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This is to certify that the
thesis entitled

A Simplified Statistical Method For Field Evaluation Of
Sprinkler Irrigation Systems

presented by

Mohamed Eldaw Mohamed Elwadie

has been accepted towards fulfillment
of the requirements for

M.S. Agricultural Technology

degree in
and Systems Management

 

 

 

 

Date JUly 31, 1995

 

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Michigan State
Universlty

 

 

 

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TO AVOID FINES Mun on or More data duo.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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A SIMPLIFIED STATISTICAL METHOD FOR FIELD EVALUATION OF
SPRINKLER IRRIGATION SYSTEMS

By

Mohamed Eldaw. Mohamed. Elwadie

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

1995

ABSTRACT

A SIMPLIFIED STATISTICAL METHOD FOR FIELD EVALUATION OF
SPRINKLER IRRIGATION SYSTEMS.

By

Mohamed E. M. Elwadie

Sprinkler irrigation has become increasingly popular in the recent years, because of
continuous innovations and improvements in the method. However, water distribution
uniformity is an important factor attracting the attention of many researchers, because of
its direct impact on crop productivity and the environment.

In this thesis, a simplified statistical method for field evaluation of sprinkler
irrigation systems is presented. The method is based on the estimated coefficient of
variation CV (low/high) and estimated confidence limits. The method can be applied to
the evaluation of any sprinkler irrigation system when 18 catch can depths are randomly
selected. The coefficient of determination (R2) together with 95% confidence limits were
used to compare this method with methods already in practical use.

When the CV (low/high) of solid set sprinkler was compared to the CV (actual) ,
R2 = 0.96. On the other hand, when CV (18) was compared to CV(actual) R2 = 0.94.
Further comparison of CV (low/high) to CV (18) yielded R2 = 0.97.

With regard to Turf grass sprinklers, a comparison of CV (actual) to CV
(low/high) resulted in R2 = 0.99. Comparing CV (actual) to CV (18) yielded, R2=O.99.
When CV (low/high) was compared to CV (18) gave R2 = 0.99.

As for the center-pivot system, a comparison of CV (Heermann) to CV (low/high)

from simulated data yielded R2 = 0.94. When the actual data were statistically analyzed , a
comparison of CV (Heermann) to CV (SCS) resulted in R2 = 0.93. In addition, when CV
(Heermann) was compared to CV (low/high) R2 = 0.95. Further comparison of CV (SCS)
to CV (low/high) yielded R2 = 0.99. Finally, a graphical technique for estimating the
statistical uniformity of the the proposed method is presented.

It can be concluded that, the “three lowest and three highest” method is practically
applicable for field evaluation of sprinklers inigation systems. It includes the advantages
of being very simple, easy to use and is based on statistical analysis. In addition, it is a
very useful tool for conservation of energy used for crop production and conservation of

water to the farmer and the environment.

T 0
my siblings Aisha and Balla, who sacrificed their lives for us

ACKNOWLEDGMENTS

The author wishes to thank the Rotary Foundation of Rotary International for their
generous financial support through Freedom from Hunger Scholarship. Without their
financial support this work could not have been achieved.

My utmost appreciation and gratitude goes to my major professor Dr. V. F. Bralts
whose tireless support and guidance provided me with inspirational energy to undertake
this research.

I am, sincerely grateful and thankful to Dr. R. Von Bernouth, the Chairperson,for
his contineous financial assistance and technical support to finish this research.

I must also extend my appreciation and gratitude to my committee members: Dr.
Fred Nunberger and Dr. Paul Reike for accepting to share the reading and editing and for
their constructive evaluation of this work.

I fiJlly indebted to Dr. Rogers Neimyers, my Rotary Host Counselor, for providing
and creating suitable environment for my studying throughout my stay in Michigan.

Many of my friends and colleagues have helped, in no small measure. I would like
to mention few of them who have provided invaluable contribution to this work Dr.

Mahmoud Mansour, Neba Ambe, Alioune Fall, and Barry Boubakr.

ii

TABLE OF CONTENTS

LIST OF TABLES ................................................... iv
LIST OF FIGURES .................................................... v
ABBREVIATIONS ................................................... vii
I. INTRODUCTION .................................................. l
A. Background ................................................. 1
B. Overview ................................................... 6
C. A Scope and objectives ......................................... 9
II. LITERATURE REVIEW ........................................... 11
A. Soil-water-plant relations ...................................... 11
B. Methods of irrigation ......................................... 20
C. Types of sprinkler irrigation systems .............................. 22
D. Parameters for sprinkler irrigation evaluation ....................... 23
E. Sprinkler system capacity requirements ............................ 33
F. Sprinkler uniformity .......................................... 36
G. Irrigation Efficiency Terms ..................................... 46
H. Summary ................................................... 56
III. METHODOLOGY ................................................ 57
A. Research approach ........................................... 57
B. Theoretical development ....................................... 62
IV. RESULTS AND DISCUSSION ...................................... 69
A. Solid set sprinklers test ....................................... 69
B. Solid set sprinklers on Turf ..................................... 75
C. Center-pivot systems ......................................... 81
D. Nomograph for sprinkler irrigation system uniformity estimation ........ 87
V. CONCLUSIONS AND RECOMMENDATIONS ......................... 89
APPENDICES ...................................................... 91
Appendix A. Solid set sprinklers data .............................. 91
Appendix B. Turfgrass sprinklers data ............................... 98
Appendix C. Center-pivot system data ............................. 105
REFERENCES ..................................................... 109

iii

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

Table 10.

Table 1 1.

Table 12.

Table 13.

Table 14.

LIST OF TABLES

Major world irrigated areas ................................... 3
Inigated area in the United States .............................. 4

Characteristics of irrigation development in the US from 1974 to 197 9
by region ................................................ 5

Range in available water-holding capacity of soils of different texture . . 14

Effective crop root depths that would contain approximately 80% of
the feeder roots in a deep, uniform, well-drained soil profile ......... 15

Typical peak daily and seasonal crop water requirements in difl‘erent
climates. ................................................ 16

Guide for selecting management-allowable deficit, MAD, values for

various crops ............................................ 18
Typical values of C used in Hazen-Williams equation .............. 27
Recommended C-values for plastic ............................ 30
Coefficient of variation of solid set sprinklers .................... 71
Coefficient of variation for sprinklers on Turf .................... 77
Coefficients of variation for center-pivot from simulated data ........ 81
Coefficients of variation for center-pivot from actual data .......... 82

Values of maximum depths at different coefficient of variations and
known minimum depths. ................................... 87

iv

Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.

Figure 8.

Figure 9.

Figure 10.
Figure 11.
Figure 12.

Figure 13.

Figure 14.
Figure 15.
Figure 16.

Figure 17.

LIST OF FIGURES

A typical solid set sprinkler layout ............................. 7
A Typical Center-pivot system layout ........................... 7
Dimendionless energy gradient curve .......................... 26
Nomograph for drip irrigation uniformity estimation ............... 42
Application efficiency under sprinkler irrigation .................. 53
Deficit irrigation for 100% efficiency .......................... 53
Application efficiency relationships ............................ 54

Application efficiency, coefficient of variation and percentage deficit

relationships ............................................. 55
Topographic distribution of water from solid set sprinklers .......... 61
Surface distribution of water fi'om solid set sprinklers .............. 61
Standard normal distribution curve ............................ 63
A comparison of CV (actual) to CV (low/high) ................... 72
A comparison of CV (actual) to CV (low/high) with 95%

confidence limits .......................................... 72
A comparison of CV (actual) to CV (18) ....................... 73

A comparison of CV (actual) to CV (18) with 95% confidence limits. . . 73
A comparison of CV (low/high) to CV (18). ..................... 74

A comparison of CV (low/high) to CV (18) with 95% confidence
limits .................................................. 74

V

Figure 18.

Figure 19.

Figure 20.

Figure 21.

Figure 22.

Figure 23.

Figure 24.

Figure 25.

Figure 26.

Figure 27.

Figure 28.

Figure 29.

Figure 30.

Figure 31.

Figure 32.

A comparison of CV (actual) to CV (low/high) on turf. ............ 78

A comparison of CV (actual) to CV (low/high) with 95% confidence

limits on turf. ............................................ 78
A comparison of CV (actual) to CV (18) on turf .................. 79
A comparison of CV (actual) to CV (18) with 95% confidence

limits on turf. ............................................ 79
A comparison of CV (low/high) to CV (18) on turf ............... 80
A comparison of CV (low/high) to CV 18 with 95% confidence

limits on turf. ............................................ 80
A comparison of CV (Heermann) CV (low/high) ................. 83
A comparison of CV (Heermann) to CV (low/high) with 95%
confidencelimits .......................................... 83
A comparison of CV (Heermann) to CV (SCS) .................. 84
A comparison of CV (Heermann) to CV (SCS) with 95%

confidence limits. ......................................... 84
A comparison of CV (Heermann) to CV (low/high). ............... 85
A comparison of CV (Heermann) to CV (low/high) with 95%

confidence limits .......................................... 85
A comparison of CV (SCS) to CV (low/high). ................... 86
A comparison of CV (SCS) to CV (low/high) with 95%

confidence limits .......................................... 86
Nomograph for sprinkler irrigation system uniformity estimation ..... 88

vi

AW

ASAE

CV

Low/high

ABBREVIATIONS

available water holding capacity, which is the difference between field
capacity and permanent wilting point, decimal.
American Society of Agricultural Engineers.
Roughness coefficient, dimensionless.
Coefficient of variation, percentage and equal o/>‘<‘.
Diameter of pipe, mm (inch).
Soil Conservation Service, distribution uniformity.
Water application efficiency, percentage.
Soil Conservation Service pattern efficiency.
Water application efficiency.
Food Agriculture Organization of the United Nations.
Field capacity, percentage.
Dimensionless fiiction factor.
Acceleration due to gravity, mZ/s.
Head loss due to friction, m.
Pipe length, m.
Sum of three-low depths and the sum of three-high depths method, based

on the estimated coefficient of variation and estimated confidence limits.

vii

PWP

PVC

R2
SCS
Slvfl)
SURFER
UC

UCC
UCH

UCW

U.S.

XI

Management-allowable deficit, decimal.

Operating pressure, Kpa (Psi).

Permanent wilting point, percentage.
Polyvinylchloride.

Flow rate in Us.

Reynold number, dimensionless.

Coefficient of determination.

Soil Conservation Service.

Soil moisture deficit equal 50% of the Available water.
Computer software, version 4.5, 1991.

Uniformity coefficient of variation of the irrigation system, percent.
Christiansen uniformity coefficient.

Hart uniformity coefficient.

Wilcox and Swailes uniformity coefficient.

United Nations.

United States of America.

Standard deviation

Average depth of application, mm (inch).

Confidence level desired.

viii

I. INTRODUCTION

A. Background

Irrigation has enabled many nations to establish ancient civilizations in the semiarid
and arid regions, such as the Egyptian civilization on the River Nile and the Chinese
civilization on the banks of the Yellow River. Irrigation is one of the oldest technologies,
but improvements in irrigation methods and practices are still being made. The future will
require even more innovations and improvements because of the competition for limited
water resources.

Agricultural production in general, and the production of food in particular has not
kept up with need. In 197 7 the Food and Agriculture Organization (F A0) of the United
Nations (UN) estimated that the total global irrigated area was 233 million hectares (ha),
and that would increase to about 273 million ha by 1990, Jensen (1983). Buringh et al.
(1975), estimated that, of 3419 million ha of potential agricultural land in the world, 470
million ha could be irrigated. A summary of irrigated area by regions and countries was
presented by Zonn (1974) and reproduced by Fukuda (1976). A brief summary is
presented in Table 1, (estimates in Table I differ slightly from those of the FAQ). In 1979,
the FAO estimated irrigated agriculture to represent only 13% but the value of its crop
production was 34% of the total world arable land. Since the end of World War II, the

development of sprinkler irrigation has been very extensive. One of the factors that helped

2

in the successful development of sprinkler irrigation was the introduction of the light
weight aluminum pipes. This basically reduced the initial investment cost in equipment.
Other factors include, improvements in sprinkler design and couplings, and fittings. By
1950 Keller and Bliesner (1990) better sprinklers and more efficient pump, further reduced
the cost and increased economic accessibility of sprinkler irrigation systems, hence
accelerating widespread use of the method. More recently, the self-propelled center-pivot
sprinklers, which gained popularity in the 19603, have provided a means for relatively low
cost, high frequency automatic irrigation with a minimum labor cost. Additional
innovations are continually being introduced to reduce labor cost and increase the
efficiency of sprinkler irrigation.

Table 2 shows the increase in US. irrigated land area since 1939. The largest
recent percentage increases occurred in the subhumid and humid south and southeast
states. But the largest increase in the total area occurred in the semiarid central and
southern great plains, Table 3 Jensen (1983). He suggested that 32% of the total irrigated
area in the US (20 million ha), was under sprinkler irrigation The largest increase in
sprinkler irrigated areas are in the arid pacific northwest and the semiarid great plains.
Furthermore, in the subhumid cornbelt and arid pacific northwest 84 and 54 percent,
respectively of the total irrigated area are under sprinkler irrigation. Sprinkler irrigation
has grown in popularity, because sprinkler irrigation systems are adaptable and suitable for
a wide variety of cropping systems. Also, they are adaptable to all irrigable soils, different

topographies, and because sprinklers are available in a wide range of discharge capacities.

Table 1. Major world irrigated areas.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Agricultural Land
Continent and Country Cultivated Cultivated Land Percent
Irrigated Irrigated
ha (1000s) ha (1000s

Afiica 214,000 8,929 4.2
Asia, excluding USSR 463,000 164,640 35.5
Australia and Oceania 47,000 1,701 3.6
Eume, excluding US SR 145,000 12,774 8.8
North and Central America 271,000 27,431 10.1
South America 84,000 6,662 7.9
USSR 233,000 11,500 4.9
Total 1,457,000 233,637 16.0

 

Adapted from Jensen, (1983).

 

4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2. Irrigated area in the United States.
US. Census data Irrigation Journal data
Year Total Inigated Area in Rate of Total Irrigated Area in Rate of
the US Growth the US Grth
ha (10003) ac (10003) percent ha (10003) ac (10003) percent

1939 7,278 17,893 - - - -

1944 8,312 20,539 2.7 - - -

1949 10,484 @906 4.8 - - -

1954 11,960 29,552 2.7 - - -

1959 13,421 33,164 2.3 - - -

1964 14,997 37,057 2.2 - - -

1969 ”$2 39,122 1.1 - - -

1971 - - - - - -

1972 - - - 20,215 49,951 -

1973 - - - 20,834 51,480 3.1
1974 16,691 41,243 1.1 21,461 53,029 3.0
1975 - - - 21,871 54,044 1.9
1976 - - - 23,032 56,911 5.3
1977 - - - 23,658 58,459 2.7
1978 20,700 51,000 3.0 23,834 58,893 0.7
1979 - - - 24,746 61,148 3.8

 

 

 

 

 

 

 

 

Adoptedfi'om Jensen, (1983).

 

5

 

 

 

 

 

 

Table 3. Characteristics of irrigation development in the US from 1974 to 1979 by
region .
Total Area Irrigated Sprinkler Irrigated
1974 to 1979 1974 to 1979
Region ha (10003) percent ha (10003) Percent percent
of total

Arid Southwest, (AZ, CA) 4,010 4,470 11 561 835 28 19
Arid Pacific Northwest, (ID, OR, and 2,963 3,153 7 1,006 1,664 65 53
WA)
Semiarid Central Mountains, (CO, MT, 4,587 4,280 -7 529 559 6 13
NV, UT, and WY)

 

Semiarid Central and South Great Plains, 7,343 8,987 22 1,766 2,884 63 32
(KS, NE, NM, OK, and TX)

 

 

 

 

 

 

 

 

 

 

Subhumid Combelt, (IL, IN, MN, MO, 261 602 131 172 504 193 84
and WI)

Subhumid and Humid, South and 1,993 2,511 26 504 799 59 32
Southwest, (AR, FL, GA, AL, MS, NC,

and SC )

 

 

Adapted from Jensen, (1983).

B. Overview

Hydraulic design is the most important factor in the ultimate success or failure of a
sprinkler irrigation system. A significant amount of research has been done in this area.
To assist in the improved design of sprinkler irrigation, Christiansen (1942), developed the
coefficient of uniformity as an indicator of a design's distribution uniformity. Heermann
and Hein (1968) modified Christiansen's uniformity coefficient for center-pivot sprinkler
systems. In addition to the coefficient of uniformity, Christiansen (1942) developed an
adjustment factor for the head loss along a lateral due to sprinkler output. Merriam and
Keller, (197 8) developed the distribution uniformity concept. Bralts et al. (1983 a, and b),
developed the statistical uniformity concept for evaluation of drip irrigation systems. The
design of sprinkler irrigation submain units for optimal sprinkler uniformity is very
important, because once the nozzles, the laterals and the main components have been
chosen, very little additional flow control is possible. Thus, the engineer making the
design decision regarding pipe size as well as nozzle and sprinkler selection, must have a
method of determining submain unit Sprinkler uniformity at the design stage.

Sprinkler irrigation systems, figure 1 (Solid set sprinkler) and figure 2 (Center-
pivot), consist of water supply and a pump, followed by a network of mainlines, (mostly
pipes of steel, asbestos or recently of polyvinylchloride (PVC), and laterals made of either
aluminum, PVC, or polyethylene, and sprinklers. In addition to delivery for irrigation,
sprinkler irrigation systems can be an effective means for the application of chemicals, i.e.

fertilizers, pesticides, herbicides, descants, and defoliants.

