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Order Number 8911086
Active microwave remote sensing of a natural, tallgrass prairie
and a projected disk component model to explain the behavior of
a modified dielectric disk model
Martin, Robert David, Jr., Ph.D.
Kansas State University, 1988
UMI
300 N. Zecb Rd.
Ann Arbor, MI 48106
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ACTIVE MICROWAVE REMOTE SENSING OF A
NATURAL, TALLGRASS PRAIRIE
AND
A PROJECTED DISK COMPONENT MODEL
TO EXPLAIN THE BEHAVIOR OF
A MODIFIED DIELECTRIC DISK MODEL
by
ROBERT D. MARTIN, JR.
B.S., Texas A&M University, 1982
M.S., Texas A&M University, 1984
A DISSERTATION
submitted in partial fulfillment of the
requirements for the degree
DOCTOR OF PHILOSOPHY
AGRONOMY
KANSAS STATE UNIVERSITY
Manhattan, Kansas
1988
Major Professor
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TABLE Of CONTBNTB
Page
TABLE OF C O N T E N T S ........................................ i
LIST OF T A B L E S .......................................... iii
LIST OF F I G U R E S .......................................... v
ACKNOWLEDGEMENTS .........................................
x
CHAPTER ONE - INTRODUCTION ..............................
1
CHAPTER TWO - LITERATURE REVIEW ......................... 5
INTRODUCTION ............................................. 6
ACTIVE MICROWAVE REMOTE 8ENSING OF 80IL MOISTURE . . . . 9
Soil Parameters
............................ . . . . . 9
Dielectric P r o p e r t i e s ...............................10
R o u g h n e s s ........................................... 12
Sensor P a r a m e t e r s ..................................... 14
Frequency R e s p o n s e ................................... 14
Angular R e s p o n s e ..................................... 16
Po l a r i z a t i o n ..........
17
crop cover influence on c*'s Relationship
to Soil M o i s t u r e ................................... 20
ACTIVE MICROWAVE REMOTE SEN8ING OF V E G E T A T I O N ......... 22
Field S t u d i e s ......................................... 23
M o d e l i n g ................................................25
Simple Physical M o d e l s .............................. 25
Mathematical M o d e l s .................................29
Field A p p r o a c h ..................................... 29
Intensity A p p r o a c h .................................31
C O N C L U S I O N ................................................35
R E F E R E N C E S ................................................37
CHAPTER THREE - C-BAND 8CATTER0METER MEASUREMENTS
OF A NATURAL, TALLGRA88 PRAIRIE
. . . .40
A B S T R A C T .................................................. 41
I NTR O D U C T I O N ............................................. 43
MATERIALS AND M E T H O D S ................................... 45
Location and Site D e s c r i p t i o n ........................ 45
Radar M e a s u r e m e n t s ..................................... 46
Soil M e a s u r e m e n t s ..................................... 49
Vegetation M e a s u r e m e n t s .............................. 52
RESULTS AND D I S C U S S I O N ................................... 53
Correlations Between a* and Vegetation Parameters
. .53
Correlations and Partial Correlations
Between a ’ and Leaf Water P o t e n t i a l ................56
Correlations Between a* and Expressions
of Soil M o i s t u r e ................................... 62
i
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Page
C O N C L U S I O N S ............................................. 73
R E F E R E N C E S ....................................
. .76
CHAPTER FOUR - A PROJECTED DISK COMPONENT MODEL TO
EXPLAIN TEE BEHAVIOR OF A MODIFIED
DIELECTRIC DISX M O D E L .................... 79
A B S T R A C T .................................................. 80
INTRODUCTION ............................................. 82
MATERIALS AND M E T H O D 8 ................................... 83
Site D e s c r i p t i o n ....................................... 83
Vegetation M e a s u r e m e n t s .............................. 84
Soil M e a s u r e m e n t s ..................................... 87
Radar M e a s u r e m e n t s ..................................... 89
RESULTS AND D I S C U S S I O N ................................... 91
Attenuation Measurement R e s u l t s ...................... 91
Unmodified Disk Model R e s u l t s ........................ 94
Modification of the Disk M o d e l ....................... 106
Modified Disk Model Results
........................ 106
Projected Disk Component
Model.................... 130
Projected Disk Component
Model Description ...... 131
Projected Disk Component Model Results .............. 137
Results of the MDM Explained by the P D C M ............ 143
Implications of the PDCM Results beyond the MDM
. .145
C O N C L U S I O N S ............................................ 148
Appendix A. Calculation of the Horisontal and
Vertical Components of a Projected Disk...............151
R E F E R E N C E S ...............................................157
ii
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LIST OF TABLES
Table
Page
2.1. Radar frequencies and equivalent wavelengths.
7
3.1. Konza site locations and burn histories.
47
3.2. Soil properties for each year and treatment.
50
3.3. Summary statistics of the vegetation parameters
for all years and treatments.
54
3.4. Correlation coefficients for o* versus various
vegetation parameters for all ^ears and
treatments and all polarization combinations
for the 45* view angle.
55
3.5. Correlation coefficients for o* versus leaf
water potential and partial correlation
coefficients for a ’ versus leaf water potential
given volumetric s<5il moisture for the combined
1985 and 1986 data.
57
3.6. Correlation coefficients for a* versus
volumetric soil moisture for all polarizationview angle combinations, years and treatments.
64
3.7. Linear regression equations of a* (HH15) versus
each expression of soil moisturecr(independent
variable) for 1984. RMSE is the root mean
square error.
67
3.8. Linear regression equations of a ’ (HH15) versus
each expression of soil moisturetr(independent
variable) for 1985. RMSE is the root mean
square error.
68
3.9. Linear regression equations of o' (HH15) versus
each expression of soil moisturetr(independent
variable) for 1986. RMSE is the root mean
square error.
69
3.10. Regression coefficients and statistics for the
combined data sets of all three years for those
expressions of soil moisture which exhibited
groupings of the sensitivity of o' (HH15) to
soil moisture into burned and unbUrned classes.
70
iii
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Table
Page
4.1. Two-way path loss (attenuation) values (in dB)
for the sunflower canopy using 15* angle of
incidence.
92
4.2. Percentage of total canopy fresh weight.
93
4.3. Variable inputs to Eom and Fung's model used to
produce the results seen in Figures 4.3-4.10
and 4.13-4.28.
108
4.4. Inputs to the disk model which were treated as
constant for the four days represented in
Figures 4.3-4.10 and 4.13-4.28.
109
4.5. Linear regression statistics for measured (inde­
pendent variable) versus predicted (dependent
variable) a^ using the UDM and the MDM.
127
4.6. Linear regression statistics for measured (inde­
pendent variable) versus predicted (dependent
variable) a*
using the UDM and the MDM.
r1n
128
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LIST OF FIGURES
Figure
2.1
2.2
2.3
3.1
3.2
3.3
3.4
4.1
4.2
4.3
Page
"Relative contributions of coherent and
diffuse scattering components for different
surface-roughness conditions: (a) specular,
(b) slightly rough, (c) very rough." (Ulaby
et al., 1982b)
13
"Angular response of scattering coefficient
for ... five fields for high levels of
moisture content at (a) 1.1 GHz, (b) 4.25
GHz, and (c) 7.25 GHz." (Ulaby et al., 1978)
15
"Angular dependence of the depolarization
ratio of a smooth surface." (Ulaby et al.,
1978)
19
Soil moisture release curves for all years
and treatments.
Points on the lines are not
measured values, but are shown to aid in line
identification.
51
Backscattering coefficient (W45) versus leaf
water potential for the burned and unburned
treatments.
60
Mean leaf water potential versus day of year
for the burned and u n b u m e d sites.
Standard
error bars indicate one standard deviation
about the mean.
61
Scatter plot and lines-of-best-fit of the
backscattering coefficient (HH15) versus
volumetric soil moisture for the burned and
unbumed, 1984 sites.
63
Relationship of volume of water displaced by
an immersed sunflower plant to the wet weight
of the sunflower plant.
86
Dielectric constant versus volumetric soil
moisture for the sunflower field.
88
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
96
v
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Ficrure
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
Page
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
97
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
98
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
99
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
100
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
101
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
102
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
103
The measured leaf angle distribution for a
sunflower canopy.
104
Probability density functions for the leaf
inclination angles of five theoretical canopy
types.
107
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
110
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
111
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
112
vi
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4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
4.26
4.27
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
113
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
114
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
115
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
116
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH
polarization.
117
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
118
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
119
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
120
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
121
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
122
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
123
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
124
vii
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Ficrure
4.28
4.29
4.30
4.31
4.32
4.33
4.34
4.35
Page
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W
polarization.
125
The vertical projection (V) of a unit, planar
disk rotated azimuthally from 0 to 360* as
viewed from nadir.
Each curve represents a
disk at a different angle of inclination
indicated by the number (the disk normal's
angle in degrees from zenith) beside the
curve.
134
The vertical projection (V) of a unit, planar
disk rotated azimuthally from 0 to 360* as
viewed 45* from nadir.
Each curve represents
a disk at a different angle of inclination
indicated by the number (the disk normal's
angle in degrees from zenith) beside the
curve.
135
The vertical projection (V) of a unit, planar
disk rotated azimuthally from 0 to 360* as
viewed 90* from nadir.
Each curve represents
a disk at a different angle of inclination
indicated by the number (the disk normal's
angle in degrees from zenith) beside the
curve.
136
The horizontal projection (H) of a unit,
planar disk rotated azimuthally from 0 to
3 60° as viewed from any angle from nadir to
90* off-nadir.
Each curve represents a disk
at a different angle of inclination indicated
by the number (the disk normal's angle in
degrees from zenith) beside the curve.
138
The horizontal delta function (H1) for five
disk inclination angles (indicated in legend
at bottom of graph).
139
The vertical delta function (V') for five
disk inclination angles (indicated in legend
in lower left of graph).
140
The horizontal component (HN) of the disk
integrated over all azimuths and inclination
angles for the five theoretical canopy types.
141
viii
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Ficrure
4.3 6
A.4.1
A.4.2
A.4.3
Page
The vertical component (V") of the disk
integrated over all azimuths and inclination
angles for the five theoretical canopy types.
142
The projection of a unit, planar disk onto
the hv-plane.
153
Geometry used in solving for the horizontal
component of a unit, planar disk rotated in
three-dimensional space. The dashed line
represents the intersection of the ab-plane
(cross-hatched area) with
the
disk.
154
Geometry used in solving for the vertical
component of a unit, planar disk rotated in
three-dimensional space. The dashed line
represents the intersection of the ab-plane
(cross-hatched area) with
the
disk.
156
IX
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ACKNOWLEDGEMENTS
A number of people generously helped me and influenced
me on this project and I would like to take this
opportunity to thank them.
I wish to express my sincere appreciation to Dr. E. T.
Kanemasu, committee chairman, for his professional and
personal guidance during the course of this study.
I would also like to extend my gratitude to Dr.
Mary Beth Kirkham, Dr. James Koelliker, and Dr. Loyd Stone
for serving on my committee and reviewing this manuscript.
Thanks are extended to the following individuals for
their respective roles in the successful completion of this
dissertation.
Dr. Ghassem Asrar for his ideas and enthusiasm for
this project.
Dr. David Brunfeldt for his help in maintaining the
radar equipment, his patience when explaining the
fundamentals of radar, and his insights on the future of
radar remote sensing.
Dr. Ranga Myneni and Bruce Burnett, friends and
colleagues, for their opinions and insights on different
aspects of this work and the world in general.
Dr. Paul Chen and Dr. Adrian Fung, for generously
allowing me the use of their model and their help with
modifying the model.
Mr. Dale Reed for his help in maintaining the field
equipment and his good hearted insights on everything from
raising children to growing wheat.
Ms. Janet Killeen for providing student workers at
critical times in the project despite the great demands on
this precious commodity for other projects.
Dr. Marvin Bauer, for allowing me the time to complete
this dissertation after hiring me to work at the Remote
Sensing Lab, University of Minnesota.
The National Aeronautics and Space Administration for
supporting in part this work under Grant NAG-5-389.
Special thanks are extended to my family in Texas.
Though we were many miles apart, your support and
encouragement over the years has come through loud and
clear.
Finally, I would like to say thank you to my wife Jean
and my son Ben. Thanks, Jean, for the countless ways in
which you helped me in my graduate career and for your
patience in this long journey. Thank you, Ben, for helping
me put my work in its proper perspective.
x
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CHAPTER OMB
INTRODUCTION
I
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Over the past 14 years, a great deal of research has
been focussed on determining the potential use of active
microwave remote sensing in agricultural and natural
resource applications.
The interest in active microwave
remote sensing stems from the ability of radar to penetrate
cloud cover and to provide its own source of illumination.
Most of the research to date has concentrated on
determining the optimal sensor configuration for the remote
detection of soil moisture, but there has also been some
effort to determine the sensitivity of active microwave
systems to vegetation canopy parameters.
A review of the
work in active microwave remote sensing over the last 14
years is presented in the following chapter, Chapter Two.
In 1983, a series of experiments were initiated by
NASA/JSC under the Mobile C-Band Scatterometer and Optical
Radiometer for Vegetation Characteristics Estimation
Research (MCSORVCER) program.
One purpose of the program
was to increase the information base of the C-band (i.e.,
4.75 GHz frequency or 6.3 cm wavelength) backscattering
properties of a variety of vegetation types.
These types
included mixed deciduous forests, cypress and pine stands,
aspen and black spruce stands, a peach orchard, a crop of
sunflowers, and tallgrass prairie.
Chapter Three of this dissertation reports the
findings of three summers of C-band scatterometer
measurements of a tallgrass prairie.
It can be viewed as a
2
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step in furthering our understanding of what the C-band
backscattering coefficient tells us about the various
canopy elements and soil parameters of a grassland area.
The objectives of this study were to (1) determine the
degree of correlation between soil moisture and the
backscattering coefficient and (2) determine the degree of
correlation between various grass canopy parameters and the
backscattering coefficient for a tallgrass prairie.
Included in the MCSORVCER program was a model
development and field verification effort to further the
understanding of the physical basis of C-band microwavecanopy interactions.
The complex structure of vegetation
canopies has made estimation of vegetation parameters more
difficult than the estimation of soil moisture.
Modeling
efforts coupled with the field studies may provide a better
understanding of these canopy-energy interactions, thus
increasing the amount of information that can be gained
from radar measurements of vegetation targets.
As part of the field verification effort, C-band
scatterometer measurements of a crop of sunflowers were
used to test the disk model developed by Drs. H. J. Eom and
A. K. Fung in 1984 (see Chapter Four for reference).
This
study included an evaluation, modification and reevaluation
of the original model.
In addition, a new model, the
Projected Disk Component Model, was written to aid in the
explanation of the behavior of the modified disk model.
3
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The results of this study are presented in the final
chapter, Chapter Four.
Additional research is needed to help realize the
potential of radar remote sensing.
It is to this end that
the studies reported in the final two chapters were
undertaken.
The purpose of these reports is to contribute
new information to the current research in field
measurements and modeling in active microwave remote
sensing.
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CHAPTER TWO
LITERATURE REVIEW
5
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INTRODUCTION
As mentioned in the previous chapter, a great deal of
research over the past 14 years has been focussed on
determining the potential use of active microwave remote
sensing in agricultural and natural resource applications.
Host of that research has concentrated on determining the
optimal sensor configuration for the remote detection of
soil moisture, but there has also been some effort to
determine the sensitivity of active microwave systems to
vegetation canopy parameters.
Microwave radiation suffers far less attenuation by
the atmosphere than that experienced by electromagnetic
radiation in the visible and infrared wavelengths.
As a
result, remote sensing in this region of the spectrum
(i.e., 1 mm to 3 m wavelength)
is relatively independent of
weather conditions, though some difficulties can arise with
heavy precipitation (Moore, 1976).
The most commonly used
microwave frequencies in remote sensing are listed in Table
2.1 along with their band designations and wavelengths.
Active microwave sensors, frequently called radars or
scatterometers, generate and radiate microwave energy into
free space and detect the signal reflected back from a
target (Toomay, 1982).
Since they provide their own source
of illumination, radars can operate independently of the
time of day.
Radar data from field studies are typically collected
6
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TABLE 2.1.
Radar frequencies and equivalent wavelengths
(Sabins, 1978).
Band
Designation
Ka
K
Ku
X
C
S
L
P
Wavelength
(cm)
0.8
1.1
1.7
2.4
3.8
7.5
15.0
30.0
to
1.1
to
1.7
to
2.4
to
3.8
to
7.5
to 15.0
to 30.0
to 100.0
Frequency
GHz (10
cycles/sec)
40.0
26.5
18.0
12.5
8.0
4.0
2.0
1.0
to 26.5
to 18.0
to 12.5
to 8.0
to 4.0
to 2.0
to 1.0
to 0.3
7
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with scatterometers and reported in terms of the
backscattering coefficient (a*).
Scatterometers, a
type of radar, are designed to measure signal strength and,
thus, provide information about the scattering properties
of a target (Moore, 1983).
The generic term "radar" (an
acronym for radio detection and ranging) usually refers to
systems which make uncalibrated images, but it is also a
convenient term to use when referring to active microwave
remote sensing systems.
The backscattering coefficient
, where "t" and
"r" represent the transmitted and received polarization,
respectively)
is the radar cross-section per unit
illuminated area.
The radar cross-section (a) is defined
as "... the area intercepting that amount of incident power
of polarization t (transmitted) which, when scattered
isotropically, produces an echo at polarization r
(received) equal to that observed from a target," (Fung and
Ulaby, 1983).
This results in a*r having units of
m2/m2 (unitless).
In other words, the backscattering
coefficient "...of a given target is a measure of the
backscattering strength (power) of the target relative to
an isotropic scatterer having the same cross-sectional
area," (Ulaby et al., 1974).
The backscattering
coefficient is usually expressed in decibels (dB) since it
can vary over several orders of magnitude.
Linear values
8
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are converted to decibels by the following algorithm:
a* in dB * 10* log,„(<j\
10
Linear
).
ACTIVE MICROWAVE REMOTE SENSING OF SOIL MOISTURE
The relationship between the backscattering
coefficient and soil moisture depends on a set of target
and sensor parameters.
The target parameters of primary
importance are the dielectric properties of the soil
[represented by the dielectric constant) and the surface
geometry (called "roughness" and represented by the
standard deviation of the surface height variation (rms
height)].
The primary sensor parameters include: frequency,
angle of incidence, and polarization.
A crop cover can
also modify the relationship between the backscattering
coefficient and soil moisture.
Soil Parameters
The target parameters, dielectric constant and
roughness, play different roles in the reflection of
microwave energy back to the radar.
The dielectric
constant determines the nature of the interaction (i.e.,
reflection, transmission, or absorption) of microwave
radiation with a soil while soil roughness determines the
angular distribution of the scattered radiation.
9
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Dielectric Properties
The dielectric constant of an object describes the
propagation characteristics of an electromagnetic wave
through that medium.
An excellent qualitative description
of the dielectric constant of water is provided below
from page 9 and 10 of D. A. T. Dick's book Cell Water
(1966) .
"The dielectric constant of water is a
measure of its ability to reduce the intensity of
an external electric field and is simply the
ratio:
intensity of field across a vacuus
intensity of field across an equal layer of water
This ratio is greater than one.
The reduction of
the external field is due to its effect on the
separated charges in the individual water
molecules; the result is that each individual
water molecule tends to orientate (sic) itself
in the electric field in the same way as does a
compass needle in the earth's magnetic field.
