131
515
THS

 

17-15313 llllllllllllllllllllllllllllIIHHIIlllllllllllllllllll

2 29310515945656
LIUHAHY

/ ( 3 3 Ce > 1 Michigan State
University

 

 

 

This is to certify that the

dissertation entitled

Characterizing Irrigation Environmental Efficiency
Based on Distribution Uniformity
and Irrigation Management

presented by

Neba M. Ambe

has been accepted towards fulﬁllment

of the requirements for
Agricultural Technology

Ph.D. degree in and Systems Management

 

 

 

Date 1" 3'016

 

MSU i: an Afﬁrmative Action/Equal Opportunity Institution 042771

 

PLACE ll RETURN BOX to remove thie checkom from your record.
TO AVOID FINES return on or bdore dete due.

    

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU le An Afﬂrmetlve ActiorVEquel Opportunlty Inetltuﬂon
nuns-n1

 

This is an authorized facsimile, made from the microﬁlm
master copy of the original dissertation or master thesis
published by UMI.

The bibliographic information for this thesis is contained
in UMI’s Dissertation Abstracts database, the only
central source for accessing almost every doctoral
dissertation accepted in North America since 1861.

[M Dissertation
Services
A Bell & Howell Company

300 N. Zeeb Road. Ann Arbor, Michigan 48106
1-800-521-0600 313-761-4700

Printed in 1997 by xerographic process
on acid-free paper

DPP'I'

INFORMATION TO USERS

This manuscript has been reproduced ﬁ’om the microﬁlm master. UMI
ﬁlms the text directly Earn the orig'nal or copy arbrnitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may be
from any type of computer printer.

The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins,
and improper alignment can adversely aﬁ‘ect reproduction.

In the unlikely event that the author did not send UMI a complete
manuscriptandtherearemissingpages, thesewillbenoted. Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.

Oversize materials (e.g., maps, drawings, charts) are reproduced by
sectioning the orig'nal, beginning at the upper left-hand corner and
conﬁrming ﬁ’orn left to right in equal sections with small overiaps. Each
original is also photographed in one exposure and is included in reduced
form at the back of the book.

Photographs included in the original manuscript have been reproduced
xerographieally in this copy. Higher quality 6" x 9" black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly to

order.

UNII

A Bell a Howell Information Company
300 NorchechAnnArbor MI 48106-134éUSA
31317614700 800/521-0600

CHARACTERIZING IRRIGATION ENVIRONMENTAL EFFICIENCY
BASED ON DISTRIBUTION UNIFORMITY AND IRRIGATION MANAGEMENT

By

Neba M. AMBE

A DISSERTATION

Submitted to
4 rchigarr State University
in partial ﬁtlﬁlment of the requirements
A [hr the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultm'al Engineering

1995

UK]: number : 9631224

 

UM! Micr'ofom 9631224
Copyright 1996, by UM! Company. All rights met-red.

Thlsrnicroforrn editiouis protectedegeinst unauthorized
copying under Title 17. United States Code.

 

UM

300 North Zeb Road
Ann Arbor. MI 48103

ABSTRACT

CHARACTEerINc IRRIGATION ENVIRONMENTAL EFFICIENCY
BASED ON DISTRIBUTION UNIFORMITY AND IRRIGATION MANAGEMENT

By

Neba M. AMBE

Managing irrigation systems in an environmentally sound manner is a major challenge
to irrigation mangers. Two common performance measures are often used: statistical
uniformity - a measure of variation in the system’s applied water. and application efﬁciency -
a management parameter which is indimtive of how much of the applied water is in the root
zone. Both system performance and management strategies have an impact on the irrigated
farm’s environment. but neither of these measures quantities that impact. This study was
undertaken to answer the following research questions. Can an environmental efficiency
performance measure for irrigation management be formulated? How does application
efﬁciency (AE) vary with the application depth under an imposed areal distribution?

A deﬁnition of irrigation environmental efﬁciency is proposed. An equation for
determining its variance was formulated using system science and the propagation of error
theories. Irrigation data from center pivot irrigation systems with statistical uniformitics
from 40 to 98% were simulated using mean and standard deviations from data in the
literature and actual data from St. Joseph County. MI. Application eﬁcienciec for selected

depths (0.4 to LP. of the average applied depth) and statistical distributions were determined

for each system. The results were then used to determine irrigation environmental eﬂiciency.

The results show that: l) the statistical distribution of application etﬁciency for various
minimum application ratios (MAR - required depth divided by the mean applied depth) can
be described by a family of curves whose slopes slightly increase with the statistical
uniformity of the system: 2) application efficiency increases with MAR: the increasing rates
are a ﬁInction of the system uniformity; and 3) irrigation environmental efﬁciency (Elf) is
a function of the irrigation system and management.

Regression equations relating application efﬁciency to the minimum application ratio.
charts that relate irrigation environmental efﬁciency to application efficiency, statistical
uniformity. and the fractional area fully irrigated are presented. E“; has been used to show
and compare the statistical distribution of various center pivot systems. from two
geographical regions in the United States. and to evaluate five Michigan farms using data

from actual irrigation schedules.

DEDICATION

To
my family members
Living and Dead

and

To all
who seek protection

of the environment-

AC KNOWLEDGMENTS

Atty indebted thanks to my program directors: Professor V. F. Bra/ts for conceiving this
research idea. his motivation and encouragement to undertake this project. and Professor R D. von
Bernuth for his insight and guidance in the course of this study. Their careﬁrl direcrion and
wpervision led to the timely completion of this work Special thank to Professors T. H. Burkhardt.
E Dersch and W. H. Shayya for serving as members of my advisory committee. Their individual
and collective inputs led to the integrated approach taken in this study.

I express gratitude to John Barkley and Tim Russet of the National Resources Conservation
Service. St. Joseph C ounry. M ﬁrr their time. effort and assistance in locating the necessary data
jbr this project. Sincere thanks go to Dr. A. Go. Ads. L Arganian and P. Gardner jbr providing
the necessary assistance and a hospitable atmosphere in accomplishing this task.

Acclaim and benediction to my mother. Lum Regina and grandmorher. Nchang Monica on
whose forms I deve10ped an interest in agricultural science. and above all for providing me the
education they never got. My heartfelt gratitude to all my family who have always been supportive
of my educational goals and despite the long years of absence never gave up. Although all of them
have not lived to see the end result. their images remain ﬂesh in my mind as I write these lines.

And/inally I owe a signiﬁcant debt to my LansingCameroon family and all my friends fbr their

moral. spiritual and material support. The list is quite along one. so omission of any names is

unintentional.

PREFACE

My love and curiosity for the agricultural sciences came from assisting my mother and
grandmother with routine farm activities. Interest in agricultural research must have begun
when i asked my grandmorher, out of frustration from the tedious labor. if there was a less
tiring and time saving means of planting corn. Over the years. and drawing from my
association with the farm and its produce. [ have come to realize that a farm is not just part
of the soil or dirt, that a farmer is not just one who sows seeds, and that plants don’t grow
just because a seed is sown- There is a complex mutual association of these entities. perhaps
not realized or understood by many. How this symbiotic relationship can be maintained
provided an interesting deliberation and has been the mental requirement to pursue the work
reported in these leaves.

This work is the child of a casual conversation with Professor Bralts who emphatically
said: I believe distribution eﬂiciency and application eﬂiciency can be combined to get
environmental eﬁiciency. curd somebody ought to do it- At ﬁrst I found no interest in the
subject and he might have given up trying to convince me. An absurdity, it sounded to me,
primarily because I thought that was too abstract. far from reality and therefore a difficult

goal to pursue. But in the deep belief of my personal philosophy - nothing without hands

can challenge a human being with hands and a brain - I decided to take on the task. What
at ﬁrst sounded abstract and undoable has materialized into a dissertation, presented here in
six sections.

The ﬁrst section contains introductory information on the nature, problem, scope and
objectives of the research. Section [I contains the relevant literature reviewed. It covers
a historical perspective of the relationship between irrigation management and the
environment, the application of systems theory to irrigation management; and a discussion
of the various irrigation performance measures in current use.

Research procedures. results and discussion are presented in section [11. These are
reported as two independent papers in conformity with the publishing format of the
Transactions of the ASAE scientiﬁc journal. Each paper contains an abstract. speciﬁc
objectives. investigation procedure, results, discussion and conclusion.

Section [V is a general conclusion on the nature of the research ﬁndings, application and
relation to past works. Recommendations based on the experience and results from this
work are presented in section V. Unless indicated as a footnote. full citations on all
referenced works in the text are given in Section VI - References. Finally, details of

material that could not be included in the text can be found in the Appendices.

Neba M ME
1 December I 995
Michigan State University

vii

TABLE OF CONTENTS

LIST OFTABLES \
LIST or FIGURES ....................................................... xi
I. Introduction ............................................................... I
A. Problem statement .................................................... 3
8. Scope and objectives .................................................. 4
II. Literature Review ......................................................... 5
A. Irrigation management and the environment ................................ 5
I- Historical systems .............................................. S
2- Irrigation disasters: lessons from the past ............................ 6
3- Irrigation and resource development ................................ 8
8. Systems theory and irrigation management ................................. 9
1. System concepts ............................................... 10
2. Systems theory and approach .................................... I l
3. Rationale for application to irrigation management ................... I
4. Application to irrigation management .............................. 20
C. Irrigation performance measures ........................................ 21
l. Irrigation uniformity ........................................... 22
2. Irrigation efficiency ............................................ 29

0. Summary and discussion .............................................. 40

viii

[11. Research Procedure. Results and Discussion .................................. 42

A. Estimating irrigation application efﬁciency and its Statistical distribution ........ 43
I. Abstract ..................................................... 43
2- Introduction .................................................. 43
3- Theoretical development ........................................ 45
4. Procedure .................................................... 47
5. Results and discussion .......................................... 50
6. Conclusions .................................................. 61

B. An environmental efﬁciency performance measure for irrigation management . . . . 62

1. Abstract ..................................................... 62
2. Introduction .................................................. 62
3- Theoretical development ........................................ 65
4. Procedures .................................................. 70
5. Results and discussion .......................................... 72
6. Conclusions .................................................. 82
IV. General Conclusion ...................................................... 83
V. Recommendations ........................................................ 85
VI. References .............................................................. 87
Appendices ................................................................. 95
Appendix I. QuickBasic Program Listing ............................. 95
Appendix 2. Detailed Program Output ............................... 98
Appendix 3. Regression Coefﬁcients ............................... l02
Appendix 4. SCS-Scheduler Output: Soil Water Content ............... 103
Appendix 5. Center Pivot Evaluation Data for St. Joseph. MI ............ 108

LIST OF TABLES

Table I. Deﬁnitions of efﬁciency ................................................ 30
Table 1. Selected data from Heerrnann et al. (1992). . . . .............................. 48
Table 3. An example of a generated matrix from equation [26] ......................... 49
Table 4. Validity of AE results from the procedure of Equation [25] ................... 51
Table 5. Irrigation measures and suggesred Em clnsiﬁcation values- .................... 77

LIST OF FIGURES

Figure 1. Systems approach to problem solving (adapted from Manetsch and Park. 1993) . . . 12

Figure 2. System modeling procedure (adapted from Manetsch and Park. I993) .......... 16
Figure 3. Natural resource system ............................................... 20
Figure 4. Application efﬁciency deﬁnition sketch .................................. 32
Figure 5. inﬁltrated soil water variability ......................................... 46
Figure 6. AE frequency distributions for selected systems ............................ 52
Figure 7. Cumulative ﬁ'equency distributions from Figure 6 .......................... 5 3
Figure 8. Application efficiency as a ﬁmction of MAR and Us ........................ 55
Figure 9. Relating application uniformity to application efﬁciency and leached fraction . . . . 57
Figure [0. Relationship between AE. Us and fully irrigated area ........................ 58
Figure l l. Estimating application uniformity from AE and Us for an example problem ..... 60
Figure ll. Estimating the fractional area adequately irrigated for an example problem ..... 60
Figure l3. Bridging the gap between the physical and management aspects of irrigation . . . - 63
Figure 14. irrigation environmental efﬁciency related to MAR. Us and AE ............... 73
Figure l5. Irrigation environmental efﬁciency related to MAR. Us and irrigated area ....... 74
Figure [6. Estimating Em from AE. Us and MAR for two example problems ............. 76
Figure [7. Estimating En; fractional area adequately irrigated. MAR and Us

for two example problems ............................................. 76
Figure [8. E“; distribution of center pivot systems from Michigan and Colorado .......... 78
Figure [9. Seasonal variation of E15 for selected Michigan farms ....................... 80

xi

 

I. Introduction

If I were a tree among trees. a cat among animals.
... this problem would not an’se.’
- Albert Camus -

A riverﬂou'edﬁom Elen to water the garden-3. Generations have. and will continue
to depend on water. Throughout the entire history of the human race. irrigation - the
artiﬁcial supply of water to meet plant needs - has always been indispensable to agriculture.
In'igation is one of the basic measures for raising world agricultural production. FAO
predicts 300 million hectares of land will be under irrigation by 2000. The principal
objective of irrigation is to adequately and efficiently ﬁll the root zone with required soil
water using either subsurface. surface. sprinkler or drip method. The driving force behind
the development of each system or a shift from one system to another is the desire for more
efﬁcient water use. higher economic returns and environmental protection. Efﬁciency
depends on several factors including distribution uniformity of the applied water, irrigation
scheduling and plant-soil-water relations.

Irrigation managers and farmers are concerned with the system's efﬁciency throughout
the growing season. An ideal system would be [00% eﬂ'rcient. Unfortunately each

irrigation syStem poses some degree of non-uniformity which can be attributed to system

 

[An shard mung. ﬁr Mull ofSin'pl-a p. 38. I955.

2The river rpﬁr into [our stream. run of wind! are theﬁmrr'liar Tigris and Euphrates (Guest's. 2:10. N).

2

design and operation. soil properties and climatic factors. The result is the coexistence of
under- and over—irrigated spots in the same ﬁeld. Under-irrigation results in yield losses.
Over-irrigation produces deep percolation losses of water and plant nutrients. Percolated
nutrients pose an environmental hazard. in addition to increased cost of pumping excess
water. The farmer is often forced to make trade offs between conﬂicting environmental and
economic goals.

The climate of an area determines the amount of precipitation, which in turn affects the
amount of irrigation water to meet plant needs. Topography and soil type dictate the
irrigation method selected. Economic conditions specify the complexity of the irrigation
system and aﬁ‘ect its distribution uniformity. Socio-economic (and most recently
environmental) conditions bias the farmers' goals. decisions and consequently management
practices. These in turn affect the efﬁciency and economic outcome of the system-
Environmental pollution may be a consequence of the overall system efﬁciency.

The above describes a closed system in which energy and material flow to and fro. From
the law of conservation of flow. every system with input has an output: desired and
undesired. Too often we have focused on the desired outputs with little or no attention to
the undesired ones. Agricultural production inevitably depletes resources and may pollute
the environment. In analyzing system proﬁts. the undesired output that ends up in the
environment is given zero dollar value and the long term eﬂ’ects are ignored. This is because
external accountability across the system boundary is limited to those outputs that bring
income. We know. for example. how much corn leaves the farm. its net retums and where

it goes. However. the quantity of leached nitrates (eg. no kg per hectare: Martin. 1992)

 

 

 

3

or the amounts of soil loss from erosion are rarely considered. Vital questions are often
ignored. What is the cost of cleaning up? What are the long term ramiﬁcations. and how
long will it take before we see these effects? There is an urgent need to pay attention to
system outputs that end up in the environment.

The ever increasing demand for water and the continuous depletion and pollution of
resources clearly suggests the need for greater stewardship. Agriculture must move touwd
more eﬁcient. productive and environmentally sound practices. The work described here
examines how improved irrigation management can help assure an agricultural system that

is economically and environmentally sustainable.

A. Problem statement

Application efﬁciency is indicative of how the system is managed while distribution
uniformity is used to evaluate system performance. Both an irrigator‘s management
practices and the performance of an irrigation system can have a signiﬁcant impact on the
environment For a given efﬁcient management practice and system performance, can the
potential effect of their combined output to the environment be characterized? No. As of
now. there is no performance measure for the potential of environmental degradation

resulting from the combined performance and management of an irrigation system-

B. Scope and objectives

The work reported here contains a literature review with respect to irrigation

management and the environment. systems theory and irrigation management, and irrigation

performance measures, and research ﬁndings on methods of estimating application and

environmental efﬁciency in irrigation management. Use is made of the integrated concept

of the soil-plant-water—management system in which irrigation performance measures.

systems theory and statistical concepts are used to develop an index for characterizing the

potential environmental effects of irrigation management. The concept of irrigation

environmental efficiency is proposed and applied to selected irrigation systems.

The overall goal of this research is to develop a performance measure for environmental

efﬁciency of irrigation management practices The following are the speciﬁc objectives:

l-

’J

he)

To assess the statistical distribution of application efficiency.
To develop an environmental performance measure for irrigation systems.
To evaluate selected center pivot systems and some Michigan irrigated farms using

the new parameter-

 

 

I I. Literature Review

Irrigation. afnecessity. involves a trude-oﬂ’between production.
and some environmental value: ... irrigation is a social contract
to sacriﬁce some environmental values ..."

- Jan van Sclrilfgnarde .

A. Irrigation management and the environment

I. Historical systems

Irrigation is one of the oldest agricultural practices in the world. Its origin can be traced
to that of the human race (Genesis. 2:10). Irrigation has been practiced on the banks and
delta of the river Nile for about 8000 years - making it the longest period of continuous large
scale irrigation (van Schilfgaarde. 1994). Historical accounts reviewed by Jensen (I980)
indicate technological developments in irrigation agriculture on the river Nile about 6.000
B.C.. drained canals in Mmopotarnia in 4.000 B.C. and the use of ﬂooding waters on the
Indus river about 2.500 B.C. Irrigation practices were in place along the Yellow river in
2.627 B.C. and in Peru about 1.000 B.C.

The dependence of early civilizations on irrigation earned them the name hydraulic
societies (James et al.. I982). These societies with government directed water control
originated in the Near Eut- Egypt and Mesopotamia thousands of years before the Christian
era and continued in India. Persia. Central Asia. parts of Southeast Asia and ancient Hawaii

(Kappel. 1974). Such societies in the Western Hemisphere. Kappel continues. ﬂourished

 

iii-tam m urn-rid mum-dormers VmCoueerveuon. somzrzo-aat. I995.

5

6

in Andean Zone. Mesoamerica (region of the Lake Mexico), Southwestern United States in
Arizona and New Mexico among the Pueblo Indians prior to the Spanish conquest. Remains
of ancient canals are still evident on both sides of the Salt River. Arizona (Taylor and
Ashcroft. I972).

Ancient irrigation systems required highly organized societies to maintain them. Sri
Lanka (Ceylon) at the turn of the century had irrigation structures as old as 2,500 years. In
the last 900 years the government built [.420 new tanks (dams) and 534 canals; at the same
time 2.355 tanks and 3.621 canals were repaired (James et al.. I982).

It has often been debated and is still unclear whether social institutions brought about
irrigation or irrigation established them (Adams. I974; James et al.. 1982; Kappel. 1974).
It is believed that the Sumerian Empire- whose bread basket was Mesopotamia. perished
because of the collapse of the irrigation system; one school of thought has it that the
irrigation system collapsed because of a detoriation in the empire‘s social structure (van
Schilfgaarde. 1994). One thing is clear: societies have disappeared and ecological disasters

have taken a toll when irrigation systems failed.

2. Irrigation disasters: lessons from the past

The history of civilization contains a litany of self-destructive irrigation developments.
Failure of the Syrian and Babylonian societies of the Near East and North Africa (Carthage)
were attributed to waterlogging and a rise in the soil water table in irrigated lands (Taylor
and Ashcroft. I972). Salt deposition in the root zone resulted to poor or no crop growth.

Seeped waters from earthen canals into adjacent lands. waterlogged lands and annual

7

malaria epidemics in the Middle East are all examples of human misery blamed on poorly
planned and managed systems (Gulhati and Smith. I967). A change in irrigation practices
following the construction of the Aswan Dam in Egypt caused waterlogging of the Nile
Delta leading to the I902 cotton crop failure. In Pakistan. it took 568 tube wells. 2.370
wells and 1.790 kilometers of installed drains to reclaim 1.040.000 ha of land. Prior to this
initiative. an estimated 20.000 to 40.000 hectares went out of production annually as a result
of salinity and water logging (White House. I964; Cantor, I970).

