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REMOTE SENSING OF THE WATER STATUS OF A BARE SOIL USING MICROWAVE AND HYDRAOLOGIC TECHNIQUES

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8426185
Mir Mohamad Sadeghi, Aii
REMOTE SENSING OF THE WATER STATUS OF A BARE SOIL USING
MICROWAVE AND HYDRAOLOGIC TECHNIQUES
Ph.D.
University o f A rkansas
University
Microfilms
International
1984
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REMOTE SENSING OF THE WATER STATUS
OF A BARE SOIL USING MICROWAVE
AND HYDROLOGIC TECHNIQUES
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
REMOTE SENSING OF THE WATER STATUS
OF A BARE SOIL USING MICROWAVE
AND HYDROLOGIC TECHNIQUES
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
by
Ali
Mir Mohamad Sadeghi, B.S., M.S.
Shiraz University, Iran, 1972
University of Arkansas, 1979
May 1984
University of Arkansas
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This dissertation is approved
for recommendation to the
Graduate Council
Dissertation Adviser:
Dr. H. D. Scott, Soil Physics
Dissertation Committee:
Dr. D. W. Brewer, Mathematics
Dr'./J. T. Gilmour, Soil Chemistry
Oi_
r ology
Dr. T. C. Keisling, Melj'e'Di
ipDr. W. P. Waite, Electrical Engineering
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TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS
vi
ABSTRACT
vii
LIST OF FIGURES
xii
LIST OF TABLES
xiv
LIST OF APPENDIX TABLES
XV
PREFACE
CHAPTER I.
CHARACTERIZATION OF SOIL PHYSICAL AND HYDRAULIC
PROPERTIES OF A CAPTINA SILT LOAM
ABSTRACT
1
INTRODUCTION
2
REVIEW OF LITERATURE
3
METHODS AND MATERIALS
13
Plot Preparation
Experimental Instrumentation
Experimental Procedure
Soil Samples
Soil Water Diffusivity
RESULTS AND DISCUSSION
Soil Profile Description
Bulk Density
Particle Density
Total Porosity
Particle Size Distribution
Moisture Retention Characteristics
Soil Water Status
Saturated Hydraulic Conductivity
Unsaturated Hydraulic Conductivity
Soil Water Diffusivity
CONCLUSIONS
CHAPTER II.
13
13
17
18
20
23
23
23
27
30
30
30
35
45
45
51
i'67
MEASUREMENTS OF THE DEPENDENCE OF MICROWAVE
REFLECTIVITY ON SOIL MOISTURE PARAMETERS IN A
DRYING SOIL PROFILE
ABSTRACT
60
iv
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TABLE OF CONTENTS (cont.)
Page
INTRODUCTION
61
REVIEW OF LITERATURE
63
METHODS AND MATERIALS
72
Measurement System
Location of Measurements
Theoretical Analysis Models
RESULTS AND DISCUSSION
CONCLUSIONS
CHAPTER III.
72
74
77
82
115
ESTIMATING EVAPORATION:
A COMPARISON BETWEEN
PENMAN, IDSO-JACKSON, AND ZERO-FLUX METHODS
ABSTRACT
118
INTRODUCTION
119
REVIEW OF LITERATURE
120
METHODS AND MATERIALS
123
Instrumentation
Meteorological Data
Experimental Procedure
123
125
125
RESULTS AND DISCUSSION
130
CONCLUSIONS
141
APPENDICES
142
LITERATURE CITED
149
v
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ACKNOWLEDGEMENTS
This dissertation is dedicated to the most important person in my
life, Janet:
my life's companion.
The author would sincerely like to thank Dr. H. D. Scott, major
professor, for his encouragement, assistance, and, in particular, his
patience throughout the study.
A sincere appreciation is expressed to
Dr. W. P. Waite for his constructive assistance.
Gratitude is also
extended to Dr. T. C. Keisling, Dr. J. T. Gilmour, and Dr. D. W.
Brewer for their expert guidance.
A special appreciation is offered to my parents, Ahmad and Shokat
M. Sadeghi and to Joseph and Janet Berrey, whose endearing love and
support made this dissertation possible.
I would like to thank Mr. Branon Thiesse, Ms. Karen Wenzelburger
and Ms. LeAnne Romano for their assistance throughout the conduction
of these experiments.
vi
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ABSTRACT
Laboratory and field experiments were conducted to evaluate the
potential application of remote-sensing and hydrologic techniques to
determine the water status of a drying soil profile.
bare Captina silt loam.
dies.
The soil was a
The experiments were divided into two stu­
The first study was three evaporation-drainage cycles which
were conducted under field conditions from late June through August,
1981.
The objectives of the first study were to evaluate the physical
and hydraulic properties of the Captina soil and to determinate the
relationships between microwave reflectivity and both soil moisture
content and soil matric potential, respectively.
For each drying
cycle, the bare soil was initially saturated and allowed to dry for
extended periods.
Frequent measurements were taken of soil moisture
potential, soil moisture content, and soil surface reflectivities.
Reflectivity measurements were made with a bistatic reflectometer
operating over the frequency ranges of 1 to 2 GHz and 4 to 8 GHz.
After the termination of the experiment, the plot was excavated to
obtain the morphological description and undisturbed soil cores of the
soil profile.
The physical and hydraulic properties of the Captina soil were
evaluated for all three drying cycles of the 1981 experiments.
The
most distinguishing characteristic of the Captina soil at the study
site was the presence of a tongue shaped fragipan located at depths
ranging from 70 to 120 cm.
The large variabilities in the soil water
transport rates through the profile, however, were due to the wavy
vii
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characteristics of the boundary between fragipan and non-fragipan
horizons.
Hydraulic conductivities as a function of soil depth and
soil moisture content were determined on the in situ plots.
Values of
the saturated hydraulic conductivities obtained from the laboratory
experiments were compared with the in situ hydraulic conductivities
when the moisture content was at the maximum wetness.
A relatively
high correlation coefficient of 0.838 was found between these parame­
ters.
Subsequently, the maximum soil water diffusivity of the Captina
soil was found to be 4.6 cm^/day.
Results of the 1981 experiments on determination of the rela­
tionships between microwave reflectivity and soil moisture parameters
showed a strong linear correlation between reflectivity and both volu­
metric moisture content and matric potential, particularly at the
lower frequencies.
However, at the higher frequencies, a similar
coherent interference pattern to those observed in the laboratory
experiment were detected.
These appear to be due to steep moisture
gradients occurring between drying layers, which is probably a func­
tion of drying time, tillage, and evaporative demand of the soil
system.
In another field experiment on the same soil but different loca­
tion, an evaporation-drainage study was conducted.
The objective of
this experiment was to evaluate the potential application of
Idso-Jackson (1979) evaporation equation on the Captina soil.
Due to
the lack of a lysimeter in field, the Idso-Jackson equation was com­
pared with the two other methods which followed somewhat different
approaches.
Two of the methods (modified Penman combination and
viii
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Idso-Jackson) are dependent only on measurements of atmospheric para­
meters whereas the third method (plane of zero flux) is dependent on
measurements of soil parameters.
The soil profile was wet up and
allowed to dry by evaporation and drainage.
Results of the second field study indicated that for the initial
two days after infiltration ceased all three methods predicted similar
evaporative losses.
Differences between the three methods occurred
when the soil moisture content at the soil surface controlled the eva­
poration rates.
Under these conditions the Penman predicted the
highest amounts of water evaporated from the soil surface.
Lower
losses by evaporation were predicted by the Idso-Jackson and zero-flux
methods.
In the case of the Idso-Jackson method this result was
attributed to the influence of clouds on albedo and the importance of
albedo in the predictive equation.
For the zero flux method the
decrease in evaporation was due to lower soil water contents and
matric potentials near the surface which resulted in lower transport
rates to the surface.
ix
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LIST OF FIGURES
Figure
1-1
Page
The schematic diagram for bare soil experiment of
the summer 1981.
14
1-2
Cross-sectional area of each bank within the plot.
16
1-3
Bulk density of Captina silt loam and standard
deviation of cores as a function of soil depth.
28
Particle density of Captina silt loam and standard
deviation of samples as a function of soil depth.
29
Particle size distribution of the profile at the
experimental plot.
31
Upper profile moisture characteristic curves from
the experimental site.
33
Lower profile moisture characteristic curves from
the experimental site.
34
Upper profile semilog transformation of the soil
moisture retention function.
36
Lower profile semilog transformation of the soil
moisture retention function.
37
1-10
Soil water content distributions in Captina soil.
39
1-11
Daily total soil water potential as a function of
soil depth.
40
Diurnal variation of matric potential at various
soil depths.
41
Comparison between average drainage rate and
average evaporation rate at the experimental site.
43
Hydraulic conductivity as a function of soil water
content at 1-3, 3-5, 5-10, and 10-15 cm depth
intervals.
47
Hydraulic conductivity as a function of soil water
content at 1-15 cm depth interval.
48
Hydraulic conductivity as a function of soil water
content in 7 selected soil depth intervals.
49
1-4
1-5
1-6
1-7
1-8
1-9
1-12
1-13
1-14
1-15
1-16
x
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LIST OF FIGURES (cont.)
Page
Figure
1-17
1-18
1-19
2-1
Hydraulic conductivity as a function of the deficit
volumetric water content from the saturation water
content at various soil depth intervals.
52
Evaporation rate as a function of time, indicating
the two stages of drying process.
54
Cumulative evaporation rate for stage II as a
function of (time)^2.
Electromagnetic spectrum, indicating the visible,
infrared, and microwave wavelengths and frequencies.
56
64
Normalized albedo as a function of volumetric water
content at various soil depths.
65
Temperature response to volumetric water content at
various seasons.
67
Relationships between relative dielectric constant
and volumetric water content for sand, loam, and
clay soils.
70
Block diagram of bistatic reflectometer
instrumentation.
73
2-6
Reflection components of the two-layer model.
78
2-7
Daily total soil water potential as a function of
depth during second drying cycle.
83
Diurnal fluctuation in soil matric potential at
various depths during the second drying cycle.
84
Diurnal fluctuation of microwave reflectivity at
1.5 and 6.0 GHz during the second drying cycle.
85
Diurnal fluctuation in soil matric potential at 1
cm depth and microwave reflectivity at 1.5 GHz as a
function of time during the second drying cycle.
87
2 -2
2-3
2-4
2-5
2 -8
2-9
2 -10
xi
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LIST OF FIGURES (cont.)
Page
Figure
Daily variation of microwave reflectivity during
the second drying cycle.
88
Cumulative evaporation during the second and third
drying cycles as a function of time.
89
Diurnal fluctuation in soil matric potential at
various depths during the third drying cycle.
90
Diurnal fluctuation of microwave reflectivity at
1.5 and 6.0 GHz during the third drying cycle.
91
Daily variation of volumetric water content at
various soil depths during the third drying cycle.
92
Microwave reflectivity as a function of soil matric
potential at various depths during the second drying
cycle.
93
Microwave reflectivity as a function of soil matric
potential at various depths during the third drying
cycle.
94
Microwave reflectivity as a function of volumetric
soil water content at various depths during the
third drying cycle.
95
2-19
Microwave reflectivity as a function offrequency.
99
2-20
Moisture release characteristic curve for 0 to 5
cm depth in Captina soil.
101
Sequential stages of soil drying for a rough
surface.
103
Microwave reflectivity as a function of time at
lower and higher frequencies during the second
drying cycle.
105
Field measured and model reflectivity as a function
of frequency for selected days during the second
drying cycle.
108
Predicted volumetric soil moisture content for the
selected days during the second drying cycle.
109
2 -1 1
2-12
2-13
2-14
2-15
2-16
2-17
2-18
2-21
2-22
2-23
2-24
xii
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LIST OF FIGURES (cont.)
Figure
2-25
2-26
3-1
3-2
3-3
3-4
3-5
Page
Positions of the steep moisture gradients (layers)
in the upper soil profile during the second and
third drying cycles.
110
Development of the crust layer during the third and
second drying cycles.
113
Volumetric water content and total soil water
potential profiles during thethird drying cycle.
131
Depth to the zero-flux plane as a function of time
during the three drying cycles.
132
Cumulative
evaporation rates calculated from IdsoJackson, zero-flux, and Penman methods during the
first drying cycle.
134
Cumulative
evaporation rates calculated from IdsoJackson, zero-flux, and Penman methods during the
second drying cycle.
135
Cumulative
evaporation rates calculated from IdsoJackson, zero-flux, and Penman methods during the
third drying cycle.
136
xiii
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LIST OF TABLES
Page
Table
1-1
On-site morphological description of Captina soil.
24
1-2
Selected physical properties of the Captina soil.
26
1-3
Particle size distribution of Captina soil.
32
1-4
Regression coeffieicnets, intercepts (A), and
slopes (B) for the semilog transformation of the
soil moisture retention data.
38
Values of the evaporation rates at 1 cm depth and
drainage rate across 122 cm soil depth during the
second drying cycle.
44
Statistical parameters of the relationship between
K and volumetric water content.
50
Comparison between two methods of determining
saturated hydraulic conductivity.
53
Selected physical properties of the Captina silt
loam.
75
Regression coefficients for reflectivity (-dB) as
a function of soil matric potential (-bar).
96
Regression coefficients for reflectivity as a
function of volumetric soil water content for the
third drying cycle.
98
1-5
1-6
1-7
2 -1
2 -2
2-3
2-4
3-1
Depth to the steep moisture gradients as a function
of time.
112
Average daily climatological data during the three
drying cycles, July 3-July 6, July 8-July 16, and
August 2-August 11, respectively.
139
xiv
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LIST OF APPENDIX TABLES
Page
Table
1
2
3
4
5
6
Reflectivity measurements from first drying
cycle, June 18 through June 22.
143
Reflectivity measurements from second drying
cycle, June 30 through July 7.
144
Reflectivity measurements from third drying
cycle, July 28 through August 1.
145
Tabulated values of the parameters used in Penman
method for three drying cycles.
146
Tabulated values of the parameters used in IdsoJackson method for three drying cycles.
147
Tabulated values of the parameters used in zeroflux method for three drying cycles.
148
xv
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PREFACE
Agricultural applications of remote sensing are becoming
increasingly important as world populations grow and the demand for
better estimates of crop yields continues to rise.
Remote-sensing
techniques are capable of estimating the soil moisture distribution of
large areas within short periods of time.
One aspect of the remote-
sensing research in agriculture relates to the estimation of water
evaporation from bare soil, from vegetation, and from open water sur­
faces.
Because of the complexity of the subject, this research
focused on the behavior of a bare soil.
Laboratory and field experiments using remote-sensing and hydrolo­
gic techniques were conducted in order to evaluate the water status of
a drying soil profile in the Captina soil.
Prior to evaluating the remote-sensing and hydrologic techniques,
it was essential that the physical and hydraulic properties of the
soil be well understood.
The soil at the experimental site was
characterized physically, morphologically, and hydrologically.
Laboratory and field studies were conducted on describing the rela­
tionships between microwave reflectivity and soil moisture parameters
under both homogeneous and nonhomogeneous soil profiles.
The poten­
tial application of the evaporation equation proposed by Idso et al.,
(1979) was evaluated for the Captina soil under subhumid climatic con­
ditions .
This study is presented in three chapters.
In Chapter 1, the
characterization of the physical, morphological, and hydrological
xv i
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properties of a Captina soil are discussed.
However, the discussion
centers on the hydraulic properties of the study site.
In Chapter 2, the relationships between microwave reflectivity and
soil water status are demonstrated.
Further, the ability of remote-
sensing techniques to detect soil moisture content and/or potential
distributions near the surface of the soil was determined.
Laboratory
and field experiments conducted to characterize these relationships
fulfill this need are described.
In Chapter 3, the estimation of evaporation from bare soil is exa­
mined.
The potential application of the most simple remote-sensing
equation to predict evaporation was evaluated.
The possible applica­
tions of the microwave results to the evaporation equation are then
described.
Each chapter is a complete unit containing an abstract,
introduc­
tion, literature review, methods and materials, results and
discussion, and conclusion sections.
The literature cited are com­
bined and listed separately.
xvii
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REMOTE SENSING OF THE WATER STATUS
OF A BARE SOIL USING MICROWAVE
AND HYDROLOGIC TECHNIQUES
Chapter I.
Characterization of soil physical and hydraulic properties
of a Captina silt loam
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ABSTRACT
An in situ experimental study was conducted on a bare plot of the
Captina silt loam.
Three evaporation-drainage cycles were conducted
from late June through August, 1981.
The physical and hydraulic pro­
perties of the Captina soil were evaluated for all three drying
cycles.
After the termination of the experiment, the plot was exca­
vated in order to obtain the morphological description of the soil
profile.
The most distinguishing characteristic of the Captina soil at the
study site was the presence of a tongue shaped fragipan located at
depths ranging from 70 to 120 cm.
The large variabilities in the
water transport data, however, were attributed to the wavy charac­
teristics of the boundary between fragipan and non-fragipan horizons
of the soil profile.
Hydraulic conductivities as a function of soil
depth and soil moisture content were determined from the jln situ plot.
Results indicated that, although hydraulic conductivity relates to
soil moisture content, the slope of the relationship between hydraulic
conductivity and soil depth increased to a maximum value within the
fragipan.
In the fragipan zone, however, a slight change in moisture
content caused a significant variation in hydraulic conductivity
value.
The values of the saturated hydraulic conductivities obtained
from the laboratory experiments were compared with the in situ
hydraulic conductivities when the moisture content was at the maximum
wetness.
A relatively high correlation coefficient of 0.838 was found
between these parameters.
Subsequently, the maximum soil water dif-
fusivity of the Captina soil was found to be 4.6 cm^/day.
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INTRODUCTION
Knowledge of the physical and hydraulic properties of a soil is
required in order to evaluate soil water movement through a drying
profile.
Among the most important characteristics of a soil, however,
are its hydraulic properties, i.e. those which contain and transport
water.
Values of hydraulic conductivity and soil water diffusivity are
two of the most common indications of the hydrological properties of a
soil.
Since there are no reliable methods to estimate these proper­
ties from the more fundamental soil properties, values of hydraulic
conductivity and soil water diffusivity must be measured experimen­
tally.
Accurate values of these soil parameters are necessary for use
in many aspects of agriculture and hydrology.
The object! •-?. of this study was to evaluate the physical and
hydraulic pr</,-
ies of a drying soil profile.