    

Sprinkler UfllI
Lateral Pipe Um!

Mainline Pipe Um!

      
            

    

       

    

\v .nnuuHHMp-wfinu
_. . .\ - a
\V m . mm n W .3.
t a in. m ...
\b . Wm“ a t

WOIOI
SOUTC.

A typical solid set sprinkler layout. (Adoptedfi'om Sichinga, 19 75).

Figure 1.

A Typical Center-pivot system layout. (Adoptedfiom Wallace, [98 7)

Figure 2.

8

The advantages of the conjunctive application of chemicals with irrigation water
include savings in labor and equipment, better timing, ease of split and multiple controlled
application, greater flexibility of farm operations, and consequently enhanced crop
production. Other functions of sprinkler irrigation systems may include crop and soil
cooling, protecting crops from frost and freeze damage, delaying fruit and bud
development, controlling wind erosion, providing water for seed germination by effective
light watering and land application of wastes. Today, sprinkler irrigation systems are
utilized on all types of soils, topographies and crops. However, the use of fertilizer
injection through sprinkler irrigation has not been fully realized. This is because irrigators
were not certain that their sprinkle systems were performing at an acceptable level of
uniformity. The problem has been a lack of field evaluation tools.

The field evaluation of sprinkler irrigation submain units is important for the farmer
to ensure acceptable performance of water distribution and chemical application; as well as

a diagnostic tool for the engineer to confirm successful design. I

In this thesis, a simplified method for the field evaluation of sprinkler irrigation
system was evaluated. This work follows the comprehensive procedure used by Bralts et
al (1983) to evaluate drip irrigation submain units by the using statistical uniformity
concept. The same procedures were adopted to evaluate the design and uniformity of
sprinkler irrigation. Then, the estimated coefficient of variation and the estimated
confidence limits were developed for sprinkler irrigation systems based on one sixth
maximum depths and one sixth minimum depths. Finally, the statistical uniformity was

calculated. The method was compared to existing methods used to evaluate sprinkler

9

irrigation systems, by using linear regression method and the results were validated. A
nomograph of sum of three minimum depths to the sum of three maximum depths was

generated to calculate the statistical uniformity of sprinkler irrigation systems.

C. Scope and objectives

The broad objectives of this study were to develop a simplified method to conserve
water, chemicals, and energy used for crop production through improved field evaluation
of sprinkler irrigation systems. Improvement of field evaluation techniques can conserve
energy by maximizing the efficiency of water use. This simplified method is, also, a very
usefirl tool to diagnose environmental concerns such as runoff water quality.

This study was, therefore, intended to develop a simplified method for field
evaluation of sprinkler irrigation systems which can be useable by the farmers. The
method described here uses uniformity estimates based upon the coefficient of variation,

and the statistical uniformity concept together with estimated confidence limits.

The specific objectives of this research were:

1. To develop the statistical uniformity concept for sprinkler irrigation
systems based on estimated coefficient of variation and estimated
confidence limits;

2. To apply the estimated coefficient of variation and the statistical uniformity
concept with estimated confidence limits to field evaluation of sprinkler

irrigation systems; and

10

To evaluate the usefillness of the estimated coefficient of variation and the
estimated confidence limits for the field evaluation of sprinkler irrigation
systems by statistical comparison of the results to methods already adopted

for field evaluation of sprinkler irrigation systems.

II. LITERATURE REVIEW

A. Soil-water-plant relations

Understanding the general concept underlying basic soil-water-plant relations and
interactions is central to the ability to design and manage sprinkler irrigation system. It is
therefore, worth clarifying the following important terms:

1. Soil water

The soil stores water needed by plants. Adsorptive and capillary forces, called
matric forces, hold significant amounts of water which can be removed and used by
plants. It is much easier for plants to obtain water from the soil when it is moist than
when it is dry because these retention forces are more significant under low water content
conditions.

Between saturation and absolute dryness are two important soil water contents
relative to the plant. These water contents, field capacity (fc) and permanent wilting
point ava), are defined respectively as the upper and the lower limits of soil water that is
available to the plants. In practice these parameters are defined as follows: Field capacity
is the percentage of water remaining in a soil two to three days after the soil has been
saturated and after free drainage has practically ceased, and permanent wilting point is the
water content of the soil after plants can no longer extract water at a sufficient rate for
wilted leaves to recover overnight when placed in a saturated environment. The water

content when the soil is at field capacity is less than saturation, while the soil is not

11

12

absolutely dry at the permanent wilting point. Neither field capacity nor wilting point is a
sharply defined quantity.

Because water between field capacity and permanent wilting point is available to
the plants, it is called the available water, (AW). The following equation is used to

compute available water:

= (fc-pWP)
AW 0,, 100 (1)

where:

AW = available water (mm, in);

D,2 = depth of the root zone (cm, in.) the depth to the soil layer that restricts

water movement;

fc = field capacity in percentage by volume; and

pwp = permanent wilting point, in percentage by volume.

Soils of various textures have varying abilities to retain water. Table 4, gives
typical ranges of available water-holding capacities, (field capacity minus permanent
wilting point) of soils of different textures adapted from Chapter 1, Section 3, of Keller
and Bliesner, (1990). These data are important to the farmer because any irrigation
beyond field capacity is an economic 1033. However, if field data were not available, these

averages are very useful in preliminary designs.

13

2. Root depth

The total amount of water available for plant use in any soil is the sum of all
available water-holding capacities of all horizons occupied by plant roots (Keller and
Bliesner, 1990). Table 5. can be used to estimate the effective root depth if actual data are
not available. The values represent the depth at which crops will obtain a major portion of

their needed water when grown in a deep, well-drained soil that is adequately irrigated.

3. Consumptive use

To address the question of system capacity that, over the life of the system will
maximize profit to the farmer, one must decide how much water the system should be able
to deliver to a crop over a given period. It is necessary to know how much water the crop
will use, not only over the entire growing season, but also during the part of the season
when water use is at its peak. It is the rate of water use during this peak consumptive
period that is the basis for determining what rate irrigation water must be delivered to the
field. Examples of typical seasonal and peak daily crop water requirements are given in

Table 6.

14

 

 

 

 

 

 

 

 

 

 

 

Table 4. Range in available water-holding capacity of soils of different texture.
water-holding capacity
range average

Texture mm/rn mm/m

1. Very coarse texture-very coarse sands. 33 to 62 42

2. Coarse texture-coarse sands, fine sands, and 62 to 104 83
loamy sands.

3. Moderatelycoarse texture-sandy loams. 104 to 154 125

4. Medium texture-very fine sandy loams, loams 125 to 192 167
and silt loams.

5. Moderately fine texture clay loams, silty clay 145 to 208 183
loams and sandy clay loams

6. Fine texture -sandy clays, silty clays, and clays 133 to 208 192

7. Peat and mucks. 167 to 250 208

 

 

 

 

Note: 1 rum/m = 0.012 mm

Adoptedfrom Keller and Bliesner, 1990.

15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5. Effective crOp root depths that would contain approximately 80% of
the feeder roots in a deep, uniform, well-drained soil profile.
Crop Root Depth Crop Depth (1n) Crop Root Depth
(111) (m)
Alfalfa 12 to 1.8 Chard 0.6 to 0.9 Peanuts 0.4 to 0.8
Almonds 0.6 to 1.2 Cherry 0.8 to 1.2 Pear 0.6 to 1.2
Apple 0.8 to 1.2 Citrus 0.9 to 1.5 Pepper 0.6 to 0.9
Apricot 0.6 to 1.4 Coffee 0.9 to 1.5 Plum 0.8 to 1.2
Artichoke 0.6 to 0.9 Corn (grain 0.6 to 1.2 Potato (Irish) 0.6 to 0.9
and silage)
Asparagus 1.2 to 1.8 Corn (sweet) 0.4 to 0.6 Potato (sweet) 0.6 to 0.9
Avocado 0.6 to 0.9 Cotton 0.6 to 1.8 Pumpkin 0.9 to 1.2
Banana 0.3 to 0.6 Cucumber 0.4 to 0.6 Radish 0.3
Barley 0.9 to 1.1 Egg plant 0.8 Safflower 0.9 to 1.5
Bean (dry) 0.6 to 1.2 Fig 0.9 Sorghum 0.6 to 0.9
Bean (green) 0.5 to 0.9 Flax 0.6 to 0.9 Sorghum 0.9 to 1.2
(silage)
Bean (lirna) 0.6 to 1.2 Grapes 0.5 to 1.2 Soybean 0.6 to 0.9
Beet (sugar) 0.6 to 1.2 Lettuce 0.2 to 0.5 Spanish 0.4 to 0.6
Beet (table) 0.4 to 0.6 Lucem 1.2 to 1.8 Squash 0.4 to 0.9
Berries 0.6 to 1.2 Oats 0.6 to 1.1 Strawberry 0.3 to 0.5
Broccoli 0.6 Olives 0.9 to 1.5 Sugarcane 0.5 to 1.1
Brussels 0.6 Onion 0.3 to 0.6 Sudan grass 0.9 to 1.2
sprout
Cabbage 0.6 Parsnip 0.6 to 0.9 Tobacco 0.6 to 1.2
Cantaloupe 0.6 to 1.2 Passion fruit 0.3 to 0.5 Tomato 0.6 to 1.2
Carrot 0.4 to 0.6 Pastures 0.3 to 0.8 Turnip (white) 0.5 to 0.8
Cauliflower 0.6 Pea 0.4 to 0.8 Watermelon 0.6 to 0.9
CelerL 0.6 Peach 0.6 to 1.2 Wheat 0.8 to 1.1

 

 

 

 

 

 

 

Adapted fiom Keller and Bliesner, 1990.

 

 

l6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 6. Typical peak daily and seasonal crop water requirements in different
climates.
Types of climate and water requirements, mm
Season Cool Moderate Hot High desert Low desert
Crop l 2 l 2 l 2 l 2 l 2
Alfalfa 5.1 635 6.4 762 7.6 914 8.9 1016 10.2 1219
Grain 3.8 381 5.1 457 5.8 508 6.6 533 5.8 508
Beets 4.6 584 5.8 635 6.9 711 8.1 732 9.1 914
Beans 4.6 330 5.1 381 6.1 457 7.1 508 7.6 559
Corn 5.1 508 6.4 559 7.6 610 8.9 660 10.2 762
Cotton - - 6.4 559 7.6 660 - - 10.2 813
Peas 4.6 305 4.8 330 5.1 356 5.6 356 5.1 356
Tomatoes 4.6 457 5.1 508 5.6 559 6.4 610 7.1 660
Potatoes 4.6 406 5.8 457 6.9 553 8.1 584 6.9 533
Truck vegetables 4.1 305 4.6 356 5.1 406 5.6 457 6.3 508
Melons 4.1 381 4.6 406 5.1 457 5.6 508 6.4 559
Strawberry 4.6 457 5.1 508 5.6 559 6.1 610 6.6 660
Citrus 4.1 508 4.6 559 5.1 660 - - 5.6 711
Deciduous orchard 3.8 483 4.8 533 5.8 584 6.6 635 7.6 762
Vineyard 3.6 356 4.1 406 4.8 457 5.6 508 6.4 610

 

 

 

 

 

 

 

 

 

 

 

 

l = Daily; 2 = Seasonal.
Adapted fiom Keller and Bliesner, 1990.

 

1 7

4. Soil moisture management

A general rule of thumb for many field crops in arid and semiarid regions is that the
soil moisture deficit, (SMD), within the root zone should not fall below 50% of the total
available water-holding capacity. This is the management allowable deficit; MAD = 50%
of AW. Because it is desirable to bring the moisture level back to field capacity with each
irrigation, the depth of water applied at each irrigation is constant (50% of total available
water holding capacity) throughout the growing season (Keller and Bleisner, 1990). This
means that the duration of each irrigation is also constant, although the frequency of
application varies as a function of changes in the rate of water use over the growing
season.

The situation is different in the humid regions, because it is necessary to allow for
rains during the irrigation period. However, the 50% limitation on soil moisture depletion
should be followed as a general guide for field crops.

Soil management, water management, and economic considerations determine the
amount of water used in irrigation and the rate of water application necessary. The
standard design approach has been to determine the amount of water needed to fill the
entire root zone to field capacity, and then apply at one application a larger amount to
account for evaporation, leaching, and inefficiency of application. The traditional
approach to the frequency of application has been to take the depth of water in the root
zone reservoir that can be extracted, assuming MAD = 50%, and, using the daily
consumptive use rate of the plant, determine how long this supply will last. This approach

is usefill only as a guide to irrigation requirements, as many factors affect the volume, and

18

the timing of application for optimal design and operation of a system.

Table 7. Guide for selecting management-allowable deficit, MAD, values for
various crops.

 

 

 

 

 

 

MAD, % Crop and root depth
25-40 Shallow-rooted, high-value fi'uit and vegetable
crops
40-50 Orchards,’ vineyards, berries and medium-rooted
row crqrs
50 Forage cropsz grain crops, and deep-rooted row crops

 

 

 

I
Somefi'eshorchardsreqturelowchADvalueedunngfiimfimshmgforsia'ng

Adapted from (Keller and Bleisner, 1990)

5. Irrigation depth
The maximum net depth of water to be applied per irrigation, d,, is the same as the

maximum allowable depletion of soil water between irrigations. It is computed by:

x 100 a (2)

where:
d, = maximum net depth of water to be applied per irrigation, mm (in);
MAD = management allowed deficit, which can be estimated from Table 4;
W, = available water-holding capacity of the soil, which can be estimated from
Table 4, mm/m; and

Z = effective root depth, which can be taken from Table 5, mm (11).

19

6. Irrigation interval

The appropriate irrigation interval, which is the time that should elapse between

the beginning of two successive irrigations, is determined by:

where:

_ d"
f'y; (3)

f = irrigation interval or frequency, days;

(1,, = net depth of water application per irrigation, to meet consumptive use
requirements, mm (in); and

Ud = conventionally computed average daily crop water requirement, or use
rate, during the peak-use month, which can be estimated from Table 6,
mm/day (in/day).

The values selected for d, will depend upon system design and environmental

factors, and it should be equal to or less than 64. When dn is replaced by d, in equation 2,

f becomes the maximum irrigation interval, j;

20

B. Methods of irrigation

Farm irrigation systems must supply water at rates in quantities, and at times
needed to meet farm irrigation requirements and schedules. It is essential that farm
irrigation systems facilitate management by providing a means for measuring and
controlling flow. The methods of applying water to the plants may be classified as

subirrigation, surface irrigation, microirrigation, and sprinkler irrigation.

I. Subirrigation

In special situations, water may be applied below the soil surface by developing or
maintaining a water table that allows water to move up through the root zone by capillary
action. This is essentially the same practice as controlled drainage. Controlled drainage
becomes subirrigation if water must be supplied to maintain the desired water level.
Water may be introduced into the soil profile through open ditches, mole drains, or pipe
drains. The open ditch method is most widely used. Water table maintenance is suitable
where the soil in the plant root zone is quite permeable and there is either a continuous
impermeable layer or a natural water table below the root zone. Since subirrigation allows
no opportunity for leaching and establishes an upward movement of water, salt

accumulation is a hazard; thus the salt content of water should be low.

2. Surface irrigation

2 1
This is the most common method of applying irrigation water, especially in arid
regions. Surface methods include: wide flooding, where the flow of water is uncontrolled,
and surface application, where the flow is controlled by furrows, corrugations, border
dikes, contour dikes or basins. To conserve water, the rate of water application should be

carefully controlled and the land properly graded.

3. Microirrigation

Increasing use is being made of microirrigation (trickle or drip) systems that apply
water at very low rates, often to individual plants. Such rates are achieved through the
use of specially designed emitters or porous tubes, usually installed on or just below the
soil surface. These systems provide an opportunity for efficient use of water because of
minimum evaporation losses, and because irrigation is limited to the root zone. Because
of their high initial cost, their use is generally limited to high-value crops. They are, also

well adaptable for application of agricultural chemicals.

4. Sprinkler irrigation

A sprinkler irrigation system uses pressure energy to form and distribute "rainlike"
droplets over the land surface, (Larry G. James, 1988). In sprinkler irrigation systems
water is conveyed from a pump through a network of pipes, called mainlines and
submains, to one or more pipes with sprinklers called laterals. A typical sprinkler system
is shown by figures 1 and 2. Sprinkler irrigation is a versatile means of applying water to

any crop, soil, and topographic condition. It is popular because surface ditches and prior

22

land preparation are not necessary and because pipes are easily transported and provide no
obstruction to farm operations when irrigation is not needed. Sprinkling is suitable for
sandy soils or any other topographic conditions where other methods may be expensive or
inefficient, or where erosion may be particularly hazardous. Low rates and amounts may
be applied, such as required for seed germination, frost protection, delay of fruit budding,
and cooling of crops in hot weather. Fertilizers and soil amendments may be dissolved in
water and applied through irrigation systems. The major concerns of sprinkler irrigation

systems is the investment costs, labor requirements, and evaporation losses.

C. Types of sprinkler irrigation systems
There are 10 major types of sprinkler irrigation systems and several versions of
each type. These types of systems may be divided into two basic groups:
1. Set systems
These operate with a sprinkler set in a fixed position. They can be further divided
to the following subgroups:
(1. Periodic move
Hand-move laterals, end-tow laterals, side-roll laterals, side-move
laterals, gun, and boom sprinklers
b. Fixed sprinkler system
2. Continuous-move systems
These operate while the sprinklers are moving. They can be subdivided into:

Traveling sprinklers, center-pivot system, linear-moving laterals.