Within a few decades of inigation in the San Joaquin and Imperial valleys (California)
[21.000 hectares of land became unproductive. Salt accumulation was to blame (Harris.
[920). Other areas included the Great Basin. Colorado. Rio Grande River and Columbia
River basins. Taylor and Aschroft (I972) cited increased salinity. low permeability
(inﬁltration) rates and soil structure deterioration in the Salt River Valley of Arizona as an
ancient evidence of unsatisfactory methods of water application-

The few cited examples clearly portray what can go wrong with poorly managed
systems- The Punjab irrigation system (Falcon and Gotsch. I971) where poor management
led to increased soil salinity stands out as one of the modern examples. In Idaho. Carter
( I980) estimated the total quantity of salt leached from a ﬁve meter deep Portneuf silt loam
at 70 metric tons/ha; the ﬁrst 14 cm of water passing out of the bottom of the soil carried 38
metric tons/ha of soluble salt into ground water over a two year period. Concern for the
environment has prompted van Schilfgaarde ( 1994) a prominent irrigation scientist to write:

Irrigation has made major contributions in the past. continuing through this day. to
feeding the world and to rationalizing the use of limited natural resources for the
common wealth: but in the process. warts have arisen and inequities have appeared

8

and unneeded insults to the environment has: occurred-
Every rose has a thorn. but the eareﬁil harvester never gets hurt- Irrigation should and ought
not to be self destructive. Society's inability to control management practices can render

irrigation systems destructive.

3. Irrigation and resource development

Irrigation relates to water resource development- James et al- ( I982) have noted that
“rarely is one farm an independent unit of inigation“ since bringing water to the farm and/or
draining the excess from the farm requires cooperation that begins with the farmer.
community and then extends to the river basin. Depending on the size and location of the
irrigated area. this can extend to national and international levels. Examples include the
Colorado River ﬂowing through a vast irrigated land in the United States into Mexico and
the Nile river rising from Ethiopia through Sudan and Egypt

In a given irrigation system. withdrawal rates that exceed recharge rates. according to
Hillel (I987). eventually deplete the source and even deprive the crop of water when it is in
most need. An irrigation system without proper drainage may become unsustainable-
Excess drainage is a potential environmental hazard Consequently. proper irrigation control
should begin at the source: groundwater. river or lake-

Irrigation is an integral part of resource development and it is a human exercise and
social endeavor (in communal systems) rather than an academic exercise. Hillel (I987) in
this regard considers irrigation projects as a place for a community of people to work

together while leading healthy and harmonious lives. This requires designing a system

9

beyond the purpose of crop production; it takes food and a clean environment to live a
healthy life.

Human beings, with their intelligence. creativity and initiative. are an important resource
in development. I-Iillel (I987) notes with regret that irrigation managers in communal
systems tend to be authoritative. and often neglect the real players of the game. Most
systems in North Africa and Asia are designed and operated by engineers for the
convenience of engineers with limited attention to the needs and desires of the farmers (van
Schilfgaarde. I994). The same can be said of the economic and agronomic aspects of
irrigation management- An essential resource is wasted if humans are deprived of the ability
to use their senses in their work. Hillel points out that people tend to cherish. and are more

careful with the products of their initiatives or where they are participants.

8. Systems theory and irrigation management

Irrigation is not an end in itself: it needs coordinated management of economic and
environmental problems. The complexity of the irrigation-farm-environment system. in
addition to uncertainties in a political and socio-economic situation call for a systems theory
application to irrigation management. Systems theory and analysis have been used
extensively in the physical sciences; its application in agriculture. particularly irrigation. is
a new and rapidly developing investigative tool (ICID. I980; Carruthers and Clark. I98 I;

Holy. I981).

IO

I. System concepts

A system is a hierarchical structure with a deﬁned boundary consisting of inter—related
components (single functioning units) that act together to achieve a Speciﬁed objective
(Ogata. I978). Its overall behavior is inﬂuenced by changes in any system component.
The boundary can either be natural or artiﬁcially ﬁxed by the investigator in conformity with
system objectives (ICID. I980) and the magnitude of complexity the investigator is willing
to tolerate. A system boundary. according to Rountree (I977), should not be regarded as
rigid lines: rather. as grey bands whose factors have diminishing effects on system
behaviour. The system concept can be extended to various phenomena (Ogata. I978)
including irrigation management (Vang and Barney. I994: Carruthers and Clark. I981;
I-Ioly. 1980.

Every system has input(s) and output(s). A system input is that factor which stimulates
a change in system behaviour. Two types of inputs are recognized. The ﬁrst type.
exogenous or environmental input is determined by factors completely independent of. or
external to the system. Weather is an example of an exogenous input in a farming system.
The second type. endogenous or controllable input is used as a means of altering system
behaviour in a desirable direction. For example the number of seeds per hectare. or volume
of water in a given period.

System output is a factor caused by a given system- It can either be used as an input into
another system or used as a performance measure of the system- A system can produce

desired and undesired outputs. The desired output is a means of satisfying a system goal

whereas the undesired output is that unwanted side effect produced by a system in the cause
of satisfying intended goals. The most challenging practice for managers and farmers is to
balance between the two in a proﬁtable manner-

A system can be characterized as dynamic or static (Ogata. 1978). In a dynamic system.
variables change with time as a result of changes in inputs and interactions among system
elements. Manetsch and Park ( I993) refer to such. as a system with memory because its
outputs depend on previous values of input variables. The output of a dynamic system
changes with time if it is not in a state of equilibrium (Ogata. I978). A static system has no

memory i.e. its output is independent of previous input variables and remains constant if its

input does change-

2. Systems theory and approach

Systems theory provides a problem solving tool in which the inter-relationships of each
part of the problem in a component is considered as well as the inter-relationships among
objectives. and the means of realizing them (ICID. I980). This. according to Chestnut
( I966). involves the overall consideration of various methods of accomplishing desired
objectives as an integrated whole where each component is designed to achieve a common
goal. Thus. a complex problem can be composed of a series of precise and speciﬁed
component tasks for solution while maintaining the unity of the system.

Manetsch and Park (I993) deﬁne systems approach as:

a problem solving methodology which begins with tentatively identiﬁed set of needs
which are acceptable or "good" in light of trade-0173' among needs and the resource
limitations that are accepted as constraints in the given setting.

[2

This approach overtly seeks to include all factors which are important in arriving at a ”good”
solution to the given problem. It also makes use of quantitative models. Most often.
simulations of these models assist in making rational decisions. Simulation involves the use
of a computer program or the functioning model of a system on which different design and
management strategies are tried.

Figure l is a summary of the systems approach as a problem solving methodology. Each
of the boxes represents a major phase of the approach- Although the arrows are
unidirectional, it is important to note that each phase is an interactive decision making
process and is composed of sub-phases. A global view of these phases will be discussed
followed by a detail look of the modeling phase. The discussion is based on the six major

phases of systems approached identiﬁed by Manetsch and Park ( I993).

 

 

 

 

 

 

 

 

 

 

 

 

 

Needs Analysis .
I .44 Implementation
Feasibility Evaluations V
Y System Operation
Modeling V
System Retirement '
V
Implementation Design :——-

 

Figure 1. Systems approach to problem solving (adapted from Manetsch and Park.
I993 ).

The approach begins with a needs anabsrls which takes into consideration the needs of

every one as well as institutions which will be involved with the proposed system. It

[3

involves interactions with policy/decision makers. managers or operators responsible for the
performance of the system. Needs analysis can be accomplished through surveys, polls,
expert Opinions and evaluation of working systems similar to that under study. If a need
exists. an explicit statement is made and this forms the basis of feasibility evaluation.

In the feasibility evaluation phase a set of feasible system conﬁgurations or management
strategies capable of satisfying identiﬁed needs are generated. It is important at this stage
to differentiate between needs and wants. A eateﬁrl analyst should question: do these needs,
in fact. exist? lfthey do. can they be stated in an operational form? This phase formulates
an explicit statement of the problem to be solved based on the identiﬁed needs.

Modeling is based on the speciﬁcations for system design or management strategy from
feasibility evaluation. In the modeling phase. mathematical models of the system
alternatives are constructed. if possible. Models are usually implemented on computers4
and validated (See System modeling below). These models are used to explore possible
trade-oﬁ's among performance criteria. assist decision and policy makers in arriving at
normative judgments about what is good or bat (Manetsch and Park 1993). This eventually
leads to the creative synthesis of better system design and/or management strategies.

Implementation design specifies the details of the system and/or the management
strategy desigied in the modeling phase. Manetsch and Park stress a "complete”
speciﬁcation of the details i.e. developing a complete set of instructions that will lead to the

operation of the desired real system. This phase also involves the complete speciﬁcation of

 

{VWQl/comptaer model: may not be possible in some cases.

14
the system structure. required data. statistical analysis. communication channels to decision
makers. etc.

The implementation phase gives physical existence to the desired system in which
management designs are brought into existence. Deﬁciencies and errors of implementation
design are detected and corrected through repetition of implementation design.

System adequacy is tested or determined in the system operation phase. In most cases.
operation reveals additional deﬁciencies that were undetected in the previous phases. It also
involves an on-line management control since it is here that management strategies
developed in the earlier phases are implemented. System theory requires that this phase be
periodically reviewed and improved upon by repeating previous phases of the systems
methodology.

The last phase of systems methodology is system retirement. This is often ignored in
most system analyses (Manetsch. personal communication). It is important to realize and
include this phase in all systems analysis. This phase requires answers to such questions as:
what happens to system components when the system is dysfunctional or has reached the end
of its economic life? Will the retired components or replaced parts pose an environmental
hazard? How long can the system operate before it is retired. and would it have made any
beneﬁcial economic returns? Such questions are an aid to deﬁning the structure of the

system.

a. System modeling

System modeling involves the representation of a given situation. It consists of
developing a mathematical model of a system suitable for operation on a computer. Dent
(1975) regards modeling as a technique with which to apply and extend astems thinking.
In its deveIOpment. Wright (1975) advises that the starting point should be a very simple
input-output model which can later on be expanded in detail with the following
identiﬁcations: major subsystems. important components and relationships within each
subsystem. links between subsystems. important environmental variables and control points.
A resulting conceptual model provides the basis for identifying the type and form of data
required.

The modeling task takes on two approaches. The ﬁrst is called the black bars approach
(Manetsch and Park. [993) where inputs and outputs can be observed and measured. but the
process of transforming inputs to outputs remains unknown or is of less importance to the
user. This approach seeks to identify a system model from data that describes the behaviour
of the system. Using various mathematical relations and statistical techniques a model is
derived as the best ﬁt to the Operational data Most of the work done in various engineering
disciplines employs the black box approach.

The second is the structural approach which begins with a careful examination of system

structure and theory to determine basic system components and linkages. An overall system

S‘Vright uses the term Black Box to refer to an Mann. though stable and independent grouping o/detail.

16

model is thus developed by modeling the characteristics of the system components and the
constraints imposed by its components. The structural approach has been used in the design
and control of both physical and non-physical systems (Mintzberg. 1976; Manetsch and
Park. 1993). Both approaches are complementary to each other and models developed from
both approaches generally give better results (Manetsch and Park. I993).

Application of models in systems research can be distinguished into two categories:
descriptive and normative (Wright. I975). The model. when used for descriptive purposes
becomes a framework for identifying system components and relationships as well as
determining the satisfactory functional relationships. The normative application requires
some objective function to evaluate different decision mles. Such functions are often

concerned with proﬁts or utility.

b. Modeling procedure

 

 

 

 

 

 

 

 

 

 

 

Six major steps (boxed) can be Feasibility Evaluation
J +1 Sensitivity Analysis .
identiﬁed in system modeling Concept Selection 5 ' Y
and Modeling '
. . - ‘ - Stability Analysis
(Frgure 2). The input of a modeling y
Model Veriﬁcation l ' Y . .
phase comes from feasibility V “‘4“ ”Wan“
. . - - 5 V
evaluation. A selected concept is 54““ "mm“ -"“ Implementation Design

 

modeled in the form of equations.

Figure 2. System modeling procedure (adapted from
block diagrams. flow charts. etc. Miami! and Park. 1993).
and implemented on a computer- This phase involves important decisions that affect the

accuracy of computer solutions. operational costs. coding language. model compatibility

17

with available computers and other soﬁware applications. speciﬁcation of model inputs. etc.
Once the model is implemented and the input-output formats are designed. the next step is
to verify that the model does indeed simulate the underlying situation. To verify means to
establish the truth. accuracy or reality of something Thus. a model is veriﬁed in relation
to absolute truth. Although one may not establish a fact with absolute certainty. hypotheses
can be tested in terms of the probability that they are true (Naylor and Finger. I967). The
process of veriﬁcation includes cross checking model results with hand calculated results.
and numerical with analytical results for agreement.

Validation is often a link to an iterative loop that leads to successive tests and reﬁnement
in a model. If the model describes a controllable system. validation must demonstrate that
the model exhibits behaviour that characterizes the system (Manetsch and Park. 1993 ). This
is achieved through reproducing past system behaviour or independent data that were not
used in constructing the model. Neter et al. (1990) state two ways of validating a model:

I. use new independent data to check model and predictive ability.

2. compare results with theoretical expectations. earlier empirical and simulation

results.

For non-existent systems. eg. using a model to design a new system. the validity of
developed model relies on the validity of the various theories and assumptions which
determined the structural form of the equations of the model (Manetsch and Park. 1993) and
the values assigned to model parameters. It also relies heavily on subjective judgement.
preferably involving the decision maker. Validation can lead to further information

gathering. data collection improved estimates of coefficients and reﬁned models. A crucial

[8

question to answer in validation is whether the model leads to better decisions than can be
obtained from using other techniques.

Sensitivity is deﬁned as the rate of change in one factor with respect to another
(McCuen. 1973; Wyseure. [986) or the change in an objective function due to perturbations
in the value of a parameter (Beck and Kenneth. I977). Sensitivity analysis determines
which decision variables (design parameters and controllable inputs) are important and
worth including in model applications. Knowledge of model parameters of lesser
importance in affecting system performance can provide additional freedom to satisfy the
necessary constraints which may apply to inputs and parameters.

Stability analysis identiﬁes the stability boundaries of the system such that critical
parameters will not be unknowingly set at values which could lead to unstable behaviour
over time as system structure or environment changes. Stability analyses employs analytical
studies based on stability theory and use of repeated simulated runs to explore stability
boundaries.

Model implementation. also referred to as experimentation. has the purpose of
comparing various treatments under exactly identical conditions. Wright gives four
objectives of model application: i) compare alternative courses of action. if) estimate system
response to changes in the level of single inputs. iii) explore the response surface generated
for diﬁ‘erent combinations of input levels. and iv) estimate the input combination required

for an optimal or minimal level of output

 

 

 

l9

3. Rationale for application to irrigation management

[CID ( 1980) offers the following justiﬁcation for employing systems theory and analysis

in irrigation management.

to

It is useful when required data for solving a problem cannot be obtained directly by
observation.

[t permits the combination of strictly scientiﬁc approaches with common sense.
subjective opinions. evaluations. intuition and experience for decision making.
Manetsch and Park (1993) have used this concept in developing a systems problem
solving procedure.

Manipulating individual components can achieve maximum effectiveness for the
whole system.

It‘s an excellent decision tool in the phase of uncertainty where the decision or policy
maker can choose a line of action based on desired objectives and quantitative

comparisons of alternative solutions-

The fourth justiﬁcation ﬁnds application in a natural resource system (Figure 3) where

farmers attempt to control the soil water content in an uncertain environmental and

economic condition to achieve high yields while suiving to minimize environmental

degradation Harding ( I968) recognized the conﬂict between environmental and economic

goals and wrote:

The great challenge facing us now is to invent the corrective feedback that are
needed to keep custodians honest. We must ﬁnd ways to legitimate the authority of
both the custodians and the corrective feedback:-

20

In light of the above statement. one is tempted to call for an immediate and abrupt change
in our goal philosophies. But this is unlikely to happen over night Thus. Street ( l 990) has
suggested developing transition strategies based on the laws of thermodynamics and entropy.

This can be done through systems analysis.

4. Application to irrigation management

A typical natural resource system

1" \..
1’

 

comprises the environment . ”meme“! .

 

management. soil and irrigation system A

‘ . . .
; Irngeuon Farm %——’

 

(Figure 3). The environment provides

 

Pollutant:
. Environment LL/

The soil provides the basis for \\_’/

agricultural production. Management

conditions for existence and survival-

1

Figure 3. Natural resource system
controls the produce from the farm.

irrigation and the soil tluough tillage and the use of soil conditioners. It is important to note
that there is no control over the pollutants. yet they enter the environment which is the major
input source for the soil and irrigation- In our current drinking management practices and
economic analyses are conﬁned to the components above the broken line. Our ultimate
desire is to erase the line and have direct control over the pollutants in the system (i.e..
redirect the arrow that links management and produce such that management can control

both produce and pollutants).

2|

Figure 3 shows the management and environmental components as a dynamic function
of goals. information feedback and control. It can be considered an open system because
of the constant exchange of material. energy and information. Information provides the
manager with the state of the system based on observed inputs and outputs. The goals in
combination with these observations provide a framework for decision making i.e. system
control. The result is a set of formulated decision rules for system operation which
constitutes a management policy that is tactical or strategic (Wright. I975). One advantage
of the systems approach is that the irrigator can have both tactical and strategic goals (soil
water levels. salt contents. groundwater quality. etc.) for managing irrigation. soil and the
environment- In addition. solution sets that are feasible and efficient according to technical
and economic criteria are identiﬁed for the decision maker to compare and pass judgement.
Sufﬁce to note that farmers' practical applications of recommended practices tend to be
governed by ﬁnancial cost considerations.

The ellipse in Figure 3 tells us that nothing leaves or enters the system. Thus. we have
to be careﬁtl in pursuit of our production goals. Serious long term implications can result

in pursuit of short term economic goals. Doyle (1990) cites a Punjab irrigation study

(Falcon and Gotsch. I971) where such pursuits have led to increasing soil salinity.

C. Irrigation performance measures
Irrigation water distribution in the ﬁeld can either be measured directly or inferred from
overlapped sprinkler patterns (Hart and Heerrnann. I976) using distribution functions.

Various functions for such inference have been presented (Heermann et al.. [992; Warrick.

22

I983; Elliot et al.. I980; Hart and Heermann. I976). Most of these functions require
knowledge of the mean application depth. its standard deviation and the shape of the
distribution.

Irrigation performance measures are a way of characterizing system behaviour from
several estimates of irrigation depths at various locations. These measures determine the
degree of water replenishment in the root zone at each irrigation. the amount of runoff
and/or deep percolation and the uniformity of the applied water during irrigation
(Rauschkolb and Homsby. I994). There are at least ﬁve performance measures in the
literature (Kruse I978: Shearer. I978). This review focuses on distribution uniformity and

application efficiency as measures of irrigation uniformity and efficiency.

l. Irrigation uniformity

Irrigation uniformity refers to the variation in the amounts of water applied to locations
within an irrigated ﬁeld. Ideally. an irrigation system should apply water such that all parts
receive equal amounts. The absence of an ideal system means that some parts of the
irrigated ﬁeld receive more water than others- On one hand. if the ﬁeld is irrigated such that
all parts receive the required or desired amount. then some parts will be over irrigated. On
the other hand. if only part of the ﬁeld receives the most irrigated water to meet the required
depth. then under-irrigation will occur in some areas. Irrigation uniformity is therefore a
measure of the degree to which water is unifome distributed to the ﬁeld. There are at leasr

eight proposed ways of characterizing uniformity in the literature (see Uniformity measures

23
and coeﬂicient below). Subsurface (Hart, I972), local and global (Solomon. I983, I985)
uniformities have been described.

Local uniformity as stated by Solomon. is limited to portions of an irrigated area in a
ﬁeld (e. g. the area between four sprinklers: the area of a furrow or border strip (for surface
irrigation) or a lateral (for trickle irrigation). Global uniformity involves full ﬁeld scale
factors that are often not included in local uniformity studies (e.g- ﬁeld wide pressure
differences and edge effects in sprinkler irrigation). Hill and Keller (I980) estimated that
differences in ﬁeld wide pressures and sprinkler edge effects account for twenty percent
reduction in the uniformity coeﬁ’rcient.

The areal distribution and uniformity of water application has been used to characterize
uniformity of soil water in the root zone. I-Iart ( I972) compared the uniformity of applied
soil water and concluded that sub-surface redistribution (horizontal) approached a ﬁnal value
(85%) with time. Cohen and Bresler (I967) attribute subsurface redistribution to horizontal
matric gradients that are established in non-uniform distributions to compensate for areas
with less water. However. Sinai and Zaslavsky ( I977) found that both surface and sub—soil

characteristics can cause non-uniform sub-surface redistribution-

a. Inﬂuencing factors

Soil characteristics inﬂuence water flow over the soil surface and its inﬁltration into the
root zone thus. affecting uniformity. Brakensiek et al- ( I98I) reported variability of soil
inﬁltration characteristics even within a given textural class. In furrow irrigation. Hill and

Keller ( I980) have observed differences between wheel and non-wheel furrows- Ley and

24

Chyma (I98 I) reported a range of S - 15% standard deviation of the mean flow in furrow
ﬂow rates. Pressure variations within a pipe or resulting ﬁom ﬁeld elevation differences and
hydraulic characteristics of emitters also contribute to irrigation non-uniformity-

Initial soil water content plays a signiﬁcant role in subsurface uniformity. Redistribution
is most rapid at high water content gradients. Uniformity however. approaches a limit which
would n0t be exceeded in a reasonable length of time (Hart. I972). In one study Hart
showed that two systems with surface distributions of 60 and 70% attained a subsurface
distribution uniformity of 85%. The time taken to attain the ﬁnal value was shorter in the
70% than in the 60% system. The author then concluded that the ultimate useﬁrl distribution

might be high irrespective of the initial surface distribution.

b. Uniformity measure and coefﬁcient

All irrigation systems possess some non-uniformity in water application. Since [00%
uniformity is economically unfeasible. irrigators must accept less than ideal uniformity in
operating their systems. This calls for a performance measure - uniformity coefficient - for
assessing the uniformity of water application in irrigation systems- A review of some of the
measures follows.

