AN ABSTRACT OF THE THESIS OF
Kim C. Nielsen
for the degree of
Agricultural and Resource Economics
Title:
Master of Science
presented on
RISK/RETURN ANALYSIS OF IRRIGATION SYST
in
June 15, 1982
DESIGN AND
OPERATING RULES
Abstract approved:
Redacted for privacy
A model was developed to simulate winter wheat production on
irrigated farmland similar to that found near Hermiston, Oregon.
simulated farm is irrigated with a side roll sprinkler system.
The
A well
is located adjacent to the wheat field and the water is delivered by
an electrically powered pump.
The major components of the model are:
1.
The soil moisture component which estimates daily soil
moisture level. The soil moisture level is a function
of daily precipitation, daily irrigation and daily evapotranspiration. Evapotranspiration is calculated as a
function of measured pan evaporation, wheat plant stage
of development and the soil moisture level.
2.
The irrigation component which schedules daily irrigation
based on the decision strategies supplied by the model
user.
There are three major parts of each strategy, the
irrigation system design, the set time in hours and the
soil moisture level that initiates irrigation.
3.
The yield component of the model which estimates
wheat grain yield as a function of daily temperature,
The
daily soil moisture, and stage of plant growth.
scheduling of irrigation will create variability in the
soil moisti.'re level across the field. This variability
of soil moisture is incorporated in the yield component.
4.
The risk/returns component which calculates the net returns
and utility. Utility is equal to the average net return
minus the standard deviation weighted by a risk aversion
factor.
Wheat production was simulated for 19 years of daily weather data
from the HermIston Agricultural Experiment Station from 1963-1981.
Several strategies were compared.
The comparisons were made of the
yields, water use, irrigation costs, net returns, risk and utility of
the various strategies.
The strategies were ranked according to maximum
utility.
The results indicated that designing irrigation systems for maximum
yields did not result in the highest utility.
The optimum strategies
were those that initiated irrigation at a low level of soil moisture depletion and used a system with a relatively lower capital investment.
The average annualized investment cost f or the five strategies with the
highest yields was $76.43 per acre.
The annualized investment cost for
the five strategies with the highest utility was $57.54 per acre.
The
difference in average utility between the two groups was $19.37 per acre.
The strategy with the highest yield had a utility level of $295.77 per
acre.
The strategy with the highest utility had a utility level of $337.12
per acre.
tion.
The analysis included only those costs associated with irriga-
Utility was more sensitive to labor costs and water charges than
to the cost of energy and interest rates.
The level of risk aversion
made very little difference in the relative level of utility for the
different strategies.
If the moisture holding capacity of the soil was
reduced then the level of risk aversion made a bigger difference in the
relative level of utility.
Risk/Return Analysis of Irrigation System
Design and Operating Rules
by
Kim C. Nielsen
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the
requirements for the
degree of
MASTER OF SCIENCE
June 1983
APPROVED:
Redacted for privacy
Professor of Agricultural and Resource Economics in charge of major
Redacted for privacy
Head of Department of Agricultural and Resource Economics
Redacted for privacy
Dean of Gradua
Date thesis is presented
June 15, 1982
Typed by Teresa M. Young for
Kim C. Nielsen
ACKNOWLEDGEMENTS
The completion of the thesis is a major goal f or a student in the
attainment of a graduate degree.
At times this one aspect of the
program requirement may seem to be a formidable task for a new student.
I would like to acknowledge and express my appreciation to all of the
following people who helped me reach that goal.
Dr. A. Gene Nelson not only provided encouragement and academic
guidance as major professor but served as a positive example of
professionalism and leadership.
Dr. Marshall J. English, Department
of Agricultural Engineering, provided information and service relative
to the engineering aspects
of the thesis topic.
This service helped
to stimulate interest in other academic disciplines and broaden the
scope of my education.
Thanks are due to Manning Becker, Dr. Harry Mack and Dr. Stan
Miller for serving on the graduate committee.
Ron Rickman, Columbia
Plateau Conservation Research Center, provided information concerning
wheat production in the Columbia river basin.
I would also like to thank the faculty and staff in the Department
of Agricultural and Resource Economics for the quality education,
encouragement and positive environment they provide at 0513.
This
environment is complemented by fellow graduate students who, in a bond
of fellowship, motivated through challenging competition and encouraged
discovery through intellectual discussion.
Special thanks are due to my wife, Nancy and my parents Charles
and Ruth Nielsen for their sacrifices, love and encouragement throughout the course of my academic education.
TABLE OF CONTENTS
Page
I.
II.
INTRODUCTION
Profit Maximization and Irrigation Technology
New Technology and Farm Planning
Objectives
Thesis Organization
1
REVIEW OF LITERATURE
Estimating Yield Response to Water
Optimization in Water Use
Summary and Conclusion
7
III. METHODOLOGY
Simulation Modelling
The Yield Component
Water and Temperature Stress
The Soil Moisture Component
Evapotranspiratiori Estimation
System to be Modelled
System Design
Operating Rules
Simulation Sequence
Evaluation of Estimated Results
Summary
IV.
V.
1
4
4
5
7
9
11
13
13
15
17
19
20
22
22
24
27
28
29
MODEL VALIDATION AND SIMULATION RESULTS
Data Source
Estimation of Soil Moisture Coefficients
Estimation of Yield Coefficients
Testing Model Performance
Results
Yields and Water Use
Total Investment Cost
Net Returns
Influence of Labor Costs
Influence of Energy Rates, Interest Rates
and Water Charges
Utility Under a Water Constraint
New Strategies
Effect of Soil Moisture Capacity
Summary
30
30
SUMMARY AND CONCLUSION
Summary
Limitations of the Model
Conclusion
62
62
63
31
34
38
41
Li.2
42
50
50
55
60
65
TABLE OF CONTENTS (continued)
Page
REFERENCES
66
APPENDIX I
70
APPENDIX II
73
LIST OF FIGURES
Figures
Page
1-i
Profit Maximizing Level of Input
3-1
Wheat Production System
14
3-
Yield Response to Soil Moisture
18
3-3
Value of KCE Over Time
21
3-4
Representation of Model Field with Four Laterals
23
4-1
Evapotranspiration Response to Soil Moisture
32
4-2
Plot Layout for Hermiston Field Trials
35
3
LIST OF TABLES
Taile
Page
3-1
Lateral Design Parameters
25
4-1
Deviations of Estimated Evapotranspiration
33
4-2
Comparison of Measured Yields and Yields
Estimated by Simulation Model
4-3
Average Yields, Irrigations and Water Use
39
4-4
Total Investment for Each Strategy
43
4-5
Prices Used in Analysis
45
4-6
Ranked Utility, Net Returns and Costs
46
for Each Strategy in Dollars Per Acre
4-7
Ranked Utility, Net Returns and Costs with
Labor at $10.00 Per Hour
4-8
Ranked Utility and Net Returns with Energy Cost
51
Increase of 50%
4-9
Ranked Utility and Net Returns with Water
53
Charges of $10.00 Per Acre Foot.
4-10
Yields and Water Use for Strategies 38-45
56
4-11
Total Investment Cost for Strategies 38-45
57
4-12
Ranked Utility an
58
Net Returns with Addition
of Strategies 38-41
4-13
Ranked Utility and Net Returns for Strategies
42-45
61
Risk/Return Analysis of Irrigation System
Design and Operating Rules
CHAPTER I
INTRODUCTION
Two major inputs for the production of crops are land and water.
In arid regions of the world where rainfall is scarce and irregular
the lack of rainfall may regulate all other inputs (Martin et al.,
1976, p. 30.).
In these areas irrigation is an alternative that
will allow otherwise unproductive land to be put into production.
There has been a dramatic increase in the number of acres under
irrigation over the past several years.
In 1900 there were about
one million acres being irrigated world wide and by 1976 the number
had risen to 561 million (FAO Yearbook 1977, Enochian, 1982).
There
are approximately forty million acres of irrigated farmland in the
U.S. (FAO Yearbook 1980).
total farmland.
This accounts for about 10 percent of the
Over 80 percent of U.S. land irrigated by pumped
water is located in the seventeen westernmost states (Slogget, 1974).
Kloster and Whittlesey (1971) cite a study (Butcher et al., 1967)
indicating that 90 percent of water withdrawals from lakes, streams
and underground water supplies in Washington State were for agricultural use.
The demand for water by agriculture, municipalities and
various kinds of public projects has led to increased concern over
the efficiency of water use.
Increasing the efficiency of water
use may have several environmental, social and economic benefits
(English and Orlob, 1979; Enochian, 1982).
This study will examine
the economic benefits to individual farm firms through improved
water use efficiency in winter wheat production.
Profit Maximization and Irrigation Technology
In the past irrigation systems have been designed to meet the
maximum water demand during the growing season (Jensen and King, 1962;
2
English and Nuss, 1982).
This practice assumes that the goal of an
irrigator is to maximize crop yield.
If farmers are profit maxi-
mizers, then yield maximization may not be compatible with profit
maximization.
Profit maximization will occur when the incremental
cost of a unit is equal to the value of the additional output from
the last unit of input.
In economic terms this is where the value
of the marginal product (VMP) is equal to the marginal input cost
(MIC).
The point q' on Figure 1-1 shows the profit maximizing input
level for a hypothetical production function.
yield maximizing level of input.
The point q'' is the
As the cost of the input (q) in-
creases, the maximizing level of q will decrease.
q decreases, q' will move towards q''.
As the cost of
In recent years the cost of
irrigation has increased relative to other input and output prices.
This would imply that farmers, if they are profit maximizers, should
use less water and produce a lower yield.
Profit is not the only consideration when applying water to
crops.
Farmers are also faced with uncertainty.
Much of the
uncertainty is related to weather and random variables over which
they have little control.
In the face of this uncertainty, a farmer
may apply more water than is economically efficient in order to
reduce the risk of low yields or crop failure.
The uncertainty of knowledge concerning the amount of water in
the soil profile is one area where great improvements have been made
over the years.
In the past irrigation management was an art.
A
shovel full of soil was removed and examined for moisture content.
If the soil felt less than adequately moist then a crop would be
irrigated.
One might schedule irrigation based on whether or not
the plants appeared to be under moisture stress.
At this point,
irrigation may not prevent considerable yield loss.
A great deal of effort has gone into the development of better
methods to measure and estimace soil moisture content (Jensen at al.,
1971).
The term "scientific irrigation scheduling" is now used and
information regarding it can be found regularly in agricultural trade
and scientific journals.
The advancements of computer technology have
Yield
water use
ci''
Figure 1-1:
q
Profit Maximizing Level of Input
4
also helped.
This allows the necessary soil moisture and weather data
to be rapidly processed and made available to people who can use the
inforinat ion.
These technological improvements have led to the de-
velopment of irrigation scheduling services that are available to
farmers from both extension and commercial services (Stegnian., 1980;
Jensen, 1978).
The result is that it is now possible to get more
accurate information that can help in the allocation of irrigation
water.
New Technology and Farm Planning
The improvements in irrigation technology have removed some of
the uncertainty in the pursuit of economic irrigation efficiency.
Other areas of uncertainty exist and must be examined before appli-
cation of the irrigation innovations to farm planning is practical
(English, 1981).
The relationship between soil moisture and yield
has not yet been quantified enough for application to farm level
decision making (Arkin, 1978).
In the past more emphasis has also
been put on production efficiency than economic efficiency.
Systems
designed for production efficiency may have a greater capacity and
higher total investment than necessary for economic efficiency.
Ayer (1978) indicated a need for added emphasis on the economics
of irrigation technology for the individual decision maker.
Obj act ives
This study examines the benefits of new irrigation technology
to farm level decision making.
The new technology makes it possible
for an irrigation manager to use irrigation strategies that were not
practical earlier.
A simulation model is developed to estimate the
returns and risks of using the different strategies in the production
of winter wheat.
The strategies consist of combinations of operating
rules and irrigation system designs.
The operating rules are the
irrigation set time and the soil moisture level that initiates irrigat ion.
S
By comparing different combinations of system designs and operating rules one will be able to determine the optimal combination of
irrigation inputs for wheat production.
The sprinkler system in-
vestment costs and operating costs will be analyzed.
The simulation
model will estimate the results of using a particular system design
with different operating rules.
The comparison of the results will
determine the optimal combination of labor and capital to use in
irrigation.
One operating rule is the level of soil moisture depletion that
initiates irrigation.
The analysis of the results of different levels
of soil moisture depletion will indicate if reductions in water use
and more scientific irrigation scheduling will achieve better economic
efficiency.
A major aspect of this analysis is the cost of energy in
pumping water.
The net returns are an important factor to the profit maximizing
individual.
Improving the efficiency of the allocation of inputs
should increase the net returns.
The risk associated with the
increase in net returns is also important.
The analysis will include
an examination of the risks associated with each irrigation strategy.
The risk is measured as the standard deviation of net returns.
The objective of the thesis is to analyze the net returns and
risk associated with alternative irrigation strategies.
The strate-
gies consist of combinations of operating rules and irrigation system
designs.
Thesis Organization
Chapter II reviews literature relevant to the thesis topic.
The
review will cover literature concerning crop production functions and
the application of production functions to decision making.
It also
explains the contribution of this study to the literature.
Chapter III explains the development of the simulation model.
It contains a discussion of simulation methodology.
It also explains
6
in detail the soil moisture component and the yield estimation cornponent of the model.
Chapter IV presents the validation and results of the simulation
model.
The presentation includes analysis of the yields, water use
and economic aspects of the different irrigation strategies.
It also
discusses how risk aversion relates to the strategies.
Chapter V summarizes the thesis.
The summary identifies the
major components of the model and their relationship to the driving
variables.
The results of the simulation model are restated.
chapter contains a discussion of the limitations of the model.
limitations identify areas for further research.
The
The
'4
CHAPTER II
REVIEW OF LITERATURE
Estimating Yield Response to Water
A production function indicates the quantity of some output as
a function of the quantity of one or more variable inputs.
Such
production functions are used quite often in estimating crop yields
as a function of the variable input water.
Heady and Hexam (1978) show
many variations of the traditional production function used in estmating
crop yields as a function of water.
Legget (195) estimated a
production function for wheat using measured precipitation as the
variable input.
Kioster and Whittlesey (1971) estimated Cobb-Douglas,
quadratic and square root production functions using applied irrigation water as the input.
Johnson and Davis (1980) used soil moisture
readings to determine the total water use and estimated a linear
production function.
Each of these functions are used to estimate
yield as a function of some measure of total water use for the season.
Yaron et al.
(1973) estimated a production function using the
number of days in the season when soil moisture was above a specified
level.
The function is
I = Ml - B1 exp(-k1W12)][1 - E2 exp(-k2T))
where Y is the final yield, A, B1, k1, B2 and
are all coefficients
to be estimated, W12 is the number of days soil moisture was above
45% of the maximum soil moisture and T is the number of days from
when enough moisture is available for germination to the day of
complete germination.
This function does account for the fact that
daily water consumption is important but does not incorporate the
timing of water availability.
The traditional production function is limited in its usefulness
for analyzing optimal irrigation quantities.
The timing of water
application is important and needs to be considered.
The decision
[1
to apply water is not a one time decision.
A farm manager must
decide several times during the season how much and when water will
be allocated to the various crops.
The response of the plant to
each of these applications will vary with the physiological maturity.
In recent years, much work has been done to estimate crop pro-
duction functions that incorporate the timing of water application.
Most of these functions use some form of the relationship proposed
by dewit (1958).
This relationship is that the ratio of actual
yield to maximum potential yield is equal to the ratio of actual
water use to maximum potential water use.
Hanks (1974) divided the
season for wheat production into five stages and used the relationship described above to estimate a production function.
The equation
is
Ya
Yp
,.5
fTa\ ai
- 'ilTp)
where Ya is the actual grain yield, Yp is the potential yield, Ta is
the actual transpiration, Tp is the maximum transpiration and oi is
a weighting factor for each stae of grovth.
Doorenbos and Kassam (1979) use the ratio of evapotranspiration
to potential evapotranspiration to estimate crop production functions.
The authors interpretation of the equation is shown below.
5
Yp)
KC1(l_ETaI
1=1
ETpj
where Ya and Yp are actual and potential yield respectively, KC1 is the
yield response for the growth stage i and ETai and ETp
potential evapotranspiration respectively.
actual and
Rickinan et al. (1975) used
the ratio of available soil moisture to soil moisture at field capacity
to estimate dry matter production of winter wheat.
of the production function is shown below.
1DM. = 1DM.
e
1
TDM=E
i=l
DM.