23

D. Parameters for sprinkler irrigation evaluation

1. Basic hydraulics

The hydraulic principles of sprinkler irrigation are based upon the classical
continuity and energy equations. The following developments will follow the theory and
nomenclature used by Wu et., al., (1979) and Bralts et a1. (1983 a, b).

a. Pressure and head relationships:

The pressure of water at rest in a container at any point is equal to the
product of the unit weight of water (1000 Kg/m3 at 20°C) and the height of water above
the point, (head of water). Head is in meters (m) and pressure in Kilo-Pascal (KPa). One
meter of water = 9.81 KPa of pressure. In an irrigation system the head consists of

several components:

i. static head = difference in elevation between source and current position;
ii. pressure head = the pressure (P) divided by the unit weight of water;
iii. velocity head = the energy required to accelerate the water from rest to its

velocity (V 2/2g); and
iv. fiiction head (hr) = the energy required for water to flow (to overcome
friction) between two points at the same elevation.
b. Pipe flow equation
The flow in a sprinkler irrigation manifold pipe or lateral will be considered to have
reached a steady state. Flow will, therefore, vary spatially due to fiiction and pipe length,
but not temporally (Bralts, et al. 1983). This means that the total flow in the pipe is

changing, usually decreasing, with respect to length due to friction losses.

24

Head 1033 along a lateral is due to sprinkler output and fiiction. Any of several
empirical equations can be used to calculate head loss due to fiiction. In this thesis, only
two such equations will be discussed. The first equation, which is based on the Darcy-

Weisbach equation is as follows:

LP”
28,0 x (4)

 

Where:
hf = head loss due to friction;
f = dimensionless fiiction factor;
L = length of the pipe;
D = diameter of the pipe;
V = velocity of water in the pipe; and
g = acceleration due to gravity.
Since sprinkler irrigation laterals are considered to be hydraulically smooth and
their flow is fully turbulent then the Blasius empirical formula for turbulent flow in a
smooth pipe can be substituted for the dimensionless fiiction factor (f), (Wu and Gitlin,
1974; Howell et. al. 1981; and Bralts et. al. 1983 a, b). Figure 3. represents the

dimensionless energy gradient line, along a sprinkler irrigation lateral line, (Wu and Gitlin,

1974)

The Blasius formula for the fiiction fact f, is:

25

0.3164

0.25
Re

f:

 

(4000< Re <100000)

where:
f = friction coefficient; and
RC = Reynold number.

Watters and Keller (1978) combined equations (4 and 5) at 20°C and found:
Q 1.75
hf = 7.89 *105 (——)*L
04.75

where:
hf = head loss in meters;
Q = flow rate in Us;
D = pipe diameter in millimeters; and

L = pipe length in meters.

(5)

(6)

26

o —— comm: runaursucs, noucu me
0.1 \ ---_runwr.e~r FLOW in «room we
\ ._ .. murmur FLOW
112 ' \ ,_,_._ HAZEN-meLIAMS common

 

a: _ \
u . \
as \

0.8. \ \
0.1.. \ \

0... \\\ \
0.0.. \

"rescues unor- mmo. n. ram/am

 

\

 

 

 

o 0.1 0.2 0.3 no as as 0.7 0.8 0.3 1.0
LENGTH ”110,01.

Figure 3. Dimendionless energy gradient curve, (Wu and Giltin, 1974)

2 7
The second empirical equation which is commonly used in hydraulic design is the

Hazen—Williams formula (Keller and Karmeli, 1975; J eppson 1982):

1.852
h = 1221* 1010 (-—Q———)*L (7)
f C 1.852 D 4.871

where: C = the roughness coefficient.

Table 8 shows typical values of C for use in the Hazen-Williams equation.

 

 

 

 

 

 

 

 

Table 8. Typical values of C used in Hazen-Williams equation
Pipe Material C Value
Plastic 150
Epoxy-coated Steel 145
Cement Asbestos 140
Galvanized Steel 135
Aluminum, (with couplers every 30 ft) 130
Steel (new) 130
Steel (15 years old) or Concrete 100

 

 

 

 

Adoptdfiom James, (1988).

The Hazen-Williams equation was developed from the study of water distribution
systems that used 75 mm (3 in.) or larger diameter pipes and discharges greater than 3.2

L/s (50 gpm). Under these flow conditions the, Re is greater than 5 x 10‘, and the

 

28

formula, therefore, predicts the friction losses satisfactorily.

The Reynold number at 20°C (68°F) for water flowing through a pipe is:

(8)

:0

II

7?
D116

where:
K = conversion constant, (1.3 x 10°, for metric system; 3214 for English

system).

The friction factor f for flow in smooth pipes is given by the following classic

equation for laminar flow where Re < 2000

f=— (9)

For turbulent flow, Rc >2000.

For turbulent flow the fiiction factor f, taking Von Korman formula, becomes;

1 _ D
—5 - 1.14 + 2 log 2- (10)

29

and the relationship:

(11)

Elm

where:
E = relative roughness;
e = roughness size, (L); and
D = diameter of the pipe, (L).
An equation developed by Churchill (1977), perfectly handles the entire range of

Reynold number for determining f in all types of pipes. It lends itself to numerical

 

solutions:
1
f = 8 ((%)n + ——1——15' 12 (12)
e (K1+K2) '
where:
1 e
K = 2.457 1n ( + 0.27 — )l6
‘ ( 7 09) D (13)

(E)

K2 = (37530/Re)16

 

30

If the value of C for smooth pipe, of 150 is substituted in equation (4), the

following empirical equation is obtained:
5 Q 1.852

Equation 14 is the same as equation 7, but it incorporates a fixed value for C. The
major difference between Darcy-Weisbach and Hazen-William equations is that, the
Darcy-Weisbach equation has a fiiction factor which is dependent on Reynold Number
while the Hasen-William equation has a constant smooth pipe fiiction factor. However, it
is clear that, the Darcy-Weisbach equation represents the fiiction losses in small diameter
pipes and hoses better than does the Hazen-William formula. Furthermore, when
comparing the two equations at the same velocity, the C-value of the Hazen-Williams
equation seems to be dependent upon pipe diameter.

Howell (1981) recommended the following C-values to use with plastic pipes:

 

 

 

 

Table 9. Recommended C-values for Plastic Pipes
C-value Diameter
130 14 - 15 mm(0.58 inches)
140 18 - 19 mm (0.75 inches)
150 25 - 27 mm (1.0 inch)

 

 

 

 

Adopted from Howell, (1981).

31

Both equations (4) and (7) are generalized by Wu and Gitlin (1975), and Wu et. al

(1979), as follows:

AH=—aQ"’ (15)

where:
AH = change in head due to friction;
Q = total lateral line flow;
a = pipe constant; and

m = pipe flow exponent.

c. Sprinkler Flow Equation
In general, the relationship between pressure, or pressure head, and discharge from

a sprinkler can be expressed by the orifice equation:

q = K. (1’)”5 (16)

01'

q = K.) (17)“ (17)

32

where:

q = sprinkler discharge L/m, (gpm);

Kd = appropriate discharge coeflicient for sprinkler and nozzle combined and

specific units used;

P = sprinkler operating pressure KPa (Psi); and

H = sprinkler operating pressure head, m (ft).

The design coefficient Kd can be determined for any combination of sprinkler and
nozzle, if any value of P and the corresponding value of q are known. Because of the
internal sprinkler friction losses, Kd decreases slightly as P and consequently q increase.
However, over the normal operating range of most sprinklers, it can be assumed constant.

Equation (16) can be manipulated to yield;

P = P’ (1)2 a
q, (1 >

where;

P’ and q’ can be supplied by the manufacturer's tables; and either P and q is not
known. Also, equation (17) can be manipulated in a similar manner.

A special form of equation (16) and (17) can be modified to account for sprinkler

and nozzle plugging, (Bralts, 1983):

q = (H!) K, P‘"5 (19)

33

q = (H!) K. H ”'5 (20)

where:

a = the fraction of nozzles likely to plug.

E. Sprinkler system capacity requirements
The required capacity of a sprinkler system depends on the size of the area
irrigated, the gross depth of water applied at each irrigation, and the net operating time

allowed to apply this depth.

1. System capacity
The capacity of the system can be computed by the formula presented by (Keller

and Bliesner, 1990):

Q=K— (21)

where:
Q = system discharge capacity, L/s (gpm);

K = conversion constant, 2.78 for metric units, (453 for English units);

3 4
A = design area, ha (acre);
d = gross depth of application, mm (in);
f = operation time allowed for completion of one irrigation, days; and
T = average actual operating time per day, hr/day
2. Sprinkler application rates

The rate at which water should be applied depends on the following:

a. The infiltration characteristics of the soil, the field slope, and the crop
cover;
b. The minimum application rate that will produce a uniform sprinkler

distribution pattern and satisfactory efficiency under the prevalent wind and
evaporative demand conditions; and

c. The farm conditions and the type of sprinkler system used.

3. Computing set sprinklers application rates

The average application rate from a sprinkler is computed by:

 

(22)

where:
I = average application rate, mm/hr, (in/hr);

K = conversion constant, 60 for metric units, (93 .6 for English units);

3 5
q = sprinkler discharge, L/min, (gpm);
S, = spacing of sprinklers along the laterals, m (ft); and

SI = spacing of laterals along the main line, m (ft)

4. Computing instantaneous application Rate
To compute the average instantaneous application rate, 1,, for a sprinkler having a

radius of throw, R5, and wetting an angular segment, 8,, equation (23) can be modified as:

 

 

TE (R)2 x S0 (23)

where:
K = same as above;
Rj = radius of wetted area, 111 (ft); and

S, — angular segment, (from a top view) wetted by a stationary a sprinkler jet,

degrees.

36

F. Sprinkler uniformity

Irrigation uniformity is a concept used extensively in system design and
management. There are several factors that cause irrigation to be nonuniform under
different methods of irrigation. However, there are specific factors that affect the water
application efliciency of sprinkler irrigation systems:

i. Variation of individual sprinkler discharge throughout a lateral line;

ii. Variation in water distribution within the sprinkler-spacing area, which is

caused primarily by wind;
iii. Losses of water by direct evaporation from the spray; and

iv. Evaporation from the soil surface before water is used by plants.

1. Solid sets sprinklers

The uniformity of application is of primary concern in a sprinkler design
procedure. The areal distribution of irrigation depth from a sprinkler system is often a
result of an overlapping application pattern of many individual sprinklers at a given
spacing. The uniformity of sprinkler irrigation has been studied by many researchers. The
first pioneer to address the problem of sprinkler uniformity as an important factor affecting
the design and performance of sprinkler irrigation was Christiansen (1942). He was the
first to assign an index to the variability of sprinkler irrigation depth, and introduced a
measure of uniformity known as the Christiansen Uniformity Coefficient, (U CC), defined

as:

 

37

" I<X.-X’)1

 

UCC = 1 - Z (24)
14 nX
where:
.>’< = average depth of irrigation;
X, = observed irrigation depth; and
n = No. of observations.
The mean deviations are given by:
n X;-.?
Mean Deviations = 2| —— | (25)
#1 ”

Keller and Bliesner (1990) suggested that the test data for UCC > 70% usually
forms a bell-shaped normal distribution and is reasonably symmetrical about the mean.

Therefore, UCC can be approximated by:

= A verage (low -halj) depth of water received
.17

UCC

 

X100 (26)

However, the problem with the UCC measure is that it gives the same weight
assigned to irrigation depths above and below the mean. The result is that too little and

too much irrigation has the same effect on yield, which is not quite true. The bottom line

3 8
of this definition of uniformity is that dispersion of irrigation water is related to the mean
of the amount irrigated.
Wilcox and Swailes (1947) replaced the mean deviation of Christiansen by the

standard deviation. The result was the coefficient of variation (CV), 6/>‘< , and becomes:

UCW = I - (27)

><1|°

where:

o = the standard deviation of the sample.

The coeflicient of variation was extensively used by Bralts, et al.. (1981, 83, 84
and 87) to develop statistical uniformity concept to evaluate drip irrigation submain units.
The coefficient of variation is defined as the ratio of the standard deviation to the mean of
a sample or a population. The coefficient of variation was approached by estimating the

mean and the standard deviation. The following is a summary of how they developed the

estimation equations.

a. Estimating the standard deviation:

(Q... - Q1.) (28)

ZIN

as

where:

39

8,, = the estimate of the standard deviation of the emitter (sprinkle) flow rate;
Q“, = the sum of the observations in the upper one sixth of the distribution;

Q, = the sum of the observations in the lower one sixth of the distribution; and
N = the number of observations in the sample.

b. Estimating the mean:

qs z _(Qus + Q13) (29)

c. Estimating the coefficient of variation:

Using the above two equations, the coefficient of variation can be written as:

CVq, = 0.667 M (30)

(gas + Q13)

If 18 random measurements of sprinkler or emitter flow rate were made, it would
only be necessary to sum the three highest and the three lowest values to estimate the

coefficient of variation. The above equation can be rearranged to demonstrate the linear

nature of the terms Q“, and Q“:

_ (0.667 + CVq,)

' (0.667 - CV,,) 1‘ (31)

 

40

Thus, for any given coefficient of variation CV,” the Q“, varies linearly with Q],
Bralts, et al., (1983), also used, the inverse relationship of minimum time to

maximum emitter flow rate, so the above equation can be written as:

_ (0.667 + CVq, ) T

max — ( 0667 _ CVqS ) min (32)

 

where:
Tm = the sum of the top one sixth of the emitter flow times required to fill a
Specific volume with water; and
Tmin = .the sum of the bottom one sixth of the emitter flow times required to

Specific volume with water.

d. Confidence Limits:
The confidence limits for the coefficient of variation (CV,,) on samples from a

normal population, (Bralts and Kesner, 1983, after Sokal and Rohlf, 1969) can be

expressed as:

p (Vq - 1% SVqs Vq'qu + t% 5V) = 1 - a (33)

41

Where:
CVq = sample coefficient of variation;
t,,,2 = student t value for given a;
a = confidence level desired;
CV“q = Actual coefficient of variation for the full submain; and
SW = standard deviation of the coefficient of variation is calculated from the

equation:

 

CV
5V. = 5', 1/1 + 2 (CV92 (34)

 

Using these two equations, the confidence lirrrits for the sample coefficient of
variation, CV,, can be found. Since the confidence limits of the estimated coeflicient of
variation are dependent on the assumption of a normal distribution, the above confidence
limits can only be used as the approximate confidence limits of estimated coefficient of
variation.

They translated this relationship into a nomograph figure 4, for drip irrigation field
uniformity estimation. The same procedure will be followed for sprinkler irrigation

uniformity estimator.

42

 

 

 

 

 

 

 

 

 

 

g . 4 I8! CONFIDENCE LIMITS
.—=1
C. L.
. g 3
one :5
:_ IO
1 13
”'18
I”
v ' ‘I
3? coo
3: a . o
g lmjL‘v
h
g
‘5
E
«3 zoo
run
A A l A
o 50 in 180 zoo 250 III

SumolmoTNuMII-mlfml

Figure 4. Nomograph for drip irrigation uniformity estimation, (Bralts, 1983).

43

Hart, (1961) described a uniformity similar to UCC:

UCH=1—(%)°'5(%) (35)

Hart and Reynolds (1965) from the Hawaiian Sugar Planters' Association
proposed a uniformity coefficient similar to UCC called Hawaiian Sugar Planters'
Association (HSPA). Hart et al. (1980) showed these two coefficients are essentially the
same.

A useful term placing a numerical value on the uniformity for agricultural irrigation
is the distribution uniformity, DU, (Merriam and Keller, 1978). DU indicates the

uniformity of application throughout the field and is computed by:

DU=Axeragelomum§LdepthanateLreceixed* 100

Average depth of water received
The average low-quarter depth of water received is the average of the lowest one-
quarter of measured values, where each value represents an equal area.
The relationship between UCC and DU was approximated by, Keller and

Bleisner(1990), as:

UCC = 100 — 0.63 ( 100 - DU) (36)

01'

44

DU = 100 - 1.59 ( 100 — UCC) (37)

And the relationship between UCC and the standard deviation of individual depth

of catch observations can be approximated by:
0 2 05
UCC = 100 ( 1.0 - (—_) (—)' ) (38)
x it

Emmanuel, (1992), referred to the postulation of (Karmeli, 1977, 1978. Karmeli,
Salazer and Walker, 1978), that observations drawn from the cumulative distribution are

approximately linear and could be defined as:

Y=a+bX (39)

where:
Y = dimensionless irrigation depth;
X = dimensionless area received Y depths or less; and
a and b are the intercept and the slope on the Y-axis respectively.
Noting that the uniform distribution provides a linear cumulative distribution, they

defined the uniformity coefficient by:

45

UCL = 1.0 — 0.25 b (40)

where:
b = transformed range of dimensionless irrigation depth; and

0.25 = is the mean deviation, dividing the mean for uniform distribution.

2. Center-pivot System

The center-pivot sprinkler system is a versatile method of applying water to a large
scale agricultural area which covers about one-quarter section of a land area. The method
developed because of an increased demand for agricultural labor. The effectiveness of this
method can be evaluated using the guidelines of ASAE. Bittinger and Longenbough
(1962) were the first to develop a mathematical model for center-pivot uniformity.
Heerman and Hein (1968), solved the mathematical expression for the application rate and
the application depth to develop a weighted coefficient of uniformity for center-pivot

system in the form of:

. ES. (41)

 

 

 

where:
Cn = coefficient of uniformity (Heermann and Hein);
D, = catch can depth at distance S from the pivot center; and
S, = distance from catch point to the center of the pivot.
Marek et a1 (1986) used the coefficient of variation to develop an areal-weighted

uniformity coefficient in the form of :

 

 

1:1 ' (42)

 

 

Cu =100 1.0 - N NN'I

 

 

 

 

G. Irrigation Efficiency Terms
1. SCS Pattern Efficiency
The on-farm irrigation committee, (Kruse 1978), defines pattern efliciency as:

EPLQ = i r

Average depth of water applied
This is not an efficiency term as the name suggest but a distribution index and it is

similar to the low quarter distribution.