Christiansen (I942) deﬁned and used the ﬁrst uniformity for sprinkler irrigation as:

Uc =[1 - M] 100 [ll
AV"

where Uc is the Christiansen uniformity coefficient; le; - ul is the sum of the absolute

difference between each measured value (x.) and the mean (u); N is the number of

25
observations. The author selected 84% as the minimum acceptable level of water
distribution for any particular irrigation method.

Dabbous (I962) cited a second coefficient developed in 1955 based on a range of

estimated water depths. The mathematical representation is given by [2]

- 2(tr - L)
”a ‘ TIT ‘"

where H and L are the highest and lowest values of irrigation depths respectively. The
coefﬁcient uses the mid point of the range as a measure of central tendency. Solomon

( I983) reported a modiﬁcation of equation [2] given by Rainbird Sprinkler Manufacturers

 

Us 2 [3]

where u is the mean applied depth and H and L as previously deﬁned.

A third uniformity measure came into the literature in I947 (Wilcox and Swailes) as

U,=1-9—=t-cv [4]
u

where c is the standard deviation from the mean applied depth. u. and cv. the coefﬁcient of
variation. This coefﬁcient has also been referred to as the Wilcox-Swailes uniformity (Su.
1979) or the statistical uniformity (Bralts et al.. I981). The measure found application in
the development of combined statistieal uniformity measures or variance equations in drip

and surface inigation (Bralts et al.- 198 I: Iaynes and Clemmens. I986; Clemmens. I99I).

26
Another uniformity coefficient which makes use of the standard deviation but based on

a normal distribution of irrigated depths introduced in I965 (Hart and Reynolds) is

U =1-o.193 av [5]

Solomon (I983) lists two advantages of equation [5]: (i) it makes use of the standard
deviation of the data in the same way as equation [4] and (ii) its numerical value in most
instances is similar to Christiansen's uniformity coefﬁcient. equation [I]. The two equations
are numerically equivalent for normally disuibuted irrigation depths. UH has also been
referred to as the Hawaiian Sugar Planters Association uniformity coefficient

In I964. Benami and Hore proposed the "A" coeﬂ'rcient and deﬁned it as

M. - MD,

A = I.66
M. - MD, [6]

where M, and Mg are respectively the mean depths above and below the mean application
depth. and the MDs their respective mean deviations. According to Solomon ( I983) the
signiﬁcance of [6] has not been recognized and its later use in the literature is limited to
those works reviewing it or comparing it to other measures. Hart and Heermann (I976) see
"no particular advantage" of using equation [6] in place of "other established distribution
parameters". probably because of the complicated use of the absolute deviations.

Karmeli ( I977. I978); Karmeli et al. (I978) formulated a uniformity coefﬁcient similar
to Christiansen's but based on the linear cumulative distribution function for sprinkler

irrigation depths. equation [7].

U: = r - 0.256 [3 [TI

where B is the slope of the cumulative distribution line. This measure has been used in
optimal irrigation scheduling to minimize deep percolation.

The Soil Conservation Service (Dabbous. I962) proposed pattern efficiency (PE) as a
measure of uniformity deﬁned as the ratio of the mean of the low quarter irrigated depth to
the mean depth. The term efﬁciency may be misleading as this measure does not assume

a management scheme. Hart and Reynolds (I965) suggested a statistical version of PE as

DU = I - l-27 cv [8]

where cv is the irrigation system’s coefﬁcient of variation. For a nortnal distribution. the
mean of the low quarter is approximately 127 times away from the standard deviation below
the mean (Solomon. I983). Thus the numerical value from the SCS deﬁnition and [8] are
equal so long as the irrigated depths are normally distributed. PE has been referred to as
distribution uniformity (Kruse. I978) or trickle emission uniformity (Hill and Keller. I980;
Keller and Karmeli. I974a).

Keller and Karmeli (I974b) further suggested an "absolute emission uniformity".

equation that includes the average ratios of maximum and minimum emitter ﬂow rates.

EU. = LP: . 3-1] I00 [9|
2 q. q.

E
where qu = average of lowest one-quarter of emitter flow rates; qll = average of all emitter
flow rates and q. = average of highest one-eight of emitter ﬂow rates. The authors
recommended a design EU greater than 90%.
The On Farm Irrigation Committee (Kruse. I978) recommended distribution uniformity

(DU. equation [8]) and Christiansen's uniformity (Uc, equation [I ]) as uniformity measures.

c. Uniformity interrelationships

Warrick ( I983) presented analytic relationships between Christiansen's uniformity [I],

distribution uniformity. [4]. and the coefﬁcient of variation for six statistical distributions-

These were generalized as:

U'=l.l3cv; cv<0.2$

Uc-I-O.8cv; cv<0.$

DU = -0.6 + 1.6 U... cv < 0.25

In addition. the author tabulated exact analytical relationships between cv. equations [I] and

[8] for the normal. log-normal. uniform. specialized. beta and gamma functions. Other

relationships include:

Ur - 0.985 Uc - 0.011 [13]

Uc = 0.958 U” - 0.030 [14]

U, : 0.020 U:- - 0.920 Uc - 11227 [15]

29
Equations [13] through [IS] are from Karmeli et al. (1978). Hart and Heermann (I976) and
Seniwongse et al- (l972) respectively.
Hart and Heermann ( I976) expressed difﬁculties in evaluating real distributions due to
scarcity of data points for analysis. One constraint is the cost of collecting these data sets.

This may explain why most uniformity studies tend to be local rather than global.

2. Irrigation efﬁciency

The term eﬁ’tciency presupposes 0r assumes a management scheme and is generally
understood as a measure of an obtainable output from an input. Efficiency of an irrigation
system practically relates to the consumption of the available resources. Low efficiencies
indicate excess water not used by plants. The lost can be reflected in the pumping cost of
water. Irrigation efﬁciency is constrained by natural resources. applied technology. human
behaviour and socio-economic conditions (Thompson. I988). Thus. efficiency can vary
from place to place and from one farm to another in the same region.

Different concepts and deﬁnitions ofeﬂiciency (Table I) have been used to evaluate the
efficient use of water. Robinson (I978) lists six components included in the evaluation of
irrigation efﬁciency: the water applied. soil and water quality. energy consumed. labour.
investment/return on investment and net production. The 'On F arm Irrigation Committee'
(Kmse. 1978) deﬁnes irrigation efﬁciency as the ratio of the average depth of irrigation
water beneﬁcially used to the average depth of irrigation water applied. This deﬁnition is
rather ambiguous as beneﬁcial use can cover a wide range of activities ranging from salt

leaching, crop needs. pesticide or fertilizer application. etc. Some authors have limited

30

 

 

 

 

 

 

 

 

 

 

 

Deﬁnitions of efﬁciency
Title Deﬁnition: Ratio of .. Source
I . Application efﬁciency a) water in root zone to water delivered to ﬁeld. I
b) volume of irrigation water manned by crops in I
an irrigated area to volume applied in area plus I
volume for intentional leaching.
c) b) + correction for effective rainfall. l
d) net inches required to replace soil moisture in root
zone to inches applied-
e) useful water volume to total volume delivered. 3
0 Product of tmiformity coefﬁcient and system 4
efﬁciency.
2. Application (pattern) average low quarterdcpth of water inﬁltrated and 5
efﬁciency of low quarter stored in the root zone to the average depth of
water applied.
3. Consumptive use normal consrnnptive use of water to net arnotmt 6
depleted in root zone.
4- Inﬁltration amount of water inﬁltrated to applied. 7
5- Irrigation application percent of irrigated water stored in soil root zone. I
efﬁciency
6. Irrigation efﬁciency a) volume of irrigation water eonsrnned by crops in I
an irrigated area to volume applied in area.
b) ET of applied water to norm! of applied water. 8
7. Optimum irrigation maximum yield value to seasonal water applied. I
efﬁciency
8. Storage efficiency a) quantity in root zone during irrigation to amount 9. I0
needed in root zone prior to irrigation.
b) water stored in the root zone a percent of total I I
applied-
9. Water distribution a) absolute average deviation to mean depth I0
efﬁciency b) average low quarter depth of water infiltrated to
average depth of water inﬁltrated the quarter of the
area receiving the least amormt of water.
IO. Water use efﬁciency a) dry weight of crop to ET depth. I I

water beneﬁcially used to amount delivered.

I = Aljibury. I978: 2.3 3 Robinson. I978: 4 = Kimbcll et al.. I990; 5 = Krnse. I978: 7 2-
Tsakiris- I985: 9 = Anyoji and Wu. I994: 6.8.I0 = RauschKolb and Homsby. I994: II =

lsraelson and Hansen. I967.

3|

beneﬁcial use to crap needs. The argument as to what constitutes beneﬁcial use in addition
to a lack of Speciﬁcs in deﬁnitions makes the comparison of irrigation efﬁciency in different
regions or cultures rather illusive.

In order to make an unbiased comparison of system performance, it is imperative that
the deﬁnition of irrigation efﬁciency be agreed upon. Such a deﬁnition should be
comprehensive enough to warrant use in all available situations and "include some objective
characterization of the beneﬁts of using the established relationships between the input

variables of the irrigation system considered” (Y itayew, I987).

0. Application efﬁciency: definition and signiﬁcance

Figure 4 shows the distribution (curved line) of applied or inﬁltrated water in a soil
proﬁle and four regions (A A0, B and C) that describe an irrigated proﬁle. The average
depth of applied water is represented by the broken line at which half of the ﬁeld receives
more than the average and the other half less than the average. The root or required depth
or minimum application ratio, RA (Chaudhry, I978) is shown by the horizontal solid line.

"A" is that fraction of the ﬁeld or met volume that would received at least the required
depth at the. end of an irrigation period. while "AD” (I - A) is the deﬁciently irrigated
portion. The average depth inﬁltrated in A0 is DA. "B” is the fraction of the soil proﬁle that
has not received any of the irrigated water: it is interesting to note that a portion of this
proﬁle belongs to the root zone. "C" represents the soil proﬁle receiving the excess water.
Efficiency deﬁnitions (e.g. storage, leaching and application) relate to one or more of the

described areas of Figure 4.

32

Area fraction

0.0 0.2 0.4

0.6 0.8 1.0
0.0 W,, .. ..

I I I 1 I I I

 

 

 

 

 

” l
AD
- A : doficitly .
Am _ fully irrigated area . im-gamdﬁ
> /
)9 0.5 '— al., ---4
- . /.._..... V0
53 [JA ' m (moored) am , ’ ‘ average depth
In ' 3 ‘ In An
2 D- // cl
., ,x' non-Irrigated area
4
2‘ 1.0 _--_\rem-22ﬂ£l_%/_,.z _________ __.
u .. 6.. ’1’, 4
3 0’45“
= . 6\ ‘05
I! v- 9 -' ..
Q. / 9‘
E 0* ‘
L. 1 .5 — / -1
O _ ’ ‘
C ,'
..I
2.0 4411114114411_1_1111111111

Figure 4. Application eﬁ'rciency deﬁnition sketch.

ASAE (I 993) deﬁnes application efficiency (AE) as the ratio of the averaged depth of
irrigation water inﬁltrated and stored in the root zone to the average depth of water applied.

expressed as a percent. The deﬁnition can be expressed in terms of areas in the ﬁgure as

..‘LZL‘LL
Ar-AD‘C

[15]

Application efﬁciency is one of the most predominant indices for comparing
management practices (Lamack and Niemiera. I993), irrigation. cropping and tillage
systems (Yonts et al.. [991). As an important index in evaluating an inigation system.

application efﬁciency indicates the excess water applied to the ﬁeld (Walker. 1979). This

33
would include the amount lost to deep seepage and run off (Clemmens. I991; Tsakiris.
1985).

Application efﬁciency can be used to make an economic judgement on proposed
installations of various systems (Chaudhry, 1978). Furthermore, it describes the effects of
both management decisions and operational characterisﬁcs of an irrigation system (Shearer.
1978). Poorly managed inigation systems result in excess water loss as deep percolation
from the root zone. Lost water is costly to inigators and posses an environmental hazard.

Applieation efficiency is a function of a system’s Operational time (Y adav et al., 1986)
or the gross depth required (Chaudhry, 1978), as well as indicates the potential available
water in the root zone to plants. (von Bernuth. I993; equation [17]). Estimates of
application efficiency in addition to seasonal ET can be used to determine seasonal water
budgets and as a guide for irrigation management. High AEs will require low water
amounts regardless of the ET (Rauschkolb and Hornsby, I994)- Kimbell et al. (1990) have
derived water requirements for sprinkler irrigated alfalfa from application efficiency.

Nitrogen fertilizer is an important plant nutrient. Because its fate in the soil is
unavoidably linked to that of water (Rauschkolb and Hornsby, 1994) there is a need to pay
closer attention to the question of application efﬁciency in irrigation management. The
concentration of nitrogen near the soil surface (when ammonium is applied) and the amount
of nitrate leached are proportional to the quantity of water applied at that location or leached
out of the root zone.

Applieation efﬁciency gives no indication of the adequacy or uniformity of the system

(Walker. 1979). For example one can achieve a 100% efficiency with severe under—

34
irrigation (Anyoji and Wu, 1994) even with poor uniformity (Shearer, 1978) or in cases

where deep seepage is considered beneﬁcial.

0. Inﬂuence on application efficiency

Several factors signiﬁcantly influence application efﬁciency: the rate of root
deveIOpment and the active root depth; the inigation method; the required amount of water
to recharge the depleted soil proﬁle. and soil type. Assuming the same system duration and
application rate. sandy soils will have a lower AE than clay soils. since larger amounts of
water will leave the sandy root zone during irrigation than in the clay soil.

Low AE values under shallow rooted crops. or continuous irrigation early in the growing
season when the crop canopy does not cover the entire soil surface and the root system is
limited to around the crop. This is because irrigating the entire surface results to massive
evaporative loses (Y adav et al.. I986). In addition, any inﬁltrated water in non-rooted areas
eventually ﬁnds its way below the tilled layer as deep percolation.

Application rates greater than the soil's intake rate distort the surface distribution pattern.
Low Spots where water accumulates or passes are over-irrigated and will have low AE.
High spots from which water runs off will receive less water and consequently low AE
(Taylor and Aschroft. 1972). In addition. Till and 805 (1985) mention uniformity and the
amount of water leaching (deep seepage) including wind (Seginer et al-. 1991) as some of

the factors that influence application eﬁ'rciency.

35

c. Application efﬁciency relations

There exists a relationship between AE and crop available water (von Bernuth; 1993):
4
AW = —"— AE [ 17]
"I

where AW = available water, d“ = net depth of applied water and m = mean application
depth. Hart and Reynolds (1965) developed tabulated relationships between application
efﬁciency, application ratio and coefficient of variation (cv) based on a Gaussian distribution
of inﬁltrated depths. (They deﬁned application ratio as the average depth of water at the
point of lowest application to the average depth required.)

Chaudhry (1978) presented AE. analytically and graphically, as a function of the
coefficients of variation and skewness for various application ratios for both Gaussian and
gamma distributions. The relationship allowed for quantitative evaluation of skewness
effects. The author further showed a direct proportion between the average loss (I - AE),
deep percolation and cv when the depth of water required for adequate irrigation equals the
average depth supplied.

Howell ( 1964) using various asymmetries for the same cv showed a dependence of AE
on skewness. The results showed an increase in AE for positive asymmetry with a minimum
application ratio less than or equal to one and a decrease for negative skews with a minimum
applieation ratio greater than one. Chaudhry (1977) later conﬁrmed these results for ﬁxed
application rates.

Warrick et al. (1989) showed that as the amount of water applied increases the area. A.

fully irrigated increases and application efﬁciency decreases. They also noted that as the

36

coefﬁcient of variation for a given water level increases, both AE and A tend to decrease.
Their work contains tabulated values for ﬁve cuss of the specialized power, log-normal and
normal ﬁrnctions.

AB is a function of the application depth which may not necessarily equal the cr0p need
(Chaudhry, I978). Hillel ( 1987) noted that AB is a function of sprinkler uniformity rather
than soil properties so long as the application rate does not exceed the soil's intake rate. The
dependence of application efﬁciency on uniformity von Bernuth (1993) is the basis for

calculating application efﬁciency.

d. Application efficiency determination

Application efﬁciency determination is based on the amount of water replenished in the
root zone at a given irrigation, runoff, deep percolation and the system's distribution
uniformity. For a normal distribution of applied water depths. application efﬁciency can be
ealarlated by integrating the probability density ﬁrnction (Warrick et al., 1989; Anyoji and

Wu; 1994). One result from such a calculation is

A5 = I - (27!)'°5 cv e ”'5‘ ‘ Acv [18]

where cv is the coefﬁcient of variation for applied depths and A is the area receiving at least

the required depth. Another equation developed by Chaudhry, (1978) is

AE =1 - a; D‘(I — A) [[9]

37

where RA is minimum application ratio; D A is the average deﬁcit and "l - A" is the
deﬁciently irrigated area. The equations involve the normal distribution function which does
not have an explicit solution.

In recognition of this, Walker (1979) devel0ped equation [20] (from a polynomial that

estimates the Gaussian function) as a function of the area deﬁcitly irrigated and cv.

A5 = l - t 3.634 - 1.12311; + 0.003113” ) cv [20]

where AD is the area of the ﬁeld that is deﬁciently irrigated. The author discourages the use
of the equation when AD is below l0%; prediction errors rapidly increase to [0%.

Clernmens ([99 I) gives a similar equation that makes use of the area deﬁciently irrigated.

A R .(1 -A)U
AE= ° ° [le

MoeL

 

where A is the fraction of the ﬁeld that is adequately irrigated; R0 is the target or required
depth; U0 is average depth in the area less than RD; MD is the average depth inﬁltrated and
L represents surface losses as runoff. No associated errors are reported. The author has also

”ven tables that relate A5 to the fraction of the area with adequate and deﬁcit irrigation. and

storage efﬁciency.
Howell ( I964) calculated AE as
21:. - x) '

I
AE=—1--—-———— 22
t! z: [I

38
where :g is the minimum application depth on an area, a; p is the average depth applied; it.
is the various measured depths and "+" indicates the sum of positive deviations only. For

x1| = in AB was related to Christiansen's uniformity, UC, as

A5 : 0.50 + Uc) [23]

When the mean application depth equals the root zone depth. the maximum possible AE

when there is no over-irrigation is expressed as (von Bemuth. 1993)

A15 = [1 - 0.5(1 - (16 1100)]. [24'

Rauschkolb and Hornsby (1994) have summarized water application efﬁciencies for a
variety of crops. different locations and inigation systems. Although water application
efﬁciencies may vary from 30 to 90%. they noted small differences in application
efﬁciencies for well managed systems (70-85% in sprinkler systems. 70-95% for surface
level systems and 80—90% in drip systems).

The Soil Conservation Service (English and Nuss. I980) recommended a 65%
application efficiency. Some water districts require higher values. [n 1993 efﬁciency
requirements in the Southwest Florida Water Management District" were 75% and 80% for
existing and new permits respectively. Efﬁciency goals (irrespective of the type of permit)
have been set for 80% by 1997 and 85% by January 1, 200! respectively for row crops.

strawberries and citrus.

 

6 Water Use Permit Information Manual: Honda We Gide. Basis of review for water use per-nut
qppEarrions. and design aids.

39

Thompson (1988) evaluated l6 irrigation projects of the Bureau of Reclamation using
data from 1963 to 1984. Nine had AE less than 40%, four between 40 and 65%, and 3
above 65%. The author concluded that efﬁciency time patterns showed no evidence of
progressive improvement in efﬁciency. Two projects had statistically signiﬁcant trends and

both were towards lower efﬁciency levels.

e. Improving application efficiency

lzadi et al. ([991) presented two procedures for maximizing application efﬁciency in
surface inigation and suggest the use of a target depth. Decreasing the mean depth of
application increases AE but the area adequately irrigated is reduced (von Bemuth. 1993).
To increase the depth of water in an area with the least amount of water by x% would imply
increasing the total application by x%. This causes signiﬁcant increases in deep percolation
when the percent area receiving adequate inigation is increased (Kruse, I978). Higher
system efﬁciency increases AE as the amount of deep percolation decreases while the area
adequately irrigated is increased. This is constrained by the cost of installing and
maintaining a high uniformity system. von Bemuth notes that while it is technically feasible

to achieve [00% system uniformity, it is economically unfeasible.