When they are thus orientated (sic), however, the
minute fields due to the separated charges in the
individual water molecules add together instead
of cancelling one another as they do in the
normal random orientation.
The resulting field
due to the oriented molecules is in such a
direction as to oppose the original external
electric field, the intensity of which is
therefore reduced as described above.
Hence the
size of the dielectric constant is related to the
intensity and separation of the charges, i.e. to
the dipole moment, of the water molecule."
Since the dielectric constant of water is about 80
(unitless) and that of the solid component of soil is about
5, the soil's dielectric constant is largely dependent on
10
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the amount of free water present in the soil (Thorne and
Russell, 1947).
Increasing the dielectric constant of the
soil by increasing moisture content results in an increase
in the amount of microwave energy reflected by the soil.
It is a well documented fact that increases in soil
moisture content result in increases in the backscattering
coefficient (Ulaby, 1974; Ulaby and Batlivala, 1976; Ulaby
et al., 1978; Bernard et al., 1982).
This relationship,
however, does not apply to soil moisture conditions that
exceed saturation because of the occurrence of specular
reflectance (Dobson and Ulaby, 1981).
It is customary in this type of research to express
soil moisture on a volumetric basis (i.e., volumetric soil
moisture).
A study conducted by Dobson and Ulaby (1981)
found that expressing soil moisture content as a percentage
of field capacity (mf) (where field capacity is defined as
the volumetric moisture content at -32.5 KPa) removed the
soil textural-dependence of the linear relationship between
o°r and soil moisture.
The importance of this finding
is that it allows for textural differences to be taken into
account when estimating soil moisture from radar data which
covers a wide variety of soils.
This is particularly
important for data obtained from airborne radars which may
include coverage of a large number of soils.
For studies
covering only one soil or very similar soils, the use of
volumetric soil moisture is preferred because the
11
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dielectric constant of soils is proportional to the number
of water dipoles present in a volume of soil (Dobson and
Ulaby, 1986).
Roughness
A wave impinging on a soil surface is subject to
scattering in all directions and reflection in the specular
direction.
It is the backscattered component of the
scattered energy that a radar measures.
The portion of energy scattered in all directions is
referred to as the 'diffuse component' while the specularly
reflected portion is referred to as the coherent component.
Each component's relative contribution to the angular
radiation pattern is determined by the roughness of the
soil surface.
As surface roughness increases, the
contribution of the coherent component decreases while that
of the diffuse component increases.
illustrated in Figure 2.1.
This relationship is
When the angular radiation
pattern consists of only a diffuse component, the surface
is said to be Lambertian.
While a rougher soil surface leads to a larger
diffusely scattered component, it does not necessarily lead
to a larger backscattering coefficient.
As will be seen in
the next section, the influence of surface roughness
depends on the three sensor parameters.
12
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N \^\
Reflected Power is Entirely
Coherent and e, • e. Scattering
Pattern is a Delta Function
(3)
Coherent Component
Oiffuse Component
Scattering Pattern Consists of
Large Coherent Component and
Small Oiffuse Component
(b)
Scattering Pattern is Composed
Entirely of Diffuse Component.
For Lambertian Surface,
o° (e,«,) ■ og cos e cos e,
(c)
FIGURE 2.1.
"Relative contributions of coherent and
diffuse scattering components for different surfaceroughness conditions: (a) specular, (b) slightly rough,
(c) very rough." (Ulaby et al., 1982b)
13
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Sensor
Frequency Response
Whether a soil surface can be judged rough or smooth
depends on the frequency of the electromagnetic wave
generated and received by the radar (Ulaby et al., 1982b).
A given soil surface viewed at a high frequency (shorter
wavelength), such as 7.25 GHz and at a low frequency
(longer wavelength), such as 1.1 GHz, will appear
electromagnetically rougher to the higher frequency system.
This difference in perceptions of roughness between
different frequencies is reflected in the angular response
of the backscattering coefficient and is illustrated in
Figures 2.2a-c.
From these figures, the conclusion can be
drawn that distinctions between soils of differing
roughness decrease with increasing frequency.
This does
not mean, however, that roughness effects are removed by
making all soils appear equally rough by using higher
frequencies.
Increasing frequency actually makes the radar
more sensitive to soil roughness for all soil moisture
conditions while at the same time reducing the radar's
sensitivity to soil moisture (Ulaby and Batlivala, 1976).
Studies have shown that a frequency of around 4 GHz
maximizes a ’r sensitivity to soil moisture while
minimizing the influence of surface roughness and
vegetation cover (Ulaby and Batlivala, 1976; Ulaby et al.,
1978).
14
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Soil
res
Moisture
Height (gc«i°l In
(cm)
lop lea
< t.l
0 .4 0
2 .2
0 .15
1 .8
1.1
0 .1 9
0 .14
1.0
o .ia
-15
i i
-20
-25
-M
0
10
Frequency: 2 .2 5 M r
fre q u e n c y ! 4 .2 5 W i
Frequency! I.IG H r
20
10 0
10
20
10
0
20
10
Angle o l In cide n ce • (O egrcesi
Angle o f In c id e n c e e (Degrees)
Angle o f Incide n ce e (Degrees)
(a )
(D l
(c l
FIGURE 2.2.
"Angular response of scattering coefficient
for ... five fields for high levels of moisture content at
(a) 1.1 GHz, (b) 4.25 GHz, and (c) 7.25 GHz." (Ulaby et
al., 1978)
10
Angular Response
The angle of incidence (6) is the angle at which the
radar views the target with respect to nadir.
Ulaby (1974)
showed early-on and, in subsequent studies, that the back
scattering coefficient from a soil decreases with
increasing e and that the rate of decrease varies with the
degree of soil roughness.
Ulaby and Batlivala (1976) found
that the backscattering coefficient of a rough soil
experiences less change with increasing 9 than that of a
smooth soil (see Figs. 2.2a-c).
Ulaby et al.
(1978) observed that for 9's < 10* smooth
surfaces yielded higher a *s than did rough surfaces;
however, this trend was reversed for 9's > 10* (Figs. 2.2ac) .
The higher <7* for the smooth field when viewed at
e < 10* was due to the proximity of the sensor to the
specular angle and the interception of the specular
component of the reflected radiation.
For the rough field,
the coherent component was negligible at all angles.
The
higher cr^s for the rough field when viewed at 9 > 10*
were due to the greater backscattered diffuse component of
the angular radiation distribution.
The radar response to
soils possessing the same moisture content but different
degrees of surface roughness was found to be essentially
independent of surface roughness for 9 » 10*.
For this
reason, in addition to Ulaby's (1975) finding that 9 = 10*
minimizes the influence of a crop canopy on radar return
16
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from a soil, 10* has been chosen as the optimum angle of
incidence in radar remote sensing of soil moisture.
Polarization
Polarization describes the orientation of the electric
field strength vector relative to the plane of incidence
(Long, 1975).
The plane of incidence is defined as the
"...plane formed by the normal to the surface and the
direction of propagation of the incident wave" (Suits,
1983).
A horizontally or perpendicularly polarized wave is
oriented perpendicular to the plane of incidence while a
vertically or parallel polarized wave is oriented parallel
to the plane of incidence.
A change in polarization due to
reflection, scattering or propagation is referred to as
depolarization.
In the literature, HH stands for a horizontally
transmitted, horizontally received wave.
W
represents a
vertically transmitted, vertically received wave.
These
two configurations are often called the like-polarized
configurations.
HV and VH are referred to as the cross­
polarized configurations since the transmitted and received
configuration are orthogonal to each other.
Polarization or depolarization of an electromagnetic
wave by a target plays a part in the measured,
backscattered radiation, but it is not as significant as
the roles played by roughness, angle of incidence, or
17
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frequency when viewing a soil surface.
Using a ratio of
CTh*
v/ah” as an indicator of depolarization, Ulaby et
al.
(1978) found little dependence of depolarization on
soil moisture, but did find an angular dependence when
viewing smooth soils (Fig. 2.3).
The angular dependence of
depolarization, however, was found to decrease with
increasing frequency.
The decrease in angular dependence
with increasing frequency was due to the associated
increase in soil roughness at higher frequencies.
When
viewing a very rough surface, the angular dependence of
depolarization was found not to exist at either high or low
frequencies.
In studying the effect of row orientation on
a * , Ulaby et al.
for HH or W
(1979) found no row direction dependence
at a frequency of 4 GHz.
From this evidence,
they chose 1ike-polarization configurations as an optimal
characteristic for radars used in soil moisture remote
sensing when
operating at frequencies greater than 4 GHz.
In terms of the backscattering coefficient, the
angular dependence of polarization translates into a*
nh
not decreasing as rapidly as
does when 9 is
increased. This difference disappears on rougher soils or
when using higher frequencies (Brunfeldt, 1986).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0S
*5 •
R
-10 -
OS
.
A
Frequency
Soil
Moisture
(GHZ)
7.25
7.25
1.1
1.1
m, (g cnr1)
0.03
0.34
0.03
0.34
-
o
rms Height g• 1.1cm
e
o
Wet
7 25 GHz
°
ra
a
£
-30.
5
10
15
20
25
30
Angle of Incidence e (Degrees)
FIGURE 2 . 3 .
" A n g u la r dependence o f t h e d e p o l a r i z a t i o n
r a t i o o f a smooth s u r f a c e . " (U la b y e t a l . , 1 9 7 8 )
19
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crop Cover Influence on c*'s Relationship to Soil Moisture
The sensitivity (i.e., the slope of the linear
relationship between a ’f and soil moisture) of the
backscattering coefficient to soil moisture is reduced by
the presence of a vegetation cover.
reasons:
This occurs for two
l) the vegetation cover contributes a
backscattering component of its own and 2) the radar signal
is attenuated in its travel through the canopy to the soil
and back (Myers, 1983).
Ulaby et al.
(1979) found that the sensitivity of o ’
to soil moisture for a vegetatively covered soil is
decreased as the frequency or angle of incidence is
increased.
As e is increased, the path length of the wave
through the canopy is increased thus increasing attenuation
and backscattering by the canopy.
As frequency is
increased, the scattering components of the vegetation
(e.g., leaves and stalks) increase in size relative to the
wavelength, thus increasing the canopy contribution to the
backscatter at the expense of the soil's contribution.
The
extent to which different crops affect the sensitivity of
o ’ to soil moisture depends in a large part on the
vegetation parameters (e.g., water content, height, shape
and density).
In this same study, they also looked at the effect of
row direction relative to the radar viewing direction and
the way this affected
.
They found no row direction
20
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dependence for the HV configuration at any frequency
between 1 and 8 GHz, but a strong dependence for HH and W
configurations for frequencies lower than 4 GHz.
The strong
dependence of the like-polarization configuration on row
direction is due to the high coherent component reflected
back to the radar when 9 is perpendicular to the slope of
the furrow.
While the HV configuration was found to be
independent of this effect, it is an undesirable
configuration because the transmitted power would have to
be boosted around 10 or 20 dB to get the equivalent
performance of the like-polarization.
In a study conducted in 1982 by Ulaby, Aslam and
Dobson, it was shown that the relative contribution of the
vegetation to backscatter was dependent upon the moisture
content of the soil.
They found that when soil moisture
was less than 50% of field capacity (where field capacity
is defined as the volumetric moisture content at -32.5 KPa)
the backscattering contribution of the vegetation limits
the ability of the radar to predict soil moisture with an
acceptable degree of accuracy.
mf when mf < 50%.
In fact, c* overestimates
This results in a loss of sensitivity
(decrease in slope) when compared to predictions for a bare
soil.
For mf > 50%, the soil contribution dominates the
backscatter and the estimates of soil moisture from a*
tr
are very similar for bare and vegetated fields.
While the loss of sensitivity of a ’r to soil
21
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moisture has been emphasized, it is important to remember
that sensitivity and correlation are two different things.
The findings for correlation coefficients for bare and
vegetated fields are variable.
In the two above mentioned
studies, comparisons of correlation coefficients between
bare and vegetated fields are indirect, but some results
are presented separately in the papers.
The Ulaby et al.
(1979) study found a correlation coefficient of 0.92 for
<j * versus soil moisture for vegetated fields and a
correlation coefficient of 0.86 for the bare soil condition
when using a frequency of 4.25 GHz, 0 * 10*, and a
polarization of HH.
The authors do not attempt an
explanation of this difference, but it is obvious that a
strong linear relationship between <j(* and soil moisture
exists for both bare and vegetation-covered soils.
ACTIVE MICROWAVE REMOTE SENSING OP VEGETATION
A vegetation canopy possesses a great many more
dielectric discontinuities (i.e., plant surface-air
interfaces) than does a soil.
For this reason, the nature
of the electromagnetic wave-target interaction is
considerably more complex and less understood than that
exhibited by a soil surface.
Field studies using radar
observations of vegetation canopies have produced mixed
results up to this point, but they do show some promise in
estimating certain biophysical parameters.
In an attempt
22
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to better understand the energy-matter interaction between
microwaves and vegetation canopies, there has been a
considerable effort devoted to modeling these interactions.
The following is a brief summary of some of the findings
from field studies and modeling efforts over the past 14
years.
Pield Studies
In one of the earliest studies, Ulaby (1975)
determined that W
and cross-polarization configurations
were more sensitive than HH to crop type.
He further
suggested that for purposes of crop classification, a dual
frequency (4-5 GHz and 7 GHz or higher) and dual
polarization ( W and cross) would probably yield the best
results.
In a subsequent paper, Ulaby et al.,
(1975), narrowed
the suggested radar parameters to one polarization (W )
two frequencies (9 GHz and 16.6 GHz).
and
They found that this
configuration would allow them to achieve a 2 dB difference
between milo and soybeans at 9 GHz and a 3 dB difference
between corn and alfalfa at 16.6 GHz.
They also found that
an angle of incidence between 30* and 65* maximized their
crop discrimination ability by reducing soil moisture
effects.
Ulaby and Bush (1976a), when working with corn, found
a vary strong correlation (0.96) between o* and the
23
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normalized water content of the c o m
(i.e., this is the
mass of the water in the vegetation divided by the product
of the plant height and the field's plant density).
This
was achieved using a frequency of 17 GHz and a 50* angle of
incidence.
With this configuration, they found as much as
a 5 dB difference between the a*p of irrigated and
nonirrigated c o m .
The difference in radar response to the
two crops was attributed to differences in plant geometry
and water content.
When looking at alfalfa, Bush and Ulaby (1976) found
significant soil effects from short stands, but the
attenuation by tall stands masked any soil effects when
viewed at nadir.
Unfortunately, when alfalfa was viewed
at off-nadir angles, temporal variations in o'r showed
no consistent responses to any canopy parameters.
In an attempt to estimate leaf area index (LAI) from
<j * , Ulaby et al.
(1984) made some interesting findings.
For sorghum and corn, they found that the <j * of the
canopy was dominated by the leaf contribution when LAI was
greater than 0.5.
An LAI of less than 0.5 resulted in the
soil and stalks becoming important contributors to a*p.
For wheat, they found that the leaf contribution was
important as long as the heads were not present.
These
findings were made using a frequency of 13 GHz, 9 = 50*,
and a polarization of W .
This study also included a
24
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modeling effort which will be described in the following
section.
Modeling
In an effort to better understand the behavior of
electromagnetic wave interactions with vegetation-soil
complexes, many scientists have turned to modeling for
answers.
The types of models used can be separated into
two groups:
1) empirical or semi-empirical, semi-
theoretical models relating o* to vegetation-soil
parameters and 2) complex mathematical models which
simulate the EM wave interaction with the vegetation-soil
complex.
Simple Physical Models
The first type of model can range in complexity from
a simple regression of
to a biophysical paramater
such as plant water content to a semi-empirical, semitheoretical model in which the regression is based on the
hypothesized functional relationships of the scattering
processes involved.
The simple regression models are generally used in
preliminary experiments to determine simply if a
relationship exists between o* and a canopy or soil
parameter.
This approach was used by Ulaby and Bush in
their study with corn (1976a) in which they found a strong
25
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linear relationship between a* and the canopy water
content normalized for canopy height.
They found a similar
relationship in wheat between a* and canopy moisture
on a wet weight basis though they expressed the equation in
exponential form since they were working with a ’ in
linear units instead of decibels (Ulaby and Bush, 1976b).
The more involved semi-empirical, semi-theoretical
models are designed to determine the respective
contributions of the canopy and soil elements to the radar
return.
These models are theoretical in that the canopy is
represented by a medium of known attenuating and scattering
characteristics such as a cloud of water droplets or a
dielectric slab.
This representation requires that the
canopy's biophysical parameters be expressed in terms
relevant to the theoretical canopy (e.g., canopy moisture
content might be expressed in kg of water per m3 of canopy
volume rather than the traditional percentage of wet
weight).
These models are empirical in that they contain
several coefficients which are obtained from a regression
or multiple linear regression analysis of a* to a
selection of canopy and soil components.
This approach has been used by several researchers.
Bush and Ulaby (1976) used this type of model when they
modeled an alfalfa canopy as a dielectric slab.
This model
worked well for predicting a* at near nadir viewing
angles and allowed the researchers to examine the influence
26
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of canopy height on at* ;
however, its estimates of a ’f
away from nadir were poor.
In 1978, Attema and Ulaby
modeled alfalfa, c o m , milo and wheat as a cloud of water
droplets.
In addition to finding good agreement between
predicted and observed a^s (r*0.70 to 0.99), their
model provided estimations of the attenuation of the
vegetation layer and the relative contributions of the soil
and vegetation to the radar return.
Later, Ulaby et al.
(1984) extended the original cloud model to a multi-layer,
cloud model to allow them to differentiate further the
contributions of different canopy elements (represented by
different layers) to the radar return.
modified cloud model of Ulaby et al.
In addition, the
(1984) allowed an
examination of the relationship between a* and LAI
since it included an LAI input (unlike the original model)
rather than just volumetric canopy moisture.
comparisons of
In
predicted by the model to LAI measured
in the field, the authors found (for LAI > 0.5 and no heads
present) an rJ=0.62 (rms=0.8 dB) for corn, an r1=0.74
(rms=0.6 dB) for sorghum, and a r**0.90 (rms=1.2 dB) for
wheat.
(Note: rms is the root mean square, but is more
commonly known as the standard deviation.)
More recently,
Paris (1986) modified the original cloud model to accept
inputs of individual canopy component biophysical
parameters (e.g., mean leaf area) rather than aggregate
canopy parameters (e.g., LAI).
This allowed him to examine
27
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the effect of changing leaf size on the radar return.
By
using the area of the average green c o m leaf as a driver
of the model, he attained agreement between predicted and
measured a^s of r=0.96 compared to an r=0.83 when
driving the model with the canopy water content.
significant improvement in the prediction of a*
This
indicated
that green leaf size might be a better descriptor of
microwave interaction with a c o m canopy than simply using
vegetation water content.
In all of these studies, the soil's contribution was
determined from a simple linear model which was then
modified by the attenuating characteristics of the
overlying medium.
Both types of models (simple regression and semiempirical, semi-theoretical) serve a useful purpose.
The
simple regression models provide an indication of
relationships between a* and target components while
the semi-empirical, semi-theoretical models provide a more
detailed look at the relative contributions of the various
target components to the radar return.
Neither of these
two model types provide much insight into the mechanics of
energy-matter interactions between vegetation canopies and
microwave radiation.
For that purpose, a more complex
mathematical treatment is required.
28
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Mathematical Models
Models using a more rigorous mathematical approach to
simulate microwave radiation interaction with vegetation
have generally followed either a field approach or an
intensity approach.
For the field approach, the scattering
problem is formulated in terms of Maxwell's wave equations.
