18 Nitrogen Uptake by Corn ............. 112
19 Plot 22 Summary Nitrogen Balance ......... 112
20 Plot 23 Summary Nitrogen Balance ...... ... 113
A-l Daily Climatic Data, Matchett Farm, 1976 (Month:
April) ..................... 163
A- 2 Daily Climatic Data, Matchett Farm, 1976 (Month:
May) ...................... 164
A-3 Daily Climatic Data, Matchett Farm, 1976 (Month:
June) ...................... 165
A- 4 Daily Climatic Data, Matchett Farm, 1976 (Month:
July) ...................... 166
A- 5 Daily Climatic Data, Matchett Farm, 1976 (Month:
August) ........... .......... 167
A-6 Daily Climatic Data, Matchett Farm, 1976 (Month:
September) ...................
A- 7 Daily Climatic Data, Matchett Farm, 1976 (Month:
October)
A- 8 Daily Climatic Data, Matchett Farm, 1976 (Month:
November) .................... 170
B-l Matchett Farm Evapotranspiration Parameters, 1976. 171
C-l Evapotranspiration Per Growth Stage of Corn . . . 172
D-l Corn Yields and ET of Each Plot ......... 173
F-l Wheat Yields and ET of Each Plot ......... 182
XII
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ACKNOWLEDGMENTS
The authors are deeply indebted to the many individuals who
diligently and meticulously attended to the field work and
laboratory analyses. In particular, we appreciate the continued,
extensive efforts of Mr. George Bargsten who was responsible for
field operations, Ms. Barbara Mancuso who was in charge of the
laboratory, and Mr. John Bargsten who ably assisted in the
laboratory.
The efforts by the Project Officer, Dr. James P. Law, Jr.,
in cooperatively facilitating the construction activities, and
then later the research program, by his willingness to meet with
the Principal Investigator whenever necessary and to rapidly
respond to requests certainly contributed to the successful
pursuit and conclusion of this research and demonstration
project.
Much of the research reported herein resulted from the
efforts of J.W. Hugh Barrett while pursuing a Ph.D. degree.
Dr. Wynn R. Walker is to be thanked for the helpful discussions
at the inception and during the course of the study and Dr.
Robert Danielson for his review of this work and his subsequent
suggestions. In addition, Dr. Danielson made available material
related to his own research which was of considerable benefit.
Special thanks are due to Dr. David Karmeli of the CSU Depart-
ment of Agricultural and Chemical Engineering and the Technion
Israel far discussions which gave the theoretical concepts of
this study their impetus, and to Dr. Ed Sparling for his
assistance with economic principles.
In preparing the report drafts and final copy, we sincerely
appreciate the efforts of Ms. Susan Kuehl and Ms. Sue Eastman
for the typing and Ms. Hanae Akari for the drafting.
Gaylord V. Skogerboe
J.W. Hugh Barrett
Berry j. Treat
David B. McWhorter
Xlll
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SECTION 1
INTRODUCTION
BACKGROUND
From the time that man first developed the art of
artificially applying water to the land he has been faced with
the problem of how to best allocate the available water supply
to his crops. Before the advent of river regulation his
alternatives were limited, as in many areas he had to take the
water in the spring when it was available, spread it over the
area he could command and hope that the flow would be sustained
sufficiently long to bring the crop to the stage of harvest.
But what of that low flow late in the season? Should it
be spread to all of the land area being cropped, or should it be
restricted to a smaller area from which maximum yields could
be obtained? Even with the advent of river regulation, in which
the flow can be adjusted to meet the fluctuating demands of the
crops, should an attempt be made to irrigate as much land as
possible with the water allocated to irrigation, or should peak
yield be striven for on a smaller land area?
In some areas, the question has been answered (but not
solved) by allocating a water supply which is sufficient to
fully satisfy the crop needs of the given irrigated area. Often,
in fact, the allocation is greatly in excess of the requirements
of the crops (i.e., Grand Valley). Even in this case, though,
the application of water will have an associated cost for water
delivery, as well as environmental detriments, and the question
of the optimal depth of water application will still exist.
The question takes on perhaps greater significance in
situations where the quantity of water available for irrigation
is less than adequate to supply the potential crop requirements
over the available land area. This is a fairly common case and
may be due to a variety of causes in addition to inadequate or
unregulated river flows. For example, the availability of
groundwater has induced many farmers to irrigate until the point
has been reached in many regions where the water is being with-
drawn at a rate faster than it is being replenished. The
realization that the groundwater supply is finite, coupled with
the high cost of pumping from an aquifer with a declining
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phreatic level, has caused an economic, and in some areas, legal
limit to be placed on the quantity able to be withdrawn. In
many areas of the world, legal volumetric limits are also ex-
tended to surface water supplies.
Similarly, farmers irrigating from on-farm reservoirs, in
which intermittent runoff is captured, usually have available
to them a supply less than adequate to provide full crop water
requirements over the irrigable land area. Irrigation based
on the uncertainty of supply often associated with on-farm
water conservation must make the best possible use of the avail-
able resource. Any water carryover from one season to the next
reduces the risk of failure in the ensuing season.
Some irrigation districts operate a water market in which
farmers may rent or lease their excess water to those requiring
additional supplies. If the irrigator has the opportunity to
rent or lease the excess water he must decide to what level his
irrigation should be restricted. A farmer could conceivably
increase his economic return by properly managing a smaller
volume of water and disposing of the excess so saved.
In recent years there has been a growing concern with
water quality degradation resulting from irrigated agriculture.
The solutions to this problem have been identified as improved
water management practices. However, improving the present
practices of allocating and using water to achieve high levels
of irrigation water management requires a fundamental knowledge
of crop yield-water use functions.
In addition to the physical and economic reasons outlined
above, social and political factors may also intrude to cause
the available water supply to be spread over a larger area than
that which would allow total satisfaction of crop needs. These
may not necessarily include the host of other environmental,
social and economic causes which compete for the water that was
once reserved almost exclusively for agriculture.
Those irrigation planners who have considered the problem
of optimal depth of irrigation application are divided on the
answer. Many would appear to agree with Stewart, et al. (1973)
who state in the case where water is limited in relation to the
available land area, that:
the optimal seasonal (irrigation) depth for profit
maximization will be one unit (or as few units as
practicable) greater than (irrigation) at the economic
break-even point.
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On the other hand, Hillel (1972) feels that:
Traditionally, the great fallacy in water management
has been the tendency to save water per unit of land
area, in order to "green up" more land. Some of the
agricultural planners in Israel, as well as in other
arid countries, have fallen prey to this fallacy. We
must remember that our basic aim is not to save water
but to increase production efficiency by optimizing
the water supply (and other environmental variables)
so as to maximize plant response. The best chance
of increasing production efficiency by water manage-
ment is to obviate water stress and prevent water
from becoming a limiting factor in plant growth.
PROJECT OBJECTIVES
A total of eight objectives were outlined for this research
project. They are as follows:
1. Evaluate the effects of various irrigation practices
on the amount and chemical quality of return flows.
2. Evaluate the effects of various irrigation practices
on crop yields and fertilizer requirements.
3. Demonstrate that improved farm management of irri-
gation water can reduce the mineral content of
return flows.
4. Demonstrate that improving the chemical quality of
irrigation return flows through better farm irri-
gation practices is profitable due to increased
crop yields and reduced fertilizer expense.
5. Provide a better understanding of the manner in
which water quality degradation takes place as
a result of irrigation.
6. Develop recommendations regarding irrigation systems,
methods, and practices which will minimize the
chemical quality of return flows while maintaining
a good crop environment and maximum benefits from
the consumed water.
7. Develop procedures for projecting the findings of
this study to basinwide evaluations.
8. Provide useful information for future salinity
studies concerned with farm management.
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An accompanying report, "Irrigation Practices and Return
Flow Salinity in Grand Valley" addresses the objectives 1, 3, 5,
7 and 8. This particular report addresses objectives 2, 4 and
6, with particular emphasis upon the relations between irrigation
practices and crop yields, and only limited emphasis on fertility,
Objective 6 is also covered extensively in a companion project
report, "Evaluation of Irrigation Methods for Salinity Control
in Grand Valley." All of these reports have been delineated to
serve the needs for the final report in this series, "'Best
Management Practices' for Salinity Control in Grand Valley."
The objectives of this study were expanded to determine
the correct seasonal depth of irrigation water to apply under
any water supply situation. In the case where the water supply
is limited relative to the available land area, the determi-
nation of the optimal depth of application will determine the
area able to be commanded by the water supply. In the case
where water is plentiful relative to the available land area,
the determination of the optimal depth of application will
determine the quantity of water that must be supplied. The
objective is to develop an answer that has universal rather
than site-specific application and to show the impact of ir-
rigation methods and management practices on the interrelation-
ship between the water supply, land area and profits.
APPROACH TO STUDY
The optimal allocation of irrigation water will obviously
depend on the relationship between yield and the crop's water
supply. Data on this relationship have been collected since
the late 19th century and some of the most comprehensive and
revealing studies are reviewed in Section 4. Only in recent
years have the equipment and techniques become available to
enable yield to be related to evapotranspiration under field
conditions. An endeavor has been made to review the available
literature on this subject.
As the body of knowledge is not large and as there is
difficulty in drawing common conclusions from the published
reports, an experiment was undertaken with hybrid corn (Zea
mays L.) and winter wheat in order to partially fill the infor-
mational gap and to provide firsthand insights into the
reaction of crops to stress at different stages of growth. This
experiment was carried out near Grand Junction in the Grand
Valley of western Colorado.
Using the Grand Valley results in conjunction with the
results of other researchers, a method has been developed to
determine the economically optimal seasonal depth of water
application under conditions of both limited and plentiful water
supply. Every effort has been made to arrive at a general
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result having universal application, rather than to develop a
complex computational procedure of limited and specific ap-
plication. A basic hypothesis has been that if the depth of
application can be obtained with an accuracy which is within
the limits of accuracy of application of the given irrigation
method, then this will be of far greater value than a complex
computer model that may obtain the answer with a little more
precision, but which may, in fact, be spurned in practice be-
cause of its complexity (although this is not to deny the value
of such models in the appropriate solution). In addition, the
results obtained by such a model would only be as good as the
parameters and constraints upon which it is based, which, in an
agricultural situation, are often difficult to model any better
than idealistically. The objective has been to see if a correct
answer exists that only depends on the relative magnitude of
the parameters rather than on absolute magnitudes.
As the optimal allocation of irrigation water depends on
the relationship between yield and water applied, factors
affecting the form of that relationship obviously will affect
the calculations of the optimal depth of allocation. Factors
which will influence the relationship include the degree of
dependence of the crop on irrigation, the management practices
under which the crop is grown, and the inherent limitations of
the irrigation system used to water the crop. Viewed from the
opposite perspective, an examination of the factors affecting
the crop yield-water use functions will allow an evaluation of
those factors in terms of their impact on farmer profitability,
return flow salinity, and downstream detriments.
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SECTION 2
CONCLUSIONS
This field study has capitalized on recent research results
of other investigators to substantiate the functional relation-
ship between water use and crop yields. This research has
focused upon the implications of this relationship in reducing
the salt load from the Grand Valley that is presently reaching
the Colorado River. Many of these conclusions are applicable to
all irrigated areas.
1, In this study, the crops were subjected to different
irrigation regimes and the yields of mature dry mat-
ter forage, and grain, as affected by the different
regimes, were compared. The timing of moisture defi-
cits has a significant effect on dry matter yields as
well as on grain yields. The result appears reason-
able when it is considered that the grain component
of many crops makes up a substantial portion of the
dry matter yield.
2. The corn crop was differentiated into three growth
stages after establishment, designated successively
the vegetative, pollination and grain-filling periods.
Stress was applied in one or more of these periods by
eliminating irrigation. The crop was harvested for
both grain and dry matter.
a. A notable effect was the severe depression
of yield caused by stress during the pol-
lination period. Any evapotranspiration (ET)
deficits occurring in this period alone
would appear to restrict the upper limit of
both grain and dry matter yields, irrespec-
tive of subsequent irrigations.
b. If deficits have also occurred in the
vegetative period, the crop may be somewhat
conditioned to stress and the detrimental
effect of the pollination period stress may
be lessened in terms of water use efficiency.
In this case, a late irrigation is likely
to elicit a small positive response.
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c. Where the crop has been well watered through
the first two growth stages, irrigation
during the grain filling period may be of
no benefit to yields and may even be detri-
mental, particularly to grain yields.
d. Maximum efficiency, in terms of grain
yield per unit of water used by the crop,
occurred when irrigated through the
vegetative and pollination stages of
development.
e. Forage yield results showed that the
vegetative stage was the more critical
period with respect to water deficits and
dry matter production. The highest return
on water use was 279 kg per cm, occurring
when the crop was irrigated only through
the vegetative stage of development.
f. Maximum yields of forage corn was obtained
by those treatments where the corn was
irrigated during the vegetative and later
growth stages. A substantial saving in
water can be achieved by the elimination
of irrigation during the maturation stage
of development (grain filling) and at the
same time, maintain yields of grain and
forage at a high level.
g. An important result which is not unique
to this study is that the maximum ET of a
crop does not necessarily correspond to
the maximum yield. This was found for
corn and wheat.
3. The wheat grown in this experiment was subjected to
different irrigation treatments only in the latter
stages of its development (from the late boot stage
onwards) and was harvested only for grain. The crop
was differentiated into two subsequent growth stages-
the anthesis period and the grain filling period.
a. Little response to irrigation in the grain
filling period occurred, irrespective of
earlier irrigations.
b. Irrigation during the anthesis period was of
considerable benefit, although stress during
the earlier shooting stage may even have
limited the effectiveness of this irrigation.
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4. To determine the economically optimal allocation
of irrigation water to a given crop, the relationship
between the yield of the crop and its use of the sup-
plied water must be known. Studies of this relation-
ship, particularly those considering the yield of
the reproductive organ of the crop, have generally
resulted in a curvilinear line of best fit being
drawn through a scatter of data.
5, More recent studies, including that undertaken
herein, indicate that this scatter of data largely
results from the time of occurrence of water defi-
cits in relation to the stage of growth.
a. Crops are far more sensitive to moisture
stress during some stages (i.e., polli-
nation in corn) than others.
b. If a crop is supplied a seasonal quantity
of water less than its potential require-
ments, exaggerated yield reduction could
occur if the deficit occurs during periods
of such sensitivity.
c. The scatter in data can be considerably
reduced, therefore, if deficits are so
timed that they cause the least yield
reduction for the given quantity of water
supplied.
6. If crop yields are plotted against evapotranspiration
(ET) rather than the quantity of water supplied, the
data will fall on a straight line, this line repre-
senting the upper bound of yield for a given quantity
of ET.
a. When the upper bound on yield is plotted
against the water supply available to the
crop,,a concave downwards function results.
b. The horizontal difference between the
linear function and the curvilinear
function is the amount of water supplied
but not used in the evapotranspiration
process, i.e., losses.
c. High water application efficiencies will
be associated with small losses, resulting
in a yield versus supplied water function
which will be close to linear.
8
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7. All of the conclusions drawn from this study are
based on functions representing the upper bound
of the yield-water use relationship, i.e., those
representing irrigation regimes in which any
deficits are sequenced to occur at the least
damaging times.
a. This premise is reasonable in that it
represents the ultimate goal of the
irrigation farmer.
b. The linear yield-water use (ET) function
may be thought of as the ideal, with
curvilinear relations diverging from the
linear function representing deviations
from the ideal.
c. The relative proximity of the field
production function to the ideal allows
an evaluation of irrigation management
practices and irrigation system
performance.
8. On heavy soils, such as encountered in Grand Valley,
irrigation can be halted before the crop has reached
physiological maturity, allowing the stored soil
moisture to carry the crop through to harvest, which
will:
a. Improve crop yields.
b. Allow the soil to be drier for harvest.
c. Allow better utilization of interseasonal
precipitation.
d. Retain more nutrients in the root zone,
particularly nitrogen, for use by
subsequent crops.
9. Although very efficient irrigation practices were
used in this research, the results based on vacuum
extractor data clearly showed that most of the
losses of nitrate fertilizer by deep percolation
occurred early in the irrigation season. These
fertilizer losses would have been more dramatic
if the usual irrigation practices employed by
farmers in Grand Valley had been used.
-------
10. The relationship between crop yields and water use
has formed the basis of the analysis to determine
the economically optimal seasonal depth of irrigation
water to apply. Both the analyses used and the re-
sults obtained will differ depending on whether water
is relatively scarce or relatively plentiful.
11. In the case where the quantity of water for irrigation
is limited relative to the available land area, the
correct seasonal depth of water to provide is that
which will satisfy the ET requirements of the crop,
plus a small margin for leaching salts from the root
zone, rather than spreading the limited water supply
over too much land.
a. For systems with very high application
efficiencies, such as 90 percent for trickle
irrigation, the correct depth of water appli-
cation may be obtained by dividing the ET
corresponding to the method of irrigation by
the efficiency.
b. For systems with low efficiencies, the problem
becomes more complex. An important considera-
tion is whether a change in the method of water
application would be appropriate, particularly
when the large quantity of irrigation return
flows resulting from an inefficient system re-
sults in significant water quality degradation.
12. In the case where the quantity of water available
is plentiful relative to the land area, the correct
irrigation policy is to apply a seasonal depth of
irrigation water which will allow close to maximum
yields to be attained. The shape of the yield
production function, which is dependent on the irri-
gation efficiency, will determine "how close."
a. For highly efficient irrigation, the
production function will be only slightly
nonlinear and the objective should be to
irrigate to achieve maximum yields.
b. For less efficient irrigation, the correct
depth of application for the farmer will
depend on the price ratio (ratio of mar-
ginal cost of water to marginal net income),
while the application depth will be considerably
less in those cases where the irrigation return
flows cause water quality degradation.
10
-------
13. The water allocation model ultimately depends on
the mathematical relationship between crop yield
and water use. Therein lies its inherent weakness,
a. To use yield versus water supply (or water
applied) functions destroys any uniqueness,
and hence predictive capability, of the
relationship.
b. The unique yield versus ET relationship
can be used, but the efficiency of appli-
cation for each area to which it is applied
must be known in order to determine the
optimal allocation.
11
-------
SECTION 3
RECOMMENDATIONS
The conclusions resulting from this particular research
effort have led to the following recommendations that should be
incorporated into an "action" salinity control program for
Grand Valley.
1. An awareness program should be undertaken to acquaint
irrigators with the advantages of terminating the
irrigation of corn and grain crops earlier than is
presently practiced in the Grand Valley. There are
benefits in both reduced salinity and increased crop
yields.
2. Improved agronomic practices should be given as much
consideration as the construction of physical improve-
ments when implementing a full-scale salinity control
program in Grand Valley. Farmers will be more recep-
tive to adopting improved agronomic practices at the
same time that physical improvements are constructed.
Improved agronomic practices can provide substantial
benefits to farmers, thereby facilitating also the
adoption of improved irrigation methods and practices,
which in turn will provide substantial benefits to
downstream water users because of reduced salinity
concentrations.
3. Improved agronomic practices should be incorporated
into the irrigation scheduling service to be provided
under the action salinity control program for Grand
Valley. An effective irrigation scheduling service
should use improved irrigation practices based upon
an evaluation of each field in the Valley.
4. Existing agronomic research from other locations in the
West should be reviewed in order to develop irrigation
guidelines for each of the major crops that take into
account the requirements for irrigation return flow
quality control.
12
-------
5. The economic advantages to farmers in adopting more
advanced irrigation methods, such as sprinkler or
trickle, should be documented in a style that is mean-
ingful to farmers. These irrigation methods have
definite advantages for reducing the salt loads reaching
the Colorado River, as well as increasing crop yields.
Salt loads will be reduced because of significant re-
ductions in deep percolation losses early in the season
and a smaller reduction late in the season as a result
of earlier termination of irrigation. Crop yields will
be increased as the result of increased fertilizer use
efficiency, a more favorable root-zone environment for
crop growth and earlier termination of irrigation.
These interrelations are becoming increasingly important
for farmers to understand.
13
-------
SECTION 4
CROP RESPONSE TO IRRIGATION REGIME
CROP 'YIELD-WATER USE FUNCTION
Crop yield-water use functions form the basis for decisions
regarding the allocation of irrigation water. An explanation
of the importance and uses of production functions has been
given by Minhas et al. (1974):
To study the question of economically optimal use of
water, we need to know the exact shape of the crop
response function to different quantities of water
used by the crop throughout its growth cycle. For
instance, consider a large reservoir system. The
problems of scheduling the operations of the system
include decisions on the timing of water releases
and the allocation of water among crops. The allo-
cation decisions are relevant also for the operation
of tube wells or run-of-the-river irrigation systems.
Unless we have the knowledge of the marginal producti-
vity of water allocated to each crop at different
stages of its growth, we cannot arrive at an optimal
set of decisions. This knowledge is required also
in determining the extent of the command area of an
irrigation system. A production function for each
crop, in which yield is related to dated inputs of
water, will provide such knowledge.
Crop production functions in this study are considered
particularly within the framework of on-farm allocation of a
limited supply of irrigation water; however, this allocation is
the starting point in deciding the allocation of water within
the overall system, to which the results are equally applicable.
Decisions on allocations may be among projects, as well as
among crops, soil types and locations within projects. The
decision could be between agriculture versus other uses. The
production functions will affect the design of water conveyance,
distribution and irrigation systems, since they should determine
the scheduling of water releases and consequent irrigations.
Production functions also allow the economic impact of water
shortages in irrigated agriculture to be assessed.
14
-------
Some of the earliest production functions were obtained by
researchers investigating the effects of precipitation and soil.
moisture on dryland crop yields. Cole (1938) studied the
relationship between annual precipitation and the yields of
spring wheat on the Great Plains. Taking1 272 data points from
14 research stations in the northern Great Plains over the
period 1906-1935, he obtained the linear regression equation:
yield = (precipitation-8.02)2.19 (1)
with a correlation coefficient of 0.74, where the yield was
measured in bushels per acre and the precipitation in inches
for the year ended 31st July. Cole recognized that it may have
been more satisfactory to use the precipitation from the actual
date of one harvest to the next, in order to more nearly repre-
sent that moisture available to the crop, but this would intro-
duce data not so readily available or readily determined. Using
31st July as the year end placed the data close to harvest and
allowed uniformity of data. When the yield and precipitation
of the 14 stations were averaged for each of the 30 years, Cole
obtained from the 30 data pairs the regression equation:
yield = precipitation-10.07)3.19 ....... (2)
with a correlation coefficient of 0.88.
Leggett (1959) related the yield of wheat in eastern
Washington dryland areas to available moisture and nitrogen for
the years 1953-1957. He obtained the regression equation:
yield = 5.8(SM + R) - 23.8 (3)
with a correlation coefficient of 0.87, where SM is the available
soil moisture in the spring and R is the rain which fell during
the growing season. A higher correlation coefficient (0.91)
between yield and total moisture was obtained for the experiments
conducted under annual cropping and a lower correlation coeffi-
cient (0.77) for those conducted on fallowed ground. Curvilinear
regression analysis of the data did not improve the relationship
between yield and total available moisture and therefore Leggett
assumed the relationship was linear over the range of moisture
and yield considered.
Attempts to develop production functions for irrigated
crops have been numerous, for the reasons mentioned at the
beginning of this section. Comparison of the production
functions obtained by different researchers is difficult as
different coordinates are often used. The ordinate is
15
-------
generally expressed as yield. In some cases relative yield is
used, where the yield is expressed as a percentage of the
maximum yield obtained at that location. The latter method may
allow some degree of transferability of production functions,
with the relative yield at one location multiplied by the maxi-
mum yield at another thereby giving (theoretically) the absolute
yield at the second location for the given quantity of water.
Many terms have been used for the abscissa, ranging from
transpiration to the amount of water applied. For comparitive
and useful purposes/ a common and reproducible term is obviously
required. Evapotranspiration would appear the most suitable as
it is usually computed or measured, although it may be dependent
on the method of water application. Using transpiration would
overcome this objective, but measurement under field conditions
is difficult. Using the amount of water applied as the abscissa
makes comparison of crop production functions difficult, as they
will then vary with the method of irrigation and the practices
adopted.
Different shapes of the function relating yield to water
use have been obtained by different researchers. The strongly
linear relationship between wheat grain yield and precipitation,
obtained by Cole (1938) and Leggett (1959), has been supported
by container and field experiments which have demonstrated for
many crops a linear relationship between yield and water use
until maximum yield is obtained. Perhaps more numerous, however,
are the field experiments showing that the relationship between
yield and applied water is concave downwards. In this instance,
the curve rises monotonically to a maximum value of yield and
then in some cases flattens to a plateau, while in other cases
the curve shows a decrease in yield with increasing water use.
Some of the more illustrative experiments and studies in
which crop yield-water use functions were obtained are reviewed
to show alternative forms of the function and to allow an
examination of the parameters involved. This includes both
linear and nonlinear functions. The review forms the basis for
the resolution of the form of the relationship, which is
presented in a subsection below.
Until the development of the neutron meter for rapid, non-
disturbing soil moisture measurement, accurate measurements of
crop evapotranspiration were practically limited to experiments
carried out in containers. This is still largely true for crop
transpiration measurements. One of the most comprehensive
studies of the dry matter yield-transpiration relationship was
undertaken by de Wit (1958), who studied a wide range of data
collected for common field crops grown in containers from which
evaporation was controlled or measured. The results of many of
the observations are presented in Figure 1. in the cases
where the relationship varied from linear, de Wit considered
this to be associated with poor aeration of the root system.
16
-------
50r
25
50r
25
I50r
100
50
-------
Explanation of Data Sources.
referenced in de Wit, 1958).
(Details in original publications,
a~j
graph k:
graph 1:
graph m:
graph n:
graphs o, p;
graphs q, r:
Data from Sohultz (1.9;/).
Availability of water between (V) 76-95%,
(A) 57-95%, (Q) 38-95%, (Q) 19-95%,
(O) 0-95% of the water holding capacity of
the container, a: serradella; b: mustard;
c: sorghum; d: hairy vetch; e: carrots;
f: oats; g: meadow foxtail; h: meadow fescue;
i: red clover; j: white clover.
Crop: peas. Data from Boonstra (1934).
Availability of water (V) 90, (A) 70, (Q) 50,
(Q) 30% of water holding capacity. Average
two varieties harvested around July 10, 1930.
Crop: oats. Data from Van der Paauw (1949) .
(A) wet and (Q) dry series.
Crop: corn. Data from Haynes (1948) .
(^) initially water only (plant died) ;
(Q) small portion of roots sparingly
irrigated (plant died) ;
irrigated field capacity at permanent
wilting perc. ;
(A) irrigated to permanent wilting perc. to
field capacity at 20 inches Hg pressure
at;
(V) water table 6 inches below soil surfaoe.
Crop: alfalfa. Data from Scofield
(O) infrequently irrigated;
(Q) frequently irrigated;
(O) sub irrigated.
(1945)
Crop.: oats. Data from Dillman (1931) .
(O) severe wilting during heading and
milking stage;
(Q) severe wilting during heading stage;
(O) regular supply of water.
o: Newell; p: Mandan.
Crop: corn. Data from Kiesselbach (1916) .
q: 1910. «>) 35, (Q) 45, (Q) 60, (V) 80
and (A) 100% of the water holding
capacity.
r: 1913. (Q) 50, (p) 70 and (A) 95% of the
water holding capacity.
Figure 1 (continued).
18
-------
To allow transferring or comparing results from different areas,
he proposed the relationship:
yDM
where yDM = total dry matter yield
T = total transpiration during growth
E = free water evaporation
o
The coefficient m varied for different crops, while the exponent
n was found to be about 1 for the Great Plains of the USA and
about 0 in the Netherlands. Although data were unavailable,
de wit hypothesized that there probably are regions where the
value of n is somewhere between 0 and 1.
Arkley (1963) developed a method of comparing directly
yield-transpiration functions obtained at diverse sites. In
doing so, he took data from many experiments in the literature
where plants were grown in containers with evaporation from the
soil prevented, for example, by sealing all openings in the
containers with wax. Arkley plotted the yield of dry matter
versus transpiration corrected for mean relative atmospheric
humidity during the period of most active growth (H) whereas
de Wit had used a correction based on free water evaporation.
Graphs of dry matter yield versus T/(100-H) were plotted for a
wide range of crops from sites around the world; the crops
included barley, oats, wheat, corn, millet, alfalfa, carrots
snapdragons and weeds. All the graphs showed a linear relation-
ship with a very high correlation coefficient. In most cases,
the line of best fit also passed through the origin, showing
that yield of dry matter was directly proportional to the
transpiration. Arkley concluded that deviation from a straight
line with increasing moisture revealed the effect of overirri-
gation, while reversal in the slope of the line suggested
waterlogging or poor aeration in the soil.
Hanks et al. (1969) plotted the cumulative dry matter
yields of wheat, oats, millet and grain sorghum obtained at the
United States Department of Agriculture (USDA) Central Plains
Field Station at Akron, Colorado, against evapotranspiration.
In all cases, a strong linear relation existed. For sorghum,
an estimate of evaporation from the soil (Es) was made and sub-
tracted from evapotranspiration to allow an estimate of
transpiration. The data showed a high linear correlation of
yield with transpiration (coefficient of determination of 0.97),
with the line of best fit passing through the origin. Hanks
et al. (1969) consider this to be a strong evidence that for
grain sorghum, dry matter production is directly proportional
to transpiration. The yield versus evapotranspiration and yield
versus transpiration relations are shown in Figure 2.
19
-------
NJ
O
8000
7000
6000
T 5000
o
xj
a>
,"4000
3000
2000
1000
h- V
• Lysimeters 1966
A Lysimeters Dry 1967
o Lysimeters Irr. 1967
Sampled Dry 1967
a Sampled Irr. 1967
Yield = 208ET-l640
0 r2 = 0.977
10
20 30
ET, cm
Yield versus evapotranspiration
40 50
8000
7000
6000
32
•2 4000
3000
2000
1000
Yield=254T(est)-l92
r2 = 0.970
Lysimeters 1966
A Lysimeters Dry 1967
o Lysimeters Irr. 1967
v Sampled Dry 1967.
o Sampled Irr. 1967
j_
b.
0 10 20 30 40 50
T(est) = ET-Es(est), cm
Yield versus transpiration
Figure 2. Relation of cumulative dry matter yield of grain sorghum to evapotranspiration
and transpiration (from Hanks, et al., 1969).
-------
A linear relationship between dry matter yield and
evapotranspiration was also obtained by Hillel and Guron (1973)
in a well-monitored 5-year experiment with corn in Israel. The
relationship between grain yield and evapotranspiration was also
found to be linear. Both relationships are shown in Figure 3.
