SUBSURFACE DRIP IRRIGATION SYSTEM ...

SUBSURFACE DRIP IRRIGATION SYSTEM DEVELOPMENT AND MODELING OF WETTING PATTERN DISTRIBUTION

A Thesis Presented to the Graduate School Faculty of Agriculture, Alexandria University In Partial Fulfillment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY In

Agricultural Engineering

By

Mohammad Nabil Bahgat Mohammad El-Nesr

For more information and further queries please contact me at [email protected]

2006

Advisors' Committee: Prof. Dr.\ Samir Mohamed Ismail, Professor of Irrigation Systems' Engineering, Agricultural Engineering Department, Faculty of Agriculture, Alexandria University. Dr.\ Tarek Kamal El-Din Zein El-Abedin Assistant Professor of Irrigation Systems' Engineering, Agricultural Engineering Department, Faculty of Agriculture, Alexandria University. Prof. Dr.\ Mohamed Mohamed Abdou Wassif Professor Emeritus of Soil, Soil Conservation Department, Water Resources and Desert Soils Division, Desert Research Center.

SUBSURFACE DRIP IRRIGATION SYSTEM DEVELOPMENT AND MODELING OF WETTING PATTERN DISTRIBUTION

Presented By

Mohammad Nabil Bahgat Mohammad El-Nesr

For the Degree of

DOCTOR OF PHILOSOPHY

In

Agricultural Engineering Examiners' Committee:

Approved

Prof. Dr.\ِ Azmy Mahmoud El Berry, Professor of Agricultural Engineering, Cairo University

Prof. Dr.\ Mahmoud Abdel Aziz Hasan, Professor of Agricultural Engineering, Zagazig University

Prof. Dr.\ Samir Mohamed Ismail, Professor of Agricultural Engineering, Alexandria University.

Dr.\ Tarek Kamal El-Din Zein El-Abedin Assistant Professor of Agricultural Engineering. Alexandria University.

Date:16/9/2006

Dedication To the Souls of My Father, grandmothers, & grandfathers To My Mother To My pacemaker Dr. Nagat ElNesr To My aunt Hoda, My Uncles Salah, Galal, and Yousry To my sisters and all my family To Masged ElHedaya Mosque To my professors and colleagues To all of the desert researchers And Finally To the future, to my Children Merna and Mohannad ElNesr

ACKNOWLEDGEMENTS I would like to thank my prime supervisor, Dr. Samir M. Ismail, Professor of Agricultural Engineering, Head of Agricultural Engineering Department, Faculty of Agriculture, Alexandria University, for suggesting this research problem, his continuous guidance and advice during the entire stages of this work. Thanks to Dr. Tarek K. Zien El-Abedeen, Assoc. Prof. of Agric. Eng., Agric. Eng. Dept., Fac. of Agric., Alex. Univ., for his generous encouragement, helpful Ideas, and for his patience in thorough review of the manuscript. Many thanks to Dr. Mohammad M. Wassif, Prof. Emeritus of Soil, Former Chairman of the Water Resources and Desert Soils Division in the Desert Research Center (DRC), for his lasting encouragement, continuous support, for his guidance in the field work, and for reviewing the manuscript. My thanks to All Staff Members of the Agricultural Engineering Department, Fac. of Agric., Alex. Univ., who are my professors, for their support during my undergraduate and post graduate studies, and for their release of the ingenuity talent of the department's students. My thanks to Dr. Ismail Abd El Galeel, Prof. of Horticulture, and President of the DRC, former director of North Sinai Research Station; for his great help and endless support during the field work. Thanks also should be to All Staff of the North Sinai Research Station, especially Eng. AbdulRaheem, Eng. A. Abdel Fattah, and the field laborer Taha ElSaiidy for their cooperation, and attention during the field experiments. Many thanks to my colleagues in the Soil Conservation Department of the DRC, especially Eng. M. El Farra, and Dr. H. Heikal for their help in some field trips, and Dr. M. Kilany for his help in the soil analysis in lab. Many thanks to Dr. Gamal Abd El-Naser, professor of soil physics in the Faculty of Agriculture (Saba Pacha) Alex. University, for his help in providing the Hydrus 2D software which was used for the current model validation. Finally, I wish to express my deep thanks to the patience, support, and encouragement of My Wife who suffered a lot during the whole stages till this work is done. In addition, many thanks, gratitude, and appreciation are to my Twin-sister, for her great help on the final stages of this work.

ii

TABLE OF CONTENTS Dedication ...... ................................................................................................................ i Acknowledgements........................................................................................................... ii Table of contents.............................................................................................................. iii List of figures.... ............................................................................................................... v List of tables...... .............................................................................................................. xi Nomenclature.... ............................................................................................................ xiii Abstract

...... ........................................................................................................... xvii

Chapter I: INTRODUCTION ........................................................................................... 1 Objectives ............................................................................................................... 2 Chapter II: REVIEW OF LITERATURE......................................................................... 3 1 Subsurface drip irrigation present and future ....................................................... 3 1-1 Advantages of subsurface drip irrigation ................................................... 3 1-2 Disadvantages of subsurface drip irrigation. .............................................. 5 2 Subsurface drip irrigation field researches. ......................................................... 6 2-1 SDI effect on crop yield. ............................................................................ 6 2-2 SDI compared to other systems.................................................................. 6 2-3 Subsurface drip irrigation system design ................................................... 6 3 Modeling Surface and subsurface drip irrigation. .............................................. 11 Chapter III: MATERIALS AND METHODS................................................................ 18 1 Field Experiment ................................................................................................ 18 1-1 Field Experiment Location....................................................................... 18 1-2 Site description and land preparation. ...................................................... 18 1-3 Field Experiment Objectives. ................................................................... 21 1-4 Treatments ................................................................................................ 21 1-5 Planted Crops ........................................................................................... 23 1-6 Field layout............................................................................................... 23 1-7 Measurements and field observations ...................................................... 26 2 Model Development ........................................................................................... 29 2-1 Basic Soil-water relationships' equations ................................................. 29 2-2- Soil parameters' values............................................................................ 33 2-3 Modeling Procedure and assumptions...................................................... 35

iii

2-4 Modeling difficulties and special considerations ..................................... 55 2-5 Model developing language and user interface ....................................... 61 Chapter IV: RESULTS AND DISCUSSION................................................................. 63 1 Field experiment results: .................................................................................... 63 1-1 Yield of crops ........................................................................................... 63 1-2 Tartoufa yield. .......................................................................................... 63 1-3 Tomato results. ......................................................................................... 69 1-4 Visual observations .................................................................................. 72 1-5 System evaluation and future investigations. ........................................... 78 2 Field soil moisture patterns: ............................................................................... 79 3 Model justification and utilization ..................................................................... 88 3-1 Field-measured data validation ................................................................ 88 3-2 Comparative validation to Hydrus 2D model........................................... 89 4 Model-based studies:.......................................................................................... 96 4-1 System construction studies ..................................................................... 96 4-2 Soil physical modeling studies ............................................................... 113 4-3 Mathematics of modeling studies.......................................................... .126 Chapter V: SUMMARY AND CONCLUSION........................................................... 134 Chapter VI: REFERENCES ......................................................................................... 138 APPENDIXES ........................................................................................................... 148 Chapter VII: ARABIC SUMARY................................................................................ 163

iv

LIST OF FIGURES Number

Caption

Page

2-1

Typical subsurface drip irrigation field layout

7

3-1

Field experiment location, in north Sinai

18

3-2

Field preparation before laying pipe lines.

20

3-3

Installing the dripper lines.

20

3-4

Installing the access tubes.

22

3-5

Field experiment layout shows all blocks and crops locations.

24

3-6

Field experiment scheme for one crop shows all treatments in one Block.

25

3-7

Calibrating the neutron probe.

27

3-8

Calibration curve of the Neutron Moisture meter

28

3-9

Study element scheme for ground drip model.

36

3-10

Finite difference grid of the current model.

38

3-11

The full Jacobian of the first stage of single surface source

46

3-12

The full Jacobean Matrix of the second stage of single surface source

48

3-13

The Jacobian matrix of the first stage of a subsurface system.

50

3-14

Flowchart of the main procedure logic

51

3-15

Different types of matrices system.

55

3-16

Convergence and over relaxation of fields.

56

3-17

Soil water retention curve SWRC of a course textured soil

59

4-1

Tartoufa yield as affected by physical barrier existence

65

4-2

Tartoufa yield as affected by the physical barrier existence and burying depth..

65

v

Number

Caption

Page

4-3

Tartoufa yield as affected by the hydraulic barrier existence and burying depth.

66

4-4

Tartoufa yield as affected by hydraulic barrier existence

66

4-5

Tartoufa yield as affected by hydraulic and physical barrier

69

4-6

Tartoufa yield as affected by burying depth

69

4-7

Tomato yield as affected by physical barrier.

70

4-8

Tomato yield as affected by hydraulic barrier.

70

4-9

Moisture distribution for the surface treatments, tartoufa early growth season

80

4-10

Moisture distribution for the surface treatments, tomato early growth season

80

4-11

Moisture distribution for the 10 cm depth treatments, tartoufa early growth season

81

4-12

Moisture distribution for the 10 cm depth treatments, tomato early growth season

81

4-13


82

4-14


82

4-15


83

4-16


83

4-17

Moisture distribution for the surface treatments, tartoufa late growth season

84

4-18

Moisture distribution for the surface treatments, tomato late growth season

84

4-19

Moisture distribution for the 10 cm depth treatments, tartoufa late growth season

85

vi

Number

Caption

Page

4-20

Moisture distribution for the 10 cm depth treatments, tomato late growth season

85

4-21


86

4-22


86

4-23


87

4-24


87

4-25

Field measured moisture content increment values compared to model predicted values for surface drip treatment measured at times 5, 10, 15, 20, 30, and 45 minuets after infiltration start.

90

4-26

Field measured moisture content increment values compared to model predicted values for bilateral 20,40 cm treatment measured at times 5, 10, 15, and 20 minuets after infiltration start.

91

4-27

Field-measured versus model-predicted values of soil moisture increase after infiltration, for a surface dripper line with no barriers

92

4-28

Field-measured versus model-predicted values of soil moisture increase after infiltration, for a surface dripper line with hydraulic barrier

93

4-29

A comparison of water content isolines between the current model and Hydrus 2D output diagram.

94

4-30

A comparison of snapshots between the current model and Hydrus 2D output diagram of simulating water movement in sandy soil through a 3L/h emitter for 60 minuets, cumulative volume of 3 Liters.

95

4-31

Moisture pattern of applying 5L through a 8l/h emitter in a sandy soil.

98

vii

Number

Caption

Page

4-32 a, b

"Drip Chartist" output patterns of 2 Liters water application, just after emission stopped, after 20 min, and after 6 hours of redistribution, for different gap sizes between bilateral surface-subsurface drip irrigation.

100

4-33 a

"Drip Chartist" output patterns of 2 Liters water application, after emission stopped, after 20 min, and after 6 hours of redistribution. For different upper lateral depths, where the lower later at fixed distance=6 cm.

103

4-33 b


104

4-33 c


105

4-34

Simulation time and simulation steps in application and redistribution as affected by upper lateral location and gap space.

107

4-35 a

"Drip Chartist" output patterns of 2.5 Liters water application, just after emission stopped , after 20 min, and after 6 hours of redistribution, for different depths of a 30 cm width physical barrier

109

4-35 b


110

4-35 c


111

4-36

Physical barrier dimensions effects on simulation time and steps

112

4-37

Wetting pattern and simulation charecteristics as affected by emitter discharge.

114

4-38

Effect of saturated and residual water content on the shape of the wetting pattern and on the simulation duration.

116

& 101

viii

Number

Caption

Page

4-39

Effect of beginning water content, and saturated hydraulic conductivity values on the shape of the wetting pattern and on the simulation duration.

117

4-40

Effect of some soil characteristics fitting parameters' values on the shape of the wetting pattern and on the simulation duration.

118

4-41

Effect of soil texture class on the shape of the wetting pattern and on the simulation duration.