1
Ka KW
A simplified form
I?]
where DM1 is the dry matter yield in period i, e is the base of the
natural logarithm, Ka is the coefficient for soil moisture, KW
a weight-
ing factor for stage i and TDM is the total dry matter production for the
season.
Ka is estimated using the log equation given by Jensen et al.
(1970) and
Ka = ln(100ASM + l)/ ln(l0l)
SMFC
where ASM is available soil moisture, SMFC is soil moisture at field
capacity and in is the natural logarithm.
The production functions of
Hanks (1974) and Doorenbos and Kassam (1979) are also essentially
relationships between soil moisture and yield.
This is due to the
procedure they use to estimate transpiration and evapotranspiration.
Optimization in cater tJse
Several approaches have been used to find the optimal
allocation of water to crops.
With the traditional production
function this would simply be a matter of taking the derivative
to find the marginal physical product.
The basic principle of
optimization could then be used to allocate water (Henderson and
Quandt, 1980, pp. 74-98).
Minhas et al. (1974) estimated separate
production functions for two periods in the growing season and used
this approach to allocate water to wheat.
Mathematical programming models that arrive at optimum solutions
have also been used.
Flinn and Musgrave (1967) developed production
functions for eight periods during the growing season.
These
production functions were incorporated into a dynamic programming
model to show how such models could be used in the allocation of
water.
Kumar and Khepar (1980) used separable programming to find
the optimal cropping patterns under various water quantity constraints.
The most common technique is to use a simulation model that
estimates the results of various irrigation strategies.
The objective
of this type of model is to make comparisons among strategies and not
necessarily to arrive at the optimum strategy.
Rydzewski and Nairizi
(1972) used a simulation model to compare three different water
delivery systems.
Simulation was used by Ahmed et al. to compare
different irrigation strategies in the production of grain sorghum
in South Central Texas.
Morey and Gilley (1973) used a simulation
model to compare wheat yields in Minnesota under different irrigation
strategies and soil types.
The objective in both of these projects
was to maximize yield with respect to water use.
As stated pre-
viously the goal of a farmer may be economic optimization.
et al.
Yaron
(1973) used simulation to compare irrigation strategies based
on soil moisture with a strategy based on a predetermined time schedule.
The results indicated that irrigation based on soil moisture information
could lead to higher economic efficiency of water use.
Harris and Mapp (1980) compared two irrigation strategies in the
production of grain sorghum in Oklahoma.
The first strategy was to
apply 3.0 inches of water five times during the season.
The second
was to irrigate 0-9 times during the season at different levels.
The
analysis showed higher net returns under a flexible irrigation strategy.
The optimal schedule was determined ex post and could not be applied to
farm decision making.
Zaveleta et al. (1980) compared the optimal economic allocation
of water in grain sorghum production.
Situations of perfect weather
knowledge and conditional expectations of precipitation amounts were
compared.
A comparison was also made of the optimal policy with con-
ditional expectations of weather and three fuel curtailment scenarios.
The study indicated that introduction of stochastic elements could
result in increased water use and a reduction in net returns.
This
study also lacked analysis of decision strategies that could be useful in irrigation planning for farm managers.
Mapp and Eidman (1975) used simulation to compare two irrigation
strategies in the production of grain sorghum, wheat and corn in
Oklahoma.
The first strategy was to irrigate the crop with the highest
value of the marginal product first.
to grain sorghum.
The second strategy applied only
Grain sorghum was irrigated if the expected yield
11
reduction from not irrigating was greater than 10 bushels.
The rule
used soil moisture and days to maturity to estimate yield loss.
The
research indicated a higher net profit with a decision rule based on
expected yield loss.
This strategy did have greater risk as measured
by the standard deviation of net profit.
The advantage of a simulation model is that it allows the complex
soil moisture, climate and other plant growth relationships to be more
easily incorporated into the model.
Attempts are also underway to
develop simulation models that will be available to farmers, extension
personnel and irrigation district managers etc. to evaluate contemplated
system changes and operating strategies (Anderson and Maass, 1974;
Ritchie et al., 1978).
Most of the simulation models discussed have examined the relationship of water quantity to yield and net returns.
One aspect that has
been given less attention is irrigation system design.
As mentioned
previously, the timing of water application is an important aspect of
a production function dealing with crop yield.
The design of the
system will determine how often water can be applied to the field.
In
addition the amount of labor required to apply a specific amount of
water will also vary with the design.
Summary and Conclusion
The traditional production function does not adequately estimate
crop yield as a function of water.
The non-tradional functions
(Hanks, 1974; Doorenbos and Kassam, 1979; and Rickmanetal., 1975)
which estimate yield as a function of relative water use over different
growth stages are more appropriate.
The non-traditional function is
better for estimating yields but is more difficult to use in the optimization of water use.
This difficulty would dictate the use of mathematical
programming or simulation modelling.
Simulation modelling is used in
most cases to analyze efficiency of water use.
The decision to apply less water will result in both operating
and capital cost reductions (English and Nuss, 1982).
If the system
capacity is reduced to take full advantage of reduced water use, it
12
will be more constrained during years of higher than normal water
demand.
The average yields and net returns over several seasons will
fluctuate more than with a higher capacity system.
This study will compare how irrigation system designs and operating
rules affect wheat yields, net returns and risk.
The model will include
a winter wheat yield estimation component, a soil moisture component,
a risk/returns analysis component and weather data.
The simulation
model will be designed to demonstrate how weather variability and system
design combine to affect the result of operating rules.
13
CHAPTER III
METHODOLOGY
Simulation Modelling
The term "simulation model" may include mathematical programming
techniques (Dent and Blackie, 1979, p. 10).
It is important when
discussing simulation modelling to explain what definition is being
used.
Markiand (1979, p. 53) defines simulation as "... an experimental
technique that usually results in a series of answers, anyone of which
may be acceptable to the manager."
This concept seems to be most
common (see Dent and Blackie, 1979; Charlton and Thompson, 1970 and Held
and Helmers, 1981) and is the definition used here.
The wheat produc-
tion simulation model estimates yields and net returns given a particular
decision strategy.
The model does not contain an algorithm to determine
the optimal strategy.
The model to simulate winter wheat production will consist of a
grain yield component, a soil moisture component, an irrigation component and a risk/returns analysis component.
Elements entering the model
to interact with these components are called "driving variablest' (Dent
and Blackie, 1979, p. 6).
Controllable and uncontrollable driving
variables are entered into the simulation model.
Precipitation,
evaporation and temperature are the uncontrollable variables.
Precipita-
tion and evaporation enter the model and interact with the soil moisture
component.
Temperature affects plant growth and interacts with the
yield component.
The controllable variables are irrigation operating
rules and system design.
These two variables will interact with the
irrigation component to determine the rate of daily water application.
The soil moisture component will determine a soil moisture level which
is an input to the yield component.
The yield and water application
affect the total returns and costs.
Figure 3-1 shows the relationship
between the components.
The remainder of the chapter is devoted to
explaining the development of the components and their relationship to
the driving variables.
Precipitation
Evaporation
Decision Rule I
(System Design
4J
Returns
Figure 3-1:
J,
P
Return
Wheat Production System
Costs
H
15
The Yield Component
According to Martin, et al. (1976, P. 90) the cumulative growth
of most plants over time will have a shape similar to that of a sigmoid
curve.
This curve depicts two phases of plant growth.
During the
first phase the rate of plant growth is increasing over time.
At the
inflection point this phase ends and the rate of growth declines over
the second period.
Jose (1974) used a combination of two functional forms to describe
this type of curve.
During the period from the end of winter dormancy
to the inflection point an exponential form is used.
This type of a
form, for explaining plant growth, was introduced by Hackenberg in 1909
(Evans, 1972, p. 190).
It is called the "monetary analog" because the
form is the same as that used in continuous interest compounding.
The
equation is
Yl = Aert
(3-1)
where A is the initial amount or the intercept in a production function,
e is the base of the natural logarithm, r is the continuous rate of
growth, t is the length of the time period and Yl is the cumulative
growth through time t.
Equation 3-1 gives a measure of Yl at the end of period t.
the simulation model a daily response to yield is needed.
For
The daily
function is
= Aert -
(3-2)
where AYl
equal to
Yl
is the grain yield response in day t.
et_)er
and Yl
is equal to Aert.
These equalities can
be used in equation 3-2 and the daily response is
rt
r(t-l)
AYl=Ae -Ae
= Aet l)r
= Yl_
(3-3)
(er_i)
1Ylt = Yli.k
-
The value ert is
AetU
16
where LYl
is the daily yield response,
is the total yield to
day (t-l) and k is a constant equal to (er_i).
For the period from the end of t (t') to plant maturity the function
used is commonly known as a Spiliman function (Heady and Hexam, 1978,
p. 38).
The Spillman function is derived from the sum of a decreasing
geometric series (Spillman, 1923) which is shown in equation 3-4.
(3-4)
= j-- (l-c')
S
where S
is the sum of the series over n, a is the first element of
the series, c is the common ratio of each element to the preceeding
element and n is the number of elements in the series.
As n goes to infinity S
value of S.
will be equal to
and is the maximum
In using the equation as a production function,
the maximum yield from t
stituted for a and S
to maturity.
is
The variable t'' is sub-
is the final yield for the second period.
Equation 3-5 is the form of the geometric series as the production
function.
(3-5)
Y2 = M(1-c
ti'
where Y2 is the total addition to yield from t' to t, and t'' is
(t-t'), and N is the maximum possible yield () and c is the rate
of diminishing marginal production.
A function for daily yield response is needed for the second
period.
to
In the geometric series the additional value a
ac'.
This value an corresponds to the daily increment of
yield for day t'' in the function.
For the purpose of clarity in
the presentation nip is used in place of a
daily growth is
(3-6)
is equal
Y2t
= mpc1
and the function for
17
Water and Temperature Stress
Equations 3-3 and 3-6 simulate the maximum potential growth on
a daily basis.
than optimal.
No allowance is made for conditions that are less
When temperature and/or soil water is less than
optimal, the actual daily growth will be less than the maximum
potential growth.
The function used to explain the relationship
between soil moisture and yield is that used by Rickman et al. (1975)
represented in Figure
3-3 and equation 3-7.
KA = ln(l00.ASM/SNFC + 1)/ln(iOl)
(3-7)
where KA is the normalized response of growth to soil moisture, and
ASM Is the available soil moisture, SMFC is the available soil
moisture at field capacity and in is the natural logarithm.
The relationship between grain yield and temperature is more
difficult to quantify.
Rickman et al.
(1975) estimated a normalized
response function of dry matter accumulation to temperature.
This
relationship is not applicable when trying to estimate grain yield
(Pickman, 1982).
The author attempted to adjust the function in
order to apply it to grain yield but had little success.
blem was the lack of yield data for more than one season.
The proThe
effect of temperature is represented in the model as hot or cold
extremes.
The relationship is
(3-8)
TX = 0 for 37°F > TA > 104°F
(3-9)
TX = 1 for 37°F < TA < 104°F
where TX is the normalized response of yield to temperature and TA
is the average daily temperature.
The effects of temperature and moisture are now incorporated
into the daily yield response functions.
The approach taken by
Jose (1974) and Pickman et al. (1975) is to use the products of the
temperature and moisture function in the production function.
In the
model presented here the daily yield function is multiplied by the
18
KA 1.
1.0
ASM
SMFC
Figure 3-2:
Yield Response to Soil Moisture
19
minimum of TX and KA.
The practice of using the minimum input is
not uncommon in estimating production functions of two or more
essential inputs (Waggoner and Norvell, 1979).
This is based on
the assumption that growth is limited to the smallest amount of any
necessary input.
Equation 3-3 and 3-6 become -respectively.
(3-10)
,Y1t = Y1ti,.k.mi.n(KATX)
= mp.ctl.min(KA,TX)
(3-11)
for
for t >t'
where k, c, and mp are coefficients to be estimated.
is also an estimated
The value t'
lue.
The Soil Moisture Component
A model is also needed to calculate available soil moisture
(ASM) and evapotranspiration (ETA).
simply a bookkeeping technique.
The calculation of ASM is
Soil moisture inflows are added
to ASM and the outflows are subtracted.
(3-12)
ASM
= ASMt
i
+ bIRRt
1
+ PRCPt
i
ETAt
i
where ASM is available soil moisture, b is irrigation efficiency,
IRR is irrigation water applied, PRCP is rainfall, ETA is actual
evaportranspiration arid PNF is water runoff from the soil surface.
If after three days since the last wetting ASM is greater than
soil moisture at field capacity (SMFC), the difference is assumed to
be lost to percolation.
rainfall.
Initial soil moisture is a function of winter
The relationship is
(3-13)
SE = 74.52-.l47WM
(3-14)
ASM0 = (SE/lOO).WMI
where SE is storage efficiency, WM is winter rainfall in centimeters,
ASM0 is initial soil moisture and WMI is the winter precipitation it
inches (Glenn, 1981).
Irrigation efficiency (b) was assumed to be a
relationship between soil moisture and gross irrigation application.
20
The relationship estimated by the author is
b = l.07284-.30377.IRR/Depl
(3-15)
where b is the irrigation efficiency, Depi is the soil moisture depletion
(SMFC-ASM) and IRR is the gross water application.
The irrigation
efficiency multiplied by IRR gives the amount of moisture added to the
soil profile.
The value b is constrained to vary between .10 and .92.
The model allows the user to determine irrigation.
Precipitation is
acquired from historical data and runoff is considered negligible.
SMFC
is a predetermined parameter depending on soil type and rooting depth.
Evapotranspiration Estimation
The calculation of ETA is more complicated.
A common practice
is to calculate reference evapotranspiration using climatological
data (Jensen, et al., 1971).
Hanks (1974) calculates ETA by using
measured pan evaporation data.
Bates, et al. (1982) examined the
relationship between pan evaporation and ETA in the Columbia River
Basin.
The purpose was to develop "a coefficient of evapotranspiration
which is easily applied for the improvement of irrigation practices and
water conservation."
In this model ETA will be calculated using the
approach of Bates, etal. (1982) and adjusting it for soil moisture
deficits.
(3-16)
The process is outlined below
ETA
EVAPKC
where EVA? is pan evaporation, and KC is a coefficient for soil
moisture level, plant stage of growth and wetness of soil surface.
(3-17)
KC = KCEKN + KS
where KCE is pan evaporation coefficient, KS is an adjustment for ETA
after wetting and KN is adjustment for the level of available soil
moisture.
The value KCE was approximated by Bates et al. (1982) and is shown
in equation 3-18 and Figure 3-3
(3-18)
KCE = (-1.968 x i0)t3 + (2.029 x 102)t2 + 56.062
21
1.
60
Figure 3-3:
Value of KE Over Time
120
days
22
where t is the number of days since winter dormancy.
The value for
KS was approximated by Jensen et al. (1971) is
(3-19)
KS = (.9-KCE)8 for D
1
(3-20)
KS = (.9-KCE)5 for D
2
(3-21)
KS = (.9-KCE).3 for D
3
where D is the number of days since the last wetting by irrigation or
precipitation.
System to be Modelled
The production unit to be modelled is a 160 acre winter wheat
farm near Hermiston, Oregon.
The model farm will be irrigated by a
side-roll sprinkle irrigation system.
The spacing of the risers and
nozzles is 60 ft. and 40 ft. respectively.
2640 ft. by 2640 ft.
The field dimensions are
The mainline runs through the middle of the
field so each lateral is 1320 ft. long.
The riser spacing is 60 ft.
This gives a total of 88 sets with 44 on each side of the mainline.
A 250 ft. well is located next to the field.
Figure 3-4 represents
the field to be modelled.
As stated the field is divided into 88 sets.
It is assumed that
each side of the mainline will be irrigated identically and that the
yield response will also be the same.
one side of the field or 44 sets.
The model will only simulate
The simulation model will estimate
daily soil moisture and yield f or each set.
it is assumed that the
farmer will irrigate the first set and proceed to the end of the field
before returning to irrigate a second time.
The irrigation component
of the model schedules the irrigation for each set.
If enough precipita-
tion occurs to raise the soil moisture level to field capacity then
irrigation is stopped.
the Hermiston area.
first set.
It is quite unlikely that this would occur in
When irrigation begins again it will start on the
23
2640'
Lateral
Lateral
0
'V
N
-4
'-4
Lateral
z
Lateral
0 Well
Figure 3-4
Representation of Model Field withFOur Laterals
24
System Design
The simulation model compares the net returns of using different
systems and operating rules.
The author designed the different systems
using a computer model developed by Marshall English, Assistant Professor
of Agricultural Engineering, Oregon State University.
of system design is the number of laterals.
with 10, 8, 4 and 2 laterals.
of water flow.