The intensity approach is based on radiative transfer
theory and formulates the problem in terms of average power
(Ulaby et al., 1986).
In both methods, the soil is
considered as a dielectric slab with only surface
scattering characteristics (i.e., no volume scattering
within the soil).
Both methods have their drawbacks.
The field approach
suffers from the practical inability to deal with multiple
scattering phenomena and relies on first order scattering
approximations.
While the field approach can deal with
multiple scattering phenomena, it cannot consider
diffraction effects in computing the individual
contribution from multiple scattering (Ulaby et al., 1986).
Field Approach:
In most cases, the field approach models the
vegetation canopy as a continuous, inhomogeneous medium
bounded above by air and below by soil.
The term
"inhomogeneous" refers to the dielectric perturbations
which occur randomly within the medium.
These
29
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perturbations represent the dielectric discontinuities
which occur in a volume of space consisting of air and
vegetation.
Canopy parameters are expressed in terms
relevant to the theoretical medium.
These include the
percent volume of vegetation and the average dielectric
constant of the medium (estimated from a dielectric mixing
formula using water, solids and air).
The field approach first determines the mean (or
coherent)
field within the medium by use of the wave
equations (Fung, 1982).
The electromagnetic wave
transmitted (scattered) into the air above the canopy (and
detected by the radar) is determined from a transmittance
function and the mean field in the medium through a process
called "first order renormalization" (Fung, 1979).
Finally, the scattering coefficient is calculated from the
scattered field and is expressed in terms of the average
scattered power (Fung, 1982).
Studies using this approach include Fung and Ulaby
(1978), Fung (1979), and Tsang and Kong (1981).
Since
these studies differed primarily in the method of
mathematical approximation used to determine the mean field
within the medium, the reader is referred to the original
papers for an indepth discussion of the mechanics involved
in these types of approximations.
Only the comparison of
their results with field data will be discussed here.
Tsang and Kong's (1981) paper dealt primarily with the
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
mechanics of a modification to Fung and Ulaby's (1978)
approximation to the mean field, but failed to test their
modification against any field data.
As such, it is
difficult to gauge their contribution to this type of
modeling effort.
Fung and Ulaby (1978) and Fung (1979)
tested their models and found that agreement between the
measured and predicted a* was best for view angles
greater than 30* off-nadir and for canopies which were
weakly scattering (i.e., lacked substantial losses due to
multiple scattering).
The lack of agreement between the
measured and predicted a*
for strongly scattering
canopies was attributed to the inability (from a practical,
computational standpoint) of the field models to deal with
multiple incoherent scattering (Fung et al., 1987).
The
lack of agreement between the measured and predicted a *
at view angles less than 30* off-nadir were attributed to
the models' assumption of a plane boundary (rather than a
rough surface) between the canopy and soil (Fung, 1979).
Intensity Approach:
The intensity approach most often models the canopy as
a collection of discrete scatterers of known geometry and
scattering characteristics.
This method begins with the
field approach to determine the scattered field for an
individual scatterer at a given orientation.
The scattered
field in the direction of observation is then converted to
31
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a power or intensity level.
This process is repeated for
the scatterer at all possible orientations within the range
of angles specified.
The transfer of energy through the
canopy is tracked as the combined emissions and extinctions
of power from all scatters using radiative transfer
methods.
Converting the scattered field to a power level
dramatically reduces the amount of information necessary to
characterize an individual scatterer's contribution to the
scattered radiation from the canopy.
This reduction in
data permits the modeling of multiple scattering since the
model does not need to keep track of all of the EM field
information (e.g., phase matrices) beyond the original
computation of the scattered field (Chen, 1988).
One advantage of the intensity approach over field
approaches is that it allows the user to change the
orientation and size of the scatterers.
This is analagous
to changing the leaf angle distribution and leaf size of
the canopy.
To date, the number of studies using the intensity
approach to model radar returns from vegetation is small.
These studies include Eom and Fung (1984), Eom and Fung
(1986), and Fung et al.
(1987).
As with the discussion of
field approaches, the reader is referred to the original
articles for an indepth discussion of the mathematics
involved in this type of modeling.
Only a general
32
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description of the results of these studies will be
provided here.
Eom and Fung (1984) developed a scatter model for
dielectric disks in which they accounted for multiple
scattering by use of a method called "matrix doubling."
Since leaves can be somewhat disk-like in appearance, this
model has the advantage of allowing canopy inputs which are
more similar to actual canopy measurements (e.g., leaf
size, thickness, and range of orientations) than could be
used in a continuous medium model.
The model compared well
with the absolute values (within ± 2 dB) and angular trends
of measured values for soybean.
To model radar returns from coniferous forests, Eom
and Fung modified the disk model in 1986 to use needle-like
scatterers rather than disks.
Unfortunately, the study
failed to compare the modeled results with field
measurements, though their findings did indicate that
needle orientation appears to play a major role in
determining the angular trend of a ‘
f.
Fung et al.
(1987) further modified the original disk
model to allow the individual disks (or needles) to be
within the Fresnel zone of one another.
Previously, their
model had assumed that the disks were within the far zone
of one another.
[The far zone can be thought of as the
region far enough away from the leaf such that
contributions of radiated energy from different parts of
33
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the leaf appear to be in phase with each other (Toomay,
1982).]
Their rational for the modification vas that
within the Fresnel zone "... the Fresnel effect causes
phase changes and therefore cancellations among
contributions from the same leaf."
The overall effect vas
to reduce slightly (i.e., approximately 1 dB) the a*
when compared with predictions made with the far-zone
assumption, though the effect vas most noticeable in the
disk-shaped leaves.
Few comparisons were made with field
measurements in this study, but those that were made showed
good agreement with field measurements as did the original
disk model.
When compared to predictions made with the far
zone assumption, the needle-like leaves were found to
increase or decrease a*r depending on the view angle.
Though their modification resulted in differences of less
than 2 dB between the Fresnel zone and far-zone
assumptions, it vas an important contribution to the
modeling effort since leaves are often more closely spaced
within the canopy than the previous models had permitted.
In other words, while the modification resulted in only
minor improvements in the predicted values,
it was
theoretically more sound than the far-zone assumption
because it allowed the disks to be as close to each other
as leaves in a real canopy.
34
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CONCLUSION
Active microwave remote sensing of vegetation and
soils has been studied for approximately 14 years with the
hope of exploiting the cloud-penetrating and sunlightindependent capabilities of radar systems for assessing and
inventorying crops and natural resources.
During this
time, a considerable amount of effort has gone into
determining the effect of different target characteristics
on radar returns and the optimal sensor parameters for
maximizing the information sought from active microwave
measurements.
Field work and empirical studies have demonstrated
that the interaction of microwave energy with soilvegetation complexes can yield important information about
the moisture status of the target as well as information
about other biophysical features (e.g., LAI).
Estimations
of soil moisture from radar measurements have proven to be
quite accurate, but the complex structure of vegetation
canopies has made estimation of vegetation parameters more
difficult.
Modeling efforts coupled with the field studies
may provide a better understanding of these canopy-energy
interactions, thus increasing the amount of information
that can be gained from radar measurements of vegetation
targets.
There is hope that active microwave remote
sensing can provide estimates of LAI under high LAI
conditions in which visible and infrared wavelength methods
35
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lose their sensitivity.
If vegetation parameter estimates
from radar data can be improved, microwave remote sensing
will provide an essentially weather-independent means of
monitoring vegetation and soil moisture.
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REFERENCES
Attema, E. P. W. and F. T. Ulaby (1978), Vegetation modeled
as a water cloud, Radio Science. 13:357-364.
Bernard, R . , PH. Martin, J. L. Thony, M. Vauclin, and D.
Vidal-Madjar (1982), C-band radar for determining
surface soil moisture, Remote Sens. Environ.. 12:189200
.
Bush, T. F. and F. T. Ulaby (1976), Radar return from a
continuous vegetation canopy, IEEE Trans. A n t . Prop..
24:269-276.
Brunfeldt, 0. R. (1986), Personal communication, April 18.
President, Applied Microwave Corporation.
Chen, M. F. (1988), Personal communication, May.
Assistant
Research Professor, University of Texas at Arlington,
Wave Scattering Research Center.
Dick, D. A. T. (1966), Cell Water. Butterworths,
Washington, D.C. pp. 9-10.
Dobson, M. C. and F. T. Ulaby (1981), Microwave
backscatter dependence on surface roughness, soil
moisture, and soil texture: part III - soil tension,
IEEE Trans. Geosci. Rem. Sens.. 19:51-61.
Dobson, M. C. and F. T. Ulaby (1986), Active microwave
soil moisture research, IEEE Trans. Geosci. Rem. Sens..
24:23-36.
Eom, H. J. and A. K. Fung (1984), A scatter model for
vegetation up to Ku-band, Remote Sens. Environ.. 15:185200 .
Eom, H. J. and A. K. Fung (1986), Scattering from a random
layer embedded with dielectric needles, Remote Sens.
Environ.. 19:139-149.
Fung, A. K . , M. F. Chen and K. K. Lee (1987),
Fresnel
field interaction applied to scattering from a
vegetation layer, Remote Sens. Environ.. 23:35-50.
Fung, A. K. and F. T. Ulaby (1983), Matter-energy
interaction in the microwave region, pp. 115-164, In J.
E. Estes and G. A. Thorley (eds.) Manual of remote
sensing, volume 1, 2nd edition, American Society of
Photogrammetry, Falls Church, Virginia.
37
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Long, M. W. (1975), Radar reflectivity of land and sea.
Lexington Books, D. C. Heath and Company, Lexington,
Massachussets.
Moore, R. K. (1976), Active microwave systems, pp. 234-290,
In J. Lintz, Jr. and 0. S. Simonett (ed.) Remote sensing
of environment. Addison-Wesley Publishing Company,
Reading, Massachusetts.
Moore, R. K. (1983), Radar fundamentals and scatterometers,
pp. 369-474, In J. E. Estes and 6. A. Thorley (ed.)
Manual of remote sensing, volume 1, 2nd edition,
American Society of Photogrammetry, Falls Church,
Virginia.
Myers, v. I. (1983), Remote sensing applications in
agriculture, pp. 2111-2228, In J. E. Estes and G. A.
Thorley (ed.) Manual of remote sensing, volume 2, 2nd
edition, American Society of Photogrammetry, Falls
Church, Virginia.
Paris, J. F. (1986), Probing thick vegetation canopies with
a field microwave scatterometer, IEEE Trans. Geosci.
Remote Sens.. 24:886-893.
Sabins, F. F., Jr. (1978), Remote sensing: principles and
interpretation. W. H. Freeman and Company,
San Francisco, California.
Suits, G. H. (1983), The nature of electromagnetic
radiation, pp. 37-60, In J. E. Estes and G. A. Thorley
(ed.) Manual of remote sensing, volume 1, 2nd edition,
American Society of s for mapping soil moisture, IEEE
Trans. Geosci. Elec. 14:81-93.
Toomay, J. C. (1982), Radar principles for the non­
specialist. Lifetime Learning Publications, Belmont,
California.
Ulaby, F. T., C. T. Allen, G. Egger III and E. Kanemasu
(1984), Relating the microwave backscattering
coefficient to leaf area index,
Remote Sens. Environ..
14:113-133.
Ulaby, F. T., A. Aslam and M. C. Dobson (1982), Effects of
vegetation cover on the radar sensitivity to soil
moisture, IEEE Trans. Geosci. Remote Sensing. 20:476481.
38
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Ulaby, F. T., P. P. Batlivala and M. C. Dobson (1978),
Microwave backscatter dependence on surface roughness,
soil moisture, and soil texture:
part I - bare soil,
IEEE Trans. Geosci. Elec.. 16:286-295.
Ulaby, F. T . , G. A. Bradley and M. C. Dobson (1979),
Microwave backscatter dependence on surface roughness,
soil moisture, and soil texture: part II - vegetationcovered soil, IEEE Trans. Geosci. Elec.. 17:33-40.
Ulaby, F. T. and T. F. Bush (1976a), Corn growth as
monitored by radar, IEEE Trans. Ant. Prop.. 24:819-828.
Ulaby, F. T. and T. F. Bush (1976b), Monitoring wheat
growth with radar, Photoar am. Eng. Rem. Sens.. 42:557568.
Ulaby, F. T . , T. F. Bush and P. P. Batlivala (1975), Radar
response to vegetation II: 8-18 GHz band, IEEE Trans.
Ant. Prop.. 23:608-618.
Ulaby, F. T., J. cihlar, and R. K. Moore (1974), Active
microwave measurement of soil water content, Remote
Sens. Environ.. 3:185-203.
Ulaby, F. T . , D. Held, M. C. Dobson, K. C. McDonald and T.
B. A. Senior (1987), Relating polarization phase
difference of SAR signals to scene properties, IEEE
Trans. Geosci. Remote Sensing. 25:83-92.
Ulaby, F. T . , R. K. Moore and A. K. Fung (1982b), Microwave
remote sensing; active and passive. Volume 2 . AddisonWesley Publishing Company, Reading, Massachusetts.
Ulaby, F. T . , J. Cihlar, and R. K. Moore (1974), Active
microwave measurement of soil water content, Remote
Sens. Environ.. 3:185-203.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER—THREE
C-BAND SCATTEROMETER MEASUREMENTS
OF A NATURAL/ TALL0RAS8 PRAIRIE
Accepted for publication by
Remote Sensing of Environment
on February 26, 1988.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ABSTRACT
C-band (4.75 GHz frequency, 6.3 cm wavelength)
scatterometer measurements were made of a tallgrass prairie
in an attempt to determine the relationship between (1) the
backscattering coefficient and different expressions of
soil moisture and (2) the backscattering coefficient and
various canopy parameters.
The findings of this study
support those made in previous studies in terms of the
optimum polarization and view angle selection for soil
moisture work (i.e., near-nadir view angles and like
polarizations).
In contrast to previous studies, it was
found that view angles of 30* and 45* also produced strong
correlations with soil moisture.
In addition, there were
two new findings regarding the effect of prairie vegetation
on the C-band backscattering coefficient.
The first was a
moderately strong correlation and partial correlation
between a* and leaf water potential, which indicates some
capability of C-band measurements in detecting extremes in
the water status of prairie vegetation under shallow soil
conditions.
The second was the finding that site
differences (primarily differences in vegetation) due to
burn treatments appeared to be sufficient to cause
significant differences in the sensitivity of a^r to soil
moisture. The site differences could not be removed by any
known expression of soil moisture.
These two findings were
surprising since previous radar studies had reported
41
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minimal vegetation effects when using a frequency and view
angles such as those in this study.
42
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INTRODUCTION
Over the last several years there has been a
considerable amount of research dedicated to radar remote
sensing in which bare soils (Chang et al., 1980; Dobson and
Ulaby, 1981; Sadeghi et al., 1984; Ulaby, 1974; Ulaby and
Batlivala, 1976; Ulaby et al., 1978; 1984) and traditional
agricultural crops (Bernard et al., 1982; Bush and Ulaby,
1976; Paris, 1986; Ulaby, 1975; Ulaby et al., 1984; 1979;
1975; Ulaby and Bush, 1976) have served as targets.
Grasslands, with only a few exceptions (Jackson et al.,
1981; Jackson and O'Neill, 1985), have not received the
attention of these other targets.
In view of the global
importance of grassland areas, this lack of attention is
unfortunate.
Grasslands occupy approximately 17% of the earth's
land surface (Ajtay et al., 1977) and 28% of the United
States (Bailey, 1978). Located in remote regions and often
covering huge expanses, these areas are better suited to
monitoring by remote sensing methods than to more costly
and time consuming traditional methods of condition
assessment.
The original range of native grasslands in North
America has been greatly reduced by farming's need for flat
or gently sloping lands with deep, rich soils.
As a
result, much of the remaining grasslands have been
relegated to marginal lands with thin soils, rough
43
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topography, and low rainfall.
These areas, lacking the
water storage capacity of deep soils, are particularly
sensitive to periods of low or no rainfall.
Often found in the semi-arid regions of the world,
grasslands are occasionally subject to severe drought.
In some cases, the detection of dry conditions in a
grassland might prove useful in pinpointing potential
grassfire areas or better forage areas.
In the extreme
case, the timely detection of the onset of drought
conditions might help reduce the catastrophic consequences
which accompany major droughts by providing disaster-relief
agencies with more time to prepare.
The following is a discussion of the findings of three
summers of C-band, field scatterometer measurements of a
tallgrass prairie. It can be viewed as a step in furthering
our understanding of what the C-band backscattering
coefficient tells us about the various canopy elements and
soil parameters of a grassland area.
The objectives of this study were to (1) determine the
degree of correlation between soil moisture and the
backscattering coefficient and (2) determine the degree of
correlation between various grass canopy parameters and the
backscattering coefficient for a tallgrass prairie.
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MATERIALS AMD METHODS
Location and Site Description
This study was conducted during the summers of 1984,
1985 and 1986 on the Konza Prairie Research Natural Area
(KPRNA) located near Manhattan, Kansas (39*9'N, 9 6 ’40'W).
The KPRNA is a 3487 ha tallgrass prairie preserve with a
mixed species composition and a silty clay loam (Udic
ustoll) as the predominant soil type. In a detailed
vegetation study of the KPRNA, approximately 39 species of
grass have been identified with big bluestem (Androooaon
gerardi Vitman), little bluestem (A*. scooarius Michx.), and
Indian grass (Sorahastrum nutans (L.) Nash) being the three
dominant species (The Tallgrass Laboratory, 1984).
The
varied spatial distribution of so many species creates a
complex canopy unlike any found in traditional monoculture
crops.
The different sites for each year consisted of a
burned and an u n b u m e d treatment making a total of six
treatments (three different sites with two treatments per
site) on which microwave, plant parameter and soil
measurements were made.
Burned and unburned treatments
were chosen to provide two different grass canopies.
Burning is a common range management practice used to
remove the previous seasons' senescent vegetation.
The
senescent vegetation lies as a thick, insulating mat on the
ground reducing soil warming and the availability of
45
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photosynthetically active radiation (PAR) to the new
season's growth.
Burning during the spring removes this
"litter layer," thus allowing the young vegetation to take
full advantage of the PAR and warmer soils during a time
when rainfall is usually abundant.
Table 3.1 provides the
Konza site identification label and the burn treatment
history for each site used in this study.
Radar Measurements
The radar used in this study was a C-band
scatterometer with a 4.75 GHz center frequency (6.3 cm
wavelength) and a 3.4*, 3 dB beamwidth.
The sensor was one
of three units built by the University of Kansas Remote
Sensing Laboratory and is called the Microwave
Scatterometer C-band (MS-C).
A boom truck served as a
mobile platform for the MS-C providing a minimum slant
range of 9 m from the target and a means of extending the
scatterometer over the target.
Instrument control and data
acquisition were accomplished with a Hewlett-Packard HP41 CV handheld computer while an HP digital cassette drive
and a thermal printer were used for data storage and
inspection, respectively.
Scatterometer measurements were expressed in teems of
the backscattering coefficient
units of decibels (dB).
((7 *)
and are reported in
The subscripted ”t" and "r" serve
as a reminder that the backscattering coefficient has both
46
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TABLE 3.1.
Konza site locations and b u m histories.
-1984B
U
SITE
-1985U
B
Konza Site
Location :
1C
IOC
ID
10D
2De
Burn History
Scheduled
Burn Frequency
(years)
1
10
1
10
2
Years Burned
Including Year
of Interest
1978
1981
through
1984
1979
1976
through
1985
-1986B
U
1980
1982
1984
1986
UD
NONE
1980
NOTE: B and U sites were located adjacent to each
other during each year.