A recent and comprehensive endeavor to develop methods for
predicting crop yields has been made by the Consortium for
International Development (1976) experimenting with corn at
Davis, California; Yuma, Arizona; Logan, Utah and Fort Collins,
Colorado. One of the objectives was to develop production
functions which reflect influences on yields of different water
supply levels and moisture tensions within the root zone at
different stages of crop growth. This was achieved by the
experimental design in which all irrigation after the establish-
ment of the crop was from a single sprinkler line parallel to
the rows through the center of the plots. The closely spaced
sprinkler heads threw a triangular water pattern such that
maximum water application occurred at the sprinkler line, taper-
ing evenly away with distance (see Figure 4.) The growing
season was divided into three time periods (growth stages) after
establishment of the crop, these periods being the vegetative
period, the pollination period and the maturation period. Con-
trol plots received water during all three growth stages. This
treatment was designated III, with each I representing irrigation
in the corresponding growth stage. Other plots had irrigation
halted for the duration of one or more growth stages. The
absence of irrigation during a particular stage was designated
by the symbol 0. For example, where the crop received water in
the vegetative and maturation period, but not in the pollination
period, the treatment was designated 101. This arrangement
allowed severe deficits to be imposed during different stages of
growth. in addition, different degrees of stress were imposed
within a given treatment, with those plants furthest from the
sprinkler line being most severely stressed.
For the control treatment, and generally within any given
treatment, the relationship between yield and ET, in most
cases, was strongly linear, for both dry matter and grain
production. The upper bound on all of the data was also linear.
As an example, a plot of the data relating yield to ET at Fort
Collins is shown in Figure 5. Here, the yield associated with
the highest values of ET can be seen to decline from those of
the same treatment with a lower ET, which if Arkley's (1963)
suggestion is followed, indicates poor aeration in the root
zone.
The extrapolation of the upper bound line intercepts the
abscissa to the right of the origin. This is in contrast to
the correlation with transpiration, discussed above, in which
the line passes through the origin. Hanks et al. (1969)
also extrapolated the linear regression line down to zero yield
21
-------
e
o
20
2
0)
^ 10
>s
k_
Q
10
o
(V
8
^
«/>
c
° 6
0)
2 2
*
O 1966
• 1967
O 1968
A 1969
D 1970
I
1
100 200 300 400 500
Seasonal Evapotranspiration, mm
600
Figure 3.
Relation of dry matter and grain yield of corn
to seasonal evapotranspiration (from Hillel
and Guron, 1973).
22
-------
Sprinkler Line
Different Treatments
Rain Gauges
Rows
Pattern of Water Distribution
Figure 4. Schematic of the experimental layout adopted
by the Consortium for International Development,
23
-------
Ft. Collins, 1974
Treatment Symbol
100 200 300 400 500
ETf mm
Figure 5. Corn dry matter yields from several irrigation
timing treatments, related to seasonal evapo-
transpiration depths, Fort Collins, 1974 (from
Consortium for International Development, 1976}
24
-------
to find for four experimental crops a positive value of ET
required before any yield was obtained. Evidently, with non-
forage crops, a considerable proportion of the water used is
required to bring the crop to the stage of reproduction. Unless
this basic amount of water is available, no yield will result
(Downey, 1972). Leggett (1959) found, for example, that approxi-
mately 100 mm of water are required to bring wheat to the
heading stage under dryland conditions in eastern Washington.
There appears to be a distinct intercept or threshold value of
evapotranspiration below which production of grain is negligible,
The threshold evapotranspiration value may be due largely to
the water loss caused by direct evaporation from the soil sur-
face as well as perhaps to the occurrence of some transpiration
in late season from the senescing plants after cessation of
growth. It is still possible, therefore, that production is
proportional to net transpiration during the main growing
season (Hillel and Guron, 1973).
One of the most comprehensive studies of crop yield-water
use relationships has been compiled by Shalhevet et al. (1976)
for a wide range of crops grown at a number of locations in
Israel over the period 1954-1971. Production functions are
presented in graphic and algebraic forms in terms of relative
yield and net or gross water application. The authors used
relative yield rather than absolute yield as a simple way of
presenting data from different locations and years in a uniform
manner. Net water application was the actual amount of water
added to the soil following an irrigation, rather than the
amount actually delivered. The authors used this parameter to
reduce variability due to application efficiency and soil
conditions. In all the experiments reported, irrigation effi-
ciency was 80-90 percent, and the authors felt that by correct-
ing for efficiency, the data obtained may also be applied to
conditions other than those of the experiments. A linear
regression was applied to the data of most field crops in the
range from zero to 95 percent relative yield. Good fits were
obtained for wheat, sorghum, grain and forage corn, cotton and
tomatoes, with coefficients of determination ranging from 0.70
to 0.97. Curvilinear functions were fitted to the results of
sugar beets, where the abscissa was net water application in the
spring, and to alfalfa, where the abscissa was gross water
application. Regression analysis gave indeterminate results
for orchard crops.
As mentioned earlier, results showing a nonlinear
relationship between yield and water use are probably more
numerous than linear relationships. For example, in an experi-
ment in which grain sorghum was grown in lysimeters, Howell and
Hiler (1975) found only a weak correlation between yield and
seasonal ET (linear correlation coefficient equal to 0.64). In
experiments conducted by Evans et al. (1960) in the Willamette
25
-------
Valley of Oregon, where yield of unhusked cobs of sweet corn
was plotted against consumptive use under four different moisture
treatments, the four points so obtained fall on a concave down-
ward curve in both years of the experiment. These results would
appear incompatible with the results reviewed up to this point,
except that the effect of the timing of the water deficits has
not been included. The importance of the timing of deficits,
including the effect on the results of Howell and Hiler (1975),
is discussed in the next section.
Musick and Dusek (1971) plotted seasonal water use against
yield in experiments with different water treatments conducted
during 1963-1965 at the USDA Southwestern Great Plains Research
Center at Bushland, Texas. From the scatter obtained, the
lower yielding treatments can be represented by a linear rela-
tionship. The higher yielding treatments indicate that under
conditions of good water management, the seasonal yield-water
use curve is a curvilinear diminishing return relationship within
the range of about 300 to 660 mm. The authors conclude that
the function is not an explicit relationship but may vary con-
siderably depending on various factors that affect both yields
and water use. As will subsequently be shown, one of those
factors relevant to their study may well be the amount of water
lost below the depth of soil moisture measurement, in this case
to 120 cm during the growing season and to 180 cm after planting
and after harvest.
The analysis was expanded by Musick et al. (1976) who took
the data collected by themselves and other researchers over the
period 1956 to 1971 at Bushland and plotted relative grain
yield against seasonal soil-water depletion from the 0 to 120 cm
soil depth, as shown in Figure 6. Data were collected for
grain sorghum, wheat and soybeans and a quadratic equation was
fitted to all scatter diagrams with a high degree of success
(coefficient of determination ranging from 0.57 to 0.99 for the
12 plots and being above 0.84 for 10 of them). In one case,
however, the fitted curve was concave upwards and in nearly all
cases a straight line would have fitted the data equally as
well up to the point where maximum yield was first obtained,
i.e., for the lowest amount of water depleted. Higher levels
of seasonal depletion were achieved by irrigating to maintain
a higher moisture content in the root zone and hence losses due
to percolation beyond the 120 cm depth would be expected to be
proportionally higher at the higher depletion levels.
In another series of experiments at Bushland and at the
Texas A & M North Plains Research Field at Etter, Shipley and
Regier (1975) and Shipley (1977) obtained curvilinear relation-
ships between yield and applied water for corn, grain sorghum
and wheat. Different yields were obtained for a given water
quality, depending on the stage of growth during which the water
was applied. By taking only the peak yield associated with a
26
-------
100
80
60
40
20
0
100
70
60
40
20
r-7470 kghflj
1956 Sorghum
'= 426-4l.8x-l.054x2,.
«D r* = .89
!» SE= ±16.2%?
ov>
7950 kg ho'
1958 Sorghum
y =-2765+ I86.8x-3.038x*
r* =.86
SE = ±II
i
100
80
,0 60
6s-
» 40
1 20
0V/
8500 kg ho
1963 Sorghum
y=-738+48.9x-0.7llx2
rz =.89
SE=±6.3%
_o
0>
cc
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
- 7360 kg ho'1 ^
« r* = .9l
/ SE = ±9
±9.8%
-8040 kg ha'1
1957 Sorghum
= -!362+93.0x-l.480x2
CD ri -. .99
? SE=±2.7% T
CD
&
1965 Sorghum
*y =-454+30.2 x-0.4!2x2
r* = .57
SE=±I0.6
1956 Wheat
y=-1667+l26.4x-2.264x*
r2 = .90
SE = ±I2.6%
=-791 + 54.3x-0.828 x*
•7660 kg ho
1964 Sorghum
y=-987+68.9x-l.096x2
rz = .94
SE=±5.2%
_l I 1 L-
vA
1971 Sorghum
y =-430+30.0x-0.429x*
rz -- .74
SE=±8.8%
_J I 1 L_
•
1956 Wheat
y s-434+24.0x-0.647x2
r4 = .85
SE=±6.9%
__] I 1 L-
1967 Wheat
= -l090+48.8x-l.42lx2
SE = ±6.6%
Figure 6.
'22 26 30 34 38 42 22 26 30 34 38 42
Total Soil Water 0-120 cm Depth, cm
Relationship of soil-water depletion in the 0 to
120 cm depth to relative yield (from Musick et
al., 1976).
27
-------
given depth of application, a quadratic expression was able to
be fitted to the results. This expression represented the
optimum yield function and was used in subsequent analysis.
TIMING OF DEFICITS
The major factor contributing to the scatter in the results
obtained by the many researchers is undoubtedly the timing of
water deficits. Numerous investigators have shown that a water
deficit occurring at one stage of growth will have a different
effect on yield as compared with a deficit occurring at another
stage. For the same amount of evapotranspiration, the yield
may be expected to differ. For example, Robins and Domingo
(1953) found that soil moisture depletion to the wilting per-
centage for one or two days during the tasseling or pollination
period of corn results in as much as a 22 percent reduction in
grain yield and periods of 6 to 8 days gave a yield reduction
of about 50 percent. Yield reductions due to the absence of
available water after the fertilization period appeared to be
related tov the maturity of the grain when the available water
was removed. Following maturity, the depletion of the available
soil moisture had no effect on yield. Denmead and Shaw (1960)
found that corn subjected to moisture stress at silking was the
most severely affected as far as grain yield was concerned.
Moisture stress in the vegetative stage (prior to silking)
reduced yield by 25 percent, moisture stress at silking reduced
yield by 50 percent and moisture stress in the ear stage (after
silking) reduced yield by 21 percent. Barnes and Woolley (1969)
found a two-eared variety of corn more tolerant to moisture
stress at pollination and blister kernel stages than a single-
eared variety.
Downey (1972) found that a constant soil moisture stress
tends to reduce the yield of nonforage crops almost as a linear
function of the severity of the stress. When differential stress
is applied, however, the effects are very much related to the
timing of deficits. Severe water stress in corn during female
meiosis (very early stage in the development of the grain),
although for only a short period (8 days), dramatically reduced
yield even though seasonal evapotranspiration was 90 percent of
that giving maximum yield. A period of water stress following
pollination and continuing until maturity also severely reduced
the effectiveness of water applied in other growth stages.
Yield was only about 50 percent of maximum even though ET was
90 percent of that giving maximum yield. On the other hand,
water stress during male meiosis (or while the crop was young)
increased water use efficiency. Downey concluded that if, of
necessity, water is to be restricted, then it would be most
desirable that it be restricted during the period of early
growth.
28
-------
From their work with grain sorghum, Howell and Hiler (1975)
also concluded that the timing of the occurrence of a water
deficit was more critical with regard to yield effects than the
magnitude of the deficit. If a water deficit must occur, they
suggest the bud through bloom period should be avoided and small
water deficits occurring in several periods are preferred to a
large deficit occurring in any single growth stage.
Similarly, Stewart et al. (1974) made a number of recom-
mendations for managing water in corn production based on three
years of research at Davis/ California:
1. If there is to be a mild seasonal ET deficit (to
10 percent), it is best imposed wholly during the
vegetative period. If that is not possible, the
latter part"of the grain period is nearly as
acceptable. Avoid any deficit in the pollination
period if there has been no deficit in the pre-
ceding vegetative period.
2. Moderate seasonal ET deficits (10-25 percent) must
be distributed through at least two growth periods
(one of which must be the vegetative period).
3. Severe seasonal ET deficits (25-50 percent) require
distribution through all three major growth periods.
These recommendations for grain sorghum and corn are in
general agreement with the conclusions of Salter and Goode (1967)
who reviewed a wide range of literature. In addition, Salter
and Goode have summarized research on the yield response to
water at different stages of development for a wide variety of
crops, ranging from cereal crops to orchards and from vegetable
crops to flowers.
A number of researchers have observed that the yield
response to a moisture deficit at a particular growth stage
may~not be a function of that growth stage alone, but may be
affected by the degree of stress in earlier growth stages.
There may be a tendency for stress imposed at any one stage to
harden the plant against damage from stress at a later stage as
far as grain yield is concerned (Denmead and Shaw, 1960). With
corn and tomatoes, moderate soil water stress before flowering
gave higher yields than did little or no soil water stress,
when the post-flowering pericid was one of moderate water stress
(Fischer and Hagan, 1965). Stewart et al. (1975) also found
for corn that where there had been an earlier ET deficit in the
vegetative period, the negative effect of a pollination period
deficit was greatly blunted. The earlier water stress reduced
plant size, and this appeared to "condition" the crop so that
a following pollination period deficit had less negative effect
on yield. The conditioning effect was not shown to operate on
grain sorghum.
29
-------
RESOLVING THE YIELD-WATER USE FUNCTIONAL RELATIONSHIP
In the literature reviewed above, a considerable amount of
evidence has accumulated to indicate that, up to the minimum
amount of ET producing the maximum yield, the relationship
between yield and ET is linear. The correlation appears to be
even higher when total dry matter is considered as compared to
grain yields. The scatter in results using grain yields may be
somewhat reduced when rainfall or other factors reduce stress
during critical periods. Where severe stress is deliberately
imposed during a critical growth stage, such as by Stewart et
al. (-1975) at Davis, a wider scatter may result.
However, two inconsistencies remain to be resolved: (a)
to explain the results of those researchers who obtained a
curvilinear relationship between yield and water use; and (b)
to show how a unique relationship between yield and ET can hold
when it is known that the same ET deficit can give different
yields if imposed at different times, or conversely, how the
same yield can be obtained for different values of ET.
The first problem is probably due to a combination of two
causes. Firstly, when water is applied in excess of the amount
required for maximum yield, "water use" and to some extent
evapotranspiration, increases while yield remains constant or
decreases. A decrease in yield is particularly apparent if
waterlogging reduces soil aeration (Downey, 1972). This,
coupled with the scatter of data due to the timing of deficits,
allows a curvilinear function to be fitted to the plotted data.
Secondly, in most cases, the abscissa is not evapotranspiration,
but rather applied water or some similar parameter. In this
case, the curvilinear nature of the function may be due to
water losses incurred between water applied (or supplied) and
the final use of some portion of that supply in evapotranspiration.
The difference between the two functions is well illustrated
in Figure 7, in which the curved line represents the relation-
ship between yield and the seasonal depth of irrigation water
applied, or yield and field water supply (which includes avail-
able soil water,at planting plus rainfall) and the straight line
represents the relationship between yield and ET. The difference
between the straight line and the curved line, shown as "nonET"
on the figure, represents the xvater applied (or supplied) that
is not consumed, i.e., losses. The convexity of the applied
water function illustrates that these losses increase percentage-
wise as the point of fully satisfying ET demands is approached.
The losses could be due to evaporation, surface runoff or deep
percolation below the root zone. When Hillel and Guron (1973)
took particular care to calculate the drainage component of the
field water balance, the relationship between grain yield of
corn and seasonal evapotranspiration was strongly linear.
30
-------
'J 1 1 000
| 10000
| 9000
gS 8000
£ 7000
^ 6000
| 5000
~ 4000
•o
• 3000
> 2000
c
s 1000
o
°c
-
-
-
-
-
3-(ET from ASWP + R)-*
-
-
-
iiiii
-------
The problem of developing a unique relationship between
yield and evapotranspiration has received considerable attention
from Stewart and associates at Davis. They recognized that
irrigation programming registers a dual effect on yield (Stewart
and Hagan, 1973). The first effect is inevitable, the second is
manageable. The primary effect is that of water shortage, per
se. Thus, any seasonal ET deficit is inevitably associated with
some minimum fractional reduction in yield below maximum. A
secondary reduction in yield may result from the timing of the
ET deficits, with those occurring during more sensitive or
"critical" growth stages of the crop in question causing a
relatively larger decrease in yield. Such losses are avoidable
through informed water management, which has the effect of
orchestrating the sequence of ET deficits so that yield loss is
minimized (Stewart et al., 1976). The Davis experiments have
shown that when ET deficit sequencing is optimal (i.e., any
deficits are timed so that they cause the least possible reduc-
tion in crop yield), the relationship between yield and seasonal
ET is quite well represented by a straight line function for
corn, grain sorghum, and pinto beans. If the upper bound of
yield is related to the depth of water applied, rather than ET,
a curvilinear relationship will result.
PREDICTIVE MODELS
Many attempts have been made to develop a functional
relationship between yield and water inputs, taking into account
the different effects on yield of water deficits at different
stages of growth. Moore (1961) developed a model to allow cal-
culation of the net variable income associated with each irri-
gation cycle, allowing calculation of the optimal time to apply
irrigation water. Moore used as a basis for this analysis a
hypothetical relationship between the relative rate of plant
growth and the mean soil moisture stress in the active root
zone, shown in Figure 8 for different soil types. For one
irrigation cycle, relative growth is the area under the moisture
release curve (relative growth rate versus soil-water depletion) ;
Gri =
"_
where Gr^ is the relative growth during the i irrigation cycle
expressed as a percent of potential growth, or
Gr.
r
o
ei
g(x) dx
x 100
= Iei ............. (6}
32
-------
Relative
Growth
Ratet
Percent
Sandy Soil
Loam Soil
Clay Soil
Available Moisture Depletion, Percent
100%
Figure 8. Variation in relative growth with available moisture
depletion for sandy, loam and clay soils (from
Moore, 1961) .
where In- is the fraction of potential growth for one irrigation
cycle, e1 is the moisture depletion percent at which the irri-
gation cycle is terminated and g(x) is the functional relation-
ship of relative growth to percent moisture depletion.
For an entire irrigation season,
n
Gr = £
TQ . T
(7)
where t. is the length in days of the ith irrigation cycle and
T is the length in days of the irrigation season.
For the special case where 9-j is constant for each
irrigation cycle throughout the season,
n
Gr =
ti
(8)
because for the entire season,
n
(9)
33
-------
Moore recognized the need for further refinement in the
method, especially in regard to the nature of the effect of
different amounts of soil moisture stress at different time
periods upon production of different plant parts and the effect
of moisture stress on the different stages of plant development.
However, the model allowed him to proceed with the economic
analysis of the value of irrigation water applied within any
one irrigation cycle and to determine an optimal irrigation pro-
gram which could bring into account varying water prices and
changing commodity prices during the growing season.
Hall and Butcher (1968) sought to develop a method which
could be used to assure that the seasonal distribution of water
was optimal (within the accuracy of the data and the postulates)
for each point on the overall production function. The authors
recognized that the magnitude of crop yield reductions due to a
soil moisture deficiency may depend almost as much on when the
soil moisture deficiency occurs as it does on the total magni-
tude of the seasonal shortage. They postulated that if Ymax is
the maximum yield of a crop under given conditions and if
the soil moisture is kept at field capacity, wf, through all
growth periods of the crop, then the yield would be Ymax.
However, if the soil moisture fell to a value w-j_ less than wf
during the ith growth period only, but remained at wf for all
other growth periods, then the resulting yield, y, could be
expressed as :
which defines a^ under the condition of the postulate. As aj_
depends on the magnitude of the soil moisture content, w^, it
may be expressed as a^ = a-^fwi). The authors then postulate,
for the given conditions, that the yield to be expected when two
or more of these time periods have deficiencies can be calculated
by the multiplicative function:
y = ar(Wl).a2(w2).a3(w3)...an(wn) Ymax ..... (u,
The authors proceeded to the development of the methodology
for optimal irrigation timing, using this expression as the
objective function of a dynamic programming problem (maximize y)
subject to the constraints of water supply, allowable soil
moisture levels (wilting point to field capacity) and water
balance in the root zone.
Jensen (1968) related yields to the effects of limited soil
moisture (resulting in reduced water use during a growth stage)
on the depvelopment of the marketable product of a determinate
flowering crop, by the multiplicative expression:
34
-------
n (SL\*i
i-i \EV i
(12)
where y/Ymax represents the relative yield of the marketable
product from an agricultural crop; (ET/ETp)i represents the
relative total evapotranspiration during a given stage of
physiological development (ET is the actual use of water and
ETp is the use of soil moisture was not limiting) and AI repre-
sents the relative sensitivity of the crop to water stress
during the growth stage i. The right side of the equation is a
product. Therefore, severe water stress, as indicated by
reduced water use, during a single growth stage could reduce the
yield of the marketable product severely. The magnitude of A
for specific growth stages would depend primarily on the sensi-
tivity of plant growth to water stress during each growth
period. The primary implication of the model is that the yield
of the marketable product of a farm crop may not be linearly
related to total water use when plants are stressed.
The Stress Day Index Model (Hiler and Clark, 1971) is an
additive type expressed as:
n
£
max max i=l
where CS.^ is the crop susceptibility factor which expresses the
fractional yield reduction resulting from a specific water
deficit occurring at growth stage i. A is the yield reduction
in kilograms per hectare per unit of Stress Day Index (SDI),
where:
_X_ = 1.0 - Y^— £ [CS±(1.0 - !£-)..] . . . (13)
n
SDI = £ (SDi x
and SD is the stress day factor which expresses the degree of
water deficit in the specific growth stage:
SD = (1.0 - H ................ Q.5)
The crop susceptibility factor (CS) is a -function of the deficit
factor. This functional relationship has not been postulated
but has been taken as linear based on other research. If CS is
assumed to be a linear function of the deficit,
35
-------
CS = a(1.0 -
(16)
then, the original equation can be written (Howell and Hiler,
1975) as:
= 1.0 -
"max
A
max
n
£
i=l
[a.(1.0 -
ET
ET
• . (17)
Yaron and Strateener (1973) developed a soil moisture
simulation model based on evapotranspiration predictions. Using
wheat data, the authors fitted parameters to a Cobb-Douglas type
function, an exponential function and a Mitscherlich function.
The last gave the most reasonable yield estimate obtainable
under optimal conditions and was chosen as the "best estimate"
and as the basis for the analysis of optimal irrigation policy.
The Mitscherlich equation is:
n
y =
max
^ (1 - B±(
(18)
where y is the yield, Ymax is the maximum yield, i is an index
of the growth stage (i=l,...,n), xi is a dimensionless soil
moisture index and B-^ and k^ are parameters (Blank, 1975) .
Another single crop model was presented by Minhas et al.
(1974), who first developed an evapotranspiration prediction
model for wheat as a function of available soil moisture only.
The function was of the form:
f (x) = (1 - e"
- 2e
~rx
(19)
where r is a parameter fitted from the data, x is the available
soil moisture (ASM) in the root zone, x is the ASM at field
capacity and f(x) is the ratio of actual to potential ET.
Actual ET is then the product of f(x), potential ET and an
assumed scaling factor which varies with the maturity of the
crop. Parameters were fitted using wheat data from Delhi,
India, and tested against alfalfa data reported in 1968 by
Mustonen and McGuiness (Minhas et al., 1974).
With an adequate ET prediction function, the authors used
regression to fit parameters to the multiplicative function:
36
-------
where y is the yield and x^ is the relative evapotranspiration
in period j. The parameters a and b. are fitted from data.
Hanks (1974) developed a simple model, based on earlier
models, for both dry matter yield and grain yield, with the
main emphasis on the former. The equation to relate dry matter
yield, y, to transpiration is taken from that of de Wit (1958) :
y = mT/EQ (21)
where T is transpiration, Eo is average fresh water evaporation
rate and m is a crop factor. This equation had been confirmed
by Hanks et al. (1969). Four different methods of relating T
to T (potential transpiration) were used in verifying the
model, all giving reasonable results. Soil evaporation (Es) is
assumed to be related to potential soil evaporation (E?p) and
the time since last wetting (t) by the empirical relation:
ES = vvt)1/2 (22)
where tD is the time when Es = E (assumed one day). The
potential transpiration, Tp, is calculated from:
Tp = ETp ' Esp (23)
To estimate grain production, Hanks used the method of Jensen
(1968) which has been described above.
Stewart et al. (1976) developed two models which utilized
estimates of anticipated ET deficits and growth stage sensiti-
vities to predict actual ET and yield for the season. The
models were developed for pinto beans, but the authors consider
them to have equal applicability to both grain sorghum and
corn.
Model 1 (Stewart et al., 1976) is referred to as the
Growth Stage Model and is given by the additive expression:
/ETM. - ETA.
y - ymax ' Ymax .£ YRRi I V?7. / (24)
37
-------
where ETf4 is the total ET requirement for the season, ET]y[. is
the ET requirement for growth period i, ET&- is the actual ET in
growth period i and YRR^ is the yield reduction ratio in growth
period i, defined as the ratio of percent yield reduction to
percent ET deficit.
Model 2 is referred to as the ET Deficit Sequence Model and
is expressed as:
= Y - Y
max max
(25)
where $0 is the yield reduction ratio, where ET deficit
sequencing is optimal, and 3 is the yield reduction ratio pre-
dicted for the season, based on the actual ET deficit sequence
and on the growth period sensitivities found by research.
Obviously, the expression in brackets may be simplified. However,
the first term in the brackets represents the inevitable yield
loss and the second is the additional loss due to suboptimal ET
deficit sequencing. The authors consider this separation of the
yield losses to give Model 2 an advantage over Model 1.
The eight crop production functions described above have
been presented as a review to acquaint the reader with the
divergent approaches to predicting the anticipated yield from a
given quantity of water. The basis for development of the
various models range from data collected from extensive field
trials to some rather questionable assumptions.
Yaron and Strateener (1973) and Minnas et al. (1974) rely
on data from a number of years to establish their production
functions. Howell and Hiler (1975) tested the model of Minhas
et al. and those of Jensen (1968) and Hiler and Clark (1971)
on a limited amount of data from a variety of sources and found
that all of the models, which are quite similar in formulation,
represented the experimental data accurately within the range
of data. Hanks (1974) found that his model gave a good fit of
predicted versus measured dry matter yield of sorghum in
Colorado, corn dry matter and grain yields in Israel and corn
grain yields in Nebraska, with various water application treat-
ments. The Stewart et al. (1976) models were developed from
data collected at Davis, California, and await independent
verification. The Moore (1961) model and the Hall and Butcher
(1968) models were developed from theoretical considerations
and would appear difficult to apply.
38
-------
The functions described herein are about evenly divided
between multiplicative type functions and additive type
functions. Both cannot be correct for a given situation. The
multiplicative function indicates, for example, that if growth
is only 70 percent of potential for a particular growth stage,
then the maximum yield attainable by the crop is 70 percent of
potential. According to the additive theory, 70 percent of
potential growth in a particular time period would only result
in potential yields being reduced by 30 percent of that parti-
cular time period's potential contribution. The overall reduc-
tion would be considerably less if there were a number of time
periods considered.
Multiplicative functions meet two important conditions that
exist in the relationship between actual yield and moisture
availability. Firstly, if the soil moisture during all stages
of growth is at field capacity, or evapotranspiration is at the
potential rate, then there is no stress and yield equals Ymax.
Secondly, if soil moisture is entirely depleted, or evapotrans-
piration ceases in any growth period, then the plant dies
regardless of the moisture regime in other growth stages and
yield equals zero. This condition is usually not met by an
additive function.
The multiplicative function, however, may break down when
stress occurs in a number of growth stages. _For example, if a
yield reduction of 0.8 occurs due to stress in an early growth
stage alone, the final yield is y = 0.8 Ymax. If a yield reduc-
tion of 0.6 occurs due to stress in a later growth stage alone,
v = 0 6 Y™=v If, in another experiment, the crop receives
these'restive amounts of stress in both growth stages, with
no stress in other growth stages, the anticipated yield accord-
ing to the multiplicative theory would be y = 0.48 Yma How-
ever, experiments with some crops have revealed a conditioning
effect as discussed earlier and so the actual reduction in
yield would not be as great as shown here The conditioning
effect is not taken into account by the mulitplicative functions
discussed above, and these may be expected to underestimate
yields where conditioning occurs.
The development of crop production functions cited above,
and by other researchers not cited, has been stimulated^ the
desire to achieve the objectives outlined at the beginning of
this section. The process has been to develop a production
function for use in determining the optimal irrigation program,
the optimal irrigated area, or whatever objective is desired.
For the case of researchers such as Jensen (1968), Hiler and
Clark (1971) and Stewart et al. (1976) the production function
has been developed separately. Other researchers, such as
Moore (1961) and Hall and Butcher (1968), have developed the
production function en route to developing the methodology for
39
-------
optimal irrigation programming. As stated by Minhas et al.
(1974), the exact shape of the crop production function must
be known before the question of economically optimal use of
water can be resolved. The point is made by Blank (1975) that
an adequate theory is not generally accepted and that currently
available data are not sufficient to conclusively adopt any of
the production functions described. In other words, the
endeavors of researchers to develop optimal irrigation programs
and allocations (i.e., Dudley et al., 1971a, 1971b), while
providing valuable insight into the physical processes, will
find little application until the form of the crop yield-water
use function is known more precisely.
40
-------
Section 5
EXPERIMENTAL DESIGN
PURPOSE OF EXPERIMENT
The literature reviewed in the preceding section has
revealed an apparent dichotomy in the form of the relationship
expressing crop yield-water functions. The difference between
the forms of the relationship would appear resolved by taking
into consideration the measure of water used in the abscissa.
Researchers plotting yield against applied water generally
obtain a concave downwards function. The advent of more advanced
research tools, particularly the neutron probe for soil moisture
measurement, has allowed recent researchers to plot yield against
ET, obtaining a linear upper bound on the results.
The purpose of this experiment was to confirm whether the
results of the recent researchers could be substantiated. One
year of experimental results could not be expected to provide
sufficient data on which to base extensive conclusions regarding
optimal water allocation. However, if the data gave markedly
different results from the limited experimental data available,
the universality of the published data would be open to question.
On the other hand, if the data conformed to that obtained by the
other researchers, it would appear reasonable to extend their
results to different areas. This experiment was conducted in a
manner which would allow comparison with published results.
Where possible, the yield of both grain and dry matter was
obtained.
DESCRIPTION OF PLOTS
The plots used for the field trials are located on a
23-acre (9.3 hectare) area of leased land situated to the north
°f Grand Junction, Colorado. The farm is bounded on the north
by the Government Highline Canal and on the east by a natural
channel known as Indian Wash (Figure 9) . .
The location of the water supply lateral running through
the farm divides it into three sections (Figure 10). In 1976,
alfalfa was grown in Field I, corn in Field II, wheat in the
northern section of Field III and Jose Tall Wheatgrass in the
41
-------
City of
Grand Junction
Scale
Figure 9. Location map of the project area.