The study was con­
ducted during tVie summer of 1981 on bare soil.
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REVIEW OF LITERATURE
The soil is a highly dynamic and complicated system.
It consists
of solid components which are irregularly fragmented and associated in
an undefined geometric patterns.
50% of the soil volume.
The solid component occupies nearly
The other half of the soil volume consists of
various proportions of liquid and gases.
At optimum soil moisture
contents for plant growth, water and air occupy the same volume per­
centage, each approximately 25 percent by volume.
soil volume taken up by air and water,
With so much of the
it is obvious that air and
water play a vital role in various aspects of agriculture.
However,
the most important of soil phenomena are those physical properties
which are dependent upon the interactions between the solid components
and the liquid in the pores (Childs,
1969 and Hillel,
1971).
When water is applied to the soil through precipitation or irriga­
tion, depending on soil physical characteristics,
the water moves down
through the soil profile or flows over the soil as surface runoff.
The portion which infiltrates will be redistributed through the soil
profile as a result of variations in soil water potential.
The move­
ment of water in the soil profile generally occurs under two con­
ditions:
however,
saturated or unsaturated.
The saturated condition,
is a special case of the unsaturated condition and occurs
when the moisture content is maximum.
The basic law, which describes water movement in soil, was first
proposed by Darcy, the French hydraulic engineer in 1856.
Darcy,
through a series of experiments, obtained the proportionality of the
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flux of water to the hydralic gradient.
This relationship in a three
dimensional form is commonly expressed as,
q = -K x V H
[1]
where q is the soil water flux (m/sec), K is the proportionality fac­
tor which is known as the hydraulic conductivity (m/sec), and V H is
the gradient of the hydraulic head in three-dimensional space.
Equation [1] is the more exact and generalized expression of the
Darcy's Law, which is presented in differential form.
Solution of the
differential form of the Darcy's equation for a particular soil system
is possible, if the boundary conditions are specified.
For the
drainage flux from a soil profile, the vertical distance from the soil
surface, the zero water flux across the surface, and the assumption
that, no net lateral soil-water flow should be specified.
The negative sign in Darcy's equation is used so that positive
values of the flux occur in the positive flow direction.
Powers,
1972; Childs,
1969; Hillel,
1971).
(Kirkham and
The total hydraulic poten­
tial is the summation of the gravitational potential, Hg, pressure
potential, Hp, matric potential, Hm, and osmotic potential, Ho and
additional terms which are not practically important are possible.
Under soil conditions existing in Arkansas, concentration of solutes
in the soil are not significantly high, therefore, the osmotic poten­
tial, Ho, is generally taken as zero.
Under saturated conditions,
values of gravitational and pressure potentials are considered,
whereas for unsaturated conditions,
the important component potentials
are matric, Hm, and gravitational potentials, Hg.
4
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Darcy's law, however, is not applicable to all situations of flow
through porous media.
of less than unity;
The law seems to be valid for Reynolds numbers
that is, Darcy's law applies only as long as the
flow of liquid through the poroud medium is laminar.
Experiments have
shown that the linearity of the variation of the flux as a function of
soil total hydraulic gradients fails at high values of flow velocity
(Hillel, 1971).
Equation [1] is commonly used to evaluate a situation where a
steady-state flow or near steady-state prevails, that is, the flux
remains constant at any point along the conducting system.
In the
field, most soil water transport processes occur under transient-state
conditions, where the magnitude and the direction of flux and
hydraulic gradient vary with time.
of mass is required.
Therefore, the law of conservation
The law of conservation of mass states that in
any confined system mass can neither be created nor destroyed.
Consequently, in a small volume element of soil, the rate of increase
of flux, q, with distance must be equal to the rate of decrease of
water content, with time, t.
In the three-dimensional system, the law
of conservation is expressed as,
where q is the flux in Darcy's law, equation [1],
the flux in three-dimensional space.
V is the gradient of
By substituting equation [1]
into equation [2] the general soil water flow equation is obtained,
30
r - = V.K.VH
[3]
3t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where V H is the gradient of the hydraulic head in three-dimensional
space (m) and K is the hydraulic conductivity (m/sec).
The assump­
tions made in deriving equation [3] are that inertial forces are
negligible in comparison to the viscous forces, the porous medium is
continuously connected, the temperature is isothermal, the soil is
homogeneous and isotropic, and the chemical and biological reactions
do not have a significant impact on the conducting system.
Equation [3] in one dimensional form can be written as:
3t
3z
L
|
This form of the transient-state flow equation can be applied for the
saturated conditions.
Since the components of the hydraulic head, H,
for saturated conditions are the pressure head, hp, and the gravita­
tional head, Hg (the elevation above the reference level), the
hydraulic gradient in equation [4] can be resolved into two components
as,
30 _ 3 t v
3t
3z L
For vertical flow
,3 (Hp+Hg)'
9z
•
[5]
l, and equation [5] becomes,
3z
1® =
3t
f (iSE.+ 1)]
K
3z I
whereas, in horizontal flow
3z
3 Hg/ 3 z
[6]
]
=0,
and equation [5] may be
reduced further to,
3® _ 3_ f w 3 H^ I
3t “ 3x L
3x ' j
[7]
Equation [7] applies to transient-state, horizontal flow of water
through saturated porous medium.
The parameter K represents the
6
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saturated hydraulic conductivity or the permeability.
In many soils,
the hydraulic conductivity does not necessarily remain constant
(Hillel,
1971).
Childs (1950) has pointed out that the permeability
may decrease with time due to the percolating water and releasing
dissolved air into the pores, swelling of colloidal particles, mecha­
nical blocking by movement of the smallest particles into the pores,
the possible growth of microorganisms in the pores, and the chemical
effects of the flowing liquid upon the materials.
Permeability could
also increase with time due to solution in the percolating water of
the initially entrapped air.
As a result, the pores which are filled
with water obviously are effective in conducting the water through
soil, the effective porosity is, however,
limited to those which are
filled with water.
For all these reasons,
the value of the saturated hydraulic con­
ductivity should not be considered as an exclusive property of the
soil alone, since its magnitude is dependent upon the attributes of
soil and water together (Hillel,
1971).
Although flow through the saturated soil is important, usually
flow in the field occurs in an unsaturated condition.
Quantitatively
describing water movement through unsaturated conditions requires the
determination of soil water potential, soil water content, and unsa­
turated hydraulic conductivity relationships.
The difficulty here is
the dynamic nature of these parameters and commonly the solutions to
unsaturated flow problems are obtained through the indirect methods of
analysis, based on approximations or numerical techniques.
The formulation of the flow through unsaturated conditions is
nearly similar to the equations describing the saturated conditions.
7
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The question is whether or not Darcy's law is valid for the unsa­
turated processes.
Kirkham and Powers (1972) point out that in some
porous mediums, the use of Darcy's law does not lead to proper
results, while there are many flow problems for saturated and unsa­
turated soils where the application of Darcy's law leads to valid
results.
However, the derivation of the equation of continuity is not
based on the assumption that Darcy's law is valid.
Equation [7] can be modified for unsaturated flow in a one dimen­
sional system, to give
The difference between equations [7] and [8] is that the hydraulic
conductivity is now a function of either matric potential or moisture
content of the soil (Hillel, 1971 and Kirkham,
1972).
The most impor­
tant change in the transition from saturation to unsaturation is the
decrease in magnitude of the hydraulic conductivities.
Hillel (1971)
has reported that sometimes this decrease in K can be several orders
of magnitude as suction increases from 0 to 100 KPa.
Several methods have been developed to determine hydraulic conduc­
tivity both under saturated and unsaturated soil conditions.
These
methods may be classified as field methods, laboratory methods, and
the calculation from soil physical properties such as pore size
distribution.
Methods for measuring hydraulic conductivity of
saturated soils in the laboratory were reviewed by Klute (1965a) and
for measurement in the field by Boersma (1965a).
Bouma et al. (1971)
and Basak (1972) studied the effect of soil structure on saturated
hydraulic conductivity.
Gumbs (1974) compared the laboratory measure-
8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ments with the field values of the saturated hydraulic conductivites
and proposed a simple linear regression which adequately predicted
saturated hydraulic conductivity from the percent coarse sand.
Baker
(1977) investigated the influence of 5 major factors in the crust test
for in situ measurement of hydraulic conductivity.
In 1979, Fadl
modified an apparatus to measure hydraulic conductivity of undisturbed
soil cores in the laboratory.
His technique could simultaneously
control the two traditional errors caused by side wall flow and the
destruction of the soil structure.
Marshall (1958) showed that the
saturated hydraulic conductivity was related to the size distribution
of the pores.
pore geometry.
However, the difficult part was to characterize this
Laroussi, et al. (1981) suggested that the geometri­
cal characteristics of the porous media can be used to calculate the
hydraulic conductivity in saturated flow.
Laboratory measurement of unsaturated hydraulic conductivity can
be obtained when the flow system is either under steady-state or
transient-state conditions.
Under steady-state conditions, flux and
water content remain constant with time, whereas, in transient-state
conditions, these parameters may vary.
Measurements based on steady-
state conditions are more convenient and often more accurate.
The
difficulty, however, may be to establish the flow of water through the
soil sample, in which flux, gradient, and water content are constant.
Hillel and Gardner (1969) investigated the effect of impeding layers
at the surface on the unsaturated hydraulic conductivity values.
The
results indicated a decrease in conductivity values corresponding to
lower water contents of the transmission zone as the impeding layer
9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
became thicker.
Many investigators also have conducted laboratory
experiments to characterize the effect of soil texture,
pore-size
distribution, and various soil sample dimensions on the values of
unsaturated hydraulic conductivities (Elzeftawy et al.,
al.,1976; Bouma et al., 1971; Baker,
1975; Ahuja et
1977).
Field methods are considered more reliable and represent the
most accurate values of hydraulic conductivity of the soil.
Richards
et al. (1956) and Ogata and Richards (1957) were among the first to
conduct field experiments to estimate hydraulic conductivity using
tensiometer and gravimetric water content data.
Nielsen et al. (1964)
reported that the most common and satisfactory measurements of soil
water potential, and hence the hydraulic gradient have been made with
tensiometers.
However,
they mentioned that the major disadvantages of
the field method are the limited range of moisture contents obtained
at the greater depths, and the fact that values of hydraulic conduc­
tivity are restricted to soil moisture contents for potentials greater
than -0.5 bars (which is the useful range of the common tensiometer).
The relationship between hydraulic conductivity and soil-water
pressure for various soil depths was reported by Nielsen et al.
(1964); Rose et al. (1965); and van Bavel et al.
(1968).
Rose et al.
(1965) have shown that the hydraulic conductivity may be determined in
the field over the entire range of water content, on a soil of nonuniform profile.
The equation was derived using the water balance
based on Darcy's law,
<V
!| dz)dt) {(|BL + 1)jT)-l
[9J
10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where (Kz ) is an average hydraulic conductivity over time interval T =
c 2 “ C1 (sec); P is the rate of precipitation;
gation; E is the rate of evaporation.
I is the rate of irri­
This equation is for a given
volume of vegetation-free soil, where the upper boundary is the soil
surface and the lower boundary a plane at depth z (cm); tj and tz are
the times of observations of consecutive profiles (sec).
Errors
caused by estimating evaporation could be avoided by covering the sur­
face after irrigation.'
In the course of the determination of the hydraulic conductivity,
scientists have become aware of the major disadvantages of the field
and laboratory methods.
Keisling et al. (1977) studied the inherent
variability of soil parameters under field conditions.
They found
that the variability caused from location to location had a major
influence on the variation of soil-water conductivity.
The distribu­
tion of the water flux over space and time was examined by Warrick et
al.
(1976).
They were concerned with the effective utilization of
field-measured soil data, including effects of spatial distribution.
In this field study, the plot was prepared to determine the in
situ hydraulic conductivity as a function of water content and
pressure head.
The method used is known as the "zero-flux".
This
method which also is based on Darcy's law and the equation of con­
tinuity was first proposed by Richards et al.
modified by Arya et al. (1975).
(1956) and then was
During the redistribution of moisture
content in the soil profile, zones of upward and downward movement of
water occurred simultaneously and were separated by a plane of
"zero-flux".
The location of the zero flux plane in the profile at
any time could be identified where the hydraulic gradient, and there-
11
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
fore, the soil water flux is zero.
With this method the plot was
nearly saturated and then allowed to dry due to the drainage and eva­
poration.
Water contents at various soil depths were obtained from
the tensiometer and water retention data.
Average daily hydraulic
gradients were plotted as a function of soil depth, the depth to the
plane of the zero-flux was found to be where the sign of the hydraulic
gradients changed from negative to positive.
However, the precise
depth was obtained by linear interpolation between the two depths.
The position of the plane of zero-flux varies with time after
infiltration of
water ceased.
Knowledge of the rate of change of
water content, hydraulic gradients, and the position of the zero flux
plane at any time would allow K(
0 ) to be calculated from:
[ 10 ]
and
•b
[ 11 ]
where z is the depth to the plane of zero-flux, and za and zj, are the
depth above and below the zero-flux plane, respectively.
The upper
boundary is the 1 cm soil depth, where the first microtensioraeter is
located and the lower boundary is the depth to the position of the
tensiometer located at the bottom of the soil profile.
Volumetric
water content may be obtained from the moisture characteristic curves
for each horizon.
12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
METHODS AND MATERIALS
Plot Preparation
This study was conducted from late June through August,
1981.
The
experimental site was located on the west side of the Main Experiment
Station, at Fayetteville in an area mapped as Captina silt loam.
A plot with dimensions of 3.66 x 3.05 m^ was constructed by
removing the grass vegetation and confining the area with a wooden
frame.
The boards of the frame were placed into the soil to a depth
of approximately 20 cm, leaving 10 cm above the soil surface; this was
designed to confine the soil moisture redistribution within the plot
area.
A drainage ditch also was added around the plot to detect
lateral movement of water caused by rainfall into the plot area.
A
wooden frame roof consisting of three pieces of corrugated fiberglass
was constructed in order to keep out precipitation after the satura­
tion of the plot and during the drying cycle.
The roof was made of
three sections so that it could be easily removed to allow access to
the instruments used to monitor soil water movements.
The roof was
sloped at 10% to prevent leakage caused by the accumulation of water
from rainfall (Figure 1-1).
Experimental Instrumentation
After the initial preparation, the plot was instrumented with
three banks of tensioraeters (macro and microtensiometers) with mercury
13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
SIDE VIEW
TENSIOMETER
ACCESS TUBE
MICRO-TENSIOMETER
SOIL TARGET
3m
TOP VIEW
Figure 1-1
The schematic diagram for bare soil
experiment of the summer 1981.
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
manometers.
These tensiometers were positioned at 1, 3, 5, and 10 cm
depths for microtensiometers, and at 15 cm increments ranging from the
soil depth of 15 cm to 137 cm for macrotensiometers.
Each microten-
siometer was made by grinding the cup end off of a ceramic cup (1
bar porous ceramic, 6 cm long, 0.6 cm O.D.,
1 m m wall thickness).
The
ceramic material was connected via nylon tubing from one side to the
mercury manometer and from the other side to a brass clamp.
The
macrotensiometer consisted of a porous cup (1 bar porous ceramic, 5 cm
long, 2 cm O.D., 3 mm wall thickness), connected through a PVC tube to
a manometer.
Each bank contained one neutron probe access tube in
order to complement the tensiometers (Figure 1-2).
Tensiometer data along with the access tubes measurements were
used to determine the soil moisture potentials and corresponding
moisture contents at various depths for each bank.
In order to minimize the effect of the plot boundary on the ten­
siometers, attempts were made to keep the distance between ten­
siometers and plot boundary more than 15 cm; the same distance also
was used to locate the access tubes and the tensiometers.
This was
done to detect the effects of the water in the tensiometers on the
neutron probe readings.
Figure 1-2 shows the cross-sectional area of
each bank and indicates the location of the two types of tensiometers
which were used in this study.
Due to the importance of the soil
moisture status at the surface, microtensiometers were placed with
small increments at 1, 3, 5, and 10 cm soil depths.
15
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TO Hg MANOMETERS
TENSIOMETERS
ACCESS t u b e
y
Ocm
AP
LQ
£V
AP2
18 cm
15 cm
29 cm
31cm
45 cm
Bt2
46 cm
61 cm
Bt3
61 cm
74 cm
76 cm
Btx
91 cm
102 cm
107cm
117 cm
122 cm
137cm
Figure 1-2
140 cm
Cross-sectional area of each bank
within the plot.
16
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Experimental Procedure
After the plot was instrumented, water then was applied to the
plot through a perforated plastic garden hose.
A steady-state was
established between the application rate and infiltration rate of
water in the plot, in order to keep water from ponding on the soil
surface.
The application rate was found to be approximately 1.4 cm of
water in an hour.
The wetting process at this rate was continued
until the plot appeared saturated.
Immediately after the plot was considered to be saturated, time
zero, the time when all surface water infiltrated the soil, was
assumed to be the beginning of the drying cycle.
The plot then was
allowed to dry simultaneously by evaporation and drainage.
Measurements taken included tensiometer readings, neutron probe
measurements, and soil gravimetric samples.
At the initiation of the
drying cycle, the soil was nearly saturated and the rate of water
movement decreased sharply with time.
Therefore, measurements of the
water status were taken every two hours for approximately three days.
As the soil dried by evaporation and drainage, the frequency of the
measurements were reduced to three times a day, morning, solar noon,
and late afternoon.
Later the frequency of measurements was reduced
to two times a day, and finally to one daily measurement in the after­
noon.
There were three drying cycles; the first drying cycle was
stopped in the fourth day due to a heavy rain, which caused flooding
in the plot.
The second and third drying cycles were complete cycles.
The data obtained from each cycle included soil samples and ten­
siometer readings.
17
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Soil Samples
Five soil cores with the dimensions 6 cm x 5 cm and five disturbed
soil samples were taken from the depths corresponding to the ten­
siometer positions.
Soil cores samples were used to determine
saturated hydraulic conductivity, moisture retention characteristic for
pressures less than one bar, and bulk density.
Undisturbed soil
samples were used to determine particle density, particle size distri­
bution, and moisture retention characteristics for pressures ranging
from one to fifteen bars.