B - burned site
U - unburned site
47
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a transmitted and Received polarization.
Measurements were
made using three transmit-receive polarization combinations
and three view angles making a total of nine polarizationview angle combinations.
Transmitting and receiving
polarizations could be set independently to a horizontal
(H) or vertical (V) configuration.
The three polarization
combinations used in this study were HH, HV, and W
where
the first letter denotes the transmitting polarizaton and
the second letter denotes the receiving polarization.
The
three view angles used were 15*, 30*, and 45* from nadir.
Measurements were labelled according to their polarizationview angle configuration so that, for example, a label of
HV30 would indicate a horizontal transmitting polarization,
a vertical receiving polarization, and a view angle of 30*
from nadir.
When triggered, the HP-41CV collected 30 backscatter
measurements from the MS-C over a 30 second time interval.
The 30 raw data values, their mean, and other information
(e.g., slant range, view angle, polarization)
were then
stored on the digital cassette tape. A summary of the data
(e.g., angle of incidence, polarization, mean a*r) was then
printed out on the thermal printer.
Spatial averaging of
the a ‘ measurement was achieved by driving the truck
alongside each of the sites during the 30 second, data
collection period.
48
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Soil Measurements
Eight soil samples (0 to 6 cm depth) were taken from
within each site concurrently with each set of
scatterometer measurements.
From the wet and dry weight of
these samples, the soil water content (i.e., gravimetric)
was determined.
Soil bulk densities (0 to 6 cm depth) were
determined from eight undisturbed cores taken from each
site near the end of the measurement season and were used
to convert the gravimetric soil moisture to volumetric
terms.
Soil properties for each site are listed in Table
3.2.
The moisture release characteristics of each
treatment's soil was determined in the laboratory with a
gas pressure, moisture extraction technique using ceramic
plates and cellulose acetate membranes (Klute, 1986).
The
moisture content of each soil was determined for -32.5,
-43.2, -100, -500, -1000 and -1500 KPa soil water
potentials (note: -1 bar = -100 KPa).
Expressing the soil
water potential as a logarithm required the use of the
absolute value of the soil water potential rather than the
customary negative value.
From these data, the logarithmic
relationship between soil water potential and volumetric
soil moisture can be determined for each soil.
This
allowed an estimate of the soil water potential given the
volumetric moisture content.
Figure 3.1 illustrates the
relationship between the soil water potential and
49
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U1
o
Soil properties (0
-1984-
6 cm depth) for each year and
SITE -------------------1985------- ----- 1986—
B
U
B
U
Soil
Property
B
u
Sand (%)
22
23
27
31
22
20
silt (%)
50
48
50
46
54
58
Clay (%)
28
29
23
23
24
22
clay
loam
clay
loam
loam or
silt loam
loam
silt
loam
silt
loam
1.04
1.03
0.79
0.69
0.83
0.77
4.5
4.4
o
•
to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.2.
treatment.
4.7
7.8
7.2
Soil Texture
Bulk Density
(x 10 kg/m3)
Organic
Matter (%)
B - burned site
U - unburned site
ISOOt
—
Burned 1984
Unturned 1984
-9- Burned 1985
1200
-0
Unturned 1985
■*
Unturned 1986
Burned 1986
Soil
900
Water
Potential
(K P a >
600
0.05
I'M II il i
0.15
0.2
0.25
0.3
0.35
0.4
Volumetric Soil Moisture (m3/m3)
FIGURE 3.1.
Soil moisture release curves for all years and
treatments.
Points on the lines are not measured values,
but are shown to aid in line identification.
51
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volumetric soil moisture (i.e., the moisture release curve)
for each soil.
All expressions of soil moisture were derived from one
or more of the following:
1) the wet and dry weights of
the soil samples, 2) the bulk densities and/or 3) the
moisture release curves.
The soil moisture expressions
tested in this study are listed below.
1) Gravimetric soil moisture,
(units: %, g/g or kg/kg)
2) Volumetric soil moisture,
%, c m / c m or m / m )
(symbol: m ),
9
(symbol: m ) ,
v
3) Logarithm of soil water potential,
none)
(units:
(units:
4) Percentage of m at -32.5 KPa, (similar to the
"percentage of field capacity" used in previous
studies), (units: %)
5) Percentage of m at -1500 KPa, (similar to the
"percentage of lilting point" used in previous
studies), (units: %)
6) Percentage of m between -32.5 and -1500 KPa,
(often referredvto as the "percentage of
available water"), (units: %).
Vegetation Measurements
Agronomic measurements consisted of the wet and dry
weights of the green vegetation, the dry weights of the
senescent vegetation and green leaf area index (LAI)
measurements.
A total of nine samples were taken once a
week during the microwave measurement period from each site
using a 0.1 m J frame.
From these measurements, the percent
moisture content was determined for the green vegetation on
52
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both a wet weight and dry weight basis.
Canopy height
measurements were made once per week in 1985 and 1986 for
the green grass and for the litter layer.
This measurement
allowed the calculation of the moisture content of the
vegetation normalized for canopy height (Ulaby and Bush,
1976).
since agronomic measurements were not always made
on the same day as radar measurements, a cubic spline
smoothing procedure (Kimball, 1976) was used to provide
estimates of the vegetation parameters between measurement
days.
The summary statistics of the agronomic parameters
are listed in Table 3.3.
As part of another experiment, leaf water potential
measurements were made (using the pressure bomb method) on
these sites during the last two years (Retta, 1986), some
of which coincided with our radar measurements.
Only seven
of these measurements in 1985 and five in 1986 coincided
with the radar measurements.
This necessitated the
combination of the data sets from these two years to
determine their correlation with a ’ .
tr
RESULTS AMD DISCUSSION
Correlations Between a * and Vegetation Parameters
Table 3.4 shows the correlation between the vegetation
parameters and the backscattering coefficient (HH45, HV45
and W 4 5 )
for all years and sites.
These data suggest that
the plant parameters are poorly to moderately correlated
53
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TABLE 3.3. Summary statistics of the vegetation parameters
for all years and treatments.
VEGETATION
PARAMETER
STATISTIC
-------------- SITE------------1984--1985--1986
U
B
B
U
B
U
Moisture
Content on
Dry Weight
Basis (%)
MEAN
STD. DEV.
MINIMUM
MAXIMUM
116
56
60
263
96
32
42
161
97
11
74
120
110
1
109
114
197
12
174
216
124
5
114
131
Moisture
Content on
Wet Weight
Basis (%)
MEAN
STD. DEV.
MINIMUM
MAXIMUM
50
10
36
71
46
7
34
60
49
3
42
54
51
0
51
52
62
3
60
66
52
4
49
62
Live, Dry
Weight
Phytomass
(kg/ha)
MEAN
STD. DEV.
MINIMUM
MAXIMUM
2919
694
941
3548
3318
919
901
4226
2433
180
2181
2783
2749
99
2464
2862
2789
320
219
3371
2869
569
1812
3824
Moisture Con­
MEAN
tent Normal­ STD. DEV.
ized for Can­ MINIMUM
opy Height
MAXIMUM
(kg/m )
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
0.52
0.09
0.23
0.63
0.49
0.09
0.41
0.71
1.27
0.04
1.22
1.30
0. 65
0. 07
0.59
0. 78
LAI
MEAN
STD. DEV.
MINIMUM
MAXIMUM
1.29
0.42
0.57
1.85
1.20
0.43
0.47
1.82
1.07
0.11
0.71
1.15
0.95
0.16
0.81
1.33
1.73
0.11
1.46
1.79
1.31
0.22
0.89
1.67
Senescent
Vegetation
(kg/ha)
MEAN
STD. DEV.
MINIMUM
MAXIMUM
1130 6945
768 1618
104 4462
2215 11809
888 8986
535 1965
0 5880
1849 12098
919
378
496
1427
6524
1771
3671
8245
GREEN
CANOPY
HEIGHT
(m)
MEAN
STD. DEV.
MINIMUM
MAXIMUM
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
0.39
0.23
0.14
0.93
0.52
0.04
0.44
0.58
0.53
0. 08
0.33
0.53
0.53
0.05
0.48
0.61
LITTER
HEIGHT
(m)
MEAN
STD. DEV.
MINIMUM
MAXIMUM
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
0.00
0.00
0.00
0.00
0.12
0. 01
0.11
0.14
0.00
0. 00
0.00
0.00
0.11
0.01
0.10
0.12
B - burned site, U - unburned site, N.A - not available
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.4.
Correlation coefficients for a° versus various vegetation
parameters for all years and treatments and all polarization combina­
tions for the 45° view angle.
Site
BURNED
1984
1985
1986
UNBURNED
1984
1985
1986
LAI
Dry
Weight
of Green
Biomass
Moisture
Content
on Dry
Weight
Basis
Moisture
Content
on Wet
Weight
Basis
HH45
HV45
W45
HH45
HV45
W45
HH45
HV45
W45
0.31*
0.46**
0.31
0.33
-0.06
0.45
-0.05
-0.31
-0.16
-0.42**
-0.32*
-0.50**
0.18
0.36
0.08
-0.24
-0.05
-0.32
0.63**
0.73**
0.78**
0.64*
0.44
0.72*
0.23
-0.02
0.29
0.61**
0.75**
0.75**
0.61*
0.33
0.71*
-0.17
0.27
-0.08
HH45
HV45
W45
HH45
HV45
W45
HH45
HV45
W45
-0.09
0.30*
-0.00
0.03
0.24
0.02
-0.35
-0.12
-0.45
-0.58**
-0.24
-0.55**
0.19
-0.02
-0.26
-0.30
-0.06
-0.41
0.55**
0.79**
0.75**
0.05
0.47
0.44
0.38
0.02
0.41
0.55**
0.79**
0.75**
-0.13
0.26
0.26
0.16
0.57
0.38
Polariza­
tion View
Angle Com­
bination
* - significant at the a=0.05 level
** - significant at the a=O.Ol level
N.A. - Not Available
Moisture
Content
Normalized
for Canopy
Height
N.A.
N.A.
N.A.
0.62*
0.18
0.65*
0.61
0.73
0.75
N.A.
N.A.
N.A.
0.00
0.25
0.02
-0.01
0.63
0.02
with o ’r .
Not only were the correlations weak, they were
inconsistent between years (e.g., positive one year and
negative the next).
Both the target and the sensor may have contributed to
the weak correlations between a* and the vegetation
parameters.
The sensor was configured (i.e., 4.75 GHz
frequency) to optimize soil moisture sensitivity in part by
minimizing sensitivity to vegetation (Ulaby, 1975; Ulaby et
al., 1979).
At this frequency, the thin, narrow leaves and
stalks of the grass canopy would be considered "small"
relative to the 6.3 cm wavelength of the microwave
radiation.
In addition to the canopy elements being small
in comparison with the wavelength, the vegetation was
relatively sparse.
When compared to corn, milo, soybeans,
and other crops used in previous studies (Ulaby, 1975;
Ulaby
and Bush, 1976; Ulaby et al., 1975; 1979; 1984), the
grass
canopies' height, phytomass, and LAI (Table 3.3)
would
appear low, making it likely that a grass canopy is a
less attenuating medium than the canopies of these other
crops.
Correlations and Partial Correlations Between a ’ and Leaf
Water Potential
The correlation coefficients for a ’ versus leaf water
tr
potential were quite strong (see Table 3.5), particularly
for W 4 5 on both the burned and unburned treatments.
It
56
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
TABLE 3.5. Correlation coefficients for o* versus leaf water
potential and partial correlation coefficients for o* versus leaf
water potential given volumetric soil moisture for tfte combined
1985 and 1986 data.
Burned
Measurement
Label
in
-'J
HH15
HH30
HH45
HV15
HV30
HV45
W15
VV30
VV45
Correlation
Coefficient
0.82**
0.77**
0.82**
0.79**
0.69*
0.79**
0.80**
0.83**
0.85**
Partial
Correlation
Coefficient
0 .6 6 *
0.36
0.56
0.52
0.39
0.51
0.49
0.57
0.69*
* - significant at the a=0.05 level
** - significant at the a=0.01 level
Unburned
Partial
Correlation Correlation
Coefficient Coefficient
0.59*
0.53
0.61*
0.70*
0.45
0.63*
0.47
0.51
0.75**
0.40
0.32
0.44
0.59
0.16
0.50
0.07
0.24
0 .68 *
should be remembered, however, that the small size of the
1985 and 1986 leaf water potential data sets necessitated
their combination for the correlation analysis.
As such, a
direct comparison of the correlations of a ’f with leaf water
potential cannot be made to the correlations of a ‘r with the
other five vegetation parameters.
A partial correlation analysis was performed in an
attempt to determine the degree of correlation between a'r
and leaf water potential at given volumetric soil moisture
contents.
The limitation of this analysis is that the
soils were thin (approximately 10 to 30 cm in depth) which
resulted in a high degree of dependence of the leaf water
potential on the near surface soil moisture.
This
dependence is particularly strong over the range of
volumetric soil moisture for which this analysis was run
(i.e., 0.07 to 0.28 m3/m3 for the burned sites and 0.08 to
0.26 m3/m3 for the unburned sites).
Over these ranges,
small changes in m^ result in large changes in the soil
water potential (see Fig. 3.1) which in turn cause changes
in the leaf water potential.
On a deeper soil, a plant's
access to soil moisture at greater depths would reduce the
dependency of leaf water potential on the near surface soil
moisture.
Under these conditions, the relationship between
a* and leaf water potential might not be as strong as that
in the shallow soil case.
Table 3.5 lists the partial correlation coefficients
58
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for the leaf water potential versus a* at all polarizationview angle combinations given volumetric soil moisture.
As
expected, the coefficient values decreased for the partial
correlation, but the correlation remained high enough for
W 4 5 on both the burned and u n b u m e d treatments to suggest
that a'r was responding, in part, to the leaf water
potential.
This finding is consistent with previous
findings (Ulaby and Bush, 1976; Ulaby et al., 1975) about
a°
r 's greater sensitivity to vegetation at higher angles of
incidence (e.g., 45* or greater).
HH15 on the burned
treatment had almost as strong a partial correlation as
W45,
thus indicating that the grass canopy has some effect
on o'r even at low angles of incidence.
Figure 3.2 shows the linear relationship between a ‘r
and leaf water potential for the burned and unburned
treatments for the combined 1985 and 1986 data.
The
relationship is moderately strong with some scatter in the
data.
Since the leaf water potential is the average of
three to six species, it is possible that this scatter
could be due, in a large part, to the variability in the
leaf water potential between individual plants or species
(see Fig. 3.3).
Whatever the cause of the variability, the
implications of this finding remain that it may be possible
to detect extremes in the water status of prairie
vegetation using C-band scatterometer data taken at high
angles of incidence (e.g., 45*).
59
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• Unburned
Y=2.32X-11.73
r2-0.57
RMSE-0.80
Backscattering
Coefficient
(dB)
•1 8
••
-22
-3 .5
-3
-2.5
Leaf Water Potential (MPa)
FIGURE 3.2.
Backscattering coefficient (W45) versus leaf
water potential for the burned and unburaed treatments.
60
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BURNED
•2.5
SITE
LEAF
WATER
POTENTIAL -3.s
(MPa)
o 1985
•1.5
• 1986
UNBURNED
■zs
SITE
LEAF
WATER
POTENTIAL -is
(MPa)
170
ISO
190
200
210
DAY OF YEAR
FIGURE 3.3.
Mean leaf water potential versus day of year
for the burned and unburaed sites.
Standard error bars
indicate one standard deviation about the mean.
61
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Correlations Between a ' and Expressions of Soil Moisture
As in previous studies, the backscattering coefficient
was found to be linearly related and highly correlated with
volumetric soil moisture.
The linear trend between o ’ and
tr
m^ can be easily seen in Figure 3.4.
Table 3.6 lists
the correlation coefficients for all polarization-view
angle combinations, years, and sites for o ’ versus
volumetric soil moisture.
W15
followed by HH15 had consistently high
correlation coefficients (i.e., r > 0.8) for all
treatments.
For this reason, W 1 5 and HH15 were used in
all subsequent statistical analysis of the relationship
between a ’ and soil moisture.
This finding also lends
additional support to previous studies of the optimal
scatterometer configuration for soil moisture remote
sensing work.
While W 1 5 and HH15 had the highest correlations with
soil moisture,
it should be noted that the correlations of
o ’ with soil moisture were stronger for the 30* and 45“
view angles than previous works would have indicated (Ulaby
and Batlivala, 1976; Ulaby et al., 1978; Ulaby et al.,
1979).
The implication of this finding is that spaceborne
radars may not need to be restricted to near-nadir view
angles for satisfactory detection of soil moisture in
grasslands.
A variety of soil moisture expressions were tried in
62
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HH15, 1984
o
Burned
•
Unbumed
— Burned
Predicted
-
Backscattering
Coefficient
(dB)
Unbumed
Predicted
oo*
•12
0 .0 5
°°o
0.1
0.1S
0.25
0.3
0.35
0.4
Volumetric Soil Moisture (m3/m3)
FIGURE 3.4.
Scatter plot and lines-of-best-fit of the
backscattering coefficient (HH15) versus volumetric soil
moisture for the burned and unbumed, 1984 sites.
63
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TABLE 3-6.
Correlation coefficients for o* versus volumetric
soil moisture for all polarization-view ancjle combinations,
years and treatments.
PolarizationView Angle
Combination
HH15
HH30
HH45
HV15
HV30
HV45
VV15
W30
W45
B
1984----U
0.93**
0.94**
0.94**
0.96**
0.96**
0.93**
0.90**
0.92**
0.94**
0.92**
0.94**
0.92**
0.90**
0.93**
0.81**
0.87**
0.83**
0.85**
B
1985----U
0.88**
0.82**
0.71**
0.68**
0.70**
0.69**
0.84**
0.79**
0.75**
B - burned site
U - unburned site
* - significant at the a=0.05 level
** - significant at the a=0.01 level
0.86**
0.76**
0.45
0.76**
0.76**
0.60**
0.93**
0.79**
0.23
1986
B
0.97**
0.97**
0.80*
0.71*
0.59
0.74*
0.97**
0.96**
0.94**
U
0.81*
0.75*
0.74*
0.69
0.86**
0.67
0.93**
0.89**
0.73*
an attempt
to determine which expressions reduced the site
dependence
of the relationship between a* and soil
moisture.
The degree of site dependence was found to vary
with the manner in which soil moisture was expressed.
To test the degree of site dependency, a statistical
comparison
(i.e.,
sensitivity of or*
analysis of covariance) of the
to soil moisture (i.e., slope values)
was
made for each expression of soil moisture for HH and W
polarizations at the 15* angle of incidence. Since there
were 6 treatments, there were a total of 15 pairwise
comparisons to be made of the slopes of the six regression
lines for each expression of soil moisture.
One finding from this comparison was that when soil
moisture was expressed in gravimetric terms, percent of the
-32.5 to -1500 KPa my difference (i.e., % available water),
or as the logarithm of the soil water potential, the slopes
of a° versus soil moisture for each site could be
tr
statistically grouped into burned and unburned categories
when using the HH15 configuration.
In other words, the
sensitivity (slope) of o* to gravimetric soil moisture,
percent of the -32.5 to -1500 KPa my difference, and to the
logarithm of the soil water potential was the same for all
years on the burned site.
unburned site results.
The same can be said of the
The sensitivity of a ‘f to the above
mentioned soil moisture expressions was, however,
statistically different (for 0=0.05) between the burned and
65
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unburned sites.