4 7

2 Irrigation Efficiency

There are many different irrigation efficiency concepts now in existence and they
are widely used. However, the most commonly used definition is the ratio of beneficially
used water to total water applied, Chaurdry (1978).

Application efficiency is different from irrigation efficiency and is the ratio of water
stored in the root zone to total water applied. Many attempts have been made to
standardize irrigation efficiency terms, e.g. The On Farm Irrigation Committee, and Kruse

(1978)

3. Application Efficiency
There are different available definitions in the literature, which vary according to
the particular use. However, this term should include the effect of losses due to

nonuniformity of application, spray drifts, evaporation, and pipe losses.

4. Water Use Efficiency
Irrigation efficiency sometimes is defined as water use efficiency. Israelsen and

Hansen (1962) defines water use efficiency as:

 

E - 100 W"
a — W (43)

48

 

where:

Eu = water use efficiency;

W, = water is beneficially used; and

Wd = water delivered to the farm.

5. Water Application Efficiency

Water application efficiency is defined as:

E - 100 W‘
a — wf (44)

where:

E, = water application efficiency;

Ws = water stored in the root zone during irrigation; and

Wf = water delivered to the farm or irrigation system.

Wallace (1987) also refers to common sources of losses of irrigation water during
water application including surface runoff, (Rf), and deep percolation below the root zone,

(Dr). The sum of these losses and water used is equal to total water delivered.

Wf = W. + Rf + Df (45)

49

According to this equation water application efficiency (E,) can be defined as:

W-(R +D)
_ f f f
Ea—IOO f (46)

 

When the incorporation of leaching these definitions are radically changed, because
water in this case is considered to be beneficially used.

Application efficiency is not an indication of irrigation uniformity or adequacy.
Figure 5, illustrates how, with deficit irrigation, an application efficiency of 100% may be
achieved under sprinkler irrigation (Wallace 1987, refers to Wu and Gitlen, 1981).
Figure 6, shows a common application efficiency found under sprinkler irrigation. In
figure 6, area A is adequately irrigated, area B is in deficit irrigation, while area C is

excessively irrigated. Using these areas, then, application efiiciency may be defined as:

E:—
" A+C (47)

Bralts et al., (1984) have defined application efficiency for drip irrigation as:

V 1 - P V 1 -
Ea = 100 '( D) = 100 ’( D) (43)
3600 Q, T

 

 

50

where:

VI = the volume of water applied, m3;

PD = irrigation deficit expressed as decimal;

V, = irrigation volume required, m3;

Q, = the actual discharge to the submain per second, m3 ; and

T = irrigation time in hours.

The above equation is illustrated in figure 7. Wallace (1987).

Bralts (1984) used the coefficient of variation when the irrigation volume applied
equals the irrigation volume required, then the irrigation deficit is equal to 0.40 times the
coefficient of variation. As a result the application efficiency can be determined by the

equation:

Vr( 1 — PD)
Ea = 100 V = 100 (1 - 0.4 CV) (49)

 

Figure 8, shows this relationship.

Hart and Reynolds, (1965) assumed that the standard deviation and the mean
drawn from a population sample adequately represent the actual mean and the variance of
the total population. Then, they used the coefficient of variation to analyze irrigation

system design. They used the normal probability density function:

51

 

e F i 3 (50)

Where:

N = number of observations;

q = class interval;

x = the value of an occurrence;

$2 = the mean of the sample; and

s = the standard deviation.

They, also, assumed that the population is continuous and that it is possible to
determine the fraction of the total number of observations falling between two points with

an equation:

-f)2

13
Ay = f e S (51)

 

Replacing Ay with a, a with >‘<H, , and B with co, the equation becomes:

52

-0.5 —__(x'£)2

fl

Q
II
M
3
:1
,El‘\. 8
m

 

(52)

where:
a = the fiaction under the normal curve from x = >‘<H, to x = co;
52H, = minimum application on the area a; and
H, = the fraction of the mean application (>7) 2 over the area a.
This equation can be used to compute the fraction of irrigated area in excess or

deficit.

Figure 5.

Figure 6.

53

 

 

 

 

Application efficiency under sprinkler irrigation, (Wallace, 1987)

 

 

 

Deficit irrigation for 100% efficiency, (Wallace, 1987)

 

54

FRACTION or AREA. a.% '

0 20 40 60 80 100
r I I fi

 

 

p
L

0.5 1-
b
L
b

1.0

 

 

   
 

Coefficient of Variation of
Emitter Flow ltotall. Vq - 0.10

1.5 I-

A - Water stored in root zone

B - Water lost due to deep seepage

C 3 Deficit

G - Ratio of the required irrigation depth X;
to the mean irrigation depth X

L X - Mean irrigation depth

RATIO OF DEPTH, X;/X

1

 

2.0

Figure 7. Application efficiency relationships (Bralts, 1984)

55

 

   

 

 

 

 

111-259.
1&1
fl
8
i
u
g N Vq'dedmflww
i
9
11.
a
111
s 70
3
t
9
.1
5 to
M, J L 1 1 1 1 1 r L._ 1 1
ottfflOlZlfifllNfilC 133
"W?“ DEFICIT. '0. 3
Figure 8. Application efficiency, coefficient of variation, and percentage deficit

relationships, (Bralts, 1984).

56

H. Summary

Sprinkler irrigation uniformity is the measure of spatial variability of the
application of water to an irrigated area. Although a large number of uniformity measures
have been in widespread use, none of them can claim to absolutely represent all the
characteristics of a real distribution. An extensive research has been done in this area.
However, the most common statistical measures are Christiansen's uniformity and the
coefficient of variation. The problem with Christiansen uniformity, is its susceptibillity to
arbitrariness of performance measurement. On the other hand, the coefficient of variation
uses the squares of the deviation from the mean rather than the deviations themselves. It
uses two statistical moments, the standrd deviation and the mean. Therefore, it gives a
better measure of dispersion.

The On-F arm Irrigation Committee was trying to provide standardized definitions
for irrigation efliciency terms, (Kruse, 1978). However, all the definitions of efficiency
terms are based on theoretical studies and lack empirical investigation and statistical
techniques. In addition, there are statistical relations between irrigation uniformity and
efficiency. Therefore, there is no simple or efficient method for field evaluation of
sprinkler irrigation systems. In this thesis, a simplified statistical method based on the
estimated coefficient of variation and statistical uniformity conceptwill be presented for the

field evaluation of sprinkler irrigation systems.

III. METHODOLOGY

A large body of theoretical research has been published regarding the various
aspects of sprinkler irrigation uniformity. The Literature Review indicated that most of
the work was concentrated in the area of variability of water distribution. However, there
is a lack of empirical research in this area. It was also apparent that a number of studies
followed traditional procedures advocated in the past by the Soil Conservation Service,
(SCS), and the American Society of Agricultural Engineers, (ASAE). These procedures,
despite their usefirlness, were tedious and laborious as well as time consuming. Many
attempts have been made to apply the coeflicient of variation and the statistical uniformity
concept to evaluation of sprinkler irrigation, however, there was no extensive research
made to investigate the practical usefulness of these concepts. In this study, 18 randomly
selected application depths were compared to the methods already in practical use by
applying the estimated coefficient of variation and estimated confidence limits. The latter
is called three low and three high method.

A. Research approach

There was a need to develop a simple, easy, quick, and relatively accurate method
to evaluate the irrigation uniformity of sprinkler irrigation systems. The ultimate goal was
to conserve water and energy for the irrigator as well as to maximize his profit.

The following approaches were adopted to achieve the stated research objectives.

57

58

Objective 1.
Develop the statistical uniformity concept for field evaluation of sprinkler irrigation

systems based on the estimated coefficient of variation and estimated confidence limits

Research approach:

The procedure presented by Bralts and Kesner (1983) to develop an equation for
determining the coefficient of variation for drip irrigation from randomly selected times to
fill a specific container was applied to estimate the coefficient of variation for sprinkler
irrigation systems from Similarly selected depths.

The estimated coefficient of variation was calculated by first, independently
estimating the standard deviation and the mean. The coefficient of variation was then
obtained by dividing the standard deviation by the mean. The method used for estimating
the standard deviation uses the difference between two quantities drawn from the tails of
the normal distribution curve of observed values. The same method will be applied to
develop an equation for estimating the mean. A complete procedure to develop equations
for estimated coefficient of variation and estimated confidence limits was presented in the

theoretical development.

Objective 2.
Apply the estimated coefficient of variation and the statistical uniformity concept

with estimated confidence limits to field evaluation of sprinkler irrigation systems.

59

Research approach

During this stage of analysis, collected data from sprinkler irrigation were analyzed
according to ASAE recommendation to compute the coefficient of variation. Then the
estimated CV was calculated for 18 randomly selected depths fi'om the actual data. The
three-low and three-high method will be applied to calculate the estimated CV. Finally,
the coefficient of variation was also computed for 18 depths by the standard deviation
method.

The software “SURFER, version 4.15. 1989.” and hand picked methods were
used to randomly select 18 depths for solid set sprinklers and center-pivot system
respectively.

The software “SURFER” was used for the following reasons:

1. It shows topographic and surface maps of the water distribution as

illustrated by figures 9 and figure 10;

2. It gives better chance of random selection; and

3. It closely estimates the unrecorded data points during the time of data

collection, because it uses ”minicurve” method with an accuracy of

(0.995).

Objective 3.
Evaluate the usefirlness of the estimated coefficient of variation and the estimated
confidence limits for field evaluation of sprinkler irrigation systems by statistical

comparison of the results to the methods already adopted to evaluate sprinkler systems.

60

Research approach

The coefficient of variation from the actual data was compared to the estimated
coefficient of variation calculated by the “three-low and three-high method”. Then the
coefficient of variation resulted from 18 depths was, also, compared to the CV actual and
CV (low/high). The results were statistically tested using the coefficient of determination,
(R2) for field evaluation of sprinkler irrigation systems.

A nomograph was constructed by plotting the sum of three-lowest depths against
the sum of three-highest depths. Then, either the statistical uniformity or the coefficient of

variation can easily be found if one knows the required inputs.

61

30 min. Run with low South Breeze
28.00 6.

10.00 4 00 32.00 100.00

100.00 100.00
4..
.._
L 52.00 52.00 N
.93
.x
.S
L— 64.00
0. 64.00
U")
o 46.00 46.00
L
0-
_._;
_gn_ 25.00 2300
Q

 

10.00 10.00
10.00 25.00 46.00 64.00 82.00 100.00

Dist. from Sprinkler ft

The sprinklers were located in the corners of the square.

Figure 9. Topographic distribution of water from solid set sprinklers.

 

Figure 10. Surface distribution of water from solid set sprinklers.

62

B. Theoretical development

The procedure presented by Bralts and Kesner (1983) to develop an equation for
deterrrrining the coefficient of variation for drip irrigation from 18 randomly selected times
to fill a specific container will be followed to estimate the coefficient of variation for
sprinkler irrigation systems.

The development of a statistical method for estimating the coeflicient of variation,
i.e the standard deviation over the mean, was approached by first, considering methods,

for independently estimating the standard deviation and the mean.

1. Estimating the standard deviation:

The method used for estimating the standard deviation uses the difference between
two quantities drawn from the tails of the normal distribution curve of observed values,
Figure 11.

For a normal distribution using the sprinkler flow rates, q (liters per hour), as the
random variable, the sum of the observations in the upper portion of the distribution can

be expressed as:

Q.=Np[ci+Sq(Z..,)l (53)

where:

Qu = the sum of the observations in the upper portion of the distribution;

63

N = the number of observations in the sample;
p = the proportion of the observations in the upper portion of the
distribution(0<p<0.5);

= the mean sprinkler flow rate;

S q = the standard deviation of sprinkler flow rates; and

Zn, — the mean abscissa in the upper portion of the standard normal variate, (u

=0, 0 =1).

It can be shown that Zup = y/p, where y is the ordinate height of the normal

probability density firnction.

 

 

e (54)

Figure 11. Standard normal distribution curve, (Bralts, 1983).

64

Np represents the number of observations in the upper portion of the distribution.

Expressing the sum of the lower portion in similar manner:

Q1 : Np I (I _ Sq (211)] (55)

Where:
Ql = the sum of observation in the lower portion of the distribution; and
Z1,, = the mean abscissa in the lower portion of the standard normal variate.
Based on these equations and the observation that Zup = y/p = 2,, the estimate of

the standard deviation of sprinkler flow rate, S,I is derived in the equation of the form:

1
Sq = m [Qu' Q1] (56)

An example of this method is presented by Bralts (1983). He used p equal to one
sixth, (p = 0.167), for which y = 0.25. In this case, Sq can be expressed as the difference
between the sums of the upper and the lower one-sixth of the distribution divided by one
half of the number of observations. Then the estimated standard deviation is given by the

equation:

65

2
Sq: = N [ Qus - le ] (57)
Where:
Sq, = the estimate of the standard deviation of sprinkler flow rate when p =
0.167:
Q... =

the sum of the observation in the upper one sixth of the distribution; and

Q, = the sum of the observation in the lower one sixth of the distribution.

2. Estimating the mean:

Since we assumed a normal distribution which is symmetrical about the mean, the

estimated mean sprinkler flow rate a, can be found by:

1

 

— : +
q 2pNlQ, Q,] (58)
Setting p = 0.167, the above equation becomes:
i=310 +0.1 (59)
N US 3

Where all variables were as previously defined

66

3. Estimating the coefficient of variation:

The coefficient of variation (CV,) is defined as the standard deviation (8,) divided

by the mean(q'). Then the equation for CVq becomes:

 

1 —
=§a=2legu Q1] (60)
q ‘7 4 ..
2pN[Qu Q1]

01'

CV _ PIQu_Q1]

‘1 yiQ,+Q,1 (6‘)

Setting p = 0.167, for which y = 0.25, will result in the estimated coeflicient of

variation as follows:

( Qus _ Q13 )
CV = 0.667
4: (Q... + Q...) ‘62)

If 18 random measurements of sprinkler or emitter flow rate were made, it would

only be necessary to sum the three-highest and the three-lowest values to estimate the

67

coefficient of variation. The above equation can be rearranged to demonstrate the linear

nature of the terms Q,,, and Q,:

_ (0.667 + CV,,)
“3 _ (0.667 - CV,,) ” (63)

 

Thus, for any given coefficient of variation CV the Q“, varies linearly with Q,

<18,

Bralts, et al., (1983), also used, the inverse relationship of minimum time to

maximum emitter flow rate, so the above equation can be written as:

_ ( 0.667 + CVq, )
"‘3" ' ( 0.667 - C11,) mi“

 

(64)

The above equation can be modified to replace the time to fill specific container

by the depths collected in each catch can. As a result equation (61) becomes:

( 0.667 + CV )
= 9‘ - (65)
m“ ( 0.667 - CVq, ) "“n

 

6 8
4. Estimating the confidence limits:
The confidence limits for the estimated coefficient of variation are in the literature
review using equations (42). The confidence limits for the coefficient of variation (CV,)
on samples from a normal population, (Bralts and Kesner, 1983, after Sokal and Rohlf,

1969) can be expressed as:

(CV, - tg SVqs CVJSCVq + 1% SVq) = l — 01 (66)

The standard deviation of the coefficient of variation can be calculated from the

equation:

 

 

CVq ([1 + 2 (CVq)2 (67)
JZTV

S =

CV,
Since these estimated confidence limits of estimated coefficient of variation are
dependent on the assumption of normal distribution,, these, limits can only be used as

approximate confidence limits of the estimated coefficient of variation.

IV. RESULTS AND DISCUSSION

A. Solid set sprinklers test

In this part of the analysis, data from Sichinga thesis (1975), Appendix A, were
input to the software “SURFER” to select 18 catch can depths. The coeflicients of
variation were calculated from the actual data by the standard deviation method, the by
three-low and three high method, and finally, CV3 were computed from 18 depths using
the standard deviation method all with 95% confidence limits, Table 10.

The objective was to apply the estimated coefficient of variation to field evaluation
of solid set sprinklers. Then to compare the results of estimated coefficient of variation to
the method already in practical use. Figure 12, illustrates the relationship between the
estimated CV from (low/high) to the CV from actual data calculated by standard deviation
method. Then the CV from actual data were compared to CV(18) calculated by standard
deviation method, as can be viewed by Figure 14. In addition, CV (low/high) was
compared to CV (18).

From figure 12 it can be seen that the estimated CV (low/high) is highly correlated
to the coefficient of variation from actual data with R2 = 0.956 with 95% confidence
limits.

Figure 13 shows the estimated confidence limits between the CV (low/high) and
the actual data. A comparison of CV from actual data to CV (18) yielded R2 = 0.94 with

69

7O

95% confidence limits as it can be seen from figure 14 and figure 15.

Figures 16 and figure 17 show the relationships between the CV computed by the
three-low and three-high method compared to the CV from 18 depths for set sprinklers.
The coefficients of variation are highly correlated with R2 = 0.97 at 95% confidence limits.
From the above analysis of the linear regression of the CVs calculated by the three
methods, it is clear that there was no significant difference to use either of these methods
for the calculation of the coefficient of variation. It can be concluded that, the three-low
and three-high method is highly applicable for the field evaluation of solid set sprinklers,
it is very simple, easy and based on statistical background. In addition, it is quick, and
could conserve time and money for the farmer. Furthermore, it is a very usefirl tool for

conservation of energy and water to the farmer and the environment.