122

4-42

Effect of moisture model, conductivity model, and different numerical integration methods on the shape of the wetting pattern and on the simulation duration.

124

4-43

Effect of cubic spline fitting usage with different moisture models and different numerical integration methods on the shape of the wetting pattern and on the simulation duration.

125

4-44

Wetting pattern and simulation characteristics as affected by Simulation Panel area.

128

4-45

Wetting pattern and simulation characteristics as affected by grid unit length.

130

4-46

Wetting pattern and simulation characteristics as affected by number of iterations

132

4-47

Effect of time increment factor for two applied volume cases on the shape of the wetting pattern and on the simulation duration.

133

A-1

The main output screen of the model.

148

A-2

“Grid” tab in model options.

149

A-3

“Time” tab in model options.

150

A-4

“Soil” tab in model options.

151

A-5

“Soil Hydraulic Functions” tab in model options.

152

A-6

“Sources” tab in model options.

153

A-7

Construction panel alternatives in “Sources” tab.

154

ix

Number

Caption

Page

A-8

“Grid” tab in model options.

155

A-9

“Output” tab in model options.

156

A-10

“Defaults” tab in model options.

157

A-11

“Time Step Browser” form.

158

A-12

Different output scenes of single isolated dripper.

159

A-13

Different output scenes of two isolated drippers, 34cm apart.

160

A-14

Summary of inputs as exported by the model.

161

A-15

Wetting front advance steps in sandy soil by 3l/h isolated emitter as simulated by the current model. Left sequence shows simulation before reaching isolation sheet, while right sequence shows simulation after reaching the isolation.

162

x

LIST OF TABLES Number

Caption

Page

3-1

Experimental site soil texture and particle size distribution percent

19

3-2

Soil moisture characteristic curve values of the experimental site soil.

19

3-3

Some soil properties of the experimental site soil

19

3-4

Summary of field treatments

23

3-5

Soil physical properties according to its texture

34

4-1

ANOVA table of "total tartoufa yield" variable

64

4-2

ANOVA table of "marketable tartoufa yield" variable

64

4-3

Total tartoufa yield as affected by main effect and interactions between independent treatments.

67

4-4

Marketable tartoufa yield as affected by main effect and interactions between independent treatments.

68

4-5

ANOVA table of "Tomato yield" variable

70

4-6

ANOVA table of "Tomato root average weight" variable

71

4-7

ANOVA table of "Tomato plant weight (w/out fruits)" variable

71

4-8

ANOVA table of "Tomato fruit count" variable

71

4-9

ANOVA table of "Tomato fruit average weight" variable

72

4-10

Tomato yield as affected by main effect and interactions between independent treatments.

73

4-11

Tomato root average weight as affected by main effect and interactions between independent treatments

74

4-12

Tomato plant weight without fruits as affected by main effect and interactions between independent treatments

75

4-13

Tomato fruit count as affected by main effect and interactions between independent treatments.

76

4-14

Tomato fruit average weight as affected by main effect and interactions between independent treatments..

77

xi

Number

Caption

Page

4-15

Experimental site soil properties

89

4-16

Simulation time, and simulation steps in application and redistribution for different gap spacings

102

4-17

Default soil physical parameters of case-study 2-1

115

4-18

Studied values for each soil parameter, where default values of each parameter is bolded

115

4-19

Soil properties of some soil texture classes in the model case-study

120

4-20

Grid dimensions of each case-study when the grid unit is fixed

127

4-21

Grid dimensions of each case-study when the grid area is fixed

127

4-22

Time increment factor values, allowable iterations values, and accumulative volume values used in study 3-2

131

xii

NOMENCLATURES Sorter Symbol

Meaning

Dimensions

1.00 English Symbols E1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

C D (q) E FC Fi Fis g h i is j K ks l m M n N p P P PC q R Rc (i) Rmax RR

Water capacity of soil Water diffusivity of soil Evaporation rate Water content at field capacity discharge of water discharge of water at the boundary of saturation Denotes the vertical position in the Jacobean matrix The soil water pressure head taken positive for unsaturated soils (denotes suction) Finite difference grid number in radial direction Finite difference grid number at saturated boundary Number of the time step Soil hydraulic conductivity Soil saturated hydraulic conductivity Finite difference grid number in vertical direction An empirical constant affects the shape of the retention curve Maximum number of grid units in the vertical direction An empirical constant affects the shape of the retention curve Maximum number of grid units in the radial direction Denotes the horizontal position in the Jacobean matrix Porosity Total head Personal computer Emitter discharge Radial Axis in cylindrical coordinates Radius from emitter of element at grid position i Radial length of the simulated area Element radius ratio

[L-1] [L2T-1] [LT-1] [L3T-1] [L3T-1]

[L]

[LT-1] [LT-1]

[L] [L3 T-1]

[L]

xiii

Sorter Symbol S (θ) SOR t

1 1 1 1

u UBR V v Va VBR Vc w X Z z ze Zmax

1 1 1 1 1 1 1 1 1 1 1 1

Meaning

Dimensions

Matric flux potential at θ water content Successive over relaxation Time An integration temporary variable represents the water content variable Unbalance ratio Applied volume Water vertical velocity Actual out volume from the emitter[L3] Volume balance ratio Calculated volume on the grid Wetted width of the wetting bulb Horizontal axis Vertical axis Wetted depth of the wetting bulb Vertical grid location of the buried emitter Vertical length of the simulated area

[L2T-1] [T]

[L3] [LT-1]

[L3] [L]

[L] [L]

Roman Symbols Symbol 2.01 α

γ γg 2.052

εb

2.051 ε 2.06 Φ 2.10 ϕ 2.121

λ

2.122 λps 2.14 ν

Meaning Dimensions Pronunciation An empirical parameter whose inverse is often referred to as the air entry value or [L-l] Alpha bubbling pressure The always-saturated diameter of [L] gamma subsurface emitter The number of the always-saturated grid [L] gamma units of subsurface emitter Small decimal less than 0.1 in volume epsilon balance Allowable error epsilon Equations matrix Phi Gravitational head Finite difference grid unit length (grid spacing) A pore-size distribution parameter affecting the slope of the retention function The number of iterations counter

[L]

phi

[L]

Lamda Lamda p s. Nu

xiv

Symbol 2.17

Θ

2.17 θ 2.17 θAr

Meaning Dimensionless water content or effective degree of saturation, or the reduced water content

Dimensions Pronunciation Theta

Soil moisture content

Theta

Entrapped air content

Theta a r

Initial wetness of soil

Theta beginning.

2.17 θd 2.17 θini

The desired soil moisture content

Theta d

Initial wetness of soil

Theta i n i.

2.17 θr 2.17 θs

The residual water content of the soil

Theta r

The saturated water content

Theat sat.

2.17

End limit of integration to find the matric flux potential

Theta v

2.17 θwr 2.17 θws

Actual residual water content

Theta w r

Actual Saturated water content

Theta w s

2.18 ρ(t) 2.19 σ

Time dependent wetting radius

2.17

θb

θv

Rho of t

The accumulative flow

3

[L ]

Sigma

2.20 τj 2.20 τδ 2.23 ω

Time-step

[T]

Taw j.

Time step

[T]

Taw delta

2.23 Ω 2.25 ψ

Unknowns matrix

2.26

A coordinates variable (r direction in cylindrical coordinates) The corresponding equation to grid location i,l

2.26

The error matrix Matric suction

ξ ζ i,l

2.27 ϒ 2.30 ℜ

3.00 3 3 3 3 3 3 3

Omega [L]

Psi

[L]

xi Zeta

The pore-connectivity parameter

iota

The Jacobean matrix

Jacobian

Abbreviations {Dp} {Is} {Tb} 1D 2D 3D ADI

Depth variable Physically isolated treatment Hydraulically isolated treatment One dimensional Two dimensional Three dimensional Alternate direction implicit method

[L]

xv

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

4.00 4 4

Symbol ALN ANOVA BC BCM BD BDF BDN DDF DDN GDF GDN MCM MF-D MF-K MFP MUR PDC PWC VG WP

Meaning Dimensions Pronunciation Alternate linear-nonlinear method Analysis of variance Brookes and Corey Burdine's conductivity model Bulk density [M L-3] Symbol of the Single subsurface dripper with physical barrier case Symbol of the Single subsurface dripper without physical barrier case Symbol of the Double dripperline with physical barrier case Symbol of the Double dripperline without physical barrier case Symbol of the Single surface dripper with physical barrier case Symbol of the Single surface dripper without physical barrier case Mualem's conductivity model Diffusivity based matric flux potential [L2T-1] Conductivity based matric flux potential [L2T-1] Matric flux potential [L2T-1] Modified unbalance ratio Primary drainage curve Primary wetting curve Van Genuchten Permanent Wilting point water content

Non English words Egyptian measure of land area. 1 Fd.=4200 m2 Tartoufa Jerusalem artichokes plant Fd.

[L2]

Feddan

xvi

ABSTRACT.

A

new technique in subsurface drip irrigation (SDI) was developed. The technique is called The Hydraulic Barrier or Bilateral SDI. It aims to barricade water from escaping far from the root zone through deep percolation. Its idea is to bury a secondary dripper line beneath the primary one so as the wetting pattern of the new system is enhanced to cover the root zone. The technique was tested through a field experiment on two crops and it was proved to have a noticeable effect on the crop yield. A mathematical computer model (Drip Chartist) was developed as well. This model is able to simulate surface and subsurface drip irrigation, with and without the hydraulic barrier, with and without the conventional physical barrier. The model was validated in field and through a comparison with previous trusted model (Hydrus 2D). Validation to the "Hydrus 2D" shows high coincidence between the two models. While the results show high correlations with field data with little under estimation. Several studies were performed on the computer model; which lead to important results in the drip irrigation systems design field.

Keywords: Subsurface drip irrigation, bilateral, hydraulic barrier, physical barrier, computer model, ADI finite difference.

xvii

INTRODUCTION Desert soils suffer from high temperature, lack of water, and poor plant-nutrients as well. These problems made it essential to use the most efficient irrigation system in conveying water to the plant without wasting any of the scarcely-found water resources. According to this, the drip irrigation system is the most suitable system to desert conditions, due to its high conveying efficiency, water conservation, and due to the precise ability of fertilizers and chemicals additions through it so as to enrich the desert soil's poverty in plant essential nutrients. One of the most important developments of the drip irrigation system is the subsurface drip irrigation system (SDI). This system is defined as the slow frequent application of water to the soil profile through emitters placed along a delivery line placed beneath the soil surface (Neufeld, et. al. 1999). It could also be defined as the application of water below the soil surface through emitters, with discharge rates generally in the same range as drip irrigation (ASAE, 1999). In other words, it is the low-pressure, low-volume irrigation system that uses drip tubes buried below the soil surface, (Alama & Broner, 2000). The SDI has too many advantages due to the dry soil surface. It, however, has some disadvantages as a result of the deep percolation problem due to the closeness of the dripping source to the far edge of the root zone. Some solutions to this problem were presented by some investigators (will be discussed in Chapter II) concerning laying a physical barrier under the root zone in order to force water to spread horizontally or to stay within the root zone, however, the major drawback of this solution is the technical and economical problems to trench a wide and deep furrow to lay the physical barrier in. This furrow's width is 5 to 10 times wider than what is needed for just burying the dripper line. Moreover, the hazard of air lack may appear in the root zone due to the moist environment created by the physical barrier, in addition to root dwarfness hazard. Therefore, a new method was tried which was called the Hydraulic Barrier system or the bilateral subsurface drip system. This new method barricades water without performing such problems. The hydraulic barrier method could be briefed as burying a secondary pipeline similar to the primary one but beneath it, and dividing the required water volume between the two pipes. The purpose of this is to formulate the water pattern so as to increase its width and hence to increase the available water in the shallow root zone. This technique, as seen, requires no extra trenching width, and does not cause air lack or root dwarfness. In order to check the validity of the new technique, several field experiments should have been done on the construction alternatives, and comparing the new method by the existing ones. Doing that research in the field is costly and exhausting. The only way to achieve that is to model the system so that hundreds of simulation experiments could be made easily and reliably. Hence, A computer simulation model has to be done, with the ability to simulate both existing and new methods, including surface drip, subsurface drip, bilateral drip, and physical barrier simulation. Therefore the objectives of the current study

1

could be summarized in the following: Objectives 1.