The model compares systems
The next design consideration is the rate
The system will either deliver water at a full irriga-
tion level or at a lower level.
examined.
The first aspect
Two different levels of pumping are
These levels will be explained in conjunction with the operat-
ing rules.
Operating Rules
Two different types of operating rules are analyzed.
The first is
the set time and the second is the level of soil moisture when irrigation is started.
With 8 and 10 laterals, set times of 23 hours and 11
hours were considered.
level of 6 inches.
inches.
With
The analysis assumes a maximum soil moisture
The soil moisture levels used are 5.0 inches and 3.0
2 and 4 laterals, set times are 11 hours and 7 hours and
moisture levels of 5.0 inches, 3.0 inches, and 2.0 inches were used as
alternatives for initiating irrigation.
The set time, rate of water flow, soil moisture depletion and the
uniformity of water distribution combine to give a measure of irrigation
adequacy.
An irrigation adequacy of approximately 87 percent is consid-
ered full irrigation by the Soil Conservation Service.
This means that
87 percent of the area irrigated receives at least enough water to fill
the soil profile.
The remaining 13 percent of the area will receive less
water than soil moisture depletion.
rates are considered.
As mentioned previously, two pumping
The two rates are those that would achieve approxi-
mately 87 and 50 percent adequacy given the maximum daily ETA and the
sprinkler system capacity.
It is also assumed that the uniformity of
the water distribution is normal.
Table 3-1 shows the lateral designs,
set time and adequacy levels that are used in the simulation model.
25
Table 3-1
Lateral Design Parameter
Irrigation1
Strategy
Laterals
Adequacy
Set Hourly App.2 Cycle3
Time
Time
Rate
System4
Capacity
10
87
23
.17
9
.43
10
87
23
.17
9
.43
10
87
11
.18
5
.44
10
87
11
.18
5
.44
5
10
50
23
.11
9
.29
5
10
50
23
.11
9
.29
7
10
50
11
.11
5
.28
10
50
ii
.11
5
.28
8
87
23
.20
11
.42
LO
8
87
23
.20
11
.42
LI
8
87
11
.22
6
.44
L2
8
87
11
.22
6
.44
L3
8
50
23
.14
11
.29
L4
8
50
23
.14
11
.29
15
8
50
11
.14
6
.28
16
8
50
11
.14
6
.28
17
4
87
11
.42
11
.42
18
4
87
11
.42
11
.42
19
4
87
11
.42
11
.42
20
4
87
7
.44
8
.42
21
4
87
7
.44
8
.42
22
4
87
7
.44
8
.42
23
4
50
11
.28
II
.28
24
4
50
11
.28
11
.28
25
4
50
11
.28
11
.28
26
4
50
7
.30
8
.28
27
4
50
7
.30
8
.28
28
4
50
7
.30
8
.28
29
2
87
11
.74
22
.37
30
2
87
11
.74
22
.37
L
3
26
Table 3-1
(Continued)
Irrigation1
Strategy
1
Laterals
Adeguacy
Set Hourly App.2
Time
Rate
Cycle3
Time
System4
Capacity
31
2
87
11
.74
22
.37
32
2
50
11
.44
22
.22
33
2
50
11
.44
22
.22
34
2
50
11
.44
22
.22
35
2
50
7
.55
15
.26
36
2
50
7
.55
15
.26
37
2
50
7
.55
15
.26
SCS measurement of irrigation, 87 percent is considered full
irrigation.
2 - Evaporation loss at 8 percent.
3 - Cycle time is the number of days to irrigate the entire field.
The values are rounded up to the whole number.
4 - System capacity is the net application per irrigation divided
by the cycle time.
27
Other information in Table 3-1 is the application rate and system
capacity.
The application rate is the rate of water application in
inches per hour.
This is important because if the rate is too high
the soil will not absorb the water and run-off will occur.
Table 3-1
shows that a system with two laterals and 11 hour sets must have an
This
application rate of .74 in/hr. to achieve 87 percent adequacy.
is a relatively high rate of application but is not unreasonable.
There are soils in the Hermiston area with intake rates of .80 in/hr.
System capacity is a measure of daily application.
If a person
were to move the laterals often enough to irrigate the entire field in
one day then system capacity is the maximum amount of water the system
can apply to each acre.
System capacity is equal to the net application
per irrigation divided by the number of days to irrigate the entire
field.
Net application is equal to the set time multiplied by the
application rate.
For example, strategy 1 (Table 3-1) has a set time
of 23 hours, a net application rate of .17 inches per hour and a cycle
time of 9 days.
The system capacity is
(23 x .17)19
where .43 is the system capacity.
.43
Comparable calculations made using
the data shown in Table 3-1 will not always result in a measure of
system capacity equal to that in Table 3-1.
This is due to rounding
errors.
Simulation Seguence
Daily weather data were acquired from the Hermiston Agricultural
Experiment Station.
The most consistent data were available from 1963.
Weather data for 1963-1981 were used for the model.
it is assumed
that this period represents the normal distribution of weather in the
area.
Winter rainfall is for the period November 1 to March 31.
season from the end of winter dormancy is April 1 to July 20.
The
It is
assumed that the crop will be established in the fall.
The model calculates the soil moisture for each set beginning on
April 1.
If the soil moisture, of the first set, is below the
28
designated moisture level for irrigation then the irrigation cycle
will begin.
The beginning of irrigation is based on the first set only.
The irrigation component schedules the irrigation for all the sets beginning with the first set.
laterals and the set time.
The scheduling 15 based on the number of
Soil moisture may return to the level to
begin irrigation on the first set before the last set has been irrigated.
In this situation the irrigation for the earlier irrigated sets will be
postponed i.e., no set will receive a second irrigation before all sets
have received the first irrigation.
The process is repeated for each
day in the season and for each year in the simulation process.
The
yield response to temperature and soil moisture is also estimated daily
for each set.
Evaluation of Estimated Results
The simulation model does not arrive at an optimum solution.
results of each strategy must be considered outside of the model.
The
The
method of evaluating the results of the winter wheat production model
is outlined below.
Net returns are calculated for each year.
The net returns exclude
charges for cultural practices (other than irrigation), taxes, depreciation, etc.
The returns to irrigation are the only ones considered.
The average return and standard deviation of net return are calculated.
This is the average and standard deviation of each strategy over the
simulation period (19 years).
The utility of each strategy is measured
and
(3-22)
U = NR-RSD
where U is utility, NR is the average net return for a particular
strategy. SD is the standard deviation of NR and R is a coefficient
to weight SD according to the risk aversion of a manager.
R will vary
from zero to two for the risk neutral manager and most risk averse
manager respectively (Brink and McCarl, 1978).
29
Summary
A discussion of simulation modelling was presented.
Simulation
is considered a technique of estimating results of various strategies.
Optimization in simulation is less defined than in mathematical programming.
The optimum may be a sub-jective evaluation of the manager.
A simulation model for the analysis of winter wheat production in
Hermiston, Oregon was presented.
The model consists of yield, soil
moisture, irrigation scheduling and risk/returns analysis components.
The driving variables are weather and system design and operating
rules.
Weather and strategies (design and operating rules) are un-
controllable and controllable variables respectively.
The production
unit to be modelled was described with a discussion of the different
strategies to be used on the farm.
is also presented.
The sequence of simulation events
The strategies are evaluated on the basis of utility.
Utility is the average net return minus the standard deviation
weighted by a risk aversion factor.
30
CHAPTER IV
MODEL VALIDATION AND SIMULATION RESULTS
A simulation model must be validated to verify that the sequence
of simulated events is correct and that the model predictions are
consistent with actual wheat production relationships.
The model des-
cribed in Chapter III was coded in FORTRAN for the use on the CYBER 170
computer located at Oregon State University.
the validation process.
This chapter describes
The results of the estimation of model co-
efficients are presented along with a brief discussion of the process
for testing the model logic.
The wheat production system was simulated
for the different strategies and the results are given.
Data Source
During the 1981 crop season, the Department of Agricultural
Engineering at Oregon State University conducted experiments near
Hermiston, Oregon to determine the effects of deficit irrigation on
evapotranspiration and wheat yield.
The data acquired from the field
trials were used to estimate the coefficients for the plant growth
and soil moisture models.
Four treatments from the field trials were
used to estimate the necessary model coefficients.
All of the treat-
ments were irrigated to field capacity by April 1, 1981, and were
irrigated at 100 percent of soil moisture depletion at different intervals thereafter.
W13 and Wl4 were irrigated in 1 week intervals.
and T15 were irrigated at 2 week intervals.
T13
T2A3 and T2A5 were irrigated
at 3 week intervals and T3A3 and T3A4 at 4 week intervals.
The reader
is referred to Nuss (1981) for a detailed discussion of the experimental
design.
The coefficients were estimated using an iterative technique.
Rasmussen and Hanks (1978) used a similar procedure to estimate a
model and found that the results were comparable to those achieved
through regression.
The values for the coefficients were chosen randomly
31
and entered into the model.
to the measured data.
The predicted results were then compared
The sum of the deviations (SD) and the average
of the sum of the squared deviations (MSD) were computed for the
various combinations of random values.
Incremental changes were made
in the random value and MSD and SD were re-calculated.
The process was
repeated until only small changes occurred in SD and MSD.
The objective
was to find a set of values that minimize SD and MSD.
Estimation of Soil Moisture Coefficients
For the moisture component of the model the value to be estimated
is KN.
Daily ETA values were used for the estimation procedure.
The
best fit was achieved when a function is used similar to that shown in
Figure 4-1.
This function shows that the value of KN increases in a
manner described by a cubic function, then KN is constant until a particular level of ASM/SMFC is reached.
The function coefficients were
estimated and the results are shown below.
KN
(4-1)
1 for
> .45
SMFC
2
KN = b1 ASM
- b2 ASM
SMFC
SMFC
(4-2)
for ASM
< 45
SMFC
where b1 and b2 are equal to 14.13 and 20.60 respectively.
A comparison is made of actual and estimated evapotranspiration in
Table 4-1.
Three models are compared.
The first two models, entitled
Nuss Log and Nielsen Log respectively, are comparisons of works by
Nuss (1981) and the author.
The method used to estimate ETA is in both
cases a log model used by Jensen et al. (1971).
In equation 3-16 the
author uses pan evaporation (EVAP) to calculate ETA.
In an equivalent
calculation Nuss (1981) uses, in place of EVAP, climatological data
and estimates reference evapotranspiration using the Penman equation.
The value for KN is
(4-3)
KN = ln(100
ASM/SMFC + 1)/ln(101)
where all the variables are the same as defined previously.
The third
model, entitled Nielsen Cubic, is the function described in equations
4-1 and 4-2.
The numbers in the table are the values of the total
32
IKN
1.0
.5
.5
1.0
ASM
SMFC
Figure 4-1:
Evapotranspiration Response to
Soil Moisture
33
Table 4-1:
Deviations of Estimated Evapotranspiration
Deviations from cumulative
Measured ETA (Hundredths of inches)
Nuss
Nielsen
Nielsen
Log
Log
Cubic
Plot
Code
Total
Measured
ETA (inches)
W13
15.90
37.40
97.56
39.06
W14
16.47
-65.76
18.58
-40.21
T13
16.79
-76.38
25.55
-25.00
T15
17.96
-232.28
-44.50
-78.54
T2A3
14.44
114.57
75.93
10.22
T2A5
15.00
50.00
8.49
-56.89
T3A3
13.09
257.48
236.67
175.23
T3A4
13.75
304.72
193.72
131.28
389.75
613.00
155.15
30,035.94
14,043.52
7,652.12
dev
(dev)2
8
34
predicted ETA minus total measured ETA in hundredths of inches. The
table also shows the sum of the deviations and the mean of the sum of
squared deviations.
Estimation of Yield Coefficients
The comparisons between predicted and measured yield were
slightly more difficult to make.
tables 4l and 4-2
access tube.
The plot codes Wl3, W14, etc. shown in
are a description of a particular neutron probe
The measured yields were taken between the access tubes.
The predicted yields were estimated using the information from the
access tubes.
Measured yields used for comparisons to validate the
model are therefore the average of the plot yield on each side of the
acöess tube (see Figure 4-2).
Values were estimated for k, mp, c, t, and Yo (A in equation
3-i) using the iterative technique described above.
functions are shown below
(4-4)
= Yt1.k.min(KA,TX) for t < t'
Y2t =
(4-5)
The daily yield
.
.
. .1
mp.ctt.min(,TX) fort> t'....O
where k, mp, c, t', arid Yo are equal to .0672, 978.64, .79, 54 and
100 respectively.
Table 4-2 shows the results from the estimated model.
are in pounds per acre.
The yields
The sum of the deviations and the mean of the
sum of squared deviations are given.
The results were compared with
those by Rasmussen and Hanks (1978) and the accuracy compares favorably
based on the mean of the sum of the squared deviations.
Testing Model Performance
After the component coefficients had been estimated the performance
of the simulation model was tested.
The objective is to verify that the
relationships between components have been described consistent with the
production system.
It is also to check for logic errors that may
.J.w.
1
fl
and
S
2
3
measured yield
S
=
sprinkler lateral
=
access tube
Yield used to estimate model for access
tube 2 is equal to:
+
2
Figure 4-2:
Plot layout for Hermiston Field Trials
36
Table 4-2:
Plot
Code
Comparison of Measured Yields and Yields Estimated by
Simulation Model
Estimated
Yield
Measured1
Yield
Dev.
(pounds per acre)
Wl3
6226
W14
6380
6317
63
T13
6052
6754
-702
T15
6377
6460
83
T2A3
5711
5506
205
T2A5
5677
5890
-213
T3A3
4807
4526
281
T3A4
4807
4675
132
5896
330
2dev
(dev)2
13.76
99,468
8
1
Data sheets from Department of Agricultural Engineering, Oregon State
University, field trials, John Madsen property, Hermiston, Oregon, 1981.
37
have occurred in the programming process.
Testing the model logic is
quite subjective and the method used by the author is outlined below.
The process was to change specific parameters and constrain variables
to normal and extreme values.
The system was simulated for a small sample
of data and the results examined.
During the process several intermediate
results that flow between components were also examined to verify that
they were correct and/or realistic.
For example, the daily soil moisture
values, daily precipitation and daily irrigation values were printed to
verify the soil moisture component.
Irrigation and daily precipitation
were constrained to extreme values to check the soil moisture component
under different situations.
The irrigation component was validated along
with the soil moisture component.
The testing of the model indicated that it functions properly.
modifications were minor.
Most
The reader should be aware of two changes that
were made as a result of the testing.
The first modification was that if
available soil moisture is totally depleted before June 1, then crop
failure is assumed.
after June 30.
The second was that irrigation will not take place
This is the approximate time period that irrigation is
stopped in the Hermiston area.
In conclusion, the author feels that the model described can be used
to adequately estimate yields.
son made with other models.
does have limitations.
This conclusion is based on the compari-
Recognition is given to the fact that it
Soil moisture and crop yield data from other years
and locations would be helpful and could be used to improve the model.
This is particularly true for determining the role that temperature plays
in yield prediction.
Results
The production of winter wheat was simulated for 19 years of weather
data.
The effect of different irrigation strategies was evaluated.
Each
strategy is a combination of a particular set of operating rules and system
design.
The yields, water use, net returns, and variability of net returns
were examined.
The strategies are compared on the basis of utility.
Utility is the average net returns minus the weighted standard deviation
38
of net returns.
The standard deviation is weighted according to the
degree of risk aversion.
The remainder of the chapter is devoted to a
discussion of the simulation results.
Yields and Water Use
Table 4-3 shows the wheat yield and water use for each strategy
(see Table 3-1 for specification of strategies).
rable 4-3 also shows
the average number of irrigations and the ratio of actual evapotranspiration (ETA) to potential evapotranspiration (ETP).
Potential evapotrans-
piration is the value of ETA when the plant is not subject to water stress.
It is the maximum value of water use by the plant.
The calculation of
ETP is
ETP = EVAP.KCEKN
where EVAP, KCE and KN are defined the same as in equation 3-17, but the
value of KN is a constant equal to 1.0.
The ratio is greater than 1.0
for some strategies due to the value KS (equation 3-17).
increased soil moisture after irrigation or precipitation.
of potential evapotranspiration excludes KS.
KS accounts for
The estimation
Strategies that have fre-
quent irrigations at low moisture depletion levels will have a cumulative
ET that is greater then cumulative ETP.
The highest yield was obtained with strategy 3.
124.69 bushels per acre.
The yield is
The highest five yields are 124.69, 123.72,
122.46, 122.31 and 121.67 for strategies 3, 11, 7, 15 and 20
respectively.
