Measurement and simulation of soil water status under field conditions

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Title:
Measurement and simulation of soil water status under field conditions
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xi, 167 leaves : ill. ; 28 cm.
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English
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Stone, Kenneth Coy, 1959-
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Subjects / Keywords:
Soil moisture -- Measurement   ( lcsh )
Soil moisture -- Florida   ( lcsh )
Soil moisture -- Mathematical models   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1987.
Bibliography:
Includes bibliographical references (leaves 163-166).
Statement of Responsibility:
by Kenneth Coy Stone.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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aleph - 000943136
notis - AEQ4824
oclc - 16767007
sobekcm - AA00004850_00001
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Full Text









MEASUREMENT AND SIMULATION OF SOIL WATER STATUS
UNDER FIELD CONDITIONS







By

KENNETH COY STONE


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1987


i













ACKNOWLEDGEMENTS


.The author would like to express his appreciation to Dr. Allen G.

Smajstrla for his guidance, assistance and encouragement throughout this

research. The author would like to thank his other committee members

for their support and guidance throughout this research and in

coursework taken under their supervision.

The author also expresses his appreciation to the Agricultural

Engineering Department for the use of its research and computing

facilities. Appreciation is also expressed to other faculty and staff

members in the department for their assistance.

Special goj~tude is expressed to the authors family for their

continuous support and encouragement throughout his studies.

Finally, the author would like to express his very special

gratitude to his wife, Carol, for her drafting expertise, patience and

continuous support and encouragement.













TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS . . ii

LIST OF TABLES . . . v

LIST OF FIGURES . . .. vi

ABSTRACT . . . x

CHAPTERS

I INTRODUCTION . . 1

II REVIEW OF LITERATURE . . 4

Measurement of Soil Water Status . 4
Soil Water Content Measurement . 4
Soil Wafer Potential Measurement . 8
Automation of
Soil Water Potential Measurements . 11
Water Movement in Soils . . 15
Soil Water Extraction . . 20

III METHODS AND MATERIALS . . 26

Equipment . . 26
Instrumentation Development . .. 27
Field Data Collection . . 30
Model Development .. . . 33
One-Dimensional Model . 36
Two-Dimensional Model . 41
Soil Water Extraction . 50

IV RESULTS AND DISCUSSION . . 54
Instrumentation Performance . 54
Field Data Collection . . 60
Model Verification . . 70
Model Operation with Field Data . 94
One-Dimensional Model . 102
Two-Dimensional Model . 109
Model Application . . 116

V SUMMARY AND CONCLUSIONS . . 124

Microcomputer-based Data Acquisition System 124
Field Data . . 124








Modeling Soil Water Movement and Extraction 125
Model Applications . . 125
APPENDICES

A. Alternating Direction Implicit Finite Differencing. 126
B. Listing of Soil Water Movement and Extraction Model. .137

REFERENCES . . . 163

BIOGRAPHICAL SKETCH ................ 167












LIST OF TABLES


Table 3-1.


Table 4-1.



Table 4-2.



Table 4-3.



Table 4-4.


Microcomputer-based data acquisition system
components and approximate costs .

One-dimensional distribution of water extraction
for a 15 day drying cycle for young citrus trees
with and without grass cover . .

Two-dimensional distribution of water extraction
for a 15 day drying cycle for young citrus trees
with grass cover . .

Two-dimensional distribution of water extraction
for a 4 day drying cycle for young citrus trees
with and without grass cover . .

One-dimensional distribution of water extraction
for a 4 day drying cycle for a grass cover crop
at water depletion levels of 20 kPa and 40 kPa .


. 28



. 68



. 69



. 73



. 76













LIST OF FIGURES


Figure 2-1.

Figure 3-1.

Figure 3-2.


Figure 3-3.


Figure 3-4.



Figure 3-5.


Figure 3-6.


Figure 3-7.


Figure 4-1.


Figure 4-2.


Figure 4-3.



Figure 4-4.


Figure 4-5.


A typical soil water characteristic curve .

Layout of lysimeter system. . .

Details of individual lysimeter soil water status
monitoring system. . .

Location of tensiometers in 1985 field experiment
for young citrus trees in grassed and bare soil
lysimeters. . . .

Location of tensiometers in 1986 field experiment
for young citrus trees in grassed and bare soil
lysimeters. . . .

Schematic diagram of the finite-difference grid
system for the one-dimensional model of water
movement and extraction. . .

Schematic diagram of the finite-difference grid
system for the two-dimensional model of water
movement and extraction. . .

Effect of the relative available soil water
and potential soil water extraction rate on the
soil water extraction rate. . .

Calibration curve of output voltage versus
pressure applied for pressure transducer No. 1. ..

Calibration curve of digital units versus
voltage applied for the analog-to-digital
circuit used. . ...

Comparisons of mercury manometer manually-read
and pressure transducer automatically-read
tensiometer water potentials during drying cycles
for 2 tensiometers in the laboratory. .

Comparisons of mercury manometer manually-read and
pressure transducer automatically-read tensiometer
water potentials for all laboratory data. .

Evaluation of pressure transducer-tensiometer No. 1
by comparison of mercury manometer manually-read
and pressure transducer automatically-read water
potentials in the field. . .


5

31


32



34


35



38


44



53


55



57



58


59



61








Figure 4-6.


Figure 4-7.



Figure 4-8.



Figure 4-9.


Figure 4-10.



Figure 4-11.



Figure 4-12.



Figure 4-13.


Figure 4-14.


Figure 4-15.


Figure 4-16.


Figure 4-17.


Figure 4-18.


Figure 4-19.


Evaluation of pressure transducer-tensiometer No. 2
by comparison of mercury manometer manually-read
and pressure transducer automatically-read water
potentials in the field. . .

Evaluation of pressure transducer-tensiometer No. 3
by comparison of mercury manometer manually-read
and pressure transducer automatically-read water
potentials in the field. . .


Evapotranspiration rate from the 1985 field
experiment with a 20 kPa soil water potential
treatment young citrus tree with grass cover.

Evapotranspiration rate from the 1985 field
experiment with a 20 kPa soil water potential
treatment young citrus tree with bare soil..

Evapotranspiration rate from the 1986 field
experiment with a 20 kPa soil water potential
treatment young citrus tree with grass cover.

Evapotranspiration rate from the 1986 field
experiment with a 20 kPa soil water potential
treatment young citrus tree with bare soil..

Evapotranspiration rate from the 1986 field
experiment with a 20 kPa soil water potential
treatment with a grass cover. .

Evapotranspiration rate from the 1986 field
experiment with a 40 kPa soil water potential
treatment with a grass cover. .


Soil water potential-soil water content
relationship for Rehovot sand. . .

Hydraulic conductivity-soil water content
relationship for Rehovot sand. . .

Simulated results of soil water content profiles
for infiltration into a Rehovot sand under
constant rain intensity of 12.7 mm/hr. .

Simulated results of soil water content profiles
for infiltration into a Rehovot sand under
constant rain intensity of 47 mm/hr. .

Soil water potential-soil water content
relationship for Yolo light clay. . .

Hydraulic conductivity-soil water content
relationship for Yolo light clay. . .


62


vii


63


. 66


* 67



71



72



74


75


79


80


81


82


83


84








Figure 4-20.


Figure 4-21.


Figure 4-22.


Figure 4-23.


Figure 4-24.



Figure 4-25.


Figure 4-26.


Figure 4-27.


Figure 4-28.


Figure 4-29.



Figure 4-30.



Figure 4-31.



Figure 4-32.


Figure 4-33.


Soil water potential-soil water content
relationship for Adelanto loam. . 85

Hydraulic conductivity-soil water content
relationship for Adelanto loam. . 86

Simulated results of soil water content profiles
for infiltration into a Yolo light clay with
initial pressure potential at -66 kPa. 87

Simulated results of soil water content profiles
for infiltration into a Yolo light clay with
initial pressure potential at -200 kPa. 88

Simulated results of soil water content profiles
for infiltration into a Adelanto loam with
initial pressure potential at -66 kPa. 89

Soil water potential-soil water content
relationship for Nahal Sinai sand. 90

Hydraulic conductivity-soil water content
relationship for Nahal Sinai sand. . 91

Simulated results of dimensionless soil water
content distribution for infiltration into a
Nahal Sinai sand at 57 min of infiltration time. 92

Simulated results of dimensionless soil water
content distribution for infiltration into a
Nahal Sinai sand at 297 min of infiltration time. 93

Two-dimensional model simulated results of soil
water content profiles for infiltration into a
Rehovot sand under constant rain intensity
of 12.7 mm/hr. . . 95

Two-dimensional model simulated results of soil
water content profiles for infiltration into a
Rehovot sand under constant rain intensity
of 47 mm/hr. . . 96


Evapotranspiration rate from the second drying
cycle of the 1985 field experiment with a 20 kPa
soil water potential treatment young citrus tree
with grass cover. . .


Distribution of evapotranspiration through the
daylight hours. .. . 99

Soil water potential-soil water content
relationship for Arredondo fine sand. ... 100


viii


. 98








Figure 4-34.


Figure 4-35.


Figure 4-36.


Figure 4-37.


Figure 4-38.


Figure 4-39.


Figure 4-40.


Figure 4-41.


Figure 4-42.


Figure 4-43.


Figure 4-44.


Figure 4-45.


Figure 4-46.


Figure 4-47.


Figure 4-48.


Figure 4-49.


Hydraulic conductivity-soil water potential
relationship for Arredondo fine sand. .

Simulation results for the one-dimensional model


with field

Simulation
with field

Simulation
with field

Simulation
with field

Simulation
with field

Simulation
with field

Simulation
with field

Simulation
with field

Simulation
with field

Simulation
with field

Soil water
treatments

Soil water
treatments


data for the 150 mm depth. .

results for the one-dimensional model
data for the 300 mm depth. .

results for the one-dimensional model
data for the 450 mm depth. .

results for the one-dimensional model
data for the 600 mm depth. .

results for the one-dimensional model
data for the 900 mm depth. .

results for the two-dimensional model
data for the 150 mm depth. .

results for the two-dimensional model
data for the 300 mm depth. .

results for the two-dimensional model
data for the 450 mm depth. .

results for the two-dimensional model
data for the 600 mm depth. .

results for the two-dimensional model
data for the 900 mm depth. .

potentials for the three irrigation
at the 300 mm depth. . .

potentials for the three irrigation
at the 900 mm depth. . .


Soil water storage for the three irrigation
treatments. . . .

Cumulative irrigation for the three irrigation
treatments. . . .

Cumulative drainage from the soil profile for
the three irrigation treatments. .