[3 Global and local efficiency
in dealing with irrigation water efﬁciency, one distinguishes between global and local
eﬁiciency, to borrow from Solomon (1983). in global efﬁciency, it's the overall efﬁciency

of the watershed that is important while in local efficiency or on-farm irrigation efﬁciency

40

(Robinson, 1978) relates to the net amount of water applied per unit area from crop
consumption. According to global eﬁ'tciency advocates, users up stream need not wony
about efﬁciency; only the last user down stream should. This is because the excess water
re-enters the underground water and is pumped and used over and over again. Although
little water is lost in the process. maintaining water quality becomes a problem (Robinson.
1978). Except in communal systems, global efﬁciency is not economically efﬁcient or
beneﬁcial to the users up stream. Striving for global efficiency without caution may result

to an ecological disaster.

D. Summary and discussion

Inefﬁcient and non-uniform systems tend to waste water. nutrients and energy.
Management and system improvement allow for a high rate of application efficiency in any
given system. Soil and water quality are the most delicate to manage in an irrigation set up.
While we desire a high quality soil through proper leaching (removal) of salts from the soil
over the years. we do not want leaching to occur to the point where underground or
surrounding water contamination is likely to occur.

Resource exploitation, soil degradation, water resource depletion and pollution are
insidious trends of the past prevalent in today's society. Lessons from history show that
great losses. costs and consequences await us, unless there is an effort on our part to improve
irrigation management inigation agriculture should not be self destructive: it has supported
most areas through millennia and has been the economic basis of societies through recorded

history.

M

The design and management of irrigation systems contain more than the engineering and
agronomic inputs. Human, economic and environmental factors must be taken into account.
Many factors involved in crop production should and must be evaluated in an integrated
management system. This calls for a systems approach in irrigation - a missing link in
today's irrigation design and management practices.

In general, efﬁciency assumes a management scheme relating the output of a system to
its inputs. When used as a performance measure, the term provides a basis on which to
make decisions regarding system operations, which system components and to what extend
need adjustment It serves as a tool for comparing different systems. In irrigation
management, environmental efﬁciency will signify the level of potential pollutants entering
the environment.

Application efﬁciency is an important irrigation performance measure. Apart from its
indirect estimation using the equations in the section Application eﬂiciency determination,
direct ﬁeld measurement under sprinkler irrigation have not been documented. Furthermore,
there is a need to investigate the impacts of management practices on application efﬁciency
as well as the probability of such efﬁciencies under various management strategies.

Although there is wide recognition of the environmental concerns in irrigation
management. attempts to address those concerns still emphasize the single discipline
approach. There is a nwd to incorporate the systems approach in irrigation management and

provide the farmer with a tool to make environmentally sound decisions.

III. Research Procedure, Results and Discussion

.. when you cannot measure rt. when you cannot express it or numbers.
your knowledge rs ofa meagre and unsatisfactory kind. '
- Lard Keir-m -

This section is divided into two papers. written in the format of the Transactions of the
ASAE scientiﬁc journal. Each paper has an abstract. an introduction. speciﬁc objectives.
procedures. results and conclusions. Both papers are related. but can be read in any order
without loosing much content. The works cited in each of the papers can be found in Section
VI - References.

Paper A deals with application efﬁciency determination under various statistical
uniforrnities and applieation ratios- The results presented include the statistical distribution
of applieation efﬁciency. and graphical and mathematical relationships between application
ratio and system uniformity.

Paper 8 discusses. ﬁ'om systems theory. a method of characterizing environmental
eﬁiciency of irrigation management. A new performance measure in irrigation management
termed irrigation environmental efﬁciency is proposed and graphically related to other
commonly used irrigation measures. The measure is applied to some existing irrigation

systems and management.

 

sﬁsm and mung. n: Pairwise! Revrew. vol. \liii p. 134. 1934.

42

43

A. Estimating irrigation application efﬁciency and its statistical distribution

1. Abstract

A common performance measure in irrigation management is application efficiency
(AB). The popularity of this index prompts the following research questions: How does AE
vary with the applied depth of water under an imposed areal distribution? What is the AE
uniformity in a given setting? This purpose of this study was to determine the statistical
distribution of application eﬁiciency for a range of minimum application ratios (required
depth divided by the mean applied depth) - 0.4 to ll. Irrigation ﬁ'om center pivot systems
were simulated assuming a normal distribution function. A new term for characterizing
application efﬁciency. application uniformity (AU). is introduced based on a statistically
derived uniformity coefﬁcient. Regression equations relating AE to AU. minimum

application ratio and statistical uniformity are presented.

2. Introduction

One of the most commonly used performance measures in irrigation is application
eﬁiciency (AE). AP. is deﬁned as the ratio of the average depth of irrigation water inﬁltrated
and stored in the root_zone to the average depth of water applied. expressed as a percent
(ASAE. [993). Although some researchers have noted that this measure gives no indication
of the adequacy or uniformity of irrigation (Anyoji and Wu. 1994: Walker. [979: Shearer.
1978). it does show how much water is lost ﬁ'om the ﬁeld as runoff and/or deep percolation
(Clemmens. I991: Tsakiris. [985: Walker. 1979). Lost water is costly to farmers and posses
an environmental hazard since the fate of most nutrients is linked to that of water. Assuming

a uniform mixture. the amount of nitrate leached in a given spot in the ﬁeld is proportional

44
to the quantity of water leached out of the root zone at that location (Rauschkolb and
Homsby, 1994).

Besides environmental concerns. AE can be used for comparing management practices

(Lamack and Niemiera. I993). irrigation. cropping and tillage systems (Yonts er al.. [991 ).

As an evaluation index. it can be used to make an economic judgment on the insrallation of
variors proposed systems (Chaudhry. I978). The measure has also been used in determining
a system's operation time (Yadav et al.. 1986: Wu and Gitlin. 1983). the potential available
water in the root zone to plants. (von Bemuth. [993) and the gross depth required (Chaudhry.
1978). Furthermore. it describes the effects of both management decisions and operational
chametcristics of an irrigation system (Shearer. 1978). Clemmens (l99l) and Warrick et al.
(1989) related application efﬁciency to the area receiving full irrigation. Warrick et al.
tabulated values for ﬁve cases of the specialized power. normal and log-normal functions.

Estimates of application efﬁciency in addition to seasonal evapotranspiration (ET) can
be used to determine seasonal water budgets. Kimbell et al- (1990) derived water
requirements for sprinkler irrigated alfalfa from application efﬁciency. Low application
eﬁiciencies and high ETs indieate large quantities of water to meet plant needs (Rauschkolb
and Hornsby. I994).

The calculation of application eﬁiciency depends on the assumed required depth - a
function of the allowable soil water depletion. The allowable depletion is commonly based
on rules of thumb such as 0.5. 0.25. etc. of the ﬁeld eapacity. However. other factors such
as economics. labor availability. sources and methods of water supply. social and cultural

habits can affect irrigation timing and the application depth. The application or required

4S
depth. as such. may not necessarily equal the root zone depth. thus affecting AE.
Three questions arise: Can AE be estimated from a given application ratio and statistical
unifomtity? How does application efficiency vary with the application ratio under a given
imposed areal distribution? What is the nature of its statistical distribution for a given

setting? The quest for these answers is the focus of this paper.

3. Theoretical development
The following discussion assumes that excess water applied for leaching requirements
is considered a loss since it cannot be recovered by plants. once out of the root zone. If the
fraction of an irrigated ﬁeld. X. receives an applied or required depth. w. then the ratio of w
to the mean applied depth is termed minimum application ratio (MAR). (Chaudhry. I978).
The areal distribution of water under sprinkler irrigation is the result of overlapping
precipitation patterns from several individual sprinklers (Chaudhry. I978). The irrigation
depth over the ﬁeld varies due to spatial variability in soil properties (Brakensiek et al..
1981). However. for a soil with constant soil properties across the ﬁeld and assuming no
translocation. soil water variability is strictly due to non-uniformity of the irrigation system.
In either case. some areas will be over-irrigated and others under-irrigated (Figure 5). For
a constant root depth (represented by the horizontal solid line) which may or may n0t deﬁne
the required depth. non-uniformity (not necessarily the only factor) will lead to variability

in application efﬁciency.

46

One“ “3'.“

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'J LIL'U“U 4"

 

 

 

 

 

 

 

 

 

 

§[

 

Figure 5. lnﬁltrated soil water variability.

[nﬁltrated water depths. w,- . can be measured at discrete points where each point
represents a small arm. Application eﬁiciency. for each A. can be calculated for a given

required or root zone depth as follows:
.45, = RD [25]

where A15 is the application efﬁciency of a given small am i. RD is the required or root
depth and w; is the inﬁltrated water depth in the 1“ location in the ﬁeld. Since the depths.
wi, over the entire am deﬁne an inﬁltrated distribution. AE in a similar manner. will have
a distribution that is dependent on PD. The application efficiency for the proﬁle can be

obtained as an average of AE. i.e..

47

‘4 "E' [261

whose standard deviation is:

v l
.2; (AE. - .m- ’ [27]

N-l

 

SD"? ‘-’

where N is the total number of observations. Equation [27] is a measure of the variation of
application efﬁciency within the proﬁle. SDAE can be standardized by dividing equation
27] by [26] to obtain the coefﬁcient of variation. CV AB

A uniformity coefﬁcient for AE. can be derived and termed application uniformity as
.40 = (r - CV‘EHOO [23]
Equation [28] compares with the statistical uniformity coefﬁcient (Bralts et al.. 1981).
US = (l - cnroo [29]
and provides a statistical description of application efﬁciency as well as the uniformity of the

irrigated depths within the root zone.

4. Procedure

Eight data sets ﬁ'om Heermann et al. (1992) were reproduced using MINlTAB's normal

distribution algorithm (Minitab. [993). The data were originally collected by the Soil

48

Conservation Service under various center pivot systems with different uniformity
distributions. 1hese sets were selected to represent a wide range of distribution uniformities.
Selected sets with their respective means and standard deviations are shown in Table 2.

Table 2. Selected data from Heermann et al. ([992).

 

System ID Mean. mm Std. Dev.. mm Us

 

SCS44 21.6 12.8 43.1
scs06 5.3 2.65 50.0
scs03 30.7 1 1.96 61.0
scs10 15.7 5.37 65.8
“ sc531 13.0 3.85 70.4
scs04 14.8 2.86 80.7
scs15 33.1 439 86.7
$625 24.2 2.18 91.0

 

Three hundred data points were simulated for each set using a QuicleBasic computer program
(Appendix 1). To ensure the accuracy of the simulated data. the average and standard
deviations were compared with the reported values. Each simulated value represented an
inﬁltrated depth. w. for a given location. Eleven required depths were selected at regular
intervals. Application eﬁiciency for each set was calculated according to equation [26}.
Table 3 shows part of an output ﬁom one sample set. For an inﬁltrated depth of 36.0
mm. the application efﬁciency at location 2. for example. (w-_.) is 52.5% for an 18.9 mm
required depth or 0.6 minimum application ratio (MAR). At the same location for a

37.7mm required depth (MAR = 1.2). the application eﬁiciency is 100% (w: < RD).

49

Table 3. An example of a generated matrix from equation [26]

Mean inﬁltrated depth I 31.4 mm: Us = 61.8%

 

 

lnﬁltrated Application efﬁciency for required depths
N depth

m 12.6 18.9 25.2 31.4 37.7
(0.4). (0.6) (0.8) (1.0) ( 1.2)
1 22.5 55.9 83.8 100.0 100.0 100.0
2 36.0 35.0 52.5 69.9 87.4 100.0
3 35.0 35.9 53.9 71.8 89.8 100.0
4 40.7 30.9 46.4 61.8 77.3 92.7
296 16.0 78.7 100.0 100.0 100.0 100.0
297 31.7 39.7 59.5 79.3 99.1 100.0
298 31.3 40.2 60.3 80 .4 100.0 100.0
299 41.2 30.5 45.8 61.0 76.3 91.6
300 23.1 54.3 81.5 100.0 100.0 100.0
Average A2 46.3 65.1 795 89.2 95.2

Std. Dev. 20.17 21.40 18.62 13.96 9.21

CV. 43 .6 32.9 2.3.4 15 .7 9.7

LU. 56.4 67.1 76.6 84.3 90.3

 

° Minimum application ratio

The average application efﬁciency. its standard deviation and the corresponding
uniformity were calculated in accordance with equations [26] through [28]. Two commonly
used equations in estimating application efﬁciency were used to validate the approach in
[26]. These represent equations [30] (Clemmens. 1991) and [31] (Walker. 1979) which are

presented below using the authors' natations.

50

.4 R ’ (I " A"!
Ea = OM ' L D [30}
o

 

where A is the area fully irrigated. R0 is the required depth. U0 is the average depth
inﬁltrated in the deﬁciently irrigated area. MD is the mean inﬁltrated depth and L represents

losses due to surface runoff and evaporation (neglected in this study).

1.2)]

Ea = 1 - (3.634 - 1423,13" - 0.00340 )cv [31]

where AD is a fraction of the area that is deﬁciently irrigated “and cv is the coefficient of
variation of the applied depth.

An application eﬂiciency distribution pattern for each required depth was determined at
5% intervals. Regression equations relating application efﬁciency to minimtun application

ratio were ﬁtted to the polynomial:
y = a - a.x '- ~ an: [32]

where a‘ through a“ are ﬁrnctional coefﬁcients of system uniformity. ((Us - statistical
uniformity): y is the application efﬁciency. x is the minimum application ratio (of n‘h order
polynomial). All equation parameters were determined using SigmaPlot's curve ﬁt procedure

(Jendel Scientiﬁc. 1994).

5. Results and discussion
A detailed output of the results is presented in Appendix 2. A comparison of the results

from the above procedure with other methods is shown in Table 4- There is a good

)l

agreement with results from Clemmens' equation. But for the MAR of 0.4 at cv = 30 and
MAR of 0.4 to 0.8 at cv = 39. the discrepancy between the results is less than 10%.
Generally. the error tends to reduce with a decrease in cv or an increase in the application
ratio. A similar trend was observed in comparison with the Walker equation but. with a
signiﬁcantly higher error (>13°/o) for the 0.4 and 0.6 application ratios in all but cv = 19.
Walker cautioned the use of the equation when the deﬁciently irrigated area was less than
10%. The fractional area receiving minimum irrigation in these cases was below the 10%
margin and this. may explain the large observed differences.

Table 4. Validity of AB results from the procedure of Equation [25].

 

 

 

Application Emciency
cv MAR Regression Equation 30 Equation 31
Equation (Clemmens 1991) (Walker. 1979)
0.4 40.3 40.0 69.8
0.6 60.4 60.0 69.8
9 0.8 805 80.0 78.0
1.0 97.1 96.5 96.7
1.2 100.0 98.6 100.0
0.4 41.8 40.0 40.8
0.6 62.4 59.9 56.3
19 0.8 80.9 783 76.7
1.0 93.5 92.4 93.0
1.2 98.9 99.5 99.1
0.4 44.0 39.8 34.2
0.6 63.9 58.8 55.5
30 0.8 80.3 75.5 75.7
1.0 91.5 88.3 89.3
1.2 97.1 96.8 96.5
0.4 46.3 39.0 33.0
0.6 65.1 56.9 54.7
39 0.8 79.5 72.3 73.2
1.0 89.2 84.7 85.9

1.2 95.2 93.7 93.7

 

 

 

 

 

Ratio
+1.0
+05
+05
+0.7
+0.8
+0.9
-o— 1.0
-o— [,1
+12

 

 

 

 

   

 

 

3"
O

  

7. ' ‘ i
0.8§— 3:315
r “3‘35"“
179637
a '.
é" 014'-
021- . -
(1015“-
0 20 40 60 80 100

 

warden-x.
Figure 6. AE ﬁequency distributions for selected systems.

(lurrltllsc frurua'y

(lurizllvc auras-y

(lattrlallw [tummy

(\llldtllu: liupuay

 

 

 

I ' I I # I V

 

 

 

 

 

 

 

 

 

'-°:

 

 

‘13 l: Lg-m-x.
0.6 {-

 

 

n3 lt-Lgssam

06%-
L

014 i-

 

Arriinim 6076:529-
Figure 7 Cumulative frequency distributions from Figure 6.

 

0.01m

     
  

    

-o—u4
—o-O.5
45-06
-9--07
or 08
—o-Q9
—o—Lo
—o--l.1
-o-l.2

54

Figure 6 shows a frequency distribution of applieation efﬁciency over application ratio
ranges of 0.4 to 1.2. For a given system. the distribution tends to shift toward 100% AB
with an increase in the minimum applieation ratio. Two peaks can be observed - a ﬁxed peak
at 100% AE for all cases and one to its left that varies with AE. These peaks seem to suggest
a dependency on each other. For example. as the application ratio increases the peak at
100% AB increases while the other peak decreases. The increase in the peak at 100% AB
stems from the fact that more of the applied water is within the required depth.

The cumulative frequency distribution is shown in Figure 7. The curves portray a
consistent and repeated trend in all systems. However. the higher the system uniformity the
steeper the slopes and the wider the spread between the curves.

ET demands generally increase with the growing sexon partly because of an increase in
the active root volume and plant canopy. This implies that the required depth. and
consequently the application ratio. will increase with the root zone depth. Therefore. the
shape of the cumulative application eﬁciency function over the season will depend on the
actual inﬁltrated water depth. The actual AE. statistieal distribution can be described by non-
dimensional curves as shown it Figure 7. For any given system the seasonal application
efﬁciency can be characterized by a "arnily of curves similar to those in Figure 7. where the
curves to the left represent early season and those to the right. late season. These curves
suggest application efﬁciency is not a constant. but a variable value for any given
management practice throughout the season.

Application efﬁciency generally increases with minimum application ratio for all

uniformities (Figure 8). These results support an earlier ﬁnding where von Bernuth ( 1983).

55

using a proﬁt function demonstrated that the optimal coefﬁcient of uniformity increases with
the mean irrigation water applied. However. with reference to slopes of the system curves
in Figure 8. A15 in lower uniformity sy5tems increases at a slower rate than higher
uniformity systems. The difference in the slopes account for the system curves crossing over
at about the 0.7 MAR. A detailed look at where the curves converge revealed that all but the

40. 50 and 98 Us curves (extreme cases) cross over at 0.72 MAR (73% AE).

   
    

 

   
    

 

 

10° :. . . . | r . l ‘ riﬁr—f :22")
l' ’ 3
90 E— :6
80 E-
E i
3; 70 :- -:
8 = 3
so 60 E- v 3
O
1: 50 E- : .il
2 b .5
'5 : ta ::
g ‘0 L’ A “-1
a E o 3
< 30 :7 ‘ 1
E o 3
: o 98 3
‘10 :- — titted ‘3
5 :1
o l ' l l I ' L ' ' I ' ' ' i 1 ' ' 1 l ALLL ' I 1L4
0.0 0 2 0.4 0.6 0.8 1.0 12

Minimum application ratio

Figure 8. Application efﬁciency as a function of MAR and Us.
Figure 8 shows that below 0.7 MAR a 50% uniformity system has a better eﬁiciency than

a 90% uniformity system. For example. consider two systems: 1 and II with a statistical
uniformity of 50 and 90% respectively. At 0.4 MAR system i has an AE of 48% and system
[Ihasa40% AE. ATO.9 MARsystemlha583% AEandsystem lIhas90%AE. Butthey

both have about 72% at 0.7 MAR.

56

A “1 statistic" testing the signiﬁcance of Us on AE in the range of 0.6 to 0.8 (near the
cross-over) showed no signiﬁcant difference (a = 0.05). At 0.7 MAR the AE range is 1.9%.
4.9% at 0.6 MAR and 4.4% at 0.8 MAR. The 0.6 to 0.8 MAR interval may be signiﬁcant
for three reasons. First. AE decreases with uniformity below 0.6 MAR. This implies that
large volumes of water and nutrients are leached out of the root zone. Lost water is costly
to producers. Leeched nutrients pose an environmental hazard and reduce yields. Second.
AE increases with unifomiity above 0.8 MAR but this is n0t necessarily a desired goal in a
case where all of the soil's available water has been depleted. This is because the fractional
area that is adequately irrigated decreases with increasing AE (Clemmens. 1991). Third. the
relative AE insensitivity to system uniformity at around 0.7 MAR seems to suggest that
value as an ideal application ratio. especially if an irrigator has no knowledge of the system
uniformity in use.

The relationship between application efﬁciency and the minimum application ratio

(Figure 8) can be amused by the following polynomial:

.45 = a. - 11.8%!le - arWARz - 6.54.181 [33]

where MAR is the minimum application ratio and a0, a). a 1. and a3 are functional coefﬁ-
cients of system uniformity. The mathematical representations of these coeﬂicients are

expressed in [34].