42
-------
Field I
Canal
Field
Jf
Scale
si^sess
0 50 100 200 feet
100 meters
Field HI
Figure 10.
Map of the Matchett Farm fields used for the
study area.
43
-------
southern section of Field III. Field I consisted of 16 plots/
Field II of 32 plots and Field III contained 10 plots of wheat
and 5 of wheatgrass. The location of the plots within each
field is shown on Figures 11, 12 and 13.
Because of the particular requirements of earlier experiments
at the farm, not all plots are of equal size. Plots in Fields I
and II are all nominally 100 feet by 100 feet (30.5 by 30.5
meters) while Field III consists of 6 plots of 100 feet by 100
feet, 2 of 200 feet by 40 feet (61 by 12 meters), 2 of 300 feet
by 40 feet (91.5 by 12 meters) and 5 of 500 feet by 40 feet (152
by 12 meters). (English units are used here as these were the
units used during construction.)
Water supply to the plots came from the lateral mentioned
above. The water was diverted into aluminum main supply lines
running north-south along the western edge of Fields I and III
and the eastern edge of Field II. From the main supply line the
water was measured through V-notch weirs into gated pipe running
east-west across the top of each row of plots. In the case of
Field II, the water was first pumped from the lateral into an
elevated tank to provide sufficient head to fill the gated pipe.
The ground surface of the farm slopes to the south and the
whole area is underlain by Mancos Shale generally 2 to 4 meters
below the surface, with isolated areas as shallow as 0.4 meters
and as deep as 7 meters. The shale generally dips to the south-
west with some undulation. The plots were formed by excavating
a trench along the lines dividing the plots to a depth slightly
below the top of the shale. A plastic curtain was then placed
vertically in the trench to divide the individual plots. The
lower edge of the curtain was sealed to the shale by backfilling
to the original elevation of the shale with compacted clay. A
drainline, encased in a gravel filter material, is located
inside the curtain (Figure 14) and is continuous around the
plot. The curtain was raised vertically to within approximately
a meter of the ground surface and held in place by backfilling
with the excavated material. Water entering the drainline
leaves the plot area via solid pipeline which transports it to
a measuring station where quantity and quality can be monitored.
SOIL CHARACTERISTICS
Soils on the experimental farm are, in general, silty clay
loams derived from the underlying Mancos Shale. Some variation
in the profile exists, with a layer of more sandy textured soil
being encountered in many plots about half a meter below the
surface. Sandy layers, where encountered, are generally from a
few centimeters to one-half a meter thick.
44
-------
8
10
13
15
12
Roadway
Figure 11. Location of plots in Field I,
45
-------
o
5
TJ
O
O
tr
1 7
2 1
25
29
18
22
26
30
Shale Too
_^_ Deep for
Plots
37
Q
41
45
38
42
46
19
23
27
31
33
. 35
39
43
47
20
24
28
32
34
36
40
44
<
•
h
48 j
«*
a
In
V
5
si
3
3
^Roadway
Drain Line
to
Indian Wash
Figure 12. Location of plots in Field II,
46
-------
o
TJ
O
O
cr
Buffer
Zone
49
50
52
53
54
55
57
56
58
59
60
61
62
63
Figure 13. Location of plots in Field III
47
-------
00
Wafer
fable
Shale
Figure 14. Plot cross-section with drain details,
-------
During the course of construction in 1973, the soil surface
was heavily compacted. This severely hampered cultural and
irrigation activities during the first two seasons particularly,
and areas that were heavily trafficked were still found to have
very low infiltration rates in 1976.
Bulk densities are quite high for the soil type, averaging
1.45 gm cm'3 in the plow layer and 1.55 gm cm ^ deeper. The
moisture retention characteristics of the soil vary slightly
from plot to plot and with depth. The water content at field
capacity (one-third bar pressure) is about 37 percent by volume.
The saturation witer conlent is about 45 percent (Avars, 1976).
Wilting point (15 bar pressure) is about 20 percent by volume.
As mentioned in the preceding section, the depth from the
soil surface to the underlying shale bedrock varied markedly A
map showing the contours of the depth to shale from the ground
surface is presented in Figure 15.
The desert climate of the area has restricted the growth of
nativfvegetation* thereby causing the soils to have a low
nitrogen content due to the absence of organic matter. The
mineral aoil is hioh in bicarbonate and sulphate salts of sodium,
£££iuTiagne8i£ and calcium, ^though natural phosphate
exists in thP soils it becomes available too slowly to supply
?he needs of cultivated crops. Other minor elements such as
iron are available (Ayars, 1976).
any .
for Lunity Analysis. Soil s^fles were ejected
9
soil cor..^.J.K.n fro; the
tr^
conductivity of the saturated extract ranged from 1.5 to 5.5
pL centie, : the average
during the preceding
winter to be about 2.
IRRIGATION REGIME
ThP ar-Pai-Pst latitude for experimentation was with the
corn In Field ??wh?ch was sown and harvested within the period
under She abhors 'control . Experimentation with different
irrigation reaimes was carried out with the alfalfa, but the
expeSen? was u^imately abandoned as the effects of different
treatments in earlier years and in preceding cuttings carried
over ?he watering schedule of the wheat was out of the authors'
49
-------
Figure 15. Depth to shale bedrock from ground surface,
in meters.
50
-------
control until mid-May 1976, by which time the effects of early
spring moisture stress were evident.
Field II was watered as a single unit over the period
3rd-10th May, following sowing. The gated pipes were then
installed across the top of each row of plots. Over the period
8th-llth of June, when the corn was approximately 15 to 20 cm high,
all of the plots were individually irrigated again with
approximately a 45 mm watering.
The corn was then differentiated in three subsequent
growth stages. Stage I was from the emergence and establishment
stage through the main period of vegetative growth preceding
tasseling. Stage II was the pollination period from tasseling
to the blister kernel stage , and Stage III was the grain filling
period from blister kernel to physiological maturity. These
growth stages coincide with those of Stewart, et al. (1975)
although some subjectivity is involved in the differentiation
between growth stages.
Water was applied to the corn weekly during one, two or
three of the growth stages, giving eight different treatments
(Figure 16). Each treatment was replicated four times. The
eight plots within a replication were grouped contiguously to
provide approximately equal depth to shale within the replication.
Those plots being watered within a growth stage were
watered once a week with a net amount calculated to be slightly
in excess of the crop requirements. Thus, in the early stages
it was planned that the watered plots would receive approxi-
mately 40 mm per week, rising to 65 mm per week during the
period of peak demand. Stressing during a particular growth
stage was achieved by eliminating all irrigation from the
stressed plots during that growth stage. Rainfall which fell
during the growing season was light and infrequent, allowing a
high degree of stress to be applied.
The wheat plots were similarly differentiated according to
growth stage, although to a somewhat limited scale due to experi-
mental work with the wheat not beginning until the spring
following its winter dormancy. All plots were watered during
the week beginning 17th of May, when in the late boot stage, after
which two growth stages were considered, the anthesis period and
the grain filling period. Three plots reqeived water only
during the first stage (1-0), two plots received water only
during the second stage (0-1), three plots received water during
both stages, (I-I), and two plots received no water at all
during both of these stages (0-0). Approximately 50 mm (net) of
water was applied per week to those plots being irrigated.
51
-------
to
Growth Stage: 0
I Pre-emergence plus
I Post-emergence
Irrigation
5 Irrigations
Legend:
I = Irrigation
0= Non-irrigation
m
4 Irrigations Designation
0-0-0
v^rm
I
fo"
o-o-i
o-r-o
O-I-I
I-0-0
I-O-I
I-I-O
I-I-I
Plant
Secondary Rooting
Tassel
Blister Kernel
Mature
Emerge a Estobish | Veqetotive Period
6 Weeks
29th April 13th June
Pollination Period
Grain Filling Period
!3thJu.y * ***! 5th August 5 """i 7th September
Figure 16. Irrigation treatments for corn,
-------
FERTILIZER TREATMENTS
Following the 1975 crop/ the fertility level was determined
by compositing samples from paired adjacent plots and fertilizer
was applied that autumn at the rates shown in Table 1. These
rates were chosen on the basis of an alternative experimental
design which was ultimately abandoned. Subsequently, nitrate
levels for each plot were determined during the season by plant
leaf analysis.
The fertilization treatments were designed to ensure a good
stand of the crop and to evaluate nutrient losses due to excess
irrigation. Field II was the principal study area for fertiliza-
tion studies. The corn grown in this field was fertilized to
obtain two levels of nitrogen. The alfalfa, wheat and Jose
Tall Wheatgrass grown in the remaining plots were fertilized
uniformly based on nutrient analysis of the surface soils.
Alfalfa was grown in Field I and was fertilized initially
with phosphate to establish the crop and was again fertilized
with phosphate in subsequent years to maintain its vigor. The
fertilization was done uniformly over the entire field.
The wheat crop, Field III-N, received the recommended
quantities of nitrogen, potassium and phosphate based on a yield
goal of 8.7 m^/ha. The recommendation is contained in the
Colorado State University publication, "Guide to Fertilizer
Recommendation in Colorado." A uniform rate of fertilization
was maintained over the field.
The corn test plots, Field II, received fertilization such
that two levels of nitrogen were achieved in the surface soils.
The goal was an equivalent of either 100 ppm nitrogen or 60 ppm
nitrogen in the soils. This goal was achieved by: (1) analyzing
the surface soils for nutrients; and (2) based on existing
nitrate levels, half the plots were selected for fertilization
to 60 ppm and the remaining to 100 ppm.
The soil samples used for analysis were taken from adjacent
plots and mixed. Soils were mixed for only two plots per
analyzed sample. This means that adjacent plots received the
same fertilizer treatment; i.e., plot 17 and 18.
By using the approximation (Ludwig and Soltanpour, 1975),
that 10 ppm nitrogen is roughly equivalent to 40 kg per hectare
of nitrate nitrogen in the top 30 cm of soil, the nitrogen
required to achieve a specific nutrient level was computed.
The amount of potassium and phosphate fertilizer required
was computed based on recommendations found in the fertilizer
guide. The fertilizer was applied on the paired test plots
using a fertilizer drill. All fertilizer was carefully weighed
53
-------
TABLE 1. FERTILIZER ADDED TO FIELD II, 1976
Rate of Fertilizer Application (kg ha"1)
Plot
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
NH4N03(33%)
0
0
298
298
488
488
0
0
190
190
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P205(44%)
132
132
132
132
132
132
78
78
78
78
78
78
132
132
78
78
78
78
78
78
0
0
78
78
78
78
78
78
78
78
0
0
ZnS04(36%)
0
0
0
0
15
15
15
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
15
0
0
15
15
0
0
54
-------
to insure proper levels of fertilization. The design of the
experiment was dictated by the soil analysis and was random due
to this fact.
The plant leaf analysis was carried out by taking 100
leaves from the rows designated for sample harvesting at the
time when approximately 75 percent of the field showed silk
emergence (5th August). The second leaf down from the top ear
was removed for analysis. The leaves were air dried, ground and
analyzed for total nitrogen using the semi-micro Kjeldahl method,
55
-------
Section 6
FIELD OPERATIONS
CULTURAL PRACTICES
Field I was planted to the Resistador variety of alfalfa in
the spring of 1974. Before sowing, the field had been fertilized
with 44 percent superphosphate (P20q) applied at the rate of 335
kilograms per hectare. No further fertilizer was added prior to
or during the course of the study herein described. No weed or
insect treatments were found to be necessary.
Field II was planted to corn in the three preceding crop
years and again in 1976. The first two years yielded poor crops
due to late sowing and the compacting effects of plot construc-
tion traffic. Yields from well-watered crops in 1975 were below
the Valley average. In 1976, the Pioneer variety 3369A was sown
on 29th of April. Both the insecticide Thiamet and the herbicide
Lasso were applied prior to sowing. The corn was sown with a
four-row planter to give a population of approximately 50,000
plants per hectare.
Following emergence and establishment of the plants,
interrow cultivation for weed control was carried out at the
beginning of June, followed two weeks later by a surface applica-
tion of 2,4-D at a rate of 0.6 litres per hectare to control
weeds in the rows. A second interrow cultivation was carried
out on 20th of June. Those weeds which persisted in the rows
designated for sample harvesting were removed by hand hoeing.
In late July, a minor infestation of Western Corn Rootworm
and Corn Ear Worm was detected in the crop. Only minor damage
occurred before control measures were taken on 30th of July when
Parathion was applied from the air at a rate of 0.56 kilograms
per hectare.
Field III was planted to the New Gains wheat variety in
October 1975. Prior to planting, the field was uniformly ferti-
lized with 44 percent ?205 at a rate of 90 kilograms per hectare
of the fertilizer. The wheat was broadcast sown at a rate of
112 kilograms per hectare. The fields were surface-irrigated
with furrows spaced at 30-inch (76 cm) centers.
56
-------
FIELD DATA COLLECTION
The principal activities throughout the crops' growing
seasons were the application of water to the crops, monitoring
the moisture balance in the root zone, and measuring the amount
of fertilizer passing beyond the root zone.
The method of water application was the same for each
field. Gated pipe ran across the upper end of each row of
plots, as shown in Figure 17. Water measured into the pipe
through the V-notch weir (Figure 18) was conveyed to only one
plot in the row so that all of the measured water was applied to
that plot. Surface runoff from each plot was measured with a
1-inch (25 mm) Cutthroat flume set in the taildrain at the
outlet from the plot, as shown in Figure 19. :The point of
outflow of the subsurface runoff could be measured. No sub-
surface runoff was noted from any of the plots during the course
of the study. A running total of net water application (inflow
minus outflow) was recorded on a prepared sheet/ with the
irrigation halted when the desired depth of water had been
applied.
Unfortunately, an error had been made in the original
calibration of the V-notch weirs. This error was not discovered
until July 14, 1976, when an independent check was made. Until
that time, 18 percent less water than intended had been applied
per irrigation. At the same time an attempt was made to prevent
surface runoff from the plots. The resulting ponding at the
ends of the furrows, coupled with the shortage of applied water,
caused an unintentional moderate stress to the plants around the
middle of the rows during the early stages of the experiment.
The effects were more noticeable in some plots than others.
Soil moisture was measured weekly by neutron moisture probe
(Figure 20) in the corn plot and by gravimetric means in the
wheat plots. The measurements are described in more detail in
Section 7.
HARVESTING OPERATIONS
The 32 plots of corn in Field II were partially harvested
for forage yield measurements on 17th of September and the remaining
unharvested portions of each plot were harvested for grain on
the 10th and llth of November.
Forage yield estimates were made by harvesting two rows on
each side of the neutron probe access tubes for a total of four
rows per plot, or a total area of 600 square feet (55.7 m2) per
plot. The harvest was accomplished by manually cutting each
stalk at ground level, as shown in Figure 21. In order to
eliminate any border affects, a 60 foot (18.3 meter) length from
57
-------
Figure 17. Watering of corn plots using gated pipe.
Figure 18.
Measurement of water applied to the plots using
a V-notch weir.
58
-------
Figure 19.
Measurement of surface
runoff from the plots
using a Cutthroat flume
Figure 20. Measurement of soil
moisture using a
neutron meter.
-------
Figure 21. Harvesting corn for dry matter yield
Figure 22. Weighing corn samples for dry matter yield,
60
-------
the center of the rows was harvested and the ends were left
standing. A row was also left on each side of the access tube
row to exclude plants possibly damaged while taking moisture
measurements during the season. The total fresh plant weight
from each plot was determined by weighing the sample on a spring
tension scale, shown in Figure 22. Four representative plants
from each plot were then weighed, air-dried, chopped, weighed,
dried on a forced air oven, and reweighed. The dry weight of
the harvested material was calculated on the basis of the
moisture percentage of the sample. A few of the samples suffered
some squirrel damage while being air-dried; however, this was
compensated by taking the average weight of .the remaining un-
damaged cobs, multiplying by the number of original cobs and
adding this weight to the sample weight.
Grain yield estimates were made by harvesting three rows on
each side of the previously harvested forage rows, with the six
rows per plot giving a total area of 900 square feet (83.6 m2)
per plot. To eliminate any border effects, a 60 foot (18.3
meter) length from the center of the row was sampled. The
harvesting was carried out using the three row "Oliver" combine,
shown in Figure 23. The grain was collected in a sack held
under the elevator outlet to the combine bin and the weight
determined on a spring tension scale. The kernel moisture
percentage of each grain sample was determined using a "Motomco"
moisture meter. The grain weight per sample area was converted
to kilograms per hectare at 15.5 percent moisture.
Field III contained 10 wheat plots of variable dimensions;
consequently, the harvested area varied according to the width
and length of each plot. The wheat was harvested on 27th of July
using the "Hege 125" experimental plot combine shown in Figure
24, which has a 4-foot (1.2 meter) wide cutting head. For the
plots measuring 100 feet x 100 feet, two swaths were cut through
the plot, each being 20 feet (6.1 meters) from the sides of the
plot. For the plots measuring 40 feet x 200 feet and 40 feet x
300 feet, only one swath was cut through the plots, this being
located near the center of the plots. The grain was collected
in sacks and later weighed on a spring tension scale. Grain
bushel weight was also determined for each sack of grain and
averaged for each plot. The dimensions of each cut,was measured
and the sampling area calculated for each plot. This was used
to give a yield estimation for each plot in kilograms of grain
per hectare.
61
-------
9^^^
• '***!>
Figure 23. Combine used for harvesting corn grain samples
Figure 24. Combine used for harvesting wheat samples
62
-------
Section 7
EVAPOTRANSPIRATION
DATA COLLECTION
Climatic data were collected in the southern part of Field
III on Matchett Farm. The weather station was located in a field
sown to Jose Tall Wheatgrass. Readings were taken every morning,
including weekends, at approximately 8 a.m. The daily data
obtained are listed in Appendix A for the period from April 1, to
November 9, 1976.
Maximum and minimum temperatures were recorded on a
hygrothermograph as well as on a maximum and minimum thermometer.
The thermometer readings were used in the ETp estimates as it was
felt that these are inherently more accurate.
Rainfall was constantly monitored with a tipping bucket rain
gauge, with the registrations recorded on a strip chart. The
tipping bucket was activated by each 0.01 inch (0.254 mm) of
rainfall.
Relative humidity was continuously recorded on the
hygrothermograph. The recorded value is that which occurred at
the time of minimum temperature, and generally corresponds to the
maximum value for the day.
Solar radiation values were read from the solar radiometer
located in the weather station. The value read from the inte-
grator in the morning of a particular day was subtracted from the
value read in the morning of the subsequent day, with the counts
multiplied by the calibration factor of 0.200 to giv$ the value
of measured solar radiation for that day (R ) in langleys
(calories cm~^) per day.
During the early part of the season the solar radiometer was
out of order and values of Rs were obtained from the Agricultural
Research Service (ARS) weather station located in the valley.
These values were obtained for a period of 54 days after the
solar radiometer was repaired on the llth of May so that a cor-
relation between the ARS values and the CSU values could be ob-
tained. The overlapping data was matched best by a power curve
fit:
63
-------
(Rs'cSU ' 1-569(RS) " - °-916) ..... !26)
and this function was used to fill in the missing Rg data at
Matchett Farm during late April and early May.
Wind run was measured with an anemometer located 2 meters
above the ground. Over the period 7th of August to 20th of
September the anemometer was broken and wind run data was ob-
tained from the Weather Bureau station located at Walker Field
approximately 2 kilometers to the northwest. Measurements at
this location are made 6.7 meters above the ground. Windspeed
at an elevation of -2 meters can be approximated from measurements
made at other elevations using the power law:
W~ = W (2/z)°*2 (Pair et al . , 1969, p. 105) . .(27)
4. Z
where z is the elevation in meters at which W is measured.
Using this relationship,
<»2>CSU= (W6.7>WF(67f>°'2 = ° "785 (W6 .7> WF ' ' ' (28)
data from Walker Field, (Wg,7)wF' were collected for July through
October and plotted against the available CSU records for the
same period. A better fit to the data was actually obtained
using:
CSU= °-833(W6.7>WF ............. (29>
and this relationship was used to fill in the missing data.
Evaporation was measured in a U.S. Class A pan set on a
platform with the pan rim 45 centimeters above the ground. The
surrounding field was planted to Jose Tall Wheatgrass for a
distance of approximately 125 meters in the direction of the
prevailing wind. The values of evaporation given in Appendix A
are direct readings from the pan and, hence, rainfall amounts
must be added to give the net value of evaporation for the day.
Consequently, some readings on days in which rainfall occurred
are negative.
Two volumetric lysimeters, one meter square and 0.5 meters
deep, were planted to subterranean clover and set level with the
ground surface. Each lysimeter was supplied water from a tank
approximately 1.5 meters high and 32 centimeters in diameter,
with the level of the water in the lysimeter maintained approxi-
mately 10 centimeters below the soil surface by a float valve.
64
-------
The lysimeters began to give unrealistically high values of
in early June. In July, one lysimeter was excavated and
inspected for leaks. No leaks were found and the lysimeter was
returned to the ground. At the same time the subterranean clover
overhanging the sides of both lysimeters was trimmed. Although
this overhang did not appear significant at first, on measurement
it was found to have increased the transpiring surface area by
approximately 65 percent. After cutting, ET values reduced
significantly, although an instantaneous reduction was not
apparent (see Figure 25).
Soil moisture in the corn crop was measured weekly by
neutron moisture probe at 30 cm intervals to a depth generally in
excess of 180 cm, or to shale, whichever occurred first. Two
access tubes were placed in the bed of the center row of each
plot, 25 feet (7.6 meters) apart and equidistant from each end of
the plot. Moisture in the top 15 cm of soil was measured gravi-
metrically. Because neutron probe access tubes could not be
installed without damage to the growing crop, soil moisture
measurements in the wheat crop were made gravimetrically each
week to a depth of 120 cm or to shale, whichever came first. By
integrating the moisture measurements over the depth of measure-
ment, changes in root-zone soil moisture storage from week to
week could be calculated.
COMPARISON OF METHODS OF ET CALCULATION
A comparison of the computed and measured values of
for the 27 week period of consideration during the summer o
1976, is given in Table 2 and is plotted in Figure 25. The
ETp values computed by the Penman method and the Jensen-Haise
method, calibrated for local conditions, were in very close
agreement. Over the 27-week period, the ETp computed by the
Penman method was 1309 millimeters, or 2.8 percent higher than
the 1273 millimeters computed by the Jensen-Haise method. The
percentage difference on a week-by-week basis was usually higher,
although for two-thirds of the time the weekly values of ETp
computed by the two methods were within 10 percent of each other.
The biggest difference was 22 percent.
Errors in ETp estimates using weekly time periods are to be
expected. Jensen and Wright (1976) found an estimated standard
error of 1.0 millimeters per day at Kimberly, Idaho, using daily
data, with this error decreasing inversely, with the square root
of the number of days for time periods up to 30 days. Therefore,
the variation in estimates of weekly ETp using the Penman or
Jensen-Haise method is to be expected.
Pan evaporation over the first 24 weeks (after which water
in the pan was frozen) was 90 percent of ETp calculated by the
Penman method. The discrepancy was much less over the first 12
65
-------
CTv
1 1 1 1 1 1 1 1 1
Values from
Jensen ( 1973)
Values Obtained
from Soil Moisture
Measurements
Establishment Vegetative Pollination Grain Filling
10 12 14 16
Week Number
18
20 22 24 27
Figure 25. Variation of crop coefficient with time.
-------
TABLE 2. COMPARISON OF POTENTIAL EVAPOTRANSPIRATION ESTIMATES AND EVAPORATION DATA
a\
Estimated Potential Evapotranspiration, mm per week Evaporation
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Modified Julian
Date
64-70
71-77
78-84
85-91
92-98
99-105
106-112
113-119
120-126
127-133
134-140
141-147
148-154
155-161
162-168
169-175
176-182
183-189
190-196
197-203
204-210
211-217
218-224
225-231
232-238
239-245
246-252
Interval
May 3-9
10-16
17-23
24-30
May 31- June 6
June 7-12
14-20
21-27
June 2 8- July 4
July 5-11
12-18
19-25
July 26-Aug. 1
Aug. 2-8
9-15
16-22
23-29
Aug. 30-Sept.5
Sept. 6-12
13-19
20-26
Sept. 27-Oct.3
Oct. 4-10
11-17
18-24
25-31
Nov. 1-7
TOTAL
Penman Jensen-Haise Lysimeter
29.5
56.7
33.9
46.9
66.4
68.9
63.3
58.3
70.6
76.2
61.4
57.7
55.2
63.2
59.0
53.6
54.3
60.0
30.7
45.6
26.8
33.1
31.1
33.8
26.6
22.5
23.6
1309
29.5
52.4
36.5
46.7
61.2
54.0
58.1
60.5
71.9
76.3
66.0
65.6
61.5
52.5
55.9
55.3
58.7
57.9
37.6
43.3
27.5
30.4
28.7
28.1
19.3
17.1
20.2
1273
North
31.5
27.2
32.2
52.9
86.3
106.8
120.3
124.9
148.2
136.1
112.2
87.7
58.6
61.2
45.8
58.9
64.3
62.2
32.0
47.0
43.7
43.4
19.3
19.7
South
19.7
25.6
27.8
39.8
71.2
87.3
104.4
107.1
128.0
117.1
82.7
74.3
54.4
51.4
45.4
43.3
50.2
47.5
31.6
37.1
17.8
25.2
10.0
15.0
Use
Average
25.6
26.4
30.0
46.4
78.8
97.1
112.4
116.0
138.1
126.6
97.5
81.0
56.5
56.3
45.6
51.1
57.3
54.9
31.8
42.0
30.8
34.3
14.7
17.4
USER
(including
rainfall)
mm per week
27.6
38.9
28.7
37.1
50.9
54.3
39.8
44.7
52.6
56.5
49.5
47.2
45.3
47.3
47.0
42.9
44.6
44.4
27.8
34.5
26.2
25.8
18.6
50.3
42.1
43.1
56.4
65.6
65.2
67.8
66.3
64.6
63.7
60.4
48.6
49.7
51.6
44.0
52.3
51.1
27.0
38.6
18.4
21.9
22.9
24.4
1115
-------
140
CTi
CO
Penman
— Jensen - Haise
— Average lysimeter
Class A pan
0
12 15
Week Number
Figure 26. Computed and measured water use.
-------
weeks. Hanks and others at Logan, Utah, found uncorrected pan
evaporation a good measure of ETp (Consortium for International
Development, 1976).
Although the uncorrected pan evaporation results are in good
agreement with the values of ETp calculated, a pan factor correc-
tion would normally be expected. Published values indicate a pan
factor of 0.7 for the given conditions (Doorenbos and Pruitt.,
1975, Table 19) . Using this factor, the calculated value of
seasonal ET would be :
ET = 0.7 x 1115 x j. ............. (30)
= 410 mm
where 1115 is the evaporation (including rainfall) in millimeters
up until the time the water in the pan froze, and 650/1236 is a
representation of the seasonal crop factor (ET/ETp by Penman's
method) . This value of ET is well below that which would be
reasonably expected and indicates the necessity of locally
calibrated values of the pan factor in using pan evaporation as a
measure of ETp.
The good agreement between the three methods discussed above
would indicate that ETp may be estimated on a seasonal basis with
a reasonable degree of reliability using any of the methods
provided they are locally calibrated. The closer agreement
between the Penman and Jensen-Haise methods, compared to pan
evaporation, would point in their favor, but without accurate
lysimeter measurements, a definite conclusion cannot be drawn.
The lysimeter data are obviously in error during the first
half of the season, as discussed earlier. Average lysimeter
values of the remainder of the season are in quite good agreement
with the computed values, but the discrepancies between the
readings from the two lysimeters in many cases makes an average
reading of dubious value.
The values of ETp calculated from the USER data would appear
unduly low. The peak value following tasseling of 47.3 milli-
meters per week corresponds to an average of 6.8 millimeters per
day which would appear too low for fully grown corn.
Weekly estimates of ETp using combination equations cannot
be expected to have great accuracy, as discussed above. Estimates
by the Penman method were used for the weekly ET computations for
the corn, as the Penman equation incorporates more of the factors
influencing evapotranspiration.
69
-------
CROP WATER USE
Consumptive use of water by a well-watered crop may be most
accurately obtained by growing the crop in a lysimeter in the
field. Such an arrangement was not possible in this experiment,
where volumetric lysimeters sown to subterranean clover were
located adjacent to the experimental plots. As described
earlier, the lysimeters were found to be malfunctioning during
the course of the experiment and hence evapotranspiration of the
well-watered plots was computed using Penman's combination equa-
tion. Evapotranspiration was calculated on a weekly basis as the
crops .were watered on a weekly schedule.
For the corn crop grown in Field II, the calculated values
of potential evapotranspiration were multiplied by a crop coeffi-
cient (Kco) to obtain crop evapotranspiration. The crop coeffi-
cients used are those presented by Jensen (1973) . Using the
coefficients presented, the calculated seasonal ET was exces-
sively high (840 mm). Doorenbos and Pruitt (1975) consider the
maximum crop evapotranspiration for corn grown under arid
conditions to be 700 mm. Therefore, two adjustments were made
to the crop coefficients:
1. As the crop was "watered up" after planting, the crop
coefficient was taken as zero in the two weeks preceding emer-
gence, rather than having values ascribed from the week of
planting.
2. A check of the soil moisture measurement data showed
that, by Week 21 (22nd September), moisture extraction from the
root zone had ceased. A straight line was therefore drawn on
the crop coefficient curve from the value at Week 17 (23rd
August) to zero at Week 21. This closely accords with the values
of Doorenbos and Pruitt (1975) . The effect of this adjustment
on the weekly crop coefficients as given by Jensen (1973) is
shown in Figure 26.
The tabulation of the weekly crop coefficients and compu-
tation of the maximum crop evapotranspiration is given in Table
3. The parameters used in calculating potential ET by the
modified Penman method are given in Appendix B. Effective
cover was assumed to occur ten days after the well watered plots
reached about 50 percent tasseling. Therefore, the date of
effective cover was 31st of July which was 93 days after
planting and 75 days after emergence.
Moisture measurements were made weekly using the neutron
probe, in most cases to a depth exceeding 180 cm, or to the
underlying shale. The water balance (applied water + rainfall +
change in soil moisture storage) was summed for each of the
growth stages shown in Figure 26. The water balance generally
exceeded the crop evapotranspiration computed as described above,
70
-------
TABLE 3. COMPUTATION OF ET FOR WELL-WATERED CORN CROP
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Date
May 3-9
10-16
17-23
24-30
May 31- June 6
June 7-13
14-20
21-27
June 28-July 4
July 5-11
12-18
19-25
July 26-Aug. 1
Aug. 2-8
9-15
16-22
23-29
Aug. 30-Sept. 5
Sept. 6-12
13-19
20-26
Sept. 27-Oct. 3
Oct. 4-10
11-17
18-24
25-31
Nov. 1-7
Kco
0
0
0.08
0.21
0.25
0.31
0.40
0.49
0.61
0.71
0.81
0.90
0.95
0.98
0.99
0.99
0.95
0.72
0.48
0.25
0
0
0
0
0
0
0
Penman
ET (mm)
29.5
56.7
33.9
46.9
66.4
68.9
63.3
58.3
70.6
76.2
61.4
57.7
55.2
63.2
59.0
53.6
54.3
60.0
30.7
45.6
26.8
33.1
31.1
33.8
26.6
22.5
23.6
ET
(mm)
0
0
3
10
17
21
25
29
43
54
50
52
52
62
58
53
52
43
15
11
0
0
0
0
0
0
0
TOTAL
650
71
-------
indicating that some water was lost to drainage. There was not
sufficient drainage that it could be measured as outflow from the
plots. In those cases where the water balance for a particular
growth stage was less than the computed crop evapotranspiration,
this lower value was used for crop ET.