Core samples were used to determine
saturated hydraulic conductivity by the constant head method using
Darcy's
Law as follows;
K = QL
where Q
is the volume of water
/ (At*
V H)
[1]
in cm^,A isthe cross sectional area
of the soil cores in cra^, L is the length of the core samples in cm,
V H is the net pressure head on the soil core in cm, and t Is time of
collecting a known volume of water in hr.
In order to show the uniformity of the Captina soil, water con­
tents were plotted against the natural logarithm of matric potentials,
the regression line was defined by the following equation:
H
= a exp (b
0)
[2]
Tu
where a and b are regression constants,
Hm is matric potential,
0V
is volumetric water content.
18
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Bulk density was determined by dividing the weight of dry soil in
each core by its volume.
The disturbed soil samples were used to
determine particle density by the pycnometer method, particle size
distribution by mechanical analyses, and soil moisture characteristics
for pressures more than one bar (Black et al.,
1965).
Unsaturated hydraulic conductivity was determined from the
hydraulic gradient and soil water flux using the zero-flux method.
In
a soil profile, which is subjected to both evaporation and drainage,
the zero flux plane will separate the portion of soil water which
moves upward in response to evaporation from that which moves downward
in response to drainage.
this plane.
However,
there is no water movement across
The flux of water at any depth is obtained by integrating
the rate of change in moisture content (obtained from the moisture
release curve) with time for a distance from the zero flux plane to
the depth in question.
Hydraulic gradients were obtained from ten-
siosstsr measurements at various sell d a p th f •
The position of the
plane of zero-flux moves downward as the soil profile dries.
The
hydraulic conductivity can be determined by dividing the soil water
flux by the potential gradient as follows;
K(0)_ = { /0 (3£)dz}/(2S“)
a
z, 3z
9z ~
a
a
r_.
L3J
3z
zb
where a and b are the depths in soil profile above and below the depth
of zero flux plane, Z and K(
0 )a, K( 0 )b are the hydraulic conduc-
19
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tivities corresponding to the water contents at specified depths a and
b (Arya et al., 1975).
Functional relationships were developed between hydraulic conduc­
tivity and both volumetric water content, © v and deficit volumetric
water content from the saturation, (© s - © v).
The equations are
described as follows:
K(0) = K(0S ) exp (60v )
[5]
K(0) = K(0S ) exp
[6 ]
where K ( 0 S ) and
S(0s - ©v )
6 are regression constants and K(©v ) represents the
hydraulic conductivity at saturation, where © s = © v .
Daily flux of liquid water across the 1 cm soil surface or daily
approximate evaporation was calculated, using Eqs.
[3] and [4].
The
evaporation rates were then plotted as a function of time during each
drying cycle.
This was done to identify the stages of evaporation.
Soil Water Diffusivity
The soil water diffusivity, D, for the Gaptina soil was calculated
in two ways, depending upon the water content; for the water contents
during the first stage of evaporation, D was determined from the K at
that water content and the slope of the water retention curve
(specific water capacity).
The relation between D, K, and specific
water capacity is described as follows:
[7]
20
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For the water content at the beginning of the second stage of eva­
poration or less, D was determined from the solution of unsaturated
flow equation as described by Fick's first law
F = -D
[8 ]
where F is the flux of water (cm^/cm^ * sec).
Combining Eq.
[8] with the law of conservation of mass gives the
equation which has become known as Fick's second law.
[9]
According to Crank (1956), Eq.
[9] can be solved analytically for
a semi-infinite slab with constant diffusivity, D.
To calculate flux
at the upper boundary, the solution is as follows,
F = (0. - 0O ) (D/irt)^
where:
[1 0 ]
0 i = the initial water content, water content at the
beginning of stage II.
© 0 = the water content at the soil surface, assumed to be
zero.
Cumulative evaporation, E, can be obtained by integrating Eq.
[10]
with respect to time.
E = 2 (Qi - 0q ) (Dt/tr)^
[1 1 ]
21
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For further simplification we assumed the coefficient, A to be
A = 2(0± -0o )(D/u)^
t12^
E = kit"2
[13]
Then
In order to calculate the soil water diffusivity for evaporation
stage II, the cumulative evaporation was plotted against the square
root of time in days; coefficient A is the slope of the regression
line.
Knowing the magnitude of this coefficient, and the values of
and 0O, the soil water diffusivity was calculated using Eq.
[12].
22
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Q
RESULTS AND DISCUSSION
Soil Profile Description
A soil profile description made at the study site is given in
Table 1-1.
The soil is in an area mapped as Captina silt loam.
The
Captina soil is described as a moderately well drained, slowly per­
meable, and dominated in the lower horizons by a firm, brittle fragi­
pan.
It is classified as a Typic Fragiudult in the fine, silty,
mixed, mesic family.
The most distinguishing characteristic of the Captina soil at the
study site is the presence of a fragipan located at depths ranging
from 70 to 120 cm.
The boundary between fragipan and non-fragipan
horizons was found to be wavy (tongue shaped).
This wavy boundary
will cause large variabilities in the transport of water within this
region of the soil profile.
The Ap horizon, the first 18 cm of the
top soil, has a fine granular structure, whereas in Ap2 a massive
structure was observed from 18 to 30 cm.
The B horizon starts at the
30 cm depth, where a sudden change in color from brown to yellowish
brown was observed.
Data in Table 1-2 represent the selected physical
properties of the Captina profile at the study site.
Data are pre­
sented for bulk density, particle density, total porosity, percent of
sand, silt, and clay, and saturated hydraulic conductivity.
Bulk Density
Two zones of relatively high bulk density were identified in the
profile.
The first peak was near the bottom of the Ap horizon.
In
23
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Table 1-1:
On-site morphological description of Captina silt loam.
Horizon
Depth
(cm)
Ap
Ap2
0-18
18-29
Description
Dark grayish brown (10YR 4/2) silt loam; weak
fine granular structure; friable; few fine
roots; clear smooth boundary.
Brown (10YR 5/3) silt loam with few fine faint
yellowish brown (10YR 5/4) mottles; massive
structure; friable; common fine roofs; numerous
dark grayish brown (10YR 4/2) worm and root
channels; many discontinuous pores (1-4 mm
dia.); 1% coarse fragments; clear wavy boun­
dary.
Bt
29-45
Yellowish brown (10YR 5/4) silt loam; weak
subangular blocky structure; friable; few fine
roots; numerous dark brown ( 10YR 4/3) worm and
root channels; few pores (1-6 mm dia.); clear
smooth boundary.
Bt2
45-61
Yellowish
brown (10YR 5/6) silt loam; medium
subangular blocky structure; friable; thin
patchy yellowish brown (10YR 4/5) clay films on
vertical faces of peds; few fine roots; few
pores (1-1.5 ram dia.); clear wavy boundary.
Bt3
61-72
Yellowish brown (10YR 5/4) silty clay loam;
moderate medium subangular blocky structure;
thin patchy yellowish brown (10YR 5/4) clay
films on vertical faces of peds; few fine
roots; a few dark grayish brown (10YR 4/2)
coatings in root channels; few fine pores; 5%
coarse fragments; clear irregular boundary.
Btx
72-102
60% consists of red (2.5YR 5/6) silty clay
loam; moderate medium subangular blocky struc­
ture; firm; thin patchy red (2.5YR 5/6) clay
films on vertical and horizontal ped faces; no
roots; many fine black Fe-Mn stains; clear wavy
boundary.
40% consists of red (2.5YR 4/6)
heavy silt loam with many common medium
distinct fine permanent pinkish gray (7.5YR
6/2) and yellowish brown (10YR 5/6) mottles;
weak medium prismatic structure; very firm,
slightly brittle; common pores (0.5-2 mm dia);
many coarse distinct black Fe-Mn stains on
prism faces; clear wavy boundary.
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1-1:
On-site morphological description of Captina silt loam,
(continued)
Horizon
Depth
Bx
102-117
Red (2.5YR 5/6) silty clay loam with common
fine prominent dark yellowish brown (10YR 4/6)
and some yellowish brown (10YR 5/4) mottles;
prismatic structure; firm and brittle; common
pores (0.5-2 m m dia.); many firm black Fe-Mn
stains on prism faces, 10% coarse fragments;
clear wavy boundary.
Bt
117-140
Red (2.5YR 4/4) silty clay loam with many
coarse medium distinct pale brown (10YR 6/3)
and yellowish brown (10YR 5/4), common coarse
distinct pinkish gray (7.5YR 6/2), and a few
fine prominent strong brown (7.5YR 5/6)
mottles; moderate coarse subangular blocky
structure; firm reddish brown (2.5YR 4/4) and
dark yellowish brown ( 10YR 4/4) clay films;
vertical gray seams; common fine black Fe-Mn
stains and nodules; gradual wavy boundary.
Description
25
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26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
this horizon, bulk density ranged from 1.27 gm/cm^ at the surface to
1.41 gm/cm^ i-n the lower depth of the same horizon.
This increase in
bulk density within the same horizon was due to the presence of a plow
pan.
Bulk density remained essentially constant around 1.40 gm/cm^
along the Ap2 horizon starting at 18 cm to the end of the B1 horizon
at 45 cm.
The second bulk density peak was found in the fragipan.
In
the fragipan zone which ranged from Btx to BX, values of bulk den­
sity were higher in comparison to the non-fragipan horizons.
However,
the maximum values of the bulk densities in the fragipan increased to
1.64 g/cm^, which is considered to be relatively high for silt loam
soils.
The overall average bulk density of the soil profile was 1.47
gm/cm^.
This value compares favorably with the average bulk density
of 1.51 gm/cm^ found in 1976 by Paetzold on the same soil but at a dif­
ferent location.
The data in Figure 1-3 show the variation in bulk
densities as a function of soil depth.
Particle Density
Variations of particle density as a function of soil depth are
shown in Figure 1-4.
Generally values of particle density were
nearly constant in a soil profile which is morphologically uniform.
The minimum value for particle density in Captina profile as 2.49
gm/cm^j which was found near the soil surface.
This value is con­
sidered to be low which is probably due to the presence of higher
organic matter content near the soil surface.
Values of particle den­
sity increased to 2.62 g/cnP at the 30 cm depth and remained fairly
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
SOIL BULK DENSITY Ig/cm ^i
1.2
2.0
1.4
CAPTINA SOIL
CYCLE 2
20
■
40
DEPTH
| cm I
60
80
100
120
140
Figure 1-3
Bulk density of Captina silt loam and
standard deviation of cores as a function
of soil depth.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
PARTICLE
2 .3
DENSITY (g /c m 3 )
2 .5
2 .7
2 .9
20
DEPTH
| cm )
40
60
80
CAPTINA SOIL
100
CYCLE 2
120
1401
Figure 1-4
Particle density of Captina silt loam and
standard deviation of samples as a function
of soil depth.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
constant in a small range from 2.61 to 2.64 gm/cra^ throughout the soil
profile (Table 1-2).
Total Porosity
Porosity ranged from 0.49 cm^/cm^ in the Ap to 0.374 in Btx
horizon.
Data in Table 1-2 indicate that if particle density is
fairly constant, the variation of porosity in the soil profile is
inversely related to the magnitude of the bulk density.
Particle Size Distribution
Particle size distribution was determined using mechanical analy­
ses (Blake et al., 1965).
The data in Figure 1-5 show the accumula­
tive distribution of particle size throughout the soil profile.
Captina soil is dominated by a large quantity of silt.
largest textural component was clay.
The
The second
The lowest amount of clay of 10%
was found near the surface in the Ap horizon; the highest quantity of
clay was 30% which was found in the B23t horizon.
The sand fraction
was the lowest percentage size fraction in the profile and varied from
25% in Ap to 18% in Btx.
The maximum sand content was 40% and was
found in the Bt horizon.
This is probably due to the fact that this
soil was formed from the weathering of sandstone.
The data in Tables
1-2 and 1-3 show the particle size distributions of the Captina soil.
Moisture Retention Characteristics
The functional relationships between moisture content and matric
potentials less than one bar are shown in Figures 1-6 and 1-7.
The
maximum moisture content of 0.432 cm^/cm^ was found at saturation in
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a>
,c
u
u
cO
0)
fH
iH
iw
O
a
o
xs
u
U-J
0
3
<
C
o
4J
P
•H
U
S
<
4J
CO
•H
•
■u
O
rH
P.
0)
N
rH
•H
CO
CO
4J
a)
rH
a
•H
4-)
U
CO
Ph
C
0)
e
iH
U
0)
a
X
<u
m
I
a;
u
D
GC
•H
3 0V ±N 3 0 H 3 d
Nouvwwns
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1-3:
Particle size distribution of Captina silt loam.
Percentage Composition
CSi
MSi
FSi
Total
Silt
Total
Clay
25.5
35.7
22.5
6.0
64.1
10.4
SIL
13.8
28.6
32.4
22.6
6.3
61.3
10.1
SIL
7.4
11.1
22.9
32.1
24.5
6.7
63.3
13.8
SIL
2.0
6.8
10.5
21.0
31.9
24.7
6.3
62.9
16.1
SIL
0.7
1.6
6.1
9.7
18.5
29.3
21.8
8.1
59.2
22.3
SIL
0.2
0.4
1.3
5.9
9.5
17.3
29.2
17.6
8.4
55.2
27.5
SIL
88-93
0.4
0.5
1.4
6.1
9.6
18.0
27.9
18.4
6.0
52.3
29.7
SICL
103-108
0.4
0.6
1.4
6.3
10.1
18.8
29.9
17.7
9.6
57.2
24.0
SIL
118-123
0.8
0.8
1.6
6.4
29.9
39.6
11.7
15.7
7.8
35.1
25.3
L
133-138
0.7
0.7
1.3
5.7
9.9
18.3
27.6
17.5
11.6
56.7
25.0
SIL
Depth
Interval
(cm)
VCS
CS
MS
FS
0-5
0.7
1.1
2.3
8.7
12.6
11-18
1.4
1.8
2.6
8.9
28-33
0.9
1.4
2.1
43-48
0.6
1.1
58-63
0.4
73-78
VFS
Total
Sand
Textural
Classification
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 .6 0
0.50
AP 0 *1 0 cm
Bt 2 8 - 4 8 cm
Bt2 5 8 - 6 3 cm
0.40
0.30
0.20
CAPTINA SOIL
CYCLE 2
0.10
0
-100
-200
-4 0 0
600
-7 0 0
•8 0 0
•9 0 0
-1000
MATRIC POTENTIAL I cm)
Figure 1-6
Upper profile moisture characteristic curves from
the experimental site.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.60
o.so
o B I2,B x
7 4 -9 4 cm
1 0 4 -1 0 9 cm
■ Bt
1 2 0 -1 2 5 cm
0.40
0.30
0.20
CAPTINA SOIL
0.10
CYCLE 2
0
100
-200
-3 0 0
-4 0 0
-6 0 0
-7 00
-8 0 0
900
1000
MATRIC POTENTIAL|cm|
Figure 1-7
Lower profile moisture characteristic curves from
the experimental site.
the Ap horizon, and the minimum value of 0.271 cm^/cm^ was found at
the 1 bar pressure in the B21t horizon.
The BX2 horizon retained
relatively lower amounts of moisture than the horizons above and
below.
This is possibly due to the presence of the fragipan in this
horizon.
In order to determine if the data fit equation [2], the
moisture retention data was transferred into semi-log plots.
The data
in Figures 1-8 and 1-9 describe this functional relation for Ap and
Bit horizon.
The correlation coefficients ranged from 0.984 at the Bt
horizon to 0.967 at the Bx horizon.
Higher values for the slopes of
the regression lines were obtained in the deeper horizons which is
possibly due to the accumulation of clay particles in the soil profile
due to the restrictive nature of the fragipan.
The higher the slope
of the regression line, the higher the dependence of water content on
matric potential.
coefficient values,
The data in Table 1-4 represent the correlation
intercepts, and slopes of regression lines along
with the mathematical models for each soil horizon.
Soil Water Status
Evaluation of the soil water relations is the most important step
in the interpretation of the functional relationships between soil
moisture and reflectivity of the soil, especially near the soil sur­
face.
The data in Figures 1-10 through 1-12 represent the daily mean
volumetric water contents, daily total hydraulic potentials, and diur­
nal variation in matric potentials as a function of soil depth.
A
comparison between the broken line (Theoretical saturation line), and
the solid line (line representing the variation in water content at
the beginning of the drainage cycle) in Figure 1-10 indicated that the
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2
Hm » 3 .2 7 x 1 0 o x p |-2 8 .a s e v I
1
r3. 0.989
AP HORIZON
I sieq | uih ' 1 V|JLN3X0d
ai
01H1VH
CAPTINA SOIL
CYCLE 2
001
0
0.1
04
0.2
0.5
0.6
SOIL WATER CONTENT, 0 v |c m 3/cm 3 1
Figure 1-8
Upper profile semilog transforma­
tion of the soil moisture reten­
tion function.
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Hm a t6 » 1 0 o x p |- 3 a 2 8 9 v
ai
MATRIC
POTENTIAL ,Hm I bars |
St HORIZON
CAPTINA SOIL
CYCLE 2
001
ai
0.2
0.3
0.4
0.5
0.6
SOIL WATER CONTENT, 6v|cnP/cm^ I
Figure 1-9
Lower profile semilog transforma­
tion of the soil moisture reten­
tion function.
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1-4.
Soil
Horizon
Regression coefficients (R^), intercepts (A), and slopes
(B) for the semilog transformation of the soil moisture
retention data.
R^
A
B
Ap
0.980
8.09 + 0.46
-28.85 + 1.37
Bt
0.984
7.38 + 0.37
-30.28 + 1.24
Bt2
0.981
9.99 + 0.53
-35.85 + 1.62
Bt3
0.981
10.02 + 0.53
-35.98 + 1.62
Btx
0.971
15.12 + 0.96
-48.32 + 2.77
Btx
0.971
15.12 + 0.96
-48.32 + 2.77
Bx
0.967
18.19 + 1.21
-59.58 + 3.61
Bt
0.873
23.14 + 3.51
-73.42 + 9.32
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
VOLUMETRIC WATER CONTENT (cm 3/cm 3 |
0.24
0.28
0.32
0.36
040
0.44
20
CAPTINA SOIL
40
SOIL DEPTH
I cm I
CYCLE 2
60
80
days after
saturation
100
Figure 1-10
Soil water content distributions
in Captina soil.
39
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TOTAL P O T E N T IA L|bars!