Evaluating the effect of bilateral tubing, lateral depth, and the physical barrier, on the crop yield and on the wetting pattern around the dripline through field experiments.

2.

Developing a simulation model of both the surface and subsurface drip irrigation systems; that can show the effect of soil type, soil-water characteristics, lateral burying depth, lateral spacing, physical barrier, and the effect of multiple tubing as well.

3.

Studying the surface and subsurface systems parameters effect on the wetting pattern, using the developed model.

2

REVIEW OF LITERATURE 1. Subsurface drip irrigation present and future Subsurface drip irrigation (SDI) is one of the oldest modern irrigation methods but relatively recent advances in plastics technology and SDI equipment have made it more affordable and long-lasting, (Neufeld, et. al. 1999). However, present technologies and future expectations made the future of irrigation is underground i.e. the subsurface drip irrigation (Zoldoske, 2000). The future of SDI is very promising, including its use in wastewater systems, and especially in areas where water conservation is important or water quality is poor. SDI is a very precise irrigation method, both in the delivery of water and nutrients to desired locations and the timing and frequency of applications for optimal plant growth, (Camp et. al., 2000). SDI is suitable for almost all crops and especially for high-value fruit and vegetable crops, turf and landscapes, (Alama & Broner, 2000).

1-1. Advantages of subsurface drip irrigation. 1-1-1. Dry soil surface Properly managed SDI systems wet the root zone uniformly throughout the field while maintaining a dry soil surface thereby reducing water losses due to evaporation. That is, evaporation of water from the soil surface will be limited to vapor diffusion because of the mulching effect of the dry soil and fewer salts will accumulate at the surface, (Phene, 1988). A dry soil surface also reduces weed growth and allows implement traffic even during irrigation, (Neufeld, et. al. 1999). Due to dry soil surface, orchards' stains or fruit-rot (like Alternaria late blight caused by "Alternaria Alternata" fungus), fully disappeared only after using subsurface drip irrigation and hence over 40% increase in yield, and over 60% increase in total profit due to both yield increase and herbicides costs saving (Katz, 1995). Equipment traffic through the field will be easier and less cumbersome because all pipes and laterals are buried. In addition, the soil surface is kept dry after the initial irrigation for germination, thus, traction through the field should be improved and less soil compaction should result, (Phene, 1988). Fields' areas can be entered by foot or vehicle during or immediately after an irrigation event. It no longer requires letting the field dry or turning the system off during special or planned activities, (Zoldoske, 2000).

1-1-2. Bypassing soil-surface problems Any soil surface crusts which usually cause infiltration problems will be bypassed and infiltration will not be a problem. Non-uniformity of application usually associated

3

2-3-2. Subsurface drip irrigation system layout A typical system layout (Fig. 2-1) consists of a settling pond (where possible), pumping unit, a hydrocyclone separator (when a pond is not feasible to take out the coarse materials), chemical injection unit, filtration unit equipped with back-flush control solenoid valves, pressure regulators, air vent at manifold, and PVC delivery system to carry the water to the field, (Alama and Broner, 2000).

1. Air vent 5. Manifold 9. Main line 13. Filter 16. Pumping pond

2. Pressure gage 6. Submain 10. Pressure gage 14. Surface water 17. Pump

3. Flushing clamp 4. Flow meter 7. Buried line 8. Pressure regulator 11. Auto valve 12. Valve 15. Chemical injection pump

Fig (2-1): Typical subsurface drip irrigation field layout. Source: (Alama and Broner,2000)

2-3-3. Importance of proper design Subsurface drip irrigation pipelines' hydraulic characteristics are the same as ground drip ones, however, improper design of either causes partial or full system failure especially due to water lack on field ends, on this situation mainly emitters' clogging by salt and sand particles may increase significantly on the low-flow emitters in the subsurface drip irrigation system. Some designers prefer higher capacity driplines, because they are less subject to plugging and allow more flexibility in irrigation scheduling.

7

However, higher capacity driplines typically require shorter lengths of run to maintain acceptable uniformity, (Lamm, et. al. 1997). Successful operation of an SDI system begins with a proper hydraulic design which satisfies constraints dictated by crop, soil type and characteristics, field size, shape, and topography, water source and supply. Disregarding design constraints will likely result in a system that is costly in both time and money and surely increases the chance of system failure. System failure might result in the loss of the total capital investment. It should also be noted that an improperly designed SDI system is less forgiving than an improperly designed center pivot sprinkler system. Water distribution problems may be difficult or impossible to correct for an improperly designed SDI system, (Lamm, et. al. 2003).

2-3-4. Lateral spacing The dripline spacing is obviously an important factor in system cost, as economics suggest wider spacings. However, wide spacing will not uniformly supply crop water needs and will likely result in excess deep percolation on many soil types. The dripline spacing is dictated by the lateral extent of the crop root zone, lateral soil water redistribution, and in-season precipitation. Soils that have a restrictive clay layer below the dripline installation depth might allow wider dripline spacing without affecting crop yield, (Lamm, et. al. 2003).

2-3-5. Driplines burying depth The installation depth is also related to the crop and soil type. Deep installations reduce the potential for soil evaporation and also allow for a wider range of tillage practices. There may also be some reduced potential for chemical, biological and root plugging of the emitters for the deeper installations. However, deep installations may limit the effectiveness of the SDI system for germination and may restrict availability of surface-applied nutrients, (Lamm, et. al. 2003). Drip lateral depth is an important consideration, drip laterals located at 0.6m were too deep to provide adequate moisture early when Faba beans were small, and plants grew better when laterals located at 0.25 to 0.45m deep. (Bryla et al. 2003) Camp (1998), stated that in his review that lateral depth was seldom a treatment variable in SDI research, so little can be said about crop yield differences with lateral depth. Lateral depth was probably optimized for site conditions, and soil and water characteristics. In some cases where several lateral depths were evaluated, little yield differences was evident. Also, Camp et. al.,(2000) deduced that little crop yield difference was reported in experiments where several lateral depths were evaluated. DeTar et al. (1996) found that the optimum burying depth for dripper line of potato was 8 to 46 cm. Other researchers found that 20 to 70 cm are acceptable depths for crops where tillage is an important consideration for it. Shallower depths (10 to 40 cm) are good for wide spread crops like alfalfa and turf grass. Generally, laterals in SDI systems are installed at depths of 0.1-0.5m, with shallower depths on coarse-textured soils and slightly deeper on finer-textured soils. In

8

The inverse trickle irrigation design process starts with an estimate of the wetted soil volume, normally the end result of the design process, this initial estimate becomes the objective of the design process. (Zur 1996) For a perfect wetting pattern, the dimensions of wetted soil must agree with some constrains; its depth must coincide with the root system, while its width must be related to the in-row spacing between emitters. (Zur 1996)

2-3-11. Physical water barrier Deep percolation is a big problem in coarse textured soils, however, this problem exists in both dripping systems (surface and subsurface) but its' effect is worst in subsurface drip irrigation, because when water is applied on top of a coarse textured soil, it took some time (depending to the infiltration rate) to run away from the root zone, surely this time will decrease if the dripping source is closer to the end of the root zone. The main avenue for water losses under this system is deep percolation, which is highest during the seedling stage and declined with the increase of root system. (El-Berry, 1989). On the other hand, Phene et. al, (1992a) showed that deep percolation losses and runoff can be reduced with properly designed and managed SDI systems. Barth (1995), suggested laying an impermeable polyethylene foil below the lateral pipes, however, he used a 60 cm wide, 0.06 mm thick plastic sheet laid on depth 30 to 40 cm, he deduced that this physical barrier had significantly increased the amount of water held in the root zone, either from dripper line or from rain, and limited the deep percolation. He stated also that the V shape of it increases the amount of water stored. In addition, he developed a special installation equipment to release the dripper line and the V shaped plastic foil simultaneously into the soil without disturbing the natural soil profile. Welsh et al. (1995) developed a technique to increase horizontal flow of water applied through SDI, this technique is called vector flow™. This technique involves placing an impermeable V shaped line just below the dripper line, i.e., the dripper line is laid over the small V shaped stripe which is only 7.5 cm wide (3 inches). They deduced that this technique lets 70% of the water applied spread up to 90 cm wide in the upper 15 cm of soil, from a 3.5 L/h dripper in a sandy loam soil, while only 25% of the applied water spread without the technique.

3 Modeling Surface and subsurface drip irrigation. The easiest way to model infiltration is to simulate a one-dimensional model normally in vertical "Z" direction downward soil surface. More accurate studies should be in two or three dimensions (2D or 3D); however the latter was not studied widely due to lack of high computer speeds till the near past. Campbell (1985) stated that unlike flood and sprinkler irrigation systems modeling, drip source infiltration modeling cannot be accepted in any way to be modeled in less than 2D. Drip source infiltration can be represented in a very satisfactory way in 2D cylindrical coordinates for point source and 2D Cartesian coordinates for line source, Brandt et al. (1971).

11

Assouline (2002) conducted experiments to study the effects of micro-drip and conventional drip irrigation on water distribution and uptake, and compared the results with the HYDRUS-2D model. He found that micro-drip results in more water content in the layer of 0-30 cm and less water in the lower layers, while conventional drip irrigation causes higher water content values in lower layers (outside the root zone). The compared software agrees with the experimental results. Cote et al. (2003) conducted a comparative study for analyzing soil wetting and solute transport in subsurface trickle irrigation. They proved the importance of the need to account for differences in soil hydraulic properties and solute transport when designing irrigation and fertigation management strategies; otherwise it will result in inefficient systems. El-Shaalan (2003) conducted a lab-study of subsurface drip irrigation under different lateral spacing in order to evaluate the tube characteristics, lateral spacing, impermeable layer depth, operation pressure, and water quality on water movement in the soil, the study was done on a laboratory sand tank, all of the studied properties had a significant effect on water distribution. The measured values were correlated well to Bower-Schilfgaarde, 1963 equation. Khalifa et al. (2004) investigated a model which simulates water movement in sandy soil under surface point source emitter, they used 2D simulation and solved Richard's equation by ADI method with some pre-simplifications and approximations, ElGindy et al. (2004) performed the model validation and concluded that the model agreed with the measured data significantly.

17

MATERIALS AND METHODS 1 Field Experiment 1-1 Field Experiment Location A field experiment was conducted in the North Sinai research station of the Desert Research Center in "El-Shaikh Zowayed" city, 30 km east of "El-Arish", and 12 km west of "Rafah" on the Egyptian-Palestinians' borders.

Fig(3-1) Field experiment location, in north Sinai

1-2 Site description and land preparation. The experiment site was almost flat, because it was leveled during the preparation of the experimental station. The soil was almost homogeneous; with medium to fine sandy texture up to 60 cm depth, no rocks or obstructions found in the soil surface and profile within the root depth. Soil texture and particle size distribution according to FAO (1970) are illustrated in Table (3- 1).

18

Table (3- 1). Experimental site soil texture and particle size distribution percent. Particle size

From (mm)

>2.0

1.0

0.5

0.25

0.10

0.063

1 αh ≤1

(3.20)

Another smooth function with attractive properties is the equation of van Genuchten (1980), further referred to as the VG-equation:

Θ=

θ − θr 1 = n θs − θ r 1 + (α h )

(

)

(3.21)

m

Where: α, n and m are empirical constants affecting the shape of the retention curve. m value can be calculated as a function of n according to the suggested conductivity model m= 1-1/n for the Mualem conductivity model and m= 1-2/n, for Burdine conductivity model Mualem (1976) and Burdine (1953), respectively. However, most of the soils have 1< n < 2, and m must be positive, i.e. Unlike Mualems' model; Burdine's model could not be used with most of soil types. van Genuchten, et al. (1991) combined Mualems' Conductivity Model (MCM) and Burdine's one (BCM) with the VG, and BC retention models, and hence derived some smooth, simple, and durable functions which can be shown in the following: Hydraulic conductivity model from MCM & VG:

(

1 ⎛ K ( Θ ) = K S Θ ⎜1 − 1 − Θ m ⎝

ϒ

)

m

⎞ ⎟ ⎠

2

(3.22)

Where ϒ, is the pore-connectivity parameter estimated by Mualem (1976) to be about 0.5 as an average for many soils, Ks is the saturated hydraulic conductivity.