Burned site radar data showed a greater
sensitivity (higher slopes) to soil moisture than that seen
for the u n b u m e d site data.
Because of the clear separation of burned and unburned
site regression equations when using these three
expressions of soil moisture, it may be possible to use two
soil moisture prediction equations (one for burned sites
and one for u n b u m e d sites) on an operational basis by
using visible and near-infrared wavelength reflectance
data.
The capability of distinguishing burned from
unburned sites using Thematic Mapper wavelength bands has
already been demonstrated for grasslands using field
radiometers (Asrar et al., 1986).
When compared for volumetric or other expressions of
soil moisture, the slope comparisons ranged from five to
eleven pairs of similar slopes with no useful groupings.
None of the soil moisture expressions resulted in a
complete removal of site dependency.
The regression
coefficients and statistics for ff{* (HH15) versus each
expression of soil moisture for each year are given in
Tables 3.7, 3.8, and 3.9.
For the three expressions of
soil moisture which exhibit groupings of the sensitivity
into burned and unburned classes, the regression
coefficients and statistics for cr{*
r (HH15) versus soil
moisture for the combined data sets of all three years for
these soil moisture expressions are given in Table 3.10.
66
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TABLE 3.7. Linear regression equations of a ’ (HH15) versus
each expression of soil moisture (independent variable) for
1984. RMSE is the root mean square error.
Independent
Variable
(Y)
1)
2)
3)
4)
5)
6)
Burned Site
Unburned Site
Gravimetric Soil
Moisture (m^)
Y=0. 307<y* -16.00
Y=0.222(7* -15.73
Volumetric Soil
Moisture (mv )
Y=29.52(J* -16.00
Y=21. 56(7*
-15.73
tr
Percentage of
-32.5 KPa mv
Y=0.106a*-16.00
Y=0.076(7* -15.73
Percentage of
-1500 KPa mv
Y=0.045a*-16.00
Y=0.037a*-15.73
Logarithm of
Soil Water
Potential
Y=-3.711(7* -0.31
Y=-2. 412(7* -4.75
Percentage of
-32.5 to -1500
KPa mv Difference
Y=0. 061<7* -11.54
Y=0.039(7* -12.04
tr
tr
tr
tr
tr
tr
tr
tr
tr
tr
tr
r*
0.87
0.85
RMSE
1.10
0.86
67
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TABLE 3.8. Linear regression equations of a* (HH15) versus
each expression of soil moisture (independent variable) for
1985. RMSE is the root mean square error.
Independent
Variable
(Y)
Burned Site
Unburned Site
1) Gravimetric Soil
Moisture (ing ')
Y=0.304(7* -13.82
Y=0.163(7* -13.83
2) Volumetric Soil
Moisture (mv )
Y=38.50(7* -13.82
Y=23.53(7° -13.83
3) Percentage of
-32.5 KPa mv
Y=0.106(7* -13.82
Y=0.076ff*-13.83
4) Percentage of
-1500 KPa mv
Y=0.045(7*
-13.82
tr
Y=0.037(7* -13.83
5) Logarithm of
Soil Water
Potential
Y=-3 .732(7* +2. 07
Y=-2.082(7“
-4.93
tr
6) Percentage of
-32.5 to -1500
KPa mv Difference
tr
tr
tr
tr
Y=0. 062(7* -9.28
_ _ _ _ _ _ _ _ _ _ tr_ _ _ _ _ _ _ _
tr
tr
tr
tr
Y=0.035(7“ -11.25
_ _ _ _ _ _ _ _ _ _ tr_ _ _ _ _ _ _
rJ
0.78
0.74
RMSE
1.43
0.80
68
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TABLE 3.9. Linear regression equations of a* (HH15) versus
each expression of soil moisture (independent variable) for
1986. RMSE is the root mean square error.
Independent
Variable
(Y)
Burned Site
Unburned Site
1) Gravimetric Soil
Moisture (mg)
Y=0.373(7° -15.07
Y=0.174a*-14.26
2) Volumetric Soil
Moisture (my )
Y=44.75(7°
-15.07
tr
Y=22.52a *-14.26
3) Percentage of
-32.5 KPa my
Y=0.136(7* -15.07
Y=0. 068(7° -14.26
4) Percentage of
-1500 KPa mv
Y=Q. 056(7° -15.07
Y=0.031(7° -14.26
5) Logarithm of
Soil Water
Potential
Y=-4.819(7° +5.28
Y=-2.222(7°
-4.33
tr
6) Percentage of
-32.5 to -1500
KPa my Difference
Y=0. 081(7° -9.47
Y=0.038(7° -11.17
tr
tr
tp
tp
tr
tr
tp
tr
tp_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ tr
r2
0.93
0.65
RMSE
0.95
1.18
69
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TABLE 3.10. Regression coefficients and statistics for the com­
bined data sets of all three years for those expressions of soil
moisture which exhibited groupings of the sensitivity of o* (HH15)
to soil moisture into burned and u n b u m e d classes.
tr
Gravimetric Soil
Moisture (mg')
Statistic
B
U
0.337
0.214
-15.88
r1
RMSE
Slope
Y-intercept
Logarithm of
Soil Hater
Potential
Percentage of
-32.5 to -1500
KPa mv Difference
U
B
U
-4.067
-2.447
0.067
0.040
-15.46
1.41
-4.46
-10.92
-11.87
0.80
0.83
0.77
0.82
0.78
0.82
1.52
0.91
1.63
0.93
1.61
0.92
B - burned site
U - unburned site
RMSE - root mean square error
B
The greatest reduction in site dependency was found
in expressing soil moisture as a percentage of the -1500
KPa volumetric moisture content in which 11 of the
comparisons resulted in similar degrees of sensitivity with
4 remaining different for the o=0.05 level.
To say that
all 15 comparisons resulted in all slopes being similar
would have required us to compare the slopes at an alpha
level of 0.0002.
In other words, we can say with 99.98%
certainty that at least one of the slopes is different from
one of the other slopes.
We definitely cannot say that one
prediction line is adequate for predicting soil moisture
for all six treatments.
Since expressing soil moisture as a percentage of the
-32.5 KPa or the -1500 KPa volumetric soil moisture
(expressions which have been claimed to greatly reduce site
dependence due to textural differences [Dobson and Ulaby,
1981; Schmugge, 1980; Ulaby et al., 1978; 1979]) did not
remove the site dependence, this suggests that the site
differences were due to differences other than soil texture
(e.g., vegetation cover).
This conclusion is further
supported by the fact that the soil textures for all sites
and years were relatively similar (Table 3.2) while some of
the vegetation characteristics were not (Table 3.3).
This finding was unexpected given that studies prior
to this one (Ulaby, 1975; Ulaby and Bush, 1976; Ulaby et
al., 1979; 1975) have indicated that the frequency and view
71
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angle used in this study are considered relatively
insensitive to vegetation, particularly since the amounts
of vegetation encountered in this study would be considered
low as compared with traditional agricultural crops.
Of the eight agronomic parameters listed in Table 3.3,
the greatest difference between burned and u n b u m e d site
vegetation cover is the presence of the senescent
vegetation (litter) layer
on the u n b u m e d sites.
While in
a dry state, this layer probably has a negligible effect on
a° measurements.
tr
Moistened from a rain shower or from
absorbing the morning dew, this layer may make a
significant contribution (at the expense of the soil
moisture's contribution) to the radar backscatter.
In this
way, the presence of a litter layer on the u n b u m e d sites
may account for the lower sensitivity of a*r to soil
moisture on these sites.
It should be pointed out that
measurements were never made when free water droplets were
present on the vegetation surfaces.
In addition to the overlying litter layer, there is a
layer of partially decomposed grass (detritus) which
constitutes the top layer of soil.
Other investigators
(Schmugge, 1987) have noted a relationship between the
frequency of burning treatments and the sensitivity of
microwave radiometers to soil moisture.
On sites which are
less frequently burned, the thickness of the detritus layer
is correspondingly thicker and the sensitivity of the
72
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microwave radiometer to soil moisture is lower.
The
detritus layer thickness may also play a role in the
sensitivity of o*p to soil moisture.
CONCLUSIONS
As in previous studies, a high degree of correlation
was found between the C-band backscattering coefficient and
soil moisture.
This strongly indicates the capability of
C-band radar as an instrument for estimating soil moisture
for grassland areas.
The grass canopy parameters, on the
other hand, were only moderately correlated with o* .
C-
band radar appears to have only a marginal capability for
estimating vegetation parameters for grassland areas.
In
the case of one vegetation parameter, leaf water potential,
even a marginal estimation capability may be useful.
Many of the findings described in this study support
those made in previous studies in terms of polarization and
view angle selection for soil moisture work (i.e., low
angles of incidence and HH and W
polarizations work best).
In contrast to these previous studies, it was found that
30* and 4 5 ’ view angles also resulted in fairly strong
correlations with soil moisture.
The implication of this
finding is that sp a c e b o m e radars may not need to be
restricted to near-nadir view angles for estimating soil
moisture in grasslands.
73
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In addition, there were two new findings regarding the
effect of prairie vegetation on the C-band backscattering
coefficient.
The first was the moderately strong
correlation and partial correlation between at* and
leaf water potential.
The implication of this finding is
that it may be possible to detect extremes in the water
status of prairie vegetation using C-band data.
Such
detection capability might prove useful in detecting those
areas most affected by drought in remote regions.
It
should be stressed, however, that the correlations between
<j* and leaf water potential may simply be the result
of the leaf water potential's dependence on the near
surface soil moisture under shallow soil conditions.
Additional study is required to determine if the
correlations remain as strong for deep soil conditions.
The second finding was that the presence of small
amounts of vegetation, such as those encountered in this
study, appears to be sufficient to cause statistically
significant differences in the sensitivity of a * to soil
moisture for different grassland sites.
These differences
do not appear to be removed by using any known expression
of soil moisture or by using HH and W
angles of incidence.
polarizations at low
HH15 appears to offer the advantage
of neatly separating the sensitivities of o* to some
expressions of soil moisture (i.e., gravimetric soil
moisture, percent of available water, and the logarithm of
74
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the soil water potential) into burned and unburned
treatments.
While W 1 5 did show groupings and differences
in the sensitivity of a ’r to soil moisture for different
treatments and years, there were no useful groupings as
with HH15.
Unfortunately, the three expressions of soil
moisture for which this holds true are not necessarily the
preferred expressions for all soil moisture work.
The implication of the latter finding is that at least
two soil moisture prediction algorithms, one for burned
treatments and another for u n b u m e d treatments (litter
present and litter absent), should be used in any soil
moisture estimation program which uses HH15, C-band
backscatter data from grassland areas to estimate these
three expressions of soil moisture.
The decision of which
algorithm to use for which sites could be determined by
visible and near-infrared reflectance data.
An alternative
approach to dealing with this site dependent relationship
is to investigate the use of a slightly longer wavelength
(e.g., 6 to 8 cm) scatterometer system.
If indeed the site
dependence is due to vegetation differences between burned
and unburned treatments, a slightly longer wavelength might
remove the vegetation effects while retaining an acceptable
degree of sensitivity to soil moisture.
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REFERENCES
Ajtay, G. L . , P. Ketner and P. Durigneaud (1977),
Terrestrial primary production and phytomass, in The
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Klute, A. (1986), Water retention: laboratory methods, in
Methods of soil analysis. 2nd ed., part I, (A. Klute,
Ed.), Amer. Soc. Agron, Inc. and Soil Sci. Soc. Amer.,
Inc., Madison, WI. pp.635-662.
76
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Paris, J. F. (1986), The effect of leaf size on the
microwave backscattering by corn, Remote Sens. Environ..
19:81-95.
Retta, A. (1986), Personal communication and unpublished
data, E. T. Lab, Kansas State University, Manhattan, KS.
Sadeghi, A. M . , G. D. Hancock, W. P. Waite, H. D. Scott and
J. A. Rand (1984), Microwave measurements of moisture
distributions in the upper soil profile, Water Resources
Res.. 20:927-934.
Schmugge, T. J. (1980), Effect of texture on microwave
emission from soils, IEEE Trans. Geosci. Remote Sens..
GE-18:353-361.
Schmugge, T. J. (1987), Personal communication. Kansas
State University, Manhattan, KS.
The Tallgrass Laboratory, (1984), Konza Prairie. Division
of Biology, Kansas State University, Manhattan, KS,
p p . 20.
Ulaby, F. T. (1974), Radar measurement of soil moisture
content, IEEE Trans. Antennas Propaqat.. AP-22:257-265.
Ulaby, F. T. and P. P. Batlivala (1976), Optimum radar
parameters for mapping soil moisture, IEEE Trans. Geosci.
Electron.. GE-14:81-93.
Ulaby, F. T., P. P. Batlivala and M. C. Dobson (1978),
Microwave backscatter dependence on surface roughness,
soil moisture, and soil texture: part I - bare soil, IEEE
Trans. Geosci. Electron.. GE-16:286-295.
Ulaby, F. T. (1975), Radar response to vegetation, IEEE
Trans. Antennas Propaqat.. AP-23:36-45.
Ulaby, F. T . , C. T. Allen, G. Eger III and E. T. Kanemasu
(1984), Relating the microwave backscattering
coefficient to leaf area index, Remote Sens. Environ..
14:113-133.
Ulaby, F. T . , G. A. Bradley and M. C. Dobson (1979),
Microwave backscatter dependence on surface roughness,
soil moisture, and soil texture: part II - vegetationcovered soil, IEEE Trans. Geosci. Electron.. GE-17:33-40.
Ulaby, F. T. and T. F. Bush (1976), Corn growth as
monitored by radar, IEEE Trans. Antennas Propaqat.. AP24:819-828.
77
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Ulaby, F. T . , T. F. Bush and P. P. Batlivala (1975),
Radar response to vegetation II: 8-18 GHz band, IEEE
Trans. Antennas.Propaqat.. AP-23:608-618.
Waite, W. p., A. M. Sadeghi and H. D. Scott (1984),
Microwave bistatic reflectivity dependence on the
moisture content and matric potential of bare soil, IEEE
Trans. Geosci. Remote Sens.. GE-22:394-405.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER f o p r
A PROJECTED DISK COMPONENT MODEL
TO EXPLAIN THE BEHAVIOR OF
A MODIFIED DIELECTRIC DISK MODEL
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ABSTRACT
The disk model developed by Eom and Fung (1984) was
tested against a set of field measurements of o'r from a
crop of sunflowers.
The model overestimated a ’r early in
the crops development, but decreased the overestimate as
the crop matured.
Since the model, in its original
configuration, assumed a uniform distribution over the
range of specified disk inclination angles, the author
modified the model to accommodate canopies with nonuniform
leaf angle distributions (e.g., planophile)
those found in the field.
similar to
The modification had a
significant influence on the shape of the response curve
for calculated a ’ versus view angle (particularly for the
vertical polarization case), but failed to reduce the over­
estimate in the early growth stages.
While the model now
has the added capability of incorporating measured leaf
angle distributions into its calculations, additional
modifications (e.g., incorporating row structure
information) may be a necessary to improve the model's
performance with row crops.
Modification of the original disk model led to the
development of a separate model, called the Projected Disk
Component Model (PDCM), to help explain the behavior of the
modified disk model.
The PDCM was written to provide the
user with a "radar's view" of a disk canopy by describing
the canopy geometry in terms of a radar's polarization
80
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configuration.
By reducing several types of theoretical
disk canopies to a simple, quantitative measure of their
constituent horizontal and vertical components, the PDCM
provides an indication of the degree of coupling that could
occur between a disk canopy and a horizontally or
vertically polarized EM wave.
In this way, the author was
able to gain a general idea of how the MDM would respond to
certain types of canopies.
The PDCM may also provide some
insight into the influence of leaf orientation on
polarization phase differences.
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INTRODUCTION
In 1983, a series of experiments were initiated by
NASA/JSC under the Mobile C-Band Scatterometer and Optical
Radiometer for Vegetation Characteristics Estimation
Research (MCSORVCER) program.
One purpose of the program
was to increase the information base of the C-band (i.e.,
4.75 GHz frequency or 6.3 cm wavelength) backscattering
properties of a variety of vegetation types.
The result of
these experiments has been several publications on the
subject using C-band scatterometers and a variety of
targets.
Among the targets were mixed deciduous forests
(i.e., water oak and red maple), cypress and pine stands
(Wu, 1986), aspen and black spruce (Pitts et al., 1988),
peach trees (Paris, 1986), and tallgrass prairie (Martin et
al., 1988).
Included in the MCSORVCER program was a model
development and field verification effort to further the
understanding of the physical basis of c-band microwavecanopy interactions.
Some of the results of this effort
can be seen in the papers of Pitts et al.(1988) and Paris
(1986).
As part of the field verification effort, the
study described here was undertaken to test the volume
scattering model of Eom and Fung (1984) with a crop of
sunflowers.
The model tested in this study was actually a
later version of the disk model which had been modified by
Dr. Paul Chen to accept ranges for two rather than three
82
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Eulerian angles of rotation.
Since sunflower canopies have nonuniform leaf angle
distributions (Shell and Lang, 1975), the model was
modified to incorporate leaf angle distributions (e.g.,
planophile) which were nonuniform and continuous over the
entire 0 to 90* leaf angle range.
Having made the
necessary modifications, the view angle response of the
modified disk model (MDM) was found to be difficult to
interpret for certain canopy types.
As a result, a second
model (the Projected Disk Component Model or PDCM) was
written to provide some insight into the MDM's behavior for
different canopy types.
Presented in this paper are the results of a
comparison of measured to predicted values from Eom and
Fung's disk model; a description of a modification to the
disk model to include nonuniform, continuous leaf angle
distributions; the comparison of the measured to the MDMpredicted values of o* ; the theory behind the Projected
Disk Component Model; the interpretation of the PDCM
results as they relate to the MDM and the potential for the
PDCM to explain phenomena (e.g., polarization phase
differences) other than the behavior of the MDM.
MATERIALS AMD METHODS
Site Description
This experiment was conducted during the summers of
83
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1985 and 1986 at the Ashland Agronomy Research Farm located
approximately 6 km southwest of Manhattan, Kansas.
The
crop was grown on a Eudora silt loam soil (coarse-silty,
mixed, mesic Fluventic Hapludoll)
in the same field for
both years.
The cultivar used for this experiment was a variety
(Triumph 585) of sunflower (Helianthus annuus L.).
Planting dates were May 23, 1985 and May 22, 1986.
The
rows were oriented north-south and were spaced
approximately 0.76 m apart.
Sunflower was chosen because it is a physically large
crop (thus ensuring interaction of the crop with the C-band
microwave radiation) and because the canopy can be
considered disk-like.
While the leaves are in fact
chordate in shape, their width is approximately equal to
their length (like that of a disk).
Vegetation Measurements
Canopy height and growth stage were measured
concurrently with the radar measurements.
Canopy height
was measured at several locations within the field using a
meter stick.
Growth stage was estimated visually using the
growth scale described by Schneiter & Miller (1981).
Leaf area index (LAI), vegetation moisture content,
average number of leaves per plant and leaf thickness were
measured on a weekly basis throughout the growing season.
84
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LAI was measured using an optical area meter.
Vegetation
moisture content was determined from the wet and dry
weights of the individual canopy components (i.e., stalks,
leaves and seed heads).
The total number of leaves and the
total leaf area for the sample provided the information to
calculate the average leaf diameter for the sample.
Leaf
thickness was measured in the field using a caliper.
It
was found not to vary appreciably from 0.7 mm throughout
the season.