71

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 10. Coefficient of variation of solid set Sprinklers.

Sample CV (Actual) Number of CV (low/high) CV (18)

Number Points
1 0.109769 79 0.135037 0.144037
2 0.143215 79 0.135333 0.147215
3 0.14791 79 0.156848 0.148938
4 0.16619 79 0.166750 0.176876
5 0.1721 79 0.170628 0.185219
6 0.176896 79 0.173960 0.187173
7 0.184164 79 0.175526 0.190243
8 0.1855 79 0.182231 0.190909
9 0.189543 79 0.183667 0.194137
10 0.193973 79 0.188600 0.195064
11 0.19494 79 0.191877 0.210257
12 0.251356 79 0.204519 0.218163
13 0.26348 79 0.253648 0.265199
14 0.285035 79 0.276561 0.295780
15 0.356115 79 0.325366 0.310588

 

 

 

 

 

 

 

CV (low/high)

CV (low/high)

72

 

 

 

 

 

 

 

 

 

0.4
112 = 0.96 %
y=0.031+0.8l"x '
0.3 —
0.2 — 0
0
0.1 _
1:1 line
0.0 I I I
0.0 0.1 0.2 0.3 0.4
CV (actual)
Figure 12. A comparison of CV (actual) to CV (low/high).
0.4
95% confidence limits
0.3 —
0.2 — f: a
J";
0.1 —
0.0 I I I
0.0 0.1 0.2 0.3 0.4
CV (actual)

Figure 13. A comparison of CV (actual) to CV (low/high)
with 95% confidence limits.

cv (18)

CV (18)

73

 

0.4

'= 0.94
y = 0.05 + 0.77 '- x

 

 

 

 

 

0.0 0.1 0.2 0.3 0.4
CV (actual)

Figure 14. A comparison of CV (actual) to CV (18).

 

 

 

 

0.4
95% confidence limits
0.3 e .
e
0.2 _.
‘/
0.1 —
0'0 l l T
0.0 0.1 0.2 0.3 0.4
CV (actual)

Figure 15. A comparison of CV (actual) to CV (18)
with 95% confidence limits.

CV(18)

cv (18)

74

 

 

 

 

 

 

 

 

0.4
R2 = 0.97 M
y=002+095‘x
0.3 — . '
0.2 —
O
0.1 _
lfllme
0.0 I I I
0.0 0.1 0.2 0.3 0.4
CV (low/high)
Figure 16. A comparison of CV (low/high) to CV (l 8).
0.4
9596confidencelhnhs ‘————'——"€E,-
0.3 _.
0.2 _.
O
0.1 —
0'0 1 l 1
0.0 0.1 0.2 0.3 0.4
CV (low/high)
Figure 17. A comparison of CV (lowllrigh) to CV (18)

with 95% confidence limits.

7 5
B. Turfgrass sprinklers

Data for this part of the results were obtained from Saffel, 1993, Hancock
Turfgrass Research Center, Department of Crop and Soil Science, MSU, Appendix B.
Actual data were entered into the software “SURFER” to select 18 catch can depths. The
coefficients of variation were calculated for the actual data, three-high and three-low for
18 depths, and from 18 depths by standard deviation methods. Table 11 shows the
coefficients of variation for each method.

The objective of this part of the research was to apply the estimated coefficient of
variation to the field evaluation of sprinkler irrigation on the turfgrass. Also the estimated
coefficient of variation was compared to methods already in practical use. The linear
regression analysis was used to statistically compare these coemcients of variation
methods.

Figures 18 and figure 19 illustrate the relationship between the CV from the actual
data to the estimated CV calculated by three-low and three-high from 18 randomly
selected depths. As it can be seen, the estimated CV (low/high) is highly correlated to the
CV of the actual data with R2 = 0.99 at 95% confidence limits.

Figures 20 and figure 21 show the relationships between the CV calculated from
18 randomly selected depths and the CV calculated from actual data with both computed
by the standard deviation method. These two methods are, also, highly correlated with R2
= 0.99 at 95% confidence limits.

When the estimated CV calculated by the three-low and three-high method was

compared to the CV from 18 depths computed by the standard deviation methods, the two

76

methods show a close relationship, with R2 = 0.99 at 95% confidence limits, as shown by

figure 22 and figure 23.

77

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 11. Coefficient of variation for sprinklers on turf.

Sample CV (Actual) Number of CV (low/high) CV (18)

Number Points
1 0.162 100 0.152 0.161
2 0.249 100 0.259 0.249
3 0.269 100 0.279 0.269
4 0.272 100 0.281 0.272
5 0.279 100 0.282 0.280
6 0.288 100 0.283 0.288
7 0.303 100 0.301 0.303
8 0.306 100 0.319 0.305
9 0.306 100 0.324 0.307
10 0.307 100 0.333 0.307
11 0.341 100 0.333 0.341
12 0.357 100 0.356 0.356
13 0.387 100 0.392 0.388
14 0.413 100 0.415 0.413
15 0.432 100 0.437 0.432
16 0.456 100 0.453 0.456

 

 

 

 

 

 

Data were obtained from the T urfgrass Hancock Research Center, Saffel 1993.

 

78
0.5

 

 

’ = 0.99 >
y = 6.43 + 0.99 " x

0.4 _

0.3 -—

0.2 —-

CV (low/high)

0.1 —

 

1:1 line
0'0 l I l l l

0.0 0.1 0.2 0.3 0.4 0.5

 

 

CV (actual)

Figure 18. A comparison of CV (actual) to CV (low/high) on turf.
0.5

 

 

95% confidence limits

//

\\

0.4 _
/

0.3 .3 /

0.2 —

CV (low/high)

0.1 2

 

 

0.0

 

l l l l
0.0 0.1 0.2 0.3 0.4 0.5

cv (actual)

Figure 19. A comparison of CV (actual) to CV (low/high)
with 95%confidence limits on turf.

cv (18)

79
0.5

 

 

1=o.99
y=-1.81+ 1.00 r x

0.4 _
0.3 —
0.2 _
0.1 —
1:1 line

00 l l l l
0.0 0.1 0.2 0.3 0.4 0.5

 

 

 

CV (actual)

Figure 20. A comparison of CV (actual) to CV (18) on turf.

cv (18)

0.5

 

95% confidence limits /

 

 

 

 

00 l j l l
0.0 0.1 0.2 0.3 0.4 0.5

cv (actual)

Figure 21. A comparison of CV (actual) to CV (18) with 95%
confidence limits on turf.

80

 

 

 

0.5 ’
R’=0.99
y=-1.77+0.99‘x
0.4 _
A 0.3 —
E
>
U 0.2 _
0.1 __ 1:1 line
0'0 l 1 l 1

 

 

0.0 0.1 0.2 0.3 0.4 0.5
CV (low/high)

Figure 22. A comparison of CV (low/high) to CV (l 8) on turf.

0.5

 

95% confidence limits

0.4 _.

0.3 —

CV (18)

0.2 _.

0.1 -

 

 

 

0'0 l I l j
0.0 0.1 0.2 0.3 0.4 0.5

CV (low/high)

Figure 23. A comparison of CV (low/high) to CV (18) with 95%
confidence limits on turf.

C. Center-pivot system

The coefficients of variation for this analysis were computed from the simulated
data from Pandey,(1989, Appendix C. using the Heermann equation, and the estimated

coeflicients of variation using the three-low and three-high method without weighting as

81

done by Heermann and Hein and are presented in table 12.

 

 

 

 

 

 

Table 12. Coefficients of variation for center-pivot from simulated data.
Sample Number CV (Heermann) Number of Data CV(low/high)
Points
1 0.155 135 0.146
2 0.259 34 0.262
3 0.289 34 0.275
4 0.346 34 0.277
5 0.46 40 0.456

 

 

 

 

 

Data were obtained fiom Pandey 1989.

Actual data collected by Soil Conservation Service (SCS) at St Joseph, Appendix
C, were analyzed and the coefficients of variation were computed by, the Heermann

equation, the Soil Conservation Service (SCS) equation, and the three-low and three-high

method as shown in Table 13.

 

82

Table 13. Coefficient of variation for center pivot from actual data.

 

 

 

 

 

 

Sample CV (Heermann) Number of CV (SC S) CV (low/high)
Number Data Points

1 0.135 61 0.150 0.160

2 0.16 49 0.180 0.196

3 0.261 27 0.260 0.272

4 0.278 27 0.280 0.287

5 0.334 25 0.280 0.296

 

 

 

 

 

 

 

Data were obtained from Soil Conservation Service, St. Joseph, 1995.

The objective was to apply the estimated CV to the field evaluation of center-pivot
system. The CV calculated by the Hermann method from simulated data was compared to
the coefficients of variation computed by the three-low and three-high method from
selected catch can depths. The two methods were closely correlated with R2 = 0.93 at
95% confidence limits as can be seen in figure 24 and figure 25.

When the actual data were analyzed, a comparison of CV (Heermann) to CV
(SCS) resulted in R2 = 0.93 with 95% confidence lirrrits as illustrated by Figure 26 and
Figure 27. When the same CV (Heermann) was compared to CV (low/high) resulted in
R2 = 0.95 with 95% confidence limits as can be viewed in Figure 28 and Figure 29.
Further comparison of CV (SCS) to CV (low/high) yielded R2 = 0.99 with 95%

confidence limits as can be seen in figure 30 and figure 31.

CV (low/high)

CV (low/high)

0.5

83

 

0.4 __

0.3 _

0.2 —-

0.1 2

 

0.0

 

=-4'. +0.93‘x

1:1 line

 

 

0.0

l 1 1 l
0.1 0.2 0.3 0.4 0.5

CV (Heermann)

Figure 24. A comparison of CV (Heermann) to CV (low/high).

0.5

 

0.4

0.3

0.2

0.1

0.0

 

95% confidence limits

 

 

 

0.0

l I l l
0.1 0.2 0.3 0.4 0.5

CV (Heermann)

Figure 25. A comparison of CV (Heermann) to CV (low/high)

with 95% confidence limits.

cv (SCS)

cv (SCS)

84

 

 

 

 

 

 

 

 

 

 

 

0.4
’ = 0.93
y = 0.07 + 0.70 " x

0.3 _

0.2 —

0.1 _.

0.0 I I I

0.0 0.1 0.2 0.3 0.4
CV (Heermann)
Figure 26. A comparison of CV (Heermann) to CV (SCS).
0.4
95% confidence limits ——9
0.3 —
O

0.2 —
O

0.1 .—

0.0 I I I

0.0 0.1 0.2 0.3

CV (Heermann)

Figure 27. A comparison of CV (Heermann) to CV (SCS) with
95% confidence limits.

 

CV (low/high)

cv (low/high)

8 5
0.4

 

1 = 0.95
y = 0.08 + 0.70 * x

 

 

 

 

 

0.0 I I I
0.0 0.1 0.2 0.3 0.4

CV (Heermann)
Figure 28. A comparison of CV (Heermann) to CV (low/high).

0.4

 

95% confidence limits

 

 

 

 

0.0 I I I
0.0 0.1 0.2 0.3 0.4

CV (Heermann)

Figure 29. A comparison of CV (Heermann) to CV (low/high)
with 95% confidence limits.

0.4

86

 

 

 

 

’ = 0.99
y=0.01+0.99‘ x

0.3 _.
E“
3 0.2 _
.9.
>
U

0.1 —

1:1 line
0.0 I I I
0.0 0.1 0.2 0.3 0.4
CV (SCS)

Figure 30. A comparison

of cv (SCS) to cv (low/high).

 

0.4

95% confidence limits

CV (low/high)
o .c
N M
1 1

P
p—o
l

0.0

_..——-——->

/

/

 

 

 

0.0 0.1

I I
0.2 0.3 0.4

CV (SCS)

Figure 31. A comparison of CV (SCS) to CV (low/high)
with 95% confidence limits.

87

D. A nomograph for sprinkler irrigation uniformity estimation.

The following equation will be used to construct a nomograph for sprinkler

irrigation systems.

The following values of maximum depths were obtained, if the values for the minimum

“m" _ ( 0.667 - CVqS) mi“

_ ( 0.667 + CVqS)

 

(66)

depths were taken from the randomly selected 18 depths at different confidence limits and

difi‘erent estimated coefficient of variations.

 

 

 

 

 

 

 

 

Table 14. Values of maximum depths at different coefficient of variations and known
minimum depths.
Dmin Dum Dm Dm,x Dmax Dmax
cv=0% CV= 10% cv=20% cv=30% CV=40%
0 O O O O O
50 50 67.65 92.83 131.70 199.80
100 100 135.30 185.65 263.50 399.60
150 150 203.00 278.48 395.00 599.40
200 200 271.00 371.31 527.00 799.25
250 250 338.00 464.00 658.72 999.06
300 300 406.00 556.95 790.50 1198.88

 

 

 

 

 

 

 

 

88

 

 

?
00
“0»,

A
8
l
‘60,.
Q“
“E.
o

8
a

‘3!»
% .

90%
4 \w/0

Sum of three highest depths

§
|
‘0.

 

 

 

 

l l l l l
0 50 100 150 200 250 300

Sum of three minimum depths

Figure 32. A nomograph for sprinkler irrigation systems
uniformity estimation.

Example:
If we take the first 18 randomly selected set of depths from

appendix B, as follows:

42, 86, 98,100,101,104,l33,136,142,156,161,184,189,
202, 203, 204, 223, 227.

Sum of three lowest depths = 42 + 86 + 98 = 226 ml
Sum of three highest depths = 204 + 223 + 227 = 654 ml

From the x-axis (sum of three lowest depths) we read a value of 226,
then we read from the y-axis (sum of three highest depth) a value of 654,
then we proceed untill the two lines intersect where the uniformity
coefficient of the system = 67%

V. CONCLUSIONS AND RECOMMENDATIONS

Conclusions

The objectives of this research have been addressed in full. The estimated
coefficient of variation has been developed for the field evaluation of sprinkler irrigation
systems. The estimated coefficient of variation has been applied to evaluate the
distribution uniformity of sprinkler irrigation systems. In addition, the estimated
coefficient of variation was found to be very usefial tool for the field evaluation of
sprinkler irrigation systems. The method has been verified for the field evaluation of
sprinkler irrigation systems, by using the linear regression method with the estimated
coefficient of variation statistically correlated to the method already in practical use.

The method was found to be very simple, applicable to sprinkler irrigation systems,
and easy to handle by the farmer. In addition, it conserves time and money for the farmer
and conserves water and energy for crop production. As a result it is environmentally
sound

The specific conclusions were:

1. Solid set sprinklers: the estimated coefficient of variation from 18 random
depths for this system was statistically correlated to the coefficient of
variation from the actual data. The two methods were highly correlated at
95% confidence limits. The method could be easily applied for the field

evaluation of this system.

89

9O

2. Turfgrass sprinklers: the estimated coefficient of variation was statistically
compared to coefficient of variation from the actual data, and there was no
significant difference at 95% confidence limits to use either of these
methods for the field evaluation of this system.

3. For center-pivot system: the estimated coefficient of variation closely
approximated the statistical uniformity when compared to coefficient of
variation fiom actual data computed by the Heermann method.

4. A simplified statistical method for the field evaluation of sprinkler irrigation
systems has been developed from randomly selected 18 catch cans depths

. using the three-low and three-high method.
5. A nomograph to estimate the coefficient of variation or statistical

uniformity for sprinkler irrigation systems has been presented.

Recommendations
1. Analysis of other factors affecting irrigation uniformity such as pressure,
sprinkler spacing, nozzle diameter, and wind speed in the comparison.
2. Incorporation of other environmental factors, such as spacial variability of
soil type which may also affect the irrigation uniformity.
3. Comparison of coefficient of variation from Heermann equation to
coefficient of variation from Mariek equation together with estimated

coefficient of variation.

REFERENCES

APPENDIX A

Solid Set Sprinklers Irrigation Data

91
Appendix A

Solid set sprinklers irrigation data

Data were obtained from Sichinga, 1975. M.S. thesis, Depart. of Agr. Engineering, MSU.
Water distribution from Rainbird 30 E-TNT sprinklers, at varied nozzle diameter,
pressure and wind speed.

setl

X X X

0.05 0.04 0.04 0.04 0.05 0.05 0.07
0.05 0.05 0.05 0.06 0.07 0.07 0.07 0.08 0.05 0.05 0.07 0.07 0.08
0.03 0.04 0.06 0.08 0.07 0.07 0.07 0.06 0.05 0.07 0.07 0.07 0.07
0.04 0.04 0.06 0.07 0.07 0.07 0.07 0.06 0.06 0.07 0.07 0.07 0.07
0.05 0.05 0.06 0.06 0.07 0.07 0.08 0.07 0.06 0.07 0.07 0.06 0.07
0.05 0.06 0.06 0.05 0.06 0.06 0.07 0.08 0.07 0.05 0.05 0.06 0.05
0.05 0.04 0.04 0.08 0.05 . 0.03 0.05
X X X

Figure 1. Water distribution from Rainbird 30 E-TNT sprinklers, 1/8 inch (3 mm) nozzle
X = position of sprinklers

Set2

X X X

0.08 0.03 0.07 0.07 0.04 0.07 0.08
0.06 0.04 0.04 0.06 0.07 0.08 0.07 0.04 0.05 0.07 0.07 0.07 0.08
0.03 0.03 0.04 0.04 0.06 0.04 0.07 0.03 0.05 0.06 0.06 0.05 0.07
0.04 0.03 0.03 0.04 0.04 0.04 0.04 0.03 0.05 0.07 0.07 0.04 0.04
0.04 0.03 0.03 0.04 0.04 0.05 0.08 0.07 0.04 0.05 0.06 0.05 0.05
0.04 0.03 0.04 0.04 0.05 0.07 0.07 0.06 0.05 0.04 0.04 0.07 0.05
0.04 0.03 0.04 0.07 0.04 0.04 0.05
X X X

Figure 2. Same as Figure 1, except wind spwd was 3.23 mph (1.44 m/s).