-0.1
-0 .3
-0.4
OAYS AFTER SATURATION
20
40
60
E
u
X
w
Q
80
_j
CAPTINA SOIL
O
(/>
CYCLE 2
100
120
140
Figure 1— 11
Daily total soil water potential as a function
of soil depth.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
15 cm
-200
10 cm
— -4 0 0
_i
5 cm
3 cm
-6 0 0
.@1 cm
-8 0 0
CAPTINA SOIL
CYCLE 2
-1000
40
80
120
160
200
TIM E I hours I
Figure 1-12
Diurnal variation of matric potential at
various soil depths.
240
plot was nearly saturated at time zero.
The data in Figure 1-11
illustrate the variation of daily total hydraulic potential as a func­
tion of depth.
The total potential line at the start of this drying
cycle (day zero) indicated that the profile was saturated from 100 cm
soil depth to the deeper profile.
A positive slope indicates water
moving upward, while a negative slope indicates the downward movement
of water.
The diurnal changes in soil matric potential at the selected
depths are presented in Figure 1-12; the maximum diurnal variation was
observed during the first few days at the beginning of the drying
cycle, especially for the 1, 3, and 5 cm depths.
These results indi­
cate the dynamic nature of soil water flux in the surface of a field
soil which is subjected to diurnally varying environmental conditions.
Similar results were obtained by Jackson et al. (1973).
A comparison was made between the rate of drainage and the rate of
evaporation on the study plot (Figure 1-13).
The average drainage
rate decreased from 2.56 cm/day to 0.712 cm/day within 24 hours,
followed by a slow change in drainage rate after the first day of
the drying cycle.
From the second day during the drying process, the
rate of evaporation and the rate of drainage were decreasing uni­
formly.
These results indicated that as long as the profile is
saturated the fragipan did not inhibit the rate of drainage through
the profile.
However,
the fragipan effect has become more prominent
in the redistribution of the water content later in the drying period.
Data in Table 1-5 represent the evaporation rate across the 1 cm depth
and the drainage rate across the 122 cm depth of the soil profile
during the second drying cycle (longest drying cycle).
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.5
FLUX OF
WATER
I cm/day)
CAPTINA SOIL
CYCLE 2
2.0
1.5
drainage rate
1.0
evaporation rate
0.5
0.0
0
1
2
4
3
5
6
7
DAYS AFTER THE CESSATION OF INFILTRATION
Figure 1-13
Comparison between average drainage rate and
average evaporation rate at the experimental
site.
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1-5:
Date
(day)
Values of the evaporation rate (flux) at 1 cm depth and
drainage rate (flux) across 122 cm depth during the second
drainage cycle.
Evaporation Rate
cm/day
Drainage Rate
cm/day
7-1-80
0.420
2.560
7-2-80
0.341
0.712
7-3-80
0.472
0.268
7-4-80
0.318
0.168
7-5-80
0.242
0.106
7-6-80
0.203
0.093
7-7-80
0.158
0.051
1
7-8-80
0.031
7-9-80
—
0.056
7-11-80
—
0.025
7-14-80
—
0.019
7-17-80
—
0.006
^The flux of water at the soil surface could not be calculated because
the microtensiometers did not operate at that degree of dryness.
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Saturated Hydraulic Conductivity
Values of saturated hydraulic conductivity (Table 1-2) were deter­
mined on undisturbed cores taken at selected depth intervals using the
constant head method (Klute, 1965a).
The K values ranged from 1.10
cm/day in the fragipan to 65.3 cm/day in the Bt horizon.
The second
lowest value of K was obtained in the 13-18 cm depth interval, which
is probably due to the existence of the plow pan in this region.
The
variation in K in the fragipan corresponded to those of bulk density;
the higher the bulk density, the lower the K.
Due to the massive
structure of the Ap2 horizon, K was significantly low at 3.55 cm/day.
The magnitude of the K increased in the B t , Bt2, and Bt3 horizons,
which is possibly due to the blocky structure of these horizons.
A
vast variation in K was found in the Btx, Bx and Bt horizons which are
in the range of fragipan.
Since the boundary between fragipan and
non-fragipan was found to be wavy (tongue shaped), the soil core
samples for determination of the K values could have been taken from
the non-fragipan region of the profile.
Unsaturated Hydraulic Conductivity
Unsaturated hydraulic conductivity was determined iii situ as a
function of soil depth, hydraulic gradient, and soil moisture content.
The
situ methods have shown to be more reliable than the laboratory
methods in determining unsaturated hydraulic conductivity (Richards et
al., 1957).
The "zero flux" method (equations 3 and 4) were used to determine
K in the field.
The magnitude of the in situ hydraulic conductivities
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
decreased with soil water content and soil depth.
The high values of
K were obtained for hydraulic conductivity in all selected depths at
the beginning of the drying cycle, the values of K became smaller as
drying of the profile continued.
The data in Figures 1-14 and 1-15
represent the linear regressions between the logarithm of the unsa­
turated hydraulic conductivity and soil moisture content for selected
depth intervals within 15 cm of soil surface.
Due to the importance
of the moisture status near the soil surface, the K values were deter­
mined separately for each selected depth intervals.
were plotted as a function of soil water content.
The K values then
The linear
regression line in Figure 1-15 was obtained when values of k and
from all depth intervals within the surface 15 cm were considered
collectively.
The maximum slope of the regression curves were
obtained in the fragipan and a relatively high slope was found between
10 to 15 cm depth which is due to the presence of the plow pan.
The
hydraulic conductivities of the 7 soil depth intervals below 15 cm
soil depth were determined and were plotted as a function of soil
water content (Figure 1-16).
The slopes of the regression curves
range from 44 in the Ap to 131 in the Btx.
Regression coefficients, r^, ranged from 0.956 at Ap2 to 0.855 at
Bx and Bt.
The data in Table 1-6 show the magnitude of the
selected parameters which describe the mathematical model for the
functional relationships between unsaturated hydraulic conductivity
and volumetric soil water content.
Results indicated that, although K
relates to soil moisture content, the slope of the relationship bet­
ween K and soil depth increased and the maximum value of the slope was
found within the fragipan.
In the fragipan zone, however, a slight
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CAPTINA S IL T
LOAM
9 2nd DRYING CYCLE
& 3rd DRYING CYCLE
/
X
/
•
A
A
A
•
A/
A //
/
‘
•
1 — 3 cm
*
°
5 — 10cm
K> 4 .2 4 x 10~1 ex p (59 8vl
K » 1 .0 x 1 0 6 8 x p |2 9 .8 e v |
r Za 0 .9 6 9
rZ = 0 .9 0 2
/
A,
^
•
•
HYDRAULIC
CONDUCTIVITY, K fc m /d a y l
•
A
X
Sa
s'
•
s/9
•
/A
y®
3 — 5 cm
0.32
A
10— 15cm
K a 4 .2 4 x l0 ”^ e *p l5 1 8^ l
•
0.30
/
A
K = 1.4xld"8oxp |4 0.19 v |
2
r s 0 i8 9 4
0.34
0.36
0.38
r2 = 0 .9 4 2
0.40
Q 30
0.32
0.34
0.38
038
0.40
042
SOIL WATER C 0 N T 6 N T ,e » |c m 3/cm 3 |
Figure 1-14
Hydraulic conductivity as a function of soil
water content at 1-3, 3-5, 5-10, and 10-15 cm
depth intervals.
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
HYDRAULIC
CONDUCTIVITY
| cm/day |
CAPTINA SILT LOAM
1 —15 cm
2 Qd DRYING CYCLE
0.1
3Ld DRYING CYCLE
0.01
e
K = 6.O5x1O_9e x p (4 4 .2 5 0 v!
r2= 0 .8 7 Q
0.001
0.30
0.32
0.34
0.36
0.38
0.40
0.42
SOIL WATER CONTENT!cm3/cm 3 1
Figure 1-15
Hydraulic conductivity as a function of
soil water content at 1-15 cm depth
interval.
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1T
HYDRAULIC
CONDUCTIVITY|cm/day |
CAPTINA SOIL
CYCLE 2
.Oil
.28
.30
.32
.34
.36
.38
.40
SOIL WATER CONTENT|cm3/c m 3 )
Figure 1-16
Hydraulic conductivity as a function of.
soil water content in 7 selected soil
depth intervals.
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1-6:
Statistical parameters of the relationship between K and
volumetric water content Captina silt loam.
Horizon
(b)
Intercept
(cm/day)
Slope
r2
Ap
6.05 x 10-9
44.25
0.870
15-31
Ap/Ap2
2.56 x 10-9
53.98
0.956
31-46
Bt
8.39 x 10-11
66.34
0.931
56-61
Bt2
5.18 x 10-13
79.29
. 0.910
61-76
Bt3/Btx
1.93 x 10-16
96.00
0.936
76-91
Btx
8.50 x 10“ 23
131.35
0.911
91-107
Btx/Bx
7.17 x 10"18
101.93
0.945
Bx/Bt
1.25 x 10“ 18
107.62
0.855
Depth
Interval
(cm)
1-15
107-122
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
change in moisture content caused a significant variation in hydraulic
conductivity values.
A comparison was made of the K values obtained using the labora­
tory method and the theoretical method.
In this method the LnK
values were plotted as function of the deficit volumetric water con­
tent from the saturation volumetric water content,
( ®s - Ov ).
The
data in Figure 1-17 represent the regression curves which describe the
function relationships between unsaturated hydraulic conductivity and
@s ~
®v)»
Theoretical values for K were obtained by assuming the
volumetric water contents be the same as the volumetric water content
at saturation, that is
®s =
®v •
With this assumption, the K values
were the same as the saturated conductivity values and the magnitude
of the K at saturation was the value of the intercept of the
regression model.
Data in Table 1-7 represent the values for K deter­
mined in the laboratory by the constant head method, and the theoreti­
cal method obtained from the functional relationships between K and
( 0 s — Ov).
A relatively high correlation coefficient of 0.838 was
found between these parameters.
Soil Water Diffusivity
The values of evaporation during the drying process were nor­
malized to the potential evaporation rates obtained for the same
period of time from both pan-evaporation data and Penman method deter­
mined for the same experimental site (Saulsberry et al., 1982).
The
average normalized evaporation rates then were plotted as a function
of time after the cessation of infiltration (Figure 1-18).
This was
done to identify the classical stages of the soil water evaporation.
51
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10
CAPTINA SOIL
HYDRAULIC
CONDUCTIVITY I cm/day |
CYCLE 2
.004
.024
.044
.084
.064
.104
.124
DEFICIT VOLUMETRIC WATER CONTENT FROM SATURATION ( cm3/cm 3 1
16s - ©vI
Figure 1-17
Hydraulic conductivity as a function of
the deficit volumetric water content from
the saturation water content at various
soil depth intervals.
52
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Table 1-7:
Depth
Interval
(cm)
Comparison between two methods of determining saturated
hydraulic conductivity.
Horizon
Saturated Hydraulic Conductivity, K
----------------- c.m/day-------------------Calculated
Experimental
15-31
Ap/Ap2
24.40
17.89
31-46
Bt
61.00
38.05
46-61
Bt2
57.00
22.96
61-76
Bt3/Btx
12.70
23.71
76-91
Btx
8.60
13.74
91-107
Btx/Bx
3.60
8.56
Bx/Bt
2.78
9.91
106-122
53
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.50
STAGE I
CAPTINA SOIL
CYCLE 2
0.40
>s
a
"O
s
E
o
UJ
STAGE II
cc
z
Oi
o 0.20
£
DC
o
a.
$
UJ
0.10
0
0
1
2
3
4
5
6
TIME | days |
Figure 1-18
Evaporation rate as a function of time, indicating
the two stages of drying process.
7
Soil water diffusivity for the evaporation at stage II was calcu­
lated from data shown in Figure 1-19.
Cumulative evaporation, E
during stage II (drying period from July 1 through July 7), were
plotted as a function of square root of time (day).
also used by Black et al., 1969.
This method was
The coefficient, A in equation (13)
was the slope of the regression line and was determined to be 0.62
cm/day.
Weighted-mean diffusivity was 4.6 cm^/day using equation [12]
with the assumptions that ®o, which the water content at the boundary
(x = o) is equal to zero, and0i to be the magnitude of the water con­
tent at the beginning of stage II for 0 to 20 cm soil depth.
The
value for ®i was experimentally determined to be 0.25 cm^/cm^-
Black
et al. (1969) obtained a diffusivity value of 13 cm^/day on a sandy
soil.
55
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CUMULATIVE
EVAPORATION ( mm^O/day |
10.0
8.0
CAPTINA SOIL
6.0
CYCLE 2
4.0
SLOPE ( A |“=6.2 mm ^ O /ld a y s l^ 2
2.0
0
1
2
3
4
TIME I days )1/2
Figure 1-19
Cumulative evaporation rate for
stage II as a function of (time)'2.
56
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CONCLUSIONS
The physical properties, hydraulic characteristics, and morpholo­
gical descriptions of the Captina soil were evaluated in this in situ
field study.
The results from the three drying cycles discovered the
following conclusions.
1.
The most distinct characteristic of the Captina soil was the pre­
sence of a fragipan located at depths ranging from 70 to 120 cm.
The boundary between fragipan and non-fragipan was found to be
wavy (tongue shaped), which caused large variabilities in the soil
water transport.
The fragipan contained less silt and sand, but
more clay in comparison with the horizons above.
This resulted in
the restriction of drainage from this soil profile, but did not
inhibit the drainage completely.
2.
Hydraulic conductivity,
as a function of volumetric soil water
content was determined in situ at various soil depth intervals
ranging from 1 to 130 cm.
When the logarithms of hydraulic con­
ductivity were plotted as a function of volumetric soil moisture
content, the maximum slope of the regression curves were in the
fragipan; a relatively high slope also was found between the 10 to
15 cm depth.
plow pan.
The latter was probably due to the presence of the
Consequently, a small change in moisture content within
the fragipan and plow pan resulted in a significant change in
hydraulic conductivity values.
3.
A relatively high correlation coefficient of 0.838 was obtained
between the saturated hydraulic conductivities determined on
57
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undisturbed cores in the laboratory and the in situ hydraulic con­
ductivities when the moisture content assumed to be at its maximum
wetness.
4.
The soil water diffusivity of 4.6 cm2/day was calculated for the
Captina silt loam.
This agreed well with the value obtained by
Paetzold (1976) on the same soil but at a different location.
58
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REMOTE SENSING OF THE WATER STATUS
OF A BARE SOIL USING MICROWAVE
AND HYDROLOGIC TECHNIQUES
Chapter II.
Measurements of the Dependence of Microwave Reflectivi
on Soil Moisture Parameters in a Drying Soil Profile
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ABSTRACT
Field experiments were conducted to determine the relationships
between microwave reflectivity and both soil moisture content and soil
raatric potential.
This study was further continued to investigate the
ability of microwave systems to detect the moisture status of silt
loam soil exhibiting abrupt changes in moisture content near the sur­
face .
A bare Captina soil initially was saturated and monitored for
extended periods of drying.
Reflectivity measurements were made with
a bistatic reflectometer operating over the frequency ranges of 1 to 2
GHz and 4 to 8 GHz.
A strong linear correlation was found between
reflectivity and both volumetric moisture content and matric poten­
tial, particularly at the lower frequencies.
However, at the higher
frequencies, coherent interference patterns similar to those observed
in a previous laboratory experiment were detected.
These patterns
appeared to be due to steep moisture gradients occurring between
drying soil layers near the surface.
The development of these layers
is a function of drying time, tillage, and evaporative demand placed
on the soil.
60
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INTRODUCTION
Moisture content near the soil surface is an important parameter
to agriculture, hydrology, and, thus, to civilization.
The amount of
this moisture serves as either an input or boundary condition in
hydrological, meteorological, and agricultural yield models.
crop yield models used rainfall as an input.
Early
Studies of the response
of crops to various environmental elements indicated that crop yields
are more closely related to soil moisture than to any other single
meteorological factor (Baier et a l ., 1968).
However, the application
of these crop models is hindered by the need for frequent measurements
of the moisture status near the soil surface.
Since classical methods
of soil moisture measurement are incapable of meeting the demand for
rapid measurements over large land areas, remote sensing techniques
have received considerable attention as a means of fulfilling this
need (Lundien,
1967; Ulaby et al.,
1978; Waite et al.,
1973).
The purpose of this study was to measure directly the relationship
between microwave reflectivity and both soil moisture content and soil
water matric potential.
The study was further continued to investi­
gate the effect on microwave reflectivity of steep moisture gradients
in the near surface soil profile under field conditions.
To
accomplish this involved moisture status measurements of nonhomogeneous field profiles under a wide variety of moisture and drying con­
ditions.
A two-layer reflectivity model previously developed in the
laboratory was extended to multiple layers ('■'25) capable of calcu­
lating the surface reflectivity from a generalized moisture profile
consisting of five linear segments.
The five segment moisture profile
61
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was capable of simulating the formation of two dry layers within the
soil volume by selecting two segments to have a very steep moisture
gradient.
The multiple frequency reflectivity measurements obtained
were modeled by means of the five segment profile and the multilayer
reflectivity program to estimate the near surface moisture profile.
This method of profile determination by means of curve fitting was
required since the variations in moisture content near the surface
occur over such small depth intervals that other means including gra­
vimetric sampling are not feasible.
Multiple frequency microwaye
measurements of this type appear to have the capability of estimating
the moisture profile in the near surface of the soil volume.
62
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REVIEW OF LITERATURE
Continuous estimates of soil moisture, particularly near the sur­
face, are required for many agricultural models.
The traditional
means of estimating soil moisture, including gravimetric sampling,
rely on point measurements, which are not practically applicable to
large land areas.
Remote sensing techniques show two potential advan­
tages over the traditional means; 1) a continuous response to the
variation in moisture content, and 2) applicability to large land
areas.
In studies of the remote sensing of soil moisture, three general
regions of the electromagnetic spectrum have been used.
visible (or shortwave),
2-1).
These are:
infrared (or longwave), and microwave (Figure
Each region has shown good correlation with soil moisture con­
tent for a particular application (Idso et al., 1975).
Reflected
radiation in the visible spectrum (albedo) has been demonstrated to
have excellent correlation with soil moisture content in the upper few
millimeters of the soil surface (Idso et al., 1975; Jackson et al.,
1976).
Unfortuneately, at these wavelenghts, penetration is slight
and sensitivity decreases once the first few millimeters of the soil
surface dry (Figure 2-2).