. 101


. 104


. 105


. 106


. 107


. 108


. 111


. 112


. 113


. 114


. 115


. 118


. 119


. 120


. 121


. 122












Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


MEASUREMENT AND SIMULATION OF SOIL WATER STATUS
UNDER FIELD CONDITIONS

By

KENNETH COY STONE

May 1987

Chairman: Allen G. Smajstrla
Major Department: Agricultural Engineering


Irrigation of agricultural crops is one of the major uses of fresh

water in Florida. Supplemental irrigation is required in Florida

because the predominant sandy soils have very low water holding

capacities, up to 70% of the annual rainfall occurs during months when

many crops are not grown, and rainfall is not uniformly distributed.

Under these conditions the scheduling of irrigation becomes extremely

important. The timely application of irrigation water can result in

increased yields and greater profits, while untimely applications could

result in decreased yields and profits, and leaching of nutrients.

A low cost microcomputer-based data acquisition system for

continuous soil water potential measurements was developed. The system

consisted of tensiometer-mounted pressure transducers, an analog-to-

digital converter and a portable microcomputer. The data acquisition

system was evaluated under laboratory and field conditions. Excellent








agreement was obtained between soil water potentials read with the data

acquisition system and those read manually using mercury manometers.

Experiments were conducted utilizing the data acquisition system to

monitor soil water potentials of young citrus trees in field lysimeters

to determine model parameters and to evaluate model performance.

Evapotranspiration, soil water extraction rates and relative soil water

extractions were calculated from the soil water potential measurements.

Two numerical models were developed to study the movement and

extraction of soil water. A one-dimensional model was developed to

describe a soil profile which is uniformly irrigated such as one which

is sprinkler irrigated. The model was used to simulate soil water

movement and extraction from a young citrus tree with grass cover in a

field lysimeter. Simulated results were in excellent agreement with

field observations.

A two-dimensional model was developed to describe a nonuniformly

irrigated soil profile as in trickle irrigation. The model was used to

simulate the two-dimensional movement and extraction of soil water from

a young citrus tree with grass cover in a field lysimeter. The model

results were in excellent agreement with field observations.













CHAPTER I
INTRODUCTION
Irrigation of agricultural crops is one of the major uses of fresh

water in Florida. It was reported (Harrison et al., 1983) that in 1981,

41 percent of the fresh water use in Florida was for irrigation of more

than 800,000 hectares of agricultural crops. Three reasons cited for

supplemental irrigation in Florida were 1) sandy soils have very low

water holding capacities, 2) up to 70 percent of the annual rainfall

occurs during months when many crops are not grown, and 3) rainfall is

not uniformly distributed even during months of high rainfall.

Because no control can be placed on when and where rainfall occurs,

researchers must focus their attention on managing the soil water

content in the plant root zone. One method of managing the water

content in soils is to apply small amounts of irrigation water at

frequent intervals. In the absence of rainfall, this provides

agricultural plants with adequate water for growth and also minimizes

losses from percolation below the root zone. With rainfall

interactions, irrigation scheduling is more difficult; the objective is

to minimize irrigation inputs (maximize effective rainfall) while

optimizing production returns. Because of the complexity of these

interactions, numerical models are useful tools to study them. Many

researchers have developed models to use in the study of soil water

management (Smajstrla, 1982; Zur and Jones, 1981). These models allow

many different irrigation strategies to be investigated without the cost

normally associated with field experiments. These models involve









analyses of infiltration, redistribution, evaporation and other factors

which affect the movement and uptake of soil water by plants.

The objective of this research was to develop a data collection

system and a numerical model which together will provide researchers

with information needed for developing and validating models of soil

water movement, crop water use and evapotranspiration. The

instrumentation system developed will record soil water potentials on a

real time basis in order to provide input data for model verification

and validation. A microcomputer based instrumentation system will allow

the computer to monitor inputs and make decisions based on the input

data. The microcomputer will have the ability to monitor and control

events in the field.

Two numerical models will be developed to study the movement and

extraction of soil water. A one-dimensional model will be developed to

describe the movement and extraction of soil water in a soil profile

which is uniformly irrigated. A two-dimensional model will be developed

to describe the movement and extraction of soil water from a soil

profile which is not uniformly irrigated such as trickle irrigation.

The specific objectives of this research were:

1. To develop and test instrumentation for the real-time

monitoring of soil water potential under agricultural crops.

2. To record the dynamics of soil water movement and water

extraction under irrigated agricultural crops.

3. To develop a numerical model to simulate the soil water

extraction patterns observed under agricultural crops as a

function of irrigation management practices and climatic

demands.





3


4. To demonstrate the use of the numerical model in evaluating

and recommending irrigation strategies.













CHAPTER II
REVIEW OF LITERATURE

Measurement of Soil Water Status

The measurement of soil water can be classified into two

categories: (1) the amount of water held in a given amount of soil (soil

water content), and (2) the potential, or tension with which the water

is held by the soil (soil water potential). These properties are

related to each other (Figure 2-1) and describe the ability of a soil to

hold water available for plant growth.

Soil Water Content Measurement

Several methods are available to measure soil water content. The

gravimetric method is the standard method of determining the soil water

content. This method consist of physically collecting a soil sample

from the field, weighing it, and oven drying the sample to constant

weight at 105 C. The difference in weights before and after drying is

the amount of water removed from the sample. Water contents can be

calculated on a weight basis, or on a volume basis if the soil volume or

bulk density was measured when the sample was taken. An advantage of

the gravimetric method is that it requires no specialized equipment.

Disadvantages are that it is laborious and time consuming. Destructive

sampling is required and sampling may disturb a location sufficiently to

distort results. This method does not lend itself to automation.

Neutron scattering allows the nondestructive measurement of soil

water content. A neutron moisture meter may be used in the field to











-107






-106-=





105
-10



-1 -
10






-103





-102-


0.0 0.1 0.2 0.3 0.4 0.5

SOIL WATER CONTENT (mm/mm)
Figure 2-1. A typical soil water potential-soil water content curve.








rapidly and repeatably measure water contents in the same location and

depth of soil. An access tube must be installed in the soil to allow a

probe to be lowered to the desired soil depth for measurements.

The neutron scattering method operates on the principle of nuclear

thermalization. Fast neutrons are emitted from a radiation source

located on a probe which is lowered into the soil. These neutrons lose

energy as they collide with hydrogen atoms in the soil and are slowed or

thermalized. Thermalized neutrons are counted by a detector which is

also located on the probe. The number of slow neutrons is an indirect

measure of the quantity of water in the soil because of the hydrogen

atoms present in water. Because the neutron method counts only hydrogen

atoms, the method must be calibrated for each specific soil type and

location. This is especially true for soils with variable quantities of

organic matter because the neutron meter will also count hydrogen atoms

in the organic matter and cause errors in the water content

measurements.

With the neutron method, a spherical volume of soil is sampled as

neutrons are emitted from the source. The radius of the sphere varies

with the soil water content from a small radius for wet soils to 20 or

30 cm for very dry soils. This measurement over a relatively large

volume is an advantage for homogenous soils with no discontinuities.

However when discontinuities such as water tables exist, their exact

locations cannot be detected accurately. Aribi et al. (1985)

investigated the accuracies of neutron meters when measuring water

contents near boundaries. They found that significant errors occurred

when readings were taken within the top 0.4 meters in an unsaturated

soil profile.








Another disadvantage of the neutron method is that the equipment

cost is high. The radioactive material contained in the neutron meter

is also a disadvantage because of the health hazards associated with

radiation. The automation of a neutron meter would be very expensive

and extremely complicated.

Gamma ray attenuation is a method which can be used to determine

the soil water content. This method determines soil water content by

measuring the amount of gamma radiation energy lost as a radiation beam

is directed through a soil. The method depends on the fact that gamma

rays lose part of their energy upon striking another substance, in this

case soil water. As the water content changes, the amount of

attenuation will also change.

Various types of gamma radiation instruments are available. One

type is intended for laboratory or stationary use. This instrument has

the source and detector parallel in line at a fixed distance apart, and

a soil column is placed between them. The source and detector are then

moved along the length of the soil column to determine the water content

distribution in the column. This would not be practical for field

application.

A second type of gamma radiation instrument has been developed for

field application. This instrument requires that two parallel access

tubes be installed into the soil. The source is placed in one access

tube and the detector in the other. Radiation is focused into a narrow

beam between the source and detector, and soil water content can be

measured in very thin layers of soil.

Another type of gamma radiation instrument consists of a stationary

detector located at the soil surface and a source located on a probe








which is lowered into the soil. The relationship between the source and

detector is known, and thus changes in density with depth can be

measured accurately with this instrument. Because the detector is

located at the soil surface, the instrument is limited to the top 30 cm

of the profile.

Gamma radiation instruments are expensive, and they can be

hazardous due to the radioactive source. This type of instrument would

be very difficult and expensive to automate.

Additional research has been conducted to utilize other soil

properties which would lend themselves to rapid methods of soil water

content determination. Fletcher (1939) conducted work on a dielectric

method of estimating soil water content. He used a resonance method to

determine the dielectric constant of the soil. This type of instrument

consists of an ocillator circuit and a tuned receiving circuit. The

instrument is placed in the soil and allowed to equilibrate. A variable

capacitor in the receiving circuit is then tuned to resonance, and the

capacitor reading is correlated with the soil water content. This

instrument must be calibrated for each soil in which it is used. Such a

device is not known to be commercially available.

Most of the methods discussed produce indirect measurements of soil

water content. Soil water content is calibrated to other factors such

as neutron thermalization, gamma ray attenuation or dielectric

properties. Only the gravametric method yields a direct measure of soil

water content.

Soil Water Potential Measurement

An alternative to the measurement of soil water content is the

measurement of soil water potential. A tensiometer measures the


_Y __








potential or tension of water in the soil. The tensiometer consists of

a closed tube with a ceramic cup on the end which is inserted into the

soil and a vacuum gage or manometer to measure the water potential in

the tensiometer tube. The tube is filled with water, closed and allowed

to equilibrate with the soil water potential. As the soil dries, water

in the tensiometer is pulled through the ceramic cup. The soil water

potential which pulls water through the ceramic cup is registered on the

vacuum gage or manometer. This force is also the hydraulic potential

that a plant would need to exert to extract water from the soil.

Therefore, a tensiometer measures the energy status of water in the

soil. Tensiometers left in the soil for a long period of time tend to

follow the changes in the soil water potential.

The hydraulic resistance of the ceramic cup, the surrounding soil,

and the contact between the cup and soil cause tensiometer readings to

lag behind the actual tension changes in the soil. Lags are also caused

by the volume of water needed to be moved through the cup to register on

the measuring device. The useful range of tensiometers is from 0 to -80

kPa. Below -80 kPa air enters through the ceramic cup or the water

column in the tensiometer breaks, causing the tensiometer to fail. This

measurement limitation is not serious for irrigated crops on sandy soils

because most of the available water for plant use occurs between 0 and

-80 kPa.