32

developed a model that can estimate soil properties from clay and sand percentage in soil. Collected data from all above mentioned references were summarized in table (3-5). Table (3-5) Soil physical properties according to its texture Texture Class Light textured soils Medium textured soils Heavy textured soils

Sand Loamy Sand Sandy Loam Loam Silt Silty Laom Sandy Clay Loam Clay Loam Silty Clay Loam Sandy Clay Silty Clay Clay

Wilting Point Residual wat. WP %Vol θr (%Vol) Min. Avg. Max. Min. Avg. Max. 4.50 6.36 8.50 4.50 7.26 13.71 4.85 7.32 10.90 4.85 8.07 15.58 3.87 8.90 13.20 3.87 8.96 20.82 6.09 11.09 15.60 6.09 12.25 26.61 3.40 7.92 9.50 3.40 11.57 30.64 6.45 11.36 19.69 6.45 13.74 30.76 6.33 14.20 17.50 6.33 12.46 26.76 7.92 16.13 20.00 7.92 15.44 32.99 8.90 18.13 21.80 8.90 17.75 38.40 10.00 20.36 29.40 10.00 16.85 32.83 7.00 22.01 32.60 7.00 17.60 42.34 6.80 24.13 35.90 6.80 18.10 44.47

Saturation Wat. Cont. θS %Vol Texture Class Min. Avg. Max. Sand 34.5 37.6 43.0 Light textured Loamy Sand 35.1 38.7 41.5 soils Sandy Loam 38.1 41.3 45.6 Loam 39.9 44.3 48.9 Medium Silt 40.5 42.9 48.9 textured Silty Laom 38.2 45.3 50.7 soils Sandy Clay Loam 38.4 45.0 48.3 Clay Loam 41.0 47.9 50.8 Silty Clay Loam 43.0 50.3 52.2 Heavy textured Sandy Clay 38.0 46.5 51.8 soils Silty Clay 36.0 50.0 54.7 Clay 38.0 50.3 55.2

Bulk Density BD g/cm^3 Min. Avg. Max. 1.62 1.68 1.73 1.55 1.65 1.72 1.44 1.54 1.64 1.35 1.44 1.56 1.55 1.57 1.58 1.30 1.42 1.64 1.37 1.39 1.41 1.30 1.33 1.35 1.27 1.27 1.27 1.28 1.33 1.38 1.20 1.24 1.28 1.19 1.24 1.29

Hydraulic conductivity K Cond. cm/min Min. Avg. Max. 0.047000 0.214198 0.495000 0.019667 0.105774 0.243194 0.009500 0.047453 0.073680 0.005833 0.027508 0.047000 0.004167 0.045821 0.057833 0.007500 0.034221 0.060667 0.002183 0.005001 0.009160 0.004000 0.004371 0.005681 0.001167 0.004483 0.007715 0.001500 0.002922 0.007882 0.000330 0.004334 0.006674 0.001667 0.004213 0.010243

van Genuchtin alpha Texture Class Light textured soils Medium textured soils Heavy textured soils

Sand Loamy Sand Sandy Loam Loam Silt Silty Laom Sandy Clay Loam Clay Loam Silty Clay Loam Sandy Clay Silty Clay Clay

van Genuchtin n

α Min. 0.0353 0.0347 0.0267 0.0111 0.0066 0.0051 0.0211 0.0158 0.0084 0.0270 0.0050 0.0080

Avg. 0.0902 0.0794 0.0509 0.0236 0.0113 0.0126 0.0401 0.0174 0.0092 0.0302 0.0106 0.0115

Field Capacity FC %Vol Min. Avg. Max. 11.80 13.71 15.92 13.20 15.58 18.10 17.00 20.82 24.00 22.90 26.61 30.10 30.10 30.64 31.20 23.40 30.76 40.19 25.30 26.76 28.50 30.50 32.99 34.94 38.40 38.40 38.40 27.40 32.83 38.80 37.80 42.34 47.80 37.30 44.47 50.40

n Max. 0.1450 0.1240 0.0750 0.0360 0.0160 0.0200 0.0590 0.0190 0.0100 0.0334 0.0162 0.0150

Min. 2.6800 1.7466 1.4484 1.4737 1.3700 1.4100 1.3298 1.3100 1.2300 1.2067 1.0900 1.0900

Avg. 2.9299 2.0133 1.6692 1.5169 1.5235 1.5363 1.4049 1.3623 1.3751 1.2184 1.2054 1.1715

Max. 3.1798 2.2800 1.8900 1.5600 1.6769 1.6626 1.4800 1.4145 1.5202 1.2300 1.3207 1.2529

34

2-3 Modeling Procedure and assumptions 2-3-1. Modeling targets. The current model consists of several modules of soil-water relationships. These modules agree in the main equation and differ in initial and boundary conditions to simulate the following circumstances: •

Single surface dripper with/without physical barrier. For simplification these modules are called GDF, and GDN respectively, where GD stands for ground dripper, F: with physical isolation, N: with no physical isolation.

•

Single subsurface (buried) dripper with/without physical barrier, modules BDF, and BDN respectively, where BD stands for buried dripper.

•

Double dripper lines, with/without physical barrier, modules DDF, and DDN respectively, where DD stands for double dripper-lines. These dripper lines must have at least one of the laterals buried. I.e. either both lines are subsurface, or one surface and one subsurface.

2-3-2 Theoretical assumptions •

The soil is assumed uniform, homogeneous, and isotropic.

•

The initial water content should be uniform, and no sensible water movement initially in the soil θ = θini , where θini is the initial soil moisture content.

•

Darcy's law applies in both saturated and unsaturated zones.

•

While infiltration, soil water at any point in the system can either increase due to infiltration, or remain unchanged, i.e., it cannot decrease at any time.

•

The hydraulic conductivity of the soil, and all its derived functions, are differentiable, continuous and single valued functions of the moisture content.

2-3-3. The basic model For the simplest model "GDN", consider a field that is being irrigated with a set of emitters, spaced at 2x, and 2y as shown in Fig. (3-9) where: z direction is considered positive downward. Therefore the element of which we can study is bounded by the plans X=0, X=x, Y=0, Y=y, Z=0, and Z=z, where z is not a fixed boundary, but it should be taken far enough of the expected wetting front during the modeled experiment time.

35

Fig(3-9) The Study element scheme for ground drip model. To ensure non interference between emitters or any other wetting sources, the flow must vanishes through the plans X=0, X=x, Y=0, Y=y, and Z=z. [not Z=0], therefore at time t >0, ∂θ ∂x = 0 at X plans, ∂θ ∂y = 0 at Y plans, ∂θ ∂z = 0 at Z=z plan. To define the boundary conditions of plan Z=0, some considerations should be taken: •

This plan is divided into two zones, the first is the wetted zone, from the emitter (X=0, Y=0) to a moving boundary which increases with time ρ (t ) , has a wetting radius ρ (t ) = x + y . The second zone is the dry zone from ρ (t ) to the end of the grid X=x, and Y=0. 2

2

•

Water flows through the emitter discharge q should instantly infiltrate into the soil, or evaporates to air, hence a film of water pond occur with no runoff, so, the water content within the wetted zone is equal to the water content at saturation θ = θs .

•

Outside the wetted zone, no water occurs at surface, so either no water reaches this zone, or the infiltrated water is exactly equals the evaporated water. From Darcy's Equation (3.5) for downward water movement, it can be said ∂θ + K (θ ) , where E is the evaporation [LT-1], from the MFP that: E = − D (θ ) ∂z ∂S definition, Eq. (3.12), ∴ E = − + K (θ ) ∂z

•

Inside the wetting zone, the integration over plans X, and Y of the net water, which evaporates and infiltrates into the soil is equals to the corresponding emitter flow, and since the element 0-x,0-y,0-z is only quarter of the emitter wetting zone then the following formula can apply:

36

time-step should be repeated with the new value of the Φ i(ν +1) . Assuming convergence of the diffusivity function, the operation will complete within 7-10 iteration steps.

The Jacobian matrix ℜ The Jacobian matrix hereby is the backbone of the model; nonetheless, any differences in the boundary conditions from model to model will be reflected mainly in this matrix, but as mentioned before, it is the locale partial differentiation of the zeta function ζ i ,l with respect to the moisture content variable. For more clarification, Zeta function of the GDN model will be discussed in details here: For any point in the grid, with the coordinates (i, l), equation (3.38) could be applied except for the points whose coordinates belong to the range of any of the boundary conditions (3.39) to (3.45). The derivation of the zeta function of the point that only belong to equation (3.38) could be as simple as to say that zeta equals the difference between the right and the left hand side of the equation where as zeta equals or tends to zero if the proper values of (θ) are entered in all locations in the formula. j +1

θi ,l 2 − θi j,l ⎛ S i j+1,l − 2S i j,l + S i j−1,l S i j+1,l − S i j−1,l = −⎜ + 2 ⎜ τj 2 (2i − 1)λ 2 λ ⎝

ζ i ,l

⎛ S j + 2 − 2S j + 2 + S j + 2 i ,l +1 i ,l i , l −1 −⎜ 2 λ ⎝ 1

1

1

⎞ ⎟⎟… ⎠ 1 j+ j +1 K i ,l +21 − K i ,l −21 ⎞ ⎟ − 2λ ⎠

(3.49)

Multiplying by λ2.τ/2 and rearranging:

(

j + 12

ζ i ,l = λ 2 θi ,l − θi j,l

)

⎡⎛ j S i j+1,l − S i j−1,l ⎞ j j S 2 S S − + + ⎢ ⎟+ i ,l i −1,l τ j ⎢⎜⎜⎝ i +1,l (2i − 1) ⎟⎠ − 2 ⎢⎛ j + 1 1 1 1 1 ⎢⎜ S 2 − 2S j + 2 + S j + 2 − λ K j + 2 − K j + 2 i ,l +1 i ,l i , l −1 i ,l +1 i ,l −1 ⎢⎣⎝ 2

(

)

⎤ ⎥ ⎥ ⎥ ⎞⎥ ⎟ ⎠ ⎦⎥

(3.50)

For 1 iS

0 2τ D

−τ ( λK + 2D ) 4

λ 2+ τ D

τ

0

−τ ( λK + 2D ) 4

λ 2 +τ D

0

0

−τ ( λK + 2D ) 4

i

i

i

i i

i i

i i

−τ ( λK + 2D ) 4 i i

i

i

i

i

i

i • •

i

i

i

i

i

i

i •

0

0

0

0

i

i

i

i

−τ ( λK + 2D ) 4

λ 2+ τ D

0

0

0

0

i

i

i

i

0

−τ ( λK + 2D ) 4

λ 2+ τ D

0

0

0

0

i

i

i

i

0

0

−τ D 2

( λK −2D )

4

τ

4

τ

( λK −2D )

4

λ 2 +τ D

τ

( λK −2D )

i

4

τ

( λK −2D )

4

M +1

⎞ ⎟ ⎟ 0 ⎟ ⎟ ⎟ ⎟ 0 ⎟ ⎟ ⎟ ⎟ 0 ⎟ ⎟ ⎟ i ⎟ ⎟ ⎟ i ⎟ ⎟ i ⎟ ⎟ i ⎟ ⎟ ⎟ i ⎟ ⎟ ⎟ i ⎟ ⎟ ⎟ 0 ⎟ ⎟ ⎟ τ ( λK −2D ) ⎟ 4 ⎟ ⎟ τ ⎟ D ⎟ 2 ⎠