In addition, the albedo of different dry
soils varies widely, thus, there is little hope of developing a rela­
tionship between soil moisture content and visible spectrum not
requiring a priori knowledge of soil characteristics (Idso et al.,
1975).
Surface temperature measurements made in the thermal infrared
region have also been shown to correlate well with the surface
63
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
THE ELECTROMAGNETIC
SPECTRUM
WAVELENGTHE E
E
•<
to
O
•<
NY
sSW
CM
E
E
,
E
o
CM
gamma!
EE
E
to
o
X X
om
x
O
o
n
i
i
-R A Y
I__
E
o
L__
X-RAY
l— U V -
RADIO-BANDS
LAUDlO
MICROWAVE-I
■INFRARED
j
ON
4>
1 0 0 GHz
19
10
1017
10
~«F
1GHz
^
P
io"
10°
10
10°
10
FREQUENCY , Hz
Figure 2-1
Electromagnetic spectrum, indicating the visible,
infrared, and microwave xvavelengths and frequencies.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o 0.28
Q
ca
_j
<
0.5
Q
Ul
O.2
N
<
cm to Surface 0
0.20
Ln
0.12
0.00
0.08
0.16
0.24
VOLUMETRIC WATER CONTENT |cm3/Cm 3|
I From idso ,et al. ,1975a I
Figure 2-2
Normalized albedo as a function of volumetric
water content at various soil depths.
moisture content of bare soil where the soil is uniform (Figure 2-3).
Where the soil is non-uniform a fair estimate of soil moisture matric
potential may be obtained.
While this technique appears to offer
sensing of moisture at a greater depth than visible spectrum measure­
ments, it is severely hampered by the presence of even slight amounts
of vegetation.
In addition, both visible reflectance and thermal
emission models for estimation of soil moisture require knowledge of
the solar radiation (irradiance and insolation) which is frequently
unavailable.
Microwave wavelengths have substantially more penetration capabi­
lity.
At these lower frequencies, penetration of vegetation cover is
significant, and the sampling depth of the measurement may be on the
order of several centimeters depending on the soil moisture content.
Sampling depth is defined as the maximum depth for which a moisture
estimate is provided by the measurement.
The results of the radar
experiment by space shuttle Columbia in November,
in the December 3 issue of Science magazine.
1981 were reported
The radar operated for
eight hours, providing images of land varying from the tropical
forests in the Amazon to the deserts of North Africa.
The sands in
the Arabian Desert were extremely dry with rainfall occurring once
every 30 to 50 years.
The results showed that radar waves penetrated
extremely dry sand to depths of several meters and discovered ancient
buried irrigation channels.
Measurement programs in the microwave region have followed two
distinct approaches; one employing passive radiometric measurements,
66
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MAR. 71 □
MAY 73 •
JUL. 70 A
AUG. 72 e
SEP. 73 o
DEC. 73 V
S 24
16
8
0 L.
0.00
0.08
0.16
0.24
0.32
VOLUMETRIC WATER CONT£NT(cm3/cm3)
(From Idso etal.,1976b|
Figure 2-3
Temperature response to
volumetric water content
at various seasons.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and the other using active radar backscattering measurements.
Both
approaches have demonstrated excellent correlation with soil moisture
content.
However, there are significant differences between the
active and passive techniques which result in differing recommended
operating frequencies for the measurement of soil moisture.
The dif­
ference in frequency would in turn be expected to produce a signifi­
cant difference in the vegetation penetration capability and the
sampling depth.
Passive microwave studies (Jackson et al., 1981; Newton et al.,
1981; Schmugge et al., 1980) have consistently shown the lower
microwave frequencies (L band) to be superior for the measurement of
soil moisture.
The increased penetration capability of the lower fre­
quencies improves both the response from beneath vegetative cover and
the sampling depth.
In addition, the effects of surface roughness are
decreased for these longer wavelengths thereby giving improved sen­
sitivity.
Active microwave studies (Ulaby et. al.,
1978-1979) have concluded
that the optimum sensor configuration is a frequency of near 5 GHz and
an incident angle of between 7 and 20 degrees.
This selection is dic­
tated by the necessity to minimize the effects of surface roughness.
Even here it has been shown that periodic components of roughness,
such as that produced by tillage, present severe problems (Fenner et
al., 1981; Waite et al., 1980).
The sensitivity of both active and passive microwave systems to
soil moisture is due to the large difference between the dielectric
constant of free water ( ^ 8 0 )
1967; Ulaby et al.,
and of air dry soil, 3 to 7, (Lundien,
1974; Wang et al., 1980).
68
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Programs utilizing both types of sensors have exhibited a pronounced
dependence upon soil texture.
However, Cihlar et al. (1974)
demonstrated that for a specific wavelength,
the effect of soil tex­
ture was reduced in the response of relative dielectric
soil moisture content (Figure 2-4).
constant
to
It has also been shown by
Schmugge (1980) that the variations in passive measurements due to
soil texture may be significantly reduced by expressing the soil
moisture as a percentage of field capacity.
Field capacity is the
amount of water in the soil two or three days after saturation when
free drainage has practically ceased.
For clayey soils this is fre­
quently taken as approximately the water content at a -0.33 bar matric
potential.
However,
in coarser-texture soils, the matric potential at
field capacity may be less negative.
Dobson and Ulaby (1981) have
likewise postulated that a textural dependence of backscattering
measurements may be removed with
a normalization based on matric
potentials between -0.3 and -2.0 bars.
Both active and passive measurement programs have concluded that
the sampling depth of the measurement is dominated by the air-soil
interface and is on the order of a few centimeters depending on the
surface moisture content.
Some differences in using multilayer models
for prediction of the response have resulted from the use of both
coherent and incoherent models (Burke et al., 1979; Wilheit et al.,
1978; Schmugge et al.,
1980).
Studies involving the direct measurement of penetration depth have
been conducted on homogeneous soil-water samples in the laboratory.
Under field conditions the moisture depth profile is not normally
69
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28 I- (Cihlar & Ulaby, 1974
Sand
24
Loam
H-
Z
Clay
to
z
o
REAL PART
o
O
£
H
O
ID
IU
Q
>
IMAGINARY
PART
5
K
0.0
0.1
0.2
0.3
0.4
03
VOLUMETRIC WATER CONTENT
Icm^/cm® I
Figure 2-4
Relationships between
relative dielectric
constant and volumetric
water content for s a n d ,
loam, and clay soils.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
uniform and may vary extensively, particularly near the surface.
Most
field programs designed to evaluate microwave remote sensing of soil
moisture have used correlation techniques between system response and
relatively large sample averages of the moisture depth profile.
In
particular, there remains some question as to the effect of the
moisture distribution within the sampling depth (Lundien,
1967).
71
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METHODS AND MATERIALS
Measurement System
Microwave reflectivity data were gathered utilizing a bistatic
reflectometer system measuring at a specular angle of 45° and with a
slant range of 3.75 m.
The reflectometer system featured separate
antenna support platforms of the same construction for both transmit
and receive and used dual, standard gain, horn antennas for the bandwidths of 1 to 2 GHz and 4 to
GHz.
8
A 1 to 2 GHz and a 4 to
8
GHz
antenna were mounted on each antenna support platform in a parallel
side-by-side arrangement.
The transmitter portion of the system con­
sisted of a microwave sweep oscillator mainframe with individual sweep
plug-ins for the 1 to 2 and 4 to
8
GHz bandwidths.
Receiver implemen­
tation was accomplished using a network analyzer as a ratiometer, a
storage normalizer, and an x-y plotter to furnish a permanent record
of the data.
Figure 2-5 shows a block diagram of the laboratory
bistatic reflectometer system.
The system configuration was the same
for both the laboratory and field measurements.
System calibration was external and employed a thin sheet of alu­
minum.
The calibration procedure involved placing the aluminum sheet
on the top of the soil sample box and making a swept frequency
measurement of the power reflected from the aluminum sheet.
After
removal of the aluminum plate, a swept frequency measurement of the
reflected power from the bare soil sample was made.
The ratio of
these two swept frequency measurements eliminated system parameters
and gave the reflectivity of the bare soil.
A more detailed descrip-
72
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TRANSMIT
ANTENNAS
RECEIVE
ANTENNAS
'I'
V
'f \ '
Y Y
V
SOIL
TARGET
SWEEP
OSCILLATOR
NETWORK
ANALYZER
STORAGE
NORMALDZER
X-Y
RECORDER
Figure 2-5
Block diagram of bistatic reflectometer
ins trumentat i o n .
tion of a bistatic reflectometer using this calibration procedure is
given in Waite et al. (1973).
Location of Measurements
The experiment was conducted at the University of Arkansas
Agricultural Experiment Station.
Measurements were conducted on a 3.7
m x 3 ra plot of bare Captina silt loam.
The Captina soil is modera­
tely well drained, slowly'permeable, and dominated in the lower hori­
zons by a firm brittle fragipan.
It is classified as a Typic
Fragiudult and has a predominant silt loam texture in the profile.
The fragipan is located at depths ranging from 0.7 to 1.2 m.
The
boundary between fragipan and non-fragipan horizons is wavy (tongue
shaped) and causes significant variations in the redistribution rate
of water within the soil profile.
Data in Table 2-1 present selected
physical characteristics of the Captina soil at the study site.
Data
from the moisture retention characteristics indicate that the Ap hori­
zon is capable of retaining 0.342 cm-Vcm^ of water at -1.0 bar
pressure and the B2t horizon retains 0.271 cm^/cm^ of water at the
same pressure.
The fragipan retained lower amounts of moisture than
the horizons above it in the profile.
The plot was instrumented with three banks of mercury tensiometers
positioned at depths of 0.01, 0.03, 0.05, and 0.1 m using raicrotensiometers, and at 0.152 m depths ranging from 0.15 to 1.37 m using
macrotensiometers.
Each microtensiometer was made by grinding the cup
end off of a ceramic cup (one bar porous ceramic,
O.D., 1 m m wall thickness),
6
cm long,
0.6
cm
the ceramic material was connected via
74
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2-1:
Depth
Interval
Selected physical properties of the Captina silt loam.
Horizon
(cm)
Bulk
Density
(g/era3 )
Particle
Density
Particle Size Distribution
Sand
Silt
Clay
_
(g/cm3 )
_
y
10
__
K Sat
era/day
Total
Porosity
(era3 /cm3 )
0-5
Ap
1.27
2.49
25.5
64.1
10.4
6.19
0.490
13-18
Ap
1 .41
2.56
28.6
61.3
10.1
3.55
0.449
28-33
Ap2/Bt
1.39
2.62
22.9
63.3
13.8
32.23
0.469
43-48
Bt/Bt2
1.39
2.60
21.0
62.9
16.1
43.87
0.465
58-63
Bt2/Bt3
1.50
2.62
18.5
59.2
22.3
21.05
0.427
73-78
Btx
1.58
2.61
17.3
55.2
27.5
26.38
0.395
88-93
Btx
1.64
2.62
18.0
52.3
29.7
1.10
0.374
103-108
Bx
1.54
2.62
18.8
57.2
24.0
16.01
0.412
118-123
Bt
1.53
2.63
39.6
35.1
25.3
3.82
0.418
133-138
Bt
2.62
18.3
56.7
25.0
65.30
—
---
nylon tubing from one side to the mercury manometer and from the other
side to a brass clamp.
The macrotensiometer consisted of a porous cup
(1 bar porous ceramic, 5 cm long, 2 cm O.D., 3 mm wall thickness),
connected through a PVC tube to a manometer.
After instrumentation,
the soil surface was tilled lightly and leveled.
Water was applied at
a steady-state rate lower than the maximum infiltration rate until the
profile was nearly saturated.
Microwave reflectivity and soil water
status were monitored during three drying cycles for the plot.
Soil
water matric potential was monitored for all cycles and gravimetric
samples for water content were taken during the third drying cycle.
The test plot was protected from rainfall by a sloping roof
approximately 1.0 to 1.5 m above the surface and extending well beyond
the plot boundaries.
Measurements were taken six times daily at the
start of each drying cycle with the frequency of measurement
decreasing as the plot dried.
The first drying cycle extended for
only four days at which point a wind and rain storm destroyed the pro­
tecting roof and deposited an undetermined amount of water on the sur­
face.
The roof was rebuilt, the soil profile resaturated, and the
second drying cycle which lasted twenty-four days, commenced.
The
profile was again saturated and the third drying cycle was conducted
lasting eleven days.
During the third drying cycle, gravimetric soil
moisture samples were taken in
2
cm measurements to a depth of 18 cm.
At the conclusion of the third cycle, the plot was excavated to deter­
mine the morphological description and physical characteristics of the
soil profile, and to take undisturbed soil cores for moisture reten­
tion characteristics at depths corresponding to those of the ten-
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
sioraeters.
The undisturbed soil cores were used to determine the soil
bulk density and the saturated hydraulic conductivity by the constant
head method.
Particle density was calculated using the pycnometer
method and particle size distribution was determined by mechanical
analysis.
(More evaluation of the physical properties of the experi­
mental site is given in Chapter 1.)
Theoretical Analysis Models
The geometry of the two-layer model used to calculate the reflec­
tivity of the prepared profiles measured in the laboratory is shown in
Figure 2-6.
In this model, medium A is in the air space above the
soil surface and media B and C are homogeneous layers with different
moisture content, the electromagnetic field in medium A consists of
the incident component, a reflected component due to the air-soil
interface, and an infinite number of reflected components from the
interface between soil medium B and soil medium C.
the field in
medium B consists of an infinite number of both upward and downward
traveling waves.
Medium C is considered essentially infinite in
depth, thus the field has no reflected components and consists of only
an infinite number
of transmitted
The components
in each region
closed form.
This
result is then
wave impedence formulation.
components.
may be summed and
identical to that
expressed in
obtained using a
The total field reflection coefficient
medium A is given by;
r 1 + T0 e- 2 YB dB
1.0 +
e - ^ B dB
[ 1
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E incident
E reflected
medium A
medium 5
medium C
tw o-layer model
Figure 2-6
E transmitted
Reflection components of the twolayer model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where
^
is the reflection coefficient due to the abrupt change in
permittivity between media A and B while
^3
is the reflection coef­
ficient due to the interface between media B and C.
the total reflec­
tion coefficient given by equation [1 ] may be viewed as a surface
reflection summed with a subsurface reflection that is altered in
phase and attenuated in magnitude due to the thickness and dielectric
properties of medium B.
The square of the field reflection coefficient is defined as the
power reflectivity and for the two-layer model may be expressed as,
2
2
|ri I + | r 3 | e-^aBdB+2| r 1 I | r 3 |e-2aBdB cos(23BdB+0i-03 )
2
1.0+1r ! I | r 3 1V 4aBdB+21r 1 11r 3 1e~2<*BdBc0s (28BdB-e 1-03)
where
03
and
©3
are phase angles, <*B is the attenuation factor in medium
B and SB is the phase factor in medium B.
If the real part of the complex permittivity for each medium is
much greater than the imaginary part, which is the normal case for
soils, then the real part of the reflection coefficient will also be
much greater than the imaginary part for the condition,
eC > eB > £A
Under these conditions the phase angles
and
01
©3
are negligible and the
minima of the power reflectivity occur where,
cos( 2 0 BdB) =
or when
2 (3B
d B
-1
is an odd multiple of
it
.
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
26gdg = (2n + 1) tt
[3]
Since
[4]
we may express d g as
dB = (2 n +
1)
[5]
^
Equation (5) shows that when the propagation distance d g in medium B
is an odd multiple of a quarter wavelength,
the surface and subsurface
components will be 180 out of phase leading to a reflectivity minimum.
Obviously when the propagation distance yields a phase shift that is a
multiple of
2
tt
, a maximum will result.
At least a bound on the relative magnitudes of the permittivities
may be obtained from the following considerations.
Where the minimum
reflectivity approaches zero, equation [2 ] requires,
[6 ]
This in turn requires,
r3I > lrl
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
which says the subsurface component must be greater than the surface
component of the reflectivity,
this leads to the following rela­
tionship between the relative permittivities of media B and C,
- Tan 0A
2
+ Sin 2 0A
'A
which for normal incidence ( ®A = 0 ° ) reduces to
2
ec' f
I£b I
Where the profile is continuous, as under field conditions,
this model
is extended by approximating the continuous change in permittivity by
multiple homogeneous layers.
For the field surfaces measured in this
program, a three or five segment linear moisture profile was required
to model adequately the reflectivity response with frequency.
81
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RESULTS AND DISCUSSION
Reflectivity values at frequencies of 1.5 and 6.0 GHz along with
values of soil matric potentials, and volumetric water content for
three drying cycles are given in Appendix Tables 1, 2, and 3, respec­
tively.
The daily soil water potential during the second drying cycle
within the surface 15 cm and the remainder of the profile, is shown in
Figure 2.7.
The negative slope of the curves for the first day indi­
cate that the initial direction of soil water flow was downward; i.e.,
water was draining from the profile.
The positive slope in the sur­
face horizons after the first day indicate that the direction of flow
was upward as a result of evaporation.
The variation in matric potential at various depths during the
second drying cycle is shown in Figure 2-8.
The amplitude of the
diurnal variation is greatest at 1 cm and decreases with depth.
At a
given depth the amplitude of the diurnal variation increases during
the first 2 to 3 days and then decreases depending on the rate of
water loss from that depth.
The tensiometers ceased to function at
approximately -0.80 bar; thus, the data record ceases first at the
cm depth and then at deeper levels as the soil dries.
1
The variation
in reflectivity at 1.5 GHz and 6.0 GHz for the same interval is shown
in Figure 2-9.
There is obviously a strong correlation between the
reflectivity and the matric potentials shown in Figures 2-8 and 2-9,
particularly at the lower frequency, early in the cycle, and at the
shallower depths.
The maximum diurnal change occurred at the 1.5 GHz
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TOTAL POTENTIAL lb«r»l
0
•0 .2
-0 4
-0 .6
•0.8
CAPT1NA SILT LOAM
2nd O ftVtna CYCLE
1S
E
o
CAPTINA SILT LOAM
2 n d O ffrm Q CYCLE
n
Figure 2-7
Daily total soil water
potential as a function of
depth during second drying
cycle.