Evapotranspiration from plots not receiving water was
obtained by measuring the soil moisture in the crop root zone
each week with the neutron probe. In these plots, no drainage
was taking place, allowing ET to be obtained by taking the dif-
ference in soil moisture between successive weeks, plus rainfall.
Rainfall was extremely light during the growing season and hence
was taken as fully effective. The ET derived for each growth
stage is shown in Appendix C.
Because of the late start in data collection, the crop water
use computations for the wheat must be considered less accurate.
As soil moisture data were not collected until mid-May, the ET
for the preceding period was taken as the difference between the
moisture content at field capacity and the moisture content at
the time of 'first measurement, plus the intervening precipita-
tion. The intervening precipitation, totaling 102 mm, was well
distributed (the maximum daily total was 15 mm, with no other
daily amounts over 6 mm) and hence was taken as fully effective.
For the remainder of the season, the crop ET was computed or
measured in the same manner as for the corn crop, using the
appropriate crop coefficient from Jensen (1973), also truncated
at the end of the season. The data are listed in Appendix F.
72
-------
SECTION 8
CROP YIELDS AND WATER USE
CORN
The variation of grain yield and dry matter yield with
evapotranspiration has been plotted in Figures 27 and 28,
respectively. A positive correlation between yield and ET exists
in both cases, with the data exhibiting a scatter similar to that
found by other researchers such as Stewart, et al. (1975) and the
Consortium for International Development (1976). The numerical
results from each plot are given in Appendix D.
As discussed earlier, scatter in the production relations
can be expected due to growth stage effects, particularly in
relation to grain yields. In the experiment conducted here, the
scatter was possibly exaggerated by variations in soil character-
istics from plot to plot. The soil texture and structure showed
slight variations throughout the field, but the major physical
difference was the variation in depth. In addition, the soil
exhibited differences in salinity level and some difference in
fertility. Insect and rodent problems may also have had some
adverse effects on the results.
Soil Fertility Affect on Yield
Fertilization of all fields for the 1976 season was based
on recommendations by the CSU Soil Testing Laboratory, Fort
Collins, Colorado. Composite soil samples from pairs of plots
were made to a depth of 30 cm. These samples were analyzed and
fertilizer recommendations made for a projected 150 bu per acre
(7476 kg per ha) yield of grain. Pairs of plots were broadcast
fertilized independently, in order to bring the field to a
constant or normalized level of fertility (Table 1).
Knowing that soil fertility differences may give erroneous
yield results in the interpretation of the irrigation data, it
was important to investigate any fertility differences that
existed within the field. The irrigation treatments placed
varying degrees of stress on the crop's ability to mine nutrients
from the soil. Plant analysis was used to indicate the fertility
status of the soil.
73
-------
0>
=
%O
in
@
"jo
5
"oi
c
2
o
I2OOO
10000
8000
6000
4000
2000
°c
Treatment Symbol
0-0-0 °
1-0-0 a * .
0-1-0 A
O-O-I v A .
- M-0 • B A
I-O-I • D ^
O-I-I
I-M v DQ v •
°* A
^ a
.<>»
o
_ _
i l i i i i
) 100 200 300 400 500 600 7C
Figure 27.
Seasonal ET, mm
Variation of grain yield of corn with seasonal
evapotranspiration.
74
-------
2
0)
18000
16000
14000
12000
10000
0)
o
2
>^
k.
o
8000
o 6000
o
4000
2000
Treatment Symbol
0-0-0 °
I-0-0 °
0-1-0 A
0-0-1 v
I-I-O •
I-O-I •
O-I-I A
I-I-I *
v a
0
-L
1
1
100 200 300 400 5OO
Seasonal ET, mm
600
700
Figure 28. Variation of dry matter yield of corn with
seasonal evapotranspiration.
75
-------
Research has shown that plant leaf analysis is a reasonably
accurate method of evaluating differences in fertility status of
the soil. The soil test data (Table 4) and the fertilization
practices (Table 1) indicate that P, K, Fe and Zn should not be
limiting to the crop. It was expected that N was the major
element influencing corn yields and was used as the indicator
element in the plant leaf analysis.
When approximately 75 percent of the field showed silk
emergence (August 5), 100 leaf samples of the second leaf down
from the top ear were obtained from the harvest rows of each
plot. They were air dried, ground and analyzed for the determi-
nation of total N content in the laboratory. The semi-micro
Kjeldahl method for total N was used for the analysis (Black,
1965). The results are shown in Table 5.
The analysis of variance revealed no significant difference
in leaf tissue N content among irrigation treatments on August 5.
Thus, it was first assumed that no significant soil fertility
differences were present among irrigation treatments. There was,
however, a high correlation (r=0.87) between the percentage N in
the leaf ti«ssue and yield of the various irrigation treatments
when the 0-0-0 treatment was excluded (Figure 29).
The percentage of N in corn leaves at near maximum yield is
reported to be between 2.5 and 3.0 (Pierre et al., 1966). Maxi-
mum yields in this experiment were in excess of the projected
grain yields for which the fertilizer recommendations were based.
It is therefore possible that higher yields could have occurred
had a higher N fertilization rate been applied (Treat, 1978).
Salinity Effects on Yield
A high salt content in the soil adversely affects the plant's
ability to absorb water and nutrients vital to its development.
This becomes especially critical when attempting to study the
effects of moisture stress on yield. High salt concentrations
impose a far greater amount of moisture stress on the plant than
normally would be imposed in a nonsaline soil. It was suspected
that if saline areas were present in the field they could
influence the yield results of the irrigation treatments.
Therefore, in order to determine if high salt concentrations
existed in the field, salinity measurements were obtained on
each plot.
Soil samples were collected to a depth of 4 feet (120 cm)
in mid~July using a soil "King" tube. A composite sample was
taken consisting of two cores from the middle harvest row on each
side of the two neutron probe access tubes, giving a total of
four cores from each plot. An analysis of the electrical con-
ductivity (EC) of the soil saturated extract and the pH of a
saturated soil paste was made in the laboratory. The results are
shown in Table 6.
76
-------
TABLE 4. SOIL ANALYSIS FROM WHICH FERTILIZER RECOMMENDATIONS
WERE BASED
PAIRED
PLOTS
17-18
19-20
21-22
23-24
25-26
27-28
29-30
31-32
33-34
35-36
37-38
39-40
41-42
43-44
45-46
47-48
MEAN
S . DEV .
pH
7.6
7.7
7.6
7.6
7.7
7.8
7.6
7.6
7.7
7.5
7.6
7.4
7.7
7.6
7.5
7.6
7.6
0.09
SALTS
mmhos/cm
7.0
4.7
2.4
4.7
3.0
4.5
3.4
4.2
3.8
4.0
5.2
4.5
3.7
3.4
5.5
4.5
4.3
1.08
%ORGANIC
MATTER
0.9
0.9
0.8
1.0
0.8
0.9
0.9
0.8
1.0
1.0
0.9
0.9
1.1
0.9
1.0
1.2
0.9
0.11
N03-N
ppm
+99
36
21
+99
39
61
73
+99
+99
70
+99
+99
78
+99
+99
+99
26.90
P
ppm
13
14
9
16
15
18
13
15
17
15
19
18
20
20
18
27
17
4.01
K
ppm
165
154
128
160
148
183
200
175
158
183
195
220
250
225
195
278
189
39.46
Zn
ppm
1.1
1.1
0.9
1.0
1.1
1.1
1.1
1.1
1.2
1.1
1.4
1.1
1.0
1.2
1.0
1.4
1.1
0.13
Fe
ppm
8.1
7.4
9.3
7.8
8.3
7.1
8.5
7.5
12.9
8.1
7.3
8.9
7.6
12.9
6.0
17.0
9.0
2.84
77
-------
TABLE 5. ANALYSIS OF VARIANCE OF PERCENT TOTAL NITROGEN IN
CORN LEAVES
Irrigation
Treatment
I-O-I
0-1-0
0-0-0
0-0-1
I-I-I
I-I-O
1-0-0
O-I-I
Mean
Source
Total
Replication
Treatment
Error
Rep
I
1.66
1.87
1.94
1.69
2.17
2.05
1.82
1.62
1.85
Rep
II
1.46
1.82
2.06
1.43
1.71
2.12
1.24
2.32
1.77
df
31
3
7
21
Rep
III
2.02
2.09
1.83
1.67
2.24
2.06
2.15
2.11
2.02
SS
3.052
1.274
1.207
1.571
Rep
IV
1.55
1.46
2.06
1.13
2.05
2.18
2.41
1.86
1.84
MS
0.091
1.172
0.075
Mean
1.67
1.81
1.97
1.48
2.04
2.10
1.91
1.98
1.87
F
1.21 NS
2.29 NS
Std. Dev. =0.27
C.V. = 14.44%
78
-------
10.0 r
1.0
Figure 29
Excluding Treatment 0-0-0
y= 5.046 (%N)-2.72
r =0.87
r2=0.75
y=3.958(%N)-l.092
1.5 2.0 2.5
% Total N in Corn Leaves
3.0
Grain yield in relation to the percent nitrogen
in the corn leaves.
79
-------
TABLE 6. pH AND THE ELECTRICAL CONDUCTIVITY OF COMPOSITE
SOIL SAMPLES FROM EXPERIMENTAL PLOTS*
EC
(wnhos./cm
Plot pH at 25° C)
Rep I
Rep II
Rep III
Rep IV
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
7.4
7.1
7.2
7.2
6.9
7.5
7.4
6.9
7.5
7.1
7.0
6.7
7.1
7.4
7.3
6.9
7.4
7.4
7.4
7.5
6.6
7.3
7.5
7.3
7.2
6.9
7.8
7.2
7.3
6.9
7.4
7.4
5.37
3.62
4.07
2.63
3.53
2.17
3.58
3.88
3.62
4.43
1.99
3.66
1.70
1.98
1.63
3.68
1.80
4.13
2.13
3.59
3.58
2.07
2.88
3.37
3.19
1.92
1.55
2.81
3.24
3.32
3.58
3.41
*pH of saturated paste, conductivity
of saturation extract
80
-------
The average electrical conductivity for all plots was 3.1
mmhos cm"1, and ranged from 1.5 mmhos cm"1 to 5.4 mmhos cm"1.
The pH values averaged 7.22, and ranged from 6.6 to 7.8. The
sodium adsorption ratio of samples collected during the previous
winter was about, 2.
The electrical conductivity of the soil saturated extract
indicates that salinity could have had a small influence on corn
yields. Bernstein (1964) reports that a small yield decrement
can be expected for corn when EC values exceed 3.3 mmhos cm"1 and
that a 10 percent yield decrement is possible for values exceeding
5.0 mmhos cm"1. Yields probably were only slightly affected in
this experiment since the two plots with the highest salinity
(17 and 26) were not stressed during the season (Treatment I-I-I).
A statistical analysis of the electrical conductivity values shows
no significant difference for either soluble salt content among
replication or for irrigation treatments (Table 7). It is
possible, however, that salinity may have caused a yield difference
between treatments I-I-O (3.07 mmhos cm"1) and I-I-I (3.86 mmhos
cm"1) due to the higher EC values for treatment I-I-I. All pH
values were found to be in a range favorable for plant development
(Treat, 1978).
Basis for Yield Analysis
An aerial view of the corn plots (Figure 30) shows the
variation in development of the crop under the different moisture
regimes. The difference between two of the plots is shown in
Figure 31.
To reduce the impact of any of these yield-reducing factors
described above, apart from ET, on yield, averages were taken
of yield and ET values for the plots making up a given treatment.
This allows easy assessment of the relative water use efficiencies
of the different irrigation treatments, as shown in Figure 32
and 33 for grain yield and dry matter yield, respectively.
(a)
The linear upper bound on the grain yield has been plotted
on Figure 32. This represents the maximum yield for a given
quantity of ET with the water applied under the regimes tested
here. Three constraints were imposed in plotting the line: (
it should pass through the point having the highest water use
efficiency; (b) a positive amount of ET is required to produce
any grain, i.e., its projection should cut .the abscissa to the
right of the origin; and (c) it should pass through the data
point corresponding to the 0-0-0 treatment.
The last point is not altogether readily justifiable,
although it is based on the results of other researchers. For
example, from their work with pinto beans, Stewart, et al. (1976)
believe that the yield reduction in Treatment 0-0-0 is primary,
with no secondary yield losses from nonoptimal timing of deficits.
81
-------
TABLE 7. AN ANALYSIS OF VARIANCE OF THE ELECTRICAL
CONDUCTIVITY FOR COMPOSITE SOIL SAMPLES TAKEN
FROM THE VARIOUS IRRIGATION TREATMENTS
(ALL VALUES IN nunhos cm~l at 25°C)
Irrigation
Treatment
0-0-0
0-0-1
I-O-I
0-1-0
O-I-I
1-0-0
I-I-O
I-I-I
Mean
AOV TABLE
Source
Total
Replication
Treatment
Error
Rep
I
2.63
2.17
4.07
3.62
3.58
3.88
3.53
5.37
3.60
d£
31
3
7
21
Rep
II
3.68
3.62
1.70
3.66
1.63
1.99
1.98
4.43
2.84
SS_
27.31
3.21
5.76
18.34
Rep
III
3.59
2.13
4.13
3.58
1.80
2.88
3.37
2.07
2.94
MS
1.07
0.82
0.87
Rep
IV
3.24
3.19
3.20
1.92
2.81
1.55
3.41
3.58
2.86
F
1.23 NS
0.94 NS
Mean
3.29
2.78
3.28
3.20
2.46
2.58
3.07
3.86
3.07
Std. Dev. =0.93
C.V. + 30.40%
82
-------
Figure 30.
Variation in corn crop resulting from different
irrigation regimes (view to the south).
Figure 31.
Difference in plant development between well-watered
corn plot (left) and stressed plot (right).
83
-------
9000
8000
« 7000
3
6000
in
- 5000
4000
.2 3000
c
'6
2000
1000
~w
I-I-Ojf /
/•H-l
Linear Upper Bound
y = 17.89 (ET)- 1937
• I-O-I
Linear Regression
y = 14.65 (ET)-857 (r2 * 0.87)
Figure 32.
100 200 300 400 500 600 700
Seasonal ET, mm
Corn grain yield versus ET: average for
each treatment.
84
-------
14000
12000
•£ 10000
JC
32~
•c 8000
0)
*—
15
6000
o
o 4000
•*—
2000
M-Oj
•1-0-0
• 0-H
0-0-1
• I-O-I
I-I-I*
Linear Regression
y =I6.55(ET)-25I3 (rz = 0.6l)
0 100 200 300 40O 500 600 700
Seasonal ET, mm
Figure 33. Corn dry matter yield versus ET: average for
each treatment.
85
-------
In other words, it is hypothesized that the genetic pattern of
root elongation and proliferation of pinto beans will, in fact,
result in the extraction of stored soil water throughout the
growing season in a time related pattern which will constitute
an optimal ET deficit sequence, provided that: (a) the soil
profile is sufficiently deep for full root development, with
moderately high water holding capacity and no structural impair-
ment; (b) the entire profile is at field capacity when the crop
is planted; and (c) little or no water is applied to the soil
during the growing season. These conditions were met in Treatment
0-0-0 with the possible slight violation in two of the plots
where the soil profile was only a little more than 200 cm deep
in places.
As the infinite combination of possible irrigation regimes
could not be tested in the experiment, it is possible that
slightly higher yields would be attainable for a given quantity
of ET. However, the high soil salinity, the inadvertent early
stressing and pest problems would probably be a greater limita-
tion on yield than the irrigation regime. The average yield of
the highest yielding treatment approximated the valley average,
while the individual highest yield was well above the valley
average (approximately 25 percent higher) and higher than those
of the better neighboring farmers.
Grain Yields
Grain yields and the analysis of variance are summarized in
Tables 8 and 9, respectively. The variance for the irrigation
treatments was partitioned into individual degrees of freedom to
assist in analyzing treatment effects.
The effects of each irrigation treatment on grain yield are
clearly seen in Figure 34. At point 0-0-0 all plots were irri-
gated the same until the start of the vegetative stage. Treat-
ment 0-0-0 received no additional irrigations from this date.
At point 1-0-0 only the pollination stage received an irrigation
and so on with -I- designating irrigation and -0- designating
no irrigation during a particular growth stage.
Grain yields for the treatments that were irrigated during
the vegetative stage (the dashed lines in Figure 34) were higher
(see Table 9) than the average for treatments not irrigated
during the vegetative stage (the solid lines in Figure 34).
Maximum yields were obtained when the corn was irrigated during
both the vegetative and pollination stages (I-I-O). Continued
irrigation through the grain filling stage (I-I-I) was of no
additional value. Partitioning of the variance associated with
those treatments receiving irrigation during the vegetative stage
(B treatments in Table 9) showed that the variance was associated
primarily with the pollination irrigations and little was
associated with irrigation during grain filling. In a similar
86
-------
TABLE 8. THE EFFECT OF IRRIGATION TREATMENT ON THE YIELD
OF GRAIN (kg/ha AT 15.5% MOISTURE)
Treatment
0-0-0
0-0-1
1-0-0
I-O-I
0-1-0
O-I-i
I-I-I
I-I-O
Rep
I
3162
5941
4615
5901
7131
4775
8301
10956
Rep
II
3429
4380
4433
4942
5144
8481
6555
8644
Rep
III
3528
5294
6105
5663
8880
4917
10051
6214
Rep
IV
5678
4582
7199
3570
5014
7092
7544
7796
Mean
3949*
5049*
5588*
5769*
6542
7067
8113
8403
Mean
6348
6126
6707
6060
6310
Yield lower than I-I-O treatment at 0.05 level.
way the variance of the grain yields (Table 9) for treatments
not irrigated during the vegetative stage was associated largely
with the pollination stage irrigation rather than with the
grain filling irrigations (compare 0-0-0 vs. 0-1-0, 0-0-1 vs.
O-I-I). The results show that irrigations during the pollination
period had a much greater effect than those during either the
vegetative or the grain filling period.
The relative importance of irrigation during each of the
three growth stages is of interest when considering water-use
efficiency. When only one growth stage was irrigated beyond crop
establishment, the best treatment was the one receiving an irri-
gation during the pollination period (0-1-0). The results
clearly demonstrate the importance of irrigation during the
pollination stage and confirms the widespread observation that
the pollination period is "critical" with respect to water
deficits and yield response. This stage should receive the
highest priority when allocating irrigation water.
87
-------
TABLE 9. ANALYSIS OF VARIANCE FOR YIELD OF GRAIN
Source of variance
Total
Replication
Treatment
A vs B
0-0-0 1-0-0
0-0-1 I-O-I
0-1-0 I-I-I
O-I-I I-I-O
within A
{0-0-0+0-O-Dvs (O-I-O+O-I-I)
(0-0-0 vs 0-0-1)
(0-1-0 vs O-I-I)
within B
(l-O-O-H-O-I)vs (I-I-I+I-I-O)
(1-0-0 vs I-O-I)
(I-I-I vs I-I-O)
Error
df
31
3
7
1
3
1
1
1
3
1
1
1
21
ss_:j: MSjf
121.00
2.04 0
64.90 9
13
24.26 8.
21.
2.
0.
26.84 8.
26.
0.
0.
54.60 2.
.68
.28
.86
08
26
42
55
95
61
06
17
60
0
3
5
3
8
0
0
3
10
0
0
F
.26 NS
.57*
.33*
.10*
.18*
.93 NS
.21 NS
.44*
.23t
.02 NS
.07 NS
Std. Dev. =1.61
C.V. = 25.5%
L.S.D. = 2372 kg/ha
* significant @ 0.05
t significant @ 0.01
x 106
88
-------
Growth Stage
I
'o
5
#
IT)
in
oo
V)
0
»-
o
9
8
6
5
4
0
0-0-0
Plant Secondary Rooting
Tassel
Blister Kernel
I Irrigation
0 Non-Irrigation
Vegetative Period
Irrigated
Vegetative Period
Not Irrigated
Mature
Emergence a Establish
Vegetative Period
Pollination Period
Grain Filling Period
29th April
13th June
13th July
15th August 17th September
Figure 34. The effects of irrigation treatments on grain yield.
-------
The vegetative period is seen in Figure 34 and Table 9 to
be the next most important growth stage to be irrigated, whereas
irrigation during the grain filling stage had little or no
benefit on grain yield. This phenomenon was also reported by
Stewart et al. (1975), who noted that in similar experiments with
corn, late irrigation had either no effect or a negative effect
on grain yield. The lack of benefit from the last irrigation
may be due to a lower need for water during this stage. It may
be that the corn plant can obtain sufficient moisture from its
own tissues or by drawing on soil moisture from its extensive
root system so that an imposed moisture stress did not occur
during this last stage of development. It is also possible that
a reduction in respiration occurred when the root-zone was kept
moist during the highly active period of grain filling. It is
evident that when adequate moisture is present during the pre-
vious stage, a water deficit is tolerable in the grain filling
period without causing grain yield losses. Under similar condi-
tions, the elimination of irrigation during this stage of
development could amount to substantial savings in water.
The suggestion has been made that early stress may have a
tendency to condition the plant against damage from stress at a
later stage as far as grain yield is concerned. Stress occurring
in the vegetative stage forces the plant to develop a more
extensive root system which helps to meet the water requirements
needed during ear development. Denmead and Shaw (1960) reported
that early moisture stress, which reduces the size of the
assimilation surface at the time of ear development, may have
little effect on grain yield; while stress imposed after the ear
has emerged has a more direct negative effect by reducing the
rate of assimilation during a critical period when photosynthesis
is being used for grain production.
Forage (Dry Matter) Yields
The literature reviewed in Section 4 indicates that dry
matter production is directly proportional to ET and that the
timing of deficits has no effect. The distribution of the data
points in Figure 33 would appear to support this view; however,
the averages tend to mask some of the scatter obtained in the
individual replications (see Appendix E, Figures E-l to E-8). In
a crop such as corn, where the grain makes up a high proportion
of the weight of dry matter (40 to 56 percent on a dry weight
basis for the treatment averages in this experiment), it would
appear reasonable to speculate that an ET deficit particularly
detrimental to grain yield would have a correspondingly detri-
mental effect on dry matter yield.
90
-------
Forage (dry matter) yields were determined by harvesting
a portion of each plot at the time the crop was normally harvested
for ensilage. The grain was well into the dent stage of develop-
ment at harvest (September 17). Yield results are shown in
Table 10.
An analysis of variance of total dry matter yield is shown
in Table 11. The treatment variance was partitioned into
individual degrees of freedom to compare irrigation treatments.
Figure 35 clearly shows the effect of the various irrigation
treatments on the yield of total dry matter. There was a highly
significant beneficial effect from irrigating during the vegeta-
tive stage (Table 11, group A vs. group B). Differences in yield
between the pollination stage and grain filling irrigations were
not signficant at the 0.05 level although the pollination stage
irrigation appeared to contribute slightly more than irrigation
during grain filling (Figure 35).
The three high yielding treatments, I-I-I, I-I-O and 1-0-0,
were all irrigated during the vegetative stage and the yield of
the 1-0-0 treatment was 11.95 T per ha. However, for some
unexplainable reason, the yield of the I-O-I irrigation treatment
was only 9.07 T per ha. It is difficult to explain why irri-
gation during the grain filling stage would cause a decrease in
total dry matter yield. Neither the N nor the soil salinity
level deviated from their means sufficiently to explain the
diverse results.
Analysis of variance (Table 11) reveals that treatments
O-o-O, 0-0-1, 0-1-0 and O-I-I were not significantly different
and yielded much below treatments receiving an irrigation in the
vegetative stage, with the exception of treatment I-O-I. Dry
matter yields for treatments 1-0-0, I-I-O and I-I-I were not
found to be significantly different.
If water is limiting and only one growth stage is to be
irrigated, these results indicate that the most efficient water-
use treatment for forage production should be one such as 1-0-0
which received irrigation only during the vegetative period. The
elimination of irrigation during both the pollination and grain
filling stages saved 50.1 cm of water (irrigation plus rainfall)
without a significant reduction in yield. The results demonstrate
the greater importance of irrigation during the vegetative stage
for forage production.
If water is available to irrigate through two growth stages,
the vegetative and pollination periods should be the most benefi-
cial. By eliminating the last period of irrigation during the
grain filling stage (I-I-O), a savings of 24.5 cm of water applied
91
-------
TABLE 10. THE EFFECT OF IRRIGATION TREATMENT ON TOTAL DRY
MATTER YIELD (METRIC T/ha, OVEN DRY)
Treatment
0-0-0
0-0-1
I-O-I
0-1-0
O-I-I
1-0-0
I-I-O
I-I-I
Rep
I
6.08
12.21
6.89
10.49
9.62
10.96
12.21
11.62
Rep
II
7.18
7.35
10.98
7.28
12.19
10.16
12.12
11.41
Rep
III
8.34
10.24
9.35
13.57
11.09
12.41
10.20
15.35
Rep
IV
9.91
6.07
9.06
9.54
9.95
14.26
17.26
15.59
Mean
7.88*
8.97*
9.07*
10.22*
10.71
11.95
12.94
13.49
Mean 10.01 9.83 11.33 11.45 10.65
Yield lower than I-I-I treatment at 0.05 level.
was achieved without a significant reduction in yield from the
maximum. The vegetative stage was clearly the more critical
period with respect to dry matter production. This differs from
grain production, where the pollination stage was of greater
importance. This relationship concurs with the findings of
Denmead and Shaw (1960), Robins and Domingo (1953), and
Kiesselbach (1950), who also found that increasing moisture stress
during the vegetative stage of growth reduced dry matter
production.
Relationships Between Grain and Dry Matter Yields
In attempting to trace the effect of water stress during
the various stages of growth and in formulating appropriate
models, researchers are faced with the problem that grain yield
can be measured only after crop maturity. On the other hand,
many of the classical studies relating dry matter yield to ET
were carried out by harvesting the forage at different stages of
maturity. One way of approximating the effect of stress on
grain yield may be by tracing the effects of stress on dry
matter yield and then relating grain yields to dry matter
(Neghassi, 1974).
92
-------
TABLE 11. ANALYSIS OF VARIANCE FOR YIELD OF DRY MATTER
Source of Variance
Total
Replication
Treatment
A vs B
0-0-0 I-O-I
O-O-I 1-0-0
0-1-0 I-I-O
O-I-I I-I-I
within A
within B
(I-O-I)vs
(I-0-O+I-I-O+I-I-I)
(I-0-O+I-I-O+I-I-I)
Error
df_
31
3
7
1
3
3
1
2
21
sst
230.00
17.37
113.04
19.60
46.55
4.90
99.50
MSt
5.79
16.15
46.90
6.53
15.52
41.64
2.45
4.74
F
1.22 NS
3.40*
9.89
1.38 MS
3.27*
8.79t
0.52 NS
Std. Dev. +2.18
C.V. + 20.44%
L.S.D. = 3.2 metric T/ha
*significant @ 0.05
tsignificant @ 0.01
93
-------
*..
Growth Stage
14
&
w
O
O
O
12
• 10
9
o
2
Q
O
n
m
i-i-.
I-CM3
Plant Secondary Rooting
To ssel
Blister Kernel
jEmergence ftEstoblith
Vegetative Period
Pollination Period
O-I-I
I Irrigation
0 Non-Irrigation
„«.«. Vegetative Period
Irrigated
_„__ Vegetative Period
Not Irrigated
Mature
Groin Filling Period
29th April
13th June
13th July
15th August 17th September
Figure 35. The effects of irrigation treatments on dry matter yield.
-------
The relationship between grain yield and dry matter yield
is plotted on Figure 36. The relationship is obviously linear,
with all but two of the data points falling within a fairly
confined band on each side of the adjusted regression line.
Excluding the two most deviant data points, the linear regression
equation is:
yG = 0.557 yDM + 370 (r2 = 0.59) (31)
where yQ is the grain yield and y_M is the dry matter yield.
The regression line has been adjusted slightly in Figure 36 to
pass through the origin, in accordance with the plots shown by
Neghassi (1974).
To use this function to predict grain yield from a
successful dry matter yield model, however, would be to ignore
the effects of stress at different stages of growth. in fact
close examination of Figure 36 indicates that some irrigation'
regimes are far more conducive to dry matter production compared
to grain production, and vice versa. Within a particular treat-
ment, the relationship between grain and dry matter yield is
basically linear (for example, Treatment 1-0-0). However, this
treatment and Treatment 0-0-0 obviously favor dry matter produc-
tion much more than say Treatments 0-1-0 and O-I-l, the data
from which are mostly on the other side of the regression line
favoring grain production. The remaining treatments do not show
any particular trend. The implication is that crops receiving
water only in the early growth stages will yield comparatively
more dry matter per unit of water than any other irrigation
regime, which is illustrated in Figure 37, where average dry
matter water use efficiency has been plotted against grain water
use efficiency. The units of kilograms per hectare-millimeter of
water have been used to provide physical meaning. (TO be
strictly correct, they could be corrected to dimensionless units
of efficiency in percent by dividing by 100.) The data fall into
two groups, in which Treatments 0-0-0 and 1-0-0 show a high
efficiency in terms of dry matter production, while treatments
0-1-0 and I-I-O in particular show a high efficiency in terms of
grain production. The remaining treatments decline in efficiencv
of both grain and dry matter production. Treatment I-O-I, which
has the lowest efficiency in both areas, nonetheless falls on
the "grain" side of a hypothetical line through the origin
dividing the two groups of points. This perhaps indicates that
while the severe stress during the pollination period (without
any preconditioning) had a drastic effect on grain yield, the
effect on dry matter yield was even more marked. Earlier, it
was suggested that this might be the case because the grain com-
ponent makes up a substantial portion of the dry matter yield
It also suggests that the classical studies relating dry matter
yield to ET, in which the forage was harvested at different
95
-------
18000
16000
14000
'o 12000
33
.2 10000
>-
8000
6000
4000
2000
Treatment Symbol
0-0-0
I-0-0
0-1-0
0-0-1
I-I-O
I-O-I
O-I-I
I-I-I
Linear Regression
/ y = 0.557 Y + 370 (r2 = 0.59)
i
0 200O 4000 6000 8000 10000 I200O
Groin Yield, kg ho"1
Figure 36. Relationship between dry matter yield and
grain yield for corn.
96
-------
30
7_
i ?s
0 "
.