All of these strategies begin irrigation at a soil
moisture level of 5 inches.
The highest yields are also with
strategies that irrigate with high frequencies and set times less
than 23 hours.
11 hours.
Strategies 3, 11, 17 and 15 each have a set time of
Strategy 20 has a set time of 7 hours.
The number of
irrigations for 3, 11, 17, and 15 and 20 were 16, 14, 17, 14 and
12 respectively.
Strategy 5 has the highest yield for any strategy
with a set time of 23 hours.
The yield for 5 is 120.08 bushels per
acre and it is ranked seventh on the basis of yield.
Table 4-3:
Average Yields, Irrigations and Water Use
;iJ
Average3cs
Yield
SD2
Yield
Max
Yield
Mm
Yield
No3
IRR
119.68
107.38
124.69
104.47
120.08
1.67
2.46
1.58
2.09
2.68
121.94
111.37
126.75
110.63
124.00
115.3?
103.24
120.36
100.86
114.33
10.
102.34
122.46
98.74
116 9'
108.45
2.30
2.40
99.09
116.98
93.96
88
105.01
8
2.07
107.59
125.84
106.34
119 91
112.21
15
122.31
1.56
2.38
2.83
2.69
2.47
125.76
111.67
122.16
103.34
125.68
119.55
101.70
112.03
98.05
116.83
14.
14
123.72
105.41
11?.84
102.66
10.
1
2
3
4
5
6
7
8
9
10
11
12
13
2.81
7'
1
i1
1.01
1.04
9.
32.81
18.14
10.
26.88
.99
6.
17.74
22.41
16.25
40 54
25.78
.91
16.
17.
12.
5.
7.
8.
5.
14.
99,91
116.92
108.45
95.82
121.67
2.63
1.72
2.07
4.43
1.65
106.78
17
108.88
123.98
96.03
112.88
105.01
89.18
117.42
106.37
94.48
117.63
102.09
90.97
1.82
3.52
3.00
2.74
4.29
110.07
105.61
122.08
107.73
104.49
103.88
90.15
111.42
97.62
85.96
6.
121.37
101.30
89.34
102.17
101.05
2.63
2.40
4.00
3.35
124,88
107.7?
101.31
109.62
107.47
115.56
96.80
83.96
97.85
96.86
11.
18
19
20
21
22
23
24
25
25
27
28
29
30
2.91
ET
Ratio
40.82
22.76
5.
16
119.91
112.21
Irr4
Water
8.
5.
3.
12.
5.
8.
5.
4.
8.
6.
4.
.
.96
.95
1.02
.91
9?
.97
37.61
19.29
1.03
.96
27.54
18.70
23.44
.97
.91
1.01
16.17
40.54
25.78
17.19
39.10
1.02
20.61
15.21
.96
.82
26.29
18.16
13.55
.96
25.52
17.12
13.38
35.61
30.54
.99
.92
.91
.99
.97
.31
.90
.78
.78
.86
.85
40
Table 4-3 : (Continued)
SD2
Yield
Max
Yield
Yield
90.19
104.75
97.55
86.16
113.36
4.63
4.45
3.76
5.23
101 .83
81 .97
2.
95.96
91.27
77.79
106.61
4.
3.31
112.94
106.67
100.5?
118.34
101.73
89.59
2.99
5.32
109.08
104.19
97.07
79.03
Average1
Yield
31
32
33
34
35
36
7
Mm
No.3
IRR
3.
2.
6.
4.
3.
1- Yield in bushels per acre
2- Standard deviation of yield
3- T1'ie average number of irrigations
4- Average gross water application in acre inches
Irr
Water
ET
Ratio
20.81
21.37
17.17
12.69
25.46
.75
.85
.80
.69
.93
18.53
13.13
.87
.73
41
The relationship between yield and water use would be expected
to be positive. The simulated results do generally have a positive
relationship between water use and yield.
The results indicate that
it is possible to reduce water application and not appreciably affect
yield.
Strategy 3. and strategy 7 received 32.81 inches and 22.41
inches of water respectively.
The yields for 3 and 7 are 124.69
bushels and 122.46 bushels respectively.
Strategies 3 and 7 are the
same in all respects with the exception of adequacy.
Strategy 3 had
an adequacy of 87 percent and 7 had an-adequacy of 50-percent.
Total Investment Cost
The total investment cost of each strategy could not be determined
before the simulation had taken place.
The lateral costs and pump
costs were available but not the mainline cost.
lire depends on the diameter of the pipe used.
The cost of the main-
The optimum diameter
of mainline pipe is a function of interest rates, the cost of energy,
total water flow and the number of hours that the system is used
durinq the season.
The more hours a system is in use, ceteris paribus,
the larger the diameter of mainline that is used.
A larger diameter
will result in higher investment costs and lower energy costs.
If a
system is used for relatively few hours during the season then a
smaller diameter of mainline is used.
energy costs.
ment cost.
This will result in higher
The cost of energy will be offset by the lower invest-
The higher energy cost is due to the increased friction
in smallerpipes.
The choice was made by consulting tables prepared
by the Department of Agricultural Engineering, Oregon State University.
The tables showed minimum cost pipe diameter for a given interest rate,
total water flow and total hours of operation.
The capital costs were
annualized by amortizing the total investment cost minus the discounted
salvage value.
The salvage value was calculated as 10 percent of the
investment in the pump and laterals.
years.
The amortization period was 15
42
The average hours of operation were calculated by the simulation
model.
The mainline diameter was chosen and total investment calculated.
Table 4-4 shows the total investment for each strategy.
The table
also indicates the combination of operat ing rules and system design
Table 4-5 shows the prices used for the
used for each strategy.
analysis.
Net Returns
Table 4-6 shows the net returns and utility for each strategy
ranked in descending order. The maximum net return and utility is
with strategy 26.
Thnet return and utility are $362.60 and $337.12
respectively.
The risk aversioncoefficient in Table 4-6 is 2.0
The
results indicate that risk does not seem to increase with the higher
average net returns.
The optimal strategies are basically the same with
a risk aversion coefficient of 0 or 2.0.
be with a lower capital investment.
The highest utility tends to
The results show that irrigating
when soil moisture reaches 5 inches is the best strategy.
Strategy 14
is the highest ranked strategy to irrigate when soil moisture is less
than 5 inches.
The utility for strategy 4 is 291.36.
Irrigating at 5 inches is probably consistent with current practices.
Farmers tend to irrigate early in the season before a high water demand
exists.
The practice is to keep moisture in the profile so the plant
will not be as stressed later in the season when there is a high water
demand.
In the middle of the season a system may not be able to meet
the water demand.
This is when water demand is high and the value of
the marginal product of water is highest.
Influence of Labor Costs
The cost of labor was changed from $4.50 to $6.00 and $10.00.
As might be expected the strategies with relatively fewer irrigations
tended to become more appealing.
labor cost of $10.00.
Table 4-7 shows the ranked results
This may be a high wage rate but could be
Table 4-4
Total Investment for Each Strategy
C)
4-)
LAT
.
HR
2
1
10
23.
2
10
3
10
23.
11.
4
10
5
10
6
10
7
10
23.
11.
9
10
11.
9
8
23.
10
8
23.
ii
8
11.
12
8
11.
13
8
23.
14
8
15
8
23.
11.
16
8
11.
17
4
11.
18
4
11.
1?
4
20
4
11.
7.
21
4
7.
22
23
4
7.
4
11.
24
4
25
4
11.
11.
26
27
28
29
30
ii.
23.
4
7.
4
7.
4
2
7.
11.
2
11.
SMI
3
HP
4
Lateral
Cost
Main Line
Cost
55000.
55000.
55000.
55000.
55000.
Pump
Cost
Total
75??.
75??.
7597.
7597.
7597.
33000.
33000.
33000.
33000.
28500.
95597.
95597.
95597.
95597.
91097.
5617.
5617.
5617.
759?.
759?.
28500.
28500.
28500.
33000.
33000.
9117.
89117.
89117.
84597.
8459?.
3.3000.
84597.
8459?.
80097.
5.00
3.00
5.00
3.00
5.00.
248.
248.
265.
265.
3.00
5.00
3.00
5.00
3.00
169.
169.
169.
244.
244.
55000.
55000.
55000.
44000.
44000.
5.00
3.00
5.00
3.00
5.00
272.
272.
156.
156.
156.
44000.
44000.
44000.
44000.
44000.
7597.
7597.
7597.
759?.
7597.
33000.
28500.
28500.
28500.
3.00
5.00
3.00
2.00
5.00
170.
280.
280.
280.
297.
44000.
22000.
22000.
22000.
22000.
5617.
7768.
7768.
7?68.
7597.
28500.
33000.
33000.
33000.
33000.
78117.
62768.
62768.
62768.
62597.
3.00
2.00
5.00
3.00
2.00
297.
297.
163.
177.
17?.
22000.
22000.
22000.
22000.
22000.
75??.
7597.
7597.
5617.
5617.
33000.
33000
29000.
29000.
29000.
62597.
62597.
58597.
56617.
56617.
5.00
3.00
2.00
5.00
3.00
176.
193.
22000.
22000.
22000.
11000.
11000.
7597.
561?.
5617.
7768.
7768.
31500.
31500.
31500.
32500.
32500.
61097.
59117.
59117.
51268.
51268.
156.
193.
288.
288.
8007.
80097.
44
Table 4-4
(Continued)
>1
w
4J
(U
LAT
1
HR
2
31
2
32
2
11.
11.
33
34
35
2
11.
2
2
ii.
7.
36
2
7.
37
2
7.
1234-
SMI
3
HP
4
Lateral
Cost
Main Line
Cost
Pump
Cost
Total
5126a.
49617.
49617.
49617.
47597.
45617.
45617.
2.00
5.00
3.00
2.00
5.00
288.
146.
146.
180.
188.
11000.
11000.
11000.
11000.
11000.
7768.
5617.
5617.
5617.
?57.
32500.
33000.
33000.
33000.
29000.
3.00
2.00
201.
201.
11000.
11000.
5617.
561?.
29000.
29000.
The number of laterals
The length of set
The level of soil moisture to initiate irrigation
Horsepower requirement
45
.1
Table 4-5:Prices Used in Analysis
Price per kilowat hour
Monthly Demand Charge
$ .0138
9.19 per HP2
Annual Hook up:
Horsepower
0-50
Horsepower
51-100
$350 + $6 per HP
Horsepower 101-200
$650 + $5 per HP
Horsepower 201-300
$1150 + $4 per HP
Horsepower 301-400
$1550 + $3 per HP
$7 per HP with a $132 minimum
Wheat is $3.80 per bushel
Labor is $4.50 per hour
Interest Rate is 12.5 percent
Lateral $5500 per lateral
Mainline cost per 100 ft.
10 inch is $651
8 inch is $526
6 inch is $325
Approximate Pump Cost Eased on Gallons of Water Pumped (GPM)
400 GPM $19,000
500 GPM $21,000
650 GPM $26,000
800 GPM $28,000
1000 GPM $29,000
1200 GPM $32,000
1500 GPM $33,000
3. - 1982 prices
2 - HP is horsepower
pump costs were nterpo1ated for GPN values between the given rates.
3
Table 4-6
Strategy
26
23
35
is
20
13
17
7
3
9
32
18
1
36
21
24
10
33
14
2
30
12
;
Ranked.Utility1Net Retwns nd Costs fo Jch Strategy in Dollars Per Acre.
TOtal
Revenue
0 and
Costs
Labor
Costs
487.90
472.88
455.69
491.70
489.12
40.4?
39.53
43.69
35.80
67.33
28.13
19.6?
14.96
35.06
28.73
473.71
482.72
470.03
492.27
497.3?
39.48
38.86
66.89
37.35
61.26
24.04
19.78
41.92
35.17
501.25
470.03
421.08
435.96
481.11
55.83
61.18
35.52
51.75
61.83
408.95
427.62
410.39
435.96
392.16
Capita]
Net
Return
SD Net
Return
Max Net
Return
362.60
359.29
352.83
346.53
334.96
12.74
13.21
14.13
13.32
9.69
387.56
385.90
378.21
370.08
359.84
333.03
325.09
316,85
313.91
337.12
332,87
324,58
319.89
315.59
12.51
12.51
58.26
82.63
78.47
340.22
335,32
325.10
330.38
322.47
365.98
362.06
348.89
355.47
344.60
315.65
309.68
307,38
299.31
295.70
315.20
310.29
307.61
302.15
299.81
38.76
19.78
9.99
12.58
24.34
88.66
78.47
46.04
58,26
88.66
318.00
310.60
329.53
313.38
306.28
11.01
8.95
335.42
333.8?
367.03
338.88
329.8?
289.66
292.94
293.77
293.33
286.48
295.77
293.29
292.40
291.36
288.38
38.88
48.12
34.32
47.02
31.28
10.90
15.15
13.58
12.58
8.03
42.34
58.10
52.53
78.47
46.04
316.83
306.25
309.95
297.89
306.80
14.50
10.23
13.81
10.86
17.05
355.63
330.50
341.63
322.93
351.43
294.07
288.52
285.99
278.16
277.76
287.82
285,80
282.74
276.16
272.70
407.21
412.69
431.66
406.22
35.19
31.56
44.49
61.63
298.31
293.44
284.94
288.22
4338
54.84
74.31
88.66
47.61
78.47
13.75
13.11
12.38
15.13
13.03
333.94
324.62
310.57
328.14
317.84
277.44
269.09
262.02
269.12
265.02
270.80
423J5
18.8?
13.38
13.57
8.5?
18.04
19.71
Cst
56.71
54.39
44.20
74.31
58.10
74.31
84.49
283.85
8.75
14.12
11.33
11.11
8.65
18.56
Net
Return
Mm
:335.07
Utility
262.21
260.19
257.96
257.79
3
Table 4-6
Strategy
29
6
16
4
19
22
25
37
8
28
31
34
:
(Continued)
Total
Revenue
0 and
Costs
Labor
Costs
Capita
Costs
Net
Return
SD Net:
Return
Max Net
Return
Net
Return
Utility
Mm
410.73
411.39
401.63
419.9?
385.19
6?.?8
32.90
31.44
41.60
42.94
9.99
15.87
24.19
21.43
8.38
82.63
72.44
88.66
58.26
285.35
279.99
273.56
268.28
275.61
14.79
12.64
14.86
12.24
20.15
322.76
310.43
311.31
301.94
334.57
262.2?
260.02
252.82
250.67
244.22
255.76
254.72
243.83
243.80
235.32
379.83
365.71
360.15
396.95
359.16
42.50
29.83
33.01
31.47
31.44
11.1?
10.14
7.72
30.39
14.74
58.10
52.53
42.34
82.63
54.84
268.05
273.21
277.09
252.46
258.13
17.13
19.88
24.5?
16.57
19.47
321.00
333.81
342.69
294.60
314.41
245.26
248.96
229,72
224.43
230.07
233.79
233,46
227.95
219.32
219.19
362.57
346.37
50.40
32.23
5.84
5.93
47.61
46.04
258.72
262.17
21.03
22.97
313.70
326.02
227,94
229,22
216.66
216.24
1- Operation and Maintenance Costs
2- Annualized at 12.5 percent over 15 years.
3- Risk aversion coefficient equal to 2.0.
47.61
3
Table 4-7:
Ranked Utility, Net
Returns
Total
Revenue
Laho
23
35
26
472.88
455.69
487.90
13
0 and
Costs
and
Costs with Labor
Capital3
Cost
Costs
Net
Return
at $10.00 Per Hour
SD Net
Return
Max Net
Return
366.65
362.81
360.33
346.45
329,37
335.25
334.55
328.23
316.14
300.93
13.98
14.53
43.95
54.39
44.20
56.71
74.31
58.26
35.52
38.86
67.33
51.75
22.20
46.04
317.32
53.43
84.49
63.84
27.95
18.84
13.98
11.70
12.40
408.95
38.88
24.23
58.10
58.26
42.34
305.93
299.85
298.01
303.50
15
491.70
35.80
9
470.03
61.18
74.31
78.47
21
24
33
427.62
410.39
392.16
48.12
34.32
31.28
77.92
43.95
33.66
30.18
17.84
10
435.96
27.95
78.4?
54.09
88,66
78.16
29.74
78.47
473.71
39.53
43.69
40.4?
39.48
33.25
62.50
43.79
17
470.03
66.89
32
421.08
482.72
489.12
435.96
5
20
18
36
43.71
58.10
52.53
46.04
14
497.3?
412.69
47.02
61.83
61.26
31.56
30
406.22
61.83
19.04
74.31
47,61
1
11
27
29
7
2
481.11
14.81
13.2?