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
■
0.1
-
0.2
-0.3
IS c m
Z
ui
H -04
£
10cm
O
(E
H
<
2
-0.5
C A P T IN A S IL T LO AM
5cm
2Qd D R Y IN G C Y C L E
-
0.6
3cm
1cm
-0.7
0
50
100
150
200
250
300
350
400
450
T IM E Ih o u isl
Figure 2-8
Diurnal fluctuation in soil matric potential at various depths
during the second drying cycle.
500
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-2
FR E Q U E N C Y
1.5 G H z
«
6 .0 G H z
&
>•
»>
-10
h
O
u
ji
IL
£ -«
*14
C A P T IN A SILT LOAM
2Qd D R YIN G C Y C L E
-19
0
50
100
150
200
2 50
300
350
400
450
T IM E (hours!
Figure 2-9
Diurnal fluctuation of microwave reflectivity at 1.5 and 6.0
GHz during the second drying cycle.
500
frequency and 1 cm depth (Figure 2-10).
In general, the reflectivity
and matric potential decreased over time and varied together.
The diurnal variations may be eliminated by examining the sequence
of measurements made at the same time each day.
2:00
Figure 2-11 shows the
p.m. measurement of reflectivity at four additional frequencies.
During the third drying cycle, the higher evaporative demand
resulted in the loss of approximately 15% more water during the first
four days after infiltration ceased (Figure 2-12).
The behavior of
matric potential, reflectivity, and volumetric water content for this
cycle is shown in Figures 2-13, 2-14, and 2-15, respectively.
The
data for matric potential and reflectivity again show a damped diurnal
variation.
This is not seen in the volumetric water content data since
gravimetric samples were taken only at
2:00
p.m. each measurement day.
The microwave reflectivity, particularly at the lower frequencies,
appears to have a high degree of correlation with both matric poten­
tial and volumetric water content.
The variation of reflectivity at
1.5 GHz as a function of matric potential and volumetric moisture con­
tent for various depths is shown in Figures 2-16, 2-17, and 2-18.
Linear regression coefficients for all depths, and both high and low
frequencies are summarized in Tables 2-2.
The high regression coef­
ficients at the shallow depths are not directly comparable as the data
record length is abbreviated due to failure of the microtensiometers
as the surface dries.
Assuming that matric potential continues to
decrease as the surface dries,
it is obvious from Figure 2-9 that the
linear correlation with the high frequency reflectivity will degrade
after approximately 120 hours.
The abbreviated record length of the
shallow potentials will thus give a higher regression coefficient than
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CYCLE 2
-200
■ -4
J -4 0 0
MATRIC POTENTIAL
•5
REFLECTIVITY
I db|
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CAPTINA SOIL
-6 0 0
1.5 GHZ ftEFLCTIVITY
-8 0 0
-9
-10
-1000
0
50
100
150
200
260
TIME I hours |
Figure 2-10
Diurnal fluctuation in soil matric potential at
1 cm depth and microwave reflectivity at 1.5 GHz
as a function of time during the second drying
cycle.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FR EQ U EN CY
1.125 G H z
1.875 GHz
4 .5 0 0 GHz
7.5 0 0 GHz
H
U
UJ
-J
s: -12
UJ
OC
•14
C A P T IN A SOIL
C YCLE 2
•16
-tel
o
50
100
150
200
250
300
3 50
400
450
T IM E I hours I
Figure 2-11
Daily variation of microwave reflectivity during the second
drying cycle.
500
3.0
CUMULATIVE
EVAPORATION |cm /day|
CAPTINA SOIL
2.5
2.0
2nd Drying Cycle
1.5
3 rd Drying Cycle
1.0
0.5
0.0
0
1
2
3
5
4
6
7
8
TIME (days)
Figure 2-12
Cumulative evaporation during the second
and third drying cycles as a function of
time.
89
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•
0.1
15cm
5cm
10cm
3 cm
CAPTINA SOIL
CYCLE 3
1cm
0
40
Figure 2-13
80
120
160
T IM E (hours!
200
240
200
Diurnal fluctuation in soil matric potential at
various depths during the third drying cycle.
320
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-2
FREQUENCY
1.5 G H z
e
6 .0 G H z
A
-8
-10
•14
C A P T IN A S O IL
CYCLE 3
-16
-18
0
40
80
120
160
200
240
280
320
T IM E Ih oursl
Figure 2-14
Diurnal fluctuation of microwave reflectivity at
1.5 and 6.0 GHz during the third drying cycle.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
VOLUMETRIC WATER CONTENTlcm3 cm3 l
0
0.05
0.10
0.15
0.20
025
0.30
0.35
DAYS AFTER SATURATION
E
_o
X
Ia
ui
a
_i
CAPTINA SOIL
CYCLE 3
16
DATA AT 2 pm
Figure 2-15
Daily variation of volumetric water content at
various soil depths during the third drying cycle.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
CAPTINA SOIL
CYCLE 2
FREQUENCY 1.5GHz
5cm
15cm
-0.2
-0.3
-0 .4
-0.5
-0.6
-0.7
SOIL M ATRIC P O T E N T IA L Ib a r s l
Figure 2-16
Microwave reflectivity as a function of soil matric
potential at various depths during the second drying
cycle.
-
0.8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-2
CAPTINA SOIL
CVCLE 3
-3
FREQUENCY 1.5 GHz
-4
-5
>-
-6
>
H
O
Ul
-I
u.
ui
(C
-7
-8
5cm
-9
15 cm
-10
0.0
-
0.1
-
0.2
-0 .3
-0 .4
-0 .5
MATRIC PO TE N TIA L
Figure 2-17
-
0.6
-0!7
Ib a rs l
Microwave reflectivity as a function of soil matric
potential at various depths during the third drying
cycle.
-
0.8
0
CAPTINA SOIL
CYCLE 3
O®
2
REFLECTIVITY
I db|
FREQUENCY 1.5 GHz
1c m
5cm
15cm
0.30
0.10
0.20
OjQ
VOLUMETRIC WATER CONTENT |cm3 cm3 )
Figure 2-18
Microwave reflectivity as a function of
volumetric soil water content at various
depths during the third drying cycle.
95
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2-2:
Soil
Depth
(cm)
Regression Coefficients for Reflectivity (-dB) as a
Function of Matric Potential (-bar).
Regression Coefficients
Cycle 1
Cycle 2
1.5
6.0
1.5
Tensiometer Record
extends only
hours
6.0
(hours)
-------- GHz1
0.970
0.861(1)
0.937
0.707(5)
(1) 150
3
0.973
0.851(2)
0.937
0.785(5)
(2) 198
5
0.975
0.849(3)
0.900
0.611(5)
(3) 222
10
0.963
0.799(4)
0.959
0.725
(4) 270
15
0.887
0.547
0.826
0.612
(5) 102
31
0.878
0.542
0.790
0.594
46
0.843
0.494
0.717
0.506
61
0.818
0.470
0.664
0.446
76
0.804
0.453
0.665
0.437
91
0.801
0.448
0.701
0.437
107
0.816
0.460
0.773
0.537
122
0.856
0.490
0.718
0.527
137
0.736
0.432
0.809
0.624
96
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
would be obtained if all records were of the same duration.
The
variation of reflectivity with volumetric moisture content is shown in
Figure 2-18 with the linear regression coefficients summarized in
Table 2-3.
Although the linear regressions would appear to yield excellent
results there are three troublesome aspects revealed by close examina­
tion of the preceding results.
These aspects, along with qualitative
explanation, are presented in the following discussion.
First, consider the behavior of the high frequency reflectivity
with time (Figure 2-9).
The loss of sensitivity initially at the
higher frequencies as the surface dries is certainly no surprise since
the sampling depth is expected to be significantly less.
the surface dries beyond the sampling depth,
asymtotically approach a constant value.
However, as
the reflectivity should
The experimental data show a
marked increase in reflectivity after approximately 120 hours.
This
reversal from the trend of the lower frequency data cannot be attri­
buted to a simple change in sampling depth.
The behavior shown is attributed to the formation of steep
moisture gradients (layers) near the soil surface.
The existence of
such layers may be deduced from the frequency variation of reflec­
tivity, a sample of which is shown in Figure 2-19.
A simple two-layer
model predicts a minimum in reflectivity where the propagation
distance in the soil is an odd multiple of a quarter wavelength.
This
sample resulted from a laboratory experiment with homogeneous layer.
For the trace shown in Figure 2-19 the minimum at 6.2 GHz corresponds
to an effective layer depth of approximately 0.4 cm.
97
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2-3:
Regression coefficients (r2) for reflectivity (-dB) as a
function of volumetric water content (cm^/cm^) for the
third drying cycle.
Regression Coefficient (r^)
Soil
Depth
(cm)
1.5
(GHz)
6.0
(GHz)
1
0.981-
0.772
3
0.959
0.753
5
0.854
0.617
7
0.697
0.359
9
0.366
0.148
11
0.594
0.184
13
0.828
0.431
15
0.439
0.149
17
0.342
0.045
98
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CAPTINA SOIL
CYCLE 2
-5
D A YS,TIM E 1400
CO
T>
tu
UJ
u.
UJ
cc
-15
-20
1
2
3
4
5
6
7
FREQUENCYIGHz I
Figure 2-19
Microwave reflectivity as a function of frequency.
8
A second problem concerns the functional relationship of reflec­
tivity with matric potential and volumetric water content.
The
results show that both matric potential and volumetric water content
are linearly related to the logarithm of the power reflectivity (db
scale), but the inconsistency is obvious since it is well known that
matric potential and water content are not linearly related.
The
explanation for this behavior may be seen from the water release curve
shown in Figure 2-20.
The initial measurement of volumetric moisture
was some six hours after infiltration ceased (time zero).
By this
time the matric potential in the upper 5 cm had already decreased to
less than -0.05 bar (Figure 2-8).
As may be seen from the water
release curve of Figure 2-20, the relationship between pressure and
water content is very nearly linear for pressures less than -0.05 bar.
The third problem deals with saturation of the reflectivity at low
matric potentials (Figures 2-16 and 2-17).
At first glance this would
appear to require a corresponding saturation in the relationship bet­
ween moisture content and pressure or that between dielectric constant
and moisture content.
However, the water release characteristic pre­
dicts that any departure from linearity at low pressure should act to
increase rather than decrease the slope of the reflectivity versus
matric potential characteristic.
Thus, in this pressure range small
variations in pressure result in larger variations in water content,
which should result in larger changes in reflectivity.
Likewise, the
results of Wang and Schmugge (1980) indicate the relationship of
dielectric constant and moisture content to be very nearly linear in
this range of high moisture content.
Any compression of sensitivity
to moisture content due to adsorbed water should occur in the region
100
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 .5 0
0.45
C A P T IN A SOIL
?E
D EPTH O TO 5 cm
o
"
e
_o
040
t2
o
0
cc
Ul
H
0 .35
1
5
0 .3 0
frUl
2
O
>
0 .2 5
0.20
-
0.2
-0 .4
-0 .6
-
0.8
-4.0
P R E S S U R E Ib a ra l
Figure 2-20
Moisture release characteristic curve for 0
to 5 cm depth in Captina soil.
of the transition moisture which is shown to correlate very well with
the wilting point for the particular soil.
Thus, it appears that
nothing in the behavior of these characteristics is capable of pro­
ducing the observed saturation.
The proposed explanation for this effect is the variation in the
effective roughness of the surface during the early stages of drying.
This may be visualized by referring to Figure 2-21.
saturated, thus homogeneous,
When the soil is
the reflectivity is essentially the pro­
duct of a roughness coefficient and the power reflection coefficient.
In this case the interaction is confined to the surface region with no
internal contributions to the reflected return.
As the soil dries,
steep moisture and matric potential gradients (layers) form beneath
the surface.
The total return is now composed of contributions from
the dry surface and the wetter subsurface layer.
As drying continues,
the moisture gradient both decreases in magnitude and moves deeper
into the soil until it is beyond the sampling depth.
At this point,
the return is again solely from the surface reflection.
In the absence of roughness,
the return from the intermediate,
layered medium will not exceed that from the saturated surface.
However,
the subsurface layer formed by the steep moisture gradient
will normally be much smoother than the surface since it will itself
be an equipotential surface.
The combined response of the inter­
mediate surface is then the superposition of the surface return that
is from a relatively dry but rough boundary and the subsurface return
from a boundary that is significantly smoother yet may involve a
significantly greater impedance discontinuity.
Under these con­
ditions it is conceivable that the total return may exceed that from
102
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-SATURATION
rORV
-T>-
BOUNDARY
WET
77//
B - INTERMEDIATE
DRY
U p> SAMPLE! DEPTH
BOUNDARY
A
C - DRV
Figure 2-21
Sequential stages of
soil drying for a
rough surface.
103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the saturated surface.
This would occur where the total return is
dominated by that of the subsurface layer.
The increase in return due
to the reduction in roughness from this layer would offset the
decrease due to having the matching layer.
If the above hypothesis is correct, there should be some evidence
in the diurnal data.
Referring to Figure 2-9, we find definite evi­
dence of this effect during the first two days of the cycle.
Close
examination reveals the increase in reflectivity observed during these
2
days is not solely due to diurnal movement of the moisture.
Superimposed on the diurnal variation are peaks in reflectivity which
develop during the daylight hours of maximum drying.
On day 1 reflec­
tivity shows an increase from 800 hrs to 1400 hrs, and on day 2 there
is an increase from 800 hrs to 1400 hrs.
diurnal variation is observed.
After day 2 only the normal
Examination of all other diurnal
cycles conducted under near saturated conditions reveal a similar
behavior of increasing reflectivity during the initial stages of
drying.
The results of the relationships between microwave reflectivity
and both soil moisture content and soil matric potential have indi­
cated a high degree of correlation, particularly at the lower frequen­
cies (Table 2-5).
However, examination of the behavior of
reflectivity with time as shown in Figure 2-22 indicates some
problems.
The regression coefficients are obviously dominated by the
decrease in reflectivity during the first
cycle.
100
to
200
hours of the
This is particularly true of the shallower depths where
failure of the raicrotensiometers occurs prior to reaching the near
horizontal portion of the drying curves.
This decrease in slope, or
104
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FREQUENCY,GHz
a 4 .5
o 1.875
O 7 .5
REFLECTIVITY
IdBI
9 1.125
-10
-12
-14
CYCLE 2
-16
-18
100
300
200
400
TIME Ihoursl
Figure 2-22
Microwave reflectivity as a function of
time at lower and higher frequencies
during the second drying cycle.
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
sensitivity, should be expected as the soil volume dries to beyond
the penetration depth at a particular frequency where the reflectivity
should asymtotically approach a constant value determined solely by
the interface between the air and the relatively homogeneous dry soil.
The low frequency curves appear to exhibit the expected behavior
and could possibly be used to predict moisture with a two segment
linear approximation to the observed near exponential decrease of
reflectivity with time.
The high frequency measurements indicate the
presence of layering effects.
The increase in reflectivity as the
soil dries that is apparent after approximately 150 hours can only be
explained by the presence of coherent layer effects wit addition and
cancellation of surface and subsurface components dependent upon their
relative phase.
Linear approximation of the drying curve will be
impossible here, as the shape will vary substantially with slight
changes in either frequency or subsurface profile.
While the field soil profiles do not have the abrupt
(discontinuous) change in moisture of artificial laboratory profiles,
they do provide exceedingly steep moisture gradients during drying
which apparently cause much the same type of behavior.
gradients refer to changes of near
2
to
1
Steep moisture
in moisture content
occurring over a depth change of approximately
0.1
wavelength.
The distribution of moisture producing the observed behavior of
reflectivity modeled by means of an approximate 5-segment linear
profile.
The profile was then used to drive the multilayer reflec­
tivity model to produce the simulated reflectivity versus frequency
curves.
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2-23 shows the variation of reflectivity with frequency
obtained for selected days during the second drying cycle along with
model results.
These results were obtained through trial and error
fitting of the observed changes by adjusting the 5-segment moisture
profile.
The predicted profiles obtained through this procedure are
shown in Figure 2-24.
The results from the nonhomogeneous field profiles indicate that
the moisture gradients within the profile during drying from satura­
tion are sufficiently steep to produce distinct coherent layering
effects.
distinct
Referring again to Figure 2-24, it may be seen that a
layer was predicted at approximately 0.4 cm.
corresponded to the observed
occurred
near
6
GHz.
this
minima in Figure 23, on day 2 that
As the surface continued to dry (day 4)
there
was little change in the depth of the first layer, however, there was
indication of a deeper layer forming as well.
the minima remaining near
6
This was indicated by
GHz while the lower frequency (1 to 2 GHz)
trace appears to dip toward a minima at a much lower frequency (longer
wavelength therefore deeper in the profile).
By day 17 both layers
were relatively well developed and there was clear indication of the
two minima.
In this case the multiple minima did not occur at odd
multiples of one-quarter wavelength, thus are indicative of separate
layers.
These results clearly indicated the dynamic nature of the water
transport within the near surface of the soil.
The depths and move­
ments indicated here are virtually impossible to measure accurately by
traditional measurements.
Figure 2-25 shows the positions of the
steep gradients (layers) in the upper soil profile during the second
107
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FREQUENCY fGHzl
2
3
4
5
j ________ i________ I________i_
0
> -5 ■ |QQ9 O
>
E
P -10
TE
o
UJ
«j
IL
UJ
s
1
8
e
model ^
21
3
4
5
6
71
8
-
-10
15-
-0
. IDAY4]
1
28
3
4
5
6
-00
-
—>j
UJ
oc
^ a c tu a l
e
-5
s
UJ
7i
. IDAY2I
0
GO
3.
>
H
>
_
___
6
CO
3.
>
o
UJ
UJ
oc
® \
e x.
•
,
N SJ
/a
. IDAY17
Figure 2-23
Field measured and model
reflectivity as a function
of frequency for selected
days during the second
drying cycle.
108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
MOISTURE BY VOLUME 1%)
0
5
10
15
20
25
30
35
0
day 2
0.5
day 4
1.0
cm
day 17
1.5
2.0
CAPTINA SOIL
CYCLE 2
2 .5
3.0
Figure 2-24
Predicted volumetric soil moisture
content for the selected days during
the second drying cycle.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TIME (daysl
0
2
4
6
8
10
12
14
16
18
20
22
24
25
5
0
2
SOIL DEPTH
[mm]
4
6
8
10
12
14
16
18
A 3Ed DRYING CYCLE
• 2nd DRYING CYCLE
20
Figure 2-25
Positions of the steep moisture
gradients (layers) in the upper soil
profile during the second and third
drying cycles.