A cubic spline technique (Kimball, 1976) was
used to interpolate canopy parameter values for days on
which radar measurements were made.
The fractional volume of the vegetation, one of the
disk model inputs, was calculated by dividing the canopy
volume per mJ by canopy height.
Vegetation volume was
estimated from the wet weights of the vegetation and was
physically measured during 1985 using an immersion
technique.
Figure 4.1 shows the relationship between fresh
weight of a sunflower plant and the volume of water
displaced by immersing the plant.
It should be noted that
the volume was measured only once during the season and
that the relationship between volume and fresh weight may
not be linear at later growth stages when much of the
canopy volume is senescent.
However, the use of fresh
weight as an estimator of vegetation volume can be
justified if one considers the majority of interaction of
the radiation to be with the moist volume of the vegetation
85
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1100 t
a
.1
Y = (1.004 x 10 )X * (8.620 x 10 )
r2= 0.999
9 °°-' RMSE = 1.117 x i d 5
700
VOLUME
x 10'6 m3 )
500
300-•
100
100
300
500
700
900
1100
W ET WEIGHT (x 103 kg)
FIGURE 4.1.
Relationship of volume of water displaced by
an immersed sunflower plant to the wet weight of the
sunflower plant.
86
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rather than with the senesced volume.
In other words,
while a mature crop of sunflowers appears to occupy a large
volume of space, the volume which interacts most
significantly with the microwave radiation is that volume
of the crop which contains moisture.
Soil Measurements
Eight soil samples (0 to 5 cm depth) were taken from
within the site concurrently with each set of scatterometer
measurements.
From the wet and dry weight of these
samples, the gravimetric soil water content was determined.
Soil bulk densities (0 to 5 cm depth) were determined from
eight undisturbed cores taken from the site near the end of
each measurement season.
Soil dielectric constant and soil surface roughness
were measured during 1986.
The soil dielectric constant
was measured on eight large (7 cm diameter) soil cores
taken from throughout the field.
technique,
A contact probe
"... based upon the capacitive characteristics
of an open-ended coaxial cable ...," described fully by
Brunfeldt (1987), was used to measure the dielectric
constant of the soil over a range of moisture conditions.
The results are shown in Figure 4.2.
Surface roughness was
measured by driving thin sheets of 1 m long sheet metal
into the ground, spray painting the soil-sheet metal
interface, tracing the profile onto paper and digitizing
87
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Real:
y = exp(6.78X ♦ 0.96)
r 2= 0.89
RMSE = 0.20
Real
Imaginary: 2
Y = 23.1X f 5.21 X
Dielectric
Constant
*
0.06
r a 0.84
RMSE » 0.47
oo
oo
Imaginary
0.05
0.1
0.15
0.2
025
0.35
Volumetric Soil Moisture (m3/m3
FIGURE 4.2.
Dielectric constant versus volumetric soil
moisture for the sunflower field.
88
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the trace of the profile.
From these data the standard
deviation and autocorrelation length of the profiles were
calculated.
Radar Measurements
Radar measurements were made throughout the growing
seasons using a C-band scatterometer with a 4.75 GHz center
frequency (6.3 cm wavelength) and a 3.4*, 3 dB beamwidth.
The sensor was one of three units built by the University
of Kansas Remote Sensing Laboratory and is called the
microwave scatterometer C-band (MS-C).
A boom truck served
as a mobile platform for the MS-C providing a minimum slant
range of 9 m from the target and a means of extending the
scatterometer over the target.
Instrument control and data
acquisition were accomplished with a Hewlett-Packard HP4lev handheld computer while an HP digital cassette drive
and a thermal printer were used for data storage and
inspection, respectively.
Scatterometer measurements were expressed in terms of
the backscattering coefficient (<7t*
r , where "t" and "r1'
represent the transmitted and received polarization,
respectively) and are reported in units of decibels (dB).
Measurements were made using three transmit-receive
polarization combinations and four to thirteen view angles
ranging from 5 to 65*.
and W
The polarizations used were HH, HV
where H means horizontal and V means vertical.
The
89
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first and second letter of the pair indicates the
transmitted and received polarization, respectively.
When triggered, the HP-41CV collected 30 backscatter
measurements from the MS-C over a 30 second time interval.
The 30 raw data values, their mean, and other information
(e.g., slant range, view angle, polarization)
were then
stored on the digital cassette tape. A summary of the data
(e.g., angle of incidence, polarization, mean a*p) was then
printed out on the thermal printer.
Spatial averaging of
the a* measurement was achieved by driving the truck
alongside the site (i.e., scanning) during the 30 second,
data collection period.
Three sets of attenuation measurements were made
during the study, two in 1986 and one in 1985.
Measurements were made at a 15* view angle using an active
radar calibrator (ARC).
The ARC was positioned at several
locations beneath the canopy for each of the three days.
Alignment with the radar was achieved by maximizing the
return voltage registered by the radar.
To identify the
degree attenuation attributable to various canopy
components, the attenuation measurements were made of the
canopy intact, decapitated (i.e., seed heads removed), and
defoliated (leaving only stalks).
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RESULTS AMD DZSCUSSIOM
Attenuation Measurement Results
Attenuation measurements of the sunflowers were made
to ensure that the canopy was a substantial enough target
for there to be significant interactions of the C-band
radiation with the canopy.
Measurements made after the
removal of various canopy elements revealed that the
greatest decrease in attenuation occurred when the leaves
were removed (see Table 4.1).
Decapitation of the canopy
(i.e, removal of the heads leaving stalks and leaves
intact) produced mixed results.
The two 1986 data sets showed a marginal increase in
attenuation for the HV and W
decapitation.
configurations after
The HH configuration in these two data sets
showed a marginal decrease in attenuation after
decapitation while all three configurations in the 1985
data set showed substantial decreases in attenuation
(i.e., roughly one-half).
A review of the biophysical
parameters of the canopies during these measurements found
that the pattern of changes in attenuation by the intact
canopy followed very closely the pattern of changes in the
percentage of the fresh weight of the canopy attributable
to the leaves (see Table 4.2).
The greatest decrease in
attenuation after decapitation occurred on day 233 of 1985,
the same day for which the percentage of fresh weight
attributable to the heads is at its greatest within these
91
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TABLE 4.1. Two-way path loss (attenuation) values (in dB)
for the sunflower canopy using 15* angle of incidence.
------- Canopy Condition --------Intact
Decapitated
Defoliated
Polarization: HH
Day Year Growth Stage
198 1986
R-3
218 1986
R-8
233 1985
R-8
19.76
16.29
18.15
19.66
15.84
9.31
2.07
2.25
2.26
Polarization: HV
Day Year Growth Stage
198 1986
R-3
218 1986
R-8
233 1985
R-8
21.98
14.25
18.79
23.53
16.82
10.44
2.23
2.62
6.45
Polarization: W
Day Year Growth Stage
198 1986
R-3
218 1986
R-8
233 1985
R-8
24.38
14.42
15.59
26.43
15.75
9.70
2.64
2.99
4.28
Intact - no modification to the sunflower canopy.
Decapitated - seed heads removed leaving only leaves
and stalks •
Defoliated - leaves and !seed heads removed leaving
only stalks.
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TABLE 4.2.
Percentage of total canopy
fresh weight.
Day
Year
198
218
233
1986
1986
1985
— Canopy Component —
Leaves Heads
Stalks
23
16
19
2
22
32
75
62
49
93
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three data sets.
It is interesting to note that the HH
configuration shows the least response in attenuation to
changes in the percentage of the canopies' fresh weight
attributable to the stalks.
This is most likely due to the
vertical orientation of the stalks and the consequent small
horizontal component presented to the impinging wave.
The increase in attenuation observed on days 198 and
218 of 1986 for HV and W
may be due to errors in the
alignment of the ARC being of the same order of magnitude
as the actual attenuation by the heads.
Though the attenuation measurements did produce some
mixed results, the measurements of the intact canopy
indicated a substantial interaction of the EM wave with the
sunflower canopy.
Unmodified Disk Model Results
The unmodified disk model (UDM) required the following
list of agronomic inputs.
• real part of the dielectric constant of the
soil
• standard deviation of the soil surface
• autocorrelation length of the soil surface
• fractional moisture content of the leaves
• radius of the leaves
• leaf thickness
• volume fraction of the leaves in the canopy
• upper and lower limit of the azimuthal
orientation of the leaf normals
• upper and lower limit of the leaf normals'
angle to the zenith
• canopy height
94
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Figures 4.3 through 4.10 show the measured and
predicted HH and W
a{* s for the sunflower canopy over a
wide range of canopy developmental stages.
In these
figures, the model has been given a 0 to 90* and 10 to 60*
range of leaf inclination angles.
In both cases, the model
assumes the leaf angle distribution is uniform over the
specified range.
As can be seen in the figures, the 10 to 60* range
typically produces results which are closer to the measured
values than the 0 to 90* range.
Since approximately 60% of
the leaf angle distribution falls within the 10 to 60*
range for a sunflower canopy (see Fig. 4.11), this is good
evidence of the model's sensitivity to leaf angle
distribution.
model for the W
The shape of the curves produced by the
configuration tend to mimick the measured
data more closely than the HH configuration.
In both
cases, the modeled results come closer to the measured
values as the canopy matures.
The presence of rows may result in an increased
specular loss and could account for the measured o* values
being lower than the modeled o*f3.
The specular loss, when
viewing the crop perpendicularly to the rows, would be
expected to be greatest early in the season when the canopy
is at less than full cover.
As the canopy develops, the
radar's view of the bare soil between the rows is
obstructed resulting in less specular loss.
Since the
95
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Backscattering
Coefficient
(dB)
o
HH Measured
—
M H O -9 0 °
Uniform
•to
•16
Day 177.1986
Growth Stage: V-18
LAI > 1.89
Mean Leaf Diameter * 0.14 m
Canopy Height = 0.65 m
Vol. Soil Moisture a 0.12
-18
Angle of Incidence (degrees from nadir)
FIGURE 4 . 3 .
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
96
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o
HH Measured
—
HH 0 - 90°
Uniform
Uniform
Backscattering
Coefficient
(dB)
•10
•14
■16
Day 197,1996
Growth Stage: R-3
LAI = 4 66
Mean Leaf Diameter = 0.18 m
Canopy Height = 1.97 m
Vol. Soil Moisture = 0.12
•18
Angle of Incidence (degrees from nadir)
FIGURE 4 . 4 .
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
97
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o
HH Measured
QH
—
HH 0 - 90°
Uniform
■2■
•
HH 10 -60 °
Uniform
•6
Backscattering •a
Coefficient
(dB)
-.0
-10
•12
•■
•14
•16
•18
Day 213.1986
Growih Stage: R-6
L A I» 3.35
Mean Leal Diameter » 0.17 m
Canopy Height» 2.16 m
Vol. Soil Moisture = 0.04
■
10
15
20
25
30
35
40
49
50
S5
60
65
70
Angle of Incidence (degrees from nadir)
FIGURE 4.5. Measured and UDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
98
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o
HH Measured
— HH 0 - 90°
Uniform
Uniform
Backscattering
Coefficient
(dB)
■6■•
•10
■14
•16•'
0
Day 241.1985
Growth Stage: R-9
LAI > 3.44
Mean Leaf Diameter = 0.18 m
Canopy Height = 2.17 m
Vol. Soil Moisture =* 0.10
5
10
15
20
25
30
35
40
45
50
S5
60
65
70
Angle of Incidence (degrees from nadir)
FIGURE 4.6. Measured and UDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
99
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o
W Measured
—
W O -90°
Uniform
Uniform
Backscattering
Coefficient
(dB)
•10
•16
Day 177,1986
Growth Stage: V-18
LAI s 1.89
Mean Leaf Diameter = 0.14 m
Canopy Height = 0.6S m
Vol. Soil Moisture = 0.12
Angle of Incidence (degrees from nadir)
FIGURE 4.7. Measured and UDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
100
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o
VV Measured
—
W O - 90°
Uniform
•
W 10 - 60°
Uniform
■e
Backscattering •a
Coefficient
(dB)
•to■
•12
■
•14
■ LAI = 4 66
Day 197,1986
Growth Stage: R-3
o.
Mean Leaf Diameter = 0.18 m
16 ■ ■ Canopy Height » t .97 m
Vol. Soil Moisture = 0.12
•18
10
IS
20
25
30
35
40
45
SO
55
60
65
Angle of Incidence (degrees from nadir)
FIGURE 4 . 8 .
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
101
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o VV Measured
OH
■z •
Backscattering
Coefficient
(dB)
—
W O - 90°
Uniform
•
W 10 -60°
Uniform
■6
••■0..
•8
•10
■12•
•14
■16
■
Day 213.1986
Growth Stage: R-6
LAI * 3.35
Mean Leaf Diameter 3 0.17m
Canopy Height = 2.16 m
Vol. Soil Moisture = 0.04
■18
to
is
20
25
30
35
40
45
50
55
so
65
70
Angle of Incidence (degrees from nadir)
FIGURE 4 . 9 .
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
102
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0
o
VV Measured
— W O - 90°
Uniform
Uniform
4
Back6 '
scattering
Coefficient '
(dB)
-10 ••
12
14
Day 241, 198S
Growth Stage: R-9
LAI a 3.44
Mean Leaf Oiameter = 0.18 m
Canopy Height = 2.17 m
Vol. Soil Moisture = 0.10
-18
0
5
10
IS
20
25
30
35
40
45
50
55
60
65
70
Angle of Incidence (degrees from nadir)
FIGURE 4 . 1 0 .
Measured and UDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
103
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SUNFLOWER
(Helianthus Annuus)
Melle, Aug. 3.1970
(reconstructed from lemeur and Blad. 1974)
Upper Layer
Lower Layer
Total Canopy
Planoofiile
Canopy
Angle
Density
Function 0a
0.6
0.4
0.2
-e ~
o
to
20
30
40
50
60
70
80
90
Leaf Inclination Angle (degrees from zenith)
FIGURE 4.11. The measured leaf angle distribution for a
sunflower canopy.
104
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model assumes a uniform spatial distribution of the disks
(i.e., does not account for row structure), the modeled
results come closer to the measured a*s as the canopy
develops and obscures the row structure.
There are several other possible reasons for the UDM's
overestimation of o ’r.
Unlike a real canopy, the disks in
the model are assumed to be of equal size.
The model also
assumes that the disks' orientation are uniformly
distributed over the range of angles specified in the
input.
Also, the model assumes that the only scatterers in
the canopy are the disks (leaves) and does not account for
the backscattering effects of stalks, petioles, or heads.
Another difference between the theoretical canopy and the
measured canopy is that the disks lack the curvature found
in leaves.
Finally, an assumption of the model may be
violated by the canopy.
The model assumes that the disks
are far enough apart from each other so that only far field
interaction among the disks occur.
This limitation was
recently addressed by Fung et al., 1987 in which the disk
model was modified to allow for near field (i.e., Fresnel)
interactions.
They found that with this modification o ’
tr
was slightly lower (e.g., less than 2 dB) for disk-shaped
leaves than without the modification.
Unfortunately, the
publication of their modification came too late to be
incorporated in this study.
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Modification of the Disk Model
As mentioned previously, the model developed by Fung,
Eom, and Chen assumed that the leaf inclination angles were
uniformly distributed over the range specified in the
input.
This is rarely the case under field conditions,
with Dr. Chen's assistance, the author was able to modify
the original model to incorporate a variety of theoretical
leaf angle distributions into the programming code.
The model was modified by multiplying the phase
function and the absorption coefficients by the probability
density function of a given canopy type at six quadrature
points over the 0 to 90* range of leaf inclination angles.
Figure 4.12 shows the probability density functions of
several theoretical canopy types described by Bunnik
(1978).
As can be seen in Figure 4.11, the measured leaf
angle density function of the total sunflower canopy is
very similar to that of a theoretical planophile canopy.
Shell and Lang (1975), also working with sunflower,
found
the leaf angle distribution to be something between that of
a planophile and a plagiophile canopy.
Modified Disk Model Results
Input values for both the UDM and the modified disk
model (MDM) are shown in Tables 4.3 and 4.4.
The graphed
results of the MDM are shown in Figures 4.13 through 4.28.
While sunflower is something between a planophile and a
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Planophile
Probability
Density
Function
Uniform
0.6 - ■
0.4 ■■
0.2
0
10
20
40
30
SO
SO
70
so
90
Leaf Inclination Angle (degrees from zenith)
FIGURE 4.12.
Probability density functions for the leaf
inclination angles of five theoretical canopy types.
107
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 4.3. Variable inputs to Eom and Fun?'s model used to
produce the results seen in Figures 4.3-4.10 and 4.13-4.28.
Day/Year:
177/86
197/86
213/86
241/85
Model Inputs
Real Part of soil
Dielectric Constant
5.89
5.93
3.45
5.28
Fractional Leaf
Moisture
0.85
0.82
0.71
0 .68
Average Leaf
Radius (cm)
7.10
8.77
8.48
8.87
0.00076
0.00070
0.00047
0.00067
0.65
1.97
2.16
2.17
Volume Fraction of
Leaves in Canopy
Physical Depth of
Leaves in Canopy (m)
108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 4.4.
Inputs to Eom and Fung's model which
were treated as constant for the four days
represented in Figures 4.3-4.10 and 4.13-4.28.
Model Inputs
Wave Number Times RMS
of Soil Surface Height
1.60
Wave Number Times Auto­
correlation Length of
Soil Surface Height
12.47
Lower and Upper Limit
of Azimuthal Distribution
of Leaves (•)
0-360
Lower and Upper Limit
of Leaf Inclination
Angle Distribution (*)
1) 0-90 for MDM
2) variable for UDM
(shown on Figures
4.3-4.10)
Leaf Thickness (cm)
0.07
Frequency (GHz)
4.75
109
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
HH Measured
—
HH 0 - 90°
Uniform
•
HH Planopnile
*
HH Erectophile
Backscattering
latterir
Coefficient
>efficie
(dB)
•1 0
■
■12•
• 14 ■
• 16 ■
Day 177.1986
Growth Stage: V-18
U l » 189
Mean Leaf Diameter = 0.14 m
Canopy Height = 0.65 m
Vol. Soil Moisture a 0.12
•ia ■
10
15
20
25
20
35
40
45
SO
55
60
65
Angie of Incidence (degrees from nadir)
FIGURE 4.13. Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
110
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Backscattering
Coefficient
(dB)
0
HH Measured
—
HH 0 - 90*
Uniform
■
HH Plagiopfiile
-
HH ExtremooNe
.
•10
■■
■12•
•14 ■
•16■■
Day 177. 1986
Growth Stage: V-18
LAI = 1 89
Mean Leaf Diameter = 0 14 m
Canooy Height = 0.6S m
Vol. Soil Moisture = 0.12
•18
10
is
20
25 20 25
40
45
SO
Angle of Incidence (degrees from nadir)
S5
60
65
FIGURE 4 . 1 4 .