£ 20
«j
'5
£
0)
IA
15
I I0
k.
5
r»
Designated Points Are Averages ,
for That Treatment /
' " / A-
1-0-0 4- /
i /
o-o-o V/o T A
a o-r-o +I"I"°
X-r+T1^"1 " *
I/ o-o-i**
/_• V
Treatments • I-O-I A Treatments
Dry Matter / v Grain
/ Treatment Symbol
/ 0-0-0 o
/ 1-0-0 a
/ 0-1-0 A
/ o-o- 1 v
/ I-I-O •
/ I-O-I .
/ O-I-I A
/ I-I-I
f 1 1 1
Figure 37.
^0 5 10 15 20
Grain, Water Use Efficiency, kg(ha-mm)"1
Water use efficiency of corn: dry matter
versus grain.
97
-------
stages of maturity, may not be particularly appropriate to the
field situation. The timing of deficits on the yield of forage
harvested at maturity may warrant further investigations, parti-
cularly with regard to the plant physiology.
Water Production and Water Use Efficiencies
The water production efficiencies (also called water applied
efficiencies) and water use efficiencies for grain and dry matter
production are given in Table 12 for the various irrigation
treatments. The water production efficiencies are inversely
related to yield, with maximum production efficiencies occurring
with the lowest yielding treatments. The high efficiencies were
due to the corn plants ability to utilize existing soil moisture
and to withstand long periods of drought stress.
TABLE 12. EFFICIENCY OF IRRIGATION WATER APPLIED AND OF' TOTAL
MEASURED WATER USE IN TERMS OF YIELD PER UNIT
OF WATER
Water Production
Efficiency*
Treatment
0-0-0
1-0-0
0-1-0
0-0-1
I-I-O
I-O-I
O-I-I
I-I-I
Dry Matter
kg/cm
684
436
280
242
244
165
182
174
Grain
kg/cm
343
204
179
136
158
105
120
105
Water-Use
Ef f iciencyt
Dry Matter
kg/cm
239
279
216
202_
224
176
206
201
Grain
kg/cm
144
149
150
129
160
128
140
137
*Values represent the average yield divided by cm. of
seasonal water applied by irrigation and from rainfall
tValues represent the total yield divided by measured
seasonal ET obtained by the water balance approach.
98
-------
The water use efficiencies are directly related to yield
with maximum efficiencies occurring in the higher yielding
treatments (Table 12). The irrigation treatments which approach
the maximum water use efficiency were irrigated during the most
critical stages of growth, particularly during the vegetative
stage for dry matter yield and during the pollination stage for
grain yield as discussed previously.
A comparison of the relationship between yield and the
amount of water supplied to the plants, and the relationship
between yield and ET, has been illustrated in Figures 38 and 39
for grain and dry matter yields, respectively. The amount of
water supplied to the plants is defined in this case as the sum
of the depth of irrigation water applied, plus rainfall, plus
the end of season depletion from field capacity in the range 0
to 190 cm (or to the underlying shale if at a depth of less than
190 cm). This assumes that all plots were watered to field
capacity at the beginning of the season to a depth of 190 cm
(or to shale). The validity of this assumption could not be
quantitatively checked but it appears highly probable.
The difference between water supply as defined and ET for
Treatment 0-0-0 would be anticipated to be smaller than for any
of the other treatments, as no additional irrigation water was
applied after the establishment period. In fact, Treatment
0-1-0 was found to have approximately the same difference, indi-
cating that all of the water applied in this treatment was
consumed. Treatment 1-0-0 was found to have a smaller difference,
created by the anomaly discussed above, but this was ignored.
Therefore, the ET abscissa was displaced to the right, compared
to the water supply abscissa, by an amount equal to this
difference. The yield versus water supply function was drawn as
a best fit through the plotted points.
In the case of grain yield versus ET, the function has
been drawn as the linear upper bound in the same manner as in
Figure 32. With the displaced abscissa shown in Figure 38, the
yield versus water supply function is tangential to the yield
versus ET function at the point corresponding to Treatment 0-0-0
but diverging away from the function at higher values of water
supply. This substantiates the point made in Section 4 that the
difference between linear and curvilinear production functions
is due to the choice of abscissa. The functions shown in
Figure 38 have exactly the same form as those presented by
Stewart and Hagan (1973) and shown in Figure 7.
Because of the scatter of data, the drawing of a dry matter
production function is more difficult and less precise. However,
a yield versus water supply function has been drawn through the
dry matter data in Figure 39 which is tangential to the yield
versus ET function (with the displaced abscissa) at lower values
99
-------
10000
ET, mm
0 200 400 600 800
i
8000
o
JC
5 6000
°v
•E 4000
o
2000
I I i i
I-I-O
O Yield versus ET
• Yield versus Wafer Supply
200 400 600 800
Water Supply, mm
1000
Figure 38. Relationship between grain yield and ET and
between grain yield and crop water supply,
for corn.
of water supply. Again, the data confirms that the difference
in the two functions is due to the choice of abscissa.
WHEAT
As the experimental control in the wheat experiment could
only be described as "fair," the results are presented more for
completeness and to confirm existing recommendations than for
any subsequent detailed analysis. The results are shown in
Figure 40, where grain yield is plotted against ET computed as
described in Section 6. As only 10 plots were included in the
experiment, the results of the individual plots are shown, rather
than the average results. The numerical results are given in
Appendix F.
100
-------
14000 i r
12000
10000
2 8000
4)
6000
4000
2000 -
200
ET, mm
400 600
800
O Yield versus ET
• Yield versus Wafer Supply
0 200 400 600 800 1000
Water Supply, mm
Figure 39. Relationship between dry matter yield and
ET and between dry matter yield and crop
water supply, for corn.
101
-------
5000
4000
3000
2000
1000
0
Individual
Treatment Plots Average
0-0 o •
1-0 o •
0-1 o •
I-I A A
i
100 200 300 400 500
Seasonal ET, mm
600 700
Figure 40.
Variation of grain yield of wheat with
seasonal evapotranspiration.
From many studies carried out on wheat, Salter and Goode
(1967) were able to draw the general conclusion that:
During the shooting and earing stages of growth, when
the development of the reproductive organs is taking
place, the wheat plant is especially sensitive to soil
moisture conditions. Shortage of water in the soil,
and also atmospheric drought, had the greatest effect
at this time in terms of loss of yield, and in many
experiments this loss was irreversible and could not
be regained by providing optimum moisture conditions
at other growth stages. Irrigation and rain have
also generally been shown to have the maximum
beneficial effect during shooting and earing.
Observation of the results shown on Figure 40 substantiates
this conclusion in respect to the effect of moisture stress
during the earing stage (when the ear is emerging from the tube
formed by the leaf sheaths). No differentiation in moisture
stress was made during the shooting stage (the stage of elonga-
tion of internodes). It is particularly noticeable that
102
-------
irrigating in the grain-filling period is of little value. The
I-I Treatment shows very little improvement in yield over the 1-0
Treatment, and Treatment 0-1 shows very little improvement over
0-0. Irrespective of the earlier treatments, the later irrigation
was virtually wasted. The early irrigation (1-0) showed a sub-
stantial increase in yield over the higher of the 0-0 treatments
in only one of the three plots, although the average of the
three 1-0 treatments is substantially higher than the average of
the two 0-0 treatments. Although the early irrigation was of
benefit, it would appear that the stress during the shooting
stage may even have limited the effectiveness of this irrigation.
103
-------
SECTION 9
FERTILIZER USE EFFICIENCY
The fertilizer treatments of the study were designed to
insure crop growth and to evaluate salt transport. The princi-
pal study area was Field II, which was used to grow corn. The
fertilization of the alfalfa, wheat, and Jose Tall Wheatgrass
was to promote crop vigor and evaluate salt transport from the
bottom of the root zone.
Due to a paucity of data from some of the drains surrounding
each plot in the test area, as a result of an experimental de-
sign that pnly supplied sufficient irrigation water to satisfy
the evapotranspiration requirements of the crop, it is not
possible to evaluate salt transport in all the test plots. The
best data are available for salt transport and fertilization on
Plots 22 and 23 located in Field II because these two plots con-
tained the vacuum extractors. The discussion in this section
will be an evaluation of the data for nitrate and nitrogen use
and nitrate transport in Plots 22 and 23.
As indicated in an earlier section, one goal of the
fertilizer treatment was to achieve a level of nitrogen in the
surface soil of either 100 ppm or 60 ppm on the plots in Field
II. The fertilizer applications indicated in Table 1 were based
on soil chemical analysis (Table 4). Plot 22 was a low level
treatment plot (60 ppm) and Plot 23 was a high level (100 ppm)
Plot 23 received no fertilizer because laboratory analysis of
the soil samples from this plot showed it was already at the
desired fertility level (99 ppm), whereas Plot 22 required a
fertilizer application of 488 kg per hectare of NH4N03 to in-
crease the soil nitrogen level from 21 ppm of NO3~N to 60 ppm.
A nitrogen balance was computed for both plots which
considered applied, extracted, residual, transported and native
nitrogen sources. Applied nitrogen totaled an equivalent of
488 kg/ha for Plot 22 and 0 kg/ha for Plot 23. The application
requirement was based on surface soil analysis and treatment
level.
The transported nitrogen was computed using volumetric and
quality data for the soil water extracted by the vacuum lysi-
meters. The leachate volumes collected in each plot have been
104
-------
expressed as a surface depth and tabulated in Table 13 for both
Plots 22 and 23. The indicated depth of water represents the
water collected between consecutive dates. For example, in Plot
23 on 6/18/76 the depth is 7.2 ram. This represents the water
extracted between 6/9/76 and 6/18/76. The vacuum lysimeter for
Plot 22 was inoperative for part of the season and the water
balance had to be completed using the change in soil moisture
storage between the beginning and end of the growing season.
The average daily flux was 1 mm for the 63 days of operation of
plot 22, while the seasonal average daily flux is estimated to
be 0.9 mm. For the comparable period, the average daily flux
in Plot 23 was 0.62 mm. The seasonal average daily flux from
Plot 23 for the 116 day test period was 0.45 mm.
The soil-water extracted each week was analyzed for nitrates
along with the other salts being studied. The nitrate values
for the weekly extracts are summarized in Table 14. Inspection
of the data for each plot does not indicate major differences
in the nitrate concentrations for the soil water extracts early
in the season for each plot. The nitrate levels begin to de-
crease in the extracts for Plot 23 after July 23, 1976. The
soil water is being extracted at a depth of roughly 3 feet be-
low the soil surface, roughly the bottom of the root zone. This
would indicate an increased usage of nitrogen by the crop. At
this time, the roots should also be reaching their maximum
development. The data indicate an improved fertilizer usage
with increased crop growth stage.
The volumetric data in Table 13 and the concentration data
in Table 14 were combined to calculate the total nitrate salt
transport. The transport calculation assumed a uniform concen-
tration for the flux equal to the water chemistry analysis at
the end of the extraction period. The calculated transported
nitrate was summed for each interval to give a total transport
value for the plot.
The data in Table 15 show that 24.2 kg/ha nitrate were lost
from plot 22 in the first 63 days of operation and 21.8 kg/ha
were lost from Plot 23 in 116 days of operation. When reduced
to an average value, Plot 22 lost 0.38 kg/ha per day and Plot
23 lost 0.19 kg/ha per day. With the levels of fertilization
being 60 ppm for Plot 22 and 100 ppm for Plot 23, the data from
the extraction indicates that a closer scrutiny of the irriga-
tions is required.
If the total transport is considered for the first 63 days
in Plot 23, the average transport value is 0.31 kg/ha per day,
which is roughly equivalent to the loss in Plot 22. The data
for Plot 23 when compared to Plot 22 show that the majority of
the nitrate loss occurs early in the season. A total of 2.1 kg/
ha was lost after July 23, 1976, which means a total of 19.7 kg/
ha were lost prior to this time in 63 days.
105
-------
TABLE 13. LEACHATE VOLUMES COLLECTED IN VACUUM EXTRACTORS
FROM PLOTS 22 AND 23 DURING 1976
Plot 22 (0-0-1)
Plot 23 (O-I-I)
Date Depth Collected (mm) Date Depth Collected (mm)
5/20/76
5/25/76
6/1/76
6/9/76
6/18/76
6/25/76
7/2/76
7/9/76
7/23/76
Total Flux
Ave. Daily Flux
for 63 days
19.3
4.6
.4
18.4 I*
8.19
5.74
2.72
2.0
2.80
64.15
1 mm
5/20/76
5/05/76
6/1/76
6/9/76
6/18/76
6/25/76
7/2/76
7/9/76
7/23/76
8/12/76
8/24/76
8/31/76
9/14/76
Total Flux
Ave. Daily Flux
5.8
3.9
5.5
4.5 I*
7.2
2.5
2.2
4.5
3.1 I
5.2 I
3.4 I
2.7 I
1.7 I
52.2
. 45 mm
Seasonal Et - 463 mm
Applied IRR - 282 mm
Rain (May 3-July 19) - 35 mm
Total Applied - 349 mm (282+67)
Soil Moisture Seepage - 220 mm
Total Est. Flux - 106 mm (349+
220-463)
Ave. Daily Flux - 0.9 mm
Irrigation applied prior to
July 23 - 42 mm
for 116 days
Seasonal Et - 510 mm
Applied IRR - 509 mm
Rain (May 3-Sept. 19) - 67 mm
Total Applied - 576 mm (509+67)
Total Loss - 562 mm (510+52)
Net - 14 mm (576-562)
*I - Indicates Irrigation
106
-------
TABLE 14. NITRATE CONCENTRATION IN LEACHATE
FOR PLOTS 22 AND 23
Plot 22
Plot 23
Date
NO-
Date
NO,
ppm
meq/1
ppm
meq/1
5/20/76
5/25/76
6/1/76
6/9/76
6/18/76
6/25/76
7/2/76
7/9/76
7/23/76
Extractor
42
36
11
18
53
40
79
85
34
Inoperative
.69
.58
.17
.30
.86
.69
1.27
1.38
.55
5/20/76
5/25/76
6/1/76
6/9/76
6/18/76
6/25/76
7/2/76
7/9/76
7/23/76
8/12/76
8/24/76
8/31/76
9/14/76
65
63
51
16
54
53
58
70
32
36
5.3
2
0
1.05
1.02
.83
.26
.87
.86
.94
1.14
.51
.59
.09
.03
0
The flux values and nitrate concentrations in Plot 23 were
lower after July 23 than earlier in the season. This occurred
even though the supply of water was being increased by irrigation
during this time period. Increases in plant growth activity and
deeper penetration of roots into the soil at-this stage of
growth probably account for the reduced loss of water and lower
nitrate concentrations.
The distribution of nitrates in the soil is shown in Table
16 for Plots 22 and 23 for Fall 1976. The values are fairly
uniform in both plots with high values being in the surface
soils and a reduction in value which is fairly uniform down to
6 feet. At 6 feet, the nitrogen levels increase. The higher
concentrations in the surface soils are a result of fertilization
and native nitrogen due to organic matter. The higher nitrate
107
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TABLE 15. TOTAL NG>3 IN LEACHATE FROM
PLOTS 22 AND 23.
Date
5/20/76
5/25/76
6/1/76
6/9/76
6/18/76
6/25/76
7/2/76
7/9/76
7/23/76
Extractor
Total
Plot 22
NO 3
(kg/ha)
8.1
1.6
0
3.3
4.3
2.3
2.0
1.7
.9
Inoperative
24.2 kg/ha
Date
5/20/76
5/25/76
6/1/76
6/9/76
6/18/76
6/25/76
7/2/76
7/9/76
7/23/76
8/12/76
8/24/76
8/31/76
9/14/76
Total
Plot 23
NO3
(kg/ha)
3.7
2.4
2.7
.7
3.8
1.3
1.3
3.1
.9
1.9
.2
0
0
21.8 kg/ha
Ave. 63 days - .38 kg/ha day Ave. 116 days - .19 kg/ha day
.085 kg-N/ha day .042 kg-N/ha day
108
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TABLE 16. NITRATE DISTRIBUTION IN
PLOTS 22 AND 23 IN FALL OF 1976
Plot 22
Plot 23
Depth
Total
NO-
Depth
172.4
Total
N03
0-1
1-2
2-3
3-4
4-5
5-6
6-7
ppm
8
2
1
3
7
4
10
kg/ha U)
39.4
9.8
4.9
14.8
34.5
19.7
49.3
0-1
1-2
2-3
3-4
4-5
5-6
6-7
Ppm
8
4
3
4
4
4
13
kg/ha*1)
39.4
19.7
14.8
19.7
19.7
19.7
64.1
197.1
(1) Assumes soil bulk density of 1.56 gm/cm3 based on numerous
field measurements for plots 22 and 23.
concentations at the lower depths may reflect that nitrogen was
transported in previous seasons to these lower depths.
The total nitrate in the soil profile was calculated
assuming a soil bulk density of 1.56 gm/cm3. One other source
of nitrogen in the soil is the nitrogen due to organic matter
in the soils.
The extraction of nitrogen by the crop is needed to complete
the analysis. The percentage of nitrogen in corn leaves was
analyzed to obtain an estimate for nitrogen uptake (Table 17).
It was assumed that the leaves would adequately represent the
dry matter. The nitrogen in the grain had a value roughly
equal to that found in the dry matter. The percent nitrogen
in the grain was calculated as percent protein divided by 6.25
Total uptake of nitrogen by corn is summarized in Table 18.
There was an estimated 233 kg/ha extracted in Plot 22 and 207
kg/ha in Plot 23. The additional yield in Plot 22 was responsible
for the higher uptake values. From Table 17 the percentage of
nitrogen present in the leaf samples for Plots 22 and 23 are
nearly equal.
109
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TABLE 17. PERCENT NITROGEN IN LEAVES OF CORN PLANTS
Plot
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
N,%
1.08
1.40
0.06
1.08
0.82
1.44
1.51
1.36
0.92
1.04
1.16
1.09
0.70
, 1.49
1.52
1.27
Plot
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
N,%
1.19
1.01
1.28
1.26
1.12
1.64
1.37
1.14
1.30
1.06
1.11
1.55
1.23
0.93
1.18
1.51
Note-100 leaves taken from rows to be harvested when
approximately 75% of field showed silk emergence (5th of
August). Second leaf from top ear taken and analyzed for
total N by semi-micro Kjeldahl method.
110
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The nitrogen balance is summarized in Tables 19 and 20 for
Plots 22 and 23. In Plot 22 there was an initial soil nitrogen
content of 96 kg/ha and an equivalent application of 200 kg/ha
with an uptake by the crop of 233 kg/ha, a residual in the soil
of 39 kg/ha and a loss of 10 kg/ha in the leachate. The nitro-
gen balance looks very good. The nitrogen loss in the leachate
was roughly 3 percent of the total available nitrogen.
In Plot 23, the plant extracted an equivalent of 207 kg/ha,
there was 45 kg/ha remaining in the soil and 5 kg/ha were lost
in the leachate. Since no nitrogen was supplied as fertilizer,
the nitrogen had to be extracted from the initial soil nitrogen,
which amounted to 490 kg/ha. The nitrogen balance is very poor.
The estimated nitrogen loss in the leachate is probably higher
than indicated; however, the only significance that can be as-
signed to this balance would be that leachate nitrogen loss is
still only a small percentage of the available nitrogen.
Nitrate transport was studied in Plot 22 and Plot 23 in an
effort to evaluate fertilizer use efficiency. The data indicate
that very little nitrate was^lost through leaching from the plots
The majority of the nitrate in the leachate was lost early in
the growing season. The nitrate loss pattern closely follows
the flux patterns of the soil water. Considering the experi-
mental design for the 1976 irrigation season, the results are
not surprising. Essentially, the plots, when irrigated, were
supplied with only sufficient moisture to satisfy the water
requirements of the plants. Therefore, there was very little
deep percolation occurring, and consequently, very little
nitrogen moved below the root zone. This result emphasizes
the importance of highly efficient irrigation practices in
achieving better fertilizer use efficiency, along with re-
ducing nitrates in the underlying groundwater reservoir.
Ill
-------
TABLE 18. NITROGEN UPTAKE BY CORN
Plot 22
Dry Matter - 10850 kg/ha
% N in Dry Matter - 1.44 156.2 kg/ha
Grain Yield - 5941 kg/ha
% N in Grain(1) - 1.3 77.2 kg/ha
233.4 kg/ha
Plot 23
Dry Matter - 9622 kg/ha
% N in Dry Matter - 1.51 145.3 kg/ha
*
Grain Yield - 4776 kg/ha
% N in Grain - 1.3 62.1 kg/ha
207.4 kg/ha
^ 'Estimate based on assumption of 8% protein in grain.
TABLE 19. PLOT 22 SUMMARY NITROGEN BALANCE
Initial Soil N as NO396 kg/ha
Total Applied N 200 kg/ha
Final Soil N as N03 39 kg/ha
Estimated Loss n.
in Leachate UJ 10 kg/ha
Plant Extracted N 233 kg/ha
296 kg/ha 282 kg/ha
TIT
Assumes a loss of 0.085 kg -N/ha day for 116 days
112
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TABLE 20. PLOT 23 SUMMARY NITROGEN BALANCE
Initial Soil N as NO3 490 kg/ha
Total Applied N 0 kg/ha
Final Soil N as NO., 45 kg/ha
Estimate Loss 5 kg/ha
in Leachate
Plant Extracted N 207 kg/ha
490 kg/ha 257 kg/ha
Assumes a loss of 0.042 kg -N/ha day for 116 days,
113
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Section 10
IMPACT OF CROP PRODUCTION FUNCTIONS UPON
ALLOCATION AND USE OF IRRIGATED WATER
The literature reviewed and the results presented to this
point indicate, for a wide range of crops, that the relationship
between yield and ET is linear. In the case of crops where the
reproductive organ or associated product is harvested (as in
cereal crops, soybeans, cotton and some vegetable crops)' the
linear relationship represents the upper bound on yield for
varying amounts of ET, at least for those crops reported herein.
Further research is required to establish the linearity (or
otherwise) of the yield functions for other crops.
The substantiation of the linearity of crop production
functions with respect to ET has a profound effect on determining
the optimal allocation of irrigation water and this in turn will
affect irrigation practices. The extent and implications of
these effects on yields and return flows will be the subject of
the remainder of this report.
Two situations may be faced in problems of water allocation.
In Case (I), irrigation water is limited, while land is available.
This is the case where, for example, wells, water rights or on-
farm reservoirs limit the water supply to an amount insufficient
to produce the maximum yield from the available land area. In
Case (II) , irrigable land is limited, while water is available at
a price. In this case, sufficient water is available to supply
the full irrigation requirements of the available land area.
A third possibility is that both water and land are limited
and in such a ratio that the maximum yield cannot be attained on
all of the available area. However, this problem reduces to that
of the first case.
The role of crop production functions in determining the
optimal water allocation will be investigated first by considering
the irrigation water to be perfectly applied (i.e., crop needs
fully satisfied, with no losses). The relevant production
function is then yield versus ET. In Case (I), this will deter-
mine the optimal land area to irrigate, while in Case (II) this
will determine the optimal quantity of water to be supplied.
114
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The determination of optimal allocation of irrigation water
under the assumption of perfect application is only a theoretical
first step in order to provide a conceptual background for the
real problem of allocation under field conditions. In this case,
which will be the next considered, loss of a portion of the
applied water will occur, the magnitude of this loss depending on
the inherent ability of the irrigation system to apply the
desired amount of water uniformly and on the management practices
associated with the use of the water.
In many areas, rainfall provides a substantial contribution
to the total water requirement of an irrigated crop. The effects
of this contribution on the determination of the optimal water
allocation is discussed next. The effect of rainfall can be
expected to be most significant under conditions where dryland
cropping is possible, where the costs of crop production are
going to be incurred irrespective of whether irrigation water is
applied or not.
The analysis outlined above is based on the consideration of
a single crop. The results are next pxtended to multiple crop
decisions.
Departures from the linear upper bound of yield-water use
production functions have been shown to be due to the timing of
water deficits. This implies that water management means more
than simply ensuring that the crop is supplied with an amount of
water exceeding its ET requirements during the course of the
growing season. An understanding of the nature of crop produc-
tion functions is a useful tool in on-farm water management.
This understanding becomes particularly important for conditions
where water is limited relative to the land area. In this case,
every unit of water saved means that additional land can be
brought under irrigation, or that more of the available water is
actually transpired by the crop, with profits consequently
increased.
ALLOCATION UNDER CONDITIONS OF PERFECT WATER APPLICATION
Perfect water application is intended to imply that water is
applied and is available to the crops in amounts exactly equalling
the ET requirement and that all of the ET requirement comes from
the applied water/ with none from stored soil moisture or rain-
fall. Losses due to inefficiency or nonuniformity are not con-
sidered to exist in this instance and additional water for
leaching is not required. This condition may be considered as
the ideal which will never be achieved in the field; however, the
concept does allow the first step to be taken towards investi-
gating the effect of actual production functions on the alloca-
tion of irrigation water. The concept implies a linear yield
versus ET function. Under certain irrigation regimes (for
115
-------
example, under the Israeli conditions reported by Shalhevet et
al., 1976) yield versus applied water functions are also found to
be linear, in which case the same analysis applies, subject to
one condition to be discussed subsequently.
Optimal Land Area
Under conditions where water is limited relative to the
available land area. Case (I), the amount of water allocated to
each unit of land (i.e., the seasonal depth of application)
automatically determines the area of land that will be irrigated,
i.e., AJ." = | (32)
where A = area of land irrigated,
Q = total quantity of water available, and
x = depth of water applied.
To determine the optimal depth of water application (x ),
the objective becomes to °P
maximize P = (0T - II)AI (33)
where P = net revenue
O_ = output (gross revenue) per unit of irrigated
area
I.J. = input (costs) per unit of irrigated area
and A_ = area irrigated.
The output in the objective function may be expressed as:
Oz = vcy (34)
where v = gross unit value of crop ($/kg),
and y = yield per unit area (kg/ha).
As the yield may be represented by the linear production function
y = a + bx, (35)
the output can be expressed as:
116
-------
0.,. = a1 + b'x, (36)
as v is a constant.
c
The input may be expressed as :
Iz = Cl + c2 + c3 + . . . + cn (37)
where the c. = cost of any operation associated with producing
1 and disposing of the crop, per unit area.
For many field crops, the cost of these operations per unit area
are:
c, = cost of seedbed preparation
c2 = cost of seed
c_ = cost of sowing
c, = cost of fertilizing
4
c- = cost of pesticides
c. = cost of interrow cultivation
6
c = cost of irrigation (labor, energy & fixed costs
of system)
c0 = cost of water
o
cq = cost of harvesting
CIQ= cost of disposing
Many of the above costs are affected to varying degrees by
the yield obtained, while some are constant per unit area for a
given crop. For example, c^ and eg are constant and c5 has been
taken as constant although conceivably at low rates of water
application where water conservation becomes critical; the value
of c5 for herbicides could possibly increase. The cost of
sowing, Co, could vary a minimal amount due to increased sowing
rates, but is essentially constant.
The cost of seed, 02? is dependent on the sowing rate, which
in turn depends on the anticipated yield. The cost of ferti-
lizer, 04, of harvesting, eg, and of disposing of the harvested
product, G^O, a1^ depend on tne anticipated or actual yield. If
yield per unit area falls below a certain minimum, eg may be
constant.
The cost of irrigating has three components: labor, energy
and the annual fixed cost of the irrigation system. The quantity
of water to be applied during the course of the season is fixed.
117
-------
If this quantity of water were applied over a large area, there
would generally be fewer irrigations at a higher cost per irriga-
tion than if the water were applied over a smaller area, receiving
more irrigations at a lower cost per irrigation. The costs will
be approximately the same, and will depend only on the quantity
of water applied. For example, with furrow and most sprinkler
irrigations, a larger area will require more sets per irrigation,
but will not be able to be watered as frequently as a smaller
area. The total number of sets, which is the principal component
of labor costs, will be exactly equal if the flow rate is the
same in either case, but could vary slightly for different flow
rates. With more capital intensive systems, such as center-pivot
or trickle irrigation, the labor input to the actual process of
irrigating is low and is fairly constant for a given quantity of
seasonal irrigation water. Variable costs of pumping (energy
plus maintenance) will also be dependent on the quantity of water
applied. The fixed cost of the irrigation system will depend on
the area and will generally tend to be cheaper per unit'area for
a larger area than a smaller area. However, as the quantity of
available water is fixed, the range in which the optimal land
area can be expected to lie is limited, and hence, the cost per
unit area would not vary greatly.
The cost of water, eg, includes only the charge for the
water. Energy costs have been included in c7 and will be con-
stant, as the total volume of water is fixed. Water charges may
be constant per unit volume or may be on an escalating scale.
In many instances, the sum of the costs of irrigating (cj
plus eg) is constant per unit volume of applied water and, for
simplicity, advantage will be taken of this fact in later
analyses. For the present case, however, the costs are separated
so that the effect of an escalating scale of charges for water
may be evaluated where appropriate.
The fixed cost of machinery, which has been included in the
above costs as appropriate, may be expected to decrease per unit
area as land area increases. However, similar to the discussion
on irrigation system fixed costs, if the range of area irrigated
is between say 20 and 30 ha, or between 2,000 and 3,000 ha, the
fixed cost of machinery per unit area will vary little.
The argument may be advanced that the fixed costs of
machinery move in quantum increments and that the marginal cost
of farming one additional hectare is much lower than the average
cost per hectare, as much of this average cost is made up of
fixed costs. A more rigorous method of analysis may, therefore,
be to consider all costs at contract rates, in which the charges
are generally made up of a fixed cost plus a variable cost
depending on area or yield. This analysis has been carried out
in Appendix G, in which it is shown that the objective function
is the same as obtained in the following analysis. This means
118
-------
that the same result is obtained irrespective of the method of
pricing.
The cost components making up Ij may be expressed as
follows, in $ per ha, by substituting a -f bx for the yield,
y, and collecting terms:
cl = al
C4 = a4
c5 = a5
C — 3. —
6 6
c? = a?
c8 = a
C9 = ag + bgx
C10 = alO + blOX
where all the a's and b's are constants, and AI is the area on
which the fixed quantity of water, Q, is applied.
The variation of c± with x may not necessarily be linear
(although this is usually the case) , but this representation is
adequate for the argument as the variation will always be mono-
tonically increasing. The expression as a linear function is for
the sake of simplicity.
Therefore, the objective becomes to:
maximize P = [a1 + b'x - (a.^ + b±x + b./Aj)] A ....... (38)
where a..^ = a-j^ + a2 + a3 + a4 + a5 + ag + a? + ag + alQ
bj = ag 4- b?
Recognizing that x = Q/Aj, where Q is a constant, the objective
function may be expressed as
maximize P = a'Aj + b'Q - (a.! A +b.Q + b.) ...... (39)
P = (a- - a±) Aj + (b- - b.) Q - b. ...... (40)
119
-------
Now, a1 (= vca) is always a large negative number as a finite
amount of ET is required to produce any yield. These relations
are illustrated in the following diagram:
y
(Yield)
a
-«>s(ET)
The term a^ is made up of positive numbers where costs are
constant per unit area or possibly small negative numbers (com-
pared to a') where costs depend on yield. The terms b'Q, b^ and
b. are all constants.