9.66
15.80
307.28
305.48
298.60
356.58
339.37
332.61
327.61
346,28
281.40
278.74
276.78
279.65
277.98
276.44
274.91
273.20
278.46
271.90
268.18
268.19
266.10
266.19
266.48
270.51
267.32
263.66
262.90
261.15
259.76
255.54
246.75
249.56
258.12
258.03
255.71
249.6?
247.84
245.44
249.66
254.89
239.64
234 93
242.49
242.91
242.89
303.67
286.43
287.74
293.35
296,99
16.58
9.55
12.04
15.23
17.92
334.88
282.52
276.53
279.48
277.08
277.75
12.24
10.41
14.91
14.62
16.15
311.66
306.91
314.34
316.75
329.80
344.69
309.95
312.80
320.99
407.21
35.19
41.93
54.84
275.24
67.78
37.35
22.20
93.14
47.61
16.17
15.13
18.59
317.03
312.31
82.63
273.14
279.15
501
55
13
dh 6o
270 6
14 82
30.16
88.66
268.36
13.88
94 17
298.4?
431.66
o
4449
6
Return
308.28
306.53
297.95
290.90
282.63
410.73
492.2?
5
34in Net
313.5:1
.
289.60
281.61
741.9?
24
240.60
Table 4-7:
(continued)
Total
.Q and
i
Labor2
Ct$
1?
6
25
22
4
31
34
16
28
8
Capita1 .Net..... $0 Net
Cot
Return
Return
Max Net
Return
Min Net.
Return
Utility
423.75
411.39
385.19
365.?1
379.83
43.38
32.90
42.94
29.83
42.50
40.08
35.27
18.63
22,53
24.83
28.4?
82.63
58.26
52.53
58.10
261.81
260.59
265.36
260.82
254.40
15.38
14.82
21.16
21.3?
18.78
301.06
296.54
326.87
324.73
311.51
239.17
236.42
232.12
233.56
228.90
231.05
230.95
223.04
218.08
216.03
360.15
419.97
362.5?
346.3?
401.63
33.01
41.60
50.40
32.23
:31.44
17.15
47.62
12.9?
13.18
53.74
42.34
88.66
47.61
46.04
12.44
267.65
242.09
251.59
254.92
243,99
25.64
15.13
21.71
23.69
18.36
336.23
281.73
308.47
320.80
289.31
218.17
219.04
221.34
222.20
216.79
216.38
211.84
208.17
207.54
202.27
359.16
396.95
31.44
31.47
.3276
67,54
54.84
82.63
240.11
215.31
21.83
21.05
301.62
266.83
207.93
180.16
(96.45
1- Operation and Maintenance Costs
2- Cost o Labor at $10.00/hour
3- Annualized at 12.5 percent over 15 years
50
considered a realistic opportunity cost of the managers labor.
Strategy
26 with 11 irrigations and set lengths of 7 hours dropped from first to
third in the rankings.
Strategies 23 and 35 moved up.
Strategies 23
and 35 had eight and six irrigations respectively.
The results of labor costs tend to be in accordance with the
attitude of farmers.
The author found that the farmers tend to
fer systems that require as few set moves as possible.
prefer 60 ft. riser spacings for this reason.
pre-
Most farmers
Their reasons seemed
to be related more to irrigation management than to labor Costs.
The high wage rate could reflect this management cost also.
Influence of Energy Rates, Interest Rates and Water Charges
Energy costs and interest rates were raised and the results
were analyzed.
of the results.
respectively.
These factors made little difference in the rankings
Strategy 26, 23, 35, and 15 still held ranks 1-4
The effects of these changes were interesting with
respect to the level of utility.
Water charges affect utility and
net returns more than energy costs.
A water charge of $10 per acre
foot reduced maximum utility to $313.38.
An increase in energy costs
of fifty percent reduced maximum utility to $317.80.
net returns are comparable.
in both cases.
The effect on
The maximum utility is with strategy 26
The magnitude of these costs needs to be explained.
Water charges of up to $50 per acre foot are realistic in some areas
of the country.
There are planned increases in the average cost per
kilowatt hour in the Hermiston area of over eighty percent at the end
of the 1982 crop season.
Utility Under a Water Constraint
The previous section explained the relationship between energy
costs, water charges and utility.
It was found that water charges
may be more important than energy costs.
With this result in mind
water constraints were imposed and the results of the simulation
model were examined.
Table 4-8:
Ranked Utility and Net Returns with Energy Cost Increase of 50%
0 and M
Costs
Labor
Strategy
Total
Revenue
26
467.90
23
35
47286
455.69
491.?0
473.71
58.68
57.33
63.71
51.83
57.02
28.13
19.67
14.96
35.06
19.71
482.72
492.27
489.12
470.03
421.08
56.0?
54.25
97.78
96.99
51.67
497.37
501.25
408.95
435.96
410.39
is
13
5
7
20
1?
32
II
36
18
24
9
1
33
10
2?
7
6
12
Capital
Costs___ Costs
56.71
Net
Return
SD Net
Return
Max Net
RetU
Mm Net
Return
Utilit
74.31
74.31
344.39
341.49
332.81
330.50
322.68
13.30
13.52
14.37
13.94
12.82
371.41
370.11
359.96
355.59
350.36
3(6.07
314.93
304,90
299.65
297,83
317.80
314.45
304.06
302.62
297.04
24.04
41.92
28.73
19.78
9.99
84.49
82.63
58.10
58.26
46.04
318.12
313.48
304.51
295.00
313.38
12.98
14.86
10.65
9.40
18.77
347.10
340.19
333.23
322.15
352.20
291.95
280.94
282.48
276.87
277.50
292.1?
88.56
80.75
57.06
?5.50
50.19
35.17
38.76
10.90
12.58
13.58
78.4?
88.66
42.34
58.26
52.53
295.17
293.08
298,85
289.63
294,08
12,56
12.10
15.35
12.00
14.33
320.21
266.32
312.17
340.08
3(8.09
327.93
262,7:3
268,66
220,05
268.8?
267.95
265.6?
265.42
470.03
427.62
481.11
392.16
435.96
88.19
70.49
89.02
45.63
68.26
19.78
15.15
24.34
8.03
(2.58
78.4?
58.10
88.66
46,04
78.47
283.59
283.88
279.09
292.46
276,65
9.23
11.09
309.90
310.46
306.31
339.40
304.39
265.55
2o4.25
258.66
262.31
254.95
265.12
2o1.?0
259.68
257.06
253.15
407.21
412.69
431.66
411.39
423.75
51.49
45.85
64.oS
47.94
63.37
18.87
13.38
13.5?
15.8?
18.04
54.84
282.01
279.15
264.78
264.95
263.86
14.50
13.73
13.16
13,42
(3.84
319.59
312.24
292.80
297.40
259.65
253,47
240.28
243.48
253.01
251.69
238,46
299,9
.214.70
54.39
44.20
;'4.31
88.66
82.63
78.4?
9.71
17.70
11.75
274.48
267,:38
28:3.25
283.22
276.21
275,04
238.10
236.19
01
Table 4-8;
(continued)
Total
16
3)
29
4
25
19
22
37
8
2i
34
401.63
406.22
410.73
419.9?
365.71
385.19
379.83
360.15
396.95
359.16
346.3?
362.57
0 and M
Labor
Costs
Capital
Costs
45.93
90.34
98.87
60.75
43.79
24.1.9
:72.44
8.57
9.99
21.43
10.14
47.61
47.61
62.98
62.50
48.62
45.92
46.14
47.38
73.90
Net
Retn
SD Net
Max Net
Retur, Bet
88.66
52.53
259.07
259.71
254.26
249.14
259.26
20.55
8.38
11.17
7.72
30.39
14.74
58.26
58.10
42.34
82.63
54.84
255.56
248.05
261.48
238.01
243.43
5.93
5.84
46.04
47.61
247.02
235.16
15.62
16.6?
15.29
Mm
Net
RetuU.ty
298.48
304.55
294.28
284.43
321.36
236.92
239.82
235.93
230.04
233.64
227.84
226.36
223.68
20.88
17.93
25.27
17.34
20.21
316.36
303.02
329.04
281.79
222.83
223.95
21271
213.81
212.20
210.93
208.74
214,07
203.01
23,63
22.04
312.74
292.97
13.01
301 .36
2i428
205.12
22312
218.16
199.75
191.07
F]
Table 4-9:
ey
Ranked tJtility and Net Returns with Water Charge of $10.00 Per Acre Foot.
Total
Revenue
0 and
Costs
2o
487.90
23
42.88
35
13
455.69
491.70
473.71
61.74
61.44
64.91
55.34
62.43
5
482.72
61.2?
15
1?
36
18
21
2.4
3
11
9
33
2?
1
10
14
14.96
35.06
19.71
24.04
41.92
Net
Return
SD Net
Return
Max Net
Return
74.31
74.31
341.34
337.38
331.62
326.99
317.2?
13.98
13.91
14.60
14.76
13.23
370.71
368.36
360.34
354.03
312.92
311.70
302.38
311.72
291.32
13.61
15.69
11.55
18.96
10.04
56.71
54.39
44.20
Mm Net
Return
313.313
309.55
302.42
297.48
347.37
310.47
303.56
294.67
292.06
344.77
340.18
334.57
351.70
321.60
286.09
277.55
279,46
275.?2
272.79
285.71
280.31
344.78
323.12
317,75
330.85
311.61
225.91
267.58
267.72
267.94
258.06
269.33
265.92
265.2o
264.66
264.18
2o3.28
254.95
255.82
253.58
250.99
99.92
53.33
100.6?
28a3
9.99
19.78
408.95
435.96
427.62
410.39
501.25
54.34
73.23
65.30
49.45
83.18
10.90
12.58
15.15
13.50
38.76
42.34
58.24
58.10
52.53
88.66
301.37
291.90
289.0?
294.82
290.65
497.3?
470.03
392.16
407.21
481.11
92.60
94.96
45.59
35.17
19,78
8.03
18.8?
24.34
78.47
78.47
46.04
54.84
88.66
291.13
276.81
292.49
284.04
272.26
13.92
9.93
18.33
15.23
319.33
306.5?
260.01
258.35
341.61
10.63
303.61
261.32
260.25
251.10
435.'6
412.69
48 51
58
8 47
'76 41
13.38
19.04
13.5?
15.8?
74.31
78.4?
277.85
267.78
265.98
265.21
1' 8'
14.55
14.73
307 18
313.36
305.60
296.73
299.85
42.3.75
2
431.óo
411.39
4.46
95.85
47.15
59.46
63.45
47.68
i
88.66
2.o3
16.02
12.99
11.91
15.08
13.23
14,11
14.30
Utility
312.11
489.12
421.08
4?0,03
12
6
28.13
Capital
Costs
84.49
82.63
58.10
46.04
58.26
5.O3
7
20
32
Labor
Costs
323,48
5' 43
250.48
246.1?
239.69
242.4
290.81
279.27
273.79
271.24
"50 7
2413.75
238.32
237.76
236.61
Table 4-9:
(continued)
Total
Strategy
30
16
4
25
19
37
28
8
31
_Revenue
0 and
Costs
M'
Labor
Costs
Capital
Costs
47.61
?2.44
88,6o
47 61
52.53
Net
Return
SD Net
Return
Max Net
Return
262.77
260.09
253.16
55 68
261.92
17.71
16.44
13.89
15 61
310.76
301.28
290.28
7 36
325.53
242.39
236.40
232.41
234.93
227.34
227,21
225.38
Y?4 45
219.45
21.58
18.66
323.81
312.19
335.19
306.50
318.41
227.31
230.08
216.32
216.3?
218.99
218.13
218.06
214.52
205.14
203.54
284.48
301 00
208.29
202.54
I9J 93
406.22
401.63
i19.9?
410 73
365.71
87.28
56.72
9' 45
41.12
8.5?
24.19
21.43
9 99
10.14
385.19
379.83
360.15
359.16
346.37
57.26
55.18
43.95
42.59
42.80
8.38
11.17
7,72
14.74
5.93
58.26
58.10
42.34
54.84
46.04
261.29
255.38
266.15
246.98
251.60
20.92
24.03
396.95
45.01
238.92
18.19
6
30.39
5 84
82.63
36
4/ ól
24
5
44.91
24
38
21.23
25.81
.
12
Net
Return
Mm
37
2
I
1
10
Utiliy
1- Includes Water Charges.
01
55
A water constraint of 22 inches was imposed.
The optimum
strategy in this situation is 32.
The net return and utility are
$329.53 and $292.40 respectively.
The risk coefficient is 2.0.
Strategy 32 is a system with two laterals and irrigation begins at a
soil moisture level of 5 inches.
Strategy 32 is the only strategy
that begins irrigation at the 5 inch level and is within the 22 inch
water constraint. The result again indicates a higher utility with
lower total investment systems.
New Strategies
The utility when initiating irrigation at a soil moisture level
of 5 inches was generally greater than when initiating irrigation at
3 inches of soil moisture.
irrigation at 5 inches.
A new strategy of irrigating at 4 inches
soil moisture was simulated.
level.
The top thirteen strategies all initiated
Four systems were analyzed at the new
The new strategies are number 38, 39, 40 and 41 and are
similar in design to 11, 15, 17 and 23 respectively.
Strategy 38 and
39 had 8 laterals and an adequacy of 87 and 50 percent respectively.
Strategy 40 and 41 had 4 laterals and an adequacy of 87 and 50 percent
respectively.
All the prices were held constant at the levels in
Table 4-5.
Strategy 41 had a utility of $327.E7 with a risk aversion
coefficient of 2.0.
This would place 41 above several other srategies
that irrigate when soil moisture reaches 5 inches.
Strategy 41 would
be preferred to 35 with a risk coefficient greater than .5. The
difference between the two in a risk neutral situation is slight.
Effect of Soil Moisture Capacity
In the strategies applied to this point risk aversion had little
effect on the optimum strategy.
(SMFC) was 6 inches.
The soil moisture at field capacity
If SMFC was lower risk might increase.
strategies were evaluated at SNFC of 4 inches.
Four
The new strategies
56
Table 4-10:
Yields and Water Use for Strategies 38-45
tl)
"-4
C)
Average
Yield
38
39
40
41
42
43
44
45
SD
Yield
Max
Yield
Mm
Yield
114.14
108.75
112.09
109.58
1' 67
113 70
88.13
107.04
86.48
117.60
113.48
116.25
114.32
2.11
1.92
2.55
120.28
117.55
119.03
119.44
118 '0
92.66
111.35
92.06
' 4'
3.22
3.10
3.35
100.00
117.30
98.84
1.41
No
IRR
9.
12.
7.
7.
13
9.
7.
5.
Irr.
Water
24.49
19.37
35.22
22.72
'1.63
14.53
24.63
15.50
ET
Ratio
1.01
.98
.99
.96
95
.82
.90
.79
57
Table 4-il:
Total Investment Cost for Strategies 38-45
U)
t,.
Lateral
Cost
Main Line
Cost
Pump
Cost
ota
LAT
HR
SMI
HP
38
39
40
8
11.
11.
4
ii.
41
4
11.
4.00
4.00
4.00
4.00
272.
170.
280k
17?.
44000.,
8
44000.
22000.
22000.
7597.
5617.
7597.
5617.
28500.
33000.
29000.
84597.
78117.
6259?.
56617.
3.00
1.50
3.00
1.50
156.
170.
163.
1??.
44000.
44000.
22000.
22000.
7597.
561?.
7597.
5617.
28300.
28300.
28300.
28500.
80097.
78117.
58097.
56117.
42
8
11.
4
8
11.
44
4
ii.
45
4
11.
3:3000.
Table 4-12:
Ranked TJtility and Net Returns with Addition of Strategies 38-41.
Total
tyevenue
23
20
13
40
38
7
11
39
9
32
3
36
21
24
10
33
27
0 and 14
Costs
Labor
Costs
Capital
Costs
487.90
472.88
459.55
455.69
491.70
40.47
39.53
38.77
43.69
35.80
28.13
19.67
16.99
14.96
35.06
56.71
54.39
489.12
473.71
467.32
482,72
470,03
67.33
39.48
28.73
58.10
74.31
58.10
38.86
66.89
19.71
17.18
24.04
19.78
472.76
492.2?
497.37
456.18
501.25
48.46
37.35
61.26
34.49
55.83
470.03
421.08
435.96
481,11
408.95
427.62
410.39
435.96
32.l6
407.21
Net
Return
SD Net
Return
Max Net
etun
Net
Return
Mm
iy
362.60
359.29
351.26
352.83
346.53
12.74
13.21
11.79
14.13
13.32
387.56
385.90
370.05
378.21
370.08
335.07
333.03
326.80
325.0?