Fig (3-11) The full Jacobian of the first stage of single surface source 46

⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝

g =0 p =0

(

−τ λ ⎣⎡ K +E ⎦⎤+ 3D

1

−τ ( λK + 2D ) 4

2

0

3 4 i

0 i i

2

)

1

2

3

4 i

i

ze

ze +1

M −1

M

2τ D

−τ D 2

0

0 i

i

i

0

0

0

( λK −2D )

0

i

i

i

i

0

0

0

( λK −2D )

i

i

i

i

0

0

0

• • i

• •

i

i i

i i i

i i i

i i i

i i i

↑

i

i

i ≤ gs ⎤ ⎥ i > gs ⎦

i

i

λ 2+ τ D −τ ( λK + 2D ) 4 0 i i

τ

4

λ 2 +τ D • i i

τ

4

↑ ←

⎡λ ⎢ ⎣0

2

i ≤ gs ⎤ ⎥ i > gs ⎦

ze

i

i

i

i

i

ze +1

i

i

i

i

i

i

i

i

i

i

i

i

i

i

M −1

0

0

0

0

i

i

i

i

M

0

0

0

0

i

i

i

i

0

−τ ( λK + 2D ) 4

λ 2+τ D

M +1

0

0

0

0

i

i

i

i

0

0

−τ D 2

←

⎡λ 2 ⎢ ⎣0

i

λ 2+ τ D

τ

( λK −2D )

4

⎞ ⎟ ⎟ 0 ⎟ ⎟ ⎟ 0 ⎟ ⎟ ⎟ ⎟ 0 ⎟ ⎟ i ⎟ ⎟ i ⎟ i ⎟ ⎟ ⎟ ⎟ i ⎟ ⎟ ⎟ ⎟ i ⎟ ⎟ ⎟ i ⎟ ⎟ 0 ⎟ ⎟ ⎟ τ λK −2D ) ⎟ ( 4 ⎟ ⎟ τ ⎟ D ⎟ 2 ⎠

M +1

Fig(3-13) The Jacobian matrix of the first stage of a subsurface system.

50

51

54

2-4 Modeling Difficulties and Special Considerations In the previous section the theoretical steps of model development were planed and shown, but while translating these steps to numerical form or to computer language, some difficulties were achieved, these difficulties and their solution will be discussed in the following:

2-4-1 Matrices solution Solving any of the matrices system normally done in a numerical form by Gauss elimination, but in the current model case this method is not suitable in most of the matrices, In the first stage solution of the FDM the system is semi-tridiagonal, while in the second stage the system is fully-tridiagonal. Tridiagonal matrix is a special case of banded matrix where the bandwidth is 3, The fully-tridiagonal system is easier to be converted to a compact form and solved in a 3×M matrix instead of N×M one, where M and N are number of matrix' rows and columns, for clarification, some matrices have hundreds of rows and columns, so solving such matrices in the 3×M form instead of N×M form saves time of several thousands of computer operations, and faster solution could be achieved. Figure (3-15) shows the different types of matrices. ⎛ a11 ⎜ ⎜ a 21 ⎜ a 31 ⎜ ⎝ a 41

a12 a 22 a 32 a 42

a13 a 23 a 33 a 43

a14 ⎞ a 24 ⎟⎟ a 34 ⎟ ⎟ a 44 ⎠

Normal matrix

⎛ a11 ⎜a ⎜ 21 ⎜ a 31 ⎜ ⎜ ⎜ ⎝

a12 a 22 a 32 a 42

a13 a 23 a 33 a 43 a 53

a 24 a34 a 44 a 54

Banded matrix

⎞ ⎟ ⎟ a 35 ⎟ ⎟ a 45 ⎟ a55 ⎟⎠

0 ⎞ ⎛ a11 a12 0 ⎜ ⎟ ⎜ a 21 a 22 a 23 0 ⎟ ⎜ 0 a 32 a 33 a 34 ⎟ ⎜ ⎟ 0 a 43 a 44 ⎠ ⎝ 0

⎛ 0 a11 a12 ⎞ ⎜ ⎟ ⎜ a 21 a 22 a 23 ⎟ ⎜ a 32 a 33 a 34 ⎟ ⎜ ⎟ ⎝ a 43 a 44 0 ⎠

Tridiagonal matrix

Compact form of a tridiagonal matrix

⎛ a11 a12 a13 ⎜a ⎜ 21 a 22 a 23 ⎜ a 32 a 33 a 34 ⎜ a 43 a 44 ⎜ ⎜ a54 ⎝

⎞ ⎟ ⎟ ⎟ ⎟ a 45 ⎟ a55 ⎟⎠

Semi-banded matrix or semi-tridiagonal matrix

⎛ ⎜a ⎜ 21 ⎜ a 32 ⎜ ⎜ a 43 ⎜a ⎝ 54

a11 a 22 a 33 a 44 a 55

a12 a13 ⎞ ⎟ a 23 ⎟ ⎟ a 34 ⎟ a 45 ⎟ ⎟ ⎠

Compact form of a semi-banded matrix

Fig (3-15) Different types of matrices system. The semi-tridiagonal system is actually a banded system but with only one element in the second upper band. There is a special solution for banded systems other than tridiagonal systems. In the current model, and any complicated finite difference models, many near-zero values occur in the calculations especially when using Newton iteration method combined with FDM, these near-zero values occurs mostly in the initial calculation steps, and caused a division-by-zero error in the computer program even when using 55

Do a loop from i = 1 to i = N

RR = 1 − ( Rc ( i ) Rc ( N ) ) Do a loop from l = M to l = 2

(

θi j,l = min θsat , θi j,l + (θi j,l −1 − θb ) × MUR × RR

)

(3.67)

Continue loop l Continue loop i Where, VBR: volume balance ratio, UBR: unbalance ratio, MUR: modified unbalance ratio, εb: small decimal less than 0.1 to ensure gradualism of volume balance even if severe unbalance occur, l: vertical direction grid numbering, M: maximum grid number of depth, i: horizontal grid numbering, N: maximum grid spacing from emitter position, RR: element radius ratio, Rc (i), Rc (N): radius from emitter of element at grid position i, N respectively, θsat: soil moisture content at saturation. In the shown procedure of volume balance, the actual and calculated volumes are compared to both volume balance ratio, and unbalance ratio as presented in steps (3.63) and (3.64). Some times unbalance ratio reaches big values (up to ±20%), and hence, correcting these values using any algorithm may lead to lack of confidence in the model results, however, the ratio of unbalance was restricted to a maximum value of εb, or half of UBR (which is less), as shown in equation (3.65), normally εb, should not exceed 0.05 because the volume balance is made mainly to escape from the over-relaxation field, after applying such small volume-correction. The whole time-step is repeated to ensure that the output pattern is actually well-adjusted by ADI and the Newton-Raphson method. As in the ADI method, volume balance modification occurs in two stages one on Z direction, and the other on R direction, the double loop (3.66) applies corrections in Z direction, while the double loop (3.67) applies corrections in R direction. In each correction stage the moisture content of the current element is raised or lowered by a small fraction equals the moisture unbalance ratio MUR multiplied by the amount of moisture increase in the previous cell, hence the errors occur mostly beside saturation, then the correction fraction is multiplied by radius ratio RR, which gives bigger corrections to element with less diameter (more close to the emission source). After applying the correction, the resultant moisture content must not exceed the saturation water content θsat.

2-4-4-Soil-water relationships Retention characteristics Most of the previously mentioned soil-water characteristics include the residual water content θr in their formula, however, most of the published papers did not show its' method of evaluation, however, the most widely used paper in this field belongs to van Genuchten et al. (1991), they determined θr as an extrapolated fitting parameter for different soil textures. Nonetheless, their model "RETC" can predict θr value from some input parameters. Still, there are some confusion between the residual water content and the permanent wilting point, this confusion was solved by Kutilek and Nielsen (1994). They define two soil properties, both called the residual water content, but one of them is 58

By inspection, the shape of the MFP function seems to be power shape, but fitting MFP to power curve fails because of the zero values at the beginning of the integration (at θ=θr). Removing the zero pair leads to high correlation coefficient and very low standard error value. Another fitting considered is the polynomial fit, acceptable fitting only occurs in the 19th degree polynomial, however, after fitting MFP to any of the mentioned models, unexpected results occur and some indefinite loops let the model freezes. Moreover, some negative values of the fitted function appear beside zero due to the coarseness of the initial function. This leads to ignoring functional-fitting of the MFP, and considering the Bézier curve (splines) interpolation. Spline is a polynomial function that can have a locally very simple form, globally flexible and smooth. Splines are very useful for modeling arbitrary and coarse functions. One of the most widely used type of splines is cubic splines (Weisstein, 1999a). A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of control points. The second derivative of each polynomial is commonly set to zero at the endpoints, since this provides a boundary condition that equations. This produces a so-called "natural" cubic spline completes the system of and leads to a simple tridiagonal system which can be solved easily to give the coefficients of the polynomials (Weisstein, 1999b). Cubic spline interpolation is a useful technique to interpolate between known data points due to its stable and smooth characteristics. Unfortunately it does not prevent overshoot at intermediate points, which is essential for many engineering applications (Kruger, 2001). Kruger (2001), suggested a solution of the intermediate points overshooting problem, this technique is called constrained cubic splines. The fitting procedure starts after defining all soil data, then 20 points of moisture ratio (Θ) were selected at equal intervals from 0 to 1, the corresponding MFP function was normally calculated, then 19 polynomial were fitted to the points. After fitting the MFP function using constrained cubic splines, no extreme values detected, no program hangings occurred, and the modeling time reduces to less than 10% of what it was before applying spline fittings.

2-5 Model Developing language and user interface The current model (called "Drip Chartist") was developed using the "Microsoft Visual Basic™ for Applications" language (VBA), however, this language is a special version of the original visual basic language which is designed to work directly on any system containing Microsoft Office™ applications with no need of special dynamic links or registry entries for the program to work, i.e. no setup for the program is required, just enable macros and run the file as any normal Office™ file. Nonetheless, the VBA language offers a Windows® user interface, such as forms and menus; hence the applications have a user-friendly interface. Detailed screen shoots of the model is found in the appendix (App 1 ). If a model was designed using a standalone programming language, the output calculations and charts must be exported to MS-Excel™, or MS-Word™ in order to be processed. But when designing using VBA, no need of exporting as the user is actually working in Excel™ environment, so processing is easier and faster.

61

RESULTS AND DISCUSSION 1 Field experiment: 1-1 Yield of crops. Statistical analysis of all field data was done in split-split-plot design with Hydraulic barrier existence (number of pipes) {Hb} as the whole plots factor, Physical barrier existence or plastic isolation {Pb} as sub-plot factor, the remainder factor is pipeline depth of burying {Dp}. The analysis of results show that only {Pb} parameter was significant by its own in most measured data, means-comparison was done as well. Detailed analyses of the results were discussed in the following. In order to simplify discussion of results, the treatments combination will be symbolized by parenthesis includes three parameters, the first is the existence of plastic barrier with the symbols Y or N, for exist and not exists respectively, the second parameter is the depth of burying as number in cm, 10, 20, 30, or 0 (for surface treatment), the last parameter is the existence of hydraulic barrier (number of pipes) and it took the numbers 1 or 2. For example, the combination treatments of plastic-isolated, single lateral, with 20 cm burying depth will be symbolized as [Y, 20, 1], while as the non-isolated, bilateral, with surface lateral will be symbolized as [N, 0, 2]. In cases of comparing main effect or double interaction, the other parameter will be replaced with the symbol "~", i.e. if a comparison of plastic barrier existence regardless of depth and number of pipes, treatment will by symbolized [Y, ~, ~], moreover, when comparing 20cm depth effect on a non-isolated treatment, regardless of number of pipes, treatment will by symbolized [N, 20, ~].