110
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and third drying cycles.
The second drying cycle extended for 24
days, but the third drying cycle was maintained for only
11
days.
Differences were attributed to the higher evaporative demand in the
third drying cycle which resulted in the loss of approximately 15%
more water during the first 4 days after infiltration ceased.
Initially, in both drying cycles a sharp increase in the depth of the
steep moisture gradient was observed within a few days.
approximately 7 to
8
After
days the layers stayed essentially constant to
the end of the drying cycle,
the second layer was detected only
during the second drying cycle at a fairly constant depth of approxi­
mately 1.5 to 1.6 cm.
The second layer was not detected in the
beginning of the drying cycle, since the moisture content above this
layer was relatively high and subsurface return was attenuated too
much to detect the interference pattern at that level.
In the third
drying cycle, the experiment should have been continued beyond day
11
to determine whether another drying layer could be detected, a fact
not known at the time the experiment was conducted.
The results (Table 2-4) of this experiment could serve in the pre­
diction of the depth of crust during the drying of the soil.
Data in
Figure 2-26 indicate the development of the crust layer during the
third and second drying cycles.
In the second drying cycle the crust
which was initially observed at a depth of 4.7 mm, rapidly reached
approximately a
6
m m depth within a few days and then stayed fairly
constant to the end of the drying cycle.
In the third drying cycle, a
crust was developed at a 3.5 m m depth and sharply increased to
the end of the drying cycle.
6
m m at
The reason that the crust was initiated
at a shallower depth in the third drying cycle was postulated to be
111
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Table 2-4:
Days Into
Cycles
Depth to the steep moisture gradients as a function of
time.
Second Cycle
layer
2 nd layer
1 st
Third Cycle *
1 st layer
1
0.470
—
0.350
2
0.500
—
0.370
3
0.560
—
0.470
4
—
—
0.560
5
0.595
—
0.570
6
0.605
—
—
7
0.615
--
—
8
0.630
—
0.610
9
0.630
1.500
—
11
0.635
1.510
0.625
14
0.640
1.530
—
17
0.640
1.560
—
21
0.640
1.570
—
24
0.645
1.580
—
^No 2 nd layer was measured because of the higher evaporative demand
during the third drying cycle.
The lower moisture contents near the
soil surface resulted in nonoperable microtensiometers beyond day 1 0
of the drying cycle.
112
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10
S£
8
u.
O
6
_
4
• 20d DRYING CYCLE
2
P
2
A 3td DRYING CYCLE
Q.
Ul
0
4
8
12
16
20
24
DAYS INTO DRYING CYCLES
Figure 2-26
Development of the crust layer during
the third and second drying cycles.
113
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due to the higher evaporative demand which caused the surface to dry
faster.
114
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CONCLUSIONS
An analysis was conducted of data obtained from the field designed
to determine the relationships between microwave reflectivity and both
soil moisture and matric potential of bare soil surfaces.
Over a
restricted pressure range (approximately 0.05 to 0.75 bar) the log of
the bistatic reflectivity has excellent linear correlation with both
moisture content and matric potential.
This is shown to be consistent
with the water release characteristics of the Captina soil.
Matric
potential demonstrates improved correlation over moisture content at
greater depths.
This result appear to reflect the better internal
correlation of the matric potential measurements.
Moisture gradients in the near surface were shown to have a signi­
ficant effect on the reflectivity response in two distinct fashions.
First, it was demonstrated that moisture gradients in the field are
sufficient to produce a distinct layering effect.
approaches
As the layer depth
X/4 a coherent interference pattern is observed, par­
ticularly in the higher frequency range (4 to
8
GHz).
demonstrated from previous results in the laboratory.
This also was
The loss of
correlation appears to limit the sampling depth of the higher fre­
quency range to something less than would be predicted on the basis of
attenuation.
The lower frequency range (1 to 2 GHz) indicated a rela­
tively higher correlation and appears to have a significantly greater
sampling depth; however, the concept of sampling depth becomes
somewhat ambiguous when applied to surfaces that behave in the
coherent layered fashion observed.
115
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Second, extremely shallow layers in rough surfaces are shown to
reduce the sensitivity to moisture of near-saturated soil.
It is pro­
posed that the increased reflection from the smoother moisture boun­
dary compensates for the introduction of the drier layer, yielding an
increased total return.
The diurnal data are shown to demonstrate
this effect of increasing reflectivity with decreasing moisture.
116
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REMOTE SENSING OF THE WATER STATUS
OF A BARE SOIL USING MICROWAVE
AND HYDROLOGIC TECHNIQUES
Chapter III.
Estimating evaporation: A comparison between Penman,
Idso-Jackson, and zero-flux methods
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ABSTRACT
A field evaporation-drainage study was conducted to compare
three methods of predicting evaporative losses from a bare soil.
Two
of the methods (modified Penman combination and Idso-Jackson) are
dependent only on measurements of atmospheric parameters whereas the
third method (plane of zero flux) is dependent only on measurements of
soil parameters.
A Captina soil profile was wet up and allowed to dry by evapora­
tion and drainage.
For the initial two days after infiltration ceased
all three methods predicted similar evaporative losses.
Differences
between the three methods occurred when the soil moisture content at
the soil surface controlled the evaporation rates.
Under these con­
ditions the Penman method predicted the highest amounts of water eva­
porated from the soil surface.
Lower losses by evaporation were
predicted by the Idso-Jackson and zero-flux methods.
In the case of
the Idso-Jackson method this result was attributed to the influence of
clouds on albedoj the impact of wind and the importance of albedo in
the predictive equation.
For the zero-flux method the decrease in
evaporation was due to lower soil water contents and matric potentials
near the surface which resulted in lower transport rates of water to
the surface.
118
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INTRODUCTION
Evaporation of water from bare soils has been a major concern for
many scientists in recent years.
It influences the time of seedling,
herbicide and pesticide application, and many tillage practices.
Evaporation is also an important factor in both managing the irrigated
and dryland farming practices.
In dryland agriculture it is the eva­
poration process that contributed to the limited water conditions.
The inadequate water supply, however,
limits the crop production.
Due to the rapid increase in populations and continual decreases
in natural resources, the need for a good estimate of crop yields has
become even more immediate importance.
However, attempts have been
made to develop a method of evaporation estimation readily adaptable
to rapid application over large areas.
Idso et al. (1979) have
applied remote-sensing techniques and proposed a rather simple
equation to calculate daily evaporation rates from bare soil.
The purpose of this study was to evaluate the potential applica­
tion of the Idso-Jackson equation to a bare Captina soil under subhumid climatic conditions.
119
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REVIEW OF LITERATURE
Evaporation of water from bare soils is the process by which the
moisture content stored near the surface due to precipitation or irri­
gation is returned to the atmosphere.
In moisture-deficient regions
the loss of water through evaporation has been estimated to be 60% of
the total amount received by soils (Hanks and Gardner,
rate of evaporation
1965).
The
influences the time of seeding, scheduling of
irrigations, herbicide and pesticide applications, and tillage prac­
tices .
Hillel (1971) stated that there are three conditions necessary for
evaporation to persist.
First, there must be a continual supply of
energy to meet the latent heat requirement.
Second, there must be a
vapor-pressure gradient between the surface and the atmosphere.
The
third condition is that there must be a continual supply of water to
the site of evaporation.
The first two conditions are external and
influenced by meteorological factors which determine the "atmospheric
evaporativity" (the maximum evaporation rate from a free water
surface),
the third condition however, depends upon the soil moisture
content, soil water potential, and soil water conductive properties.
Lemon (1956) recognized the existence of three distinct phases of
evaporation from soil surfaces.
The first stage is the loss of water
from the soil surface at a rate equal to the atmospheric evaporative
demand.
During the second stage a rapid decline in evaporation rate
occurs due to drying of the surface.
In this stage the intrinsic soil
factors govern the rate of moisture movement to the soil surface.
During the third stage of evaporation, the rate of loss of water is
120
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slow.
This stage is predominant after the moisture content in the
soil becomes relatively low.
The concept of three distinct stages of
drying was determined in the laboratory and had little meaning under
natural field conditions (Jackson,
1973; Kimball 1971; Penman,
1963).
Idso et al. (1974) have demonstrated that under field conditions, a
simple albedo measurement will characterize the transition between the
different stages of evaporation.
Several methods have been developed over the years to calculate
evaporation rates (Penman,
1977; Jackson et al.,
tations.
1948; Black et al.,
1976).
1969; Idso et al.,
Each method, however, has certain limi­
First, they are dependent on many climatological parameters
and soil surface characteristics that vary significantly from location
to location.
Second, many have been developed to calculate the poten­
tial rate of evaporation, i.e., the evaporation rate under a condition
of non-limiting water supply at the surface.
However, evaporation
rates during this stage are controlled by the energy available at the
soil surface.
As a result, the potential evaporation rate stage is
known as the energy-limiting phase (Jackson et al.,
1976).
Scientists
have attempted to overcome these limitations and have proposed addi­
tional methods to estimate evaporation rates during both the potential
rate and the falling rate stage, i.e., a period in which the surface
moisture content becomes a limiting factor (Penman,
1979; Arya et al., 1975).
1963; Idso et al.,
These methods are called combination
methods and are considered to be both independent of the season of the
year and to be the most accurate over a wide range of climatic con­
ditions .
121
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Idso et al. (1979) developed a combination equation to calculate
daily evaporation rates from bare soil.
Their equation is simple and
requires inputs of daily shortwave and longwave radiation, maximum and
minimum air and soil surface temperatures, and average albedo values
for a given day.
It is to be noted that incorporation of the surface
temperature as an independent variable in their equation integrates
the effects of other parameters such as stability, windspeed, and
water vapor deficit involved in the Penman combination equation.
However, the question that needs to be addressed is whether evapora­
tion rates from other soils and climates could be adequately described
by the Idso-Jackson method.
The purpose of this study was to evaluate the potential applica­
tion of the equation proposed by Idso et al. (1979) to a bare Captina
soil under subhumid climatic conditions.
In order to evaluate an eva­
poration equation for a particular soil and climatic condition, it is
customary to conduct a field evaporation experiment on a weighing
lysimeter (a mass balance system).
A comparison between the evapora­
tion rates calculated using the equation and the values of the eva­
poration rates obtained using lysimeter data indicate the practical
application of the equation for that particular soil and climatic con­
dition.
Due to the lack of a lysimeter we decided to compare the
Idso-Jackson equation with two other methods which were developed from
somewhat different approaches.
These two additional methods were the
Penman combination method as modified by Penman (1963) and the plane
of zero-flux method which was given by Arya et al. in 1975.
122
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MATERIALS AND METHODS
This study was conducted from late July through August, 1983.
The
experimental site was located on the east side of the Main Experiment
Station, at Fayetteville, Arkansas in an area mapped as Captina silt
loam.
The Captina soil is classified as a Typic Fragiudult in the
fine, silty, mixed, mesic family.
It is moderately well drained,
slowly permeable and dominated in the lower horizons by a firm,
brittle fragipan.
A bare plot with dimensions of 3.7 m x 3 ra was constructed by
removing the grass vegetation and confining the area with a wooden
frame.
The boards of the frame were placed into the soil to a depth
of approximately
20
cm, leaving
10
cm above the soil surface; this was
designed to confine the soil moisture redistribution within the plot
area.
Instrumentation
The plot was instrumented with three banks of tensiometers (macro
and microtensiometers) with mercury manometers positioned at 1, 3, 5,
and 10 cm depths for microtensiometers, and at 15 cm increments
ranging from soil depths of 15 cm to 90 cm.
The microtensiometers
were constructed from a ceramic tube (1 bar porous ceramic, 2.5 cm
long, 0.6 cm 0. D., 1 m m wall thickness).
The ceramic material was
connected to the mercury manometer via nylon tubing from one side and
from the other side to a brass clamp for purging.
Each macroten-
siometer consisted of a porous cup (1 bar porous ceramic, 5 cm long, 2
cm 0. D., 3 mm wall thickness),
connected through a PVC tube to a mer­
cury manometer.
123
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Each bank also contained a system of thermocouples to measure soil
and air temperatures.
The thermocouples were made following the
instruction manual by Wescor, Inc., Logan, Utah.
The thermocouples
were connected directly to a data acquisition system (Model DL-520
data logger, Wescor, Inc., Logan, Utah).
After the experiment was terminated, the thermocouples were
calibrated by comparison measurements in a stirred, temperaturecontrolled water bath at temperatures of 15, 21, 25, 29, 31, 34, 37,
40, and 42°C, respectively.
A second degree polynomial regression
equation was developed to predict the variation in the temperatures of
the water bath and the temperatures response by the data logger.
Since each sensor responded differently for a given water bath tem­
perature, the sensors were calibrated individually.
At each bank air temperatures were determined at 25, 50, and 75 cm
heights above the soil surface within the plot area.
Each ther­
mocouple was protected from direct radiation by aluminum shields.
Soil temperature measurements were obtained at 1, 3, 5, 10, 15, 30,
and 50 cm soil depths.
The thermocouples in the soil were installed
at a 30 degree slant to minimize soil disturbance and heat conduction
down the wires, and were vertically aligned with one another.
After
installation of the thermocouples at the desired depths, soil was used
to backfill and seal the hole.
lated cable, buried
20
All the wires were housed in an insu­
cm deep, and routed underground to the shelter
containing the data-logger.
Those wires which were exposed were
wrapped in aluminum foil.
Surface soil temperatures were measured with an infrared ther­
mometer (Everest Interscience Model 110).
Sensitive to infrared wave-
124
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lengths from
8
to 14 jx m ) .
The soil surface temperatures were
observed from all four sides of the plot and the values were
averaged.
Meteorological Data
An automatic recording weather station (Campbell Scientific, Inc.)
was located within
10
m of the experimental plot and was used to
moni­
tor air temperature, relative humidity, wind speed, solar radiation,
and rainfall.
Solar radiation was measured with a model LI2005 LI-COR
silicon pyranometer, relative humidity (RH) with two shaded thermistor
and RH probes (Model R01).
within the plot.
One RH probe was located above the soil
All the data were collected and recorded hourly
using a micrologger (CR21)
and a cassette tape recorder.
Incoming and reflected solar radiation over the plot were measured
by upright and inverted Eppley pyranometers located 2 meters above the
soil surface.
The pyranometers were connected to a dual channel DC
analog recorder.
Since both pyranometers had the same calibration
constant, the reflectivity values were determined from the ratio of
the reflected energy to the incoming energy.
The reflectivity within
the range of wavelengths of 0.4 - 1.2 Jim was defined as albedo.
Experimental Procedure
After the plot was instrumented, water was applied through a per­
forated plastic garden hose.
A steady-state flow rate was established
between the application rate and infiltration rate of water in the
plot in order to keep water from ponding.
The wetting procedure was
continued until the soil profile appeared saturated as indicated by
125
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the tensiometers.
After infiltration of water ceased, the drying
cycle began.
Measurements taken included tensiometer readings, soil and air
temperature readings, albedo, relative humidity, wind speed, and solar
radiation.
At the beginning of each drying cycle, the soil was nearly
saturated and the rate of water movement decreased sharply with time.
Therefore, measurements of the parameters were taken every two hours
from 8:00 a.m. to 8:00 p.m. for five consecutive days.
As the soil
dried by evaporation and drainage, the frequency of measurements were
reduced.
Three drying cycles were evaluated; the first cycle was ter­
minated after four days due to the rain.
The second and third cycles
were terminated when the microtensiometers at the
1
cm soil depth
reached - 0 . 6 bars.
Data obtained from the three drying cycles were used to calculate
daily evaporation using the Penman, zero-flux, and Idso-Jackson
methods.
Penman (1963) combined the theories of energy balance and
mass transport by the process of eddy diffusion and developed the
following equation:
E - ( ^
(Rn+ G > + ^ 1 5 . 3 6 .£<•,-«„>]
* 1-72 * 1<T2
Where E is the evaporation rate (mm/day),
pressure-temperature curve in mb/C,
Y
A is the slope of the vapor
is the psychrometer constant in
mb/C, Rn is the net radiation in G is the soil heat flux to the sur­
face in ly/day,
(ea - e^) is the mean daily vapor pressure deficit in
mb, and 15.36 is a constant of proportionality in ly/day x mb, Wf is
the wind function (dimensionless) and is expressed as
126
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where U z is the daily wind travel (Km/day) at z meters above the
ground.
The tabulation of this equation is given in Jensen (1981).
However, in this study for the calculation of net radiation in Penman
equation the daily albedo values of the bare soil were considered and
the regression coefficient values in equation [3] were selected, from
Table 6.2 in Jensen (1981) for our condition, as 1.0 and 6.21 x 10-^,
respectively.
The zero-flux method was first suggested by Richards et al.
and was later modified by Arya et al. (1975).
(1956)
This method is based on
the assumption that in a soil profile, which is subjected to both eva­
poration and drainage, there exists a zero flux plane which will
separate the portion of soil water which moves upward in response to
evaporation from that which moves downward in response to drainage.
There is no water movement across this zero flux plane.
The flux of
water at any depth is calculated by integrating the rate of change in
moisture content with time from the zero flux plane to the depth in
question.
It is to be noted that the values of soil moisture contents
were determined from the moisture release curves developed for various
soil depths of the study site.
Daily evaporation rates at the surface
were calculated as follows:
127
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where zjj + l is the soil surface and 1 < z < N is the depth of tensiometers.
The average hydraulic gradients were calculated for various soil
depth intervals.
The zero gradient was obtained by interpolating the
gradient where the hydraulic gradients changed from negative to posi­
tive values.
drying cycle.
This was calculated on a daily basis throughout the
The depths to their zero gradients were plotted against
time to determine the position of the "zero flux" boundary.
Idso et al. (1975) presented a method for calculating evaporation
of water from wet and dry soils.
Their method described both the
energy-limiting and the soil-limiting phases but did not explicitly
treat the transition phase.
In 1976 Jackson et al. utilized albedo
measurements to partition the fraction of the soil surface area
involved in the potential evaporation and the fraction exhibiting
soil-limiting evaporation.
These albedos were used to calculate
actual evaporation rates during the transition evaporation phase.
They compared the results with lysimetrically determined evaporation
rates, and concluded that this improved method could be used as a
reliable means for calculating evaporation rates during the transition
phase of soil drying.