316.85
337.12
332.8?
327.67
324.58
319.89
84.49
58.26
334.96
340.22
330.63
335.32
325.10
9.69
12.51
9.22
12.51
8,75
359.84
365.98
348.29
362.06
348.89
313.91
315.65
309.27
309.68
307.38
315.59
315.20
312.18
310.29
307.61
22.90
41.92
35.17
28.98
38.76
78.47
82.63
78.4?
72,44
88.66
322.92
330.38
322.47
320.28
318.00
9.43
14.12
11.33
12.18
11.11
339.12
355.47
344.60
347.24
335.42
300.64
299.31
295.70
293.07
289.66
304.05
302.15
61.18
35.52
51,75
61.83
38.88
19.78
9.99
12.58
24.34
10.90
78.47
46.04
58.26
88.66
42.34
310.60
321.53
313.38
306.28
316.83
8.65
18.56
333.87
367.03
338.88
329.87
355.63
292.94
293.77
293.33
286.48
294.0?
292.40
291.36
288.38
287.82
48.12
34.32
47.02
31.28
35.19
15.15
13.58
12.58
8,03
18.87
58.10
52.53
78.47
46.04
54.84
306.25
309.95
297.89
306.80
298.31
10.23
13.61
10.86
330.50
341,63
322.93
351.43
333.94
288.52
285.99
278.18
277.76
277.4
285.80
282.74
276.16
272.70
270.80
61.41
52.53
44.20
74.31
11.01
8.95
14.50
i:'.os
13.75
299.81
295.92
295.77
29:3.29
U'
Table 4-12:
Stratecjy
2
12
6
22
25
3?
28
31
(continued)
Total
Revenue
0 and M
Labor
oss
4t2.69
431.66
406.22
423.75
410,73
31.56
44.49
61.83
43.38
67.78
411.39
401.63
419.9?
385.19
379.83
32,90
31.44
4160
42.94
42.50
Net
Return
SD Net
Max Net
13.11
324.62
Mm
Net
13.38
13.57
8.57
18.04
9.99
74.31
88.66
47.61
78.4?
47.61
293.44
284.94
288.22
283.85
285.35
l238
357
15.13
13.03
14.79
328.14
317.84
322.76
269.09
262.02
269.12
265.02
267.27
15.87
82.63
72.44
88.66
58.26
58.10
279.99
273.56
268.28
275.61
268.05
12.64
14.86
12.24
20.15
17.13
310.43
311.31
301.94
334.57
321.00
260.07
252.82
250.67
244.22
245.26
52.53
42.34
82.63
54,84
19,88
24.57
16.57
19.4?
21.03
3338t
342.69
294.60
314.41
313.70
248.96
229.22
47.61
273.21
277.09
252.46
258.13
258.72
46.04
262.17
22.9?
326.02
24.19
21,43
8.38
11.17
365.71
360.15
396.95
359.16
362.57
29.83
31.47
31.44
50.40
10.14
7.72
30.39
14.74
5.84
346.3?
32.23
5.93
33.01
Capital
Costs
267.21
260.19
257.96
257.29
255.76
254.72
243.8:.3
243.80
235.32
233.79
227.94
233.46
222.95
219,32
219.19
216.66
229.22
216.24
224.4:3
230.0:.'
Ui
60
are 42, 43, 44 and 45.
Strategies 42 and 43 consist of 8 laterals
irrigating when soil moisture level reaches 3 inches and 1.5 inches
respectively.
Strategy 44 and 45 consisted of 4 laterals and
initiating irrigation when soil moisture is 3 inches and 1.5 inches
respectively.
The designs for 42-43 and 44-45 are similar to 15 and
23 respectively.
The results indicated that risk aversion may be more important at
a lower SMFC.
The maximum net returns were $337.30 and $336.33 for 44
and 42 respectively.
With a risk aversion coefficient of 2.0 the
utility was $309.91 and $313.47 for 44 and 42 respectively.
Summary
A wheat production system was simulated for 19 years of weather
It was found that a strategy with a low capital investment
data.
and initiating irrigation at a high soil moisture level resulted in
maximum utility.
The introduction of risk aversion made little difference
in the optimum strategy.
tive to labor costs and
Utility and net returns seem to be more sensiwater charges than energy costs and interest
rates.
The model also simulated two strategies with a lower moisture
holding capacity.
The net returns were greatest when initiating
irrigation at a high soil moisture level and using a system with
a low capital investment.
The introduction of risk aversion did make a
difference at the lower SMFC level.
Utility was highest when using a
system with a relatively higher capital investment when risk aversion
was added.
Table 4-13:
Strey
42
44
45
43
Ranked Utility and Net Returns for Strategies 42-45.
Total
Revenue
0 and M
Costs
477,19
447.62
370.06
372.50
34.19
37.96
31.70
29.87
Labor
Costs
32.36
18.43
11.59
21.74
Capital
Costs
74.31
53.93
52.06
72.44
Rturn_t
Net
336.33
337.30
274.71
248.44
SD Net
11.43
13.70
15.8?
14.85
Max Net
Return
355.46
362.16
304.30
282.24
Miii Net
riUtiliy
317.22
317.27
247.91
230.19
313.47
309.91
242.96
218.74
62
CHAPTER V
SUMMARY AND CONCLUSION
Summary
A model was developed to simulate winter wheat production on 160
acres of farmland similar to that found near Hermiston, Oregon.
The
major components of the model are a soil moisture component, an irrigation component, a wheat yield component and a risk/returns analysis
component.
level.
The soil moisture component estimates daily soil moisture
The soil moisture level is a function of daily precipitation,
daily irrigation and daily evapotranspiration.
Evapotranspiration is
calculated as a function of measured pan evaporation, wheat plant stage
of development and the soil moisture level.
The irrigation component
schedules daily irrigation based on the decision strategies supplied by
the model user.
There are three major parts to each strategy, the
irrigation system design, the set time in hours and the soil moisture
level that initiates irrigation.
The yield component of the model
estimates wheat grain yield as a function of daily temperature, daily
soil moisture, and stage of plant growth.
The scheduling of irrigation
will create variability in the soil moisture level across the field.
This variability of soil moisture is incorporated in the yield component.
The risk/returns analysis component calculates the net returns and utility.
Utility is equal to the average net return minus the standard deviation
weighted by a risk aversion factor.
Wheat production was simulated for a 19 year period using daily
weather data from the Hermiston Agricultural Experiment Station from
1963-1981.
Several strategies were compared.
The comparisons were made
of the yields, water use, irrigation costs, net returns, risk and
utility of the various strategies.
The strategies were ranked according
to maximum utility.
The results indicated that desfgning irrigation systems for maximum
yields did not result in the highest utility.
The optimum strategies
were those that initiated irrigation at a low level of soil moisture
63
depletion and used a system with a relatively lower capital investment.
The average annualized investment cost for the five strategies with
the highest yields was $76.43 per acre.
The annualized investment
cost for the five strategies with the highest utility was $57.54 per
acre.
The difference in average utility between the two groups was
$19.37 per acre.
The strategy with the highest yield had a utility
level of $295.77 per acre.
The strategy with the highest utility had
a utility level of $337.12 per acre.
costs associated with irrigation.
The analysis included only those
Utility was more sensitive to labor
costs and water charges than to the cost of energy and interest rates.
The level of risk aversion made very little difference in the relative
level of utility for the different strategies.
If the moisture holding
capacity of the soil was reduced then the level of risk aversion makes
a bigger difference in the relative level of utility.
Limitations of the
Model
The simulation of a biological process has limitations due to
the simplifying assumptions required.
particular system.
The model represents one
Even so, the model still provides information
that can be useful in decision making.
The simulation model may
also provide information that can help to plan the future direction
of actual experimentation.
The conclusion to the thesis is the
authors perception of the simulation modelt s major limitations and
the subsequent need for more research in those areas.
First, the estimation of wheat yield failed to incorporate some
important variables.
Fertilizer was not included.
of the effect of temperature was unsatisfactory.
modelling are continuing.
The modelling
Efforts in crop
The efforts need to continue if the yield
estimation process is going to be accurate enough for farm management
decision making.
More information is needed on how water stress, and
temperature stress early in the season affect final grain yield.
Second, the analysis did not include some constraints that are
pertinent to irrigation management.
Many farmers face water constraints.
64
The constraints may pertain to total seasonal water use or to shorter
term well capacity constraints.
The timing of water application under
water constraints needs to be incorporated with future models.
Third, the analysis examined irrigation strategies for one land
endowment.
action.
Future analysis should examine the land and water inter-
The concept of supplemental irrigation could be examined in
this context.
Fourth, there are several other aspects of irrigation system
design that need to be considered.
The model incorporated a simple
relationship between gross water application and stored soil moisture.
The stochastic nature of soil moisture distribution needs to be
considered.
Fifth, there are other sources of variation in yield i.e., response
to fertilizer, genetic variability, cultural practices, pests etc.
It
was assumed for the analysis that the response of wheat yield to soil
moisture is independent of these other sources of variation.
This
assumption means that the inclusion of these sources of risk would not
affect the relative ranking of the results.
It is important to evaluate
these risks and determine if they should be included in irrigation
management decisions.
Sixth, the model assumed that irrigation began when soil moisture
reached a given level.
An analysis of irrigation management decision
making is an area for further research.
One aspect might be the timeli-
ness of management decisions and implementation.
The author found from
conversations with farmers that the scheduling and management of irrigations is perceived as a necessary nuisance that often received less than
enough attention.
The notion of improving irrigation efficiency is
dependent upon the flow of moisture information to the manager and the
implementation of a consequent decision.
65
Conclusion
A winter wheat simulation model proved to be very helpful in
analyzing the results of different irrigation strategies.
The analysis
showed that following irrigation strategies to achieve maximum yield
were not those that achieved the highest net returns.
Higher net
returns could be had by producing at a level slightly lower than
maximum yield.
The reduction in irrigation costs were greater than
the value of the yield reduction.
The higher level of net returns was
achieved without significant increases in the level of risk facing the
wheat producer.
The author examined the major inputs relating to irrigation in
winter wheat production.
labor and water.
The inputs are capital, energy f or pumping,
The author found that the optimal irrigation strategy
was more sensitive to the irrigation equipment investment costs than to
the costs of the other inputs.
References
Ahmed, J.C., H. M. VonBavel and E. A. Hiler. "Optimization of Crop
Irrigation Strategy Under a Stochastic Weather Regime: A Simulation Study." Water Resources Bulletin. V. 12(6) 1976, pp. 12411247.
Anderson, R. L. and A. Maass. A Simulation of Irrigation Systems:
The Effect of Water Supply and Operating Rules on Production
Income on Irrigated Farms. USDA ESCS. Technical Bulletin
No. 1431.
Arkin, G. F.
"Crop Response to Available Soil Moisture." Paper
A State
presented at a symposium on Crop Response to Irrigation:
AAEA meetof the Arts Assessment of What is Known and Practiced.
ings, Blacksburg, VA. Aug. 7-9, 1978.
Ayer, H. W.
"Economic Models of Crop Response to Irrigation: A State
of the Arts Assessment.t' Paper presented at a symposium on Crop
Response to Irrigation: A State of the Arts Assessment of What is
Known and Practiced.
AAEA meetings, Blacksburg, VA. Aug. 7-9, 1978.
"EvapoBates, E. M., F. V. Pumphrey, D. C. Hane and T. P. Davidson.
transpiration Relationships with Pan Evaporation of Frequently
Irrigated Wheat and Potatoes." Unpublished Report, Oregon State
University Agricultural Experiment Station, 1982.
Brink, L. and B. McCarl.
"The Tradeoff Between Expected Return and Risk
60 (1978),
Among Corubelt Farmers." Amer. J. Agr. Econ.
pp. 259-263.
"An
Butcher, W. R., R. Gilksen, N. C. Jensen and R. S. Sutherland.
Initial Study of the Water Resources of the State of Washington."
State of Washington Water Resources Center, Pullman. Atlas of
the State of Washington III.
Rep. No. 2, 1967.
Charlton, P. J. and S. C. Thompson. "Simulation of Agricultural Systems"
Amer. J. Agr. Econ., 21(3)1970, pp. 373-389.
Dent, J. B. and N. J. Blackie. Simulation in Agriculture.
Science Publishers LTD. 1979.
Applied
"Transpiration and Crop Yields." Institute of Biological
DeWit, C. T.
and Chemical Research on Field Crops and Herbage, Wageninger,
the Netherlands, Verse-Landbouwk,onder Z. No. 69.6-s. Gravenhage,
1958.
Doorenbos, J. and A. H. Kassam "Yield Response to Water" Food and
Agricultural Organization of the United Nations, FAO Irrigation
and Drainage Paper No. 33, 1979.
English, N. J. and G. T. Orlob.
Scheduling of Irrigation."
pp. 405-414.
"Managing Returns Flows by Scientific
V. 11(6) 1979,
Prog. Wat. Tech.
67
En1ish, H. J.
"The Uncertainty of Crop Models in Irrigation Optimization."
Transactions of ASAE.
1981.
pp. 917-921, 928.
English, N. J. and G. S. Nuss. "Designing for Deficit Irrigation."
Forthcoming. ASCE IRR Drain Div.
V. 108(2) 1982.
Enochian, R. V. "Solar- and Wind-Powered Irrigation Systems" USDA
Economic Research Service AER No. 482, 1982.
Evans, E. G. The QuantitatIve Analysis of Plant (rowth.
Press, Berkeley and Los Angeles, 1972.
U. of Calif.
Flinn, T. C. and W. F. Musgrave. "Development and Analysis of InputOutput Relations for Irrigation Water." Aus. J. of Agr. Econ.
V. 11(1) 1967, pp. 1-19.
Food and Agricultural Organization of U.N.
FAO Production Yearbook.
1980.
Food and Agricultural Organization of the U.N.
FAO Yearbook, 1977.
Glenn, H. D.
Research Assistant Unclassified Crop Science, Oregon State
University. A personal conversation with the author.
December 29, 1981.
Hanks, R. J. "Model of Predicting Plant Yield as Influenced by Water
Use." Aron. J. V. 66. September-October, 1974.
Harris, T. R. and H. P. Mapp, Jr. "A Control Theory Approach to Optimal
Irrigation Scheduling in the Oklahoma Panhandle."
Southern J. of
Agr. Econ., July, 1980, pp. 165-171.
Heady, E. 0. and R. W. Hexam. Water Production Functions for Irrigated
Agriculture.
Iowa State University Press, Ames. 1978.
Held, L. J. and G. A. Helmars.
"Simulation Modelling: Potential
Univ. of Wyoming Agr. Exp.
Sta. Report No. SR-lll2, 1981.
Advantages, Uses arid Concerns.'1
Henderson, .3. N. and R. E. Quandt. Microeconomic Theory:
Approach.
3rd edition, McGraw-Hill Book Co., 1980.
A Mathematical
Jensen, H. C. "Status of Irrigation Scheduling Technology and Its
Application in the U.S.A." Paper presented at a symposium on
Crop Response to Irrigation: A State of the Arts Assesment
AAEA meetings, Blacksburg, VA.
of What is Known and Practiced.
August 7-9, 1978.
Jensen, H. E., D. C. Robb and C. E. Franzoy.
"Scheduling Irrigation
Using Climate-Crop-Soil Data." ASCE Irr. Drain Div. V. 96,
1970, pp. 25-28.
Jensen, N. C. and L. G. King. "Design Capacity of Irrigation System."
Agr. En&. J. V. 43(9) 1962.
"Estimating Soil
Jensen, M. E. and J. L. Wright and B. J. Pratt.
Moisture Depletion from Climate. Crop and Soil Data." Transactions of ASAE.
1971, pp. 954-959.
Johnson, W. C. and R. G. Davis. "Yield-Water Relationships of
Summer-Fallowed Winter Wheat.
A precision Study in the Texas
Panhandle." U.S. Dept. of Agricultural Research Results.
ARR-S-5IJuly 1980.
Jose, H. D. Decision Strategies for the Multiple Use of Winter Wheat
in Oklahoma. Ph.D.
Dissertation, Oklahoma State University,
1970.
Kioster, L. D. and N.
Irrigation Water
Washington State
Bulletin 746 No.
K. Whittlesey.
"Production Function Analysis of
and Nitrogen Fertilizer in Wheat Production."
University Agricultural Experiment Station
1971.
Kuinar, R. and S. D. Khepar.
"Decision Models for Optimal Cropping
Patterns In IrrIgation Based on Crop Water Production Functions."
4&icu1tural Water Management. V. 3, 1980, pp. 65-76.