Set3

X X X

0.04 0.04 0.03 0.04 0.03 0.04 0.04
0.08 0.04 0.04 0.03 0.04 0.04 0.08 0.08 0.04 0.04 0.05 0.06 0.06
0.03 0.04 0.04 0.02 0.03 0.04 0.05 0.05 0.05 0.04 0.05 0.06 0.07
0.03 0.04 0.04 0.04 0.04 0.04 0.04 0.06 0.05 0.04 0.04 0.05 0.06
0.05 0.04 0.04 0.04 0.04 0.06 0.07 0.06 0.04 0.04 0.05 0.05 0.05
0.08 0.05 0.03 0.04 0.05 0.06 0.07 0.07 0.05 0.04 0.04 0.04 0.05
0.05 0.03 0.03 0.03 0.04 0.03 0.04
X X X

Figure 3. Same as above except wind speed was 2.5 mph (1.12 m/s).

92

Set4

X X X

0.09 0.07 0.07 0.16 0.08 0.08 0.09
0.08 0.1 0.09 0.09 0.08 0.1 0.16 0.14 0.11 0.1 0.09 0.09 0.09
0.08 0.09 0.1 0.11 0.09 0.09 0.1 0.11 0.12 0.11 0.1 0.09 0.09
0.08 0.09 0.11 0.12 0.11 0.09 0.1 0.11 0.12 0.12 0.11 0.1 0.09
0.08 0.1 0.11 0.11 0.11 0.11 0.12 0.12 0.12 0.12 0.12 0.11 0.08
0.07 0.09 0.11 0.12 0.14 0.13 0.12 0.14 0.14 0.12 0.12 0.11 0.09
0.09 0.09 0.14 0.16 0.12 0.11 0.09
X X X

Figure 4. The nozzle diameter was changed to 5/32 inch, (4 mm).

SetS

X X X

0.08 0.07 0.09 0.1 0.08 0.09 0.09
0.08 0.09 0.09 0.1 0.1 0.1 0.1 0.12 0.09 0.09 0.1 0.1 0.1
0.08 0.08 0.09 0.1 0.1 0.09 0.09 0.1 0.1 0.11 0.11 0.1 0.09
0.07 0.09 0.11 0.11 0.1 0.11 0.1 0.1 0.12 0.12 0.11 0.11 0.1
0.08 0.09 0.11 0.12 0.12 0.11 0.11 0.11 0.14 0.12 0.13 0.12 0.09
0.07 0.09 0.11 0.12 0.14 0.12 0.12 0.12 0.14 0.13 0.13 0.12 0.1

0.07 0.1 0.14 0.16 0.1 0.12 0.09
X X X
Figure 5. Nozzle diameter 5/32 inch (4 mm), pressure 60 psi, wind speed 3.76 mph
(1.67 m/s), N.W.
Set 6
X X X
0.1 0.06 0.08 0.1 0.07 0.07 0.07

0.14 0.09 0.1 0.07 0.08 0.1 0.17 0.12 0.09 0.09 0.08 0.08 0.08
0.08 0.08 0.08 0.08 0.08 0.08 0.1 0.1 0.09 0.1 0.09 0.08 0.07
0.08 0.09 0.1 0.09 0.09 0.09 0.1 0.1 0.1 0.1 0.09 0.09 0.07
0.08 0.1 0.1 0.1 0.11 0.11 0.13 0.11 0.1 0.1 0.09 0.08 0.07
0.07 0.09 0.1 0.11 0.12 0.12 0.12 0.11 0.11 0.09 0.09 0.08 0.07
0.08 0.09 0.11 0.15 0.1 0.05 0.08
X X X

Figure 6. Same as above except, wind speed 0.45 mph (0.20 m/s), N.W.

Set7

X

0.08
0.08 0.08
0.07 0.07
0.07 0.07
0.08 0.08
0.07 0.08
0.08

X

0.05
0.07
0.07
0.07
0.07
0.08
0.09

0.05
0.06
0.07
0.07
0.08

0.06

93

0.07 0.1
0.07 0.09 0.1
0.07 0.09 0.1
0.08 0.11 0.13 0.1

0.1
0.1

0.1

X
0.1
0.1

0.11
0.12
X

0.09
0.09
0.09

0.11

0.06
0.07
0.07
0.07
0.07
0.09
0.11

0.07
0.07
0.07
0.07
0.07

0.05
0.07
0.07
0.08
0.07
0.07
0.08

0.07
0.07
0.07
0.07
0.07

X

0.07
0.07
0.07
0.07
0.05
0.06
0.06
X

Figure 7. Nozzle diameter 5/32 inch (4.0 mm), pressure 30 psi, wind speed 0.45 mph

Set 8
X
0.14

0.05

0.17 0.09 0.07 0.09
0.09 0.09 0.09 0.08

0.1 0.1
0.1 0.1
0.09 0.09
0.1
X

0.09
0.1
0.1
0.09

0.09
0.1
0.1

Figure 8. Same as above.

Set9
X
0.1
0.09 0.1
0.08 0.08
0.08 0.1
0.08 0.1
0.09 0.1
0.1
X

0.1

0.09
0.09
0.09
0.11
0.1

0.08

0.1
0.1
0.09
0.1
0.1

0.09
0.08
0.1

0.11
0.11
0.11
0.11

0.12
0.1
0.1
0.1
0.11
0.12
0.1

0.11
0.1

0.11
0.14
0.11

0.14
0.12
0.12
0.13
0.12

0.2

0.17
0.11
0.11
0.15
0.12
0.09

X

0.14
0.14
0.12
0.12
0.14
0.14
0.15
X

0.12
0.09
0.1

0.11
0.11

0.13
0.11
0.12
0.14
0.15

0.14
0.08
0.08
0.1

0.1

0.11
0.09

0.1
0.1
0.1
0.11
0.12
0.14
0.1

0.09
0.08
0.09
0.1

0.08

0.15
0.15
0.14
0.13
0.11

0.06
0.09
0.1

0.09
0.09
0.1

0.08

0.13
0.12
0.12
0.11
0.11
0.1

0.07

0.08
0.09
0.09
0.09
0.09

0.14
0.14
0.12
0.1
0.1

0.08
0.08
0.08
0.08
0.08
0.08
0.09

0.1
0.11
0.12
0.1
0.09
0.1
0.1
X

Figure 9. Nozzle diameter 3/16 inch (4.75 mm), pressure 30 psi, wind speed 3.9578

94

Set 10
X X X
0.09 0.13 0.16 0.16 0.14 0.16 0.14

0.08 0.12 0.13 0.15 0.16 0.16 0.16 0.15 0.15 0.15 0.16 0.14 0.12
0.08 0.11 0.13 0.15 0.15 0.15 0.13 0.14 0.15 0.15 0.15 0.14 0.12
0.08 0.11 0.13 0.13 0.13 0.13 0.12 0.13 0.15 0.14 0.15 0.12 0.09
0.07 0.1 0.12 0.11 0.12 0.14 0.14 0.15 0.14 0.13 0.13 0.1 0.09
0.07 0.09 0.11 0.11 0.13 0.11 0.13 0.13 0.13 0.11 0.1 0.1 0.08
0.07 0.09 0.1 0.13 0.11 0.09 0.09
X X X

Figure 10. Same as above except pressure 40 psi.

Setll

X X X

0.06 0.03 0.04 0.04 0.06 0.04 0.08
0.07 0.04 0.03 0.03 0.04 0.07 0.13 0.07 0.04 0.03 0.04 0.05 0.06
0.03 0.04 0.02 0.03 0.04 0.06 0.08 0.08 0.05 0.04 0.04 0.07 0.08
0.06 0.06 0.06 0.06 0.07 0.07 0.1 0.08 0.07 0.06 0.07 0.08 0.1
0.06 0.07 0.08 0.07 0.06 0.1 0.1 0.1 0.11 0.1 0.09 0.1 0.12
0.07 0.07 0.07 0.06 0.1 0.12 0.13 0.12 0.12 0.1 0.09 0.1 0.1
0.06 0.07 0.07 0.1 0.08 0.1 0.08
X X X

Figure 11. Nozzle diameter 1/8 inch (3.175 mm), pressure 60 psi, wind speed 7.72 mph

Set 12
X X X
0.05 0.04 0.05 0.04 0.03 0.04 0.06

0.05 0.05 0.05 0.06 0.07 0.08 0.08 0.08 0.06 0.06 0.06 0.08 0.07
0.04 0.05 0.05 0.07 0.07 0.08 0.07 0.07 0.06 0.07 0.07 0.08 0.08
0.05 0.05 0.05 0.07 0.07 0.08 0.08 0.07 0.06 0.07 0.08 0.08 0.08
0.05 0.05 0.05 0.06 0.07 0.06 0.07 0.07 0.06 0.07 0.07 0.08 0.08
0.04 0.04 0.04 0.04 0.06 0.07 0.07 0.07 0.07 0.06 0.08 0.06 0.07
0.05 0.04 0.07 0.08 0.05 0.05 0.05
X X X

Figure 12. Same as above except wind speed 5.21 mph (2.33 m/s), N.W.

95

Set 13
X X X
0.13 0.15 0.16 0.17 0.15 0.16 0.13

0.17 0.14 0.15 0.17 0.17 0.17 0.17 0.17 0.15 0.14 0.15 0.15 0.12
0.1 0.12 0.14 0.17 0.16 0.16 0.16 0.16 0.15 0.15 0.15 0.15 0.13
0.12 0.13 0.14 0.15 0.16 0.16 0.16 0.15 0.16 0.15 0.16 0.14 0.11
0.12 0.14 0.14 0.14 0.15 0.18 0.18 0.16 0.15 0.15 0.15 0.13 0.11
0.1 0.13 0.14 0.14 0.16 0.17 0.17 0.16 0.16 0.15 0.14 0.12 0.12
0.08 0.13 0.16 0.17 0.13 0.11 0.13
X X X

Figure 13. Nozzle diameter 3/16 inch (4.75 mm), pressure 60 psi, wind speed 2.5 mph

Set 14
X X X
0.12 0.13 0.2 0.21 0.17 0.23 0.18

0.17 0.12 0.14 0.19 0.21 0.23 0.22 0.2 0.17 0.2 0.23 0.23 0.18
0.1 0.1 0.13 0.18 0.2 0.2 0.15 16 0.16 0.17 0.21 0.22 0.18
0.09 0.08 0.11 0.15 0.2 0.18 0.16 0.14 0.13 0.16 0.19 0.18 0.14
0.07 0.08 0.08 0.14 0.17 0.15 0.13 0.13 0.12 0.17 0.16 0.16 0.14
0.05 0.08 0.1 0.13 0.18 0.15 0.13 0.13 0.11 0.14 0.16 0.14 0.12
0.08 0.08 0.13 0.11 0.1 0.12 0.13
X X X

Figure 14. Same as above except wind speed 7.06 mph (3.16 m/s), S.W.

Set 15
X X X
0.13 0.12 0.15 0.13 0.12 0.17 0.15

0.13 0.09 0.13 0.15 0.15 0.17 0.17 0.12 0.12 0.15 0.17 0.16 0.13
0.06 0.09 0.13 0.14 0.15 0.13 0.1 0.09 0.13 0.16 0.15 0.16 0.13
0.06 0.1 0.13 0.15 0.13 0.12 0.11 0.11 0.14 0.16 0.15 0.12 0.1
0.07 0.09 0.12 0.13 0.12 0.13 0.12 0.14 0.13 0.12 0.11 0.11 0.11
0.09 0.1 0.1 0.11 0.11 0.09 0.11 0.11 0.11 0.11 0.1 0.1 0.1
0.1 0.07 0.09 0.09 0.09 0.08 0.1
X X X

Figure 15. Nozzle diameter as above, pressure 30 psi, wind speed 2.98 mph

m
9
Z
.0

“flaw-BWNH

96

Interpolation of observed data using topographic maps by software SURFER.

l

0.06
0.05
0.04
0.04
0.05
0.06
0.07
0.05
0.04
0.04
0.05
0.06
0.05
0.06
0.06
0.05
0.07
0.06
0.05
0.04
0.04
0.05
0.06
0.06
0.06
0.06
0.05
0.05
0.06
0.07
0.08
0.06
0.06
0.07
0.07
0.07
0.07
0.06
0.07
0.07
0.07
0.07
0.07
0.08
0.07
0.07
0.07
0.08
0.07
0.06

2

0.06
0.04
0.04
0.08
0.05
0.05
0.07
0.07
0.05
0.04
0.05
0.05
0.03
0.03
0.03
0.03
0.04
0.04
0.03
0.03
0.04
0.04
0.04
0.04
0.04
0.04
0.06
0.05
0.04
0.04
0.06
0.07
0.07
0.05
0.04
0.04
0.08
0.07
0.08
0.04
0.07
0.07
0.06
0.07
0.03
0.03
0.04
0.05
0.04
0.05

3

0.04
0.04
0.04
0.03
0.03
0.03
0.04
0.05
0.04
0.03
0.04
0.04
0.07
0.05
0.05
0.05
0.07
0.05
0.04
0.04
0.04
0.04
0.03
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.02
0.03
0.05
0.04
0.04
0.03
0.04
0.06
0.06
0.04
0.04
0.04
0.07
0.07
0.04
0.05
0.08
0.07
0.06
0.06

4

0.09
0.09
0.08
0.09
0.11
0.14
0.16
0.14
0.1

0.09
0.1

0.1

0.09
0.09
0.09
0.08
0.08
0.09
0.1

0.09
0.09
0.1

0.11
0.11
0.11
0.1

0.09
0.12
0.11
0.12
0.11
0.09
0.14
0.11
0.11
0.09
0.08
0.13
0.11
0.09
0.09
0.1

0.12
0.12
0.1

0.1

0.16
0.14
0.12
0.11

5

0.08
0.08
0.09
0.1

0.12
0.13
0.13
0.11
0.09
0.09
0.11
0.1

0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.08
0.09
0.11
0.11
0.11
0.09
0.09
0.12
0.12
0.11
0.1

0.1

0.14
0.12
0.1

0.1

0.1

0.12
0.11
0.11
0.09
0.1

O. 12
0.11
0.1

0.09
0.1

0.12
0.11
0.1

6

0.08
0.08
0.08
0.08
0.1

0.11
0.13
0.11
0.09
0.07
0.06
0.07
0.11
0.08
0.08
0.08
0.07
0.09
0.1

0.09
0.08
0.09
0.1

0.1

0.1

0.08
0.1

0.11
0.1

0.09
0.08
0.07
O. 12
0.11
0.09
0.08
0.08
0.12
0.11
0.09
0.08
0.1

0.12
0.13
0.1

0.1

0.17
0.11
0.11
0.1

7

0.07
0.08
0.07
0.07
0.08
0.1

0.11
0.1

0.09
0.07
0.07
0.07
0.08
0.07
0.07
0.07
0.07
0.08
0.08
0.07
0.07
0.08
0.08
0.07
0.07
0.07
0.07
0.08
0.07
0.07
0.06
0.05
0.1

0.08
0.07
0.07
0.07
0.1

0.11
0.09
0.09
0.1

0.11
0.13
0.1

0.1

0.1

0.11
0.1

8

0.1

0.08
0.07
0.08
0.1

0.13
0.15
0.11
0.07
0.06
0.07
0.08
0.13
0.09
0.09
0.09
0.09
0.09
0.1

0.1

0.09
0.09
0.1

0.1

0.09
0.09
0.07
0.1

0.1

0.09
0.08
0.09
0.11
0.11
0.11
0.1

0.08
0.11
0.14
0.11
0.1

0.11
0.12
0.15
0.11
0.11
0.17
0.11
0.11

0.09 0.1

9

0.1
0.1
0.09
0.1
0.11
0.14
0.15
0.13
0.1
0.09
0.1
0.1
0.1
0.1
0.09
0.1
0.09
0.1
0.1
0.1
0.08
0.1
0.1
0.11
0.09
0.09
0.09
0.1
0.1
0.09
0.1
0.1
0.12
0.11
0.1
0.1
0.1
0.12
0.13
0.12
0.12
0.14
0.14
0.14
0.12
0.12
0.14
0.15
0.14
0.12

10

0.1

0.1

0.11
0.12
0.08
0.14
0.15
0.14
0.13
0.12
0.13
0.12
0.1

0.1

0.09
0.08
0.08
0.09
0.1

0.11
0.11
0.12
0.11
0.12
0.13
0.13
0.13
0.11
0.11
0.13
0.15
0.15
0.13
0.12
0.13
0.15
0.16
0.11
0.14
0.13
0.15
0.16
0.13
0.14
0.12
0.13
0.16
0.13
0.15
0.13

11

0.07
0.05
0.05
0.05
0.06
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.06
0.08
0.09
0.09
0.07
0.07
0.06
0.04
0.04
0.07
0.08
0.06
0.02
0.03
0.06
0.07
0.06
0.03
0.03
0.1