Therefore, as (a1 - a-j_)Aj is always negative, the maximum
profit will be obtained when the area of land is kept as small as
possible within the constraints.
The foregoing analysis can be qualitatively deduced by
recognizing that all costs either stay the same (07, eg, C^Q)
or increase (the remaining terms) as land area increases. At the
same time, because of the negative value of a (which was the
condition referred to immediately prior to this subsection),
supplying the full ET requirement (xmax) yields a proportionately
higher yield than some fraction of xmax. In this case, xmax is
equivalent to ETmax, the lowest value of ET for which maximum
yield is attained (but not necessarily the maximum value of ET).
The constraints have not previously been discussed, but
are: (a) land area; (b) maximum depth of applied water;
(c) capital; (d) attainable irrigation efficiency; (e) labor;
and (f) flow rate.
If the land area is to be kept as small as possible, in this
ideal case the only constraint that comes into force is to keep
the maximum depth of applied water (xmax) to that which produces
the maximum yield (Ymax). This amount of water is then x .
120
-------
The area to be irrigated is, therefore:
opt
"opt
(41)
Optimal Water Supply
In irrigating a fixed area (as defined, for example, by'
water rights or physical limitations) where water is available at
a price, the problem is to determine whether to supply the crops'
full water requirements or, if the cost of supplying the water is
high, perhaps to supply less than the full requirement. The
seasonal depth of water applied will determine the total volume
of the irrigation water supply.
To determine the optimal depth of water application, the
objective is to :
maximize p - 0^. - 1^ (42)
where p = P/A_ = net revenue per unit area
O_ = output (gross revenue) per unit area
IT = input (costs) per unit area
Again, O-j. = vcy and I-j. = GI •§• c2 + c3 + . . . + cn as before,
where c, = a.^
C2 = a2 * b2x
c3 = a3
C4 " a4 + V
c5 = a5
C6 = a6
c? - a? + b?x
C8 = a8 + V
C10 = a!0 + b!0X
The terms C2r 04, cy, eg, and C^Q all vary with yield and hence
are functions of x which varies linearly with y. The variation
of the C£ with y may not be linear functions, but in all cases
they will be monotonically increasing functions, so the effect
will be the same.
121
-------
The objective can, therefore, be generalized as:
maximize p = a1 + b'x - (aj + b.x)
(43)
10
where aj =
ai and bj = b2
!0
i.e., maximize p = a' - a. = (b1 - b.) x
(44)
As in the previous case, a1 - aj will be negative. In order
to make a profit, it will be required that:
(b' -
and also that b1
x >
> b. .
- a
(45)
If these two conditions are satisfied and the coefficient
bj is constant (does not vary with x) , then the maximum profit
is obtained when x is a maximum, subject to the constraint that
x — xmax- (If tne two conditions were not satisfied, irrigation
would not be feasible.) The depth of water to apply for maximum
profit is x
'max
and the volume to apply is Q = ATx
r J I max
The only case in which bj could vary with x is for the
charge for water. If the charge for water is on an escalating
rate, i.e., successive volumes of water have a higher price per
unit, a point may be reached where bj > b'. The optimal depth
of water to apply is that for which the last increment retains
bj < b1. An example computation using typical production costs
in relation to the crop being grown, i.e., $100 per 1,000 m3
,($123 per acre-foot) for wheat before the depth of water
applied should be less than x
max
The effect of an escalating rate of water charges compared
to a constant rate per unit of water may be represented on a
dimensionless plot as follows:
(b) Water Charges at
an Escalating Rate.
w
Water Charges at
a Fixed Rate
1.0
-------
where cw is the charge for the volume of water corresponding to a
given depth of application over a unit area, and the other terms
have been defined earlier. The relative position of the two
lines will depend on the magnitude of the water charges, while
the relative curvature of line (b) will depend on the degree of
escalation of the charges. If the escalating charges still only
represent a small portion of total production costs, line (b)
will approach the shape of line (a). A numerical example
illustrating this concept is also included in Appendix G.
Deviation from the Ideal
The foregoing two subsections demonstrate that if irrigation
water could be applied in amounts just equal to crop ET (no
losses), and that if all of the crop ET is derived from the
irrigation water (no available soil moisture or rainfall), then
the maximum profit-making policy is to make available for crop
consumption that amount of water per unit area which gives
maximum yield per unit area.
This conclusion is based on a linear production function
with a positive intercept on the abscissa. The concept developed
forms the basis for the discussion which is to follow. Applica-
tion inefficiencies have been shown to cause the production
function to deviate from a linear relationship when yield is
plotted against applied water. The next problem is to investi-
gate whether this deviation makes a significant difference
regarding this conclusion.
If rainfall and available soil moisture make a significant
contribution to the crop water supply, the yield versus applied
water function may have a negative intercept when projected on
the abscissa. Irrigation is then supplementary to the total crop
water supply. The effect of supplementary irrigation on the
conclusion drawn from the theoretical case is subsequently
investigated.
EFFECT OF APPLICATION INEFFICIENCY
Functional Concepts of Application Efficiencies
In the field situation, decisions on water allocation will
be based on yield versus applied water production functions, not
yield versus ET functions. That is, in the common situation
where the available water supply is inadequate to fully supply
crop water needs over the available land area, the available
water supply must be divided by the amount of water applied per
unit of land to arrive at the total number of land units to be
irrigated. The amount of water applied per unit of land will be
the ET divided by the application efficiency.
123
-------
No method of irrigation is capable of exactly supplying the
ET requirements of crops. Existing irrigation methods and
practices result in application efficiencies consistent with
their inherent limitations, which tend to be a function of cost
and historical water availability. In the situation where water
is abundant compared to the available area of land, the applica-
tion efficiencies will determine the amount of water needed.
Water application efficiency is defined as the ratio of the
amount of water being stored in the root zone of the soil where
it can be used by plants to the amount being applied or delivered
to the field. The term is a widely used index of the efficiency
with which water is- being used within an irrigated area, although
it is not a complete measure of the effectiveness of irrigation.
For example, it is entirely possible to irrigate with an applica-
tion efficiency of 100 percent and still fall well short of
potential yields. The application efficiency fails to indicate
the uniformity of water application, or whether enough water has
been applied to sustain the crop until the next irrigation.
Although an easily defined term, it is often quite misleading to
people not thoroughly versed in its implications (Kovda et al.
1973).
Nonetheless, the term is quite useful for comparative
purposes, particularly in the common case where excess water is
applied to the whole field, with losses occurring due to deep
percolation, surface runoff and nonbeneficial evaporation.
Bearing this in mind, efficiency of irrigation application may be
readily represented on the crop yield-water use functions as
shown in Section 8. There it was shown that the yield versus
crop water supply function could be plotted tangential to the
yield versus ET function by displacing the abscissa. The hori-
zontal difference between the two functions represents the
losses, or amount of irrigation water applied that is not con-
sumed by the crop. When the two functions are plotted on the
same abscissa, they may no longer be tangential, but rather
separated at lower values of ET or water supply, and in this
case, the difference between the two functions represents the
amount of available soil moisture and rainfall, in addition to
applied irrigation water, that is not consumed by the crop.
Obviously, difficulties arise in defining the yield versus water
supply production function when available soil moisture and rain-
fall contribute to the crop water supply. These difficulties are
discussed in the subsequent subsection.
For the two functions to be tangential at low values of ET
or water supply, it is assumed that all of the applied water is
consumed. This will generally be the case where all of the (low
amount of) applied water is provided early in the season. As the
crop's root system develops during the course of the season, it
will expand to exploit all of the available water in the poten-
tial root zone. Of course, if too much water is applied early in
124
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the season so that some water percolates below the potential root
zone, losses will occur even for a relatively low amount of ET.
Similarly, if the water is applied late in the season, the crop
will not be able to consume the available water and again losses
will occur.
To illustrate a simple case, it may be assumed that water is
applied at a constant efficiency during the course of the season.
This functional relationship is represented by the dashed
straight line as follows:
Yield versus ET
Yield
x T ieia versus Applied
x Water at a Constant
Application Efficiency
ti) Theoretical
(ii) Actual
ET or Water Applied
In reality, however, this relationship is improbable. It
could be approximately true if all the losses were removed from
the system as, for example, in the case of spray losses from
sprinkler irrigation. However, even sprinkler irrigation is
subject to deep percolation losses as additional water is applied
to overcome the effects of nonuniformity. Considering the deep
percolation losses, it may be seen that with a constant applica-
tion efficiency some of the water applied early in the season
which percolates beyond the root zone of the shallow-rooted
seedlings may become available to the crop later in the season as
the root system expands. This proportion of the loss is, there-
fore, only temporary. When the seasonal yield versus applied
water function is plotted, it may appear as the solid curvilinear
function in the above graph. Of course, all of the lines shown
represent optimal timing of irrigation applications for the given
quantity of water (x)„
If excess water were applied to a wet soil early in the
season, the resulting production function may be as follows:
125
-------
Yield
0
Yield versus ET
Yield versus
Applied Woter
Excess Water Applied to
Wet Soil Early in Season
/7
ET or Water Applied
Unique and Nonunique Functions
Crop production functions are of limited value unless they
are consistently reproducible {and therefore predictable) or at
least have the same form. The discussion in the previous sub-
section of a production function satisfying the two conditions of
linearity and a positive x-intercept showed that the same con-
clusion regarding the allocation of irrigation water is reached
irrespective of the slope of the line. If these two conditions
are not satisfied, different conclusions could conceivably
follow. If the shape of the production function differs from
year to year, area to area and farmer to farmer, and if the shape
is not predictable, then the optimal allocation of irrigation
water is equally unpredictable.
The functions reviewed in Section 4 generally plotted yield
against transpiration, evapotranspiration or applied water,
depending on the objectives of the research. The yield versus
transpiration production function is comparatively unique for a
given crop in a given area. Although it will vary slightly from
year to year depending on climatic conditions, the form of the
function stays the same. The equation for each year could be
corrected to reflect advective energy and excess radiation.
Arkley (1963) found that a correction based on relative atmos-
pheric humidity serves this purpose and he used this parameter to
correct data from different areas. For a given crop, he was able
to show a unique linear relationship between dry matter yield and
the corrected value of transpiration, irrespective of the area
(or country) in which the crop was grown. This relationship
would obviously form the ideal basis for a water allocation model
were it not for the practical problems involved. Firstly, the
linear relationship developed by Arkley (1963) and de Wit (1958)
is demonstrated only for dry matter production. (However, as a
126
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linear relationship exists as the upper bound of the yield of the
reproductive organ of many crops when plotted against ET, it
would appear reasonable to suggest that this is also true when
plotted against transpiration.) Secondly, at the present time it
is exceedingly difficult to measure transpiration under field
conditions. Therefore, although the yield versus transpiration
function would appear to be unique and readily reproducible, it
is of limited practical value due to the difficulty in quantifying
the amount of transpiration.
The yield versus ET function is not strictly unique as it
will vary slightly even within a given area due to management
practices and to variations in climatic conditions from year to
year. However, the function will still remain linear and will
represent the upper bound on yields for given quantities of water-
under a given irrigation practice and during a given season.
Consistent good management will make the function close to unique
for a given area and the function does have the advantage that ET
can be computed or measured with a fair degree of facility and
accuracy. Therefore, although this function lacks the distinc-
tive uniqueness of the yield versus transpiration function, there
is a tradeoff in terms of practicality which makes this function
very useful for a comparison of results from different areas.
Most of the predictive models reviewed in Section 4 use a rela-
tionship between relative evapotranspiration (ET/ETp) and yield
or relative yield
A number of writers have made recommendations on irrigation
amounts and timing based on the results obtained from experiments
comparing yields to quantities of applied water. These results
have been used to compute the quantities of water which should be
applied to achieve maximum yields and maximum profits. Although
the methodology used is not always sound, as shall be shown in
the following section, worse yet the function upon which it is
based (yield versus applied water) is so subjective that it is of
little value. The function will fluctuate over a wide range,
depending on the amount of rainfall during the growing season,
the amount of available soil moisture at planting and, not
insignificantly, on the water application techniques of the
individual irrigator. The contribution of all of these factors
to the crop water supply will be influenced by the soil type.
Furthermore, transferring the results obtained from research
plots to irrigated fields will be unrealistic due to the signifi-
cant differences in efficiency and uniformity. to be expected.
Also, the results of the mathematical analysis to which the
function obtained is subsequently subjected are very dependent on
the form of the mathematical expression used, as will be shown in
the following subsection.
In summary, while the yield versus transpiration function
may be the ideal on which to base subsequent analysis, the yield
versus ET function is the most practical. Although the yield
127
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versus applied water function comes closest to representing the
field case, its nonuniqueness renders it of little value in
obtaining comparative results. However, because it does, in all
its variations, represent the field case, an attempt must be made
to see if some general conclusions can be deduced from it, with
these conclusions being valid over the possible range of the
function. This is the subject of the next subsection.
Maximum Yield and Maximum Net Return
Although a unique function cannot be used to represent the
relationship between yield and applied water under field condi-
tions, the relationship can be generalized as concave downwards
and it is possible to arrive at some general results by con-
sidering just the basic shape of this functional relationship,
supplemented by some representative costs and returns.
In_considering the case of ideal water application
(preceding subsection) it was shown that the point of maximum
yield and maximum net return corresponded to the same value of
ET, viz., that value corresponding to Ymax. Conceivably, if the
relationship were of the form:
Yield
Applied Water
where both the ordinate and abscissa are plotted to a linear
scale, the amount of applied water corresponding to the point of
maximum net return may be considerably less than that
corresponding to the point of maximum yield.
In fitting a functional relationship to yield versus applied
water data, it would appear obvious that the function should not
be extrapolated beyond the range of the data. Notwithstanding,
Shipley (1977) fitted the function:
128
-------
(46)
to his data and obviously expected this function to hold over a
wider range. He hypothesi2ed that the amount of applied water
corresponding to the maximum yield could be obtained by setting
and then solving for x. Obviously overlooked is the fact that
the fitted function is not a law relating yield to applied water,
but rather a curve that happens to fit over the range of data
only. For example, the data could just as readily be fitted by
the function:
y = ax where 0.
The danger of extending the function beyond the range of the data
becomes apparent.
The amount of water corresponding to the maximum yield can
be obtained from the results presented in Section 8. ETmax is
designated as that value of ET corresponding to Ymax and may be
less than the maximum value of ET. The amount of water to apply
is
ET
x =
- R - ASM
......... (50)
where n = application efficiency,
R = effective rainfall, and
ASM = available soil moisture at planting,
provided that the efficiency is not so low that yield reducing
factors due to poor irrigation practices (for example, aeration
problems or lodging) come into play.
129
-------
For irrigation to be profitable, the cost of applying
irrigation water must be less than the return from the irrigated
product. The point of maximum net return is obtained where the
marginal cost of irrigating becomes equal to the marginal return
from the irrigated product. This can be analyzed using the
method presented by Hogg et al. (1969). Case (II) shall be
considered first, as it is easier to analyze and easier to
understand.
Case (II); In this case, the land area is fixed, with
adequate water available at a price. The expression for net
revenue per unit of land area (p) is :
P = vcy -
vwx "
(51)
where y = yield per unit area
v = value per unit of crop yield
c
x = quantity of applied water per unit area
v = cost per unit of water, and
c = cost per unit area of operations other than those
associated with irrigating.
Net revenue is maximized when the derivative of this profit
function, with respect to the quantity of irrigation water, is
set equal to zero. Assuming for the moment that c is constant,
then :
IE =
9x
v - v =0
vc vw u
(52)
Therefore,
3X
w
V
(53)
This is the result used by Shipley and Regier (1975), by
Shipley (1977) and by Stewart and Hagan (1973), although none
explain its basis. In general, it is not correct. The value of
c (for example, the cost of fertilizing, harvesting and trans-
porting) will rarely be constant, but rather, will be dependent
on yield. Some costs will be independent of yield (for example,
cultivation), so that c can be expressed generally as:
= k + v..y
(54)
130
-------
where k = constant costs per unit of area, and
v. = yield dependent costs per unit of crop yield.
Therefore, p = vcy - vwx - (k + v.y) ........... (55)
__-.
c 3x w j 3x
= 0 when
(57)
The yield dependent costs (Vj) must be less than the value
per unit of crop yield (vc) for profitability. In fact, those
costs must be considerably less, otherwise the constant costs and
water costs would make irrigation uneconomical. They probably
constitute only 10 to 30 percent of the value per unit of crop
yield, but nonetheless should be included for completeness and
understanding.
The equation for net revenue per unit area (Equation 55)
may also be expressed as:
p = Returns - Costs, (58)
where Returns = (v - v. )y (59)
and Costs = v x + k ,^Q.
The maximum net revenue is the point where the difference between
the Returns and Costs is the greatest, as shown on Figure 41.
This point, as derived above in Equation 55, is where:
3x v_ - v (61)
c j
and hence is the point where a line drawn at a slope of
vw/(vc - Vj) is just tangential to the y versus x production
function (yield versus applied water) as shown in Figure 41.
The slope of this line will determine where it is tangential to
the production function and, consequently, the optimal depth of
irrigation water to apply.
The slope of the line, which hereafter will be called the
price ratio (PR), is inherently flat and consequently is tangen-
tial to the production function at large values of x. For
example, using typical prices and costs for grain sorghum:
131
-------
o
o
o
c
3
0>
Return Function
Maximum
Net Revenue
Cos1 Function
-Yield versus Applied Water
Xopt
Depth of Water Applied (x)
Figure 41. Determining optimal depth of irrigation water to
apply where water is plentiful.
132
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VG = $0.08 per kg (- $3.50 per cwt)
vw = $0.25 per ha-mm (- $2.50 per ac-in)
v. = $0.02 per kg (= $0.50 per bushel)
then PR = 4.17 kg per ha-mm (= 0.833 cwt per ac-in).
Applying this, for example, to Shipley's (1977) production
function for grain sorghum converted to metric units and
including the preplant irrigation:
y = -927 + 29.71 x -0.0259 x2 .......... (62)
where y = grain yield in kilograms per hectare, and
x = total seasonal irrigation water, in mm,
the point of maximum profit is where:
= 29.71 - 0.0518 x = 4.17
(63)
Therefore, x = 493 mm. To this amount must be added the
effective rainfall plus the available soil moisture prior to
irrigation. Unfortunately, neither of these values are known.
However, an average of 246 mm of rain fell between the 23rd of May
23rd September during the years from which the production func-
tion was obtained, and it would appear reasonable to assume,
therefore, that at least 650 mm of water was available to the
crop. Although this estimate is somewhat crude, it does indicate
that the amount of water available to the crop was more than the
amount necessary to insure maximum possible yield, according to
figures given by Doorenbos and Pruitt (1975) .
An argument might be advanced that there is nothing to stop
the price of water from increasing, thereby increasing PR and
hence lowering the optimal depth of water application. This is
true, of course, but the key point is that the price of water can
only rise a small amount without a rise in the price received for
the crop before irrigation becomes uneconomical. Irrigation
farmers, like other farmers, are operating on a sufficiently
slender margin that the price ratio can increase very little
without irrigation becoming uneconomical. If the price of water
is increased, the value of the crop must increase. Water that is
currently highly priced is used to irrigate highly valued crops.
The price ratio, therefore, stays relatively constant. Even if
it were to vary by a factor of say two or three, which allows
generous latitude in the argument, it is still sufficiently low
that it will always be tangential to the production function at
high values of x.
133
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For example, if the price of supplying the irrigation water
increased threefold to $0.75 per ha-mm ($7.50 per acre-inch) the
optimal depth of water application would be calculated from:
29.71 - 0.0518 x = Qt08°:7^02 (64)
= 12.5 kg per ha-mm
Therefore, x = 332 mm
With only this amount of irrigation water applied, more of the
seasonal rainfall would be expected to be effective. A crude
estimate indicates that the total water available to the crop
would be well over 500 mm plus the available soil moisture prior
to irrigation. In this case, the price ratio is three times the
value originally computed and yet sufficient water should still
be supplied to allow the crop to receive very close to a full
water supply. Obviously, though, supplying only 330 mm of water
and still obtaining a high yield requires the application of
novel management practices, to be discussed in the next section.
Therefore, by using current prices and a production function
obtained from research plots, the conclusion is drawn that in the
case where the area of land to be irrigated is fixed and suffi-
cient water is available for total irrigation, the optimal irri-
gation policy is to supply close to the full water needs of the
crop. Although the price of sorghum used in this analysis has
been lower in past years, these were depressed prices and did not
reflect the costs of production. Hence, the PR used is felt to
be representative. Raising it threefold did not greatly alter
the general result.
The other parameter in the analysis, the slope of the
production function, bears closer inspection. The quadratic
expression fitted to the four data points by Shipley (1977), as
shown in Figure 42, can be seen to be actually flatter than
would be a best fit curve. The quadratic expression is tangen-
tial to a line drawn with a gradient of the price ratio (4.17)
when x = 493 mm. (The price ratio line is drawn clear of the
functions for clarity.) Drawing a curve through the four data
points would require that the curve be extended beyond the data
to be tangential to the price ratio. That is,, the quadratic
expression actually gives a lower value of x . than the true
function.
Alternatively, the four data points could be fitted with the
power function,
y = 195 x0'5867 (r2 = 0.985) (65)
134
-------
10000
9000
I 8000
"*. 7000
E
i. 6°°°
o
w 5000
c
2 4000
o 3000 r-
~ 2000
~ 1 —i r
y = -927 + 29.71 x - 0.0259 x2
xopt = 3020 mm for
Power. Function
^/^'^'-
y = I95x°-5867
= ^93 mm for
Quadratic Expression-
1000- « Data from Shipley (1977)
100 200 300 400 500
Depth of Irrigation Water Applied (x), mm
600
Figure 42. Influence of production function slope on optimal
depth of irrigation application.
also shown in Figure 42. In this case, dy/dx = PR when
x = 3020 mm. Admittedly, the power function may not be a good
expression to use over a wide range of data because it must pass
through the origin. However, over the range of the four data
points to which Shipley (1977) fitted the quadratic expression,
it fits equally as well. The point that the power function and
the preceding paragraph illustrates is that using a mathematical
expression in the analysis is far from a guarantee that the
correct value of xopt will be obtained. It also illustrates the
vast difference in the values obtained for xopt for small changes
in the shape of the function. This further detracts from the
value of using specific yield versus applied water functions for
determination of the optimal irrigation policy. Nonetheless, by
observing that the gradient of the price ratio remains relatively
low, and by observing the general shape of the yield versus
applied water function, it may be stated that the optimal irri-
gation policy is to make available to the crop close to its full
water requirements.
135
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Case (I) : In the case where the volume of water is fixed
and the land area is not limited, the objective is to maximize
profit over the total available land area, rather than profit per
unit area as above. In this case, the expression for net revenue
(P) is:
P = vcy Ax - Cw - C ............... (66)
where C = cost of water (constant for a given method)
and C = the cost of operations other than those associated
with irrigating :
i.e.,C = (k + vjY) A.J. .............. (67)
and all of the other terms have been defined earlier. Therefore,
P =
-------
Return
or
Cost
'W
Return Function
Cost Function
The optimal land area to irrigate may be obtained by setting
3P/3AJ = 0 in Equation 68.
i.e., (vc - v^)y + (vc -
- k = 0.
(71)
which may be readily manipulated to show that the optimal land
area is obtained where marginal revenue equals marginal costs,
or, by collecting terms may be expressed as:
y)(vc - v.) - k =
(72)
That is, as the return is increased by expanding irrigation to an
additional unit of area, because the total quantity of water is
fixed, yield on the remaining area must decline. The optimal
area of irrigation is where the two factors combine for the
greatest return.
Substituting
_ Q
x
the "optimizing equation" may be expressed as
(f£x - y)(vc - v.) + k = 0.
(73)
137
-------
A given production function in terms of x and y and given
cost coefficients may be substituted in this equation and solved
for x, the optimal depth of irrigation water to apply. However,
as pointed out earlier, such production functions are far from
unique (or readily available) and more general results would be
far more practical.
To incorporate the general case, a range of production
functions is shown on Figure 43. Curves 1 and 2 have been
obtained from the experimental data as plotted in Figure 38,
while Curves 3 and 4 have been drawn arbitrarily to represent
production functions more typical of field conditions. All
curves have been plotted on a common abscissa, so that Curves 1
and 2 are no longer tangential at lower values of x. Considering
x as the depth of water applied, Curve 1, originally being the
plot of yield versus ET, represents a production function at 100
percent irrigation application efficiency. The seasonal irriga-
tion application efficiency for the regime represented by Curve 2
is 82 percent, with 71 percent for Curve 3 and 48 percent for
Curve 4.
To more readily understand the effect of different depths of
water application on net revenue,
P = Return - Costs
(74)
the expressions for return and costs may be plotted against x,
the depth of water applied. This is shown on Figure 44 in
which there is one cost function and four return functions
corresponding to the four yield functions of Figure 43. The
net revenue is the vertical difference between the respective
return function and the cost function. Typical costs and prices
have been used in plotting the curves, but this is not particu-
larly significant as these will only affect the relative position
of the return functions to the cost function and will not change
the shape of either. Similarly, fixed overheads have been
ignored, as these will have just the same effect. Also, for
simplicity, the price of water has been taken as constant per
unit volume. Breaking the total cost of watering into component
parts, as done in a subsection above, only has the same effect of
changing the relative position of the cost function.
The point of maximum net revenue is where the return and
cost functions are separated by the greatest distance, i.e., where
the curves have the same slope. This point is circled on the
four return functions. The corresponding value read on the
abscissa is the optimal depth of water to apply. Referring back
to Figure 43, for Curve 1, this can be seen to be the amount
corresponding to Ymaxf as derived in the previous subsection.
The other regimes have optimal depths of water application lower
138
-------
10000
8000-
o>
.n
c
s
o
6000-
4000-
2000-
200 400 600 800 IOOO 1200
Depth of Irrigation Water Applied (x), mm
Figure 43.
Production functions for corn at different
irrigation application efficiencies.
than values corresponding to Ymax, although for the regimes
corresponding to Curves 2 and 3 it is not greatly less (91 and 86
percent of xmax, respectively). For Curve 4, it is considerably
less, with x0pt = 0.58 xraax. (xOpt = 700 mm and xmax = 1200 mm).
(For comparative purposes, it may be noted that in the case where
water is not limited with respect to land area, Case (II), using
a typical price ratio of 4 kg per ha-mm applied to Curve 4 gives
x
opt
= 0.85 x
•max-
In general, then, it may be stated that while the optimal
policy in a water abundant area is to apply close to that amount
of water giving maximum yield, in a water-short area this is not
true if irrigation application efficiencies are low. If effi-
ciencies are high, it will be true. Although these results would
appear quite reasonable by intuition, the fact that they have
always been a point of controversy has required this proof.
In Case (II), the optimal depth of irrigation water to apply
depended on the production function and on both the prices
received for and the costs associated with producing the crop.
139
-------
^*-o^ ° Return Functions.
(D
77 = 71%
77 = 48 %
Maximum
Net Revenue
for-,; = 48%
Cost Function
200 400 600 800 1000 1200
Depth of Irrigation Water Applied (x), mm
Figure 44. Variation in returns and costs with depth of
irrigation water applied.
In Case (I), the optimal depth of irrigation water to apply
depends solely on the shape of the production function. The
effect of this shape may be readily demonstrated by referring to
Figure 44. If the irrigator follows a practice resulting in a
production function the same as Curve 4 in Figure 43, a maximum
net revenue of $30,000 may be scaled from Figure 44. A differ-
ent practice resulting in a production function the same as Curve
2 would result in a maximum net revenue of $52,000 or a 73 per-
cent increase. As pointed out earlier, fixed overheads have been
deleted for simplicity and as these would have the effect of
raising the cost function, the actual effect of increasing water
application efficiency would be to increase the net revenue an
even greater percentage than calculated.
140
-------
With costs and production functions available and return
functions derived from them as shown in Figure 44, the detri-
mental effect of low irrigation efficiencies may be readily
evaluated. The losses in revenue due to poor irrigation prac-
tices are startlingly apparent. In most cases where water is in
short supply, the irrigator will endeavor to improve practices so
that little water is wasted. With relatively high efficiency so
attained, the correct policy is then to apply sufficient water so
that close to maximum yield is obtained.
If the irrigation system is such that high efficiencies are
not possible and capital is not available for improvement, the
optimal depth of water to apply is significantly less than the
depth corresponding to Ymax and could be obtained from a plot
such as shown in Figure 44 or mathematically if a reliable
expression for the production function were available. Unfor-
tunately, however, such information is generally not available
and, as pointed out earlier, susceptible to giving misleading
results. Notwithstanding, a significant general conclusion may
be drawn. That is, contrary to those who advocate spreading the
available water over as large an area as possible (subject to
applying the minimum depth that is practical or economical), the
optimal depth to apply is similar to that under more efficient
regimes and certainly greater than that which would supply the ET
requirements of the crop if none were wasted. Furthermore, it is
safer to err on the side of applying a greater depth of water
than on the side of applying less, as the return and cost func-
tions in Figure 44 converge far more slowly on the right hand
side of the optimal depth than on the left hand side.
POLICY FOR SUPPLEMENTAL IRRIGATION
Consideration will now be given to the case where rainfed
agriculture is a feasible enterprise. In this case, a greater
area may be farmed than that for which an irrigation water supply
is available. This case differs from the earlier consideration
in that this additional area may be farmed under dryland condi-
tions, whereas in the discussion prior to this, no cropping was
feasible without irrigation.
The objective now becomes to:
maximize P = (OT - IjJAj + (OD - ID)AD. (75)
subject to A = A.J. + AD
x 1 xmax
and Q = constant
141
-------
where P is the profit from the total enterprise, and Ox , Iz
and Aj have been defined earlier as the outputs, inputs and area,
respectively, associated with irrigation, and OD/ ID and AD
are the dryland counterparts. The irrigated area plus the
dryland area must be added to give the total farmed area, A,
which is constant.
As before, OT = v y (Eq. 34) ,
-L C
and IT = a.. + v_.y + — ............. (76)
Also, the profit per unit area from the dryland area (p ) is
given by :
PD ' °D - ZD .................... (77)
which in the analysis is a constant, being dependent on the
weather.
Therefore, P = vcyAI - a^ - v^yA-j. - b- + PA ....... (78)
= (vc - v^yA-j. - ajA.,. - b.. + PDA - pDAT .... (79)
However, as a., b . , pQ and A are constants,
P = (vc - VJyAj - kA-. - C ........... (80)
where k = a.. + PD.* .................. (81)
and C = b.. - pDA .................. C82)
Equation 77 will be recognized as being identical in form to
Equation 65 and may be plotted in the same manner as the
functions shown on Figure 44, which were for the case where
cropping was totally dependent on irrigation. The only differ-
ence is that now the cost function, as represented by Equation
66 will be lowered by an amount, p^, representing the increased
profit due to dryland farming. To be more strictly correct,
Equation 77 should be expressed as:
P = I(vc - v..)y + pD] Az - 3..A.J. - C , ...... (83)
142
-------
where Return = [ (VG - v )y + pQ] A.J. ,
(84)
and Cost = a.Aj + C .................. (85)
If returns and costs are plotted against x, the return functions
will increase by a constant amount, pD, compared to those shown in
Figure 44. Either way the relative shapes of all the func-
tions remain unchanged, only the relative positions of the return
functions to the cost function changes. The correct irrigation
policy, therefore, is to supply the irrigated crop with exactly
the same depth of water as calculated in the above subsection.