Legget, G. E. "Relationships Between Wheat Yield, Available Moisture
and Available Nitrogen." Washington State University Agr. Exp.
Sta. Bul. No. 609, 1959.
Mapp, H. P. and V. R. Eidman.
"Simulation of Soil Water-Crop Yield
Systems:
The Potential for Economic Analysis." Southern J. of
Agr. Econ. July, 1975, pp. 47-53.
Markiund, R. E.
Topics in Management Science.
Inc., 1974.
John Wiley and Sons
Martin, J. H., W. H. Leonard, and D. L. Stamp. Principles_of Field Crop
Production.
3rd Edition. MacMillan Publishing Co., Inc., 1976.
Mihas, B. S., K. S. Parikh and T. N. Srinivason. "Toward the Structure
of a Production Function for Wheat Yields with Dated Inputs of
Irrigation Water." Water Resources Research.
V. 10(3) 1974,
pp. 383-393.
Murey, R. V. and J. R. Gilley.
"A Simulation Model for Evaluating
Irrigation Management Practices." Transactions of the ASAE.
1973, pp. 979-983.
Nuss, G. S.
Crop Evapotranspiration of Winter Wheat, tinder Deficit
Masters Thesis, Oregon State University, 1981.
Rasmussen, V. P. and R. J. Hanks. "Spring Wheat Yield Model for
Limited Moisture Conditions." Agron. J. V. 70, Nov.-Dec.,
1978, pp. 940-984.
Rickman, R. W. Assistant Professor Soils, Columbia Plateau Conservation Research Center, Pendleton, Oregon. A personal conversation
with the author. May 10, 1982.
Rickman, R. W., R. E. Ramig and R. R. Alimaras.
"Modelling Dry Matter
Accumulation in Dryland Winter Wheat." Agron. J. V. 67(3) 1975,
pp. 283-289.
"Irrigation Management:
Ritchie, I. J., J. B. Dent and M. J. Blackie.
An Information System Approach" Agricultural Systems. V. 3, 1978,
pp. 67-74.
Rydzewski, J. R. and S. Nairizi. "Irrigation Planning Based on Water
Deficits." Water Resources Bulletin, V. 15(2), 1979, PP. 316-325.
Sloggett, G. "Energy and U.S. Agriculture:
Irrigation Pumping." 1974
USDA Economic Research Service AER No. 376.
Spillman, W. 3.
"Application of the Law of Diminishing Returns to
Some Fertilizer and Feed Data." 3. of Farm Economics. V. 5, 1923.
Stegman, E. C.
"On-Farm Irrigation Scheduling Evaluations in Southeastern North Dakota." North Dakota State Univ. Agr. Exp. Sta.,
Res. Rep. NO. 76. June, 1980.
Waggoner, P. E. and W. A. Norvell. "Fitting the Law of the Minimum
to Fertilizer Application and Crop Yields." Agron. 3. V. 71,
March-April 1979, pp. 352-354.
"Wheat Response
Yaron, D. and G. Strateener, D. Shimshi and M. Weisbrod.
to Soil Moisture and the Optimal Policy Under Conditions of Unstable
Rainfall." Water Resources Research. V. 9(5). 1973, pp. 1145-1154.
"Open-Loop Stochastic
Zavaleta, L. R., R. D. Lacewell and C. R. Taylor.
Control of Grain Sorghum Irrigation Levels and Timing." Amer. 3.
of Agr. Econ. V. 62(4).
1980, pp. 785-792.
kPPEND ICES
70
Appendix I
FORTRAN Program for the Risk/Returns
Analysis Component
PROGRAM DOL(COSTS,RESULT,OUTPUT,TAPE7CO5TS,TAPE8,TAPE6,TAPE5RESULT)
ILT,TAPE9)
ACL THE AVERAGE SEASONAL LABOR COST
'At ACRE INCH DELIVERY PER LATERAL PER SET
'AIHR THE GAILY GROSS APPLICATION RATE
'ANC POWER DEMAND CHARGE
'ANET AVERAGE NET RETURJI FOR THE SIMULATION PERIOD
ANPOW THE ANNUAL POWER HOOK UP CHARGE
'AOPC THE AVERAGE ANNUAL OPERATING COST FOR THE SIMULATION PERIOD
ATR THE AVERAGE ANNUAL TOTAL REVENUE
'ANAl AVERAGE ANNUAL WATER DELIVERY IN ACRE INCHES
'An. THE AVERAGE YEARLY YIELD PER ACRE FOR THE SIMULATION PERIOD
'AYR THE AVERAGE YIELD PER ACRE FOR EACH YEAR OF THE SUHULATED PERIOD
'CLABOR THE AVERAGE LABOR COST FOR EACH YEAR
'CML TOTAL COST OF MAI1ILINE
'CPUMP THE TOTAL COST OF THE PUMP
'CPVC COST FOR BUIEO MAINLINE
'PC THE TOTAL ANNUALIZED INVESTMENT
'FCL ANNUALIZED COST OF LATERALS
'FCNL ANNUALIZED COST OF MAINLINE
'FCPMP ANNUALIZED COST OF THE MAINLINE
'FCPVC ANNUALIZED COST OF BURIED MAINLINE
'HP PUMP HORSEPOWER
'R SET TIME
'bC SYSTEM IDENTIFICATION CODE
'100 NuM3ER OF DAYS TO IRRIGATE ENTIRE FIELD
'IS NUMBER OF SETS IRRIGATED EACH GAY
'LABOR YEARLY LABOR REQUIREMENT
'LAT THE TOTAL NUMBER OF LATERALS
'NET THE NET RETURN PER ACRE FOR EACH YEAR
NNET THE MINIMUM YEARLY NET RETURN FOR THE SIMULATION PERIOD
'OPC OPERATING COSTS FOR EACH YEAR
'OPIl SYSTEM OPERATING HOURS FOR EACH YEAR
'PKW COST OF ENGERY PER KILOWATT HOUR
'PL PRICE OF LABOR PER HOUR
'PN PRICE OF WHEAT PER BUSHEL
'PWA PRICE OF WATER PER ACRE INCH
'RI ENERGY RATE INCREASE FACTOR
'RIFL INTEREST RATE FACTOR FOR LATERALS
'RIFML INTERST RATE FACTOR FOR MAINLINE
'RIFP INTEREST RATE FACTOR FCR PUMP
'RIFPV INTEREST RATE FACTOR FOR BURIED MAINLINE
'RISK RISK AVERSION COEFFICIENT
'RHI AVERAGE YEARLY NUMBER OF IRRIGATIONS
'SALIF INTERST RATE FACTOR FOR SALVAGE VALUE
'SWAT YEARLY DELIVERY OF WATER PER ACRE IN ACRE INCHES
'TCST TOTAL INVESTMENT COST
'TCU WATER GELIVERY PER APPLICATION IN CUBIC INCHES
'TDH TOTAL DYNAMIC HEAD
'TEP AVERAGE ANNUAL MAXIMUM POTENTIAL EVAPOTRANSPIRATION
'TETA AVERAGE ANNUAL EVAPOTRANPIRATION
REAL NNET,AYR(19),SWAI(19),OPH(19),LABORCI9)
19},OPC(t9) ,CLABOR(19),NET(i.9)
DATA PKW,PL,PW/.0i3,'..5O .7/
DATA TEP,$ALIF/22.G9E2O!39,.t7O88235/
DATA RIFL,R1FHL,RIFP,RIFPV/'.150763751/
DATA </5/
PRINT','ENTER THE RISK AND THE ENERGY RATE INCREASE FACTOR
PRINTI+EXAMPLEIRATE INCREASE OF 5O IS 1.53'
REAO(',')RISK,RI
PRINT',+ENTER THE PRICE OF LABOR AND WATER'
PRINT',tLABOR i/HOUR AND WATER $/ACRE FOOT'
READ(',')PL,PWA
PWA=PWA/12
"THE COSTS OF MAINLINE IS IN DOLLARS PER 100 FEET"
"TON IS THE TOTAL DYNAMIC HEAD FOR THE MAINLINE AND IS
"CALCULATED FROM A PROGRAM FROM MARSHALL ENGLISH AG ENGIN DEPT
50 REAO(7,',END500)CPUMP,CML.CML1,CPVC,TDH
"READ INFO FROM FIM400 OUTPUT"
READ (5,IIIOC,LAT1HR,THI,TFL ,TOHI,TETA
1 FORMAT c//I3,x,I,2X,F3.o,2x,Fk.2,7x,F7.2,aX,F6.2,2x,F5.2/)
2 FORMAT(1.X,F7.2,29 1,F5.2,21X,212X,F7.2))
"TDH IS TOTAL DYNAMIC HEAD FOR SYSTEM 250 ASSUMES 200 FOOT WELL
53 FT LIFT
TDHTDH+25O+TDH1
TCUTFL'231' 60'HR
71
Appendix I (continued)
Ar=rrcu/LAT) /11k0S.O0
1S21./HRLAT
10088/IS
AIHRAI/IDO
RATIOTETA/TEP
HP(TOHTFLJ/2376
"CALCULATE THE MONTHLY DEMAND POWER CHARG444
''iULTIPLY BY FOUR FOR THE NUMBER OF MONTHS IN THE SEASON"
AMC2. 8'l. 1'. 7l 'HPl.
AMC = A NC' RI
"CALCULATE
CHARGE"''
THE ANNUAL H00%( UP
ND.HP.GT.300)THEN
HP- :3 00
t0.ANO. HP.GT.2t30THV4
-200)41.
0O.A1O.HP.GT.1OO)THEN
IGO) '5
00 .AtW. HP. GT.50)THEN
P.-")
0. AN 0. HP. CT. 15) T HEN
'RI
"CALCULATE
"13.20 AND
"5500 IS I
CPvC=C
CMLCM
TOTAL INVESTMENT FOR MAINLINE AND LATERALS"
ARE
OF PIPE NEEOEO"'
ICE THE
OF LEP4GHTS
EACH LATERAL'""'"""
3.2 C
CMLI'6 .6
FCL= LA
TCL=FC
C ST -1 CL +C ML +CP U
WRITE(9,6) IOC,LAT,HR,THI,t4P,TCL,CML,CPUPIP,ICST
FORMAT(' ',I3,3X,I2,3X,F3.0,3X,F'..2,3X,F4.O, kFli.03
FCL (FCL-. tO'FCL'SALIF ) 'RIFL
FCMLZCMLRIF ML
FCPMP (CPUMP-.10'CPUMP'SALIF) 'RXFP
FCPVC=CPVC'RIFPV
FC= FCML4FCPMP+FCPIC+FCL
FC=F C/ISO
DO 100 J1,i9
REA05,2) AYRJ) ,SWAT(J) ,OPH(J) ,t.ABOR(J)
TR(J)=PW'AYR(J)
OPC(J)=(HP'OPH(J)'.7k6'Pt(W'RI+.0006'(FCL+CPIL+CPUMP)'SMAT(J))/160
OPO (J)OPC(J) .PWA'SW4T(J)
OPCtJ)=OPC(J)+(AMC+ANPOW) /150
CLAB0R(J) (LAB3(J) 'PU /160
NET (J)=TR(J)-OPC(J)-CLABOR(J)-FC
100 CONTINUE
CALL STAT(NET,1,ANET,SONEI,SXNET)
WHET ANET-RIS'<'SCNET
CALL SORT(NET,19,XNET ,NNET)
CALL STAT(OPC,19,AOPC,SOOPC,O)
CALL STAT(TR,19,ATR,SCTR,D)
CALL STAT(LABOR,j9,ACL,SDCL,O)
CALL STAT(YR,j9,AYL..SDYL,S(YLO)
AYL= AYL/60
SDYLSDYL/6
CALL SORT(AYR.19,XTL.Yl.N)
XYLXYL/60
YLNYLN/5O
CALL STATCSWAT,lg,AWAT,SOWAT,o)
RNIAWATIAI
CALL SORTCSNAT t9,XWAT,WATN)
WRITE U,'.) IDC,AYL,SDYL,XYL,YLN,RNI,AWAT,RATIO
FORMAT(+
13,SX F6.2 5X F5.2,2F11.2,5X F3.0,SX,F5.2,5X,F5.2)
12 FORMAIC' + A9k)
GO TO 50
500 Sb P
ENO
SUBRQUTI
SORT(
"THZS SUD FINDS THE
MIN AND MAX OF AN
REAL AR(2OQ),NAX,MIN,MX,MN
MX=ARR(j)
MN=ARR(j)
00 100 I2,J
50
IF(MX.GE.ARR(I))GOTO 50
MX=ARR(I)
GOTO100
IF(MN.LE.ARR(X))GQTOIDO
MH=ARR LI)
ARRAY"44"
Appendix I (continued)
100 CONTINUE
MAX: MX
tlIN:MN
RETURN
END
SU9ROUTINE STAT(ARRAY I,AVE,STO,SKEW)
4THIS SUBRUT1NE CALULATES AVERAGE AND STANDARD DEV'
REAL ARRAY(200),M3,MZ
ss= 0
S3: 0
SUM=C
00 130 J1,I
SUN=SUM4RRAy (JI
100 CONTINUE
XBARSUH /1
00 200 J1,t
DIFF=ARRAY( J)-XI3AR
SSSS+0IFF2
S3=S3+DIFF3
ST0=S0RT(SS/(Ij))
N2SS/I
M35 3/I
SKEWM3/ (fl21. 5)
200 CONTINUE
A YE: X BAR
RETURN
END
73
Appendix II
FORTRAN Program for the Soil Moisture Component,
Irrigation Component and Yield Component
PROGRAM MOD(TAPE5,SYSDES,TAPEZ=$YSQES,TApE6,wUATA,TAPEIWOATA,
3
j OUT? U T=T A? ES
'3
"ALL
OUT?UT IS WRITTEN TO TAPE5
3,
3
A5N
$ flit ARRAY OF DAILY SOIL MOISTURE VALUES IN INCHES
'AwAT IS THE AVERAGE NUMBER OF OPERATING HOURS FOR THE IRR SYSTEM
'AVID IS THE AVERAGE YIELD PER ACRE FOR THE SIMULATION PERIOD
'AYR IS THE AVERAGE YEARLY YIELD PER ACRE
'9 IS THE IRRIGATION EFFICtEtCY
'90 THE INTERCEPT IN THE EQUATION TO CALCULATE B
'91 THE SLOPE IN HE EQUATION TO CALCULATE B
'DAY THE INDEX COUNTER FOR THE NUMBER QFAOAYSAFRQM WINTER DORANGY
'DEC IS THE VALUE TO REDUCE ASH FOR TRYING A NEW MOISTURE LEVEL FOR IRRIGATION
'DEPt IS THE LEVL OF SOIL HCISTURE DEPLETION
EPD IS THE EARLIEST POSSIBLE DATE TO RETURN AND IRRIGATE SET NUMBER ONE
'ETA IS THE CALCULATED EVAPOTRANSPIRATION
'EVAP IS THE DAILY PAN EVAPORATION
'FL IS THE HOURLY RATE CF WATER DELIVERY IN ACRE INCHES
'FLAG INDICATES THE DAY THAT ASH WAS EQUAL TO ZERO IF IT EXISTS
GPM RATE CF WATER DELIVERY IN GALLONS PER MINUTE
'HR THE SET TIME
'r IS A LOOP COUNTER
'IAVL IS THE NUMBER CF LATERALS AVAILABE TO RETURN OF A SUBSEQUENT IRRIGATION
'ID A LOOP COUNTER
'ICC STRATEGY IDENTIFICATION NUMBER