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
Ill
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2-
o
0•2
■4
HH Measured
— HH 0 - 90°
Uniform
■
•
HH Planophile
-
HH Erectophile
■
•6 ■
Backscattering
•3•
Coefficient
(dB>
■1 0 ■ ■
■ 12 ■'
14
16
Day 197.1986
Growth Stage: R-3
LAI * 4.66
Mean Leaf Diameter = 0.18 m
Canopy Height = t .97 m
Vol. Soil Moisture = 0.12
ia
10
15
20
25
30
35
40
45
50
55
60
65
70
Angle of Incidence (degrees from nadir)
FIGURE 4.15. Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
HH Measured
—
HH 0 - 90“
Uniform
■
HH Plagiophile
-
HH Extremaphile
•9
Back-
5
'•-9
scattering
Coefficient
(dB)
• to •
■12
■
• 14 ■
•16■■
□ay 197.1986
Growth Stage: R-3
LAI = 4 6 6
Mean Leal Diam eter« 0.18 m
Canopy Height» 1 .97 m
Vol. Soil Moisture = 0.12
•18
10
15
20
25
30
35
40
45
50
55
60
65
Angle of Incidence (degrees from nadir)
FIGURE 4.16. Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
113
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2t
Backscattering
Coefficient
(dB)
o
HH Measured
-
HH 0 - 90°
Uniterm
-
HH Planophile
-
HH Erectopfiile
to ■
o'*-.
• 16 ■
Day 213.1986
Growtn Stage: R-6
LAI = 3.3S
Mean Leal Diameter« 0.17 m
Canopy Height = 2.16 m
Vol. Soil Moisture = 0.04
•18 •
10
IS
20
25
30
35
40
45
50
55
60
65
70
Angle of Incidence (degrees from nadir)
FIGURE 4 . 1 7 .
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
114
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2r
a- ■
Backscattering
Coefficient
(dB)
to■
12
o
HH Measured
—
HH 0 • 90°
Uniform
•
HH Plagiophile
-
hh
Extremopnile
•o.
■
Day 213. 1986
Growth Slage: R- 8
LAI = 3.35
Mean Leaf Diameter = 0.17 m
• 16 •• Canopy Height a 2.16 m
Vol. Soil Moisture = 0.04
10
1S
20
25
20
25
40
45
SO
55
so
65
Angie of Incidence (degrees from nadir)
FIGURE 4 . 1 8 .
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
115
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Backscattering
Coefficient
WB>
.
o
HH Measured
—
HH 0 - 90
Uniform
•
HH Planopnila
-
HH Erectophile
-9.
,o.
•12 •
•16■
Day 241, 1985
Growth Stage: R-9
LAI = 3.44
Mean Leaf Diameter « 0.18 m
Canopy Height = 2.17 m
Vol. Soil Moisture = 0.10
•18•
10
is
20
25
30
35
40
45
50
55
60
65
Angle of Incidence (degrees from nadir)
FIGURE 4.19. Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
116
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2-
0
HH Measured
0-
—
HH 0 - 90°
Uniform
■2 -
s■■
Backscattering
Coefficient
(dB) ■10
■12 ■
■•
•
HH Plagiophile
•
HH Extremophile
.0
'-o.
'’0-
Day 241.1985
Growth Stage: R-9
LAI = 3.44
Mean Leaf Diameter = 0.18 m
Canopy Height = 2.17 m
Vol. Soil Moisture = 0.10
10
15
20
25
30
35
40
45
50
55
60
65
Angle of Incidence (degrees from nadir)
FIGURE 4.20. Measured and MDM-predicted backscattering
coefficient versus angle of incidence for HH polarization.
117
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0■2•
Backscattering
Coefficient
(dB)
o
VV Measurea
—
W O -90°
Unilorm
•
VV Planopnile
-
W Erectopnile
■6 ■
■8 ■
•1 0
■
•12 ■
■14 ■
•16 ■
Day 177.1986
Growth Stage: V- 1 8
LAI = 1.89
Mean Leal Diameter * 0.14 m
Canopy Height = 0.65 m
Vol. Soil Moisture = 0.12
•. o
•18•
10
IS
20
25
30
35
40
45
50
55
60
65
Angle of Incidence (degrees from nadir)
FIGURE 4.21. Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
118
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
VV Measured
—
W O - 90°
Uniform
■
VV Piagiophiie
-
VV Extreme pnile
Backscattering
Coefficient
(dB)
to■■
•t2
Day 177. 1986
Growth Stage: V-18
LAI = 1 89
Mean Leaf Diameter = 0.14 m
■16 ■• Canopy Height= 0.65 m
Vol. Soil Moisture = 0.12
•18 ■
10
15
20
25
30
35
40
45
50
55
60
65
Angle of Incidence (degrees from nadir)
FIGURE 4 . 2 2 .
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
119
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0*
•2
-4
Backscattering
latterir
Coefficient
lefficie
(dB)
■
o
VV Measured
—
W O -90°
Uniform
•
W Planopnile
-
W Erectophile
■
.....
•10
12
•14
■16
Day 197.1986
Growth Stage: R-3
LAI = 4.66
Mean Leaf Diameter = 0.18 m
Canopy Height = 1 .97 m
Vol. Soil Moisture = 0.12
•18 ■
10
IS
20
25
30
35
40
45
50
55
60
65
70
Angie of Incidence (degrees from nadir)
FIGURE 4 . 2 3 .
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
120
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
VV Measureo
— W O -90°
Uniform
0
VV Plagiophile
•2 ■ -
-
VV Extremophile
O’•
Backscattering
Coefficient
<dB>
,0 +
•12
<•* f
□ay 197.1986
Growth Stage: R-3
LAI = 4 6 6
Mean Leal Diameter » 0.18 m
Canopy Height » 1 .97 m
Vol. Soil Moisture = 0.12
10
IS
20
25
30
3S
40
45
50
55
60
65
Angle of Incidence (degrees from nadir)
FIGURE 4 . 2 4 .
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
121
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0•2 •
o
VV Measured
—
W O -90°
Uniform
•
W Planopnile
-
VV Erectophile
■4 •
Backscattering
Coefficient
(dB)
• 1 2 ••
• 16 •
Day 213. 1986
Growth Stage: R- 6
LAI - 3.35
Mean Leal Oiameter * 0.17 m
Canopy H eight» 2.16 m
Vol. Soil Moisture = 0.04
• 18 •
10
15
20
25
30
35
40
45
50
55
60
65
70
Angle of Incidence (degrees from nadir)
FIGURE 4 . 2 5 .
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
122
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
VV Measured
- W O - 90*
Uniform
VV Plagiophile
VV Sxtremophile
Backscattering
Coefficient
o
<dB> ,0 Day 213.1986
Growth Stage: H -6
LA! = 3.35
Mean Leaf Diameter = 0.17 m
i 6 .. Canopy Height = 2 . 1 6 m
Vol. Soil Moisture = 0.04
0
5
10
15
20
25
o ' - .
30
35
40
45
50
55
60
65
70
Angle of Incidence (degrees from nadir)
FIGURE 4 . 2 6 .
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
123
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
VV Measured
—
W O -90°
Uniform
•
W Planophile
-
W Eroctophile
Back-
scattering
Coefficient
m
•to «*
•12
•14
-1 6
■
-1 8
•
Day 241,1985
Growth Stage: R-9
LAI = 3.44
Mean Leaf Oiameter = 0.18 m
Canopy Height» 2.17 m
Vol. Soil Moisture = 0.10
10
IS
20
25
30
35
40
45
SO
SS
60
65
Angle of Incidence (degrees from nadir)
FIGURE 4 . 2 7 .
Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
124
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2-
Q VV Measured
0-
-
2■
W O -90*
Uniform
-
W Plagiophile
-
VV Bttremophile
Backscattering -8
Coefficient
(dB)
•10
•12
14
•16
oDay 241.1985
Growih Stage: R-9
LAI 3 3.44
Mean Leaf Diameter = 0.18 m
Canopy Height » 2.17 m
Vol. Soil Moisture =• 0.10
o-.
-18
10
IS
20
25
30
35
40
45
50
55
60
65
70
Angle of Incidence (degrees from nadir)
FIGURE 4.28. Measured and MDM-predicted backscattering
coefficient versus angle of incidence for W polarization.
125
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
plagiophile canopy, the uniform, erectophile and
extremophile canopy results are also graphed to show the
reader the contrast in the disk model output for different
canopy types.
The most noticeable effect of using the MDM is the
difference in the shape of the curves for a* versus angle
of incidence (i.e., the a^f response curve), particularly
for the vertically polarized case.
Early season over­
estimation of <r* is still a problem, though it is somewhat
reduced at the high view angles for
.
Unfortunately, assessment of the MDM's performance is
complicated by the fact that the modeled response's fit to
the measured values changes over the range of view angles.
In an attempt to compare the prediction accuracy of the UDM
and the MDM for different canopy types, a linear regression
of predicted versus measured a ' was performed for both
models and all theoretical canopy types.
The statistics
for these regressions are given in Table 4.5 for a^
and Table 4.6 for a '.
hh
From an inspection of the statistics in Table 4.5 it
can be seen that the MDM using the planophile canopy does
an equivalent or only slightly worse job at predicting a^
than the UDM using the 10 to 60* uniform distribution.
The
marginally poorer performance by the MDM is primarily due
to the overestimate of
at the lower view angles
(seen in Figs. 4.21 through 4.28).
This overestimate is
126
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 4.5. Linear regression statistics for measured
(independent variable) versus predicted (dependent
variable) a* using the UDM and the MDM.
Unmodified
Disk Model
Modified
Disk Model
Canopy
Type:
0 - 9 0 * 10 - 60* Plano- Erecto- Plagio- ExtremoUniform Uniform phile phile
phile
phile
Day
177
197
213
241
Year
1986
1986
1986
1985
--------- — — — ■
0.859
0.899
0.813
0.842
0.744
0.851
0.937
0.941
0.886
0.826
0.839
0.973
0.853
0.593
0.760
0.860
0.860
0.714
0.884
0.907
0.823
0.843
0.546
0.823
Day
177
197
213
241
Year
1986
1986
1986
1985
--------- ------0.711
0.923
0.559
0.705
0.861
1.182
1.068
1.344
SLOPES --1.195
0.302
0.927
0.178
1.605
0.264
1.855
0.387
0.659
0.550
0.954
1.133
0.832
0.677
0.902
1.199
Day
177
197
213
241
Year
1986
1986
1986
1985
-------- — _______ - INTERCEPTS —
1.387 4.583 -3.559
0.649
-0.604
-0.722
2.207 -4.924
0.350
1.477 5.976 -5.410
2.716
3.489 9.003 -4.014
■0.459
-1.624
0.227
2.231
2.023
0.881
0.970
4.242
Day
177
197
213
241
Year
1986
1986
1986
1985
--------- ------1.070
1.154
1.145
1.303
1.373
1.345
0.695
0.846
0.990
1.487
0.938
0.911
1.435
1.245
2.235
1.395
r*
RMSE ---1.599 0.467
1.814 0.628
1.910 0.404
0.776 0.392
127
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 4.6. Linear regression statistics for measured
(independent variable) versus predicted (dependent
variable) a* using the UDM and the MDM.
Unmodified
Disk Model
Canopy
Type:
Modified
Disk Model
0 - 90* 10 - 60* Plano- Erecto- Plagio- ExtremoUniform Uniform phile phile
phile
phile
Day
177
197
213
241
Year
1986
1986
1986
1985
0.747
0.879
0.614
0.705
0.865
0.882
0.612
0.647
0.702
0.756
0.412
0.509
0.790
0.886
0.936
0.914
0.833
0.898
0.873
0.862
0.667
0.824
0.490
0.601
Day
177
197
213
241
Year
1986
1986
1986
1985
0.542
0.548
0.497
0.540
0.715
0.677
0.629
0.654
0.653
0.567
0.474
0.510
0.440
0.467
0.499
0.564
0.632
0.646
0.695
0.717
0.492
0.511
0.429
0.480
Day
177
197
213
241
Year
1986
1986
1986
1985
Day
177
197
213
241
Year
1986
1986
1986
1985
----------------- INTERCEPTS--------------------0.644
-1.056 0.111 -2.640
-1.418
0.214
•0.675
-2.092 -0.463 -3.580
-1.984
0.651
-2.433
-4.103 -2.476 -4.650
-3.228
-1.256
-1.950
-3.883 -2.017 -4.012
-3.035
-0.670
1.338
0.798
1.395
1.208
1.198
0.972
1.773
1.669
1.805
1.264
2.006
1.730
0.963
0.660
0.463
0.598
1.201
0.854
0.939
0.991
1.475
0.929
1.549
1.351
128
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
due to the higher weighting of near horizontal disks by the
planophile canopy than by the 10 to 60* uniform leaf angle
distribution.
The statistics in Table 4.6 indicate that the MDM
using the plagiophile canopy provides a better prediction
of a*
nh than either the 10 to 60* uniform distribution
or the planophile distribution.
Though the r1 values
tended to be slightly higher for the erectophile canopy
than for the plagiophile canopy, the slope values in the
erectophile case were somewhat lower than 1.0 than were the
slope values for plagiophile canopy.
Both models suffered
from an overestimate of a* at high angles of
hh
incidence.
The cause of this overestimate is still
unknown.
While the modification altered the angular response of
the estimated
, it did not appear to greatly improve
the accuracy of the predicted <x^ except for day 241.
The prediction of a ’ , on the other hand, appeared to
hh
benefit from the inclusion of continuous leaf angle
distribution information into the model.
In general,
prediction performance by the MDM was found to be better
than or equivalent to that of the UDM using the 10 to 60*
uniform distribution when using theoretical canopy types
(i.e., planophile and plagiophile) which had been shown by
field work (Lemeur (1973); Shell and Lang (1975)) to be
129
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
similar to the measured leaf angle distributions of
sunflower canopies.
The test of the MDM using the sunflower crop may not
justify the modification on the grounds of improved
accuracy of estimates, but another crop might require the
flexibility in leaf angle distribution inputs provided by
the modification.
Additional modifications will be
required to incorporate other information such as row
structure and other canopy components (e.g., stalks) into
the disk model to make the simulated vegetation canopy
still more realistic.
Projected Disk Component Model
In some instances, the behavior of the MDM for
different canopy types was not initially understood.
For
example, when viewing a planophile canopy, the response
curve for a ‘ was markedly different from that of a*.
w
hh
This prompted the development of a separate model, called
the Projected Disk Component Model (PDCM), to help explain
the MDM's behavior for the different canopy types.
The
model was intended to provide the user with a "radar's
view" of a disk canopy by describing the canopy geometry in
terms of a radar's polarization configuration.
It was
hoped that by describing the disk canopy in this way, the
user could gain a some insight for how the MDM should
respond given certain types of canopies.
130
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The PDCM was based on the premise that an impinging,
polarized electromagnetic (EM) wave has maximum interaction
with those elements in the canopy which are aligned
parallel to the direction of polarization.
By reducing
several types of theoretical disk canopies to a simple,
quantitative measure of their constituent horizontal and
vertical components, the PDCM provides an indication of the
degree of coupling that could occur between a disk canopy
and a horizontally or vertically polarized EM wave.
Interpretation of the model results, though qualitative at
this point, may help explain some backscattering phenomena
observed in field experiments.
Projected Disk Component Model Description
A unit, planar disk's horizontal and vertical
projections (H and V, respectively) are found by a series
of coordinate translations and axes rotations.
The
horizontal and vertical components of an entire disk canopy
are found by integrating, weighting and averaging the
individual H's and V's over the range of disk inclination
angles and azimuthal orientations.
The disk orientation is described by the unit vector
(nQ) normal to the upper surface of the disk.
The
orientation of nQ is described in spherical coordinates by
the disk azimuth (*„)» the disk inclination angle (9o) and
n 's length which is assumed to be 1.
To be consistent
131
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
with the MDM, the disk azimuth is defined as 0 in the
direction of the observer and is measured counter-clockwise
about the center of the disk from 0 to 2*.
Disk
inclination is described by the angle between the
the zenith over the range of 0 to
Assuming that
and
t /2.
and 0Q are mutually independent, we
can write the disk normal distribution function as
^
gD - «• (eD) x ~
hocV
[i]
where g'o (9.)
o is the disk normal inclination distribution
and h (#J/2 jt is the disk normal azimuthal distribution
o o
(Ross, 1981).
The horizontal projection of the disk is defined in
the following manner
H(nr ;nB; r D) - H(0r,# r;0D, * D?ro)
[2]
where n r is the unit vector in the direction of
observation, 9^ is the view angle measured from nadir, *r
is
the azimuthal orientation of observation (always 0),
rQ
isthe radius of the disk (always 1).
and
(At this point,
the reader is encouraged to refer to Appendix A for a more
thorough mathematical and graphical explanation of the
techniques used to calculate the projections.)
Integrating the H projection of an assembly of disks
with normals inclined at 0
D
over the full 0 to 2ir azimuthal
range (i.e., the delta function) we get
132
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
For a uniform azimuthal distribution, hQ(*o) = l reducing
the equation to
o
Then, integrating over the 0 to t/2 range of disk
normal inclinations we get
T
o
T/2
[5]
o
H" can be determined for specific canopy types by
applying the weights (i.e., probability density function
values) associated with the desired canopy type to the
appropriate quadrature points during the integration
procedure.
V, V' and V" can be substituted for n, H' and H " ,
respectively, in the preceding equations and definitions to
solve for the vertical case.
Figures 4.29, 4.30 and 4.31 show the vertical
projection (V) of a unit, planar disk (i.e., radius = 1)
133
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22.5
0.3
0.6
Vertical
Projection
67.5
0.4
0.2
0
90
180
270
360
Azimuth (degrees)
FIGURE 4.29. The vertical projection (V) of a unit, planar
disk rotated azimuthally from 0 to 360* as viewed from
nadir.
Each curve represents a disk at a different angle
o f inclination indicated by the number (the disk normal's
angle in degrees from zenith) beside the curve.
134
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.8
0.6
67.5'
22.5'
Vertical
Projection
0 .4
-
0.2
0
90
180
270
060
Azimuth (degrees)
FIGURE 4 . 3 0 .
The vertical projection (V ) of a unit, planar
disk rotated azimuthally from 0 to 360* as viewed 45* from
nadir.
Each curve represents a disk at a different angle
of inclination indicated by the number (the disk normal's
angle in degrees from zenith) beside the curve.
135
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
90°
67.5*
0.8
45*
0.6
Vertical
Projection
0.4-
22.5*
0.2-
0*
O'
0
90
180
270
360
Azimuth (degrees)
FIGURE 4.31. The vertical projection (V) of a unit, planar
disk rotated azimuthally from 0 to 360* as viewed 90* from
nadir.
Each curve represents a disk at a different angle
of inclination indicated by the number (the disk normal's
angle in degrees from zenith) beside the curve.
136
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
rotated azimuthally around 360* and viewed from 0, 45 and
90* from nadir, respectively.
The numbers beside each
curve indicate the angle of inclination of the disk.
Figure 4.32 shows the horizontal projection (H) for the
same disk.
Since changing the view angle simply involves
pivoting on the horizontal axis, the horizontal projection
pattern changes with disk inclination, but remains the same
for all view angles.
Figures 4.33 and 4.34 show the horizontal (H') and
vertical (V1) delta functions, respectively, for five disk
inclination angles.
The delta functions are the disk
projections integrated over the range of azimuth angles for
a disk at a single, specified inclination angle.
Figures 4.35 and 4.36 are the horizontal and vertical
components (i.e., H" and V"), respectively, of the disk
integrated over the azimuth and all inclination angles for
the five canopy types.
Projected Disk Component Model Results
Summarizing the PDCM results, Figures 4.35 and 4.36
revealed that:
1) the vertical component of a disk canopy is
view angle dependent,
2) the horizontal component of a disk canopy is
view angle independent,
3} both the vertical and horizontal components
depend on canopy type,
137
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o’
22.5'
o.s
0.6
Horizontal
Projection
67.5
0.4
0.2
0
90
ISO
270
360
Azimuth (degrees)
FIGURE 4.32. The horizontal projection (H) of a unit, planar
disk rotated azimuthally from 0 to 360* as viewed from any
angle from nadir to 90* off-nadir.
