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MICROWAVE PROPAGATION AND BACKSCATTER CHARACTERISTICS OF VEGETATION (REMOTE SENSING, RADAR, ATTENUATION)

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8513824
W ilson, Edward A.
MICROWAVE PROPAGATION AND BACKSCATTER CHARACTERISTICS OF
VEGETATION
University of Kansas
University
Microfilms
International
Ph.D.
1984
300 N. Zeeb Road, Ann Arbor, Ml 48106
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MICROWAVE PROPAGATION AND BACKSCATTER
CHARACTERISTICS OF VEGETATION
Edward A. Wilson
B .E .E ., Ohio State University, 1969
E .E ., Ohio State University, 1973
M .S.E.E., University of Missouri, 1974
Submitted to the Department of E lectric al and
Computer Engineering and the Faculty of the
Graduate School of the University of Kansas in
p a rtia l fu lfillm e n t of the requirements fo r the
degree of Doctor of Philosophy.
Dissertation Committee
J
Ck
Dissertation defended:
August 1984
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TABLE OF CONTENTS
Page
PREFACE......................................................................................................
i
LIST OF FIGURES....................................................................................... i i
LIST OF TABLES........................................................................................ vi
NOMENCLATURE............................................................................................ ix
ABSTRACT.....................................................................................................xiv
1.0
INTRODUCTION...................................................................................
1.1
1.2
1.3
1.4
2.0
3.0
Calibration, Accuracy, and Precision......................... 28
1979 Backscatter Data........................................................ 29
1980 Backscatter Data........................................................ 37
Review of Previous Approaches......................................... 70
A Semi-Empirical Vegetation Model............................... 72
Additional Semi-Empirical Models.................................. 101
Model Comparisons............................................................... 109
Canopy Attenuation from Model.......................................... 109
ATTENUATIONDATA ANALYSIS............................................................118
5.1
5.2
5.3
5.4
6.0
1979 Backscatter Measurements........................................ 17
1980 Backscatter Measurements........................................ 22
1984 Attenuation Measurements........................................ 24
BACKSCATTERRESPONSE MODELING................................................... 69
4.1
4.2
4.3
4.4
4.5
5.0
17
BACKSCATTERDATA ANALYSIS........................................................... 27
3.1
3.2
3.3
4.0
Agricultural Applications............................................... 3
Advantages of Microwave Sensors................................... 6
Prior Research....................................................................
8
Objectives of Investigation........................................... 15
EXPERIMENTDESCRIPTION.................................................................
2.1
2.2
2.3
1
Calibration, Accuracy, and Precision...........................119
Angular, Polarization and Frequency Response of
Wheat Data............................................................................ 125
Angular, Polarization, and Frequency Response of
Soybean Data........................................................................ 128
Special Attenuation Experiments.................................... 134
ATTENUATIONMODELING......................................................................141
6.1
6.2
D ielectric Properties of Vegetation............................ 141
Vertical Stalk Absorption Loss Model...........................144
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6.3
6.4
6.5
6.6
7.0
Random Leaf Absorption Loss Model................................. 147
Random Stalk Absorption Loss Model..................
148
Wheat Attenuation Model..................................................... 149
Soybean Attenuation Model................................................. 156
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK............... 162
7.1
7.2
Conclusions............................................................................ 162
Recommendations for Future Work..................................... 164
REFERENCES................................................................................................. 166
APPENDIX A................................................................................................. A1
APPENDIX B................................................................................................ B1
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PREFACE
Any major e ffo rt such as the investigation reported herein is
not the work of a single in d ivid u al, but is the result of the
contributions
of
many
dedicated
people.
I
welcome
this
opportunity to recognize those who I feel are most responsible for
completion of this study.
My parents, Howard and Frances Wilson, provided the loving
and supportive home environment during those most important early
years of my educational experience.
my daughter,
Ju lie
provided
the
My w ife, Christine and la te r
love,
emotional
encouragement necessary to pursue this goal.
support
and
Numerous faculty and
s ta ff of the Remote Sensing Laboratory at the University of Kansas
have made direct contributions to this work.
Although there are
too many persons to acknowledge in d iv id u ally, Dr. Fawwaz T. Ulaby
deserves special
recognition.
He went far beyond his role as
teacher and advisor to provide encouragement to continue my work
despite numerous challenges.
F in a lly , I would lik e to thank the
University of Kansas for providing the academic environment and
f a c ilit ie s
for this work and the National Aeronautics and Space
Administration for providing most of the support for nry research.
i
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LIST OF FIGURES
Page
Figure
1. Configuration used to measure canopy attenuation.................. 26
Figure
2. Histogram for a ll 1979 crops combined at 35.6 GHz VV 30°
(dB)........................................................................................................ 31
Figure
3. Histogram for a ll 1979 crops combined at 35.6 GHz VV 30°
( r e a l) .................................................................................................... 32
Figure
4. 1979 dynamic range versus frequency............................................
Figure
5. 1979 frequency decorrelation for
HH p o larizatio n .................. 34
Figure
6. 1979 frequency decorrelation for
HV p o larization .................. 35
Figure
7. 1979 frequency decorrelation for
VV p o larizatio n .................. 36
Figure
8. 1979 angular decorrelation of 30° versus 50°........................... 38
Figure
9. 1979 angular decorrelation of 30° versus 70°..........................
33
39
Figure
10. 1979 angular decorrelation of 50° versus 70°........................... 40
Figure
11. 1979 diurnal response of wheat at 17.0 GHz.............................. 41
Figure
12. 1979 diurnal response of corn........................................................ 4?