Idso et al. (1979) derived a single equation to predict evapora­
tion rates from all stages by combining the equations governing eva­
poration rate during each stage of evaporation.
The equation was
presented as:
E = (3/8+5/86)(SN+1.5SLN+156) * 1.72 x 10- 2 ,
P=
(ad-a)/(ad-aw ),
LN = R a -R s
128
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where E is daily actual evaporation rate (mm/day),
solar radiation (ly/day),
is daily net
is the thermal radiation from the
atmosphere and is given by Idso and Jackson (1969), Rg is the thermal
radiation from soil using the Stephan-Boltzmann equation, a^ is dry
soil albedo, aw is wet soil albedo, and a is the soil albedo at any
given time.
In the derivation of equation [5], Idso et al. first
noted that the evaporation rate was largely proportional to net
radiation in the potential rate phase, and that net radiation was then
subdivided into two components:
thermal radiation (Lfj).
net solar radiation
(S
jj)
and net
was an external force and was assumed to
be independent of evaporation whereas Lf] was affected by surface tem­
perature.
The constants of (1.56 Lfj + 156) in equation [5] was
obtained using linear regression technique on the nighttime data when
no solar radiation was present (Idso, 1975b).
The parameter
was
defined as the partitioning factor during the transition from wet to
dry soil.
Tabulations of R^ and Rg are given in Brown (1973).
129
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RESULTS AND DISCUSSION
Soil Hydraulic Relations
Knowledge of the hydraulic properties of the Captina soil was
required before an evaluation of the potential application of the
Idso-Jackson equation could be made for the study site.
A typical
example of the water content and the total water potential distribu­
tions after infiltration ceased is shown in Figure 3-1.
These results
are from the third drying cycle (the longest drying period) and repre­
sent the 8:00 a.m. values.
A significant loss of water from the pro­
file was observed within the first 24 hours of drying,
however,
it is
during this stage of soil drying that the soil can supply water to the
surface at a rate sufficient to meet the evaporation demand of the
atmosphere.
During the initial 10 days of drying the soil moisture
content at the soil surface decreased from 0.49 to 0.28 cm-tycm^
(approximately a 40% decrease); from the 60 to 90 cm depth (fragipan
zone) the decrease in soil moisture content was 0.06 cm^/cm^ (a 15%
decrease).
The total soil water potential profiles indicated that the
profile was near saturation at the initiation of the study.
The
largest decrease in soil water potential occurred at the soil surface
whereas the smallest decrease occurred within the fragipan where the
changes in soil water content were small.
In general, as the soil
profile dried, drainage rates of water decreased rapidly.
This result
was associated with the restriction of flow of water by the fragipan.
The depths to the plane of zero-flux for the three drying cycles
are shown in Figure 3-2.
Average daily hydraulic gradients were
plotted as a function of soil depth, the daily depth to the plane of
130
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TOTAL SOIL WATER POTENTIAL (cm)
-500
E
o
W
-400
-300
-200
-100
VOLUMETRIC WATER CONTENT(cm3cm'3)
025
OS)
0.35
040
045
050
0*— days alter
Infiltration
ceased
40
&
Ui
a
=!
o
co
CAPTINA SOIL
CYCLE 3
80
100
Figure 3-1
Volumetric water content and total soil water potential profiles
during the third drying cycle.
DEPTH TO THE 2ERO
FLUXlcml
CAPTINA SOIL
CYCLE 1
40
CYCLE 3
60
0
40
80
120
160
200
TIME I hours |
Figure 3-2
Depth to the zero-flux plane as a
function of time during the three
drying cycles.
132
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zero-flux was Chen obtained by interpolating where the sign of the
hydraulic gradients changed from negative to the positive values.
Data in Figure 3-2 indicated that for the three drying cycles, the down­
ward movements of the zero-flux plane in the profile were curvilinear.
After 80 hours the slopes of the curves were less steep as the zero
flux plane moved deeper into the profile.
By 200 hours after
infiltration ceased, the plane of zero flux was located at the 90 cm
soil depth.
Prediction of Evaporation
The cumulative evaporation during the three drying cycles using
Penman, zero-flux, and Idso-Jackson methods are presented in Figures
3-3, 3-4, and 3-5.
The parameters used in the calculations for the
three methods are presented in Appendix Tables 4, 5, and
tively.
6
, respec­
These results showed that for the first two days of each
drying cycle, the variation between the amount of evaporation esti­
mated from each of those methods was not significant.
Consequently,
it may be concluded that, during the initial periods of each drying
cycle when there was no deficit of water at the surface, each of the
three methods predict similar rates of evaporation.
This two-day
drying period could perhaps be considered as first stage evaporation.
The first drying cycle was terminated after four days due to rain­
fall.
The results of the predicted evaporation, which are presented
in Figure 3-3, showed that the predicted evaporation rates were similar
for all three methods.
As the soil dried, the evaporation rates
calculated by the Penman method were slightly higher than those calcu­
lated from the zero-flux and Idso-Jackson methods.
This was expected,
133
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6.0
5.0
CAPTINA SOIL
CYCLE 1
EVAPORATION Icm l
4.0
3.0
PENMAN
2.0
IDSO-JACKSON
ZERO-FLUX
0
40
80
120
160
200
240
HOURS AFTER THE CESSATION OF INFILTRATION
Figure 3-3
Cumulative evaporation rates calculated
from Idso-Jackson, zero-flux, and Penman
methods during the first drying cycle.
134
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I
EVAPORATION
°
30 1
/ / \
M /
PENMAN
f t
2.0
CAPTINA SOIL
CYCLE 2
/
/jf
to 1“
v
/'y
40
80
120
160
200
HOURS AFTER THE CESSATION OF INFILTRATION
Figure 3-4
Cumulative evaporation rates calculated
from Idso-Jackson, zero-flux, and Penman
methods during the second drying cycle.
135
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6.0
PENMAN
5.0
4.0
EVAPORATION
Ic m l
ZERO-FLUX
3.0
IDSO-JACKSON
2.0
CAPTINA SOIL
CYCLE 3
///
1.0
0
40
80
120
160
200
240
HOURS AFTER THE CESSATION OF INFILTRATION
Figure 3-5
Cumulative evaporation rates calculated
from Idso-Jackson, zero-flux, and Penman
methods during the third drying cycle.
136
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since most of the inputs from the Penman equation come from the
atmospheric data with the assumption that there is always enough water
at the surface to meet the evaporative demand of the atmosphere.
In
this field study, the soil moisture content near the surface decreased
after two days from its maximum level required for the Penman method.
One can question whether the same would be true for Idso-Jackson
method since the only soil surface parameter involved in both tech­
niques is the albedo.
The answer is that the variation in the albedo
values in the Penman equation is not as significant as is the case for
the Idso-Jackson equation.
An increase of 10% in albedo resulted in a
10% decrease in evaporation rate using the Idso-Jackson equation,
whereas, with the Penman equation the decrease in evaporation was
approximately 1.5%.
Since the first drying cycle lasted only four
days, the effects of variation in albedo on the calculated evaporation
rates could not be adequately determined.
The second and the third drying cycles were continued as long as
the microtensiometers at the 1 cm depth could function properly.
The
soil water matric potentials at failure were between -0.5 and -0.6
bars.
The results of the second drying cycle are presented in Figure
4 and indicate a somewhat different evaporative condition than
observed during the first drying cycle.
During the first two days
after infiltration ceased, the variation in evaporation rates esti­
mated from the three methods was minimum.
Values of evaporation
calculated from the Penman method were slightly lower than those
calculated from both the Idso-Jackson and zero-flux methods.
This was
probably due to the climatological conditions during the second drying
cycle such as the high relative humidity,
low wind speed, higher
137
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
values of the maximum air temperature, less cloud cover, and a con­
tinuous increase in the albedo values (Table 3-1).
These climatologi­
cal conditions were more like those of arid regions such as central
Arizona where the Idso-Jackson equation was developed.
The higher
values of the evaporation estimated by the zero-flux method in the
second drying cycle as compared with the first drying cycle was due to
a more rapid increase in the depth of the plane of the zero-flux.
This was a result of the higher evaporative demand of the atmosphere
during the second drying cycle (Table 3-1).
It was also interesting to note that there was a decline in the
rate of evaporation for both zero-flux and Idso-Jackson methods toward
the end of the second drying cycle.
This was a result of a signifi­
cant decrease in soil water content near the surface for zero-flux
method and a considerable increase in albedo for Idso-Jackson
equation, respectively.
A decrease in moisture content near the soil
surface would result in lower transport rates of water to the soil
surface and lower evaporation rates.
Equation [1] suggests an
increase in albedo of the soil surface would also result in lower eva­
poration rates.
Meanwhile, evaporation rates calculated from the
Penman method remained relatively constant even toward the end of the
drying cycle.
This was because the rates of evaporation calculated
from the Penman method are primarily dependent upon meteorological
data only.
This result was also observed in the third drying cycle.
The cumulative evaporation for the third drying cycle is shown in
Figure 3-5.
This drying cycle, which was continued for 11 days, was
conducted during climatological conditions somewhat different than the
previous cycles.
During this drying cycle higher wind speeds (three
138
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
respectively.
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July
cycles,
Average
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the
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139
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
times more than the values obtained during the first and second drying
cycles), lower temperatures, and more cloudy days were prevalent.
Cumulative evaporation rates calculated from the zero-flux method were
higher during the first half of the drying cycle than those from the
other two methods.
This was due to a rapid increase in distance to
plane of the zero-flux (Figure 3-2) during the third drying cycle.
It is suggested that the Penman and Idso-Jackson methods may
underestimate evaporation under conditions of relatively lower
radiation and higher wind speeds.
From the results shown in Figure 3-5,
the major differences between method occurred at 72 to 96 hours after
infiltration ceased.
The average daily wind speed during this period
was 3.7 m/sec which was roughly twice the wind speed during the second
drying cycle.
Solar radiation during this same period averaged 503
ly/day compared to 556 ly/day during the second
drying cycle (Table
3-1).
As drying
the zero-flux
of the soil continued evaporative losses predicted by
method declined.
This can be attributed to the
decreased soil water contents and matric potentials near the soil sur­
face which resulted in lower transport rates of water to the surface.
Values of the evaporation estimated by Penman method were con­
sistently higher than those of the Idso-Jackson method.
The cloudy
climatic conditions during the third cycle lowered the predicted eva­
poration by the Idso-Jackson method.
The increased cloud cover caused
the albedos to be higher and consistently uniform particularly during
the initial soil drying stages.
This resulted in relatively low daily
evaporation rates predicted by Idso-Jackson method.
140
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CONCLUSIONS
The Idso-Jackson, Penman combination equations, and zero-flux
methods were used to estimate evaporative fluxes in a drying soil pro­
file under subhumid climatic conditions.
Each of the three methods
predicted similar rates of evaporation during the initial stage of the
soil drying.
However, differences between the three methods were more
prominent as the drying process continued beyond the initial stage of
evaporation.
This was attributed to the distinct characteristics of
the energy-limiting phase (when there were no deficits of water at the
soil surface) and the soil-limiting phase (when the soil moisture sta­
tus controlled the evaporation rates).
During the third and longest drying cycle, evaporative fluxes esti­
mated by the Idso-Jackson method were lower than those estimated by
both the Penman and the zero-flux methods.
A possible explanation for
this result was the significant impact of albedo on the estimated eva­
poration rates in the Idso-Jackson equation.
Under arid climatic con­
ditions such as in Arizona, where the Idso-Jackson equation was
originally developed, a steady increase in the albedo values during
the drying process occurred.
This was not the case under the subhumid
climatic conditions such as in Arkansas where values of albedo fluc­
tuated or even remained constant depending upon the presence of the
partly or completely cloudy days during the drying processes.
Consequently, cloudy conditions contributed to the lower evaporation
rates predicted by the Idso-Jackson equation.
wind,
In addition, under high
low radiation conditions, some modification may be necessary.
These results suggest that a modification for the various climatic
conditions on this method of estimating evaporation should be made.
141
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDICES
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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measurements
from
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Appendix
Table
2:
Reflectivity measurements
July 7, 1980.
from
second
drying
cycle,
June
30
S
o
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S
•H
*h
rC
00
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pH
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144
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix Table 3:
Date
7-28-80
tt
It
tl
7-29-80
II
II
II
7-30-80
II
7-31-80
ii
8-1-80
Time,
hr.
Reflectivity measurements from third drying cycle, July 28 through
August 1, 1980.
Cumulative
Time, hr.
08
000
11
003
006
009
024
027
030
033
048
054
072
078
14
17
08
11
14
17
08
14
08
14
14
102
Frequency
1.5 GHz
0.569
0.575
0.631
0.556
0.562
0.519
0.525
0.431
0.422
0.272
0.263
0.190
0.197
Reflectivity
Frequency
6.0 GHz
0.164
0.182
0.197
0.158
0.144
0.178
0.214*
0.172
0.164
0.090
0.096
0.028
0.019
^m
-cm
12
25
53
84
83
114
389
272
245
464
433
487
619
cra^/ cm3
0.420
0.417
0.400
0.380
0.380
0.368
0.325
0.330
0.340
0.320
0.320
0.315
0.310
Appendix Table 4:
Cycle
1
1
1
1
2
2
2
2
Time
(hrs)
(°C)
RH
(%)
24
48
72
96
27.5
27.5
28.4
28.6
52
58
53
49
350
286
382
322
24
48
72
96
26.2
26.9
27.9
30.3
29.1
28.2
26.9
27.8
29.0
61
53
59
46
59
56
51
42
42
313
369
402
380
389
342
336
313
282
24.6
24.3
26.2
27.7
29.5
29.4
28.3
26.8
27.5
26.9
43
42
49
49
50
49
51
46
43
46
365
337
309
325
355
312
323
306
276
279
2
120
2
144
168
192
216
2
2
2
3
3
3
3
3
3
3
3
3
3
Tabulated values of the parameters used in Penman
method for three drying cycles.
24
48
72
96
120
144
168
192
216
240
Rn
G
Wf
(ea“ed)
(mb)
(ly/d)(ly/d)(Km/d)
13
15
18
20
15
20
21
20
1.91
1.68
2.62
1.91
1.61
1.53
1.85
2.13
28
18
24
—
—
2.10
16
17
13
1.85
1.85
2.80
3.20
2.83
2.55
2.54
2.73
2.49
1.98
10
23
22
23
23
32
28
1.92
1.75
1.79
1.99
11.5
9.0
12.0
14.0
8.8
9.0
8.5
17.0
9.0
13.0
11.0
Albedo
0.765
0.765
0.769
0.754
6.14
4.85
7.21
6.17
0.14
0.15
0.15
0.16
0.16
0.17
0.18
0.753
0.759
0.768
0.787
0.779
0.771
0.759
0.767
0.778
5.17
5.95
6.55
7.45
6.69
6.28
5.92
5.56
5.64
0.740
0.738
0.753
0.766
0.783
0.782
0.772
0.758
0.764
0.759
6.24
5.90
6.54
7.18
7.36
6.84
6.58
6.64
0.20
11.0
0.17
0.17
0.18
0.19
0.19
0.19
13.0
14.0
14.0
16.0
13.0
13.5
14.0
10.0
Evap.
(mm)
0.15
0.16
0.16
0.15
13.0
16.0
11.0
A
A+r
0.23
0.20
0.23
0.24
0.24
146
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6.21
5.27
Appendix Table 5:
Cycle
1
1
1
1
Time
Rs
Albedo
RA
Ts
ta
(hrs) (°C) (ly/d) (%) (ly/d)
27.5
27.5
28.4
28.7
818
820
835
841
28.6
28.4
29.1
29.9
968
966
975
985
0.15
0.16
0.16
0.15
0.909
0.818
0.818
0.909
-150
-146
-140
-144
552
429
602
505
469
360
506
429
6.34
4.39
6.76
5.84
26.2
26.9
27.9
30.3
29.1
28.2
26.9
27.8
29.0
798
811
827
947
966
967
973
983
952
969
977
972
0.14
0.15
0.15
0.16
0.16
0.17
0.18
1.000
0.909
0.909
0.818
0.818
0.727
0.636
0.454
0.182
-149
-155
-141
-104
-135
-120
-158
-152
-127
473
574
606
610
587
532
562
541
523
407
488
515
512
493
441
460
433
403
5.68
6.51
7.33
7.69
848
832
811
825
845
26.9
28.4
28.5
28.9
29.7
27.3
28.6
29.2
28.9
24.6
24.2
26.2
27.7
29.5
29.4
28.3
26.8
27.5
26.9
772
766
798
824
854
852
834
808
820
811
24.3
24.1
23.4
24.4
26.5
25.7
25.9
25.7
26.7
27.9
915
912
904
916
942
932
935
932
945
960
0.727
0.727
0.636
0.545
0.545
0.545
0.454
0.182
0.090
0.090
-143
-146
-106
-92
582
542
488
517
544
485
511
530
489
466
483
450
400
419
441
393
408
408
372
349
2
2
120
2
144
168
192
216
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
LN
Ss
SN
Evap.
(ly/d) (ly/d)(ly/d) (mm)
24
48
72
96
24
48
72
96
2
Tabulated values of the parameters used in
Idso-Jackson method for three drying cycles.
24
48
72
96
120
144
168
192
216
240
868
0.20
0.23
0.17
0.17
0.18
0.19
0.19
0.19
0.20
0.23
0.24
0.24
-88
-79
-101
-124
-125
-149
6.68
5.84
4.91
3.99
3.02
5.93
5.38
5.20
5.31
5.66
5.24
4.61
3.10
2.47
2.02
147
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix Table 6:
Cycle
1
1
1
Time
(hrs)
2
2
120
2
144
168
192
2
2
2
2
3
3
3
3
3
3
3
3
3
Depth to the plane of
zero-flux
(cm)
24
48
72
24
48
72
96
2
Tabulated values of the parameters used in zeroflux method for three drying cycles.
11
24
60
12
27
66
70
75
72
83
90
24
48
72
96
11
47
59
70
75
120
144
168
192
216
68
79
90
90
Evaporation
rate
(mm)
6.35
4.21
6.86
6.89
5.16
8.33
7.57
6.44
4.51
4.00
3.14
6.43
7.67
7.85
7.33
6.50
4.32
4.98
2.56
2.58
148
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