57

o 48.3 - 1.4805 . 0.013211; - 2.56 x 10405J

h
ll

2 - J
a' = -153 ~ 12.8115 - 0.1760, 4 6.69 x 10 ‘US [
34]
a2 = 375 - 21.305 . 0.31905z - 1.31 x 10‘3U;
_ .2 ‘ -4 3
a3 - 179 . 9.47Us - 0.14603. 6.09 x 10 U,

The equations in [34] were developed using regression analysis. A plot of equations [33] and
[34] is shown as ﬁtted lines in Figure 8. The equations show a good ﬁt to the data (adjusted
R2 of 0.99. Appendix 3) with the following exceptions. For the Us == 98. the equations tend
to under predict at 0.9 and 1.0 MAR. and over predict at 0.6. 0.7. 1.1 and 1.2 MAR. The

largest absolute prediction error was 4% at 1.0 MAR. The error in all other cases was less

 

 

 

 

 

 

 

than 2%.
0 I'- log rFy I v T . ' . t a Y ‘r | V v—vv—r . v17 A
n - "-c 90 5 ﬂ 2 '
-‘ D 7,.
:- 1- // 3
T _ 5v * /' .J
a ... E ]__ l/
.0 z 80 1. j
I L .1
i‘ 2" 8,.ts J.
.1: 10 h- 5 70 -o-aaa 1
1— § 3. "' “‘ .l
E t -.-u0 j
*“.
an -: 3 so _ -0- m '1
3 t. -- no .:
:3 -o-aaa -§
3 " -o—aa.o 1
so - w: 30 «o-oaa ‘3
l: -- can .1
‘
‘GL ‘0 IL a a 1 ALL a ‘ 2 L] a l amgmm I 1 a . -1 A_AJ_.JI
10 50 60 70 30 90 [00

Application (mere-q - (l - Leaded [roam] I 00
1 7 1 1 t J
O 6 0.3 d 4 0 1 0 2 O I 0 0

Leeched [Faction
Figure 9. Relating application uniformity to application efﬁciency and leached fraction.

Figure 9 shows a plot of application eﬁiciency and application uniformity (AU)

58

relationships. The ﬁtted lines were obtained ﬁ'orn a ﬁfth order polynomial ﬁt whose
parameters are shown in Appendix 3. AU describes the uniformity of applieation eﬂiciency
in the soil proﬁle. The 80 to 98 U5 systems show a nearly constant AU below 80%
application efﬁciency. The ﬁgure ﬁmher illustrates that. at 80% AE a system whose
distribution uniformity is 40% will have an AU of 72%. whereas a 90% uniformity system
will have an AU of about 90%. Figure 10 offers an alternative to calculating AU from
equation [28] which assumes the availability of AE data collected in a manner described by
equation [26]. Such data are rarely available and collecting them can be time consuming and
costly. Indirect methods such as those presented by Walker (1979) and Clemmens (1991)
are often used but they do not give a corresponding standard deviation for estimating the
CVAE of equation [26].

There exists an inverse

...
O
1

§
0.
O '7'" t—r‘r‘r'r‘r‘t-r'r‘r' I" T 1" l‘ r'r‘r'rw-r‘r'

 

relationship between AE and the

area that is adequately irrigated

regardless of system tuiiformity

(Figure 10). By increasing the AE

 

Earn 60 to 80% under a 70% system

Fractional area adequately llﬂallld

9
N

uniformity the ﬁrlly recharged area

'41. L‘lJAaIJLLLIAl"

20 ‘0 IO '0 '00

decreases by 17%. The observed
Aopﬁceoon etﬁcrency

trends are consistent with previous , , .
Figure 10. Relationship between AE. Us and

ﬁndings of Wu and Gitlin (1983) fully irrigated area.

and Clemmens ( 1991). This ﬁgure can be used to make management decisions with respect

59
to the amount of area under deﬁcit irrigation for a known system and desired AE. F igures
8 and 10 show there are trade-03's among AE. system uniformity and MAR from which

producers can conveniently select design and/or management Options.

Example problem

A center-pivot sysrem has an 80% statistical uniformity coefﬁcient. The average depth of
water to be applied from the system on a ﬁeld is 23 cm. If the root depth of 18 cm is to be
completely recharged. determine: 1) application efﬁciency. 2) application uniformity. and

31 the ﬁactional area fully recharged.

Example solution
The minimum application ratio is (required depth/mean depth) = 18/23 = 0.78.
1. From equation [34]. a0 = 1.27. a. = 87.13. a: = 41.88 and a; = 43-99. Substitute

values in equation [33]: AE = 74%.

l)
O

From Figure 1 1 enter the X-axis at the 74“I AE mark. Read up to the 80% uniformity
curve (fourth curve ﬁ'om the top) and across to the Y-axis: Application uniformity

= 81%.

b3

Locate the 80% uniformity curve in Figure 12. A 74% AE corresponds to a 0.92

fractional area fully recharged.

60

 

 

 

 

     
   

 
    

 

  

O - 100
: /:
up A //§
70 -— a : : Z ,
s ’0 ’ a"
b 7

o - _ f

O k "‘

:0 - 3 so - . 6,

~ I-

a e «ea
in Q I u an
s 10 - 5 7a :- : see
u g a.

g : 1 a tee

a L ' . rte

(O - 3 50 | e eae

3 : l I ate

5 e an

& .. I 0 one

10 '- Q 50 : -—-e
I
so — 40

 

 

40 50 60 70 80 90 100
("nausea M - (I - Leeched have)!“

 

l l i. 1 l l l
0.6 0.5 0.4 1.0 0.2 0.1 0.0
Milkmen

Figure 11. Estimating applieation uniformity ﬁom AE and U s for an
example problem.

 

 

 

 

 

'.°Llrl'11_‘i ' ofthem“
E 2'.
Z Z
i- d
8 I :
3 z I
.9 - -
~ . -a
z - a
D J
2‘ - ..
g : :
O 06:- .-
= - ..
a -
o : 3
a - .4
a. ed
a " 3
h -
a .. E
E :
C u—
2 ‘-
‘5 Z
0 "tr
e.
u. 1:
h
— h
— 4
9’
no a I C I l I I
0 20 ‘0 00 00 100

Application efﬁciency

Figure 12. Estimating the ﬁactional area adequately irrigated from
A5 and Us for an example problem.

61

6. Conclusions

A procedure was deve10ped for estimating application efficiency as a function of
minimum application ratio and system uniformity. Simulated application efﬁciency results
agree with those from existing methods. Application efficiency increases with minimum
application ratio (MAR) and can be estimated as a function of statistical uniformity and
MAR. One limitation of application efﬁciency has been its inability to indicate irrigation
uniformity. Such a limitation may no longer exist: as shown in this study. a term can be
deﬁned which evaluates the uniformity of application efficiency.

Frequencies of. and variations in application eﬁicicncy with required application depths
and system uniformities have been presented. These relations serve two purposes. First.
they characterize the nature of application efﬁciency at a particular irrigation schedule
(minimum application ratio). Second. they describe the expected variation in seasonal
application efficiency (with increasing ET demand) for a given system.

StatiStical uniformity appears to have an insigniﬁcant influence on applieation efﬁciency
at 0.7 MAR. The fractional area under adequate irrigation decreases with an increase in
application efficiency regardless of system uniformity. Relationships among applieation
efficiency. statistical uniformity. MAR and irrigated area provide trade-offs from which

managers can make informed decisions.

62
B. An environmental efﬁciency performance measure for irrigation management

1. Abstract

Managing irrigation systems in an environmentally sound manner throughout the
growing season is a major challenge to managers. The purpose of this study was to develop
a new performance measure - irrigation environmental efﬁciency (E15) - for irrigation
management by combining two commonly used performance measures: application
efﬁciency (AE) and statistical uniformity (Us). Charts are presented that relate irrigation
environmental eﬂiciency to AE. Us. and the ﬁactional area fully irrigated. EIE was used to
show and compare the statistical distribution of various center pivot systems. from two
United States geographical regions. and to evaluate ﬁve Michigan farms using actual
irrigation scheduling data.

2. Introduction

Operating an irrigation system in a manner that minimizes the porential for
environmental degradation throughout the growing season is an issue of urgency today. This
stems in part from the fact that some portions of the ﬁeld. during irrigation. receive more
than the required soil water to meet crop needs. This over-irrigation leads to deep percolation
and/or runoﬁ'. Deep percolation occurs when a portion of the irrigated water moves beyond
the root zone and can no longer be recovered by plants.

One of the most important considerations in irrigation management is the system
performance throughout the growing season. In an attempt to improve on irrigation system
design. Bagley and Criddle (1956) proposed using the product of disrribution eﬁiciency and
application efﬁciency- Cuenca (1989) used that concept (which is further explored in this

paper) in determining the overall efﬁciency of surface systems. and Keller and Bliesner

63
(1990) also used this concept in estimating the required gross application depth.
Performance measures such as statistieal unifomtity (Bralts et al.. 1981) have been used
in the design and evaluation of irrigation systems without regard to the environment. This
neglect is perhaps because society has generally. by default. assigned a zero value to any
system output to the environment in its costobencﬁt analysis. There appears to be no
functional link between the engineering and agronomic aspects of irrigation management and

the environment.

53101311313an AGRONOMIC
V V

Physical Management
Distribution Uniformity Application Eﬂiciency
Us AE

 

 

Y
Irrigation Environmental
Eﬂ‘icieney
Y E, = f (Us. AE)

Minimize Environmental Degradation

 

 

Figure 13. Bridging the gap between the physical and management aspects of irrigation.
Two performance indices commonly used in irrigation management are application
efﬁciency and distribution (statistical) uniformity. Application efﬁciency is indicative of
how well the system is managed. Distribution unifonnity characterizes system performance.
Both have an impact on the immediate surrounding. but there is no index to quantify this
potential impact. The design and evaluation of irrigation systems should have an

environmental eﬁiciency term (Figure 13) that includes losses. for example from deep

percolation and system leakages.

This paper proposes a deﬁnition for environmental efﬁciency in irrigation management
and develops a variance equation for its determination from application efﬁciency and
distribution uniformity. The combination of variance approach. derived from the theory of
propagation of errors (Beers. 1957: Parratt. 1961). allows for the determination of the
variance of a parameter of interest. from variances of individual parameters (Clemmens.
1991 1. In its development. the equation parameters are either expressed as quotients. sums
or products (Mood et al.. 1974: Meyer. 1975: Clemmens. 1991).

Bralts et al. (1981) ﬁrst used the variance combination technique in trickle irrigation.
combining manufacturer's and emitter ﬁow variations. Clemmens (1988) later used the
same technique to account for factors aﬁ'ecting surface irrigation and to develop irrigation
uniformity relationships (Clemmens. 1991). Jaynes and Clemmens (1986) determined
statistical equations for the variance of inﬁltration depths using variances of different
inﬁltration components. Their results were used to calculate distribution uniformity of the
lower quartile.

Bralts et al. (1981) and Clemmens (1991) offer three justiﬁcations for the combination
of variance technique. First. the magnitude and variability of a parameter is more easily
estimated or measured than the actual distribution. Second. the impact of the variation of
each parameter on the distribution of applied water can be analyzed. Third. because the
approach uses statistical relations to integrate several factors. its use can be extended to
systems Other than those for which it was developed. or different systems can be evaluated

using the same procedures-

65

The objectives of this research were to develop an irrigation environmental eﬁiciency
performance measure in irrigation management. relate it to other irrigation measures and

evaluate selected irrigation systems and farms using this performance measure.

3. Theoretical development

A typical irrigation-farm—management system comprises four components: the irrigation
system. irrigator. soil. and the environment. Environment is deﬁned in this Study as that
portion of the irrigated ﬁeld or soil proﬁle that is excluded from the root zone.
Consequently. irrigation environmental eﬁcienq. E ,5. is deﬁned in this study as a ﬁrnction

of application efﬁciency. AE. distribution or statistieal uniformity. Us and soil type. ST.

E": = {(AE. Us. 51) [35]

Erie is a value computed ﬁom measured values of Us, AE and ST. f is a mathematical
function. ST is treated in equation [35] as a constant. The validity of a constant assumption
is based on the factthatseasonal changes in spatial variation ofST within the same ﬁeld are
considered insigniﬁeant compared to variations among ﬁelds. Us contains design parameters
and can be considered a constant in those systems where the irrigator has no control. Since
some design parameters are also management parameters and can. to some extent. be
controlled by the irrigator. Us is treated as a variable. AB is a management variable directly
controlled by the irrigator and is expected to have the most influence on E15.

Equation [35] shows that E“; can be estimated ﬁom measured quantities of AE and Us

and an observed ST. The resulting term will have an error due to the individual errors in AB

66

and Us. These errors may be correlated.

A case can be made for the dependent error assumption. For correlated errors. AB 7

and Us of unit area (i.e. AEi and Usi) can be paired “in accordance with some known

or suspected correlation" (Beers. 1957). The dependence of application efﬁciency on

uniformity (von Bemuth. 1993: Walker. 1979) suggests such a correlation between the two

parameters. Furthermore. systems with poor unifonnity tend to use more water to attain the

required depths. For example. a system that is only 50% uniform will take twice as much

water as required if the water distribution is linear (Karmeli. 1978) to meet the required

amounts if every part or a signiﬁeant portion of the ﬁeld is to receive at least the required

depth. One can. therefore. asaciate low AE locations in the ﬁeld with those areas receiving

high amounts of water. However. spatial variability in inﬁltration rates and subsurface

distribution effects are likely to weaken this correlation thus. tilting the balance towards an

independent variable assumption.

Independent errors can be assumed considering that:

l.

'J
a

La)

4.

Irrigation ﬁ'equency. applied depth and soil properties which dictate AE have no
eﬁ‘ect on Us.
Economic. social and cultural habits in most cases influence management decisions

such as allowable soil water deﬁcit. irrigation duration and depth regardless Us.

. Variations in emitter flow. operating pressure heads. distortions from wind patterns.

which constitute. Us can be measured independent of AE.

Inﬁltration rates depend more on soil physical properties than the irrigation system.

Argtnnent 3 implies that in any given observation there would be N measurements of AE and

67

Us to compute E15. A set of AE and Us values can be imagined such that E15 is computed
from randomly sampled AE.- and U51 (Parmtt. 1961). This imaginary set would represent
the actual measured values of AEi and USi.

Assuming an independent error assumption. AE and Us measurements can be averaged
to obtain uAE and pus . According to Meyer (1975). the best estimate of a function can be
obtained from a Taylor series expansion. Similarly. the best estimate of E15 (equation [35])
can be obtained using a Taylor series expansion but ignoring higher order terms as

5,5 = f( [1445 ' 5415,]. lug, ° 605.] l

[36]

 

as“. as".
= ( ) - —— 645 - 6U
f "‘5’ "US GAE l a”: S.

where 6AE,- = AEi - 14.415 and 5 Us = U55 - nu: are relatively small deviations (Parratt.

1961). An individual deviation 6 Eli: can be obtained by propagating individual errors in

 

AE and Us as follows:
‘E 5E
55 = J 5A5 '- IE 5U: 37
IE. 5.45 l a r [ 1

From statistics. the sample variance. 5:. of a measured quantity is deftned as the square of

its standard deviation. Its mathematical expression. in terms of E“; is

.V
6 z
3‘ 5") 1381

Squaring equation-[37] and substituting in [38] gives

Q

5 i at: = at: ‘5
(3.1.5.) 216.45,): . [ ‘0’!) 1160,): - 2 —-’-‘- 51—5 21545,) H609
. o ' '

 

 

ans , 5.15 an, [39]
5" _ N - 1
From the deﬁnition of the variance we obtain
. 2(64 5.1’ : mus): [401
‘5 N - 1 ' "r N - 1
The results from [40] when substituted in [39] give a variance for EIE as
S: = { EEIE - 2 65:: - z - ., 6515 65!: S [4”
En: 5A5 ‘5 (7U: "r 6.45 aus AE U,

 

 

 

From systems theory (Beers. 1957: Parratt. 1961: Doebelin. 1966). the overall inaccuracy
or error of a system can be calculated. as in equation [41] if the individual component errors
are known. These errors may be considered absolute limits. statistical bounds (i.e.. within
a speciﬁed number of standard deviations) or uncertainties on which some odds can be
accepted (Doebelin. 1966). Since most irrigation and soil properties are treated as random
variables with statistical bounds. we use the latter concept to derive a variance equation for

irrigation environmental efﬁciency-

5,5 = .15-05 [431

Taking the partial derivatives of [42] and evaluating at their mean values it. yields

69

 

 

EEIVIP

~ = ”IE

cU .
- s [4.)]
CE ,

. ‘ F

GA E U’

- = "7: 545 - 11‘ St, - "‘t', “-45 2 $45 51:, [44}

A common statistieal parameter- the coefﬁcient of variation. can be obtained by dividing [44]

by their respective means.

5211:. 33.11: S S.u.u
- 15 L, - t, as -3 as t, t, .15
1 a - ‘ ‘

“.25 “7:, ":15 "0, 11;: ”it,

[451

 

A variance equation for irrigation environmental efﬁciency is thus derived as

2 3 2 SAE SC,
CVE_ = CV“. - cry: - 2 -——-— [46]

“as "'0,

Because of the independent error mumption (Beers. 1957) in AF. and Us the covariance

(last) term in [46] goes to zero and the equation reduces to

CVz = (:va - CV5. 147]

El! 8

The resulting irrigation environmental eﬁciency term is obtained by subtracting the sqaure

70

root of [47] ﬁom one and multiplying by 100 in the manner of Bralts et al- (1981). i.e.-

E“; = (1 - cvswnoo [48]

E"; can be interpreted a a probabilistic measure of the potential to posing an
environmental hazard in irrigation management- An E"; of 40% would imply that the current
practice is six of ten times environmentally friendly or that one poses a potential

environmental concern four of every ten times-

4. Procedures

A computer simulation program (Appendix 1) was written to calculate inigation
environmental efﬁciency in accordance with equations [47] and [48] for various minimum
application ratios. application efﬁciency and uniformity values. For any given system- the
mean depth and its standard deviation descnhe its uniformity. Unifonnity values were
calculated assuming a normal distribution function. The values ranged from 40 to 90 and
reflect ranges in data from St. Joseph Irrigation District. MI and those reported in the
literature (Heerrnann et al.. 1992). CV Ag values were obtained using the procedure and
equations developed in section III-A-

Statistical uniformity. application eﬁiciency and the fractional area receiving adequate
irrigation were related to irrigation environmental efﬁciency through the E15 concept with
charts that combine non-dimensional water depths- system uniformity and application
efﬁciency. Irrigation environmental eﬁiciency classiﬁcation ranges were established based

on recommended statistical uniformity ranges (Bralts et al.- 1981).

71

Data from 65 center pivot systems in St. Joseph Irrigation District. M1 were analyzed
and clusiﬁed according to the Eu; ranges. The data were collected by the Soil Conservation
Service irrigation team for the district in 1987. 1989-1992 (Appendix 5). The results were
compared to similar data analysis from Fort Collins. Colorado (Heermann et al.. 1992). The
aim was to answer the following questions: Suppose these systems were operated at the
SCS's recommended 65% application eﬁiciency (English and Nuss. 1980). how would they
fare environmentally? What difference will it make in changing a management practice. e.g.-
by increasing the application eﬂiciency?

Five farms from St. Joseph Cormty Irrigation District. MI (whose irrigation schedules
could be matched with their respective center pivot systems) were evaluated using farmers'
actual irrigation schedules and SCS-Scheduler (Shayya and Bralts. 1994). SCS-Scheduler.
is an irrigation scheduling package that uses ﬁeld characteristics. local weather data and the
root zone water balance method for water budget updates and irrigation scheduling. Ihe
required inputs which include amotmts of water applied. rainfall events. soil characteristics
and weather information were obtained ﬁ'om farm records in the irrigation district oﬁice.

SCS-Scheduler has the capability of reporting excess water ﬁ'om either irrigation or
rainfall. Excess water is the amount of water above the soil's available water capacity for
a given depth. For each irrigation event (the day the farm was irrigated. expressed as a
fraction of the growing season). application efﬁciency was calculated as one minus the ratio
of excess irrigation water to the total water applied. From the application efﬁciency and
system uniformity. Em values for each scheduled irrigation farm were determined and related

to the percent of the growing season.

5. Results and discussion
a. Irrigation en viranmeuml eﬂicr’eney and related pejornumce measures
Irrigation environmental efficiency (Em) results for different system uniformities (Us)
and application efﬁciencies (AE) are presented graphically in Figures l4 and 15. A detailed
output of the simulation results is shown in Appendix 2.

Figure 14 shows E"; as a function of application eﬁiciency. statistical uniformity and
minimum application ratio (MAR). The figure suggeSts that a manager has two possible
options to improve an unsatisfactory current EIE value. The ﬁrst. which assumes a desired
constant application efﬁciency. is to improve sysrem uniformity. For example. with
reference to Figure 14. EIE can be increased ﬁ'orn 56% to 72% while maintaining a 70% AE.
if the system uniformity of 65% is improved to 80%. The coefﬁcient of variation. by
definition. suggests system uniformity ean be increased by reducing the standard deviation
of the mean applied depth. Improving system uniformity requires repairing and/replacing
system components and in some instances a complete overhaul of the entire system. Bralts
and Edwards (I987) discussed various options. One alternative is to increase the deﬁciently
irrigated area (Clemmens. 1991). Improving system uniformity up to 100% is theoretically

possible. but economically infeasrble (von Bemuth. I993).