Another method of measuring soil water potential is the thermal

conductance method. The rate of heat dissipation in a porous material

of low heat conductivity is sensitive to the water content in the porous

material. When in contact with a soil, the water potential in the

porous material tends to equilibrate with the soil water potential.








Phene et al. (1971) developed an instrument to measure soil water

potential by sensing heat dissipaton within a porous ceramic. The water

potential of the porous ceramic was measured by applying heat at a point

centered within the ceramic and measuring the temperature rise at that

point. Soil water potential measurements were obtained by taking two

temperature readings. The first one was taken before the heating cycle

and the second after the heating cycle. The difference between the two

temperature measurements was the change in temperature at the center of

the sensor due to the heat applied. The magnitude of the difference

varies depending on the water content of the porous block. Phene stated

that the sensor should measure the soil water potential regardless of

the soil in which it is embedded.

In experimental applications of the heat pulse device, the accuracy

of the sensor was 20 kPa over the range 0 to -200 kPa. In Florida

sandy soils such a wide range of variability would not be acceptable

because most of the available soil water is contained in the soil

between field capacity and -20 kPa. Calibration for individual soils

could improve the accuracy of the instrument. This instrument has the

capability of allowing automated data collection and is nondestructive.

The cost of the individual sensors and the associated data recording

devices is relatively high.

Soil psychrometers are instruments which can be used to measure

soil water potentials in the range of -1 to -15 bars. They operate by

cooling a thermocouple junction which is in equilibrium with the soil to

the point of water condensation on the junction, and then measuring the

junction temperature as water is allowed to evaporate. Thus the

temperature depression due to evaporation can be related to soil water


__








tension. Only small responses are obtained at potentials above -1 bar,

making this instrument unsuitable for irrigation scheduling on sandy

soils where irrigations would typically be scheduled at much greater

potentials.

Electrical resistance blocks can be correlated with soil water

potential. The blocks are placed in the soil and allowed to

equilibrate with the soil water. Resistance blocks usually contain a

pair of electrodes embedded in gypsum, nylon or fiberglass.

Measurements with resistance blocks are sensitive to the electrolytic

solutes in the fluid between the electrodes. Thus resistance blocks are

sensitive to variations in salinity of soil water and to temperature

changes. Temperatures must be measured and resistance readings

appropriately corrected.

Resistance blocks are not uniformly sensitive over the entire range

of soil water content. They are more accurate at low water contents

than at water contents near field capacity. Because of this limitation,

resistance blocks can be used to complement tensiometers to measure

soil water potentials below the -80 kPa range. They are relatively

inexpensive, and an automated data collection system may be built around

these instruments for measuring water potentials in drier soils.

Automation of Soil Water Potential Measurements

The instruments discussed may all be used to measure the status of

soil water. Most of the techniques relate a soil property to another

property which is measured by the instrument. Two of the methods allow

a direct measure of a soil property. The gravimeteric method gives a

direct measure of soil water content and tensiometers give direct

measurement of soil water potential. The gravimetric measurement method








requires destructive sampling and does not lend itself to automation.

Tensiometers may be automated by recording the changes in soil water

potential, and they do not require destructive sampling. Therefore, to

measure the status of soil water under a growing crop, an automated data

collection system using tensiometers to measure soil water potential was

chosen.

To determine the soil water potential, the water potential within

the tensiometer is measured. The tensiometer water potential is assumed

to be in equilibrium with the soil water potential. Early methods of

measuring tensiometer water potentials used mercury manometers. Later,

mechanical vacuum gauges were used. Both methods functioned well for

manual applications. Neither, however, was readily automated.

Recent interest in better understanding the dynamics of soil water

movement, and in the development of numerical models to simulate this

process, has resulted in the need for an automated system of recording

tensiometer readings on a continuous real time basis.

Van Bavel et al. (1968) used a camera to take periodic photographs

of a tensiometer manometer board. By analyzing the photographs they

were able to record changes in potentials. This procedure was, however,

laborious and did not provide continuous soil water potential records.

Enfield and Gillaspy (1980) developed a transducer which measured

the level of mercury in a mercury manometer tensiometer. The principle

of operation of their transducer was the same as a concentric capacitor.

The level of mercury in the manometer corresponds directly to the length

of a capacitor plate. A steel tube was used as the outer capacitor

plate around a column of mercury. The nylon tube which contained the

mercury column acted as the dielectric material. The capacitance of the








transducer was measured and converted to length of the column of

mercury. This instrument was found to be very sensitive to temperature

fluctuations. Further research is needed on this transducer to make it

suitable for applications in automated data collection systems.

Fitzsimmons and Young (1972) used a tensiometer-pressure transducer

system to study infiltration. Their system consisted of a pressure

transducer which was connected to many tensiometers by a system of fluid

switches. This system required substantial time lags after switching a

tensiometer to the transducer before an accurate reading could be made.

This was primarily due to changes in volume due to the elasticity of the

system. This resulted in a large scanning time in order to read all

tensiometers. Long and Hulk (1980) used a similar system.

Bottcher and Miller (1982) developed an automatic manometer

scanning device which read and recorded mercury levels in manometer-type

tensiometers. The system consisted of a computer-controlled chain-drive

mechanism which moved photocells and light sources up and down the

manometer tubes. When the scanner passed a mercury-water interface, a

change in voltage was detected by the computer. This system is

expensive, uses specially constructed rather than commercially-available

components, and is not readily expandable. It also requires the use of

a central manometer board with connecting tubing from the various

tensiometers. It has the advantage of easy verification of computer

readings by manual reading of the manometers.

Marthaler et al. (1983) used a pressure transducer to read

individual tensiometers. The upper end of the tensiometers was closed

off with septum stoppers to provide air-tight seals through which a

needle connected to a pressure transducer was inserted. The needle was








inserted into a pocket of entrapped air in the tensiometer, and the

pressure transducer output was obtained immediately. This method

introduced an error because the air pocket was compressible and was

affected by the addition of air at atmospheric pressure in the needle,

transducer, and connectors. This system was designed to minimize errors

by minimizing the volume of air introduced into the tensiometer. The

tensiometer air pockets were, however, temperature sensitive and

introduced diurnal time lags because of expansion and contraction due to

diurnal temperature changes. Also, to read several instruments, the

pressure transducer was required to be moved manually. Thus, this type

of system does not lend itself to automation.

Thomson et al. (1982) used individual pressure transducers on

tensiometers with all air purged from the system to monitor soil water

potentials. Thus, they were able to avoid lag times associated with air

pockets in the tensiometers. They were able to read pressure

transducers very rapidly by electronic rather than hydraulic switching.

A soil water potential monitoring system that used pressure

transducers as used by Thomson et al. (1982) would be able to record

data from a number of sensors very rapidly. A continuous data

acquisition system based on tensiometer-mounted pressure transducers

would provide data necessary for models of movement of water in soils,

crop water use, and evapotranspiration. The use of a microcomputer to

monitor the pressure transducers would allow the system to be programmed

to make decisions based on the input data (Zazueta et al., 1984).

Also, the cost of a dedicated data acquisition system would be greater

than that of a microcomputer-based system because of current

microcomputer costs and availability.










Water Movement in Soils

The general equations governing unsaturated flow in porous media

are the continuity equation and Darcy's Law. Hillel (1980) presented a

combined flow equation which incorporates the continuity equation

39
-= v-q S (1)
3t

where q = flux density of water,

6 = volumetric water content,

V = differential operator,

t = time, and

S = a sink or source term,

with Darcy's equation for unsaturated flow

q = K(h) VH (2)

where K = hydraulic conductivity,

H = the total hydraulic head and defined as

H = h z, and

h = capillary pressure head.

The resulting combined flow equation for both steady and transient

flows is also known as Richards equation

39
= v.(K(h}vH ) S (3)
at
For one-dimensional vertical flow, equation (3) becomes


3a a ah 3K(h)
= ( K(h)- ) S(z,t) (4)
at az az az


where z = the vertical dimension.








The sink term is used to represent the loss or gain of water from

the soil by root extraction or by application of irrigation water from a

point source.

For implicit solutions, equation (4) must be written in terms of

only one variable, soil water content or potential. By introducing the

specific water capacity, C, defined as

de
C = (5)
d h
and using the chain rule of calculus, equation (4) may be written in

terms of the soil water potential as


ah a h aK(h)
C = -- (K(h)--- ) S(z,t) (6)
at az 3z az


For two-dimensional flow, equation (3) becomes


ah a ah a ah 3K(h)
C =-= -(K(h}--) + -(K(h)-) S(x,zt) (7)
at ax ax az a z az


Thee two-dimensional flow equation written in radial coordinates

with radial symmetry may be written as


ah 1 a ah a ah aK(h)
C = -(r K(h)-) + -(K(h)-) S(x,z,t) (8)
a@t r ar ar 3z az az

The two-dimensional flow equation in radial coordinates may be used to

describe water movement and extraction of soil water from nonuniform

water applications such as trickle irrigation.

Due to the variable nature of K(h), equations (6), (7) and (8) are

highly nonlinear, and analytical solutions are extremely complex or








impossible to obtain. The nonlinearity of equations (6) and (7), and

the typical variable boundary conditions, have led to the use of

numericaI methods to solve practical problems of soil-plant-water

relationships, such as irrigation management for agricultural crops.

For one-dimensional flow, equation (6) has been successfully solved

using explicit finite difference methods by many researchers. Hanks and

Bowers (1962) developed a numerical model for infiltration into layered

soils. They solved the Richards equation for the hydraulic potential

using; implicit finite difference equations with a Crank-Nicholson

technique which averages the finite differences over two successive time

steps. Rubin and Steinhardt (1963) developed a numerical model to study

the soil water relationships during rainfall infiltration. They used a

Crank-Nicholson technique to solve Richards equation for the water

content. Rubin (1967) developed a numerical model which analyzed the

hysteresis effects on post-infiltration redistribution of soil water.

Haverkamp et a]. (1977) reviewed six numerical models of one-

dimenmsiaal infiltration. Each model employed different discretization

techniques for the nonlinear infiltration equation. The models reviewed

were solved using both the water content based equation and the water

potential based equation. They found that implicit models which solved

the potential based infiltration equation had the widest range of

applicability for predicting water movement in soil, either saturated or

nonsaturated.