1-2 Tartoufa yield. Tartoufa total and marketable yield were measured. Total yield indicates the weight of all tubers regardless of its size or state, while marketable yield indicates tubers which can be sold on market (not so-small, not broken, and not suffering of any disease's syndromes). The analysis of variance (ANOVA) shows that when "Total yield " was considered as dependent variable (Table 4-1), only factors {Pb}, {Dp}, and the interaction {Pb}×{Dp} had significant effect. This shows that hydraulic barrier {Hb} main effect and interactions are not significant on the total tartoufa yield.

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1200 Total Yield (kg/fd)

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Fig (4-5) Tartoufa yield as affected by hydraulic and physical barriers. As shown in Fig (4-6), tartoufa yield increased directly proportional to the burying depth with no significant difference neither between the pair 30cm, and 20cm, nor between the pair 10cm and 0 cm, while there was significant difference between these depth groups, this may be attributed to that tartoufa tubers which grow in the top 10 to 15cm prefer non saturated conditions. 1400 Total

Yield (kg/fd)

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Fig (4-6) Tartoufa yield as affected by burying depth

1-3 Tomato Plants. Like tartoufa, the tomato yield in the existence of physical barrier was significantly more than that of the absence of it (2.18 times more yield), as shown in Fig (4-7).But unlike tartoufa, the ANOVA showed that only physical barrier treatment had significant effect on total yield as shown in Table (4-5). This means that neither the hydraulic barrier nor the burying depth had significant effect on the tomato plant. Even though, as shown in Fig (4- 8)., the tomato yield was fewer in the existence of the hydraulic barrier. This could be attributed to the shallow root of tomato and the deep burying depth of the hydraulic barrier (at 40 cm), which took half the irrigation water away from the root system.

69

•

Although surface drip was better than subsurface drip in the greens growth on the growing season, but subsurface treatments got better yield results in both quantity and quality.

•

The symptoms of water deficiency appeared on the plants using subsurface drip without any kind of isolation (plastic sheet or another lateral line) due to high infiltration rate and deep percolation in the sandy textured soils, which take the water away from the root zone.

1-5 System evaluation and future investigations. Tartoufa tubers appear to prefer partial wetness to grow properly, however, better results reached on deeper laterals as discussed above. Moreover, the yield of Tartoufa records better results mostly on double lateral treatments. On the other hand, in most tomato results, the single tube treatments recorded better results than double tube treatments, because the latter distributes water into two points, one variable at 0, 10, 20, 30 cm, and the other is fixed at 40 cm. However, tomato root system absorbs about 75% of its needs in the top soil layers, hence, if water exists on such layers, the yield may increase. It can be said that the second dripper line in the double lateral treatment is not useful to tomato as it was laid at 40 cm depth and it took half the water away from the tomato root zone. It could be estimated that if the second lateral was buried on 20 cm depth the results could have been changed completely. The above mentioned results and remarks indicate that the double lateral technique needs more experiments on depth of burying of both lines, however, this could be achieved on field experiments or by computer modeling which can test any number of alternatives and its effect on wetting pattern and hence determine the proper depth according to plant characteristics. Another important consideration that is the economy of the bilateral technique, in this experiment, almost no large yield gain in the existence of the second lateral line, however, any economic study will show that in is not advisable to use this technique, but this is not fair as the technique still in its first investigations. Even so, the second lateral needs more research with different depths, different soils, and other techniques of application. These techniques involves applying waste water or fertilizers in one pipe, while applying fresh water in the other, or applying weed killers with water to the top pipe and waste or fresh water with fertilizers to the lower pipe. Another topic of investigation is the timing of water release in either pipe, in this experiment water released in both pipes at once. If water is released in the bottom pipe first, the moisture pattern should have been changed, another water regime could be recognize if water starts in the top pipe.

78

2 Field soil water patterns: Field measurement of soil moisture distribution under the experiments treatments was made using a field-calibrated neutron scattering meter, however, in order to take truthful results, measurements was taken after 6 to 8 hours after irrigation to ensure that water redistribution occur. Moisture measurements were taken several times during the growing season. Early and late season results will be discussed in the following. Figures (4-9) to (4-24) show the moisture distribution under surface and subsurface drip treatments in the tartoufa and tomato crops. These Figures show the treatments 'Treatments with no barriers' denoted as (N), 'Treatments with hydraulic barrier ' denoted as (H), 'Treatments with physical barrier' denoted as (P), and 'Treatments with both barriers denoted as (B). It can be noticed that the existence of the physical barrier pushes the water content's isolines (contours) upward, above its location, in the upper 40 cm of soil profile, this comparison could be seen through comparing treatment (P) to (N), and treatment (B) to (H) in Fig(4-9) for example or any of the other mentioned Figures. The hydraulic barrier's effect on moisture pattern could be noticed comparing treatment (N) to (H), and treatment (B) to (P). It increases the slope of the isolines (it lets the space between them narrower) in the space between the dripper lines. However, the hydraulic barrier's effect appears clearly (as a barrier) when the gap between the two lines is smaller. i.e., smaller gaps acts like a real barrier as shown in Figures (4-23 , and 24); where the existence of the hydraulic barrier with 10cm gap raises the water content above it as could be noticed comparing treatment (H) to (N). While in Figures.(4-21, and 22) where the gap is 20 cm the effect of the barrier is noticeable but smaller. Smaller effect could be noticed in the 30cm gap in Figures (4-19 and 20). Finally, the effect of the 40 cm gap could not be noticed as shown in Figures (4-17 and 18). Pipeline burying depth effect on the moisture profiles could be established comparing surface treatments figures (4-9, 10, 17, and 18) to buried treatments figures (411 to 16, and 4-19 to 24), however, as realized in the statistical analysis of the crops' yield, the burying depth have no clear single effect on the moisture pattern after redistribution, especially with the experimental depths chosen which are very close to each other (10, 20, 30 cm). It can be noticed in Fig (4-15B) that although water content in the bottom 40 cm is high even under the physical barrier (by side flow), but the whole profile has more water content especially in the root zone, bearing in mind that the same water amount is applied to the single and double lateral treatments. This may clarify the large crop yield of tartoufa in this depth. Soil moisture content varied due to crop water consumption, Fig (4-9) and Fig (410) show a comparison of the tartoufa versus tomato effect on soil moisture pattern under surface treatments. Lower values of moisture in the tartoufa pattern than the tomato's gives an indication that the tartoufa water consumption in higher than the tomato. Crop effect of other treatments could be observed by comparing any of the same paged Figures from Figure (4-11) to Figure (4-24).

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Fig. ( 4-9 ). Moisture distribution for the surface treatments, tartoufa early growth season No Hydraulic Barrier


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Fig. ( 4-10 ). Moisture distribution for the surface treatments, tomato early growth season

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Fig. (4-11). Moisture distribution for the 10 cm depth treatments, tartoufa early growth season No Hydraulic Barrier


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Fig. (4-12). Moisture distribution for the 10 cm depth treatments, tomato early growth season

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Fig. ( 4-23) , Moisture distribution for the 30 cm depth treatments, tartoufa crop before harvest



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Fig. (4-24) , Moisture distribution for the 30 cm depth treatments, tomato crop before harvest

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3 Model justification and utilization Once a model has been developed, it must be evaluated to ensure its harmony for the predicted behavior, this can be realized by three consequent operations: verification, validation, and output analysis. (Law, and Kelton, 1982). Fishman, and Kiviat, (1968) defined these operations as follow: “ Verification” is determining whether a simulation model performs as intended, i.e., debugging the computer program to compare step by step results to manual calculations for several program runs. The second operation “Validation” is determining whether a simulation model, as opposed to the computer program, is an accurate representation of the realworld system under study. This can be performed: by field and laboratory experiments, by comparing its results with other trusted models, or by comparing its results with published related cases. Finally, the last operation “Output analysis” is the operation in which the output of the model been revised for logic, harmony, and realism. This analysis could be done by means of statistical and mathematical methods. After performing this step, the model can be reliable and ready to use (Law, and Kelton, 1982). Model verification was carried out while and after programming stage by debugging the program line by line to ensure that no errors like overflow (division by zero), undeclared variables, mistyped variable names, or mistyped equations. Several runs were performed and compared to manually solved calculations. Testing of extremes was done as well. The model was validated to be free of all programmatic errors and typos after thorough tests. Model validation was done by comparing current model's results with fieldmeasured data. The results have been compared too with another trustful model the that made by Ragab et al. 1984, Ben-Asher et al., 1986, Thorburn et al., 2000, etc. Methods of validation and comparative results are shown below.

3-1 Field-measured data validation. In the current model; the soil was assumed to be physically uniform, and the initial water content has a constant value through all the soil profile, this situation is theoretical and is hard to be established in the real world. To overcome this situation, the comparison of wetting pattern was performed between the difference in soil moisture pattern after and before irrigation in model and in field. The current model requires some soil parameters to define the simulated soil properly. In order to find these parameters, the laboratory-measured retention values found in Table (3- 2) was entered to the computer model RETC (van Genuchten et al., 1991), which performs a neural-networks based prediction of soil properties. The predicted properties are listed in table (4-15).

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Fig (4-25) Field measured moisture content increment values compared to model predicted values for surface drip treatment measured at times 5, 10, 15, 20, 30, and 45 minuets after infiltration start.

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Soil water content (cm3/cm3) 0.00 0.05 0.10 0.15 0.20 0.25 0.00

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Fig (4-26) Field measured moisture content increment values compared to model predicted values for bilateral 20,40 cm treatment measured at times 5, 10, 15, and 20 minuets after infiltration start.

91

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Fig ( 4-27), Field-measured versus model-predicted values of soil moisture increase after infiltration, for a surface dripper line with no barriers

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Fig (4-28), Field-measured versus model-predicted values of soil moisture increase after infiltration, for a surface dripper line with hydraulic barrier

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Current Model

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Fig(4-30) Comparison of snapshots between the current model and Hydrus 2D output diagram, with the same constrains as in Fig (4-

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time steps are advancing either in a 1.x multiplication way, if the solution guess has a rapid convergence, while it advance in 0.5 multiplication way if the solution function is divergence. For example, if the current time step is 3 minuets, and the increment factor is 0.8, hence on convergence the next time step will be 3*1.8= 5.4 min. while on divergence the next time step will be 1.5 min., cumulative time is the summation of time steps, till it reaches the desired time, hence if number of time steps is small then the case variables are more consistent and stable.

4-1-1. Bilateral gap effect on soil-water pattern. One of the newly studied techniques in this thesis is the hydraulic barricading of water through a secondary buried dripper line, however, the secondary dripperline existence is not effective by it self but its relative location to the primary dripperline. This vertical space between the dripper lines is called "Bilateral Gap", which will be studied in the following. Aim of the case-study: This case-study aims to find the effect of bilateral gap on the wetting pattern and on the water availability through the root zone. Case-study's variables: Bilateral gap has been varied from 4cm to 32cm with 4cm increment, each level was evaluated just after emission stopped (before redistribution), and after 6 hours of redistribution (the experiment time starts from the infiltration beginning not end.) Case-study's parameters: All studied cases applied to a sandy soil, with a profile of 50 cm depth, and 35 cm width (radius), with grid spacing of 2.5 cm. Each case had two recorded snapshoot. One after cumulative volume of 2 liters, and the other after emission stopped and redistribution takes action for 6 hours. Redistribution was modeled the same way as infiltration; but with the emission source discharge set to zero as reported by Campbell (1985). The upper dripper line was laid on soil surface, while the secondary line was buried on different depths. Case-study's measures: In this case-study the actual output patterns from the model will be illustrated instead of the boundary lines. Simulation time and steps will be shown as well.