0.06
0.07
0.04
0.04
0.12
0.1

0.07
0.06
0.07
0.13
0.1

0.1

0.08
0.13
0.12
0.1

0.08

12

0.05
0.04
0.04

0.05

0.06
0.07
0.06
0.05
0.04
0.04
0.05
0.05
0.06
0.06
0.07
0.07
0.06
0.04
0.05
0.05
0.05
0.05
0.04
0.05
0.05
0.05
0.05
0.04
0.06
0.07
0.07
0.06
0.06
0.07
0.07
0.07
0.07
0.07
0.06
0.08
0.08
0.08
0.07
0.07
0.08
0.07
0.08
0.07
0.07
0.07

13

0.12
0.13
0.14
0.15
0.16
0.17
0.17
0.16
0.14
0.13
0.14
0.13
0.15
0.12
0.12
0.12
0.11
0.13
0.14
0.13
0.12
0.14
0.14
0.14
0.14
0.14
0.15
0.14
0.14
0.15
0.17
0.17
0.16
0.15
0.16
0.16
0.17
0.17
0.18
0.16
0.16
0.17
0.17
0.18
0.16
0.16
0.17
0.16
0.16
0.15

14

0.13
0.09
0.11
0.14
0.17
0.18
0.16
0.15
0.14
0.16
0.18
0.18
0.18
0.14
0.12
0.11
0.09
0.08
0.08
0.08
0.1

0.12
0.1

0.08
0.11
0.13
0.14
0.13
0.14
0.15
0.18
0.19
0.18
0.17
0.2

0.2

0.21
0.15
0.15
0.18
0.2

0.23
0.13
0.13
0.16
0.15
0.22
0.13
0.13
0.14

15

0.12
0.1

0.1

0.11
0.12
0.12
0.11
0.1

0.11
0.12
0.13
0.13
0.13
0.1

0.08
0.09
0.1

0.1

0.09
0.1

0.09
0.09
0.1

0.12
0.13
0.13
0.13
0.11
0.13
0.15
0.14
0.15
0.11
0.12
0.13
0.15
0.15
0.09
0.13
0.12
0.13
0.17
0.11
0.12
0.11
0.1

0.17
0.11
0.14
0.11

51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72

MEAN
STD
CV actual

WflaUI-FWNr—A

\O

10
ll
12
13
14
15
16
17
18

AVG.
STD
CV std

0.06
0.08
0.07
0.06
0.06
0.05
0.05
0.05
0.07
0.07
0.07
0.05
0.05
0.07
0.07
0.07
0.07
0.06
0.06
0.07
0.07
0.07

0.06
0.01
O. 18

0.05
0.05
0.04
0.05
0.07
0.06
0.07
0.04
0.06
0.07
0.06
0.07
0.07
0.05
0.04
0.05
0.07
0.03
0.06
0.07
0.04
0.06

0.05
0.01
0.29

0.05

0.11

0.1

0.08 0.14 0.12

0.05
0.04
0.05
0.05
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.05
0.04
0.05
0.05
0.04
0.05
0.05
0.06
0.06

0.05
0.01
0.26

0.14
0.12
0.12
0.12
0.11
0.12
0.12
0.12
0.11
0.1

0.12
0.12
0.11
0.1

0.09
0.11
0.11
0.1

0.09
0.09

0.11
0.02
0.17

0.14
0.14
0.12
0.1

0.09
0.13
0.12
0.12
0.11
0.09
0.13
0.13
0.11
0.11
0.1

0.12
0.12
0.11
0.1

0.1

0.11
0.02
0.14

0.1

0.12
0.11
0.1

0.1

0.09
0.09
0.09
0.1

0.1

0.1

0.09
0.09
0.09
0.09
0.09
0.08
0.08
0.08
0.09
0.08
0.08

0.09
0.02
0.19

97

0.09
0.09
0.09
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.08
0.07
0.07
0.07
0.07
0.07
0.07
0.07

0.08
0.02
0.19

0.09
O. 12
0.11
0.1

0.1

0.08
0.08
0.08
0.1

0.09
0.08
0.09
0.1

0.09
0.09
0.1

0.09
0.09
0.09
0.09
0.09
0.08

0.1
0.02
0.19

0.11
0.13
0.14
0.12
0.11
0.1

0.1

0.11
0.11
0.11
0.1

0.1

0.1

0.11
0.11
0.12
0.12
0.09
0.1

0.11
0.12
0.12

0.11
0.02
0.15

0.14
0.15
0.13
0.14
0.15
0.15
0.15
0.11
0.13
0.14
0.15
0.15
0.1

0.13
0.15
0.15
0.16
0.1

0.1

0.12
0.14
0.14

0.13
0.02
0.17

0.08
0.07
0.12
0.11
0.07
0.05
0.04
0.1

0.1

0.06
0.04
0.03
0.09
0.09
0.07
0.04
0.04
0.1

0.1

0.08
0.07
0.05

0.07
0.03
0.36

0.07
0.08
0.07
0.06
0.06
0.06
0.06
0.06
0.07
0.07
0.07
0.06
0.08
0.07
0.08
0.07
0.06
0.06
0.08
0.08
0.08
0.08

0.06
0.01
0.19

0.16
0.17
0.16
0.15
0.16
0.15
0.15
0.15
0.15
0.15
0.15
0.14
0.14
0.15
0.16
0.15
0.15
0.12
0.13
0.14
0.15
0.15

0.15
0.02
0.11

18 Randomly selected depths using Topographic distribution fiom software

S URFER, (using MinCurve Method)

1

0.05
0.05
0.05
0.05
0.06
0.06
0.06
0.06
0.07
0.07
0.07
0.07
0.07
0.08
0.08
0.08
0.08
0.08

0.07
0.01
0.19

CV low/high 0.18

2

0.03
0.04
0.04
0.04
0.05
0.05
0.06
0.06
0.06
0.07
0.07
0.07
0.07
0.07
0.08
0.08
0.08
0.09

0.06
0.02
0.27
0.25

3

0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.05
0.05
0.05
0.06
0.06
0.06
0.06
0.07
0.07

0.05
0.01
0.22
0.17

4
0.07
0.08
0.1

0.1

0.1

0.11
0.11
0.11
0.11
0.11
0.11
0.12
0.12
0.12
0.12
0.13
0.14
0.16

0.11
0.02
0.18
0.18

5
0.09
0.09
0.09
0.09
0.09
0.1
0.1
0.11
0.11
0.11
0.12
0.12
0.12
0.13
0.14
0.14
0.15
0.16

0.11
0.02
0.19
0.17

6
0.07
0.08
0.08
0.08
0.09
0.09
0.1
0.1
0.1
0.1
0.1
0.1
0.11
0.12
0.12
0.13
0.14
0.15

0.1
0.02
0.21
0.2

7
0.06
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.08
0.08
0.08
0.08
0.08
0.09
0.09
0.1
0.1
0.1

0.08
0.01
0.15
0.14

8
0.08
0.08
0.08
0.08
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.1
0.1
0.11
0.1
0.14
0.15

0.1
0.02
0.2
0.16

9
0.09
0.09
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.11
0.11
0.11
0.12
0.12
0.13
0.14
0.15

0.11
0.02
0.14
0.14

10

0.08
0.09
0.09
0.1

0.11
0.12
0.12
0.13
0.13
0.13
0.14
0.14
0.15
0.15
0.15
0.15
0.16
0.16

0.13
0.02
0.19
0.19

11
0.04
0.04
0.04
0.04
0.05
0.05
0.06
0.06
0.06
0.06
0.07
0.07
0.07
0.07
0.08
0.09
0.1
0.1

0.06
0.02
0.3

0.28

12

0.04
0.04
0.05
0.05
0.05
0.05
0.06
0.06
0.06
0.06
0.06
0.07
0.07
0.07
0.07
0.07
0.07
0.08

0.06
0.01
0.19
0.18

13

0.09
0.11
0.12
0.13
0.14
0.14
0.15
0.15
0.15
0.15
0.15
0.15
0.16
0.16
0.17
0.17
0.17
0.18

0.15
0.02
0.15
0.16

0.16
0.2

0.11
0.12
0.13
0.16
0.17
0.14
0.17
0.16
0.17
0.2

0.16
0.16
0.19
0.21
0.23
0.14
0.16
0.18
0.22
0.23

0.15
0.04
0.25

14
0.06
0.07
0.08
0.09
0.13
0.14
0.14
0.15
0.16
0.16
0.16
0.17
0.18
0.2
0.2
0.2
0.2
0.21

0.15
0.05
0.31
0.33

0.09
0.12
0.11
0.13
0.14
0.13
0.12
0.11
0.12
0.16
0.16
0.15
0.1

0.11
0.15
0.15
0.17
0.1

0.11
0.12
0.16
0.16

0.12
0.02
0.18

15

0.08
0.09
0.09
0.1

0.11
0.11
0.12
0.12
0.13
0.13
0.13
0.13
0.14
0.14
0.15
0.15
0.16
0.16

0.12
0.02
0.19
0.19

APPENDIX B

T urfgrass Sprinklers Irrigation Data

98
Appendix B

Turfgrass sprinklers irrigation data

These sprinkler irrigation data were obtained from Hancock Turfgrass Research Center,
Safi‘el, 1993. Dept. of Crop and Soil Science, MSU. The cups diameters were 11.46 11.4 cm.
The application rates were in mls. The sprinklers were spaced 10 m X 10 m .

Set] 46 46 46 42 46 42 42 44 50 100
64 88 70 86 96 98 102 104 104 11
40 78 74 106 114 129 146 170 135 126
30 70 90 140 152 164 170 190 160 140
30 70 112 165 184 196 190 220 180 144
40 108 169 196 214 210 220 236 180 170
50 130 194 234 250 250 236 202 184 160
70 142 206 234 270 273 260 229 186 154
98 156 226 246 274 270 263 224 220 210
101 188 186 210 244 220 222 183 154 179

Set2 89 100 120 126 122 114 108 99 98 152
61 108 148 158 162 160 162 149 146 138
23 84 140 180 205 216 205 200 176 142
21 92 154 200 222 238 236 226 198 150
30 100 160 212 227 250 240 194 206 162
34 110 172 218 240 250 255 236 210 169
52 138 180 230 222 247 260 240 210 160
70 130 178 210 222 237 249 237 192 156
76 139 160 170 187 180 170 160 150 166
64 150 106 114 120 107 109 101 96 40

$613 68 98 120 125 129 126 121 115 111 95
98 126 132 145 146 141 138 121 121 110
96 135 140 150 149 142 137 135 122 122
109 128 132 138 142 138 132 122 116 125
109 120 124 130 135 128 126 112 102 107
101 118 122 126 125 126 121 114 105 96
92 113 120 120 112 114 114 112 100 88
74 97 112 115 112 110 116 106 96 76
63 84 102 118 120 122 118 105 88 59
39 68 84 99 100 99 90 85 63 44

Set4 94 108 127 132 126 119 130 127 104 110
110 116 126 132 128 135 138 125 134
116 118 122 123 127 133 130 132 130 135
120 120 120 120 133 127 124 114 108 113
103 97 104 114 124 124 112 110 102 105
90 100 106 116 118 118 109 102 98 93
80 90 110 118 112 106 110 106 100 78
70 85 102 110 105 103 112 96 9O 75
49 77 99 112 112 112 112 108 87 66
35 50 68 75 80 78 87 81 62 52

Set 5

Set 6

Set 7

Set 8

107
120
125
120
106
94
88
73
58
52

82
96
95
104
94
84
68
50
35
20

66
76
8O
72
62
52
45
32
21
29

79
117
136
125
102
90
72
52
40
26

125
130
128
118
104
98
93
85
72
65

114
123
132
114
107
94
86
7O
60
32

90
112
124
118
99
83
70
50
36
25

92
113
123
115
96
90
78

45
52

140
144
135
123
111
112
103
100
92

77

115
130
123
118
110
103
94
90
82
48

115
121
122
115
99
90
74
67
56
38

105
120
130
115
100
99
87
81
7O
55

144
148
134
130
118
114
110
102
100
80

118
124
122
122
112
106
100
100
105
66

133
134
128
114

96
86
78
77
54

127
137
134
120
106
95
90
88
85
53

140
140
137
131
124
114
110
106
110
78

124
128
132
120
105
105
95

104
116
74

133
147
141
127
110
99
88
87
96
64

142
148
142
127
108
96

86

93
54

99

129
140
144
133
126
112
106
112
110
75

126
131
123
118
108
97

93

103
116
80

138
150
146
130
117
94

90

102
69

142
154
147

96
94
92
101
102
63

126
145
142
132
114
108
108
112
112
74

138
135
120
108
99

92
100
121
83

145
150
143
125
110
95

93

105
115
74

157
167
146
124
104
96

97

108

116
125
136
120
112
110
106
100
98

63

138
140
118
102
93
92
87
88
97
77

147
154
140
114
107
99

100
97

104
78

150
159
138
114
100
97
96
96
98
66

107
114
124
119
107
101
94

88

50

130
136
127
102
90
8O
73
72
81
64

139
137
133
108

94
90
83
86
59

142
146
138
118
94
93
85
85
81
57

80
112
123
119
102
80
80
71
60
41

130
127
125
110
94
79
67

45
45

152
125
122
111
93
87
70
58
56
38

144
140
134
115
92
80
67
66
66
52

Set 9

Set 10

Set 11

Set 12

106
130
138
132
110
106
92
80
47
50

102
130
138
116
100
97
84
75
52
38

128
127
140
132
119
110
96
75
68
40

38

41
40
55
78
88
82
65
40

132
147
157
137
124
115
112
98

85

48

141
140
138
110
98
101
96
94
80
72

134
137
145
130
122
120
120
110
94

60

62
94
119
126
129
124
120
110
88
60

150
170
136
140
130
123
122
111
107
52

147
153
140
118
110
116
102
111
115
102

140
148
148
133
123
120
126
124
119
66

86

110
128
124
128
116
114
114
102
89

157
170
158
146
128
120
114
116
123
60

142
138
140
128
122
114
116
120
125
122

140
144
144
132
120
115
130
125

68

102
128
132
124
124
122
116
122
120
115

130
144
144
137
112
113
100
107
120
60

120
124
130
141
123
112
110
112
125
115

128
130
132
131
120
106
114
118
136
60

112
128
116
127
137
132
122
120
114
130

100

124
126
130
131
116
108
91

108
112
78

120
125
125
126
118
107
100
106
114
108

125
120
120
119
110
120
107
112
122
52

122
134
118
126
132
124
126
118
120
133

125
130
120
112
98
98
90
93
108
70

128
130
125
116
104
98

94

98

105
100

125
134
111
108
88
82
85
93
111
52

144
142
125
137
124
126
127
126
122
152

110
130
122
97
91
84
80
78
86
59

120
125
130
108
100
92
84
78
76
76

120
123
1 18
92
84
74
72
66
77
44

144
156
149
131
120
118
115
128
128
132

1 10
125
124
106
89
84
72
60
48
39

114
130
137
120
100
95
80
68
60
61

116
130
130
106
88
70
52
60
6O
42

142
148
159
142
119
118
113
117
109
106

117
130
140
125
89
91
78
45
35
35

98
135
158
127
112
93
83
60
41
40

120
138
140
118
98
73
60
53
41
48

114
132
138
133
120
127
114
107
138
60

 

Setl3

Setl4

Set15

Setl6

42
26
26
30
38
54
76
70
56
40

13
34
52
60
60
50
50
36
30
14

36
52

64
60
66
64
54
46
36

84
75
46
40
34
32
31
47
60
50

43
58
70
90
104
121
124
100
70
38

18
50
80
99
112
106
72
58
40
2O

62
86
105
115
112
114
110
107
90
64

114
138
136
143
130
90
69
78
106
86

50
66
88
102
114
116
110
106
84
50

38
50
74
90
108
97
70
52
34
40

78

100
120
120
116
120
121
110
110
84

140
180
210
214
210
194
142
107
90

60

76
100
106
100
103
110
108
92
84

47
55
72
90
100
97
74
62
58
60

97

112
124
120
112
104
113
111
110
94

152
198
243
251
240
198
144
99

80

44

71
91
92
104
102
105
104
104
99
94

101
97
93
92
101
100
98

100
106

100
120
122

101

82

110
112
114
115
105
104
104
84

105

136
136
130
122
122
116
116
116
126
120

112
120
119

1116 119

111
113
110
111
110
100

152
198
240
256
242
212
152
120
103
50

120
118
110
108
110
97

160
197
232
262
249
226
193
170
154
72

105
131
112
124
122
122
110
111
106
140

140
136
132
142
140
130
118
116
114
120

110
129
128
125
122
118
105
111
110
104

152
285
323
260
270
259
234
230
200
98

122
162
146
134
132
130
120
119
142
156

135
120
110
124
130
130
108
104
110
115

116
136
140
130
122
112
105
112
118
109

156
189
212
269
290
295
280
253
218
122

136
160
164
150
140
124
116
134
140
145

101
83
96
112
152
130
104
90
90
70

116
140
141
136
123
114
115
110
107
100

192
202
220
250
294
296
280
255
212
145

106
133
154
154
130
116
120
118
111
99

26
54
98
122
137
123
104
72
50
37

100
126
132
126
119
105
106
100
91

78

220
160
190
230
280
274
249
232
222
103

ooqcnuubww—a

mhA-hh-hA-b-hhs-wwwwwwwwwwNNNNNNNN~N-H~—~——~—\o
owmqo\M-§WNHO\OWQO\M#WNflO0WQO‘M$WNt—Io\OWQC‘M&WNI—io

102
Actual data were input into the software SURFER for random selection of depths.

MiniCurve method was used for higher accuracy of 0.995.