Clark and Smajstria (1983) developed an implicit model of soil

water flow to study the distribution of water in soils as influenced by

various irrigation depths and intensities. The model simulated water

application rates from center-pivot irrigation systems with intensities








of application typical of low and high pressure irrigation systems.

Their model also simulated post-infiltration redistribution.

Rubin (1968) developed a two-dimensional numerical model of

transient water flow in unsaturated and partly unsaturated soils. He

utilized alternating-direction implicit (ADI) finite difference methods.

He studied horizontal infiltration and ditch drainage with the numerical

model. Hornberger et al. (1969) developed a two-dimensional model

to study water movement in a composite soil moisture groundwater system.

They modeled the two-dimensional response of falling water tables. They

considered both saturated and unsaturated zones in their model. The

solution method used was a Gauss-Sidel iterative technique.

A two-dimensional model to simulate the drawdown in a pumped

unconfined aquifer was developed by Taylor and Luthin (1969). The model

gave simultaneous solutions in both the saturated and unsaturated zones.

They used a Gauss-Sidel iterative method to solve the flow equations.

Amerman (1969) developed two-dimensional numerical models to

simulate steady state saturated flow, drainage and furrow irrigation.

He used ADI methods to solve both the steady state saturated flow model

and the furrow irrigation model. He also used an explicit method to

solve the drainage model.

A study of the sensivity of the grid spacing for finite difference

models was reported on by Amerman and Monke (1977). Two finite

difference models of two-dimensional infiltration were analyzed. They

solved the two-dimensional flow equations with successive overrelaxation

(SOR) and alternating direction implicit (ADI) methods. They found that

smaller grid sizes were needed in regions where the hydraulic gradients








changed rapidly. Considerable computational savings without appreciable

loss of accuracy was achieved using irregular grid sizes.

Perrens and Watson (1977) developed a two-dimensional numerical

model of water movement to analyze infiltration and redistribution.

They used an iterative alternating direction implicit technique to solve

the flow equation. Two soil types, a sand and a sandy loam, were

simulated. Nonuniform surface fluxes were applied along the horizontal

soil surface in a step type distribution pattern. They also

incorporated hysteresis of soil hydraulic characteristics into the model

to be used in the redistribution phase of the simulations.

Researchers have also utilized two-dimensional models to study soil

water movement from trickle irrigation systems. Brandt et al. (1971)

solved the flow equation in two dimensions to analyze infiltration

from a trickle source. They developed a plane flow model in cartesian

coordinates to analyze infiltration from a line source of closely spaced

emitters with overlapping wetting patterns. They also developed a

cylinderical flow model to analyze infiltration from a single emitter

when its wetting pattern is not affected by other emitters. Both models

were solved using noniterative ADI finite difference procedures with

Newton's iterative method. The results were compared to an analytical

solution of steady infiltration and a one-dimensional solution with good

results.

Armstrong and Wilson (1983) developed a model for moisture

distribution under a trickle source. They utilized the Continuous

System Modeling Program (CMSP) to simulate the soil moisture movement.

The model calculated the net flow rates into each grid. It then

calculated the change in water content by dividing the net flow rate








by the volume of soil in each grid and then multiplying by the time

step. Finally, the model calculated the new water contents from the

previous water contents plus the calculated water content changes.

Model results compared favorably with field measurements.

Zazueta et al. (1985) developed a simple explicit numerical model

for the prediction of soil water movement from trickle sources. The

model was based on the mass balance equation and an integrated form of

Darcy's law. The model produced good agreement with other results

obtained with more complicated numerical methods and analytical

solutions.

Soil Water Extraction
Water uptake by plant roots has been investigated by many

researchers. Among the first researchers to attempt to describe plant

water relations were Gradmann (1928) and van den Honert (1948). Two

approaches to modeling water extraction have been utilized to describe

the water extraction by plant roots. The first, called the microscopic

approach, describes water movement to individual roots. The second

approach, called the macroscopic water extraction model, describes water

uptake by the whole root zone, and the flow to individual roots is

ignored.

Gardner (1960) developed a microscopic water uptake model. He

described the root as an infinitely long cylinder of uniform radius and

water-absorbing properties, assuming that water moves in the radial

direction only. The flow equation for such a system is


ae la ae
-= --( r 0 ) (9)
at r ar ar








where e = the volumetric water content,

0 = the diffusivity,

t = the time and

r = the radial distance from the axis of the root.

He then obtained a solution at the boundary between the plant root

and the soil in order to maintain a constant rate of water movement to

the plant, subject to the following boundary conditions:

e = co, h = ho, at t = to, and

dh de
2 r, k(-) = 2 r, 0D (-) = q at r = r, (10)
dr dr
where k = the hydraulic conductivity of the soil,

rl= the radius of the root, and

q = the rate of water uptake by the root.

The solution of (9) subject to the initial and boundary conditions

in (10) is

q 4Dt
h ho = dh =- ( In g ) (11)
4 wk r
where g = 0.57722 is Euler's constant. The diffusivity and conductivity

were assumed to be constant, this assumption was justified because 0, r

and t are all in the logarithmic term, and dh is thus not very sensitive

to these variables.

Gardner (1960) also noted that the solution will behave as though

infinite for only very short times or for very low values of hydraulic

conductivity. Exact solutions of the problem for finite systems would

require taking the dependence of D and k upon the soil water potential

into account. Gardner also compared equation (11) with the steady-state

solution for flow in a hollow cylinder:









q b2
h ho = dr =- ( In -- ) (12)
4 rk a
where ho = the potential at the outer radius of the hollow cylinder,

b = one half the distance between neighboring roots, and

h = the potential at the inner radius a.

If b = 2Tf then equation (12) is identical to equation (11)
except for the g term which is small compared to the logarithmic term

and may be ignored.

Gardner and Ehlig (1962) presented a macroscopic water uptake
equation in which the rate of water uptake is proportional to the

potential energy gradient and inversely proportional to the impedance to

water movement within the soil and the plant. The potential energy was

expressed as the difference between the diffusion pressure deficit and

the soil suction. The impedance was expressed as the sum of plant

impedance and soil impedance. They analyzed greenhouse experiments and

obtained results consistent with the uptake equation.

Molz and Renson (1970) developed a mathematical model describing
moisture removal from soil by plant roots. The model described one-

dimensional water movement and extraction. The model used a macroscopic

water extraction term to describe moisture removal by plants. Their

formula for the extraction term was given as

R(z) D(e)
S(z,t) = T ( ) (13)
r R(z) D(e) dz
where D(e) = diffusivity,

R(z) = the effective root density,
T = the transpiration rate per unit area and
v = the root depth.






23 '


The model gave results that compared reasonably with experimental

results. The numerical solution of the Richards equation with the

extraction function was obtained using the Douglas-Jones predictor-

corrector method.

Nimah and Hanks (1973) developed a numerical model to predict water

content profiles, evapotranspiration, water flow in the soil, root

extraction, and root water potential under field conditions. Their

extraction term had the form



(Hroot + (1.05 z) -h(z,t)-s(z,t)) RDF(z) K(G)
A(z,t) = (14)
Ax AZ

where A(z,t) = the soil water extraction rate,

Hroot = the effective water potential in the root at the soil

surface,

h(z,t) = the soil matric potential,

s(z,t) = the osmotic potential,

RDF(z) = proportion of total active roots in depth increment DZ,

K(e) = the hydraulic conductivity and

Ax = the distance between the plant roots at the point

where h(z,t) and s(z,t) are measured.
Tollner and Molz (1983) developed a macrocopic water uptake model.

The extraction function assumed that water uptake rate per unit volume

of soil is proportional to the product of contact length per unit soil

volume, root permeability per unit length and water potential difference

between soil and root xylem potential. A factor which accounts for

reduced root-soil-water contact as water is removed was included in the


__








extraction function. Their model predictions were comparable with

results of a greenhouse experiment.

Slack et al. (1977) developed a mathematical model of water

extraction by plant roots as a function of leaf and soil water

potentials. The model used a microscopic model to calculate water-

upt/ke which was input into a macroscopic model of water movement and

water uptake. Water movement was described by a two-dimensional radial

flow model. The model was used to estimate transpiration from corn

grown in a controlled environment under soil drying conditions. The

model predicted daily transpiration adequately for the period modeled.

Feddes et al. (1978) developed an implicit finite difference model

to describe water flow and extraction in a non-homogeneous soil root

system under the influence of groundwater. Their extraction term

assumed the extraction rate to be maximum when the soil water potential

was above a set limit. When the soil water potential fell below this

limit, the water uptake, S(h), was decreased linearly with the soil

water potential



( h h3 )
S(h) = Smax (15)
( h2 h3 )


where h2 is the set limit below which the water uptake decreases

linearly to h3. Below h3 it was assumed that no water is extracted,

then h3 may be assumed to be the wilting point. The maximum possible

transpiration rate divided by the effective rooting depth is Smax. The

model yielded satisfactory results in predicting both cumulative

transpiration and distribution of soil moisture content with depth.








Zur and Jones (1981) developed a model for studying the integrated

effects of soil, crop and climatic conditions on the expansive growth,

photosynthesis and water use of agricultural crops. The model utilized

Penman's equation modified by Monteith to calculate the water vapor

transport from the plant to the atmosphere. It utilized a

macroscopic soil water extraction term to calculate water uptake from

the soil. The model assumed the water uptake from the soil was the

difference between the total water potential at the root surface and the

soil water potential divided by the sum of the resistance to radial

water flow inside the roots and resistance of water flow in the soil.

The model treated the water relations in plants in considerable detail.

It was successfully tested on soybeans. However the model did not take

into consideration infiltration, drainage, evaporation from the soil

surface or upward movement of water in the soil.













CHAPTER III
MATERIALS AND METHODS

Equipment
The data acquisition system developed in this research was based on

tensiometer-mounted pressure transducers. Pressure transducers used

were Micro Switch model 141PC15D. These transducers measured pressures

from 0 to -100 kPa. They produced an analog electrical output from 1 to

6 volts which was proportional to the vacuum exerted on a membrane in

the transducers. The transducers operated much like strain gages. One

side of the membrane was open to the atmosphere and the other side was

in contact with water in the tensiometer. As pressure on the water

changed, the membrane was deformed and the voltage across the membrane

changed.

The pressure transducers required an 8-volt direct current (VDC)

power supply at 8 mA each. Because a multiple-transducer system was

developed, a separate regulated power supply was used rather than the

microcomputer power supply. This assured adequate power for the

transducers.

The pressure transducers were temperature-compensated. Outputs

varied less than 1% of full scale output in the range of 5 C to 45 C.

The output voltages from the pressure transducers were interfaced

to a microcomputer through an analog-to-digital (A/D) board. The A/D

board was a Mico World MW-311 general purpose Input/Output Board. This

device had 8-bit resolution and measured input voltages from 0 to 5

volts. It had 16-channel multiplexing capability.