 

10° FjIT—FITIIr‘KﬁrKTIIIIjIjII‘IjTTII1WITI

 

 

4O

90 Lara-nae ------~- --------- "3"“ EM
2'; s‘s‘rr'"—°IL"-’gl"‘"—‘t““—§’f" _ I;
E F" l l ;\ f\ :l .3 -- ti
5% 8° :._w___.__._...... ..., : ------
'8 las"—:_ 2"" i s l I -
E i \ :\ :\ - _
g 70 :" : °°°°°° 2--°"::l~ 1
s l“ i\ LIA/'1" 11:
2 ~ 3 .3 l 3 l .
‘2 6° " a 2 5'2; 1 "3
0 l : E "I .J
c t 2 j : ..
5., ...... : .......... ......
e \/%' : z :

  

 

 

 

 

lllL

l’qujglLliLJlAl

30 4O 50 60 7O 80 90 100

 

so
Application efﬁciency

Figure 14. Irrigation environmental eﬂiciency related to MAR. Us and AE.

The second option is to increase application eﬁiciency. A sy'Stem whose statistical
uniformity is 65% and operates at 56% application efﬁciency has a 50% Em. This system
can have a 60% E“; if it is operated at 83% application efﬁciency (Figure 14). However. the
ﬁactional arm receiving at least the required application depth decreases by 0.24 (from 0.92
to 0.68. Figure 15). Using these ﬁgures the irrigator can decide on what ﬁactional area needs
to be ﬁrlly recharged to signiﬁcantly inﬂuence yield. Management decisions can be made

based on derived trade offs in Eng. area and AE-

74

 

 

 

 

     
   

 

100

90
>~
g 80
2 a -- - .. . . .
O ..
:E 70 ........... . . ......... _
o - _ :.. , ‘ L
g 60 . .. .. 3
g l
5 so Q. i
g 40 5
5 30 E
"3.
‘5 20

A
D
E
i
i
al.-3.92:..-

o I
0.0 0.1 0-2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fractional area adequately irrigated

Figure 15. Irrigation environmental eﬁiciency related to MAR. Us. and irrigated area.

Figures 14 and 15 were developed to: I) indicate the effects of possible changes in the
required depths in irrigation management assuming a consrant coefﬁcient of variation: and
2) estimate or predict irrigation environmental efﬁciency in the design and management of
irrigation systems. If the minimum application ratio and system uniformity are known. then
AE and En»: can be determined. Also. if the ﬁactional area to be fully irrigated is known for
a recommended Eu; level. MAR and Us can be selected to satisfy those conditions. The E";
charts presented bridge the gap between the agronomic and engineering aspects of irrigation
management (Figure I3. page 63). They can serve as an advisory tool for both mangers and
designers in making tactful and strategic decisions as well as suggest some practical ideas

for management options. One musr. however. recognize that other variables such as labor

75
availability. soil and climatic conditions. social and cultural habits and system capacity still

significantly inﬂuence daily or seasonal practical management decisions.

b. Example problem I

A center pivot irrigation system has a statistical uniformity of 85%. If 90% of the irrigated
area is to be fully recharged. determine MAR. E"; and AE.

Solution

Ninety percent of the irrigated area corresponds to 0.90 of the ﬁactional area adequately
irrigated. From Figure 17. locate 0.90 (circled I) and Us = 85% (3rd horizontal solid line.
in the body of Figure 17. ﬁom the top). Where the two lines intersect. read across the cloned
line: E"; = 80% and down the curved line: MAR = 0.8.

Go to Figure 16. Enter the chart at the SE = 80 tick (circled I). Follow the E";- = 80 line to
where the Us 3 85 and MAR = 0.8 lines meet. Read vertically on the x-axis. AB = 81%.
c. Example problem 2

Determine the environmental efficiency of a drip irrigation system whose uniformity is 70%
if the mean application depth is [2 mm and the required depth is 7 mm. What ﬁ-action of the
ﬁeld will be under-irrigated. Can the irrigator raise E"; to 70%?

Solution

The minimum application ratio is. required depth divided by mean depth: 7/12 = 0.58. From
Figure I7. loeate Us = 70% and MAR = 0.58 lines (boxed 2). Read across to the y-axis: E [E
= 58% and down to the x-axis: AB = 62%. From Figure l7. enter the Y-axis at E,E = 58

(boxed 2).

76

 

 

 
   

 

 
 

 

 

 

 

 

 
    

 

 

 

‘00 ..Tj f I i Y 1 I l I V I I I T I 1 I 1" - I T Tr! a 1' ' VTﬁi
: 4
‘5 so —lakrta'~.'_;m;'-"Ifjj"°'.°'g".'_""g,[";;_.~2J- "- '
g; u‘; aa‘ . . ;
a I... : | ‘ I f r
g 6330 ...._._...._.._.. ___.___ ___._..
e E" 1 3 '~ ‘
'3 ‘ i '
a 2 7° ‘ ... . 1 ’gr 1;?
o _ -
E r' ............ l -
C 6 {'— I’.’ .7.
a ﬁg?- .-
, ; . . "
s = .3
c so - ..... .. d:
2 10 -
S 3‘ ‘ Ii
... ’ ”—1
E ‘° 4’. 4,
'. l \ . 3
3° 1 r .. 1#L1 1‘.Ll 1" 4s 1. 1.: I .L r l
rs
so so so 60E] 70 so so 100

Application efficiency

Figure [6. Estimating EIE ﬁ'om AE. Us and MAR for two example
problems.

 

 

 

 

 

irrigation anvlronmanlal alllclancy (E m)

 

o . . . l' r
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 06 1.0

Fractional area adenuately irrigated

Figure I7. Estimating E"; from fractional area adequately irrigated.
MAR and Us for two example problems.

77

Move across to MAR = 0.58 to Us = 70. Move vertically to the X- axis and ﬁnd the

fractional area ﬁrlly irrigated is about 0.91. Therefore the under irrigated area is: l - ﬁrlly

irrigated area = 0.09 or 9%. For the same application efﬁciency. ElE can be raised to 70%

by increasing system uniformity to 80% (Figure I7). A 70% Eli: value cannot be achieved

by increasing AF with this system.

d. Recommended and suggested performance measures

Ideally. acceptable EIE
values should be based on
acceptable statistical
uniformity levels and the
effective root zone. Table 5
shows suggested acceptable
E"; values based on

recommended Statistical

Table 5. Irrigation measures and suggested E's

classiﬁeation values

 

 

Comment Us° CU" 5,5

Excellent > 90 > > 35
90

Very good 80 - 90 75 - 90 75 - 85

Fair 70 - 80 70 - 78 60 - 75

Poor 60 ~70 65-78 50 ~60

Unacceptable <60 <65 < 50

 

‘Us abducted from scanner a. “98”.
.0} t Clu'istraasen unifotmny maﬁicient lChrstiarrsen. l9-t2l.

uniformity values (Bralts et al.: 1981). The lowest average AE value corresponding to E";

and Us was 62%. The Soil Conservation Service (English and Nuss. I980) generally

recommends 65% regardless of system uniformity. In light of E“; . this value may be

somewhat misleading for unspeciﬁed system and management conditions. Consider a

sysrem whose statistical uniforrrrity is 60% and operates at 65% AE: both are acceptable and

recommended values. Figure I6 shows such a system has 48% Eli»: - an unacceptable. Even

at 90% AE this system will still be classiﬁed as environmentally poor.

78

The following conclusions can be made from Table 5 and Figure 16.
I . Systems with 50% statistical uniformity and below are environmentally unacceptable

regardless of the application efﬁciency and minimum application ratios.

IJ

EIE should be the guiding index in recommending acceptable values for combined

statistical uniformity and application efﬁciency.

e. Center pivot-E , E statistical distribution

 

   

s:_-;s¢:n m :92? 1555-2551 F: Cormaca heennann eta 1552

[3633 AE

i::‘:':'; 80% LE

80% Cu. Dist /

0.8

.- .-o— ._-.- --.—-—

Dlalrlbullon

   

552331

e
...‘OCOOOIIOICOOG.I.O
cocoon-....ooeooou
...

 

l
.‘ziziziiizl

nix-toil

   

 

 

£°'.f".‘."7¢‘.‘7'.u-.’.". .
a I a D e O I I a a I a

 

 

 

 

 

 

 

f
m
vrvvvvvvvvvvv
.....II
.000...

Ill
l .
ALLA AAA a

€50 50-50 00-?! 75-05 ’6 €50 50.00 “-75 75-05 ’05

Unaecapl. poor be good arealent Unacceet. poor lat good excellent

Figure 18- Ere distribution of center pivOt systems ﬁ'om Michigan and Colorado.

Figure 18 shows the statistieal distribution of evaluated center pivot systems in ﬁve E“;
categories. The right diagonal bars assume a 65% AE management while the cross hatched
bars assume an 80% AE. management. The cumulative distributions of the data are shown

as the S-curves.

79

In accordance with Table 5. 70% of the systems ﬁ'om Michigan and 75% from Colorado
fall in the fair to excellent group. There is. however. a 10% signiﬁcant difference between
the two locations in the excellent category. This difference seems to suggest that managers
in drier regions are more likely to strive for well calibrated systems than those in humid areas
where irrigation frequencies are fairly low. Both locations have a majority of the systems
in theﬁrir category. about the same proportion in the good eategory and the least proportion
in the unacceptable category.

Increasing the applieation eﬁ'rciency from 65 to 80% in the systems from Michigan
signiﬁcantly reduced the number of poor systems by 8% and increased the number of fair
systems by 14%. The fair and poor categories from Colorado were. respectively. increased
and reduced by 8%. This change was not signiﬁcant. There was no observed change in the
good and excellent categories in both locations.

These results do show that increased application efﬁciency for poor uniform syStems is
a necessity if environmental constraints are to be met. For high uniform systems
environmental efﬁciency is not very sensitive to application efﬁciency. This means that an
investment in a high uniform system pays off both environmentally and in an increased
irrigated area. In arid areas increased irrigated area means increased yields. Increasing AE
from 65 to 80 in an 80% uniform system has little impact on Ens. but signiﬁcantly reduces
the fully irrigated area. It is likely that the manager on the 65% AE schedule is more likely

to endure increased water costs.

80

ﬂ Irrigation Scheduling and E (E

90
>. 85
U
C
2
.9.
3 80
E
C
E
c 75
O
.2
>
C
O
C 70
.2
'5
.9
|-_- 65
60

 

 

 

 

 

[TITllljIIIIIIIIIIIIIITIIIIIIIﬁIlIIIITIITlI
.— -t
f are cum 0 Farm. us 1
* ~O—Lsza. 66.0% r
: . -t:- cons. use :
... . - A recs. aaass ...
- -9- R201. 67.0% 4
C U 5 -<>— Haas. 52.0w 1
-- "l
b were; —w——v d
E- -
- O---(D id
I .l
- o———<>—<>o—oo—<>—<><>
lelLUllllllLllllJllllllllllllmlyllllllsl
IO 20 30 40 SO 60 70 80 90 100

Percent of growing season

Figure I9. Seasonal variation of E“; for selected Michigan farms.

SCS-Scheduler output for the ﬁve evaluated farms are shown in Appendix 4. Evaluation
results are shown in Figure 19. Four of the ﬁve farms. on the average operated in the fair
EIE category and one in the very good category. The results show that three of ﬁve farms
were not over-irrigating for that season. It is interesting to note that the two farms that over.
irrigated in some schedules belonged to one farmer and were operated in different years

( I990 - r948 and 1991 - r085). One other farm irrigated in 1991 was H088. The farmer

maintained 100% AB in all schedules but had a poor Ens compared to R085-

81

These results show two things: I) if a farm is irrigated at 100% AE then Ens for the farm
is the system uniformity. That means no matter how hard management tries. they will never
do as well as they would like to. In other words. it is impossible to achieve a high Etta value
under the best management practice with a poor sysrem. The only alternative is to improve
the system. 2) A highly uniform system (such as r085 in Figure 19) can be operated in an
environmentally unsound manner. This is where management becomes the most sensitive
variable in the Eu; equation. These two scenario represent the extremes and are easy to
handle. The most complicated case is that in which both management variables and the
irrigation system are unstable. Management has to simultaneously stabilize its variables and
adjust system variables to compensate for the instability in the system. The danger here is
paying more attention to one set of variables. and that is something likely to happen.

The usefulness of this approach draws its strengths from the ability to operate and
manage the system within accepted limits. This raises some interesting questions. Why
would r085 bother to afford a higher uniformity system or maintain a high AE when at worSt.
the manager is still environmentally better than H088? What societal incentives are there to
move H088 to a higher level and keep r085 at the present level? Are the social. economic
and environmental beneﬁts justiﬁed by the added costs? Answers to these questions are
deﬁnitely controversial and require input from multi-disciplinary groups. Unfortunately.
such group discussions often tend to be guided by emotional and political knowledge rather

than scientiﬁc facts.

6. Conclusions

The design and management of irrigation systems require an environmental dependent
variable for various design and management alternatives. E15. with the accompanying charts.
quantiﬁes the environmental efficiency of irrigation management and system uniformity.
E";- should. therefore. be estimated in the design and operation of inigation systems.

E‘s charts presented bridge the gap between agronomic (management) and engineering
(physical) aspects of irrigation and link their operational consequences to the environment.
They serve as a tool for comparing management options whose results are environmental
protection and effective water use.

A well calibrated system can be managed in an environmentally unsound manner. Under
the best management practice inigation environmental efﬁciency cannOt be better than
system uniformity.

A large proportion of the center pivot systems used in this study fall in the fair to

excellent category of the irrigation environmental efﬁciency classiﬁcation.

IV. General Conclusion

ll’hat rs observed depends on who (3 looking “
- I" H George -

Resource exploitation soil degadation. water resource depletion and pollution are insidious
trends of the past still prevalent in today's society. Lessons from history show that great losses.
costs and consequences await us. unless there is an effort on our part to improve irrigation
management. Improved management practices and the willingness to sacriﬁce are a necessity
to balance environmental. economic and social values.

In general. eﬁiciency assumes a management scheme relating the output of a system to its
inputs. When used as a performance measure. the term provides a basis on which decisions can
be made regarding system operations. Also. it can be used to determine which system
components need adjustment. and to what extend. It’s also a useﬁrl tool for comparing different
systems. In irrigation management. irrigation environmental efﬁciency will be an indicator of
the potential to environmental pollution.

Statistical distributions of application efﬁciency for various statistieal (SyStem) uniformities
have been presented which can be used to characterize the nature of application efﬁciency at a
particular irrigation schedule (minimum applieation ratio) and/or describe the expected variation
in seasonal applieation efﬁciency (with increasing ET demand). One limitation of application

efﬁciency has been its inability to indicate irrigation uniformity- Such a limitation may no

 

°m Setennsr: a serenn/ic mqrm medrodr Williams & Norgate Ltd. London- 1936.

83

34
longer exist- as a term can be defined which evaluates the uniformity of inﬁltrated water from
irrigation.

Regression equations were developed to estimate application efﬁciency as a function of the
minimum application ratio (MAR) and statistical (system) uniformity. However. system
uniformity has no signiﬁcant influence on application efficiency at about 0.7 MAR.
Relationships among application efﬁciency. statistical uniformity. MAR and irrigated area
provide trade-offs from which managers can make informed decisions.

A new performance measure. irrigation environmental efﬁciency (E's). was presented that
can be applied to the design and management of irrigation systems. E's should therefore be
estimated in the design and operation of irrigation systems.

E‘E charts presented. bridge the gap between agronomic (management) and engineering
(physical) aspects of irrigation and link their Operational consequences to the environment. They
serve as a tool for comparing management options whose results are environmental protection
and effective water use.

Systems with 50% statistical uniformity and below are environmentally unacceptable
regardless of the application efficiency and minimum application ratios. Etta should be the
guiding index in recommending acceptable values for both system uniformity and application
efﬁciency.

About 70% of the center pivot systems used in the study fall in the fair to excellent category
of the irrigation environmental efﬁciency classiﬁcation. A well calibrated system can be
operated in a manner that is environmentally unsound. Under the best management practice- Etta

can never be better than the system's uniformity.

V. Recommendations

New combinations tn our thoughts arise from rational
associations or perhaps chance circumstances”
- W I B. Beverrdge -

The design and management of irrigation systenrs contain more than the engineering and
agronomic inputs. Human. economic and environmental factors must be taken into account.
Many factors involved in crop production should and must be evaluated in an integrated
management system. This calls for an interdisciplinary approach in irrigation design and
management.

Although there is wide recognition of the environmental concerns in irrigation
management. attempts to address those concerns still emphasize the single discipline
approach. There is a need to incorporate the systems approach in irrigation management in
order to provide managers and farmers with options from which they can make economieally
and environmentally sound decisions.

Application efﬁciency is an important irrigation performance measure. Apart ﬁ-orn its
indirect estimation using the equations in the section Application eﬂicienc'y determination.
(page 36). direct ﬁeld measurements of. or any proposed procedures in sprinkler irrigation

have not been documented. Furthermore. there is a need to investigate the impacts of

 

l0lr'trttgintltion: The art ofsetenttfic tnmttgatton. 3" Ed. (I. 89. I957.

85

86

management practices on applieation eﬁiciency as well as the probability of such efﬁciencies
under various management strategies.

Irrigation environmental efﬁciency (Em) should be the guiding index in recommending
acceptable values for both system uniformity and application eﬁiciency. As a management
tool. Etta may be useful in determining the gross amount of water to supply to any given
irrigation ﬁeld. For example. the gross depth of water application per irrigation is computed
by dividing the net depth required by the overall system efﬁciency. It is proposed that the
SyStem efﬁciency in that equation be replaced by irrigation environmental eﬁiciency: i.e
<1ng = dug/Eu; and validated under various ﬁeld conditions.

The approach used in this study. and the developed performance measure ( Etta ) should
ﬁnd application in any type of irrigation system and management. The usefulness of this
approach depends on whether the irrigation system(s) and management optionts) can be
maintained within reasonable and/or acceptable standards. It also depend on whether society
can determine if the economic and social rewards for adjusting management practices or

design are likely sufﬁcient to justify added costs.

VI. References

Adams. M. C. 1974. Hisroric patterns of Mesopotamian irrigation agriculture. In: Irrigation-
Impact on Society. Anthropological papers of the University of Arizona #25. p. 1-6.
University of Arizona Press Tuscan. Arizona.

Aljibury. F. K. 1978. Introduction to irrigation eﬁiciency and scheduling. In: Eﬂiciency in
Irrigation. The Irrigation Association: Techniml Conference Proceedings. 160-161.

Anyoji. H and I. P. Wu. 1994. Normal distribution water applieation for drip irrigation
schedules. Transactions of the ASAE. 37(1):159-l64.

ASAE. 1993. Soil and water engineering terminology. American Society of Agricultural
Engineering Standards: ASAE $526.

Bagley. LM. and Criddle- W.D- 1956. Evaluating sprinkler irrigation systems. Utah
Experiment Station Bulletin. #3 87. Utah State University.

Beck. V. J. and .I. A. Kenneth. 1977. Parameter Estimation in Engineering and Science.
John Wiley & Sons. New York. 501 pp.

Beers. Y. 195 7. Introduction to the Theory of Error. Addison-Wesley Publishing-

Benami. A. and F. R. Hore. 1964. A new irrigation-sprinkler distribution coefﬁcient.
Transactions of the ASAE. 7: 157-158.

Brakensiek- D. l... R. L. Engleman and W- J. Rawls- 1981. Variation within texture classes
of soil water parameters. Transactions of the ASAE. 24(2):355-339.

Bralts. V. F.- 1. Wu and H. M- Gitlin. 1981. Manufacturing variation in drip irrigation
unifomrity. Transactions of the A5245- 24(5):l 13-1 19.

Bralts. V. F. and D. M. Edwards. 1987. Drip irrigation and evaluation based on the statistical
uniformity concept. In: D. Hillel. ed.- Advances in Irrigation. Vol. 4:67-1 17-

Cantor. I.- M. 1970. .-I' World Geography of Irrigation. Praeger. New York.

87

88

Carruthers. 1 and C. Clark. 1981. Planning irrigation deveIOpment. Chapter 8. In: The
Economics of Irrigation. LiverPool University Press. England.

Caner. D. 1.. 1980. The impact of irrigation of ground water quality. In : .1. Eggleston. ed.
Irrigation and Drainage: Today's Challenges.

Chaudhry. F. H. 1977. Sprinkler uniformity measures and skewness. Journal of the
Irrigation and Drainage Engineering, 102 (1R4): 425-433.

 

1978. Non-uniform sprinkler irrigation application efficiency. Journal of Irrigation
and Drainage Division. 104(IR2): 165-178.

Chestnut. 1-1. 1966. Systems Engineering Tools. John Wiley and Sons. New York. 646p.

Christiansen .1. E. 1942. Irrigation by sprinkling. California Agricultural Experiment Station
Bulletin 670. University of California. Berkeley.

Clemmens. A. I. 1991. Irrigation uniformity relationships for irrigation system management.
Journal of the Irrigation and Drainage Engineering, 117(5): 682-699.

 

1988. Method for analyzing field scale surface irrigation efﬁciency. Journal of the
Irrigation and Drainage Engineering, 1 14 (I ): 74-88.