Now, however, some of this water is supplied by precipitation
during the growing season. The amount of effective rainfall to
be relied upon to satisfy some part of the crop water require-
ments could be obtained from a statistical analysis of rainfall
records. The irrigation water so saved will allow the irrigated
area to be extended so that the total area receives the depth of
water from both rainfall and irrigation calculated to be optimal
in the above subsection. That is, having identified xopt, which
will be close to xmax for highly efficient irrigation, and with
xopt now including a depth of rainfall, R,
Q
AI ~ x T^R ................... (86)
opt
MULTIPLE CROP DECISION
The preceding endeavors to find the optimal depth of
seasonal water application have been limited to the case of a
single crop. In an irrigated area, be it a farm or a district, a
variety of crops usually are grown. The results may now be
extended to the multiple crop case.
If no constraints applied, the optimal policy would be to
plant the irrigated area with the most profitable crop and supply
a seasonal irrigation requirement of xOp-t. For Case (I) , this
amount would determine the command area. For Case (II) , xopt
would determine the required water supply.
However, a number of constraints may apply to the problem.
One, which in many cases will defy a completely rational analysis,
may be termed a "cognitive constraint". This refers to the
unwillingness of an irrigator to confine his activities to one
crop. A number of reasons attend this unwillingness, including
the very real necessity to rotate crops on a given land area,
plus the overriding concern to deploy the inherent risk of
farming. Although the most profitable crop may have been
143
-------
determined from conditions prevailing at the time of planting,
conditions at the time of harvest may result in a different
ranking. This factor becomes particularly relevant when con-
sidering, for example, perennial or orchard crops versus annual
crops. Other reasons for growing additional crops may include
constraints on the flow rate of the water supply, requiring times
of peak water supply to be staggered; on labor, requiring a
staggering of periods of labor intensive activity; and on
capital, requiring the use of existing equipment. In short, the
irrigator may be reluctant or unable to commit more than a
certain proportion of his irrigable land to any one crop. While
the existing or predicted economic conditions will allow the most
profitable crop to be selected, the cognitive constraint and the
other constraints will often result in a number of crops being
planted. The objective is to determine the optimal depth of
irrigation water to apply to each crop.
As in the single crop case, the objective in irrigating a
number of crops will be to maximize the net return from the
irrigation enterprise. The profitability of each crop must first
be determined. This profitability could be in terms of per unit
of land areav or per unit depth of water.
In Case (I), where water is limited relative to the land
area, a crop having the highest return per unit of land may or
may not give the highest return per unit of water. In fact, two
crops could give the same maximum net return per unit of land,
but one may have a higher water requirement than the other. This
would indicate that the higher profitability would be associated
with the crop giving the highest return per unit of water, as the
land area may be extended while the profitability per unit land
area remains almost the same as for the other crop. While
additional costs are associated with extending the land area,
these costs generally are lower per unit area than for the
original area, so that profit is actually higher.
In Case (II), the land area is fixed and hence the most
profitable crop is that which returns the highest net revenue per
unit of land. This may not necessarily be the crop which gives
the highest return per unit of water. The cost of watering must
be included in the computation of net revenue. Although one crop
could have a higher gross return than another, it is possible
that with a higher water requirement the net revenue could be
lower.
The optimal depth of water to apply to each crop within a
multiple crop enterprise may be determined according to the
criteria developed in the above subsection for a single crop.
This will be based on profitability per unit depth of water for
Case (I) and profitability per unit of land for Case (II).
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The relative area of each crop to be grown will be
determined by the irrigator operating within the constraints
outlined above. These areas could theoretically be determined by
linear programming, or other techniques, although the physical
and cognitive constraints often allow the solution to be obtained
by inspection. The purpose here is not to describe a method
whereby the optimal crop mix might be obtained, but rather, to
determine whether xopt determined for the single crop case is the
optimal depth of water to apply to each crop when more than one
crop is grown.
Where adequate water is available to supply at least xopt,
calculated from the single crop case, to each crop, the optimal
depth for each crop in a mix of crops may be readily deduced.
Applying a depth greater than xopt increases costs while
decreasing returns and is obviously of no benefit. Reducing the
depth of water applied to one crop would be of no advantage to
any other crop, as adequate water is available, although it would
reduce costs. However, as these costs have been taken into
account in determining xopt/ the profit maximizing policy remains
to apply the individual xopt to each crop.
If the available water supply is inadequate to provide xopt
to the selected area of each crop, a decision is required to
determine whether the seasonal depth of water supplied to each
crop should be reduced, whether the area of the least profitable
crop (per unit depth of water) should be reduced, or whether the
area of all crops should be reduced on a proportional basis. The
solution may be deduced from Figure 45, where net revenue
(returns minus costs) has been plotted against the depth of
applied water. The relationship is shown for three different
crops, reflecting different responses to water and different
returns and costs.
If the seasonal depth of water applied to each crop were
reduced below x0pt' tne optimal relative area of each crop would
be where the marginal net revenue is the same for each crop, i.e.,
where the functions have the same slope. Points (a) in Figure
45, for example, correspond to depth of applied water where
marginal net revenues are equal. If
xlaAl + X2aA2 + K3aA3 = Q« • • • • (87)
where the x's are defined on Figure 45, the A's are the areas
selected for each of the three crops being considered and Q is
the total volume of available water, then the selected areas of
each crop are in the optimal relative proportions for the reduced
depth of application.
145
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Crop 2
3
C
0>
>
0>
a:
9
z
Crop 3
Depth of Irrigation Water Applied (x)
Figure 45.
Determining the optimal depth of irrigation water
to apply to each crop in a multiple crop enterprise
146
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The net revenue for any one of the crops may be increased by
reducing the area of that crop until the depth of applied water
is xopt, i.e., to where the marginal net revenue per unit of water
is zero. To maintain an optimal crop mix, the areas o,f all the
other crops should be adjusted so that marginal net revenue is
again equal, i.e., all crops should be supplied with xopt. At
this point, it will be noted that the net revenue from each crop
is maximized and net revenue from the total enterprise is also
maximized. The optimal policy, therefore, is to apply a depth of
water to each crop in the crop mix calculated to be optimal if
only one crop were being grown.
With the earlier, less profitable alternative, where each
crop was supplied with less than xopt (point (a) on the three
curves of Figure 45), the area of each crop could be determined
from Equation 84 if sufficient constraints were applied to the
areas. The x's and Q were known. Similarly, with xopt applied
to each crop, the area of each may be computed. The areas
corresponding to xa and those corresponding to xopt would not be
in the same relative proportion. For example, the area of Crop 2
would be reduced far more than the area of Crop 3, as the ratio
X2a:x2opt is far smaller than X3a:x3opf
Although it was stated earlier that the objective here was
not to describe a method whereby the optimal crop mix might be
obtained, it can be seen, in fact, that the methodology described
is appropriate for solving that problem. Knowing that each crop
should be supplied with *opt allows the relative area of each
crop to be determined if adequate constraints can be formulated.
The pertinent result here, however, is that irrespective of the
water supply situation, the profit maximizing policy is to apply
the same depth of water to each crop of a multiple crop
enterprise as would be applied if each crop were grown separately.
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SECTION 11
IMPACT OF CROP PRODUCTION FUNCTIONS
UPON WATER MANAGEMENT PRACTICES
The adoption of management practices which lead to increased
yield per unit of water applied (called hereafter "water pro-
duction efficiency" for the lack of a generally accepted term)
is of benefit regardless of the water supply situation. In the
case where water is limited relative to the available land area,
increasing the water production efficiency allows a larger area
to be irrigated with the given quantity of water. Profits may
thereby be increased. In the case where land is limited rela-
tive to water availability, increasing production efficiency
reduces the amount of water which must be applied, thereby re-
ducing costs. Unfortunately, in this case it is often found
that "water is cheaper than labor," with many farmers finding
the cost of managing water to achieve high efficiency unjustified
where the price of water is low. This is also true to some
extent even where water is limited, if the price of water is
sufficiently low.
Many practices may be adopted, however, which lead to an
increase in the production efficiency without a substantial
increase in costs. These novel management practices may be
divided into two categories: those that minimize water losses
and those that increase water use efficiency. In some cases,
these categories overlap.
MINIMIZING LOSSES
Loss of water from the farm irrigation water supply may
occur in both conveyance and application. Losses in the former
are generally due to seepage, while the latter may consist of
surface runoff, deep percolation or evaporation losses. Appli-
cation efficiency was defined earlier as the ratio of the amount
of water stored in the root zone for use by the crop to the
amount delivered to the field and hence is the ratio of ET to ET
plus these losses in application. Reducing the losses is tanta-
mount to increasing the water application efficiency.
If the water supply is limited relative to the available
land area, a number of managment practices may be adopted which
148
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make the most of the limited water supply. During the early
development of the crop, only light irrigations are required.
The ultimate root zone may then be brought close to field
capacity with subsequent irrigations to ensure that during any
later inadvertent water shortage, the crop may expand its root
system to its fullest capacity. Apart from buffering the ef-
fect on yield of possible soil moisture shortages, the deeper
root zone makes efficient irrigation easier to achieve and allows
the crop to take better advantage of heavy rains. If the ir-
rigation water supply is from on-farm storage, applying the
water early in the season for storage in the root-zone reduces
later evaporation from the reservoir as well as providing
additional storage capacity in the reservoir. In this way
losses from the water supply are reduced.
In an area where rainfall may make a substantial contri-
bution to the crop water supply, sufficient water should be
supplied during irrigation to bring the root-zone to a moisture
level less than field capacity. This may be achieved, for
example, by alternative furrow watering or by replacing just a
fraction of the soil-moisture deficit when sprinkler irrigating.
Maximum use of rainfall may thereby be achieved and the loss of
nutrients due to deep percolation reduced. The deficit allowed
to remain in root-zone soil-moisture storage would have to be
based on historical rainfall records. An exception may be
necessary during the period of peak crop water use when the
root-zone would need to be brought to near field capacity unless
rainfall is assured with a high degree of reliability.
To reduce evaporation losses, irrigations should be as
infrequent as possible within the limits set by the above re-
quirements and the type of crop. This is particularly true in
the early stages of growth when the crop canopy shades only a
small fraction of the ground surface. By allowing the soil
surface to dry out between waterings, evaporation from the soil
surface may be considerably reduced. Irrigating at night will
also lower the evaporation and wind drift losses when irrigating
with sprinklers. These two measures combined will allow
considerable water savings to be effected.
With many crops, late season irrigation has been shown to
be nonbeneficial or even detrimental to yields. This was shown
to be true for both corn and wheat in the experiment conducted
in this research effort. Water can thus be saved if these
waterings are avoided, with this water being used to extend the
irrigated area or to avoid deficits in earlier growth stages.
Ending the season with the root-zone at a lower moisture level
allows full advantage to be taken of interseasonal precipitation.
In addition, avoiding or reducing the late season irrigations
may reduce nitrogen losses by deep percolation from either the
late irrigations or from the interseasonal precipitation. The
usual nitrogen fertilizer rates result in fairly significant
149
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residual nitrogen levels at the end of the season, with this
nitrogen to be subsequently "scavenged" by future crops if
not leached from the soil profile.
From the results of the experiment with corn reported in
Section 8, it may be seen that the last four irrigations had a
detrimental effect on grain yield, as well as reducing the
seasonal water application efficiency from 82 to 64 percent.
Figure 34 indicated the disastrous effects on profitability
of these late season waterings. Fortunately, it is easier to
avoid this cause of inefficiency (by failure to irrigate) than
it is to promote it.
If the area of irrigated land is limited relative to the
available water supply, there is seldom an expressed concern to
improve application efficiencies unless the cost of the water is
comparatively high. However, improving the water application
efficiency in this case has a number of benefits, some of which
are often overlooked.
A number of researchers have shown that overirrigation can
be severely detrimental to yields. If waterlogged conditions
prevail during flowering, the oxygen diffusion rate in the soil
can be so low that basic metabolic activities of the roots are
inhibited and consequently, grain yield is severely depressed
(Downey, 1972). In this case, improved irrigation efficiency
could be of marked benefit in terms of increased returns. Water
percolating below the root-zone carries with it some of the
soluble nutrients present in the soil profile. The leaching of
nutrients from the root-zone represents a cost in terms of
reduced yields and the replacement cost of the nutrients.
In some areas of abundant water supplies, excessive runoff
accompanies deep percolation and where the soils are erosive
or the slopes relatively steep, extensive loss of topsoil occurs.
Many of the costs associated with this topsoil loss, if per-
ceived at all, are viewed as externalities, with the direct costs
being borne by downstream water users. However, as the down-
stream end of an irrigation furrow is the point of lowest dis-
charge, and usually of lowest velocity, it is often the point
of least erosion. Much of the erosion occurs higher in the
field, with the sediment deposited further downstream in the
furrow. Hence, the internal cost to the farmer, although not
always perceived, may be high.
Some of the costs associated with low water application
efficiencies are readily apparent, although, as noted above, in
some cases there may be a tendency to balance these costs
against the additional costs necessary to achieve higher effi-
ciency. This may be the case particularly with the water charges
or the cost of pumping water. In some cases, however, even
the cost of additional labor is expended unnecessarily, where
150
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additional irrigations are applied when not needed. Late
irrigations, apart from the possible losses associated with
yield reduction, may also expose the mature crop to a higher
risk of storm damage if the resulting wet soil delays harvest.
INCREASING WATER USE EFFICIENCY
Water use efficiency has been defined by Viets (1962) as
"the weight of dry matter or marketable crop produced per unit
volume of water used in evapotranspiration (ET)." it therefore
differs from water production efficiency defined above by
having ET in the denominator, rather than applied water. Metric
units are often preferable. If both the yield and ET are
expressed in units of mass, then water use efficiency becomes a
true ratio. In mass units, water use efficiency is similar to
the term "efficiency of transpiration," first attributed to
L. A. Ivanov in 1913. Efficiency of transpiration was defined
as the grams of dry matter produced per kilogram of water
transpired (Viets, 1962).
Improving water use efficiency can be accomplished by
either increasing the yield or decreasing the ET. As yield is
a linear function of ET under conditions of optimal irrigation
timing and quantities, with a positive intercept on the ET axis,
the maximum water use efficiency occurs at the ET corresponding
to maximum yield. For this quantity of ET, or any other ET,
water use efficiency can only be increased by increasing yield.
Yield improvements can be divided into two categories: those
affected by agronomic and plant genetic factors and those
affected by management factors.
The agronomic and genetic factors fall outside of the scope
of this work and shall only be listed briefly. These include
species adaptation (variety or hybrid), plant breeding, plant
shape and form, planting patterns (row spacing and planting
rate), planting date, seed quality, weed control, control of
disease and insect pests, and fertilization (Pendleton, 1966).
Management factors are those which are concerned with
achieving maximum yield for the given amount of ET, whether or
not maximum benefit has been taken of the agronomic and genetic
factors. Obviously, the two are most effective in conjunction.
Where water is cheap and abundant, the overall management
objective is to prevent water deficits at any stage of growth
in order to achieve maximum yields. In some cases, due perhaps
to maintenance becoming necessary in mid-season, deficits which
could not be foreseen at the time of planting become inevitable.
In the case where water is limited relative to the available
land area, and where the water application efficiency is low,
deficits will be necessary according to the optimal irrigation
151
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policy derived in Section 10. In either case, deficits should
be sequenced to cause the minimum reduction in yield if at all
possible. Research results, such as those presented for corn
and wheat in Section 8 and more comprehensively elsewhere (i.e.,
Salter and Goode, 1967) , will show those periods in which defi-
cits should be avoided. An understanding of the effects of the
timing of water deficits on the crop production function and the
subsequent effect on net revenue will provide a powerful tool
for profit maximization.
Many researchers and farmers have demonstrated the necessity
of coinciding the maximum water demand of the crop, determined
by its physiological requirements, with the time of maximum
atmospheric evaporative demand. This is often expressed in terms
of date of sowing. Sowing corn, for example, as early as climatic
conditions will allow ensures that the full crop canopy is
developed by the time of maximum evaporative demand and results
in higher yields provided that water is not limiting. This
practice is mentioned under the agronomic factors listed above.
If, however, there is a flow rate constraint on the available
water supply, or a labor constraint, it may not be possible to
meet the pe'ak consumptive demand even though the volume of
available water is sufficient for the crop's seasonal needs. In
this case, a crop mix may be selected in which critical growth
stages do not temporally coincide. With a single crop, planting
dates may be spread to stagger the time of occurrence of the
critical growth stage. Depending on the climate, the period of
peak evaporative demand may spread over a month or more. The
length of this spread will determine the reasonable staggering
of the planting dates.
With a constrained flow rate, the situation becomes
analogous to the supplemental irrigation situation analyzed in
Section 10, where it was shown that the available irrigation
water should be confined to an area on which a seasonal depth of
water, including precipitation, equal to or greater than the
crop ET requirements should be applied. With the constrained
flow rate, during the period of peak demand, irrigation should be
confined to an area which allows this criterion to be met, with
the remaining area irrigated when the demands are lower.
Beginning the season with the root-zone storage at or near field
capacity, or at least ensuring that it is to the desired
moisture level at the beginning of the period of peak demand,
will be of considerable benefit in allowing time to adequately
water the irrigated area within the constraints of flow rate or
labor availability. Consideration should also be given to other
methods of application, such as sprinkler irrigation or trickle
irrigation, which are better able to utilize small flow rates
than many surface methods.
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BEST MANAGEMENT PRACTICES FOR GRAND VALLEY
Much of the research results reported herein have general
applicability to irrigated agriculture. In this final sub-
section of this report, the authors will attempt to summarize
the implications of this research in implementing a salinity
control program in Grand Valley. The results of this particu-
lar research effort will be combined with the other research
efforts funded by EPA in Grand Valley in preparing the culmi-
nating report, "'Best Management Practices' for Salinity Control
in Grand Valley."
Since the Grand Valley has a limited irrigable acreage, but
a more than adequate irrigation water supply, it would be a
Case (II) area as defined in this report. The Valley contains
predominately heavy soils, which strongly influence the present
irrigation practices. Another consideration is that the mean
annual precipitation of 210 mm occurs mostly during the winter
months, with the summer rainfall occurring mostly as the result
of thunderstorms, particularly in July and August.
The most important and far-reaching result from this
research is confirming very recent reports (Stewart et al., 1976;
Shalhevet et al., 1976; Consortium for International Development,
1976) that a linear relationship does exist between crop yield
and evapotranspiration. Previous research (Skogerboe et al.,
1974) in Grand Valley has shown the necessity to reduce deep
percolation losses from irrigated croplands to substantially
reduce the salt pickup and consequently the salt load in the
Colorado River. A companion report, "Evaluation of Irrigation
Methods for Salinity Control in Grand Valley," will address the
importance of advanced irrigation methods (i.e., sprinkler irri-
gation or trickle irrigation) for substantially reducing deep
percolation losses, which is achieved by attaining high irrigation
application efficiencies. By substantiating the linear relation-
ship between crop yield and evapotranspiration, and taking into
account the physical characteristics of Grand Valley, it has
been shown in this report that crop yields will be increased by
attaining high irrigation application efficiencies. In a general
sense, this result was intuitively known. However, there are
numerous benefits in documenting this result in Grand Valley:
first of all, it removes doubts by other investigators; provides
some quantification of the benefits in increased crop yields to
be gained by employing more efficient irrigation methods and
practices; and most importantly, allows the research results
and implications to be incorporated into an action salinity
control program for Grand Valley.
Another highly important result from this crops research
is showing that irrigation of both corn and wheat can be termi-
nated much earlier than is commonly practiced in Grand Valley.
153
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Again, this result was intuitively known, but there is con-
siderable advantage in providing documentation so that this
result can be incorporated into an action salinity control pro-
gram. A practical recommendation for Grand Valley would be
the I-I-O irrigation treatment for corn, where irrigation water
is not applied during the grain filling growth stage. Although
it will take some time to gain acceptance by farmers to termi-
nate the irrigation of corn and wheat at an earlier date,
there are definite advantages to farmers in reduced labor by
eliminating one or two irrigations. This improved practice is
independent of the irrigation method being used by each farmer.
The research by Ayars (1976) has shown that interseasonal
(winter) precipitation in Grand Valley can contribute to ground-
water flow in Grand Valley, and consequently, result in increased
salt loads reaching the Colorado River. By terminating irriga-
tion of corn and wheat crops earlier than is presently practiced,
there will be more soil moisture storage available in the root-
zone for interseasonal precipitation, thereby reducing the
likelihood of winter precipitation reaching the underlying
shallow groundwater aquifer.
Earlier termination of irrigation for corn and wheat (grain
crops) in Grand Valley will result in less nitrogen fertilizer
being lost from the root-zone. Present fertilizer practices
in Grand Valley frequently result in fairly significant residual
nitrogen levels in the soil profile at the end of the season.
A combination of improved irrigation methods that achieve high
irrigation application efficiencies and earlier termination of
irrigation would result in significant increases in fertilizer
use efficiency by reducing both the quantities of fertilizer
applied and the amount that is leached below the root-zone.
Improved agronomic practices, such as the research results
reported herein, should be incorporated into the action salinity
control program to be undertaken in the Grand Valley by the Soil
Conservation Service (SCS) and U.S. Bureau of Reclamation (USER).
First of all, farmers must be made aware of the benefits to be
gained by such improved practices. Then, these improved
agronomic practices should be made a part of the irrigation
scheduling service that is to be provided under the action
program.
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Howell, T.A. and E.A. Hiler, 1975. Optimization of Water Use
Efficiency under High Frequency Irrigation - I. Evapo-
transpiration and Yield Relationship. Trans. Am. Soc.
Agr. Eng. 18(5): 873-878.
Jensen, M.E., 1968. Water Consumption by Agricultural Plants,
±n Water Deficits and Plant Growth, Vol. II, T.T.
Kozlowski, ed., Academic Press, New York, pp. 1-22.
Jensen, M.E., 1972. Programming Irrigation for Greater
Efficiency, In Optimizing the Soil Physical Environment
Toward Greater Crop Yields, Daniel Hillel, ed., Academic
Press, New York and London, pp. 133-162.
Jensen, Marvin E., ed., 1973. Consumptive Use of Water and
Irrigation Water Requirements. A report prepared by
the Technical Committee on Irrigation Water Requirements
of the Irrigation and Drainage Division of the American
Society of Civil Engineers, New York, New York.
Jensen, M.E. and W.H. Sletten, 1965. Evapotranspiration and
Soil Moisture-Fertilizer Interrelations with Irrigated
Winter Wheat in the Southern High Plains. U.S. Dept.
Agr., Agr. Res. Serv. in cooperation with Texas Agr. Exp.
Sta., Cons. Res. Report No. 4, 26 pp.
Jensen, M.E. and W.H. Sletten, 1965. Evapotranspiration and
Soil Moisture-Fertilizer Interrelations with Irrigated-
Grain Sorghum in the Southern High Plains. U.S. Dept;.
Agr., Agr. Res. Serv. in cooperation with Texas Agr- Exp.
Sta., Cons. Res. Report No. 5, 27 pp.
Jensen, M.E. and J.L. Wright, 1976. The Role of Simulation
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Annual Meeting of the American Society of Agricultural
Engineers, Lincoln, Nebraska, June 27-30, 14 p.
158
-------
Kiesselbach, T.A., 1950. Progressive Development and Seasonal
Variation of the Corn Crop. Neb. Agr. Exp. Sta. Bui.
166, 29 p.
Kovda, V.A., C. van den Berg and R.M. Hagan, eds., 1973.
' Irrigation, Drainage and Salinity. An International
Stiurce Book, FAO/UNESCO. Hutchinson and Co., publishers,
London, 510 pp.
Leggett, G.E., 1959. Relationship between Wheat Yield,
Available Moisture and Available Nitrogen in Eastern
.Washington Dryland Areas. Washington Agr. Exp. Sta. Bull.
6Q9, 16 pp.
Letey, J. and D.B. Peters, 1957. Influence of Soil Moisture
Levels and Seasonal Weather on Efficiency of Water Use
by Corn. Agron. J. 49: 362-365.
Ludwig/ A.E. and P.W. Soltanpour, 1975. Guide to Fertilizer
Recommendations in Colorado. Cooperative Extension
Service, Colorado State University, Fort Collins, Colorado
80521, January.
Minnas, B.S., K.S. Parikh and T.N. Srinivasan, 1974. Toward
the Structure of a Production Function for Wheat Yields
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Moore, Charles V., 1961. A General Analytical Framework for
Estimating the Production Function for Crops using
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Musick, J.T. and D.A. Dusek, 1971. Grain Sorghum Response
to Number, Timing and Size of Irrigations in the Southern
High Plains. Trans. Am. Soc. Agr. Eng. 14(3): 401-404,
410.
Musick, J.T., L.L. New and D.A. Dusek, 1976. Soil Water
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Neghass.i,. Habte M., 1974. Crop Water Use and Yield Models
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Pair, C.H., W.W. Hinz, C. Reid and K.R. Frost, 1969. Sprinkler
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159
-------
Pendleton, J.W., 1966. Increasing Water Use Efficiency by
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160
-------
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-------
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162
-------
I-1
cr»
U)
APPENDIX A
DAILY CLIMATIC DATA, APRIL-NOVEMBER, 1976
TABLE A-l. DAILY CLIMATIC DATA, MATCHETT FARM, 1976 (MONTH: APRIL)
Date Temperature (°F) Rainfall
Maximum
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
70
68
70
68
62
54
58
65
66
69
76
67
62
51
56
57
53
50
57
59
69
71
68
68
74
52
58
68
72
63
Minimum (ln->
33
26
28
38
39 .03
27
37
32
41
32
35
44 .01
42
41 .04
30
35 .25
33
35 .24
40
31
38
45
43
31
39
33
23
32
38
36
Max.Rel. Radiation Wind Run
Humidity (Langleys) (miles)
45
26
31
40
42
76
57
33
40
38
68
89
93
93
95
57
48
35
64
41
34
67
76
59
57
75
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
Out of Order
392*
500*
500*
500*
528*
569*
602*
532*
591*
318
151
169
236
283
196
166
199
333
196
263
436
295
208
263
275
251
124
121
215
242
27?.
262
481
542
346
134
164
271
227
Evaporation
(in.)
.301
.263
.231
.241
.180
.018
.162
.153
.262
.338
.276
.386
.194
.241
.003
.212
-.116
-.097
-.012
.168
.206
.273
.290
.235
.273
.384
.267
.224
.278
.338
Lysimeter Use (in)
North
„
—
.123
.084
.049
.062
.073
.071
.142
.107
.125
.077
.090
.019
.065
.043
.024
.150
.174
.217
.186
.181
.185
.174
.182
.224
.150
.164
.128
.084
South
—
.091
.087
.025
.060
.061
.090
.108
.088
.119
.068
.078
.010
.052
.019
.002
.000
.000
.000
.080
.118
.124
.127
.182
.132
.094
.134
.150
.139
* From correlation with Agricultural Research Service data, collected nearby.
-------
TABLE A-2. DAILY CLIMATIC DATA, MATCHETT FARM, 1976 (MONTH: MAY)
Date Temperature
Rainfall Max.Rel. Radiation Wiijd Run Evaporation Lysimeter Use (in)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Maximum
68
71
77
65
70
60
66
56
68
73
77
68
78
84
75
74
80
81
80
66
62
66
71
76
73
76
80
85
81
70
80
Minimum
31
34
43
44
41
41
42
43
43
42
49
36
36
45
44
38
42
52
55
41
50
42
41
46
41
40
45
51
49
47
43
(in.)
.04
.0'2
.26
.10
.10
.01
.14
.23
.11
.11
nuraiaity
71
55
47
50
92
80
90
98
94
72
63
56
60
55
60
60
66
51
56
87
95
98
93
91
76
80
65
45
50
66
70
(Lang leys)
648*
550*
542*
294*
622*
131*
387*
428*
428*
628*
490*
661
655
712
622
770
708
420
425
290
251
386
630
393
484
676
677
672
585
291
679
(miles)
188
198
160
206
135
165
153
128
124
214
290
196
126
159
294
168
110
103
197
91
70
121
109
161
165
101
173
188
164
185
162
(in.)
.236
.307
.271
.301
.073
.139
-.116
-.328
-.126
.180
.276
.321
.284
.227
.335
.359
.287
.318
.232
.139
.128
.030
.033
.182
.053
.220
.243
.287
.326
.274
.220
North
.028
.183
.163
.031
.207
.022
.012
.153
.131
.153
.136
.244
.232
.122
.079
.104
.261
.246
.182
.002
.014
.024
.050
.113
.198
.295
.350
.430
.360
.227
.392
South
.155
.158
.124
.012
.113
.000
.001
.004
.001
.006
.011
.132
.170
.213
.249
.225
.224
.201
.133
.001
.000
.001
.044
.088
.146
.227
.286
.346
.288
.177
.318
-------
TABLE A-3. DAILY CLIMATIC DATA, MATCHETT FARM, 1976 (MONTH: JUNE)
Date
Temperature
<°F)
Maximum Minimum
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
84
87
84
84
88
84
86
85
88
88
72
74
82
66
75
86
73
78
85
94
93
72
76
77
85
87
92
95
94
88
50
50
54
52
50
53
53
53
56
55
43
43
47
31
38
46
50
42
49
55
58
59
46
43
47
47
53
54
58
62
Rainfall Relative
, . , Humidity
(in.) (%)
77
80
48
40
48
49
61
61
61
43
36
.01 85
40
.01 95
65
49
.04 85
83
27
43
Trace 59
.04 84
87
64
41
62
47
44
45
.08 47
Radiation
(Langleys)
611
645
631
657
691
491
497
522
676
663
567
682
376
703
700
558
562
697
778
645
662
224
673
718
729
693
705
727
610
409
Wind Run
(miles)
156
224
287
237
193
333
145
205
235
402
299
249
296
201
215
278
186
202
242
224
307
207
196
156
180
165
175
143
311
338
Evaporation
(in.)