The microcomputer used was a Commodore 64. It was selected for its

programmability, its availability at local electronics supply companies,

and its low cost. An overall goal in component selection was to be able

to replace any component individually with as little down-time as

possible, and thus to assure the reliability of the system.

The microcomputer output was to a video screen, a printer, and a

cassette recorder. The cassette recorder provided storage of data for

later computations and easy transfer to other computer systems. The

printer provided a hard copy backup of data. The video screen provided

immediate interaction with the computer for programming and monitoring.

The microcomputer was programmed in the BASIC computer language.

It had approximately 32 kilobytes of programmable memory (RAM) when

using the BASIC computer language. This was sufficient to store the

calibration equations and calculated outputs from the transducer inputs.

The microcomputer also had an internal 24-hour clock which was required

for real-time data acquisition. Data acquisition system components and

approximate costs are given in Table 3-1.

Instrumentation Test Procedure
Pressure transducers were individually calibrated using a regulated

vacuum source and a mercury manometer. Measurements of transducer

voltages and mercury column heights were made at decreasing pressure

increments of approximately -10 kPa from 0 to approximately -80 kPa. To

determine whether the transducers displayed hysteretic behavior,

calibrations were continued at increasing pressure increments from -80

kPa to 0 kPa.











Table 3-1. Microcomputer-based data acquisition system components
and approximate costs.


Component Cost($)

Microcomputer 100

Printer 100

Cassette Recorder 60

Pressure Transducer 68

Tensiometer 40

Analog-to-Digital and

Multiplexing Circuit 200

Transducer Power Supply 50








A/D boards were calibrated while interfaced with the microcomputer.

Known voltages were applied to the boards and the digital outputs read

by the computer were recorded.

Calibrated pressure transducers were interfaced to the tensiometers

by drilling small holes into the walls of the tensiometers. Access

ports on the transducers were inserted into the tensiometers and the

connections were sealed with silicone sealant. The pressure transducer-

equipped tensiometers were connected to the computer using 3-lead 22

gauge electrical hookup wire.

Two tests of the functioning of the microcomputer-based tensiometer

pressure transducer system were conducted. The first was conducted in

the laboratory. Three mercury manometer tensiometers were equipped with

pressure transducers and interfaced with the microcomputer. The

tensiometers were serviced to remove air from the system. The ceramic

cups were then exposed to the atmosphere and allowed to dry for several

hours. Microcomputer readings and mercury manometer readings were taken

for comparison at random intervals during drying. Data collection

continued throughout the tensiometer range. Three replications were

taken.

The second test of the tensiometer-pressure transducer system was

conducted under field conditions. Three instrumented mercury manometer

tensiometers were installed in a field lysimeter system with grass

cover. The microcomputer was located in the field laboratory office 25

m from the sensors. Tensiometers were serviced and allowed to

equilibrate with the soil water potential. The microcomputer was

programmed to read the pressure transducers hourly. Mercury manometers

were read manually at random intervals, typically 2 or 3 times per day








during the field evaluation. Manual mercury manometer readings were

compared with the microcomputer readings to assess the accuracy of the

instrumentation under field conditions. Instrumentation was evaluated

for 3 1-week periods. Tensiometers were serviced to remove entrapped

air between 1-week analysis periods.

Field Data Collection
A field lysimeter system was used to monitor soil water status and

water uptake from young citrus trees. The field lysimeter system was

located at the Irrigation Research and Education Park in Gainesville,

Fl. Layout of the lysimeters is shown in Figure 3-1. The lysimeters

were cylindrical steel tanks with one end open. Tanks were installed

with the open end upward, exposing a circular surface production area of

2 m2. Soil profiles were 1.8 m deep. The soil in the lysimeters was

Arredondo Fine Sand, (hyperthermic, coated, Typic Quartzipsamment),

which was hand packed to approximate the physical characteristics of an

undisturbed soil profile. Drainage of excess water from the bottom of

each lysimeter was accomplished using either a porous stone or porous

ceramic cup located in the bottom of the tank as shown in Figure 3-2. A

vacuum pump removed the water from the lysimeters and the water was

trapped in PVC cylinders. The PVC cylinders were used to measure the

drainage from each lysimeter. Automated rainfall shelters were used to

cover the lysimeters in the event of rainfall. Additional details of

the construction and operation of the lysimeters were given by Smajstrla

(1985).

Data collection was conducted in two phases. In 1985 two

lysimeters were instrumented, and data were collected as described

earlier. Each lysimeter contained a young citrus tree approximately 3






31


LYSIMETERS


DRIVE UNITS


Figure 3-1. Layout of lysimeter system.









32


TO VACUUM


MERCURY
MANOMETER






NEUTRON TENSIOMETER
ACCESS TUBE > PVC
Tr ID T Kll


ii
I I
II
I I
r&:~~ ~
I; II
II j
II
II
II
Ii II
II II
II I I
II I I
I I

I,
II I

I I
II Ii
II
I II
~ ~.J ~a. L.


II
II I,
ii II
ii ___
-- 1.~


I,
I,
I,
I,
I,
I,
/,


-


DRAIN'
FILTER

Figure 3-2. Details of individual lysimeter soil water status
monitoring system.


CERAMIC \
CUP FILTER




-u
33

years old. Both lysimeters were irrigated when the water potential in

the lysimeter dropped below -20 kPa. The -20 kPa water potential
corresponded to approximately a 44% water depletion from field capacity.

One lysimeter had a grass cover crop and the second had bare soil.
These two cover practices were used to simulate different cultural
practice effects upon the young citrus in a related experiment.

Tensiometers were installed at radii of 100, 300, 500 and 700 mm
from the center of the lysimeter, and at depths of 150, 300, 450, 600

and 900 mm as shown in Figure 3-3. Data were collected with the
microcomputer based data acquisition system at 10 minute intervals and

averaged over hourly periods.

In 1986 two lysimeters with young citrus trees were instrumented
with the same water and cover treatments as in 1985. Tensiometers were
installed in the lysimeters at radii of 130, 380 and 630 mm and at

depths of 150, 300, 450, 600, 900 and 1020 mm as shown in Figure 3-4.

In addition to the two lysimeters with young citrus trees, two
lysimeters with only grass cover were instrumented. The water potential

treatments for the two grassed lysimeters were -20 kPa and -40 kPa. The

-40 kPa water potential corresponded to approximately a 50% water
depletion from field capacity.

Model Development
A computer program describing the infiltration, redistribution and
extraction of soil water was written in the FORTRAN computer language.

A Prime 550 computer was used for all computations.

Several assumptions were employed in the development and use of the
numerical models to ease the complexities associated with mathematically
describing water movement in unsaturated porous media. These











Radius (mm)


600


700 800


* location of tensiometers


Figure 3-3.


Location of tensiometers in 1985 field experiment
for young citrus trees in grassed and bare soil
lysimeters.


0 100


300


150 L


300


*


450 [


600 -


900 -


1800


1 1 7 -









Radius (mm)


380


630


* location of tensiometers


Figure 3-4.


Location of tensiometers in 1986 field experiment
for young citrus trees in grassed and bare soil
lysimeters.


130


800


150

300


450


600


1020 I


1800


I 1








assumptions were: (1) The physical properties of the soil are

homogeneous and isotropic; (2) The physical and chemical properties of

the soil are constant in time; and (3) The hydraulic conductivity and

soil pressure potential are single-valued functions of water content.

One-Dimensional Model

Equation (6) was used to describe the one-dimensional movement and

extraction of water. Finite difference methods were used to solve the

water potential based flow equation. The model used an implicit finite

difference technique with explicit linearization of the soil parameters.

The finite difference form of equation (3) was written as

k+1 k k k+1 k+1 k k+1 k+1
(h-h ) K (h -h ) -K ( h-h )
k i i i+1/2 i+1 i i-1/2 i i-1
C
i 2
At Az

k k
K K
i-1/2 i+1/2 k
+ S (16)
i
AZ
where
k k
K + K
k i i-I
K = (17)
i-1/2
2
and
k k
K + K
k i+1 i
K = (18)
i+1/2
2
The subscript i refers to distance and the superscript k refers to time.

To apply this equation to soil profiles, the soil was divided into a








finite number of layers or grids as shown in Figure 3-5. Equation (16)

was rearranged so that unknowns were on the left side of the equation

and the knowns were on the right side such that


k k k
At K At K At K
i-1/2 k+1 i-1/2 i+1/2 k+1
-( ) h + ( 1 + + ) h
2 k i-1 2 k 2 k i
Az C Az C Az C
i i i

k k k
At K At K K At
i+1/2 k+1 k i-1/2 i+1/2
- ( ) h = h + ( ) S
2 k i+1 i k k i
AZ C AZ C C
i i i


(19)


Equation (19) was written for each of the interior grids in the soil

profile. The top and bottom grids of the system required equation (19)

to be modified so that the equation would describe the boundary

conditions. The system of equations which are formed by applying

equation (19) to each grid produces a tridiagonal matrix which is

implicit in terms of h, water potential. The tridiagonal matrix was

solved using Gauss elimination. From explicit linearization, the

coefficients of the unknown h terms were known at each time step. Thus

equation (19) was reduced to

k+1 k+1 k+1
A h + B h + C h = D (20)
i i-1 i i i i+1 i

where


At K
i-1/2
A = ( )
i 2 k
Az C
i


(21)














.GRIDS
1

I

e
8
e
o
e

i-1


i+1








n


I I-t-


-----+-





----r-i----
rI
t





a I

I
i !I .
I______


Figure 3-5.


il surface

91 C1 K1
1 C K1








-1 9 C K


9 C. K.
1i 1


hi+1 i+1 Ci+1 i+1








hn 9n Cn Kn
na n n


Schematic diagram of the finite-difference grid
system for the one-dimensional model of water
movement and extraction.


!-


----- h


DZ








k
At K
i+1/2
C = ( ) (22)
i 2 k
AZ C
i

B = 1 A C (23)
i i i

k k
At K K At
k i-1/2 i+1/2
D = h + ( ) S (24)
i i k k i
Az C C
i i
Boundary Conditions. The boundary condition for the surface grid

was variable. A flux boundary condition was used to simulate

infiltration during irrigation, and a no flux boundary condition was

used for redistribution. Evaporation from the soil surface was included

in the water extraction term. Equation (20) was modified for the

surface boundary condition such that

k+1 k+1
B h + C h = D (25)
1 1 1 2 1
where

B = 1 C (26)
1 1
and


k
At Qs K At
k 1+1/2
0 = h + ( )- S (27)
1 1 k k 1
Az C C
1 1








The lower boundary was also a flux boundary and was written as



k+1 k+1
A h + B h = D (28)
n n-1 n n n
where

B = 1 A (29)
n n
and

k
At K Qb At
k n-1/2
D = h + ( ) S (30)
n n k k n
Az C C
n n


The variables Qs and Qb were, respectively, the surface and bottom

fluxes imposed on the grid system. The bottom flux was set to either a

no flow or a gravity flow boundary condition.