Each curve represents a
disk at a different angle of inclination indicated by the
number (the disk normal's angle in degrees from zenith)
beside the curve.
138
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0.9-
0.8Delta
Function
for H
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
•
0*
•
30*
0.7'
0.6 -
0.5-1
o
10
20
30
40
•
45*
50
0
SO*
x
SO
90*
70
80
90
View Angle (degrees from nadir)
The horizontal delta function (H1) for five
FIGURE 4.33.
disk inclination angles (indicated in legend at bottom of
graph).
139
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1
0.9
0.8
0 .7
0 .6 -■
Delta
Function o.s
for V
0.4
• 0*
0 .3
.
0.2
•
45*
0
60*
x
go*
0 .1 +
30*
to
20
30
—t—
40
50
SO
80
90
View Angle (degrees from nadir)
FIGURE 4.34. The vertical delta function (V') for five
disk inclination angles (indicated in legend in lower left
of graph).
140
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it
•
Planopnile
•
Erectopmlo
x
Plagiophile
0
Exlremoonila
•
Uniform
0.95”
0 .9 ”
H
Component
0.85”
I
x
x
x
O
O
O
x
x
x
x
O
O
O
O
x
O
x
O
x
O
x
O
x
O
x
O
x
O
x
O
x
O
x
x
O
O
0.8”
,0
20
30
40
50
60
70
80
90
View Angle (degrees from nadir)
FIGURE 4.35.
The horizontal component ( H " ) of the disk
integrated over all azimuths and inclination angles for the
five theoretical canopy types.
141
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0.9-■
• * a
0.8' ■
Component
!
t
fl
0.7
o .6 f
0.5' •
0.4
•
pianophile
*
Erectophila
x
Plagiophila
o
Extremopfiile
•
Uniform
10
20
30
40
50
SO
70
80
90
View Angle (degrees from nadir)
FIGURE 4.36.
The vertical component (V") of the disk
integrated over all azimuths and inclination angles for the
five theoretical canopy types.
142
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4) the maximum difference between disk canopy
types in terms of the components is found in
the vertical component at view angles greater
than 55 * and
5) all disk canopy types appear to have a
similar vertical component when viewed in the
30 to 40* range.
As stated previously, the PDCM quantifies the
horizontal and vertical components present within a disk
canopy thus providing an indication of the degree of
coupling that could be expected to occur between the canopy
and a horizontally or vertically polarized EM wave.
Restating the above observations in terms of the
polarized wave interactions with a disk canopy, Figures
4.35 and 4.36 suggest the following:
1) coupling of a vertically polarized EM wave
with a disk canopy is view angle dependent,
2) coupling of a horizontally polarized EM wave
with a disk canopy is view angle independent,
3) the degree of coupling for both polarizations
depends on canopy type,
4) the maximum difference between disk canopy
types in terms of the degree of coupling is
found in the vertical polarization case at
view angles greater than 55* and
5) all disk canopy types appear to have a
similar degree of coupling with a vertically
polarized wave when viewed in the 30 to 40*
range.
Results of the MDM Explained bv the PDCM
Extending these interpretations to the possible
effects on <j* provided the author with a general idea of
how the MDM should behave and why the MDM behaved
143
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differently for the different canopies.
In the vertical case, the PDCM indicated that a
planophile canopy would have a higher vertical component at
low view angles (e.g., 10 to 30*) and a lower vertical
component at high view angles than an erectophile canopy.
This, in turn, suggested that the
response curve
for a planophile canopy would be higher at low view angles
and lower a high view angles than for an erectophile
canopy.
of
This was indeed the case for the MDM's predictions
for the two canopy types.
The PDCM's application to the MDM in the horizontal
case was less clear than for the vertical case.
The PDCM
did not explain the decrease in o*
with increasing
hn
view angle, but it did provide a possible explanation for
the a"
hn response curve behavior of the two canopies
relative to each other.
The failure of the c*
hh
response curves to intersect or to intersect at only slight
angles for the planophile and erectophile canopies can be
attributed to the view angle independence of the horizontal
component in a disk canopy as demonstrated by the PDCM.
Also, the relative positions of the two response curves
(i.e., a* for the planophile canopy being greater than
hh
that for the erectophile canopy in most cases) can be
explained by the PDCM.
The model failed to explain and, in fact, appeared to
contradict the relative positions of the plagiophile and
144
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extremophile canopy a ’r response curves for both the HH
and W
polarizations.
The probable reason for the POCM's
failure to explain the MDM's response to the plagiophile
and extremophile canopies lies in the difference betveen
the way the MDM and the PDCM interpret the canopy.
The
PDCM averages all (high and low) values of horizontal and
vertical components over both azimuth and disk inclination
angle.
As such, H" and V" values are influenced by low
values of H and V in a way which the MDM is not.
For
example, a canopy containing some disks with a small
vertical component and some disks with a large vertical
component might result in the PDCM interpreting the canopy
as having a median vertical component.
The MDM (or a
radar) on the other hand might respond disproportionately
stronger to those elements in the canopy having the larger
vertical component while the elements with a smaller
vertical component have only a negligible effect.
The PDCM helped explain the behavior of the MDM
for certain canopy types and was particularly useful in
explaining the lesser degree of view angle dependence in
the horizontal polarization case.
It appears, however, to
be unsuited in its present form to explaining the MDM's
response to the plagiophile and extremophile canopy types.
Implications of the PDCM Results bevond the MDM
The PDCM results might have utility beyond the context
145
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of the MDM and in particular to the understanding of
polarization phase differences (PPD)
(i.e., the difference
between the phases of the received horizontal and vertical
signal voltages) observed in some crops.
In a recent article by Ulaby et al., 1987, the
authors attributed the PPD from a corn crop to differences
between the horizontal and vertical wave interaction with
the stalks and the soil surface.
Because of the senescent
condition of the leaves at the time of measurement (i.e.,
all of their measurements were made in late season), the
authors reasonably assumed that there was no substantial
interaction between the leaves and the impinging wave.
They may not have observed PPD's significantly different
from zero in the disk-like canopies that they studied
(i.e., soybean, alfalfa and clover) because of the dry
canopy conditions.
The influence of leaves on the PPD
would most likely occur earlier in the season during the
vegetative growth stages when leaf material is at its
maximum water content.
Additional research will be
required to determine if a "high-loss medium" such as a
full, moist canopy can also produce non-zero PPD's.
In Figure 4.36, the decreasing V component with
increasing view angle for all except the extremophile
canopy, suggests that an impinging, vertically polarized EM
wave would have decreasing interaction with these canopies
as view angle increases.
A horizontally polarized wave by
146
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contrast would, for the same types of canopies, have a
constant level of interaction with the disks over all view
angles.
The difference between the levels of horizontal
and vertical coupling with the disks would, in all
likelihood, manifest itself in an increasing PPD with
increasing view angle. The degree of PPD for any given view
angle would be canopy dependent and would be greatest in a
planophile canopy.
Should future field work with disk-like
canopies in the vegetative growth stages show such a
phenomenon to exist, the PDCM may provide the basis for an
explanation.
If the disk canopy also contained vertically oriented
stalks, one would expect that the decreased interaction of
the vertically polarized EM wave with the disks would allow
for greater interaction of the wave with the stalks as view
angle increases.
The PPD would then become a function of
the horizontal and vertical components of both the disks
and the stalks.
Two interesting questions arise at this
point to be addressed by future work.
At what view angle
and to what degree is the decrease in vertical coupling
with the disks offset by the increase in vertical coupling
with the stalks as view angle increases?
How is this
phenomena expressed in the PPD?
Figures 4.35 and 4.36 may have additional implications
in terms of single polarization configurations for radar.
Since the vertical component appears to be essentially the
147
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same for all canopy types when viewed over the range of 30
to 40* off-nadir, this range of view angles may prove
useful in minimizing effects due to disk canopy type
differences, thus allowing observations of other scene
factors.
Also, since the maximum difference in canopy
types is found in the vertical component at angles greater
than 55*, there may be some utility in these view angles
for canopy type discrimination by a vertically configured
system.
The difficulty of verifying these last observations in
the field lies in the fact that different disk-like
canopies have more features distinguishing them from each
other than simply the vertical or horizontal component of
their leaves.
Since vegetation canopies are not simply
collections of disks,
field verification of all of these
observations will be complicated by the effects of
branching patterns, stem size, soil surface roughness, soil
moisture, plant moisture, variable leaf size, leaf
curvature and changes in leaf angle distribution with
growth stage.
CONCLUSIONS
The disk model developed by Eom and Fung (19S4) was
tested against a set of field measurements of a* from a
tr
crop of sunflowers.
The model overestimated a* early in
tr
■*
the crop's development, but decreased the overestimate as
148
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the crop matured.
Since the model, in its original
configuration, was restricted to an assumption of a uniform
distribution over the range of specified disk inclination
angles, the model was modified to accommodate canopies with
nonuniform leaf angle distributions (e.g., planophile)
similar to those found in the field.
The modification altered the shape of the response
curve for predicted a* versus view angle (particularly
for the vertical polarization case), but did not appear to
greatly improve the accuracy of the predicted <x^ except
for day 241.
The prediction of a*,
on the other hand,
hh
appeared to benefit from the inclusion of continuous leaf
angle distribution information into the model.
In general,
prediction performance by the MDM was found to be better
than or equivalent to that of the UDM using the 10 to 60*
uniform distribution when using theoretical canopy types
which had been shown by field work to be similar to the
measured leaf angle distributions of sunflower canopies.
While the model now has the added capability of
incorporating measured leaf angle distributions into its
calculations, additional modifications (e.g., incorporating
row structure information) will be a necessary to improve
the model's performance with row crops.
To help explain the behavior of the modified disk
model, a separate model, called the Projected Disk
Component Model, was written which described the canopy
149
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geometry in terms of a radar's polarization configuration.
By reducing several types of theoretical disk canopies to a
simple, quantitative measure of their constituent
horizontal and vertical components, the PDCM provided an
indication of the degree of coupling that could occur
between a disk canopy and a horizontally or vertically
polarized EM wave.
In this way, the author was able to
gain a general idea of how the MDM would respond to certain
types of canopies for given radar polarization
configurations.
The PDCM helped explain the behavior of
the MDM for certain canopy types and was particularly
useful in explaining the lesser degree of view angle
dependence in the horizontal polarization case.
It
appears, however, to be unsuited in its present form to
explaining the MDM's response to the plagiophile and
extremophile canopy types.
Additional work with the PDCM
may provide some insight into the influence of leaf
orientation on such phenomena as polarization phase
differences observed in some vegetation canopies.
150
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Appendix A.
Calculation of tho Horizontal and Vertical
Components of a Projected Disk.
The horizontal and vertical projection of a disk,
given the disk azimuth, disk inclination angle and the
observer's view angle, can be calculated in the following
manner.
After converting the spherical coordinates (l,9o,*o)
of the disk normal vector to rectangular coordinates
(x,y,z), the vector must then be translated to the
observer's local coordinate system (p,h,v) by using the
following equations:
! X
*P
xh
: X
XV
+
+
+
V
V
V
+ a z
ip
+ a z
zh
[A2]
+ a z.
[A3]
IV
[Al]
The p-axis is the line-of-site between the observer and the
center of the disk.
If the observer is a radar, the p-axis
represents the line-of-propogation.
The h- and v-axis are
perpendicular to the p-axis and represent the horizontal
and vertical directions, respectively, as defined by the
observer.
The variable a is the cosine of the angle
between the two axes identified by the subscripts.
Since the axes are simply pivoting on the y-axis (haxis) by an amount equal to the view angle of the observer,
the translation simplifies to the following expressions:
151
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The horizontal component (H) of the disk is the
maximum value in the h dimension of the projected disk in
the hv-plane (see Fig. A.4.1) and is found by
H = dosin(0M)
[A7]
where 9^ is the angle between the line representing the
intersection of the hflB-plane with the disk and the line
representing the intersection of the pv-plane with the hnDplane (see Fig. A.4.2).
By symmetry, 9m is equal to the
angle between nQ and the h-axis.
If we let unit vector a represent nQ and we let b
represent a unit vector along the h-axis (see Fig. A.4.2),
we can solve for 9^ in the following manner:
a*b
COS (0 ) =
"
where
[AS]
- ■
1*11*1
1*1 = C(Pa)2 + (h,)1 + (vj*]*
and
[A9 ]
,
1*1 =
c(pb)1 + ( V 2 +
[A10]
Since b lies on the h-axis, pt = 0 and v. = 0 which reduces
D
D
|b| to
|b| =
The dot product for a and b is found
[All]
by
»•* = (P.) (P„) + (\) (\) +Cv.) (V
[A12]
152
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1
0.5
VERTICAL
0
-1
-1
-
0.5
0
0.5
1
HORIZONTAL
FIGURE A.4.1
the hv-plane
The projection of a unit, planar disk onto
153
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V
FIGURE A.4.2.
Geometry used in solving for the horizontal
component of a unit, planar disk rotated in threedimensional space.
The dashed line represents the
intersection of the ab-plane (cross-hatched area) with the
disk.
154
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
which, for the reasons mentioned above, reduces to
a-b = (ha) (h^ .
Taking the arccosine of c o s ^ )
[A13]
we can then find a value
for 0^ to use in solving for H.
The vertical component (V) of the disk is the maximum
value in the v dimension of the projected disk in the hvplane (see Fig. A.4.1) and is found by
v
= dj}cos(e||)
[A14]
where 9^ is the angle between the v-axis and the line
representing the intersection of the disk with the f1 vD
plane (see Fig. A.4.3).
angle between
By symmetry, 9M is equal to the
and its projection onto the hp-plane
is solved in the same way as before using equations
A5 through A7, but letting b represent the projection of nQ
onto the hp-plane (see Fig. A.4.3).
The changes in the
calculations resulting from the new role of b are due to v
D
= 0 and are as follows:
CCPb) a +
[A15]
a-b = (pa) (pb) + (ha) (h^) .
[A16]
|b| =
and
155
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V
FIGURE A.4.3.
Geometry used in solving for the vertical
component of a unit, planar disk rotated in threedimensional space. The dashed line represents the
intersection of the ab-plane (cross-hatched area) with the
disk.
156
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REFERENCES
Brunfeldt, D. R. (1987), Theory and design of a fieldportable dielectric measurement system, Proc. IGARSS '87
Symposium. Ann Arbor, 18-21 May 1987, 1:559-563.
Bunnik, N.J.J. (1978), The multisoectral reflectance of
shortwave radiation by agricultural crops in relation
with their morphologicl and optical properties. Pudoc
Publ., Mededelingen Landbouwhogeschool, Wageningen, The
Netherlands.
Eom, H. J. and A. K. Fung (1984), A scatter model for
vegetation up to Ku-band, Remote Sens. Environ.. 15:185200
.
Fung, A. K . , M. F. Chen and K. K. Lee (1987), Fresnel field
interaction applied to scattering from a vegetation
layer, Remote Sens. Environ.. 23:35-50.
Kimball, B. A. (1976), Smoothing data with cubic splines,
Aaron. J . . 68:126-129.
Lemeur, R. (1973), A method for simulating the direct solar
radiation regime in sunflower, Jerusalem artichoke, corn
and soybean canopies using actual stand structure data,
Agric. Meteorol.. 12:229-247.
Lemeur, R. and B. L. Blad (1974), A critical review of
light models for estimating the shortwave radiation
regime of plant canopies, Agric. Meteorol.. 14:255-286.
Martin, R. D., Jr., 6. Asrar and E. T. Kanemasu (1988), Cband scatterometer measurements of a tallgrass prairie,
Remote Sens. Environ., accepted for publication February
26, 1988.
Paris, J. F. (1986), Probing thick vegetation canopies with
a field microwave scatterometer, IEEE Trans. Geosci.
Remote Sens.. GE-24:886-893.
Pitts, D. E., G. D. Badhwar and E. Reyna (1988), The use
of a helicopter mounted ranging scatterometer for
estimation of extinction and scattering properties of
forest canopies, part II: experimental results for highdensity aspen, IEEE Trans. Geosci. Remote Sens.. GE26:144-152.
157
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ross, J. (1981), The radiation regime and architecture of
plant stands. Dr W. Junk Publishers, The Hague,
Netherlands.
Schneiter, A. A. and J. F. Miller (1981), Description of
sunflower growth stages, Crop Sci . . 21:901-903.
Shell, G. S. G. and A. R. G. Lang (1975), Descriptions of
leaf orientation and heliotropic response of sunflower
using directional statistics, Agric. Meteorol.. 15:33-48.
Ulaby, F. T., D. Held, M. C. Dobson, K. C. McDonald and
T. B. A. Senior (1987), Relating polarization phase
differences of SAR signals to scene properties, IEEE
Trans. Geosci. Remote Sens.. GE-25:82-92.
Wu, s. (1986).
Preliminary report on measurements of
forest canopies with C-band radar scatterometer at
NASA/NSTL, IEEE Trans. Geosci, Remote Sens.. GE-24:894899.
158
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ACTIVE MICROWAVE REMOTE SENSING OF A
NATURAL, TALLGRASS PRAIRIE
AND
A PROJECTED DISK COMPONENT’ MODEL
TO EXPLAIN THE BEHAVIOR OF
A MODIFIED DIELECTRIC DISK MODEL
by
ROBERT D. MARTIN, JR.
B.S., Texas A&M University, 1982
M.S., Texas A&M University, 1984
AN ABSTRACT OF A DISSERTATION
submitted in partial fulfillment of the
requirements for the degree
DOCTOR OF PHILOSOPHY
AGRONOMY
KANSAS STATE UNIVERSITY
Manhattan, Kansas
1988
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ABSTRACT
C-band scatterometer measurements were made of a
tallgrass prairie in an attempt to determine the degree of
correlation between (1) the backscattering coefficient
(ff* ) and different expressions of soil moisture and (2)
the backscattering coefficient and various canopy
parameters.
The findings of this study support those made
in previous studies in terms of the optimum polarization
and view angle selection for soil moisture work (i.e.,
near-nadir view angles and HH and W
polarizations).
In
contrast to previous studies, view angles of 30* and 45*
also produced strong correlations with soil moisture.
A
moderately strong correlation and partial correlation was
found between <r* and leaf water potential,
indicating
some capability of C-band measurements to detect extremes
in the water status of prairie vegetation under shallow
soil conditions.
Also, site differences due to burn
treatments appeared to cause significant differences in the
sensitivity of a' to soil moisture.
■*
tr
In a second study, the disk model developed by
Ors. Eom and Fung was tested against a set of field
measurements of a'
tr
from a crop of sunflowers.
The
*
model overestimated a"p at early growth stages, but
decreased the overestimate as the crop matured.
The author
modified the model to accommodate canopies with non-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
uniform, continuous leaf angle distributions.
The
modification altered the shape of the response curve for
predicted a* versus view angle, but failed to reduce
the overestimate in the early growth stages.
Additional
modifications (e.g., incorporating row structure
information) may be necessary.
A new model, called the Projected Disk Component Model
(PDCM), was developed to help explain the behavior of the
modified disk model (MDM).
By reducing several types of
theoretical disk canopies to a simple, quantitative measure
of their constituent horizontal and vertical components,
the PDCM indicates the degree of coupling that could occur
between a disk canopy and a horizontally or vertically
polarized electromagnetic wave.
In this way, the author
was able to gain some insight into how the MDM would
respond to certain types of canopies.
The PDCM may also
provide some insight into the influence of leaf orientation
on polarization phase differences.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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