Cohen. 0. P. and E. Bresler. 1967. The eﬂ‘ect of non-uniforrn water application on soil
moisture content. moisture depletion and irrigation efﬁciency. Soil Science Society
of A merica Proceedings. 31:117-121.

C uenca. R. H. 1989. Irrigation System Design: An Engineering Approach. Prentice Hall.
Englewood Cliﬂ’s. New Jersey.

Dabbous. B. J- 1962. A study of sprinkler uniformity evaluation methods. Master of Science
Thesis. Utah State University. Logan. Utah.

Dent. J. B. 1975. The application of systems theory in agriculture. In: G. E. Dalton. ed..
Study of Agricultural Systems. Applied Science Publishers. London.

Doebelin. E0. 1966. Measurement systems: Application and Design. McGraw-Hill. New
York.

Doyle. C. J. 1990. Application of systems theory to farm planning and control: modelling
resource allocation. In: .1. G. W. Jones and P. R. Street. eds. Systems Theory Applied
to Agriculture and the Food Chain. 89-112. Elsevier Applied Science. London and

89

New York.

Elliot. R.I... I. D. Nelson. J. C. Loftis and W. E. Hart. 1980. Comparison of sprinkler
uniformity models. Journal of the Irrigation and Drainage Engineering. 106(IR4):
321-330.

English. M. I. and G. S. Nuss. 1980. Designing for deficit inigation. In : .1. Eggleston. ed..
Irrigation and Drainage: Today's Challenges.

Falcon. W. P. and C. H. Gotsch. 1971. Relative price response. economic efficiency and
technological change: A case study of the Punjab agriculture. In: W.P. Falcon and
G. E. Dalton. eds.. Development Policy [I - The Pakistan Experience. Cambridge:
Harvard University Press.

Gulhati. N. D. and W. C. Smith. 1967. Irrigated Agriculture and historical review. In: R. M.
Hagen. H. R. Haisc and T. W. Edminister. eds.. Irrigation of Agricultural Lands.
Agronomy Monograph # ll. Amerim Society of Agronomy. Madison. Wisconsin.

Harding. G. 1968. The tragedy of the commons. Science. 143-148.

Harris. F. S. 1920. Soil Alkali. its Origin Nature and Treatment. John Wiley and Sons. New
York.

Hart. W. E. 1972. Subsurface distribution of nonuniformity applied surface water.
Transactions of the ASAE. 15(4):656-66I. 666.

Hart. W. E. and D. F. Heermann. 1976. Evaluating water distributions of sprinkler irrigatidn
systems. Colorado State University Experiment Station. Technical Bulletin No. 128.

Hart. W. E. and W. N. Reynolds. 1965. Analytical design of sprinkler systems. Transactions
of the ASAE. 8(1):83-85. 89.

Heermann. D.F.. H. R. Duke and A. M. Seratim. 1992- Distribution ﬁrnctions to represent
center-pivot water distribution. Transaction of the ASAE. 35(5): 1465-1472.

Hill. R. W. and .1. Keller. 1980. Irrigation system selection for maximum crop proﬁt.
Transaction of the ASAE. 23(2):.366-372.

Hillel. D. 1987. The Eﬁicient Use of Water in Irrigation. World Bank technical paper No.
64.

Holy. M. 1981. Irrigation systems and their role in the food crises. International Commission
on Irrigation and Drainage Conference.

90

Howell. D. T. 1964. Non-unifomiity and sprinkler application efficiency. Journal of
Irrigation and Drainage Division. ASCE(IR3): 41-53.

[C ID. 1980. The Application of System Analysis to Problems of Irrigation. Drainage and
Flood Control: A Manual for Water and Agricultural Engineers. A. W. Biswas. ed.
International Committee on Irrigation and Drainage. Pergamon Press. New York.

Israelson. O. W. and V. E. Hansen. 1967. Irrigation Principles and Practices. 3rd Edition.
John Wiley. New York.

lzadi. 8.. P. Studer and l. Mch 1991. Maximizing set-wide furrow inigation application
efficiency under ﬁrll irrigation strategy. Transactions of the ASAE. 3461:2006-2014.

James- P. W- R. J. Hanks and J. J. Jurinak. 1982. Modern Irrigated Soils. John Wiley and
Sons. New York.

Jayncs. D. B. and A. J. Clemmens. 1986. Accounting for spatial variable inﬁltration in
border irrigation. Water Resources Research. 22(8):1257-1262.

Jendel Scientific. 1994. Transforms and curve ﬁtting. SigmaPlot Scientiﬁc Graphing
Software for Windows. Ver. 2-0.

Jensen. M. 0.. (ed.). 1980. Design and Operation of Form Irrigation Systems. ASAE
Monograph No. 3. St Joseph. MI 49085.

Kappel. W. 1974. Irrigation development and papulation pressure- In: Irrigation-Impact on
Society. Anthmpological papers of the University of Arizona #25. p. 159-167.
University of Arizona Press Tuscan. Arizona.

Karmeli. D. 1977. Water distribution patterns for sprinkler and surface irrigation systems.
Proc. National Conference on Irrigation Return Flow Quality Management. Colorado
State University. Fort Collins. Colorado.

—--- 1978. Estimating sprinkler distribution patterns using linear regrssion. Transactions
of the ASAE. 21(4):682-686.

Karmeli. D.. L. J. Salazar and W. R. Walker. 1978. Assessing the spatial variability of
irrigation water applications. Document No. EPA-600f2-78-041. US. Environmental
Protection Agency. ADA. OK.

Keller. J. and R. D. Bliesner. 1990. Sprinlde and trickle irrigation. Van Nostran Reihnhold.
New York.

91

Keller. J. and D. Karmeli. I974a. Trickle Irrigation Design. Rain Bird Sprinkler
Manufacturing Corporation. Glendora. CA.

1974b. Trickle irrigation design parameters. Transactions of the ASAE. 17(4):678-
784.

 

Kelley. W. P. 1964. Maintenance of a permanent irrigation agriculture. Soil Science.
982(113-117).

Kimbell. M. K.- W. M. Miller. C. N. Mohannah and E. H. Jensen. 1990. Applied mater
required for sprinkler irrigated alfalfa in Western Nevada. Applied Agricultural
Resources. 5(4):268-275.

Kruse. E. G. 1978. Describing irrigation eﬁiciency and uniformity. Journal of Irrigation and
Drainage. Division of ASCE. 104(IRI):35-41.

Lamack. W. F. and 7.. X. Niemiera. 1993. Application method affects water application
efﬁciency of spray stake-irrigated containers. Horticultural Science. 28(6):625-627.

Ley. T. W. and W. Chyma. 1981. Furrow irrigation practices in Northern Colorado.
Transactions of the ASAE. 24(3):610-6 16.

McCuen. R. H. 1973. The role of sensitivity analysis in hydrologic modeling. Journal of
Hydrology. 18:37-53.

Manetsch. T. J. and G. L. Park. 1993. The systems approach as a problem solving
methodology. In: Systems Analysis and Simulation with Applications to Economic
and Social Systems. Dept. of Electrical Engineering. Michigan State University-

Martin. E.C. 1992. Management Strategies to Minimise Nitrate Leaching in Seed Corn
Production. Ph.D. Dissertation. Michigan State University.

Meyer. S.L. 1975. Data Analysis ﬂir Scientists and Engineers. John Wiley & Sons- New
York.

Minitab. 1993. Minitab Reference Manual. Release 9 for Windows. Minitab 1nc.. Lebanon.
PA

Mintzberg. H. 1976. Planning on the left side and managing on the right. Harvard Business
Review. July-August.

Mood- A.M.. Graybill. FA. and Boes. D.C. 1974. Introduction to Theory of Statistics.
McGraw Hill. New York.

92

Naylor. T. H. and J. W. Finger. 1967. Veriﬁcation of computer simulation models.
Management Science. 14:2.

Neter. .1.. W. Wasserman and M. H. Kutner. 1990. Applied Linear Statistical Models. 3"
Edition. IRWIN. Boston. MA.

Ogata. K. 1978. Systems Dynamics. Prentice-Hall. Englewood Cliffs. New Jersey.

Parratt. L. G. 1961. Probability and Experimental Errors in Science. John Wiley 8; Sons.
New York.

Rauschkolb. R. S. and A. G. Homsby. 1994. Nitrogen Management in Irrigated Agriculture.
Oxford University Press. Oxford.

Robinson. S. C- 1978. Measuring efficiency of surface irrigation systems. In: Eﬂiciency in
Irrigation. The Irrigation Association: Technical Conference Proceedings. 209-212.

Rountree. J. H. 1977. Systems thinking - some ﬁrndamental aspects. Agricultural Systems.
22247-254.

Seginer. 1.. D. Kantz and D. Nir- 1991. The distribution by wind of the distribution patterns
of single sprinklers. Agricultural Water Management. 12:344-359-

Seniwongse. C.- 1. Wu and W. N. Reynolds. 1972. The effects of skewness and kurtosis on
the uniformity coefﬁcient and their application to sprinkler irrigation design-
Transactions of the ASAE. 15(2):266-271.

Shayya. W. H- and V. F. Bralts. I994. SCS-Scheduler Microcomputer Irrigation Scheduling
Package. Version 3. Department of Agricultural Engineering. Michigan State
University. East Lansing. MI.

Shearer. M. N. 1978. Comparative efﬁciency of irrigation systems. In: Eﬂ'iciency in
Irrigation. The Irrigation Association: Technical Conference Proceedings. 183-188.

Sinai. G. and D. Zaslavsky. 1977. Factors affecting water distribution after uniformity
irrigation. ASAE paper. St Joseph. MI 49805.

Solomon. K. H. 1985. Global uniformity of trickle irrigation systems. Transactions of the
ASAE. 28(4):1151-1 158.

---- 1983. Irrigation uniformity and yield theory. Ph.D. Dissertation. Utah State
University. Logan. Utah.

93

Street. P. R. 1990. A systems view of commercial supply and marketing links. In: J. G. W.
Jones and P. R. Street. eds.. Systems Theory Applied to Agriculture and the Food
Chain. 159-204. Elsevier Applied Science. London and New York.

Su. M. 1979. Comparative evaluation of irrigation uniformity indices. Master of Science
Thesis. Utah State University. Logan. Utah.

Taylor. S. A. and G. I... Ashcroft. 1972. Physical Edaphology: The Physics of irrigated and
non-irrigated soils. chapter 16. W. H. Freeman and Company. San Francisco.

Thompson. S. A. 1988. Patterns and trends in irrigation efﬁciency. Water Resources
Bulletin. 24(1):57-63.

Till. M. R. and M. G. Boss. I985. The influence of uniformity and leaching on the ﬁeld
application efﬁciency. Bulletin of International Committee on Irrigation and
Drainage. New Delhi. 34(1);32-35. 60.

Tsakiris. G. P. 1985. Infiltration efﬁciency in sprinkler irrigation. Advances in Water
Resources. 8:44-47.

van Schilfgaarde. J. 1994. Irrigation - a blessing or a curse. Agricultural Water Management.
25:203-209.

Vang. H. and K. Bamey. 1994. Computer Simulation Analysis of Biological and
Agricultural Systems. CRC Press- Ann Arbor. MI.

von Bemuth. R. D. 1983. Uniformity design criteria under limited water. Transactions of the
ASAE. 26(5):1418-1421.

-—---—- 1993. Surface and Sprinkle irrigation: comparison of uniformities and eﬁiciencies.
In: A GRIT EC H 93. proceedings of the 6‘“ International Conference on Irrigation.
Tel-Avi. Israel. 3-4 May

Walker. W. R. 1979. Explicit sprinkler irrigation uniformity: efficiency model. Journal of
the Irrigation and Drainage Engineering. 105 (R2): 129-136.

Warrick. A. W.- W. E. Hart and M. Yitayew. 1989. Calculation of distribution and
application eﬂiciency for nonuniform irrigation. Journal of Irrigation and Drainage
Engineering. I 15(4):674-687.

Warrick. A.W. 1983. Interrelationships of irrigation uniformity terms. Journal of the
Irrigation and Drainage Engineering. 109 I 3): 317-332.

94

White House. 1964. Report on Land and Water Development in the Indus Plain. The White
House-Department of Interior Panel on Waterlogging and Salinity in West Pakistan.
Washington. DC. '

Wilcox. J. C. and G. E. Swailes- 1947. Uniformity of water distribution by some under-tree
orchard sprinklers. Scientiﬁc Agriculture. 27(1 1):565-5 83.

Wright. A. 1975. Farming systems. models and simulations. Chapter 2. In: Techniques and
Methods in Simulation. 17-33.

Wu and Gitlin. 1983. Drip irrigation application eﬁiciency and schedules. Transactions of
the ASAE. 26(1):92-99.

Wyseure. G. 1986. Hydrologic system modelling of the total rainfall-direct runoff
conversion. Ph.D. Thesis No. 147. Katholieke University. Leuven. Belgium.

Yadav. R.C.. V. Kurnar and V. B. Ogunela. 1986. Partitioning of rain water and its
implication on application efﬁciency of overhead irrigation. Transacrion of the
Indian Society of Desert Technology. 11(2) :91-97.

Yitayew. M. 1987. Interrelationships of performance parameters for irrigation borders.
Agricultural Water Management. 12:221-.30.

Yonts. C. D.- J. A. Smith and J. E. Bailie. I991. Furrow irrigation performance in reduced-
tillage systems. Transactions of the ASAE. 34(1):91-96.

APPENDICES

Appendix I. QuickBasic Program Listing

DECLARE FUNCTION RndNorm! (Mean!- StanDev!)
DECLARE SUB Stats (NurttArrayll ). Count'la Man!- StanDevl. CoVarl- Min!. Max!)
DECLARE SUB tabext (vte!()- srnxel. dire!- lite!- xtel. yte!)
DECLARE SUB tabbex Ivan"). arglll. inxl. duel. yte!)
CLS

OPEN ‘cz'fn.csv' FOR OUTPUT AS 8|
PRINT =1.
PRINT 81. 'SCS" G1: Us
REM USER INPUTS

Runm = 300

Mean! - 242

SW! 8 7.26: chS! 2 StanDev! I Mean!

.VISICp = .1: MRI) =- MSrcp ° Man!

alpha = 5

ARD 8 23

awe - .43: [WC 8” -alphal ‘ awc

Rquep = alpha ' awc' ARD

DIM Areat9l ). InLArrathunI‘A). AEAmyllRunISSI. LFArrayltRun 'fol
kte =90: srnxe-0!:dxe = .04
FOR i = I TO ktee l
READ Ami)
NEXT i

FOR .\I% = I TO Rural?-
Ianrtaylleﬁl = RndNormllMcanl. StanDevll
NEXT M96

FOR Rquep = MRD TO (Mean! ‘- 3 ' MRD) STEP MRD
FOR NV. - I TO Runl‘f.
1F lnl'AnayllNﬁﬁl <= Rquep THEN
AppEff = I
ELSE
AppEfl' -- Rquep I moan-gems.)
END IF
Amy-1019’.) = AppEff
NEXT NV.

CALL StatstAEAmylll. Routes AngEl. StdAE!. amt-:2. Min:- Max!)
lFevAEl> 1THEchAE!=-1!

Zinf = (Mean! - Rquepi I StanDeVE

Rinf = .788 - .3075 ' Zinfe- .0486 ' Zinf “ 2

Tint'- .788 - .693 ‘ Zinf- .0485 ‘ Zinf“ 2

CALL tabexttAmt 1. srnrre. date. kte. Zinf- FulArmt

IFFuIArea<OTHEN FuIArm=0

DefArea . 1 - FulArea

MAR - RenDep I Mean!

AngefDep - Rquep - StanDeVI ' Rinf: 'Avg. depth received in deficit area

95

96

IF Angechp < 0 THEN Angef'Dep - o
DefRario = AngefDep/ Rquep

StoEff = FuIArea * (DefArea ‘ DefRatio)
CAW = AngE! ' MAR
chE! = SQRtevAE! " 2 - chS! " 21

IF chE! > I THEN chE! =- I

EnvEfl‘. = I . GEE!

REM UNIFORMITY EFFICIENCY PER CENI‘AGES
Us! =tl -(StanDev! IMean!» ' too
AE! = Avg-A5! ' 100
SE! a SroEtT' :00
£5! = EnvF-II! ' I00
SAE!=(1-ch.E!1'100

PRINT USING $39.8 “4.8 :38} use; use my” unseat sit-m 2.888 8.8%": C52: AE!; SAE!: SEE:
EE!: CAW: Det'Ratio: FuIArca; MAR
PRINT :1. USING “us-u $88.3 88%.: m; use: “a.“ $85.38: “an"; 05!: AE!: SAEI: SE1: EEE: CAW;

DefRatio: FulArea: MAR
NEXT
PRINT SPCIZ): "US“: SPCISI: 'AE': SPCISI: 'SAE': SPCI31: 'SE‘: SPCI4): 'EE': SPCH): ‘CAW": SPC(31:
‘DefRatio': SPCIZ): ‘Arn": SPC(31:'MAR'
CLOSE 31
END

DATA 5000-5160-53 l9-5478-5636-5793-5948-6103-6255-6406
DATA .65 54-6700-6w-6985-71 2.3-7257-7389-75 1 7-7642-7764
DATA .788 I -7995-8 106-8212-83 15-8413-8508-8599-8686-8‘770
DATA .8849-8925-8997-9066-9 13 1-9192-925 1 .9306.” 57-9406
DATA .94 52-9495-9535-9573-9608-964 1-9671-9699-9726-9750
DATA .977".-.9793-98 12.9830-9846-986 1-9 875-9887-9898-9909
DATA .9918-9927-9934-994 I -9948-9953-9959-9963-9967-9967
DATA .997 1 -9974-9977-9980-9982-9985-9987-9989-9990-9992
DATA .9993 -9994-9994-9995-9996-9996-9997-9997-9998-9999
DATA .9999

FUNCTION RndNorrn! (Mam. StanDev!1
DO
RandomA! =2! ' RND-I!
RandomB! .33 ' RND- I!
Radiusl! = RandomA! “ 2 ~ RandomB! " 2
LOOP UN'I‘ILIRadiusl!< 1!):REMANDIRadius2! >0!) Mod. ‘-“'
Deviate! = RandomA! ' SORII-Z! ' LOGIRadiuslm I Radiusl!)
RndNorrn! = Mean! ~ Deviate! ‘ StanDev!
END FUNCTION

SUB Stats tNumArray!t ). Count‘lo. MeanL StanDevL CoVarL Min!. Max!)
IF Count‘l. < I THEN EXIT SUB
FOR j% - 2 TO Count‘l.
Temp! =- NumAnayIOE’o)
K7. 3 )7. - I
DO WHILE (ITernp! < NmnArrayHK'AI) AND (K26 >031
NumAnayIIKS’o - 118 NW“ K961
‘9’. 8 KY. - I
LOOP
NumArrayﬂK‘fo * II = Temp!
NEXT j‘f.