Surface infiltration. The infiltration rate during irrigation was

set equal to the water application rate until the irrigation event was

completed. The total depth of water infiltrated at any time was

calculated as the summation of the incremental infiltration volumes at

all previous time steps.

Time steps. The time steps for implicit numerical techniques can

generally be much larger than those for explicit numerical techniques,

and still maintain stability. Haverkamp et al. (1977) stated that

stability conditions must be determined by trial and error because they

depend on the degree of nonlinearity of the equations.

The time step was estimated by a method given by Feddes et al.

(1978) and used by Clark (1982):








x Az
At < (31)
1 Qmax
where Qmax was the maximum net flux occurring across any grid boundary

and x is a factor where 0.015
accommodate the rapid movement of water during infiltration and early

stages of redistribution. The value of x may be assumed to be the

maximum permissible change in water content for any grid in the soil

profile.

Updating of soil parameters. The updating of the soil parameters

was achieved by use of a tabulated search to determine the corresponding

values of hydraulic conductivity, specific water capacity and water

content for the new values of soil water potential at each time step. A

logarithmic interpolation method was used to reduce computer time. The

table was set up with linearly increasing multiples of the logarithmic

values of soil water potentials.

Mass balance. A mass balance was calculated at each time step to

check the stability of the simulation model. The method used the

initial volume of water in the profile plus the infiltration and minus

the extraction by the plant. Evaporation from the soil surface was

included in the water extraction term as extraction from the surface

grids.

Because the grid system approximates a continuous system with dis-

crete points, some error will result from the numerical calculations of

the simulation model. The error decreases as the grid size decreased.

Two-Dimensional Model

Water movement and extraction under young citrus trees was

simulated using a two-dimensional soil water extraction model. A radial








flow model may be used to describe water movement and extraction in a

soil profile which is nonuniformly irrigated as in water flow from

trickle emitters and spray jets. The radial flow model may also

describe the water extraction under widely spaced crops such as citrus.

With the assumption of radial symmetry, equation (8) was solved in

the vertical and radial directions. This equation is a second order,

nonlinear parabolic partial differential equation which expresses the

water potential distribution as a function of time and space

coordinates. No known analytical solution of equation (8) exist. Thus

it was solved numerically using finite difference equations. The model

developed in this research used an implicit finite difference technique

with explicit linearization of the soil parameters. Two solution

methods were used to solve the finite difference equations for the two-

dimensional model. It was solved implicitly using a Gauss elimination

method. Because of the time required to solve a large system of

equations by Gauss elimination, an alternation direction implicit (ADI)

method was also utilized to solve equation (8).

The finite difference equation for the solution of equation (8)

utilizing the Gauss elimination method was

k+1 k k k+1 k+1 k k+1 k+1
(h h ) K ( h h ) K ( h h )
k i,j i,j i+1/2,j i+1,j i,j i-1/2,j i,j i-1,j
C =
i,j 2
At Az

k k+1 k+1 k k+1 k+1
r K ( h -h ) r K (h -h )
i,j+1/2 i,j+1/2 i,j+1 i,j i,j-1/2 i,j-1/2 i,j i,j-1

2
r Ar










k
K
i-1/2,j


- K
i+1/2,j


- S


(32)


To apply this equation to the soil profiles, the soil was divided

into a finite number grids as shown in Figure 3-6. Equation (32) was

arranged such that the unknowns were on the left side of the equation

and the knowns were on the right side as follows


k
At K
i-1/2,j
-( )h
2 k
Az C ":
i.j


+(1+


At ( r


k+1

i-1,j


k
At ( K
i-1/2,j

2
AZ


k
K
i,j+1/2 i,j+1/2

2 k


Ar r C
i,j i,j


k
At r K
i,j-1/2 i-1/2,j
-(- )
2 k
Ar r C
i,j i,j


+ K )
i+1/2,j


k
+r K )
i,j-1/2 i,j-1/2


At K
i+1/2,j k+1
-( )h
2 k i+1,j
Az C


k
At r K
i,j+1/2 i+1/2,j
-(-- )
2 k
Ar r C
i,j i,j


k+1
h
i,j-1


k+1
h
i,j+1








(0,0)


Soil Surface


(i-Ij)


(i,j-1 (i,j) (i-,+l)


(i+1,j)


Figure 3-6.


Schematic diagram of the finite-difference grid system
for the two-dimensional model of water movement and
extraction.










k
= h
i,j


At K K
i-1/2,j i+1/2,j
- () -


- S
k


i,j


Equation (33) was reduced to


k+1
A h
i,j i-1,j


k+1
+ B h
i,j i,j-1


k+1
+C h
i,j i,j


+ h
i,j i+l,j


k+l
+ E h = F
i,j i,j+1


where


At K
i-1/2,j
A =- ( )
i,j 2 k
AZ C
i,j


At r


B = (
i,j 2


i,j-1/2 i-1/2,j

k


Ar r


At K
i+1/2,j
S (----)
2 k
Az C
i,j


At r K
i,j+1/2 i+1/2,j
E. .= (-- -----


Ar r C
i,j i,j


(33)


(34)


(35)


(36)


(37)


(38)









C = 1 A B D E (39)



k k
At K K At
k i-1/2,j i+1/2,j k
F = h + ( ) S (40)
ij i,j k k i,j
AZ C C
ij i,j
Boundary Conditions. The boundary condition for the surface grids

was a flux boundary condition which accounted for irrigation and

rainfall at the soil surface. At times when no irrigation occurred the

surface boundary was a no flux boundary. Evaporation from the soil

surface was included in the water extraction term. The modification of

equation (34) to describe the surface boundary condition was

k+1 k+1 k+1 k+1
B h + C h + D h + E h = F (41)
1,j I,j-1 1,j 1,j 1,j 2,j 1,j 1,j+1 1,j

where

C = 1 B D E (42)
1,j 1,j 1,j 1,j

k
At Qs K At
k j 1+1/2,j k
F = h + ( )- S (43)
1,j 1,j k k 1,j
Az C C

The lower boundary condition was also represented as a flux

boundary. The lower boundary in this research was an impermeable

boundary which represented the bottom of the lysimeter. The

modification of equation (34) to describe the lower no flux boundary was








k+1 k+1 k+1 k+1
A h + B h + C h + E h = F (44)
nj n-1,j nj n,j-1 n,j n,j n,j n,j+l n,j

where

C = 1 A B E (45)
n,j nj n,j n,j

k
At K Qb At
k n-1/2,j j k
F = h + ( ) S (46)
n,j n,j k k n,j
AZ C C
n,j n,j
The boundary conditions for the radial boundaries were both no flux

boundaries. The no flux boundary condition for the outer radius (j=m)

represented the outer wall of the lysimeter and was written as

k+1 k+1 k+1 k+1
A h + B h + C h + D h = F (47)
i,m i-l,m i,m i,m-1 i,m i,m i,m i+l,m im

where

C = 1 A B 0 (48)
i ,m i ,m i ,m i ,m

k k
At K K At
k i-1/2,m i+1/2,m k
F = h + ( ) -- S (49)
i,m i,m k k i,m
Az C C
n,m n,m
The boundary condition for the inner radius was also represented as

a no flux boundary. For the inner radius r(i,j) = 0, and its inclusion

into equation (8) would result in a division by zero. Therefore the

second term in equation (8) was rewritten as


1 a ah K ah a ah
-(r K(h) -) = + ( K(h) -) (50)
r ar ar r ar ar ar








dh
a no flux boundary at r = 0 implies that = 0. Then if


dh1 dh
-= 0, the lim---= 0.
dr r dr


We rewrite equation (8) as


a ah
S- ( K(h) ) +
az a z


a ah
- ( K(h) -
ar a r


a K(h)
) --
az


- S(z,r,t)


The finite difference equation for equation (51) at the inner

radius may be written as


At K
i-1/2,1 k+1
- ( )h
2 k i-1
Az C


,1


At ( K + K
i-1/2,1 i+1/2,1


+( 1+


2 k
Az C


At K
i,1+1/2
+ )
2 k
Ar C


At K
i+1/2,1 k+1
h ( ) h
i,1 2 k i+1,1
Az C


At K
.1,1+1/2
2 k
2k


At K


- K


i-1/2,1 i+1/2,1
-) -


k


or as


k+1
A h
i,1 i-1,1


k+1
+ C h
i,1 i,1


k+1
+ D h
i,1 i+1,1


+ E h
1,1 i,2


ah
C-
at


(51)


(52)


= F


(53)


I








where

k
At K
i-1/2,1
A =- ( ) (54)
i,1 2 k
Az C
i,1


k
At K
i+1/2,1
S =- ( ) (55)
1,1 2 k
Az C
i,1


k
At K
i,1+1/2
E = (-- ) (56)
i,1 2 k
Ar C
i,1

C = 1 A D E (57)
i,1 i.1 i,1 i,1



k k
At K K At
k i-1/2,1 i+1/2,1 k
F = h + ( ) -- S (58)
1,1 i,1 k k i,l
Az C C
i,1 i,1

Updating of the soil parameters, surface infiltration, mass balance

and time steps were implemented as described for the one-dimensional

soil water flow model.

The system of equations for the two dimensional model produces a

banded matrix. The matrix is a five banded matrix with the form of

















Reddel and Sunada (1970) utilized a Gauss elimination method for

the solution of a two-dimensional groundwater model. They used an

algorithm developed by Thurnau (1963) which operates only on the banded

part of the solution matrix. Computer storage is not required for the

matrix elements above or below the band. A minimum band width is

desirable and an appropriate choice of the grid numbering pattern can

reduce the total width of the band.

In this model of two-dimensional soil water movement and

extraction, a subroutine was written which used the BANDSOLVE algorithm

developed by Thurnau (1963) to solve the system of equations. A

subroutine was also written which solves equation (8) using an

alternating direction implicit method. The finite difference equations

for the ADI solution are presented in Appendix A.

Soil Water Extraction

A macroscopic soil water extraction term was used in this research.

The model used was based on actual field measurements reported in the

literature. Denmead and Shaw (1962) conducted experiments which

compared actual ET to potential ET of corn as a function of the

available soil water. Their study showed that under high potential ET

demands, the actual ET was considerably less than the potential rate

even though the available soil water was considered adequate. They also

observed that under low potential ET demands, the actual ET was equal to






51

the potential ET down to very low soil water contents. Ritchie (1973)

observed similar results in separate experiments.