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Fig(4-33c), "Drip Chartist" output patterns of 2 Liters water application, after emission stoped (20 min), and after 6 hours of redistribution. For different upper lateral depths, where the lower later at fixed distance=14 cm. 105

Sufficient water in the root zone could be established after 6 hours of redistribution when the upper dripper line's depth is up to 10cm, for any of the tested gap spaces, i.e. up to 14cm gap space. In the real world, redistribution patterns could be different especially in the [20 cm upper lateral, 10cm gap space], [14, 14], and [20, 14] cases as the wetting front reaches the lower boundary, so grid area must be expanded in these cases to ensure actual representation of the reality. Simulation time of the surface drip cases is the largest time of all cases; however, lowest time is not proportional to the upper lateral depth, but it could be established within the median of lateral depth closer to surface as shown in Fig (4-34). As stated before, simulation time and simulation steps are indicators to the complexity of the studied case. It can be said that the smaller the gap is, the more complex is the simulation due to the interference between emitters. Moreover, it can be noticed that the simulation is more complex when the emitter is closer to the upper or the lower boundary. Case-study's conclusion: It is advised to use shallower upper dripper line (from 0 to 10cm) with gap size of about 10 cm in order to enhance wetting pattern distribution in root zone. Further studies are needed to set the optimum values with relation to soil type, and emitter discharge.

4-1-3 Physical barrier effect on soil-water pattern. Physical barrier has four design parameters; depth, width, thickness, and forming shape. However, in the current model, only the first two are considered where the third is negligible, and the fourth needs flexible mesh system to be studied through, like that models which depend on finite element technique. Moreover, depth and width parameters are very important consideration in the construction economy where the trench cost depends on the soil type, soil profile, mechanization availability, and trench dimensions. Determining the optimum parameters of the physical barrier depends on gain to losses balance; however, the "Drip Chartist" can help determining gains, while trenching costs should be calculated separately. Aim of the case-study: This case-study aims to find the effect of the physical barriers width and burying depth on the wetting pattern and on the water availability through the root zone. Case-study's variables: Nine combinations of barrier's width and depth were studied; three widths (30, 40, and 50cm), and three depths (20, 25, and 30cm), in addition to a control case with no barrier. Case-study's parameters: Same as the previous case-study, but with only one surface dripper line (single lateral), and the cumulative water volume applied was 2.5 liters.

106

After 20 minuets of emission

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Fig(4-35c), "Drip Chartist" output patterns of 2.5 Liters water application, just after emission stoped (20 min), and after 6 hours of redistribution, for different depths of a 50 cm width phyisical barier

70 Application Time

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Time (s) or num. of. steps

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Fig(4-36) Physical barrier dimensions effects on simulation time and steps

25 50

30

(b) on the same isolines it will be recognized that using a larger discharge emitter does not affect the 0.11 isoline while it spread the .35 isoline to a distant location. This means that the whole pattern is being condensed in a smaller area when using a larger discharge emitter, i.e. using low flow rate emitter let the water pattern covers more area but with gradual decrease of moisture content, while using higher flow rate emitter lets the water pattern covers less area but with almost saturated zone. This could be attributed to the limitation of infiltration rate of the soil, as the higher flow rate emitter pushes a large amount of water in small time that the soil cannot redistribute to the around areas; hence water accumulates and saturated condition occurs in this small spreading area. On the other hand, lower flow rates allow lateral distribution of water as well as vertical distribution and hence it result in more area with no saturation occurrence. Considering charts (c), and (d) in Fig (4-37), it can be noticed that the faster simulated case was the 3 l/h emitter discharge, however, simulation speed and number of steps was higher before and after this value as simulation time increases up to 400% of lowest value. This could be ascribed to the saturation state occurred in the higher emitter discharge, which tends to the instability of the equations' system due to the usage of the van Genuchten equation to calculate water diffusivity and matric flux potential, this equation, however, is undetermined at saturation; hence convergence could not be achieved and the time step is being divided regularly till convergence, this is surely increase both number of simulation steps and simulation time. Case-study's conclusion: It is advised to use higher emitter discharge rates to achieve less operation time, and thus less pumping costs. On the other hand, lower emitter discharge rates lead to gradual distribution of moisture and more wetting pattern area. doing so requires more is required but with lower pressure.

4-2- Soil Parameters studies 4-2-1 Soil physical properties effect on soil-water pattern. Within the same texture, wetting pattern is expected to be affected by soil physical properties such as θsat, θres, Ks, and the retention and conductivity parameters of soil such as α, m, n, λps, and ϒ which have been described in the soil section in chapter 3. However, m and n are simply related to each other according to the conductivity model, also, λps is almost been considered as m and n product; thus, only three retention variables will be discussed in this case-study, α, n, and ϒ . Case-study's variables: Each studied variable will be studied separately while the other variables remains constant to the default values, each variable has about ten values which were studied within the acceptable range of each variable shown previously in Table (3-2). The studied values of each variable will be shown in Table (4-17) (default values are bolded):

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Depth (cm)

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Fig(4-37 ) Wetting pattern and simulation charecteristics as affected by emitter discharge. (a), and (b) Depth and width of some moisture contents' isolines repectively, (c) number of simulation steps, (d) simulation duration on the PC.

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MC value 20 10 0 0.0000

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Fig (4-40) Effect of some soil charecteristics fitting parameters' values on the shape of the wetting pattern and on the simulation duration.

1.00

2Residual water content property affects wetting pattern shape mostly in the near saturation zone as shown in Fig (4-38 d, e, and f). Depth of the near saturation isoline increases with the increment of θres while other isolines are nearly not affected except the 0.11 isoline which had a jump after the value of θres=0.10. The widths of the isolines show an increasing trend with a strange jump in the 0.926 isoline. However this jump may be due to some cumulative over shooting in the van Genuchten formulae. Simulation time of these cases is directly proportional to the θres value. 3Soil initial wetness before irrigation, or the beginning water content (θbegin) affects wetting pattern as shown in Fig (4-39 a, b, and c). Excluding the near saturation isoline, all the isolines location moves towards the increment direction of depth and width, i.e. the wetting pattern area increases with the increment of θbegin. The simulation time trend tends to increase on the increment of θbegin. 4In Fig (4-39 d, e, and f) Soil hydraulic conductivity at saturation (Ks) affects the wetting area profile widely, however, the more the Ks value, the more the depth of the specified isolines. In contrast, Ks is inversely proportional to the width of isolines. Explicitly, the increment of the Ks causes wetting area to be narrower in width and longer in depth; therefore, on the design of drip irrigation systems on higher conductivity soils the emitters must be more close to each other, and irrigation should be managed so that to give smaller amounts of water on shorter frequencies to avoid deep percolation caused by the elongation of the wetting pattern. Inversely to the θsat effect on simulation time, Ks extreme values of the tested range leads to the least simulation time, while the peak simulation time was achieved in the middle value of 0.295 cm/min which took twice the time of the 0.047 cm/min as they was simulated in 46 and 23 seconds respectively. 5The rest conductivity and retention variables' cases were plotted in Fig (440 a, b…, and i). Air entry inverse (α) effects were plotted in the upper row of the Figure, its effect is nearly like the θsat effect on wetting pattern, as it increases the wetting depth and decreases the wetting width, the least simulation time was obtained at the middle range values of α while peak time is obtained at the edges. The similarity of α plots to the θsat plots may be attributed to the direct physical relationship between them through the soil-water retention curve. 6The retention fitting parameter n seems not to affect wetting pattern within the tested range values Fig(4-40 d, e, and f), however, these values was taken as the limits of the sand textured soil in the literature as shown in chapter III. The exception of the "n=2.68" point's effect could be ascribed to that this point is the least value in range between sandy texture and the loamy sand texture, so, the soil texture may be virtuallychanged to finer texture while it is fixed to "Sandy" in the rest of cases. 7Mualem's fitting parameter (ϒ), whose value is ranged from 0 to 1 and about 0.5 for most soils, was studied for the sandy texture, and found to be ineffective to the wetting pattern and to the simulation time as well, but a strange exception in the ϒ=0.6 value, as it spread the saturation zone in depth and width, and doubles the simulation time. This could be ascribed to equation instability due to this value. The insignificant effect of on the wetting pattern supports the approximation made by van Genuchten et al. (1991) to take an average value of 0.5 to all soils.

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4-2-2 Soil texture effect on soil-water pattern. The most famous information about the wetting pattern; that it is deep and narrow in sandy soils, and shallow and wide in clayey soils. A study was done on the twelve main textures to find out the location of the previously considered isolines' values (0.11, 0.19, 0.27, and 0.35), although some of these values may not be applicable in some texture classes, but these values was considered to make harmony in all studies, however, more isolines' values may be evaluated in future studies using the current model "Drip Chartist". Case-study's variables: The twelve main texture classes were studied. Each texture has its own soil properties; the case-study was done with the default values suggested by "Drip Chartist", these values could be shown in Table (4-19): Table (4- 19) Soil properties of some soil texture classes in the model case-study. Texture Class Sand Loamy Sand Sandy Loam Loam Silt Silty Loam Sandy Clay Loam Clay Loam Silty Clay Loam Sandy Clay Silty Clay Clay

Symbol S L Sa Sa L L Si Si L Sa C L CL Si C L Sa C Si C C

θsat 0.376 0.387 0.413 0.443 0.429 0.453 0.450 0.479 0.503 0.465 0.500 0.503

θres 0.073 0.081 0.090 0.122 0.116 0.137 0.125 0.154 0.178 0.169 0.176 0.181

θbegin 0.085 0.109 0.132 0.156 0.095 0.197 0.175 0.200 0.218 0.294 0.326 0.359

n 2.930 2.013 1.669 1.517 1.523 1.536 1.405 1.362 1.375 1.218 1.205 1.171

α (cm-1)

Ks (cm/min)

0.090 0.079 0.051 0.024 0.011 0.013 0.040 0.017 0.009 0.030 0.011 0.012

0.4950000 0.2431940 0.0736800 0.0470000 0.0578333 0.0606667 0.0091597 0.0056806 0.0077153 0.0078819 0.0066736 0.0102431

ϒ 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

Case-study's parameters: All studied cases applied to a soil profile of 50 cm depth, and 35 cm width (radius), with grid spacing of 2.5 cm, and cumulative water volume of 12 liters. However, soil physical properties default values varied according to each texture.

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Case-study's results: The results of the case-study were plotted in Fig (4-41 a, b, and c), looking at chart (a), where the effect of texture class on simulation time is plotted, lead to a conclusion that heavy textured soils can be simulated faster than fine to medium texture soils, notice that the time axis scale is logarithmic. Silt texture soil was simulated in longer time compared to other texture classes. In charts (b) and (c), the wetting pattern depth and width were plotted, notice that no trend could be expected to all texture classes, as each texture class concludes many soil properties. But some trends could be noticed within the fine textured group and within the coarse to medium group. In the coarse to medium textures' group, the minimum depth of 0.35 isoline trend appears to be increasing in the coarse to fine direction. Notice that the 0.11 isoline disappears in most texture classes because it is less than the θbegin value of such texture class. In addition, the 0.19 and 0.27 isolines decrease from sand to loam direction then increases again within the first group. In the heavy textures group, the 0.35 isoline is moving deeper as the texture going finer. This could be ascribed as θres and θbegin always increase when the texture goes finer, so the 0.35 moisture content and nearby moisture content values may be found in all the soil profile soil as initial moisture content, therefore these isoline were logged in a far distance for finer textures till it disappears totally as in the [C] texture which actually have the θbegin=0.35. For the same reason, however, the width of isolines increase in the coarse-to-fine direction as shown in chart (c), also, this could explain the disappearance of the 0.11 isoline in almost all textures, and the vanishing of the 0.19 and 0.27 isolines in most texture classes. In particular, a deeper look to charts (b) and (c) may attribute the horizontal spread in the fine textured profiles, and the vertical spread in the coarse textured ones. However, the output charts of the "Drip Chartist" induce the reality that fine textured soils let the water spread horizontally than vertically, while the contrary is right for the coarser texture classes. Case-study's conclusion: Texture class affects wetting pattern shape significantly, on the coarse-to-fine direction, width of an isoline increase, while depth of the isoline decreases actually and increases relatively. However, another study is required with the relative, not absolute, wetness isolines studied (isolines which is relative to θbegin and θsat).