97

FOR j‘B’. 8 I TO Count?-
ValueSurn! = ValueSurn! *- NumAmyloﬁ‘.)
SquareSurn! = SquareSum! e NtunArrnij‘A) " 2
NEXT j-x.
Min! = NumArray!( 1)
Max! 8 NumAnay!ICount‘/ol
1F t(Count'/o .. I) \ 21' County. \ 2 THEN
Mid% - Count‘lo ‘r 2
Median! 3 (Num-krrayllMidVol ’ NW‘!Ih-Iid‘.'o - 11) I 2!
ELSE
Median! = NumArray-!(ICount‘.’o - I) x 21
END IF
Mean! - ValueSum! I Count‘/.
IF Count‘J’. -: I THBS'
StanDev! = 0!
ELSE
StanDev! ‘8 SORI(SquareSurn! - Comics ' Man! ‘ Man!) I (Counﬁ'o - In
END IF
CoVar! - SranDev! I Mean!
END SUB

SUB tabert (Vtet )- smxe. dare. kte. inx. ytc)
dume 8 ins -smxe
ire - .5 - dume Idxe
1Fite<1THENitesIELSEII-‘ire>kreTHENite-kre
yte . “elite! " (“elite - 11- stditel) ‘ Idurne -(ite - I) ' dxe) I dxe
END SUB

SUB YldNetRet
REM Environmental Yield Function
E'IT- I -pfrac:BDC=1-beta' DeICoef
YLD -= YLDrn ' E'l’f ° BDC
NetRet =(YLD ' CstI-WatCst-EEs-io ' CstEE
END SUB

98

Appendix 2. Detailed Program Output

 

 

application application storage irrigation crop fully minimum
efﬁciency uniformity efﬁciency environ. available deﬁcit ratio rm‘gated application
efﬁdency water area ratio
U. = 40
19.9 0 93.3 0 0.02 0 0.93 0.1
31.2 11.7 91 0 0.06 0 0.91 0.2
41 32 88.2 9.3 0.12 0.01 0.88 0.3
49.8 44.7 87.4 18.4 02 021 0.84 0.4
57 .6 54-1 86 24.4 0.29 0.32 0.79 0.5
64.8 61 .1 84.6 28.5 0.39 0.4 0.75 0.6
71 2 66.7 829 31 .4 0.5 0.45 0.69 0.7
76.9 71.4 81 33.5 0.61 0.48 0.63 0.8
81 .6 75.6 78.9 35.2 0.73 0.51 0.57 0.9
85.6 79.3 76.4 36.5 0.86 0.53 0.5 1
89 82.5 74 37.5 0.98 0.54 0.43 1 .1
91.8 85.3 71.6 38.2 1 .1 0.55 0.37 12
94 87.8 692 38.8 122 0.56 0.3 1.3
1.1.I = 50
16.8 0 96.4 0 0.02 0 0.96 0.1
28.6 17.3 94.5 3.3 0.06 0 0.95 02
39.1 362 93.9 19 0.12 025 0.92 0.3
48.5 48.1 93.2 28 0.19 0.39 0.89 0.4
57.1 56.8 91 .6 33.9 0.29 0.47 0.84 0.5
64.8 63.7 89.9 38.2 0.39 0.52 0.79 0.6
71 .7 692 88.1 41 .3 0.5 0.56 0.73 0.7
77.9 73.9 85.5 43.6 0.62 0.58 0.66 0.8
83 78 83 45.4 0.75 0.6 0.58 0.9
87.3 81.7 80.3 46.8 0.87 0.61 0.5 1
90.8 84.9 77.6 47.8 1 0.61 0.42 1.1
93.5 87.7 74.7 48.5 1-12 0.62 0.34 1.2
95.5 902 71 .8 49 1 .24 0-62 026 1.3
U, = 60
142 0 98.8 0 0.01 0 0.99 0.1
25.7 28.3 98.3 17-9 0.05 0.27 0.98 02
36.6 44 97.8 31.2 0.11 0.47 0.96 0.3
46.8 53.4 97.1 38.6 0.19 0.56 0.93 0.4
56.1 60.8 96 44 0.28 0.62 0.9 0.5
64.6 66.9 94.4 48-1 0.39 0.65 0.84 0.6
72.1 72.2 92.3 51.3 0.51 0.67 0.77 0.7
78.9 76.7 90 53-7 0.63 0.68 0.69 0.8
845 80.7 87.4 55-6 0.76 0.68 0.6 0.9
89.1 84.4 842 57 -1 0.89 0.68 0.5 1

92.7 87.6 81.1 58.1 1 .02 0.68 0.4 1.1

99

 

 

application application storage irrigation cop fully minimum
efﬁciency uniform‘ty efﬁciency environ available deﬁcit ratio imgated application
efﬁciency water area ratio
95.3 90.4 77.7 58.9 1 .1 4 0.68 0.3 1 .2
97 92.8 74.3 59.4 1 .26 0.68 0.2 1 .3
U, = 65
12.6 16.5 99.5 9.5 0.01 O 1 0.1
24.4 35.7 99.4 26.8 0.05 0.41 0.99 0.2
35.3 492 99 38.3 0.11 0.57 0.98 0.3
45.7 572 98.4 44.7 0.18 0.65 0.96 0.4
55.4 63.4 97.6 49.4 028 0.69 0.92 0.5
64.3 68.9 96.3 53.2 0.39 0.71 0.87 0.6
72.3 73.9 94.5 56.3 0.51 0.72 0.81 0.7
79.4 78.3 92.3 58.8 0.64 0.73 0.72 0.8
85.4 822 89.5 60.7 0.77 0.73 0.62 0.9
90.1 85.9 862 62.3 0.9 0.72 0.5 1
93-7 89.1 82.8 63.3 1 .03 0.72 0.39 1 .1
962 91.8 792 64.1 1.15 0.71 027 1 -2
97.8 942 75.3 64.5 127 0.71 0.16 1 .3
U. = 70
11.5 49.3 99.9 41.1 0.01 0.09 1 0.1
22.9 50.7 99.8 42.3 0.05 0.53 1 0.2
34 55.6 99.7 46.4 0.1 0.66 0.99 0.3
44.5 61 .9 99.4 51 .5 0.18 0.72 0.98 0.4
54.6 66.8 98.8 552 027 0.75 0.95 0.5
63.9 71.3 97.9 58.5 0.38 0.77 0.91 0.6
72.4 75.8 96.4 61.4 0.51 0.77 0.84 0.7
79.9 80 942 63.9 0.64 0.77 0.75 0.8
86.3 83.8 91.5 65.9 0.78 0.77 0.63 0.9
91 2 87.4 882 67.5 0.91 0.76 0.5 1
94.8 90.7 84.5 68.6 1.04 0.76 0.37 1.1
97.1 93.4 80.6 69.3 1. 1 7 0.75 0.23 1 2
98.6 95.6 762 69.7 1 .28 0.74 0. 1 1 .3
U. a 75
10.9 662 100 58 0.01 022 1 0.1
21 .7 662 100 58 0.04 0.62 1 0.2
32.6 662 99.9 58 0.1 0.74 1 0.3
43.3 67.8 99.8 592 0.17 0.79 0.99 0.4
53.5 71 -1 99.6 61.8 027 0.82 0.98 0.5
63.3 74.4 99 642 0.38 0.82 0.95 0.6
72.4 78 98.1 66.7 0.51 0.83 0.89 0.7
80.3 81 .8 96.2 69.1 0.64 0.82 0.79 0.8
872 85.5 93.6 71.1 0.78 0.81 0.66 0.9
92.3 89.1 902 72.7 0.92 0.8 0.5 1
95.9 92.3 862 73.8 1.06 0.79 0.34 1.1

98 95 81.8 74.5 1-18 0.78 0.18 12

100

 

 

application application storage inigation crop fully mmirnum
efﬁciency uniformity efﬁciency environ. available deﬁcit mtio irrigated application
efﬁciency water area ratio
992 97 76.9 74.8 1 29 0.76 0.02 1 .3
U. = 80
10.5 76.1 100 68.9 0.01 022 1 0.1
21 76.1 100 68.9 0.04 0.66 1 02
31.5 76.1 100 68.9 0.09 0.8 1 0.3
42 76.1 100 68.9 0-17 0.85 1 0.4
524 76.5 99.9 692 0.26 0.87 0.99 0.5
62.5 78.3 99.7 70.5 0.38 0.88 0.98 0.6
721 80.8 992 723 0.5 0.88 0.93 0.7
80.7 83.9 97.9 74.4 0.65 0.87 0.84 0.8
88.1 87.4 95.6 76.4 0.79 0.86 0.69 0.9
93.6 90.9 921 78 0.94 0.84 0.5 1
97.1 94.1 87.9 79.2 1 .07 0.83 0.3 1 .1
98.9 96.6 828 79.7 1.19 0.81 0.1 1 .2
99.7 98.4 79.1 79.9 1 3 0.79 0 1 .3
U. = 85
10.3 83.4 100 77.7 0.01 0 1 0-1
20.5 83.4 100 77.7 0.04 0.6 1 0.2
30.8 83.4 100 77.7 0.09 0.79 1 0.3
41 83.4 100 77.7 0.16 0.87 1 0.4
51 .3 83.4 100 77.7 026 0.91 1 0.5
61 .6 83.5 100 77.7 0.37 0.92 1 0.6
71 .6 84.5 99.8 78.4 0.5 0.92 0.98 0.7
80.9 86.5 992 79.8 0.65 0.91 0.91 0.8
89 89.5 97.4 81.7 0.8 0.9 0.75 0.9
95 929 94-1 83.4 0.95 0.88 0.5 1
98.3 96 89.4 84.5 1 .08 0.86 0.23 1 -1
99.6 98.3 83.9 84.9 12 0.84 0 12
99.9 99.6 81.6 85 1.3 0.82 0 1.3
U. = 90
10.1 89.5 100 85.5 0.01 0 1 0.1
202 89.5 100 85.5 0.04 028 1 02
30.3 89.5 100 85.5 0.09 0.66 1 0.3
40.5 89.5 100 85.5 0.16 0.83 1 0.4
50.6 89.5 100 85.5 0.25 0.91 1 0.5
60.7 89.5 100 85.5 0.36 0.94 1 0.6
70.8 89.5 100 85.5 0.5 0.96 1 0.7
80.8 90 99.9 859 0.65 0.95 0.98 0.8
89.8 91.9 99.1 87.1 0.81 0.94 0.84 0.9
96.5 95 96.1 88.8 0.96 0.92 0.5 1
99.4 98.1 90.6 89.8 1.09 0.9 0.1 1 .1
100 99.7 86.7 90 12 . 0.87 0 12

100 100 83.5 90 1.3 0.83 0 1 .3

101

 

 

applimuon application :1er irrigation aop fully minimum
eﬂidency uniformity ellidency environ. available deﬁa’t ratio irrigated application
efﬁciency water area ratio
U. a 98

10 98 100 972 0.01 0 1 0.1

20 98 100 972 0.04 0 1 02

30 98 100 972 0.09 0 1 0.3

40 98 100 972 0.16 0 1 0.4

50 98 100 972 025 0.061 1 0.5

60 98 100 972 0.36 0.531 1 0.6

70 98 100 972 0.49 0.797 1 0.7

80 98 100 972 0.64 0.936 1 0.8

90.1 98 100 972 0.81 0.99 1 0.9

99.2 98.9 99.2 97.7 0.99 0.984 0.5 1

 

102

Appendix 3. Regression Coefficients

 

 

gﬁ—gangm
AE = an + a, «ram 82 ma11+ a3 mar" [Equation 33]. page 56.
40 8.1500 124.64 04.28 7.08 0.9999
50 4.4800 129.67 -50.20 3.32 0.9998
60 1.7510 127.08 -33.81 -5.89 0.9999
65 0.3420 125.00 -23.91 -11.31 0.9999
70 0.3790 118.87 -7.98 4929 0.9999
75 0.0965 107.38 15.45 00.42 0.9999
80 0.9049 9276 4287 43.09 0.9999
85 23130 77.1 1 71.13 -56.09 0.9998
90 3.5600 64.21 94.07 66.58 0.9994
98 4.0700 59-52 10219 -70.28 0.9920
AU =ao + a, AE*32A52*33A53+34AE‘*35AE5 [Figure 111. page60.
40 106.7727 -1 3.6889 0.5985 0.0107 8.88605 -278e-07 0.9997
50 8.6829 -2.9786 0.2042 «0.0040 3.386-05 -1 .056-07 0.9998
60 -73.0429 7.41 00 0.1985 0.0031 242605 7.78e-08 1-0000
65 46.5055 3.2734 0.061 1 0.0008 -5.41e-06 1.87e-08 0.9998
70 55.0446 0.9449 0.0447 0.0006 246e-06 9.08e—10 0.9998
75 61.6693 0.8448 0.0526 0.0014 -1-45e-05 5.65e-08 0.9998
80 71.2514 0.8209 0.0447 0.0010 -1.03e-05 4.02e08 0.9984
85 80.5361 0.4934 0.0278 0.0007 -7.62e-06 3.30608 0.9956
90 86.0354 0.6223 0.0367 0.0009 -1.08e-05 4.61e-08 0.9922
98 87.7003 0.71 62 00420 0.001 1 -1.21e-05 5048-08 0.9883

 

 

103

Appendix 4. SCS-Sehednler Output - Soil Water Content

 

 

 

 

 

 

   

 

 

 

 

 

.. ...-mues- ..-~...-. 3:; _ ......- .-o:¢o--- .2..- .2-5-
when
max: .mxoo can: «the .230 339
o p I b b l > I b p n L D
ow ...
A .
o. . .z a... .\ ....-
~ . . .. .. ... \ \ . «mt-.3
. \ . mmzoz.
co 1 \ ION-m
. \ -
2:.- IIIII-11-IIIII-\ too.-
00..
o 3 x ..0m <1]. 6301 a: u tun-06m 05301-0 «02800 n ...-n... Lot-o
1.0.03 co..on.LL. a 3: .2 no: - Soc sconce-em
o~o>o¢b4 - 6...-.2 use...

1.0.03 c.0m I

be»: «mt-Go -

2.x.— cos-60.1....

 

 

cu-eameum ze-pcu-eu-

cub-32860080.:

 

 

1.0/4

 

 

 

 

 

 

 

 

 

 

 

 

...-3.3 ...-386 2......- 3-l _ LA .26-.295: :2..."- .55.
when
«150 aux: 3:6 vo\no 3on «two
0 - - 1 - . l:=l - - . - - - l e
.4 . .....
. ... \ .
. 4. . ... . \
ov 4 z x 19...
N .. . . ¢Uh¢3
03¢ A t .34 .3
o. \ muzuz-
. t \ ‘3..-
00 L \ v
. \ tor...
.2- .11-... 1.1.1.1.. ... .
. 2...-
o 3 c ..om < r anom- o-— u con-00m 0530.5 omzmoo " 2.x.— LOLO
1.0.03 co_.on_LL. a g: .m— an: u .300 accent-sew
£0.03 .- .oa I has: «uh-2m“. - 0...:- co_.on.LL. «nadir-.3 - :52 ...-on.

 

 

cuaaamzoa 8°.hco.¢~:

cu»:e:ooe¢o.:

 

 

105

 

ea: ._ "mmuQXm

-.~..: 2:;

 

 

 

 

 

_ ...-..- .26-ESE-

:vn.~. «5cm

 

 

 

 

 

 

 

 

«<3 9:: o~\oo ctr-0
a l 1 = r - L l .1—
ON I ‘106.
6‘ \ v
-
o.- .. .. .. 13..
~ . . .. .. \ - 5:5-
03‘ 00 I. 10*.“ $0
. muzoz.
\ 1..-.0
ca \ .
. \
.... ion-v
ac... - .
cv.-s.
o 3 6 20m <11 u canoom act-3.5 omzmoo « eta.— Logo
1.0.03 co..oo.L.-. a «neon oueoncoeu
I . 0...:- co:ooT-.... nook-30¢ - «no: 51.0....

Looo3 c_o¢

.33... «upzuo

 

 

 

audaauxum ze.h¢o.¢¢_

«whamtouezo...

 

 

106

 

 

 

 

 

 

   

 

     

 

 

 

:2. "mmwn-Xm :3... "ohm so... "22.2.0.5: 1..-a ”2.5.
- ...-.- -
3x3 3\oo «ox: «:3 at: :23
o 1 - - . . . . .
o~ 1 roo-
. 2
0v 1 1.0.—
N . lo 9.. o.- oIo as. oo- .I. on. ... .to on. so. to .6. as. ots v «uhc3
\ r .
03¢ a.- - \ 2 ~ ”6
- \ . mwxoz.
on 1 roe-m
. 2
so? 11111111111111! 13.
3....
< r a u n
u 3 c _ .o m n on ou— (Ono-um (.3016 092860 « OLA... Logo
...-:03 cozooT-L. a co: ..m aor— " 30a accent-«em

...-v.03 c_o~_ -

:5... «uhzmo " 2.3. cutout...

Sam-.501 " see: ...-on.

 

 

cuuaauzuu 26.4e6-ae.

cape-xeoocu.x

 

 

1m

 

.93.. 6386 :8... u on...—

 

 

 

 

_ ....“ £2523. ..:.2 2:5.

 

 

 

 

u h. c o
«uxoo aux: max: 3st Zxoo ouxno
o - - 1 - no
__ _. __ __
2. 1 1r...
x ..s \ v
2 .. .. \ 18..
~ . . .. . $.83
03‘ A I co. to. o. on. no. 0.... .90 ol on. 0.0 a. can .0. o. S ‘0‘.“ to
3 L s ' mmzoz.
\
A \ ION.@
GO 1 \ x v
. 1 \ too;
\\
3L . -\ f 8..
o 3 c _ .0...» 233 n: " conoom 05395 onzcou « 0%» Logo

2.: .2 an..."
:5: 5:28 .

no.03 co_.om_gx.
Loao3 :.o¢

0

<11.
m
I

0.0a coconLosw

0%... c0309.}... —o~Z.Jv_¢ . 0:02 6L0“—

 

 

mmdanmzua 8°.h¢0.88.

Kuhn-5890080.!

 

 

108

Appendix 5. Center Pivot Evaluation Data for St. Joseph. MI.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

: Average 1 , . Irrigated : \Mnd Relative

Year System tappl. depth! Chrisiansen: Statistic.” area speed humidity

inches. unifomtiy nunifor'mityE acres mph %
1987 rgent87 0.37 1 60 1 49.9 6 153.5 8.5 92
1988 ﬁle88 0.32 66 57.4 210.9 3 60
1988 myersaa - 0.31 79 73.7 124.1 10 75
1988 manhowes . 0.86 80 74.9 89.0 2 77
1988 iotka88 0.72 85 81 .2 132.4 2 41
1988 ivyod882 - 0.6 65 56.1 86.1 2 15
1988 milli88 0.72 74 67.4 58.2 5 11
1988 Ram 0.46 79 73.7 137.3 3 18
1988 ﬁeck88 0.32 . 69 612 182.3 3-4 56
1988 : ﬁnner88 i 027 : 84 80.0 T 160.7 8 78
1989 . rgemag 0.3a ' 90 37.5 ; 157.4 5 75
1989 . benquiBQ 9 0.24 80 74.9 I 162.5 5 66
1989 ‘ rcupp89 : 0.69 79 73.7 95.4 S 65
1989 dcn'p89 029 70 62.4 103.9 6 70
1989 rklein89 0.57 83 78.7 125.7 9 68
1989 agra0933 i 1.78 74 67.4 40.6 5 77
1989 dchen940 ' 1.01 85 81.2 79.5 7 81
1989 kinm3945 : 0.95 74_ 67.4 34.3 4 81
1989 dstubnex 0.32 86 82.5 50.9 2 92
1989 stubnex 5 0.85 85 812 103.2 2 92
1989 stubnex 0.74 85 812 225.9 4 76
1989 rgen1921 ' 0.74 85 81.2 225.9 5 75
1989 wwild970 i 0.63 89 86.2 309.0 3 61
1989 ebarn89 ‘ 024 80 74.9 146.3 10 78
1990 rfarmo17 ’ 1.28 80 74.9 66.6 10-12 80
1990 ‘ fgroveye . 0.43 74 67.4 175.5 3 64
1990 fgmvene - 0.79 79 73.7 147.5 4 44
1990 astutzne : 0.98 82 77.4 159.0 9 95
1990 astutzye 0.88 86 82.5 158.0 5 39
1990 mmillO34 ‘ 0.56 70 62.4 108.2 4-5 81
1990 05031.15 - 0.53 80 74.9 171.0 4-5 100
1990 dstu1201 f 0.46 as 812 148.5 4.5 66
1990 dsturbur 0.58 88 85.0 84.9
1990 mkauf190 0.59 84 80.0 422 8 89
1990 hmillz32 0.53 81 762 43.9 5 80
1990 jmgjo928 0.17 82 77.4 37.4 2 93
1990 mkauf190 0.38 70 62.4 68.7 8 89

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 Average 5 . Irrigated , 1Mnd Relative

Year System ;appl. deparIChn'siansen: Statistical! area speed :humidity

- ! inches. 1 unifomtiy !unifonnityl acres mph i °/o
1990 ' dborgSO i 0.54 i 91 762 ‘ 111.8 calm as
1990 ' 11roy90 1 0.17 ‘ 82 77.4 37.4 5-6 92
1990 ' 11111111290 2 0.33 = 71 63.7 162.9 6-7 85
1990 ' £92090 . 0.58 73 66.2 46.2 5-6 90
1990 ' mkauf390 ' 0.43 88 85.0 124.7
1991 hrnillpvi 0.31 78 72.4 74.3 4-7 74
1991 hmillida . 0.53 75 68.7 ' 208.4 8 60
1991 ' gcoom101 3 0.23 85 812 168.8 . 0-3 80
1991 «29101 i 0.19 83 78.7 91.3 ' 11911154 75
1991 1mbenne91 1 0.37 ; 81 76.2 123.6 f 5-7 62
1991 1 gentz91f 0.36 1 88 85.0 105.6 5-10 78
1991 1 ebam918 ; 0.29 77 71.2 203.6 05 75
1991 - «069150 E 0.35 e 84 80.0 155.7 5-8 80
1991 . cgrabe91 . 0.41 . 85 812 175.5 0-7 76
1991 : ebam912 5 0.45 E 91 88.7 - 30.0 . 0—3 90
1991 ebar-ex1 i 0.39 88 85.0 3 78.9 0 -
1991 ebr-ex2 i 0.38 I 85 812 116.3 none -
1991 stubny1 ': 0.38 86 82.5 3.8 5-9 65
1992 5 110111992 1 0.41 a 84 80.0 0.1 3 82
1992 ‘Jenrzhas ' 0.24 9 87 83.7 116.3 4.5 70
1992 5 gentzsax : 0.33 74 67.4 114.5 none 83
1992 5 benne92 r 0.36 81 76.2 42.1 3.5 85
1993 ‘ dstur93e i 0.27 78 72.4 43.9 5-6 80
1993 ' dstur93w ‘ 0.5 83 77.4 '42036 5-6 80

 

 

MICHIGAN STATE UNIV. LIBRnRIES
mMull“Hm“IWW1|”mWWI"WIIWIWI
31293015945656