Saxton et al. (1974) used these observed relationships in modeling

soil water movement and extraction under a corn and under a grass crop.

Smajstrla (1982) used these relationships to model the soil water status

under a grass cover crop in Florida.

The soil water extraction function used in this research was

modeled after that used by Smajstrla (1982). The soil water extraction

rate was calculated as a function of the actual evapotranspiration rate

and the current soil water status. The water extraction term was

defined as
(ET / Ri )
Si = ET RDFi Ri (59)
where Si = the soil water extraction rate per soil zone,

ET = the actual evapotranspiration rate,

RDFi = the relative water extraction per soil zone at field

capacity, and

Ri = the relative available soil water per soil zone defined as
( 6 Owp
Ri = (60)
( 6fc wp )
where 6 = the soil water content of the soil zone,

Owp = the soil water content at wilting point, and

efc = the soil water content at field capacity.
The relative water extraction per soil zone (RDF) was defined as
the percentage of water extraction for the ith soil zone when soil water

is not limiting. It may also be considered to be a rooting activity

term which indicates the percentage of active roots in the ith soil

zone.








Figure 3-7 shows the form of equation (59). Equation (59) permits
a rapid rate of soil water extraction when soil water is readily

available. As soil water is depleted, the water extraction function

produces a logarithmic rate of decline of soil water extraction. It

allows recovery of near potential rates of extraction during periods of

low potential ET and it rapidly limits extraction during periods of high

potential ET. It prevents the soil permanent wilting point from being

reached by limiting ET to very low rates as the permanent wilting point

is approached.

In this research equation (59) was used to limit water extraction

from a given soil zone as the water in that zone became less available.

Equation (59) was not used to limit the ET from the profile, only to

repartition the extraction within the soil profile.

Equation (59) was applied to calculate a water extraction rate from
each grid for each time step during model operation. The soil water

extraction rate per soil grid was then multiplied by the grid volume to

calculate the total water extraction at that time step. If the

calculated total water extraction rate was not equal to the actual ET,

the soil water extraction rates were linearly adjusted so that the

calculated and actual ET rates were equal.

The adjusted soil water extraction rates (Si) were computed as

ET
Si = S i A (61)
z Si Av
where Av is the volume of the ith soil grid.









































1.0


RELATIVE AVAILABLE SOIL WATER CONTENT


Figure 3-7.


Relationship of the relative available soil water and
potential soil water extraction rate on the soil
water extraction rate.


1.0


0.8




0.6




0.4




0.2


0.0













CHAPTER IV
RESULTS AND DISCUSSION
Instrumentation Performance
Three pressure transducers were individually calibrated to analyze
their response characteristics. A typical calibration curve (for

pressure transducer No. 1) is shown in Figure 4-1. The three

calibration equations are

Volts = 0.04812 (kPa) + 0.9861 R2 = 0.999 (62)

Volts = 0.04781 (kPa) + 0.9867 R2 = 0.999 (63)

Volts = 0.04804 (kPa) + 0.9819 R2 = 0.999 (64)

The coefficients for these equations were not significantly
different ( a = 0.05), so that for many applications one equation could

be used for all 3 pressure transducers without significant error. For

the above 3 transducers, combined equations resulted in a maximum

expected error of 0.06 kPa at 1 volt (-0.3 kPa potential) and 0.27 kPa

at 5 volts (-83.67 kPa potential). Equations could therefore be

combined for many field applications. For this research, individual

transducer calibration curves were used in order to obtain the maximum

accuracies possible with the instrumentation, and because the

microcomputer memory was adequate to permit storage of the individual

calibration curves.

In the calibration procedure, hysteresis effects were studied by
measuring transducer outputs at decreasing water potentials from 0 to

-80 kPa, followed by increasing potentials from -80 to 0 kPa. For
these transducers there were no measurable hysteresis effects.






55







6

PRESSURE TRANSDUCER
CALIBRATION

MICRO SWITCH 14PC15D



V 4-


I--
















-0 -20 -4 -60 -80 -1

PRESSURE, kPa

Figure 4-1. Calibration curve of output voltage versus pressure
applied for pressure transducer no. 1.








The A/D board was found to have a linear relationship between

voltage input and digital output as shown in Figure 4-2. The equation

which related the voltage to digital output was


Digital Units = 49.98 (Volts) R2 = 0.999 (65)

Equation (65) was combined with the individual transducer

calibration equations (62-64) to obtain relationships between

transducer-measured water potentials and the digital inputs to the

microcomputer. Equation (65) is only valid in the range of 0-5 volts

and 0-255 units for the 8-bit A/D board used. The 8-bit board,

therefore, allowed a resolution of only the nearest 0.02 volts. Greater

resolution could be achieved by the use of a 12-bit, 16-bit or other

higher resolution A/D board. A resolution of 0.02 volts is a resolution

of approximately 0.4 kPa (from equations 62-64). For this work this

degree of resolution was judged to be acceptable.

Tests of the assembled tensiometer-pressure transducer systems were

conducted in the laboratory by manually and automatically recording

tensiometer water potentials as water was allowed to evaporate from the

tensiometer ceramic cups. Figure 4-3 shows the changes in water

potential with time for 2 tensiometers. The continuous automatic

readings by the microcomputer are shown as solid lines. Open circles

show mercury manometer data that were manually read. Excellent

agreement between the automatic and manual readings was obtained. In

all cases, agreement was within 1.0 kPa.

Figure 4-4 shows a comparison of the manual and automatic readings

for the 3 tensiometers and pressure transducers tested. Agreement was

excellent, with all data points located within 1 kPa of the 100%

accuracy line.












250


0 1 2 3 4 5
INPUT VOLTAGE, VOLTS


Figure 4-2.


Calibration curve of digital units versus voltage
applied for the analog-to-digital circuit used.



























<0


to
9-

W-40
C-
0
0.
tJJ
I-


DRYING TIME, HOURS


Figure 4-3.


Comparisons of mercury manometer manually-read and
pressure transducer automatically-read tensiometer
water potentials during drying cycles for two
tensiometers in the laboratory.























to
a-6

--4
I-
UJ
Q-.





=02
LU
Q-
-44
UiJ


I-)



|-20

U~J
Of


0 -20 -40. -60


MERCURY MANOMETER WATER POTENTIAL, kPa


Figure 4-4.


Comparisons of mercury manometer manually-read and
pressure transducer automatically-read tensiometer
water potentials for all laboratory data.


-80








To evaluate the performance of the microcomputer-based soil water

potential monitoring system under field environmental conditions, 3 1-

week studies were conducted at the IFAS Irrigation Research and

Education Park. Typical results for 1 week are shown in Figure 4-5 to

4-7 for 3 pressure transducers and tensiometers. Microcomputer data

were recorded hourly and are shown as the solid line in each figure.

These lines show diurnal cycles in soil water potential and a gradually

decreasing average daily water potential as the soil dried. Water

potential changes were slow because of the low evaporative demand and

relatively inactive grass cover during the February 25 March 1 period

during which these data were collected.

The open circles in Figure 4-5 to 4-7 show manually read mercury

manometer data. Agreement between these and the automatically read data

were excellent under field conditions. The average variation between

manually and automatically read data was 0.47 kPa. This was

approximately the 0.4 kPa resolution of the instrumentation. The

maximum deviation observed was 1.76 kPa. These data demonstrated that

an accurate, effective microcomputer-based data acquisition system was

developed for automatically recording soil water potential measurements.

Because it was microcomputer-based, the system was inexpensive and

consisted of components that were readily available from local

electronics companies.

Field Data Collection
Field data were collected at the Irrigation Research and Education

Park as previously described. The data were collected for input and

verification of the numerical models developed in this research.













-60








-40








-20-


TIME, HOURS


Figure 4-5.


Evaluation of pressure transducer-tensiometer no. 1
by comparison of mercury manometer manually-read and
pressure transducer automatically-read water potentials
in the field.














-60















IaJ
UJ
0
a-





I-
Li-20-


UJ
I-


I
20


SI
40


SI
60


SI
80


SI
100


TIME, HOURS


Figure 4-6.


Evaluation of pressure transducer-tensiometer no. 2 by
comparison of mercury manometer manually-read and
pressure transducer automatically-read water potentials
in the field.


TENSIOMETER-PRESSURE TRANSDUCER
FIELD TEST NO. 2

















PRESSURE TRANSDUCER
0 MERCURY MANOMETER


' I
120


II













-60 -









-40-


L-J





-20-

z
I-.







0




Figure 4-7.


TIME, HOURS


Evaluation of pressure transducer-tensiometer no. 3 by
comparison of mercury manometer manually-read and
pressure transducer automatically-read water potentials
in the field.








The tensiometer data were used to calculate the soil water

extraction from the lysimeters. A method described by van Bavel et al.

(1968) was used to calculate the soil water extraction. Van Bavel's

method used an integrated form of equation (1) to calculate the soil

water extraction for a one-dimensional soil profile which was described

as z

Rz = -- dz qz (66)

where R, = the total soil water extraction rate for the soil profile to

a depth of z. The total soil water extraction rate calculated for the

entire profile depth z is then the ET rate.

A direct measurement of the surface evaporation was not made.

Evaporation was included in the soil water extraction from the surface

grid. The tensiometer nearest the surface was located at 150 mm. Water

extraction from this surface grid included surface evaporation and ET

for that zone. Gravity flow drainage from the lower grid was assumed.

The hydraulic conductivity for the lower grid was assigned as the flux

out of the soil profile. This was justified because observed changes in

soil water potentials for the lower tensiometer were small.

1985 Field Data. The ET rates for selected drying cycles from the

1985 field experiments are shown in Figures 4-8 and 4-9. The observed

drying cycles occurred from August 20 to September 6. Figure 4-8 is the

ET rate from the 20 kPa young citrus tree with grass cover. Figure 4-9

is the ET rate for the 20 kPa young citrus tree on bare soil. Several

data points for the tree with no grass were missed throughout the

experiment due to equipment failure. Due to these problems the tree

with no grass cover was treated as a one-dimensional profile for

analysis.









Differences between the ET rates in Figures 4-8 and 4-9 show that

the ET rates for the tree with grass cover were greater than those of

the tree with no grass cover. The higher ET rates for the tree with

grass cover were expected and were also observed by Smajstrla et al.

(1986).