4-2-3 Soil properties calc. method as affects soil-water pattern. As discussed in chapter 3, the major formulas affect soil-water infiltration relationships are the retention models (van Genuchten's (VG) and Brookes and Corey's (BC) relationships), and the conductivity models like of Mualem's and Burdine's. Moisure pattern surely affected by either formula, but to which degree? This what will be discussed in this case-study. Another calculation method that is expected to affect moisture pattern is the matric flux potential (MFP) integration method (MFP is the integration of diffusivity with relative to moisture content, as in chapter 3). Finally, the effect of cubic splines fitting on the studied variables as compared to direct integration methods was studied too.

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SUMMARY AND CONCLUSION The advantages of drip irrigation system made it the prime choice in desert reclamation and cultivation, however, burying the dripper line beneath soil surface which is called subsurface drip, increases its' benefits widely especially for the desert conditions. Doing so, on the other hand, increases the deep percolation problem. Some investigators suggest the idea of placing a physical barrier beneath the root zone, but there are some drawbacks of this method like the costs and efforts of trenching the wide and deep furrow, these problems made a must to think about a new solution of the deep percolation problem, the new suggested idea was called the hydraulic barrier method or the bilateral subsurface system. The new method aims in laying two dripper lines one beneath the other, instead of one dripper line. This modification is assumed to enhance wetting pattern shape so as to reach maximum wetness in the root zone. To verify the validity of the new technique several experiments had been done, but doing hundreds of experiments in the field was not that ease, and computer modeling could replace them effectively. For that, the objectives of the work was firstly to develop a simulation model of both the surface and subsurface drip irrigation systems; that can show the effect of all of the system parameters. The second objective was to study the effect of such parameters on the wetting pattern around the dripline by field experiments. The last objective was to perform some studies on the construction alternatives of the surface and subsurface systems using the developed model. The desired model was developed in a user friendly interface, using the Visual Basic® for Applications Language (VBA). Programs developed by this language have the compatibility to work in any PC with Microsoft Office™ system installed on it, this model is called "Drip Chartist", however, it draws the wetting pattern step by step according to any of the desired conditions, so the pattern development is easily seen and the effect of any parameter is easily observed. The "Drip Chartist" had been validated by field experiments and by comparing its results to another trusted model. The mathematical base of the "Drip Chartist" model depends on solving Richard's equation in cylindrical coordinates using finite difference technique by the alternate direction implicit (ADI) method in combination with the Jacobian expanded Newton Raphson iterative method, this technique had been trusted to be unconditionally stable with minimal accumulative error. The solution is based on selecting a time-step, during it, the grid elements is tested for balance (all elements should realize Richard equation in this time step), where the horizontal direction is considered explicit while the vertical direction implicit, if balance occur, the resultant values was entered as inputs to the second step by switching the implicit-explicit directions. If the balance was not observed in any stage, the entire calculations should be repeated with shorter time step. Otherwise if balance is verified the next time step should be longer than the previous one to insure faster convergence. At the end of each time step the accumulative volume of water is calculated and compared to that represented in the grid, if not equal (with some tolerance), the time step is rejected and recalculated from the beginning by considering the outputs of the

134

rejected time step as inputs to the new calculation, this technique is known as the Volume Balance check. After the model was successfully developed, its results were verified by debugging to manual calculations and the validated by comparison with field experiments and satisfactory correlation was achieved with some under estimation. It was also validated by comparison with another model (Hydrus 2D) and it almost coincide with it in solving a standard problem that can be applicable in both models. The field experiment was carried out as well in the North Sinai Research Station of the Desert Research Center, construction alternatives was tested in four burying depths (0, 10, 20, and 30cm), two crops (Tomato and Jerusalem Artichokes (Tartoufa)), in the existence and absence of hydraulic barrier and in the existence and absence of the physical barrier where both barriers were fixed at 40cm depth. Several measures were taken (on crop, and on moisture distribution), the results was statistically-analyzed according to splitsplit plot design, where many important conclusions were registered, what will be listed later in this chapter. Using the "Drip Chartist" model, over than ten important studies, on the factors affecting wetting pattern shape, was executed; such as the effect of dripper discharge, bilateral gap, dripper line burying depth and other important parameters. The results, conclusions, and recommendations will be listed in the following:

Field Conclusions: •

Initial irrigation by an auxiliary system is very essential to subsurface drip irrigated crops especially if no rainfall happened, till the growth of the root system can be enough to take water from the SDI.

•

Surface drip treatments got better shape of crops in the early season but SDI treatments got better yield quantity and quality.

•

Weeds totally disappear on the SDI treatments, unless it rains; hence weeds appear in a week and short-aged state.

•

In the sandy textured soils, using subsurface drip without any kind of isolation leads to plant suffering of lack of water because of high infiltration rate and deep percolation, which take the water away from the root zone.

•

None of the SDI burying depth or the bilateral system existence is effective by itself, but the interaction between each other is. However, the best combinations were the bilateral 30 & 40 cm and bilateral 20 & 40 cm, i.e., while the gap between dripper lines equals 10 to 20 cm maximum. This leads to the important conclusion that the distance between the two lateral lines is the most important variable in the bilateral method.

•

The physically barricaded surface and subsurface treatments were extremely better than other treatments, i.e., the physical barrier existence increases the yield significantly. Also the interaction between physical barrier and burying depth was

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significant in raising the crop yield, where, deeper depths (30, 20cm) got better results with the physical sheet existence. •

The interaction between physical and hydraulic barriers shows no statisticallysignificant effect on the yield quantity, with a remark that hydraulic barrier existence raises the yield in the absence of physical barrier, while it lowers the yield in the existence of physical barrier. However, this interaction is significant in the quality measures of Tartoufa, as the hydraulic barrier existence raises the crop quality in any state of the physical barrier.

•

Tartoufa tubers got better results with SDI than surface drip (DI), moreover it got better results with deeper burying depths of dripper line, while tomato gave netter results with surface drip system.

Model conclusions: •

Using volume balance check and correction is very essential to get proper simulations; however, this check should be done before accepting each time step not only at the end of simulation.

•

According to the model studies it is obviously that the best wetting pattern distribution could be achieved using gap space between the two dripper lines of 8cm to 16cm.

•

Using bilateral system in a sandy soil; shallower upper dripper line (from 0 to 10cm) with gap size of about 10 cm enhances the wetting pattern distribution in root zone.

•

It was clear that using the physical barrier in sandy soil with 30cm width at 25cm depth is very satisfactory. I.e. no need of more depth or width if the infiltration time is 20 minute.

•

The studies showed that using higher emitter discharge rates leads to achieve more saturated area around the root zone, and to lower operation time, and pumping energy

•

Wetting pattern is affected by all of the soil properties, mostly the saturated water content, the residual water content, the beginning wetness, and the saturation hydraulic conductivity.

•

Soil texture class affects wetting pattern shape significantly, on the coarse-to-fine direction, width of an isoline increase, while depth of the isoline decreases actually and increases relatively.

•

The usage of either combination of retention-conductivity models results in a different wetting pattern, however, more lab experiments needed to verify which model's combination is the best match to reality in a specific texture class.

•

Using 11 allowable iterations is very enough to ensure accurate simulations.

136

Recommended studies. •

Cubic splines usage instead of direct integration is highly recommended for its huge reduction in simulation time and as it does not affect the output pattern considerably.

•

For the finite difference grid, it is advised to use moderate to large panel area initially, and the simulation should be repeated with larger area if the minimum isoline location is less than two grid units far from the grid boundaries. It is also advised to use a grid spacing of 2 to 3 cm to ensure perfect simulation and to reduce the simulation time.

•

The bilateral technique needs more research with different depths, different soils, and other techniques of application. These techniques involves applying waste water or fertilizers in the lower pipe, while applying fresh water in the top line, or applying weed killers with water to the top pipe and waste or fresh water with fertilizers to the lower pipe.

•

Another topic of investigation is the timing of water release in either pipe and the discharge of each, in this experiment water released in both pipes at once. If water is released in the bottom pipe first, the moisture pattern should have been changed. Another water regime could be recognized if water starts in the top pipe.

•

More investigation is needed in burying the hydraulic barrier shallower than the 40 cm used in the current experiment; however, the distance between the two lines needs more field experiments to support the model results.

•

Further computer studies are needed to set the optimum gap space of the bilateral system with relation to soil type, emitter discharge, and upper dripper line's location.

•

Further computer studies are needed to set the optimum value of the upper lateral burying depth with relation to soil type, emitter discharge, and the time between irrigations.

•

Further computer studies are needed to identify the optimum dimensions of the barriers properties as affected by soil, emitter discharge, hydraulic barrier, and application time.

137

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THE APPENDIX

Appendix 1 Screen shoots of the “Drip Chartist” model inputs, outputs, and options

148

v o

n p

s r

q

t

u

w

1. 2.

“Start” button, to start simulation. “Pause” checkbox, to halt simulation for some while if it is selected, the “Time Step Browser” form appears. 3. “Options” button, to display the inputs and options form. 4. “Stop” button to end simulation. 5. Finite difference grid, shows half wetting pattern’s shape. 6. A label shows elapsed time in minuets and discharged volume in liters. 7. Legend shows color indication of moisture content range. 8. “Half plastic sheet” as simulated in the program. 9. “Trickle line” as simulated in the program. 10. Sheet “Gr1” is the graphical output, and sheet “DataGrid” is the numerical output

Fig( Fig(11),), The Themain mainoutput outputscreen screenofofthe themodel. model.

149

q

u

t

n r o s p v

w

1.

Maximum allowable finite difference grid length in [R] direction (cm)

2.

Maximum allowable finite difference grid length in [Z] direction (cm)

3.

Finite difference grid unit length in both directions (cm)=λ

4.

Right/left arrows to increase/decrease Rmax by λ each click.

5.

Right/left arrows to increase/decrease Zmax by λ each click.

6.

Right/left arrows to increase/decrease λ by 0.25 cm each click.

7.

A diagram describes variables.

8.

Tabs, each tab indicates one options/inputs group.

9.

Accept inputs and options to be applied next simulation.

10.

Reject modified inputs and options.

Fig( Fig( 22),), “Grid” “Grid”tab tabininmodel modeloptions. options.

150

1. 2. 3. 4. 5. 6.

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Maximum allowable simulation time, this time can be limited by boundary conditions in the “BCs” tab. Maximum time-step, τmax Time increment factor, α where τnext= Max[τmax,(1+α)×τprev.] Right/left arrows to increase/decrease simulation time by 1min/ click. Right/left arrows to increase/decrease τmax by 0.01 min. each click. Right/left arrows to increase/decrease α by 0.01 cm each click.

Fig( Fig( 33),), “Time” “Time”tab tabininmodel modeloptions. options.

151

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1.

Texture class drop-down menu, user can select one of 12 predefined textures or select “Custom” texture class.

2.

Texture class drop-down menu while dropped down.

3.

Saturated water content of the selected class, use slider next to the white box to change default value from minimum value of the class to maximum value of it. Using arrows performs small and slow change in value, dragging the slider head performs small-fast change, while clicking next to the slider head performs big and fast change in value.

4.

Residual water content.

5.

Saturated hydraulic conductivity.

6.

van Genuchten alpha parameter of the soil.

7.

van Genuchten yota parameter of the soil. (almost 0.5 for all soils)

8.

van Genuchten { n} parameter of the soil.

9.

The mouse while performing big change in the saturated water content slider.

Fig( Fig( 44),), “Soil” “Soil”tab tabininmodel modeloptions. options. 152

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2. 3.

4.

5. 6.

Matric flux potential calculation method, user can select either “Cubic splines” method, or direct numerical integration, the former is faster, while the latter is more accurate. Almost both methods had the same accuracy, but speed of the first method is highly significant especially in fine grids. Numerical integration method of the matric flux potential either Simpson's rule or trapezoidal rule, the latter is faster a little bit. Selected conductivity model, Mualem’s or Burdine’s model, the former can be used in most soils while the latter cannot be used unless for soils having n>2, if user selects n

SUBSURFACE DRIP IRRIGATION SYSTEM ...

SUBSURFACE DRIP IRRIGATION SYSTEM ...

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