.205
.311
.310
.427
.379
.368
.259
.323
.292
.416
.562
.352
.370
.291
.320
.380
.424
.220
.402
.478
.435
.334
.334
.349
.339
.408
.430
.387
.252
.526
Lysimeter
North
.409
.479
.582
.547
.566
.421
.454
.466
.642
.808
.602
.532
.692
.534
.609
.782
.462
.665
.769
.826
.893
.279
.691
.645
.794
.728
.849
.830
.989
.572
Use (in)
South
.325
.386
.484
.461
.464
.366
.369
.420
.565
.700
.508
.495
.370
.430
.559
.660
.391
.569
.639
.8.13
.764
.231
.576
.563
.689
.583
.719
.697
.846
.572
-------
TABLE A-4. DAILY CLIMATIC DATA, MATCHETT FARM, 1976 (MONTH; JULY)
a\
CTl
Date
Temperature
<°F)
Maximum Minimum
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
87
90
90
92
94
96
92
94
96
97
95
92
88
91
89
93
89
82
77
85
86
91
92
90
85
84
88
92
91
92
88
56
61
51
57
56
60
68
63
62
64
60
62
59
58
54
58
63
57
57
64
51
55
58
60
64
61
60
59
60
60
63
Rainfall Max. Pel.
, . . Humidity
(an.) (%)
85
59
54
40
45
42
43
58
51
54
62
66
.09 86
60
61
46
.03 54
.09 79
96
84
88
65
49
53
62
80
71
56
53
60
72
Radiation
(Langleys)
687
688
726
747
671
655
488
667
702
719
633
490
684
731
632
696
578
407
442
557
694
692
689
706
517
420
656
665
630
684
457
Wind Run
(miles)
188
190
149
208
151
194
262
176
235
230
188
169
131
173
163
127
169
152
220
146
147
154
228
127
196
152
146
133
104
215
149
Evapora tion
(in.)
.227
.343
.418
.377
.477
.393
.403
.413
.398
.461
.454
.508
.343
.370
.363
.369
.228
.118
.290
.206
.316
.348
.544
.337
.336
.207
.339
.291
.253
.383
.109
Lysimeter
North
.698
.871
.816
.980
.732
.854
.737
.776
.785
.797
.677
.566
.485
.702
.731
.695
.623
.404
.379
.522
.574
.505
.548
.492
.433
.271
.389
.391
.381
.333
.298
Use (in)
South
.594
.726
.685
.839
.685
.707
.633
.640
.608
.736
.602
.411
.413
.562
.528
.491
.406
.235
.212
.357
.433
.492
.556
.483
.393
.215
.351
.359
.323
.394
.260
-------
TABLE A-5. DAILY CLIMATIC DATA, MATCHETT FARM, 1976 (MOUTH: AUGUST)
en
Date
Temperature
(°F)
Maximum Minimum
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
80
84
78
83
86
87
84
80
85
82
82
87
83
85
83
83
85
84
84
88
90
91
87
88
91
88
82
87
89
90
85
59
58
58
57
50
54
58
56
53
53
56
51
55
52
62
57
63
55
56
56
57
59
62
52
56
61
49
50
53
55
51
Rainfall Max.Rel.
(in ) Humidity
(in.) (%)
.11 98
80
67
65
45
38
41
.10 73
80
45
.11 61
75
.06 50
70
38
47
.01 52
90
61
70
67
57
74
72
68
.01 46
93
58
50
55
83
Radiation
(Langleys)
410
529
457
629
668
668
450
228
680
434
544
640
504
623
455
610
314
573
562
619
589
391
574
574
577
452
607
599
560
476
598
Wind Run
(miles)
173
104
402
230
166
241
304*
312*
170*
208*
298*
174*
158*
210*
296*
208*
160*
198*
200*
116*
124*
194*
154*
110*
134*
194*
88*
138*
188*
180*
200*
Evaporation
(in.)
.221
.181
.311
.338
.278
.421
.275
.051
.316
.166
.251
.294
.133
.374
.327
.331
.136
.292
.254
.237
.242
.231
.260
.259
.320
.297
.318
.284
.311
.291
.369
Lysimeter
North
.135
.253
.327
.395
.358
.449
.264
.264
.293
.269
.308
.332
.243
.429
.384
.422
.214
.331
.353
.328
.343
.313
.413
.278
.376
.361
.339
.363
.393
.368
.404
Use (in)
South
.130
.228
.296
.333
.305
.355
.204
.204
.217
.209
.203
.247
.165
.307
.269
.306
.151
.236
.259
.248
.262
.233
.326
.198
.298
.265
.269
.293
.317
.292
.323
*Data from Walker Field Airport, corrected for height
-------
TABLE A-6. DAILY CLIMATIC DATA, MATCHETT FARM, 1976 (MONTH: SEPTEMBER)
01
00
Date
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Temperature (°F) Rainfall
Maximum
84
88
92
93
92
72
79
79
79
71
78
74
79
81
79
82
82
78
78
79
74
72
74
60
66
59
66
71
76
76
Minimum {int)
49
44
52
52
55
58 .01
52
47
48
52 .02
54 .01
59 .04
48
49
53
51
55
54
44
48
47 .01
44
45
50 .27
49
48
40
38
39
40
Max . Re 1 .
Humidity
(%)
63
58
52
45
44
90
95
81
54
75
80
100
88
77
55
79
60
57
56
67
57
99
86
98
98
96
99
64
60
69
Radiation
(Langleys)
572
589
629
585
515
199
524
559
467
255
400
467
530
449
307
443
501
507
503
504
319
495
325
199
273
269
448
463
518
455
WjLnd Run
(miles)
140*
126*
140*
116*
140*
132*
98*
128*
124*
72*
142*
88*
116*
94*
200*
182*
210*
170*
122*
140*
152
103
103
16
73
69
103
90
104
100
Evaporation
(in.)
.290
.270
.297
.293
.201
.029
.205
.274
.177
.043
.088
.168
.229
.178
.281
.107
.349
.231
.143
.211
.130
.167
.019
-.139
.110
-.055
.145
.147
.138
.165
Lysimeter
North
.350
.331
.337
.333
.327
.237
.280
.247
.090
.181
.192
.252
.247
.212
.262
.331
.281
.258
.286
.230
.176
.142
.143
.214
.223
.229
.186
Use (in)
South
.276
.244
.243
.251
.242
.251
.178
.222
.182
.063
.127
.141
.195
.186
.148
.199
.247
.221
.265
.138
.143
.121
.007
.002
.022
.029
.125
.119
.136
*Data from Walker Field Airport, corrected for height.
-------
TABLE A-7. DAILY CLIMATIC DATA, MATCHETT FARM, 1976 (MONTH: OCTOBER)
Date
Temperature
(8F)
Maximum Minimum
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
80
70
64
64
64
64
60
68
70
72
72
71
71
70
74
72
71
52
56
60
62
61
64
63
63
52
56
62
56
61
62
44
50
40
38
33
33
30
30
34
33
41
32
33
33
33
30
38
24
21
23
25
26
31
33
27
21
23
23
20
22
25
Rainfall Max.Rel.
. . Humidity
(m.) (%)
59
.44 63
100
80
82
73
52
67
68
59
47
75
70
71
67
64
61
72
72
55
52
76
80
71
76
82
85
75
77
73
72
Radiation
(Lang leys)
330
180
335
468
519
393
375
499
430
439
297
433
556
328
422
412
340
321
423
416
393
285
384
363
363
222
387
387
406
454
234
Wind Run
(miles)
95
136
85
83
72
199
89
100
68
142
78
146
138
81
52
116
143
119
73
103
85
78
104
131
158
186
97
86
110
117
66
Evaporation
(in.)
.096
-.400
.132
.130
.057
.176
.124
.114
.138
.164
.063
.177
.154
.144
.122
.131
.169
Frozen
Lysimeter
North
.157
.136
.124
.121
.123
.103
.094
.112
.100
.105
.087
.098
.117
.090
.134
.130
.121
Use (in)
South
.101
.042
.002
.004
.007
.054
.068
.085
.081
.096
.074
.094
.107
.072
.081
.081
.080
.040
-------
TABLE A-8. DAILY CLIMATIC DATA, MATCHETT FARM, 1976 (MONTH: NOVEMBER)
Date
Temperature
(°P)
Maximum Minimum
1
2
3
4
5
6
7
8
9
10
11
12
13
14
65
66
66
63
64
65
65
63
66
56
59
52
46
50
27
30
30
27
27
28
27
24
25
24
22
24
29
30
Rainfall Max.Rel.
.. . Humidity
dn.) (%)
69
84
74
90
76
69
66
76
72
Radiation
(Lang leys)
368
353
325
352
387
288
335
332
332
Wind Run
(miles)
114
93
117
99
104
64
82
70
86
Evaporation Lysimeter Use (in)
Un>) North South
-------
APPENDIX B
TABLE B-l. MATCHETT FARM EVAPOTRANSPIRATION PARAMETERS, 1976
j-1
-j
H
Weather Data
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Modified Julian
Date Interval
64-70
71-77
78-84
85-91
92-98
99-105
106-112
113-119
120-126
127-133
134-140
141-147
148-154
155-161
162-168
169-175
176-182
183-189
190-196
197-203
204-210
211-217
218-224
225-231
232-238
239-245
246-252
May
May
June
June
July
July
Aug.
Aug.
Sept
3-9
10-16
17-23
24-30
31- June 6
7-13
14-20
21-27
2 8- July 4
5-11
12-18
19-25
26-Aug. 1
2-8
9-15
16-22
23-29
30-Sept. 5
. 6-12
13-19
20-26
Sept. 27-Oct. 3
Oct.
Nov.
4-10
11-17
18-24
25-31
1-7
T .
mm
°C
5.3
5.2
7.8
7.6
10.2
10.0
6.9
10.2
13.9
16.6
14.8
14.7
15.7
13.3
12.6
14.2
12.6
10.6
11.6
10.3
8.5
5.3
0.6
1.3
-3.3
-5.0
-2.2
T
max
°C
18.9
24.2
22.4
25.2
29.1
27.8
26.4
28.4
32.7
34.9
31.7
30.3
31.1
28.4
28.8
30.2
30.8
31.7
24.4
26.6
20.6
22.2
18.9
22.0
15.4
14.9
18.3
T
av
°C
12.3
14.7
15.1
16.4
19.6
18.9
16.7
19.3
23.3
25.8
23.3
22.5
23.4
20.8
20.7
22.2
21.7
21.2
18.0
18.5
14.6
13.8
9.7
11.6
6.1
5.0
8.0
Relative
Humidity
.787
.609
.780
.676
.589
.553
.636
.634
.534
.507
.646
.710
.700
.584
.599
.634
.659
.571
.821
.674
.859
.734
.687
.650
.683
.771
.754
Rs
ly/day
405*
648
444
540
629
569
663
629
656
648
603
614
560
519
544
522
563
566
409
463
341
390
446
398
369
351
344
U2
mi/day
153
207
103
162
228
261
221
198
218
205
155
174
153
251*
216*
171*
144*
149*
112*
156*
93
102
108
108
99
117
96
Saturation
Vapor Pressure
(e°)T
max
21.8
30.2
27.1
32.0
40.3
37.3
34.4
38.7
49.4
55.9
46.7
43.1
45.2
38.7
39.6
42.9
44.4
46.7
30.6
34.8
24.3
26.8
21.8
26.4
17.5
17.0
21.0
(e°)T
min
9.23
8.86
10.6
10.5
12.5
12.3
9.96
12.5
15.9
18.9
16.8
16.7
17.8
15.5
14.6
16.2
14.6
12.8
20.6
12.5
11.1
8.92
6.39
6.72
4.79
4.22
5.20
* Walker Field data, corrected for height of anemometer
+ From ARS readings, using (Rg)csu = 1.569 (Rg)^15 <
0.916)
-------
APPENDIX C
TABLE C-l. EVAPOTRANSPIRATION PER GROWTH STAGE OF CORN
Treatment Plot
0-0-0 20
32
36
45
1-0-0 24
27
39
43
0-1-0 18
28
37
42
0-0-1 22
25
35
41
I-I-O 21
30
40
48
I-O-I 19
29
34
46
O-I-I 23
31
33
44
I-I-I 17
26
38
47
0
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
51
Growth
I
165
144
165
197
201
201
201
201
161
83
135
135
140
101
70
95
201
201
201
201
201
201
201
201
94
70
105
50
201
201
201
201
Stage*
II
(mm)
60
47
44
114
81
111
62
115
224
224
224
224
127
80
132
74
224
224
224
224
81
87
81
102
191
224
224
224
210
210
224
215
III
27
49
48
53
79
85
86
85
78
65
51
86
145
174
174
174
102
113
100
92
174
174
174
174
174
174
174
174
174
174
174
174
Total
303
291
308
415
412
448
400
452
514
423
461
496
463
406
427
414
578
589
576
568
507
513
507
528
510
519
554
499
636
636
650
641
*as defined in Figure 16
172
-------
APPENDIX D
TABLE D-l. CORN YIELDS AND ET OF EACH PLOT
Treatment
0-0-0
1-0-0
0-1-0
0-0-1
I-I-O
I-O-I
O-I-I
I-I-I
Plot Seasonal ET
(mm)
20
32
36
45
Average
24
27
39
43
Average
18
28
37
42
Average
22
25
35
41
Average
21
30
40
48
Average
19
29
34
46
Average
23
31
33
44
Average
17
26
38
47
Average
303
291
308
415
329
412
448
400
452
428
514
423
461
496
474
463
406
427
414
428
578
589
576
568
578
507
513
507
528
514
510
519
554
499
521
636
636
650
641
641
Dry matter yield Grain yield
(kg ha'1) (kg ha"1)
6078
7178
8337
9906
7875
10961
10162
12405
14264
11948
10494
7279
13573
9541
10222
10850
7347
10240
6070
8627
12205
12018
10196
17255
12919
6889
10978
9350
9058
9069
9622
12187
11087
9947
10711
11620
11413
15351
15592
13494
3660
3430
3528
5678
4074
4615
4433
6105
7199
5588
7132
5144
8881
5015
6543
5941
4381
5294
4582
5050
10957
8645
6215
7796
8403
5901
7943
5663
3570
5769
4776
8481
7917
7093
7067
8301
6555
10051
7544
8113
173
-------
10000
= 8000
'o
«*
10
' 6000
5 4000
o 2000
o
APPENDIX E
T 1 1 T
H-0
• 0-1-0
0-0-1® •i-o-I
1-0-0*
0-0-0
J 1 1
0 200 400 600
Seasonal ET, mm
Figure E-l. Corn grain yield versus ET: Replication I,
174
-------
10000
8000
'o
m
to
6000
•3* 4000
2 2000
i i i r
0-H
©I-I-O
©I-O-I
0-0-1© ©I~0-0
©o-o-o
I I
0 200 400 600
Seasonal ET, mm
Figure E-2. Corn grain yield versus ET: Replication II,
175
-------
10000
» 8000
V)
'5
in 6000
'O
I1 4000
c
2 2000
I I I I I
• 0-1-0
• O-I-I
• KM)
I-O-I
•o-o-r
© o-o-o
j i L
0 200 400 600
Seasonal ET, mm
Figure E-3. Corn grain yield versus ET: Replication III
176
-------
10000
8000
M
'5
6000
in
4000
4)
S 2000
I-O-O
I-I-O
I-I-I*
• 0-0-0
• 0-1-0
• 0-0-1
• I-O-I
I I
0 200 400 600
Seasonal ET, mm
Figure E-4. Corn grain yield versus ET: Replication IV.
177
-------
14000
12000
10000
8000
6000
o
"5
4000
2000
•i-r-o
• H-I
i-o-o
• o-o-i
• o-i-o
• o-i-i
'0-0-0
• I-O-I
1 I
200 400 600
Seasonal ET, mm
800
Figure E-5. Corn dry matter yield versus ET: Replication I
178
-------
14000
12000
10000
To
.2 8000
0)
6000
o
4000
2000
M-0
• I-H
• I-O-I
• 1-0-0
ii
I I
0 200 400 600 800
Seasonal ET, mm
Figure E-6. Corn dry matter yield versus ET: Replication II,
179
-------
16000
14000
2000
0.10000
JC
o>
0>
o
8000
6OOO
4000
2000
•M-I
• 0-1-0
•I-O-O
•O-I-I
O-O-I* •H-0
•KH
•O-O-O
200 400 600 800
Seasonal ET, mm
Figure E-7. Corn dry matter yield versus ET: Replication III
180
-------
18000
16000
14000
7 12000
o
.c
o»
10000
8000
o
"o
6000
4000
2000
• M-0
• I-I-I
• I-0-0
0-0-0* «0-I-I
• 0-1-0
0-0-1
0 200 400 600
Seasonal ET, mm
Figure E-8. Corn dry matter yield versus ET:
181
800
Replication IV.
-------
APPENDIX F
TABLE F-l. WHEAT YIELDS AND ET OF EACH PLOT
Treatment
0-0
1-0
0-1
I-I
Plot
51
58
49
53
56
54
57
50
52
55
Seasonal ET
(mm)
409
363
479
467
493
485
513
579
613
567
Grain Yield
(kg ha"1)
4388
3848
5011
4545
4394
4270
4157
4818
4637
4253
182
-------
APPENDIX G
EFFECT OF CONTRACT RATES ON OBJECTIVE FUNCTION
Depending on the farming operation being carried out7
contract rates usually consist of a minimum fixed price (to
cover machinery overheads) plus a variable price based on area
or yield. Typical contract costs may be expressed as follows,
where the C^'s correspond to those shown in Section 10 in the
text. The fixed cost portion of each cost is denoted by the
superscript *. Per unit area costs are no longer applicable,
so total costs will be considered. The annual fixed costs of
GI = a* + alAl
C2 = (S2 * b2X)AI
C3 = a* + a^
C4 = a4 +
-------
= a*g
C10 = VTY per unit area
= (a10
The objective is, therefore, to:
maximize P = 0 - I
= (a + bxJAj - (a..^ - a. A + t^
where a.^ = a* + a* + a* + a* + a* + a_ + ag
a. = ax + a2 + a3 + a4 + a5 + a6 + a* + a* + ag + a^
b. = b2 + b4 + bg + b1Q
(The terms composing a-^ , a^ and b^ are able to be summed
respectively as all are constants.) Therefore, the objective is
to:
ai
maximize P = [a + bx - (a. + b.x + — ) ]A
D 1 Aj -1-
which is the same as the objective expressed by Equation 37.
184
-------
APPENDIX H
OPTIMAL DEPTH OF IRRIGATION WATER TO APPLY
WITH A LINEAR PRODUCTION FUNCTION: NUMERICAL EXAMPLES
NUMERICAL EXAMPLE I:
Situation: Selected crop = wheat -
Available water = 1,000,000 m
Available land = unlimited
Yield function: y = -58.3 + 0.268x (r = 0.933)
(taken from Shalhevet, et al., 1976, for Jordan Rift and Bet
Shean Valley, Israel).
Maximum anticipated yield, Ym_jv. = 6000 kg ha
(approx. 90 bus ac).
max
Corresponding maximum water consumption x = 590 mm
Gross return on crop, v = $0.11 per kg
(approx. $3 per bus) .
Objective:
Select the optimum land area, A , to be irrigated so that
the function P = (0-I)A_ is a maximum, where
P = net revenue
0 = output (gross revenue) per ha
I = input (costs) per ha, and
A = area irrigated in ha.
Method:
0 = vcy
A 6000
y = y ~ioo
= (-58.3 + 0.268x)
= -3498 + 16.08x
185
-------
.'. 0 = (-3498 + 16.08x) (0.11)
= -385 + 1.769x $ ha"1
I = c + c2 + c3 + ... + GIO, where
c, = cost of seedbed preparation
= $25 per ha
c2 = cost of seed.
A constant seeding rate of 45 kg ha'1 has been assumed for
up to 400 mm of water consumption, then increased linearly up to
75 kg ha"1 for 590 mm of water consumption. If seed costs are
$0.37 per kg, then:
c2 = 45 x 0.37
= $17 per ha for 0 <_ x <_ 400, and
c2 = -6.718 + 0.0585X $ ha"1 for 400 <_ x <_ 590
c., = cost of sowing
= $6 per ha
c, = cost of fertilizing.
Colorado State University Cooperative Extension Service uses a
recommendation for N03-N based on the soil fertility level,
organic matter content and yield goal. The recommendation has a
functional relationship of
F = m + ny
where F is the recommended N03-N application rate in Ib N acre
and y is the yield goal in bus ac'l. For example, for a clay
loam soil having a NO3-N soil test level of 11 ppm and an organic
matter content of 1.5 percent, the relationship would be
F = -35 + 1.5y in the above units,
or F = -39 + 0.0250y
where F is in kg ha and y is in kg ha
Now, y = -3498 + 16.08x
.*. F = -39 + 0.025 (-3498 + 16.08x)
186
-------
= -126.5 + 0.402x kg ha"1
and with nitrogenous fertilizer costing $0.45 per kg (actual)
c4(N03) = -57 + O.lSlx $ ha"1.
Recommendations for other fertilizer elements are based
solely on the soil test results and are independent of the yield
goal. Therefore, assuming a phosphorus recommendation of 45 kg
ha"1 at $0.38 per kg
c4 (P2°5) = $17 Per ha
The total cost of fertilizer is, therefore,
c4 = -40 + O.lSlx $ ha"1
Cj. = cost of pesticides
= $25 per ha
c, = cost of interrow cultivation
b
= 0
Cj = cost of irrigation
= C7L + C7E + C7F' Where
c_ = cost of labor ,
c7E = variable cost of pumping (energy and maintenance)
c7 = fixed cost of irrigation equipment.
The larger the area to be irrigated, the less the number of
irrigations that can be accomplished with the fixed quantity of
water, with a higher cost per irrigation. For a smaller area,
a greater number of irrigations will be possible, each having a
lower cost. Therefore, the cost of labor will be approximately
the same, depending only on the quantity of water, which in this
case is fixed. Assume
c_T = $1 per 1000 m
/ L
= $1000 per 106m3 (Q = Ll, 000 ; 000-m3)-
= $1000/AI per ha,
as the 106m3 are to be applied to an area, Aj.
187
-------
Assume c_E = $3.00 per 1000 m3
= S3000/A per ha
c7p = $25 per ha
This cost will decrease with increasing area, but only by a small
amount within the range of areas considered.
.'. c? = 25 + 4000/Aj $ ha"1
cg = cost of water.
Consider the charges for water to be on an escalating rate of
cg = $1 per 1000 m for 0 < q <^ 250,000 m3
= $2 per 1000 m3 for 250,000 < q <_ 500,000 m3
= $3 per 1000 m3 for 500,000 < q <_ 750,000 m3
= $4 per 1000 m3 for 750,000 < q <_ 1,000,000 m3
where q <_ Q
As Q = 1,000,000 m3
c8 = $2500
= $2500/AI per ha
c_ — cost of harvesting
= $25 per ha up to 1500 kg ha plus
$0.002 per kg for greater than 1500 kg ha
When y = 1500 kg ha~ , x = 311 and cg = $25 per ha
When y = 6000 kg ha~ , x = 590 and c_ = $34 per ha
.'. CQ = $25 per ha for 0 <_ x <^ 311
and CQ = 15 + 0.0323x $ ha'1 for 311 < x < 590
y — —
c,n = cost of disposing
= $0.004 per kg in own bin + $0.0002 (kg km"1) for
hauling.
188
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Assuming a 10 km haul
C10 = $<°'004 + 0.002) per kg
= $0.006 per kg
= -21 + 0.0965X $ ha"1
Therefore, the objective function is to
10
maximize P = [0 - J c.]AT
= [-385 + 1.769x - (20 + 0.2775x + c2
+ 6500 , „ .._
A C9'JAI
AT = a
I X
1,000,000 m3
x mm
= ha where x is in mm
•JC
5 i
.*. Maximize P = -405 (—-) + (1.4265) (105) + (c^+c ) ^£
x 2 9' x
For 0 < x <^ 311,
105 5 105
P = -405 F^-) + (1.4265) (10D) + 42 (iH_)
x x
5
= -365 (^-) + (1.4265) (105)
and P is a maximum when x is a maximum.
When x = 341
P = $35,612
For 311 < x <_ 400,
5 5
P = -405(~-) + (1.4265) (105) + 32 (^-) + (0.0323) (105)
and P is a maximum when x is a maximum
When x = 400
P = $52,630
189
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For 400 < x £ 590
5 5
p = .-405(— ) + (1.4265) (105) + 8 . 282 <^-) + (0 . 0908) (105)
IK •**
and again P is a maximum when x is a maximum
When x = 590
P = $84,490
Therefore, the maximum profit is obtained when the amount of
water consumed is a maximum, up to the limit of
x = Xmax'
Therefore, the optimum area is the smallest over which the fixed
water quantity can be applied so that x does not exceed x
i.e. , A
.
opt xmax
1,000,000 m3
590 mm
= 169.5 ha
Most of the cost factors are either independent of the area
irrigated (eg) or increase with area (c]_, 03, 05, eg, Cy) .
These can be eliminated from any sensitivity analysis. The
remainder (c2, c4, c9 , and c10) all affect net profit in propor-
tion to the yield obtained from the total area. They can only
be decreased by decreasing the total yield. Decreasing the
total yield will obviously decrease gross profits by a greater
amount (otherwise the most profitable practice would be to grow
zero wheat!). Therefore, it may be seen qualitatively that the
most profitable practice is to irrigate that area, A , of crop
which will consume that depth of water, x , giving the peak
* -ii T r fflcLX
yield, Y
max
The cost factors in the profit calculation above take into
account only those variable and fixed costs associated directly
with the irrigation enterprise. From the point of view of the
farm budget, other fixed costs, such as land taxes, loan
interest and overheads, would have to be subtracted in addition
to a contingency sum for the inevitable unforeseen costs. These
factors do not affect the optimal irrigation policy as derived.
NUMERICAL EXAMPLE II:
Situation:
190
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Selected crop: wheat
Available water: unlimited
Available land: 200 ha
Yield function/ crop value and costs the same as in
Numerical Example I.
Objective :
Select the optimum quantity of water to make available for
crop consumption so that the function
p = P/Aj = 0-1
is a maximum, where p is the net profit per unit area and the
other terms are as defined in the previous example.
c, through cfi will be the same as before
c will depend on the depth of water applied:
1 mm over 1 ha = 10 m
x = S-7T mm where q is the volume of water applied per
10 3-1 rr r
unit area, in m ha
c = $25 per ha + $4.00 per 1000 m
= $25 per ha +
q = 10 X
. * . c = 25 + 0.04x $ ha"1
Cg can be expressed in terms of x. At $1 per 1000 m , the
cost per ha is $lq/1000 where q is the volume of water applied
per ha. As q = 102x, then
Cg = $0.01 x per ha for 0 < x <^ 125
= $0.02 x per ha for 125 < x <_ 250
= $0.03 x per ha for 250 < x <_ 375
= $0.04 x per ha for 375 < x <_ 500
and say CQ = $0.10 x per ha for x > 500
where the limits of q in the previous example have been converted
to limits of x by recognizing that as
x = 3-
X 10
191
-------
and q = 2§0
then x = 2000 *
cg and c,Q are as before.
The objective, therefore, is to
maximize p = -385 + 1.769x -(20 + 0.3175x + c2 + cg + CQ)
= -405 + 1.4515x - (c2 + cg + cg)
where C2, CQ, and 09 vary with x over different ranges of x.
Observation of the coefficients of x in these cost factors will
show that they are much smaller than the coefficient of x in the
expression for p, and hence, again, maximum profit is associated
with maximum x(x = xmax). If the coefficients of x in the cost
factors are increased substantially, the effect will be to make
the coefficient of x negative in the expression for p. In this
case, irrigating will not be feasible.
The remaining possibility is to increase the cost of water,
where the charge is on an escalating scale. (If the charge were
constant and substantially increased, the effect would simply be
to reduce profitability.) If, for example, water charges were
increased tenfold for up to 500 mm, so that
c8 = $0.1 x per ha for 0 _<_ x <_ 125
= $0.2 x per ha for 125 < x <_ 250
= $0.3 x per ha for 250 < x <_ 375
= $0.4 x per ha for 375 < x <_ 500
and Cg = $2.0 x per ha for x > 500
then:
when x = 200 300 400 500 590 499 501 mm
p = -184.2 -64.1 45.7 142.1 87.5 141.1 141.5 $ ha"1
192
-------
In this case, maximum profit is attained when x=500 mm,
i.e., the additional yield obtained by the crop consuming
additional water does not justify the additional water. The
breakpoint comes where the incremental charge for water jumps
from $40 per 1000 m3 to $200 per 1000 m3.
Therefore, unless the charge for water is on an escalating
scale per volume, with the maximum charge very high in relation
to the value of the crop, the most profitable practice will be
to provide the crop with the depth of water corresponding to
maximum yield.
193
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TECHNICAL REPORT DATA
{Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/2-79-149
4. TITLE AND SUBTITLE
POTENTIAL EFFECTS OF IRRIGATION PRACTICES ON
CROP YIELDS IN GRAND VALLEY
6. PERFORMING ORGANIZATION CODE
3. RECIPIENT'S ACCESSION'NO.
5. REPORT DATE
August 1979 issuing date
7. AUTHOR(S)
G.V. Skogerboe, J.W.H. Barrett, B.J. Treat,
and D.B. McWhorter.
8. PERFORMING ORGANIZATION REPORT NO,
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Agricultural and Chemical Engineering Department,
Colorado State University
Fort Collins, Colorado 80523
10. PROGRAM ELEMENT NO.
1BB770
11. CONTRACT/GRANT NO.
Grant S-800687
12. SPONSORING AGENCY NAME AND ADDRESS
Robert S. Kerr Environmental Research Laboratoi
Office of Research and Development
U.S. Environmental Protection Agency
Ada, Oklahoma 74820
13. TYPE OF REPORT AND PERIOD COVERED
y Final
14. SPONSORING AGENCY CODE
EPA/600/15
15. SUPPLEMENTARY NOTES
193 pages, 45 fig, 20 tab, 80 ref, 8 append.
16. ABSTRACT
An analysis has been undertaken to determine the economically optimal
seasonal depth of irrigation water to apply under conditions of both
limited and plentiful water supply. The objective was to determine if
general guidelines having practical utility could be postulated for all
water supply situations. An extensive range of literature pertaining to
the relationship between crop yield and the amount of water applied has
been reviewed and differences suggested 'by various authors have been
resolved. In addition, 32 plots of corn and 10 plots of wheat were
grown under different irrigation regimes in the Grand Valley of Colorado
to supplement the results.: of other researchers and to provide further
insight into the effects of stress at different stages of plant growth.
The results of the field experiments on corn and wheat show that irri-
gation can be terminated sooner than is the common practice in Grand
Valley, which will result in benefits to farmers in increased crop
yields and to downstream water users because of reduced saline return
flows reaching the Colorado River.
II
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Corn
Evapo transpiration
Salinity
Water distribution (applied)
Wheat
13. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
b.lDENTIFIERS/OPEN ENDED TERMS
Crop response/yield
Irrigation effects/
management/systems
Salinity control
Water consumption/
management
Grand Valley
19. SECURITY CLASS (This Report)
UNCLASSIFIED
20. SECURITY CLASS (This page)
UNCLASSIFIED
c. COSATI Field/Group
02 C
98 C
21. NO. OF PAGES
208
22. PRICE
EPA Form 2220-1 (9-73)
194
U. S. GOVERNMENT PRINTING OFFICE: 1979 — 657-060/5365
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