The distribution of water extraction for the two citrus tree

treatments are shown in Table 4-1. The water extraction rates are shown

as percentages of the total soil water extraction and soil water

extraction per soil zone. These values were computed for input into the

water extraction models. Table 4-1 shows the differences between the

soil water extractions for the two treatments. Approximately 97% of the

water from the tree with no grass cover was extracted from the top 750

mm of the soil profile. The water extraction for the tree with grass

cover shows that approximately 73% of the water was extracted from the

top 750 mm of the soil profile. The water extraction rates from Table

4-1 also suggest that, for the tree with grass cover, water was

extracted below the 1050 mm depth observed with the data collection

system.

A two-dimensional distribution of soil water extraction is shown in

Table 4-2 for the tree with grass cover. Table 4-2 shows that water was

extracted almost uniformly throughout the profile. Greater percentages

of weter were extracted from the inner radii of the lysimeter.

1986 Field Data. The ET rates for a selected drying cycle from

1986 field experiments are shown in Figures 4-10 and 4-11. Figure 4-10

is the ET rate from the 20 kPa young citrus tree with grass cover.

Figure 4-11 shows the ET rate for the 20 kPa young citrus tree with no

grass cover. The observed drying cycles occurred from June 16 to June



























(0
D.C.C
ul 4J 4J




CL.
C) 4J
MS



/~ *I-
SU)
r- C
V)
41~

cm
I A *' -

|0

CO C
a*)a


-E
r 4-)




0

14 O-
-a 4--w



CC
f **.- E
/ ^ cu c0


4-) Qj
0 4.)




*0-.
IL.


CC>

L3





4.. to
C>
I ~*I-








I '11. I

0 0

LOO
C)A
/ .











(&ep/ww) 3MV NOI1VNiIdSNVuOdVA3 It

U-









67


0
C+



e41

Em
*r- 41

/0. U-

C
r- 0

0 Q)
I* -X





















S.
CO C
/E *






LAO)
e- ra
a
S *L


*r-













(S p/ w J*y-J NO I U d NV^d A 2

.y s.o.








Table 4-1.


One-dimensional distribution of water extraction for a 15 day
drying cycle for Young Citrus trees with and without grass
cover.


Depth Depth Water Water Relative
Increment Extraction Extraction Water
Extraction
(mn) (mm) (mm) (mn/mm) (%)


Tree with Grass Cover

0-375 375 9.8 0.026 32.3
375-750 375 7.3 0.019 23.8
750-1050 300 8.7 0.029 28.6
below 1050 4.7 0.016 15.2

Tree with No Grass Cover

0-375 375 5.9 0.016 27.9
375-750 375 7.4 0.020 35.3
750-1050 300 7.0 0.024 33.5
below 1050 0.7 0.0023 3.3









Table 4-2. Two-dimensional distribution of water extraction for a 15
day drying cycle for young Citrus with grass cover.

Depth Depth Radius
Increment (mn)
(mm) (mm)
100 300 500 700


Relative Water
(%)


0-375
375-750
750-1050
below 1050




0-375
375-750
750-1050
below 1050


Extraction


8.59 10.46 6.92 7.66
5.65 5.79 5.46 5.65
8.03 8.26 3.94 4.07
4.21 3.45 6.33 6.04

Water Extraction
(mm)


375
375
300


2.6
1.7
2.4
1.3


3.2
1.8
2.5
1.1


2.1
1.7
1.2
1.9


2.3
1.7
1.2
1.8


Water Extraction
(mm/mm)


0-375
375-750
750-1050
below 1050


0.0070
0.0046
0.0082
0.0043


0.0085
0.0047
0.0084
0.0035


0.0056
0.0044
0.0040
0.0064


0.0062
0.0046
0.0041
0.0061









24. Differences between the two treatments showed that ET of the

tree with grass cover was greater than that of the tree with no cover,

especially early in the drying cycle. The 1220 mm depth tensiometer for

the tree with no grass did not function properly so these data were not

included in the data analysis, but this did not introduce a large

error, from Table 4-1.

The water extraction distributions are shown in Table 4-3. The

percentage of water extracted from the top layer was greater for the

tree with grass cover.

Evapotranspiration data for the two grass cover treatments are

shown in Figures 4-12 and 4-13. Figure 4-12 shows ET rates of the 20

kPa grass covered lysimeter and Figure 4-13 shows ET rates of the 40 kPa

grass covered lysimeter. Comparison of Figure 4-12 and 4-13 shows that

the ET of the 20 kPa treatment was higher than that of the 40 kPa

treatment, The grass had more water available for ET in the 20 kPa

treatment.

Table 4-4 shows the water extraction distributions for the two

grass treatments. Both distributions were similar with both having

approximately the same soil water extraction percentages for each layer.

Model Verification
The accuracy of the numerical models in simulating the infiltration

and redistribution of soil water was determined by comparison with other

computer simulations from previous works in the literature.

The one-dimensional computer model was compared to the simulations

of Rubin and Steinhardt (1963) and Hiler and Bhuiyan (1971). Their work

provided data from soils with widly different hydraulic properties and

also provided simulation results which were used for model verification.



























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Table 4-3.


Two-dimensional distribution of water extraction for a 4
day drying cycle for young citrus trees with and without
grass cover.


Depth Depth Radius
Increment (mm)
(mm) (mn)
200 600 200 600

Tree with Tree with
Grass Cover No Grass Cover


Relative Water Extraction
(%)


225
150
150
225
300





225
150
150
225
300





225
150
150
225
300


28.2 31.2 19.9 16.95
12.2 15.2 12.3 17.9
4.45 1.2 6.85 3.75
4.4 1.2 8.4 8.7
0.75 1.2 2.6 2.65


Water Extraction
(mM)

1.6 1.8 0.9 0.8
0.7 0.9 0.6 0.8
0.3 0.07 0.3 0.2
0.3 0.07 0.4 0.4
0.04 0.07 0.1 0.1


Water Extraction
(mi/mm)


0-225
225-375
375-525
525-750
750-1050





0-225
225-375
375-525
525-750
750-1050





0-225
225-375
375-525
525-750
750-1050


0.0081
0.0059
0.00046
0.00031
0.00023


0.0041
0.0038
0.0021
0.0017
0.0004


0.0035
0.0057
0.0011
0.0018
0.0004


0.0073
0.0048
0.0017
0.0011
0.0001































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Table 4-4.


One-dimensional distribution of water extraction for a 4 dry
drying cycle for a grass cover crop at water depletion
levels of 20 kPa and 40 kPa.


Depth Depth Water Water Relative
Increment Extraction Extraction Water
Extraction
(mm) (mm) (mn) (mm/mn) (%)

20 kPa Treatment Tree with Grass Cover

0-225 225 6.3 0.028 57.9
225-375 150 2.0 0.014 18.6
375-525 150 0.9 0.006 8.3
525-750 225 1.1 0.005 9.9
750-1050 300 0.6 0.002 5.3

40 kPa Treatment Tree with Grass Cover

0-225 225 3.9 0.0170 63.1
225-375 150 0.8 0.0055 13.5
375-525 150 0.5 0.0036 8.7
525-750 225 0.4 0.0019 6.9
750-1050 300 0.5 0.0016 7.8









Rubin and Steinhardt (1963) used an implicit solution of the

Richards equation in terms of water content. Their model was used to

study constant intensity rainfall infiltration on a Rehovot sand. The

soil data were presented as analytic functions which were tabulated for

use in this work. The soil hydraulic characteristics are shown in

Figures 4-14 and 4-15.

The simulated soil profile had a uniform initial soil water content

of 0.005. A uniform grid size of 10 mm was used. Figures 4-16 and 4-17

contain plots of soil water content profiles for infiltration into the

Rehovot sand. The figures show both the results from Rubin and

Steinhardt (1963) and this work. Figure 4-16 contains the soil water

content profiles for a constant infiltration rate of 12.7 mm/hr. Figure

4-17 contains the soil water content profiles for a constant

infiltration rate of 47 mm/hr. Results of this work are in excellent

agreement with those of Rubin and Steinhardt (1963).

The work of Hiler and Bhuiyan (1971) was also used to verify the

accuracy of the model developed in this work. They used a computer

model written in CMSP to solve the Richards equation. Surface

infiltration was simulated for two soils, Yolo light clay, and Adelanto

loam. The hydraulic characteristics of these soils are presented in

Figures 4-18 through 4-21.

The simulation results for these soils are presented in Figures 4-

22 through 4-24. Figures 4-22 and 4-23 show water content profiles with

time for the Yolo light clay at different initial conditions. Figure 4-

24 shows the soil water content profiles with time for the Adelanto

loam.








Comparison of results for the two soils showed excellent agreement

between Hiler and Bhuiyan's CMSP model and this work. The minor

differences between the results of the models could have resulted from

the interpolation of the soil properties.

The two-dimensional model was tested by simulating infiltration for

a Nahal Sinai sand (Bresler et al. 1971). Results were compared with a

steady-state analytical solution developed by Wooding (1968) and with an

ADI-Newton numerical simulation method presented by Brandt et al.

(1971).

These models simulated the infiltration of water into the soil from
a point source. The boundary condition used for the simulations was a

constant flux for the innermost surface grid (r = 0). The flux was set

equal to the saturated hydraulic conductivity of the soil. No flow

boundaries were used for the lower and radial boundaries. The simulated

soil profile had a uniform initial soil water content of 0.037. Figures

4-25 and 4-26 show the soil characteristics for the Nahal Sinai sand.

Figures 4-27 and 4-28 show a comparison between this work and that

of Wooding (1968) and Brandt et al. (1971). The data are presented in

dimensionless form with the relative water content defined as

S(O)/S(Bsat) where S(9) was defined by Philip (1968) as


S(O) = 0 do (67)
en
where D = the hydraulic diffusivity and en = the residual soil water

content. The total infiltration time was 57 min in Figure 4-27 and 297

min in Figure 4-28.

Figures 4-27 and 4-28 demonstrate that this model accurately
simulates the results of Brandt et al. (1971). Differences between the































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WATER CONTENT (mmu/mm)

Figure 4-14. Soil water potential-soil water content relationship
for Rehovot sand.


















102.



l-

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C-
















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SOIL WATER CONTENT (rmu/rm)

Figure 4-15. Hydraulic conductivity-soil water content relationship
for Rehovot sand.







81
















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Figure 4-18. Soil water potential-soil water content relationship
for Yolo light clay.











































0.2 0.3


SOIL WATER CONTENT (m/m)


Figure 4-19.


Hydraulic conductivity-soil water content relationship
for Yolo light clay.


84


10-1


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Figure 4-20. Soil water potential-soil water content relationship
for Adelanto loam.















1 -





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SOIL WATER CONTENT (rm/rm)

Figure 4-21. Hydraulic conductivity-soil water content relationship
for Adelanto loam.





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