ILAT THE NUM8R OF LATERALS TN THE STRATEGY
'IPC EQUAL TO ZERO IF PIPE SUBROUTINE HAS SEEN CALLEC
'IRR IS THE ARRAY OF DAILY IRRIGATIONS
'tY A LOOP COUNTER
A LOOP COUNTER
KA THE NORMALIZED RESPONSE OF ETA TO ASH LEVEL
'XC COEFFICIENT FOR PAN EVAPORATION CONVERSION 10 ETA
'KCE CROP COEFFICIENT FOR THE STAGE OF GROWTH
'KS VALUE TO INCRESE ETA AFTER WETTING
'LABOR THE HOURS OF LABOR TO IRRIGATE
'LAT THE NUMBER OF LATERALS USED FOR THE SIMULATION FOR HALF OF THE FIELD
'LPO THE LAST DAY THE SEASON TO IRRIGATE
'OPH THE ARRAY OF YEARLY SYSTEM OPERATION HOURS
'PREC Tt1E DAILY RAINFALL
'SOWAT TH STANDARD DEVIATION OF OPERATING HOURS
'SE THE SYORAGE IFFICIENCY OF WiNTER PRECIPITATION
'SET A LOOP COUNTER FOR EACH SET IN THE FIELD
'SiTDAY THE NUMBER OF SETS TH.AT CAN BE IRRIGATED IN ONE DAY
'SETS THE TOTAL NUMBER (F SETS
'St VALUE USED TO ESTIMATE KA
SMFC THE ASM AT FIELD CAPACITY
'SWAT THE AMOUNT OF cUMPER INRIGATION WATER FOR EACH YEAR
'TAR A TEMPORARY ARRAY tJSEO TO PASS VALUES TO SUBROUTINES
'1041 TOTAL DYNAMIC HEAD FOR LATERALS
'TEMP THE ARRAY OF AVERAGE DAILY TEMPERATURE
'TETA THE AVERAGE TOTAL SEASONAL ETA
TFI THE GPN MULTIPLEC BY ILAT
'THI THE LEVEL OF ASH THAT INITIATES IRRIGATION
'THIN THE MINIMUM VALUE OF 1HZ
'THIX THE $AX CF THI
'TI MAX DAILY TEMPERATURE
'12 THE MIN DAiLY TEMPERATURE
'NAT THE ARRAY OF YEARLY IRR FOR EACH SET
WM THE WINTER PRECIP iN CENTIMETERS
'wHetS THE INITIAL ASM
'WRAIN THE WINTER PRECIPITATION
'WSD STANDARD DEVIATION OF WATER USE FOR EACH SET
'YA THE ARRAY OF YEARLY YIELDS FOR EACH SET
'YR A LOOP COUNTER FOR THE YEAR OF SIMULATION
'YX 4
REAL IRR(tOO,ilG) ,XCE,KS,XC,PREC(1,111),TAR(2O3)
REAL. KA,SWATL9) LABOR(19) OPH(lg)
REAL TEHP(15,111)',WRAIN(t9,WAT(19,t0O),ASM(1UO,1i0),YA(19,10O)
INTEGER YR DAY,SETDAY,SET,FLAGtI9,100),EPD,SETS
REAL EVAP(Z911t),AYRtt
COMMON IRR,IAVL,SETDAY,YA,ASM,TEHP
DATA SMFC,SETS/.O,zs',/
DATA BO,ot,LPo/1.o7235224,.3a377oaqz,qo/
'READ THE DAILY WEATHER DATA AND CALCULATE AVERAGE DAILY TEMP
74
Appendix II (continued)
THE FILE WITH THE DAILY WEAVER DATA IS CALLED WOATA
DO 113 1Y1,19
00 15 1D1,111
REAO(1,i)T1,12,PREC(XY,IO) ,EVAP(IY,IO)
I FORMAT (6X,2F3.0 ff4.2 3X ff3.2)
TEIP( ]Y,ID)1Tt.Th/
15 CONTINUE
10 CONTINUE
''REA0 THE WINTER PRECIPITATION
THE WINTER PRECIP SHOL.LD BE AT THE END OF THE DAILY WEAVER OBSERVATIONS
AND ON FILE WOATA
REAO(1,2) (WAtN(IYJ,IY1,19)
2 FORMAT4X,F5.fl
WRITE(5,)
WITE15,')
REAO IH. STRATEGY PARAMETERS
HE S'SIEM DESIGN IFC AND THE OPERATING RULES ARE ON FILE SYSOES
75 IEAO(2,,ENO=gOO)ICC,LAT,HR,GPM,TDHL,THIX,THIN,DEC
F(GPM13B60)/11ki]k80O
TFLGPM*LA i2
ILAT:LAT'2
THITHIX
100 IF(THI.LT.THIN)GO TO 75
SETDAY24/HRLAT
VET AsU
INITIAL SOIL MOISTURE FROM WINTER PREC44
WMWRAIN(YR)/.393701
SE74. 52-. 1k7 NM
WHOISSE/IOOWRA INCYR)
IFiwpiOIS.CT. 5.00 )WMOIS6. CC
CD 135 Sc.Ti,SETS
00 136 0AY1,110
IRR(SET,OAY) =0.0
136 CONTINUE
wAr( YR,SET) 0.00
FLAG (YR ,SET)=O.0O
135 CONTINUE
IAVLSETDAY
IPC I
EPD1
DO 140 OAY1.1i0
DO 145 SEII,SETS
ASH FO THE
IF (OAY.EQ. 1) THEN
ASM( SET DAY) :WMO IS
ELSE
DEPL=SMFC-ASM(SET,DAY-i)
C C) 8eO-B1(IRR(SET,OAY-1)/OEPL)
IF(8.GT..92)B=.q2
IF(OEPL.GT.'3
IF(t3.LT. lOP 8.10
AS'(SET,0AY)ASM(SET,QAY-1)+8IRR(SET,OAY-i)+PREC(YR,DAY)
ASM(SET,CAYP ASM(SET,DAY)-ETA
E NOX F'
IF(IPC.EQ.t)GO TO 142
!F IRRIGATION IS SCHEDULED EUT SOIL PROFILE IS FULL IRRIGATION IS STOPPED
IFCASM(SET,OAYP .G1.SMFC.AND.IRR(SET,Q4y).GT.O.QOJTHEN
00 141 JSET,SETS
00 143 t:DAY,EPD
IRR(J,I)0.0
143 CONTINU
141 COWl INU
EPDDAY
1P01
END IF
142 CONTINUE
KCE=(-i.9683E-k)oAY3+(2.a2925E-2) 0AY2+56.062k(fl1
KCEKCE/100
""'COHPUTE KS VALIFS IF WATER WAS APPLISD
ASH AND
ET TO SMFC IF NECESSARY
IF(OAY-L.LE. C)THEN
KS C
IF(ASH(SET,DAY) .GT.SMFC)ASM(SET,OAY)SMFC
ELSEIF(PREC(YR,DAY).GT.G.C,OR.IRR(SET,04Y1).GT.0.C)THEN
ELSEIF(DAY-2.LE. O)THEH
75
Appendix II (continued)
KS=0
IF(ASM(SET,OA'r ,GT.SMFC)ASM(SET,OAY)=SMFC
ELSEIF(PREC(YR,DAY-1).GT.0.0.OR.IRR(SET,OAY-21.GT.G.OJTIiEN
XS=( .9-KCE) .5
ESIF (DAY-3.LE.G)THEN
IF(ASM(SET OAY).GT.SMFC)ASN(SET OAY)SMFC
ELSEIF(PEC(R,3AY-2).GT.0.0.t3R.IRR(SET,OAY3).GT.0.0)THEN
XS(.9-XCE)'.3
EL SE
XS=3
IF(AS$(SET,DAY).GT.SMFC)ASN(SET.DAY)SSNFC
NOIF
IF(KS.LT.C.0)KS*0. 0
I44*CALCULATE
IE(ASM(SET ,OAY) /SMFC.GT. .457)THEN
KAI
ELSEIF(ASMISET,OAY).GT. 0.0 )THEN
S(.1D (ASM(SET,CAY)/SMFCJ
KA =SL4231. 413 460 360 -SL' 3. 20 58 8175 89
ELSE
ASM(SET,DAY
O.0
!F ASH IS LESS THAN OR EQUAL TO ZERO THEN SET FLAG EQUAL TO THE CAY
'4CFIF( THE
ZERO MOISTURE LEVEL.3.44.*443$4
NOT. (FLAG( YR ,SET) , GT.13 ) ) FLAG(YR,SET) OAY
KA=C
ENDIF
4COMPUTE XC AND ETA
KC=KCE'KAsKS
IF(KC.GT.t) XC1
Er A=E V AP (V R, CA Y+fl KC
'CALGULATE THE TOTAL
TEl A=TETA+ET A
145 CONTINUE
IF(ASM(L OAYI.GT.THI)GCTO 140
IF(OAY.Gf.LPtflGOIO lt.3
IF(DAY.LT.EPD)GO1O 1.O
'CALL
T4E IRRIGATION SuBROuTINE'
I 0E PD
CALL PIPE(HR,FL,SETS,OAY,ID,EPO,IPC)
140 CONTINUE
4CALL THE PLANT GROWTH
CALL GROW(YR,SETS)
00 340 SEI1,SETS
00 345 OAYI,110
NAT (YR,SEI) SWAT (YR,SET) +IRRISET,DAY)
345 CONTINUE
IF(.NOT.(FLAG(YR,SET).GT.0)GO 10 340
'41F ASHO.3D BEFORE SPECIFIED DATE THEN YIELD IS ZERO''
IF(FLAG(YR,SET).CE.623G0 TO 340
YA(YR,SET):0.00
340 CONTINUE
130 CONTINUE
44CCMPUTE YEARLY YIELD AND WATER
TETA=TETA/(SETS19)
WRITE (5,6UOC, ILAT ,HR,THI,TFL,TDHI,TETA
WiITE (5, 81
8
6 FORMaT(13,2x .LA1',I2,2X ,F3. 0,2X,pk.2 .2X,TFL* i,F7.2 ,2X,
jTOHj
,Ft.2,2X,F5.2)
DO 430 YR1119
00 435 StT=1,SETS
TAR ( SET
VA ( YR. SET
405 CONTINUE
CALl. SIAT(TAR,SETS,AYR(YR),YSD)
CALL SORI(TAR,SETS,YX,YN)
'.1.0 SETi,SETS
TAR(SEI)WAT (YR. SET)
00
410 CONTINUE
CALL STATCTAR,SETS,SWAT(YR),14S0)
CALL SORT(TAR,SETS,WX,WN)
LAe0RYR)(SWAT (YR)'SE1S/(FLHR))2
OPHtYF)(SWAT(YR) 4SETSIFL)/LAT
WRITE.(5,flYR,AYR(YR),YSO,YX,YN,SWAT(YR),WSO,WX,WN,OPH(YR)
i,LA8OR YR)
7 FOHA1(I2,4(2X,F1.2),4(X,F5.2),2(2X,F7.2))
400 CONTINUE
CALL STAT(AYR,19,AYLD,YSD1
CALL ST*T(QPH,19,AWAT,SOWAI)
WRITE(S,)'AVE YIELO= ,AYLO,t S0
,AWAT,
WRITE(5,')eAVE OP HOURS
4**oE_INcREMEN1
THI AUG GO TO
THI=THI-OEC
GO 10 100
900 STOP
END
,YSD
1,SDWAT
S0
76
Appendix II (continued)
SUBROUT1tE GROW(YR SETS)
""THIS ROUTINE COPIUTES THE DAILY GROWTH OF WHEAT"
A INTERCEPT OR THE IMITIAt. LEVEL OF GROWTH
ARI ARTIFICIAL ARRAY
'ASK AVAILABLE SOIL. MOISTURE
C GROWTH COEFFICIENT FOR PERIOD AFTER I PRIME
'01 aAY COUNTER FOP. THE FIRST PERIOD
02 CAY COUNTER FOR THE SECOND PERIOD
*
1R2 ARTIFICIAL ARRAY
'1R3 ARTIFICIAL ARRAY
J INDEX FOP THE SET NUMBER
'K DAILY GROWTH COEFFICIENT FOR THE FIRST PERIOD
'KA NORMALIZED YILO RESPONSE TO SOIL MOISTURE
L COUNTER FOR THE DAY OF THE SEASON
'N MAXIMUM ADDITION 10 YIELD FOR THE SECOND PERIOD
'PIP MAX DAILY INCREMENT IN YIELD FOR THE SECOND PERIOD
RT THE DAILY CONIINUOUS GROWTN RATE
'SMFC SOIL MOISTURE AT FIELD CAPACITY
'TEMP AVERAGE GAILY TEMPERATURE
'IL THE NUMBER OF DAYS TO 7 PRIME
'12 THE NUMBER OF GAYS AFTER I PRIME
'VA ARRAY CF AVERAGE YIELD PER ACRE FOR EACH SET
'VP THE MAXIMUN POTENTIAL YIELD
REAL TEMP(i9,1t1)
REAL K,YA(19,100) ,M,MP,KA,ASM(j3O,jtO),ARI(100,jlO)
INTEGER OL,SETS,OZ,1i,T2,YR
COMMON At,IR2,IR3,YA,ftSM,1EMP
DATA RT,YP,C,A,',065,3Q5.O ,.79,100.O/
DATA Tt,T2,SNFC/k56,,.O/
KEXP<RT -i
VPtAEXP (RT'TI)
HYP-YPL
MPM' It-C)
'''INITLIE YIELD VALUES TO ZERO'"
DO i0 J:1,SETS
YA2C. 00
YA1A
"COMPUTE DAILY YIELD FCR PERIOD ONE""'
00 150 Ot=1,T1.
TKTEMPtYR,Q1+1)
TXj
IF( TX. LE 37. 1Ø) TX'O .0
KAALOGt 10O'ASH(J,O1)/5HFC.j)/ALoG(.Oj.0)
IFXA.LE.TX)THEN
V
Y At KA' K
ELSE
V
Y At 'IX' K
E N C IF
YAIYA1+Y
150 CONTINUE
"COMPUTE YIELD FCR PERIOD TWO"
DO 155 O2j,T
LC2+T1
KAALOG(1OO'ASM(J,t)/SMFC+i)/At.OG(10L.0)
TXTEMP(YR, L+L)
IF(T.LT.37. 1,O.OR,TK.GT.tQ1,)TX0
IF (KA.LE.TX)THEN
ELSE
ENGIF
YA2YA2fY
ISS CONTINUE
'''COMPUTE
TOTAL YIELDS""
YA(YR,J) YAL+YAZ
11,0 CONTINUE
RETURN
END
SU3ROU1INZ SORT(RR,J,MAX,MIN)
"THIS SOD FINDS THE MIN AND MAX OF AN ARRAY""
REAL ARR(200),MAX,MIN,MX,MN
MXARRU)
MNARR(L)
DO 100 I2,J
IF(MX.GE.ARR(I))GOTO 50
MXARR(I
50
GOTOIQU
IF(MN.LE.ARR(I))GQTOIOO
MN=ARR (I)
100 CONTINUE
MAX=MX
NIN$N
RETURN
END
77
Appendix II (continued)
SUBROUTINE PIPE(HR,Ft.,SETS,QAY,EFO,IO IPC,
'Al ACRE INCHES OF WATER DELIVERED PER APPLICATION
ENTIRE FIELD IS IRRIGATED
'OFC THE NUM!ER OF SETS THAT CAN BE IRRIGATED BEFOREON
THE FIRST SET
'EPO THE EARLIEST POSSIBLE OAT TO STARTE IRRIGATION
'HR THE SET TIHE
IRR ACRE INCHES DELIVERED TO EACH SET
EACH DAY
'ZSEIOY THE NUMBER OF SETS THAT CAN BE IRRIGATED EARLIER
SET BEFORE
ISREM THE NUMBER OF LATERAL THAT CAN RETURN TO
'THE LAST SETS HAVE BEEN IRRIGATED
LPO THE LAST DAY OF THE SEASON TO IRRIGATE
5YSTEM""
""''TMI SUBROUTItE SIIIULATES AND IRRIGATION
'""MOVEMEMT ACOSS A FIELD COMPUTES THE E4RLIEST"'''
DAY FOR
INTEGER OAY,EPO,SETS,DFC
REAL. IRR(100,1i0)
COMMON IRR,IAvL.ISETQY
DATA LPO,'90
'CALCULATE THE ACRE INCHES OP WATER DELIVERO PER APPLICATION
AIHR'FL
IPC=O
IF .NOT. (OAY,EC.EPC)) IAVLISETCY
00 200 I1,tAVt
IRR(I DAY) AI
200 COHTINU
ISRE PSEIS -IAVL
DFC ISR.EM/ISETDY
ISETIAVL+1
ISRCPISRE M-OFC'TSETDY
IAVL=ISETDYISREM
DO 205 ct,OFC
IF(OAY.KGT.LPtG0TQ 203
LSET=ISET4ISETCY-i
00 210 IZSET,LSET
IRR(I ,DAY+K) 41
210 CONtINUE
ISETSETst
205 CONTINU
203 CONTINUE
EPO=OAY'DFC+l
IO=EPO
IF(EPO.GT.LPC)GOTO 300
IFUSRE$.EQ.CJGOTO 300
00 215 ItSET,SET$
IRRtI,EP()AI
CONTINUE
215
3O0 RETURN
END
AND STANDARD OEV"
FEAL ARRAY(2OC
55=0
SUMO
00 tOO Ji,I
SUMSUM+ARRAY(J)
SS=SS +ARRAY (U) "2
100 CONTINUE
AVESUM/I
X=SS-SUM"2I
X=xI(Zli
IF(X.LT. 0.0)X*0.O
XSQRt(XI
ST 0 X
RETURN
END