1
101
98
70
50
40
30
3O
48
64
46
188
156
142
130
108
70
70
78
88
46
186
226
206
194
169
112
90
74
70
46
210
246
234
234
196
165
140
106
86
42
244
274
270
250
214
184
152
114
96
46

2
64
76
76
52
34
30
21
23
61
89
150
139
130
138
110
100
92
84
108
100
106
160
178
180
172
160
154
140
148
120
114
170
210
230
218
212
200
180
158
126
120
187
222
222
240
227
222
205
162
122

3
39
63
74
92
101
109
109
96
98
68
68
84
97
113
118
120
128
135
126
98
84
102
112
120
122
124
132
140
132
120
99
118
115
120
126
130
138
150
145
125
100
120
112
112
125
135
142
149
146
129

4
35

49

70

80

90

103
120
116
110
94

50

77

85

90

100
97

120
118
116
108
68

99

102
110
106
104
120
122
126
127
75

112
110
118
116
114
120
123
132
132
80

112
105
112
118
124
133
127
128
126

5
52
58
73
88
94
106
120
125
120
107
65
72
85
93
98
104
118
128
130
125
77
92
100
103
112
111
123
135
144
140
80
100
102
110
114
118
130
134
148
144
78
110
106
110
114
124
131
137
140
140

ACtllal data sets
6 7 8
20 29 50
35 21 47
50 32 80
68 45 92
84 52 106
94 62 110
104 72 132
95 80 138
96 76 130
82 66 106
32 25 48
60 36 85
70 50 98
86 70 112
94 83 115
107 99 124
114 118 137
132 124 157
123 112 147
114 90 132
48 38 52
82 56 107
90 67 111
94 74 122
103 90 123
110 99 130
118 115 140
123 122 136
130 121 170
115 115 150
66 54 60
105 77 123
100 78 116
100 86 114
106 96 120
112 100 128
122 114 146
122 128 158
124 134 170
118 133 157
74 64 60
116 96 120
104 87 107
95 88 100
105 99 113
105 110 112
120 127 137
132 141 144
128 147 144
124 133 130

9
50
47
8O
92
106
110
132
138
130
106
48
85
98
112
115
124
137
157
147
132
52
107
111
122
123
130
140
136
170
150
60
123
116
114
120
128
146
158
170
157
60
120
107
100
113
112
137
144
144
130

10

38

52

75

84

97

100
116
138
130
102
72

80

94

96

101
98

110
138
140
141
102
115
111
102
116
110
118
140
153
147
122
125
120
116
114
122
128
140
138
142
115
125
112
110
112
123
141
130
124
120

11

40

68

75

96

110
119
132
140
127
128
60

94

110
120
120
122
130
145
137
134
66

119
124
126
120
123
133
148
148
140
68

100
125
130
115
120
132
144
144
140
60

136
118
114
106
120
131
132
130
128

12
40
65
82
88
78
55
4O
41
44
38
60
88
110
120
124
129
126
119
94
62
89
102
114
114
116
128
124
128
110
86
115
120
122
116
122
124
124
132
128
102
130
114
120
122
132
137
127
116
128
112

13
40
56
70
76
54
38
30
26
26
42
38
70
100
124
121
104
90
70
58
43
50
84
106
110
116
114
102
88
66
50
84
92
108
110
103
100
106
100
76
6O
94
99
104
104
105
102
104
92
91
71

14
14
30
36
50
50
60
60
52
34
13
20
40
58
72
106
112
99
80
50
18
40
34
52
7O
97
108
90
74
50
38
60
58
62
74
97
100
90
72
55
47
106
107
90
98
100
101
92
93
97
101

15
36
46
54
64
66
60
64
64
52
36
64
90
107
110
114
112
115
105
86
62
84
110
110
121
120
116
120
120
100
78
94
110
111
113
104
112
120
124
112
97
100
110
111
110
113
111
116
122
120
100

16
50
60
47
31
32
34
40
46
75
84
86
106
78
69
90
130
143
136
138
114
60
90
107
142
194
210
214
210
180
140

80

99

144
198
240
251
243
198
152
50

103
120
152
212
242
256
240
198
152

_ . .mllgflf. 1

 

V5

51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
9O
91
92
93
94
95
96
97
98
99
100

mean
STD

220
270
273
250
210
196
164
129
98

42

222
263
260
236
220
190
170
146
102
42

183
224
229
202
200
190
160
136
104
44

154
220
186
184
180
180
160
135
104
50

179
210
154
160
170
144
140
126
110
100

150

107
180
237
247
250
250
238
216
160
114
109
170
249
260
255
240
236
205
162
108
101
160
237
240
236
194
226
200
149
99

96

150
192
210
210
206
198
176
146
98

40

166
156
160
169
162
150
142
138
152

159

99
122
110
114
126
128
138
142
141
126
90

118
116
114
121
126
132
137
138
121
85

105
106
112
114
112
122
135
121
115
63

88

96

100
105
102
116
122
121
111
44

59

76

88

96

107
122
123
110
95

112

58.9 48.6 17

78

112
103
106
118
124
127
133
125
119
87

112
112
110
109
112
124
130
135
130
81

108
96

106
102
110
114
132
138
127
62

87

90

100
98

102
108
130
125
104
52

60

70

78

93

103
113
135
134
110

106

75

110
112
106
112
126
133
144
140
129
74

112
112
108
108
114
132
142
145
126
63

98

100
106
110
112
120
136
125
116
50

84

88

94

101
107
119
124
114
107
48

6O

72

80

80

103
119
123
112
80

108 99.1
16.7 18.5 20.4
CVactual 0.39 0.31 0.15 0.16 0.17 0.21

116
103
93
97
108
118
123
131
126
83
121
100
92
9O
99
108
120
135
138
77
97
88
87
92
93
102
118
140
138
64
81
72
73
8O
90
102
127
136
130
45
45
64
67
79
94
110
125
129
132

69
102
90

94
117
130
146
150
138
74
115
105
93
95
110
125
143
150
145
78
104
97
100
99
107
114
140
154
147
59
86
83
90
94
100
108
133
137
139
138
56
58
70
87
93
11
122
125
152

103

78
112
108
91
108
116
131
130
126
124
70
108
93
90
98
98
112
120
130
125
59
86
78
80
84
91
97
122
130
110
39
48
60
72
84
89
106
124
125
110
34
35
45
78
91
89
125
145
130
117

96.9 107

26.8 24.6 24.6 19.3
0.28 0.23 0.23 0.18

78
112
108
91
108
116
131
130
126
124
70
108
93
90
98
98
112
120
130
125
59
86
78
80
84
91
97
122
130
110
39
48
6O
72
84
89
106
124
125
110
34
35
45
78
91
89
120
140
130
117

107

108
114
106
100
107
118
126
125
125
120
100
105
98
94
98
104
116
125
130
128
76
76
78
84
92
100
108
130
125
120
61
6O
68
80
95
100
120
137
130
114
40
41
60
83
93
112
123
155
138
98

108

52
122
117
107
120
110
119
120
120
125
52
111
93
85
82
88
108
111
134
125
44
77
66
72
74

92
118
123
120
42
60
50
52
70
88
106
130
130
116
48
41
53
60
72
98
118
140
138
120

106

25.4 18.3
0.24 0.16

133
120
118
126
124
132
126
118
134
122
152
122
126
127
126
124
137
125
142
144
132
128
128
115
118
120
131
149
156
144
106
109
117
113
118
119
142
159
148
142
60

138
107
114
127
120
133
130
132
114

115

105
84

104
104
105
115
114
112
110
82

140
106
111
110
122
122
124
112
131
105
156
142
119
120
130
132
134
146
162
122
145
140
134
116
124
140
150
164
160
136
99

11

118
120
116
130
154
154
133
106

102

120
126
116
116
116
122
122
130
136
136
120
114
116
118
130
140
142
132
136
140
115
110
104
108
130
130
124
110
120
135
70

90

90

104
130
152
112
96

83

101
37

50

72

104
123
137
122
98

54

26

97

110
108
110
118
120
119
119
120
112
104
110
111
105
118
122
125
128
129
110
109
118
112
105
112
122
130
140
136
116
100
107
110
115
114
123
136
141
140
116
78

91

100
106
105
119
126
132
126
100

89.7 106
25.5 29.9 16
0.25 0.33 0.15 0.38

72

154
170
193
226
249
262
232
197
160
98

200
230
234
259
270
260
232
185
152
122
218
253
280
295
290
269
212
189
156
145
212
255
280
296
294
250
280
202
192
103
222
232
249
274
280
230
190
160
220

174
65.7

 

WQQM-‘BWNI—

\O

10
11
12
13
14
15
16
17
18

Mean
STD
CV18

CV10w/high0.32 0.28

18 Catch can depths were randomly selected using the software SURFER .

42

86

98

100
101
104
133
136
142
156
161
184
189
202
203
204
223
227

150

53.4 50.1
0.36 0.29

64

100
130
139
146
148
152
158
166
170
190
202
209
214
227
230
244
244

174

39

44

64

68

88

106
114
118
121
122
126
128
130
132
135
137
140
140

108

52

87

94

99

101
109
110
110
112
112
113
116
116
120
122
123
123
125

108

48
52
63
72
80
84
97
99
107
110
112
114
119
125
126
133
133
134

100

33.2 17.4 28
0.31 0.16 0.28 0.34

20
32
45
81
82
82
85
88
93
94
95
104
109
1 12
1 16
122
123
128

89.5
30.5

0.32 0.15 0.28 0.39

104

29
36
37
50
63
81
91
94
102
105
119
121
127
134
137
142
144
152

98
40.5
0.41

0.42

19
26
45
52
54
78
88
88
92
99
101
102
120
123
127
142
144
146

91.4
39.5
0.43

0.44

34

50

78

85

89

100
111
111
112
112
114
117
117
118
124
125
126
149

104
28

38
4O
60
76
91
98
99
101
102
110
113
115
116
127
130
130
140
143

102
31.1

0.27 0.31

0.28 0.33

40
52
61
63
71
73
79
81
93
94
94
110
114
116
120
121
128
130

91.1
27.6
0.3

0.28

38

4O

88

110
113
114
117
118
126
126
127
129
129
132
135
138
148
153

116
31.5
0.27

0.3

40
42
58
70
83
99
102
103
104
105
108
109
110
112
118
126
140
153

99

14
26
37
4O
49
68
71
83
95
97
103
109
109
112
120
130
136
138

85.4

30.4 38.9
0.31 0.46

0.33 0.45

36

66

78

86

90

100
107
107
111
113
114
114
115
121
122
128
140
141

105
26.1
0.25

0.26

50

84

99

103
106
128
130
186
197
202
220
225
229
235
248
253
254
260

178
69
0.39

0.36

 

APPENDIX C

C enter-pivot Irrigation System Data

No

“\JO\M&WNv—h

\O

105

Appendix C

Center-pivot sprinkler irrigation data

Data were obtained from Pandey, 1989. M.S. thesis, Dept. of Agr.

Depth2 Depth3 Depth4 Depth5

inch
2
0.418
0.507
0.313
0.223
0.243
0.271
0.290
0.306
0.308
0.300
0.291
0.272
0.230
0.238
0.267
0.314
0.337
0.361
0.353
0.323
0.292
0.286
0.288
0.294
0.297
0.302
0.300
0.292
0.275
0.239
0.190
0.141
0.087
0.038

Engineering, MSU.
Distance Depth]
11 inch
1
25 0.403
50 0.491
75 0.303
100 0.217
125 0.239
150 0.265
175 0.283
200 0.296
225 0.301
250 0.293
275 0.28
300 0.263
325 0.219
350 0.227
375 0.256
400 0.301
425 0.323
450 0.346
475 0.337
500 0.307
525 0.279
550 0.274
575 0.274
600 0.28
625 0.283
650 0.285
675 0.284
700 0.278
725 0.266
750 0.232
775 0.184
800 0.203
825 0.150
850 0.103
875 0.067
900 0.063
925 0.061
950 0.058
975 0.054
1000 0.049

inch
3
0.528
0.623
0.385
0.263
0.308
0.342
0.350
0.358
0.355
0.364
0.363
0.325
0.299
0.313
0.350
0.385
0.414
0.444
0.433
0.397
0.359
0.352
0.354
0.362
0.365
0.374
0.372
0.358
0.331
0.284
0.224
0.169
0.105
0.065

inch
4
0.463
0.550
0.341
0.239
0.276
0.306
0.308
0.326
0.326
0.317
0.316
0.293
0.262
0.261
0.300
0.342
0.367
0.393
0.384
0.352
0.318
0.312
0.313
0.320
0.324
0.331
0.329
0.317
0.293
0.251
0.199
0.150
0.093
0.057

inch
5
0.413
0.511
0.336
0.356
0.295
0.332
0.356
0.387
0.391
0.382
0.357
0.338
0.285
0.284
0.335
0.381
0.411
0.437
0.427
0.404
0.365
0.337
0.363
0.360
0.341
0.342
0.371
0.374
0.357
0.307
0.249
0.177
0.084
0.037

 

Set 6 Station 11 0 10 20 30
0 1.045
100 1.427 1.428 1.327 1.187
200 1.083 1.123 1.057 1.018
300 0.948 0.974 0.935 0.934
400 0.91 0.915 0.907 0.922
500 0.898 0.892 0.893 0.904
600 0.892 0.899 0.902 0.904
700 0.936 0.943 0.937 0.924
800 0.88 0.883 0.874 0.868
900 0.876 0.868 0.846 0.849
1000 0.705 0.641 0.579 0.563
1100 0.826 0.851 0.886 0.875
1200 0.821 0.795 0.769 0.753
1300 1.063 0.912 0.758 0.626
18 hand-picked random depths:
l 2 3 4 5
0.054 0.087 0.105 0.093 0.084
0.061 0.141 0.169 0.150 0.177
0.067 0.230 0.299 0.262 0.285
0.203 0.239 0.284 0.251 0.307
0.219 0.267 0.350 0.300 0.335
0.232 0.271 0.342 0.306 0.332
0.256 0.272 0.325 0.293 0.338
0.265 0.275 0.331 0.293 0.357
0.274 0.288 0.354 0.313 0.363
0.274 0.292 0.359 0.318 0.365
0.278 0.297 0.365 0.324 0.341
0.28 0.300 0.364 0.317 0.382
0.285 0.300 0.372 0.329 0.371
0.296 0.306 0.358 0.326 0.387
0.301 0.313 0.385 0.341 0.336
0.307 0.337 0.414 0.367 0.411
0.323 0.353 0.433 0.384 0.427
0.337 0.418 0.528 0.463 0.413
CV 0.4557 0.277 0.275 0.274 0.262
Low/high
CV CV
Heermann low/high
1 0.460 0.456
2 0.259 0.277
3 0.346 0.275
4 0.288 0.274
5 0.289 0.262
6 0.155 0.146

106

1.503
1.23

1.057
0.988
0.945
0.900
0.915
0.931
0.879
0.857
0.551
0.845
0.742
0.517

0.579
0.753
0.788
0.801
0.821
0.827
0.828
0.845
0.851
0.88

0.882
0.89

0.892
0.912
0.924
0.935
0.948
1.427

0.146

50
1.888
1.212
1.021
0.95
0.916
0.89
0.904
0.925
0.878
0.854
0.543
0.834
0.716
0.408

1.863
1.109
0.958
0.935
0.907
0.884
0.909
0.909
0.872
0.843
0.586
0.838
0.676
0.279

70
1.708
1.149
0.967
0.958
0.917
0.891
0.93
0.909
0.884
0.828
0.645
0.824
1.311
0.132

80
1.620
1.170
0.967
0.922
0.890
0.893
0.94
0.901
0.881
0.801
0.712
0.814
1.277

90

1.464
1.084
0.927
0.903
0.884
0.888
0.937
0.882
0.869
0.763
0.788
0.827
1.191

 

1 07
Appendix C Cont.

Data were obtained from Soil Conservation Service (SCS), St Joseph,
Michigan, 1995, for field evaluation of center-pivot irrigation systems

System 1 System 2 System 3 System 4 System 5
Sample Distence Depth 1 Depth 2 Depth 3 Depth 4 Depth 5

number ft ml ml m1 ml ml
1 3O 0 214 59 83 90
2 60 120 50 80 104 105
3 90 130 70 60 91 140
4 120 120 190 60 70 140
5 150 90 105 64 85 97
6 180 84 154 60 64 56
7 210 82 88 56 78 75
8 240 136 80 51 75 74
9 270 l 10 80 59 76 76
10 300 234 1 16 54 70 91
1 1 330 118 69 54 78 84
12 360 120 82 60 70 40
13 390 116 82 55 70 56
14 420 104 89 58 72 55
15 450 108 89 38 74 68
16 480 98 73 44 70 69
17 510 97 92 58 74 48
18 540 122 80 59 70 43
19 570 100 72 55 67 63

20 600 1 12 80 60 70 62
21 630 120 81 49 59 62
22 660 172 80 20 80 57
23 690 180 85 40 73 69
24 720 210 96 65 59 79
25 750 216 93 63 46 56
26 780 95 16 10 60
27 810 87 0 8 56
28 840 92 55
29 870 93 61
30 900 104 56
31 930 88 62
32 960 91 60
33 990 96 61
34 1020 95 66
35 1050 78 57
36 1080 94 64
37 1110 92 64
38 1140 106 61
39 1170 85 56
40 1200 93 58
41 1230 87 69
42 1260 98 19

 

i5"‘
.1.

43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58

1290
1320
1350
1380
1410
1440
1470
1500
1530
1560
1590
1620
1650
1680
1710
1740

87
91
98
86
124
87
112
114
107
125
100
82
58
123
98

108

 

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