Figure
13. 1979 diurnal response of sorghum.................................................. 43
Figure
14. Whole plant water (kg/m2) versus stalk water (kg/m2)
for 1980 corn....................................................................................... 44
Figure
15. Whole plant water (kg/m2) versus stalk water (kg/m2)
for 1980 sorghum................................................................................. 45
Figure
16. Leaf water content (kg/m2) versus stalk wats r content
(kg/m2) for 1980 corn....................................................................... 47
Figure
17. Leaf water content (kg/m2) versus stalk water content
(kg/m2) for 1980 sorghum................................................................. 48
Figure
18. Leaf area index (m2/m2) versus stalk water (kg/m2) for
1980 corn............................................................................................... 49
Figure
19. Leaf area index (m2/m2) versus stalk water (kg/m2) for
1980 sorghum......................................................................................... 50
Figure
20. Leaf water (kg/m2) versus whole plant water (kg/m2) for
1980 corn............................................................................................... 51
ii
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Figure 21.
Leaf water (kg/m2) versus whole plant water (kg/m2) for
1980 sorghum....................................................................................... 52
Figure 22.
Leaf area index (m2/m2) versus whole plant water (kg/m2)
for 1980 corn.....................................................................................
53
Figure 23.
Leaf area index (m2/m2) versus whole plant water (kg/m2)
for 1980 sorghum................................................................................ 54-
Figure 24.
Leaf area index (m2/m2) versus leaf water (kg/m2) for
1980 corn............................................................................................. 55
Figure 25.
Leaf area index (m2/m2) versus leaf water (kg/m2) for
1980 sorghum........................................................................................ 56
Figure 26.
Backscatter (17 GHz, W , 50°) versus leaf area index
(m2/m2) for 1980 corn..................................................................... 57
Figure 27.
Backscatter (17 GHz, VV, 50°) versus leaf area index
(m2/m2) for 1980 sorghum............................................................... 58
Figure 28.
Backscatter (17 GHz, VV, 50°) versus leaf water (kg/m2)
for 1980 corn...................................................................................... 60
Figure 29.
Backscatter (17 GHz, VV, 50°) versus leaf water (kg/m2)
for 1980 sorghum................................................................................ 61
Figure 30.
Backscatter (17 GHz, VV, 50°) versus whole plant water
(kg/m2) for 1980 corn..................................................................... 62
Figure 31.
Backscatter (17 GHz, VV, 50°) versus whole plant water
(kg/m2) for 1980 sorghum............................................................... 63
Figure 32.
Backscatter (17 GHz, VV, 50°) versus stalk water (kg/m2)
for 1980 corn...................................................................................... 64
Figure 33.
Backscatter (17 GHz, W , 50°) versus stalk water (kg/m2)
for 1980 sorghum................................................................................ 65
Figure 34.
Backscatter (17 GHz, W , 50°) versus volumetric soil
moisture (gm/cm3) for 1980 corn.................................................. 66
Figure 35.
Backscatter (17 GHz, VV, 50°) versus volumetric soil
moisture (gm/cm3) for 1980 sorghum............................................ 67
Figure 36.
Observed versus predicted seasonal response for 1980
com at 8.6 GHz, VV polarization, 50°; correlation
is 0.87 and rms error is 0.66 dB................................................ 84
Figure 37.
Observed versus predicted seasonal response for 1980
corn at 13.0 GHz, VV polarization, 50°; correlation
is 0.93 and rms error is 0.45 dB................................................ 85
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Figure 38.
Observed versus predicted seasonal response for 1980
corn at 17.0 GHz, VV polarization, 50°; correlation
is 0.94 and rms error is 0.69 dB................................................. 86
Figure 39.
Observed versus predicted seasonal response for 1980
corn at 35.6 GHz, VV polarization, 50°; correlation
is 0.95 and rms error is 0.58 dB................................................. 87
Figure 40.
Comparison of model soil moisture term to model
vegetation term and total predicted o° for 1980 corn
(C l) at 8.6 GHz, VV polarization, 50°........................................ 88
Figure 41.
Observed versus predicted seasonal response for 1980
sorghum at 8.6 GHz, W polarization, 50°; correlation
is 0.95 and rms error is 1.10 dB................................................
9?
Figure 42.
Observed versus predicted seasonal response for 1980
sorghum at 13.0 GHz, W polarization, 50°; correlation
is 0.91 and rms error is 1.14 dB................................................. 93
Figure 43.
Observed versus predicted seasonal response for 1980
sorghum at 17.0 GHz, W polarization, 50°; correlation
is 0.95 and rms error is 0.95 dB................................................
94
Figure 44.
Observed versus predicted seasonal response for 1980
sorghum at 35.6 GHz, VV polarization, 50°; correlation
is 0.90 and rms error is 0.63 dB.................................................. 95
Figure 45.
Observed versus predicted seasonal response for 1980
corn at 17.0 GHz, HH polarization, 50°; correlation
is 0.93 and rms error is 0.64 dB.................................................
99
Figure 46.
Seasonal variation of albedo and optical depth for 1980
corn (Cl) at 8.6 GHz, VV polarization, 50°...............................102
Figure 47.
A comparison of corn canopy attenuation calculated from
Model A (1980 corn, C3) and canopy attenuation on
corn measured d irectly at 10.2 GHz, W polarization,
50°........................................................................................................... 116
Figure 48.
Attenuation recording of wheat at L-band, VV
polarization and 56° incidence angle.......................................... 120
Figure 49.
Attenuation recording of wheat at C-band, W
polarization, and 56° incidence angle........................................ 121
Figure
50. Attenuation recording of wheat at X-band, HH
polarization and 56° incidence angle........................................... 122
Figure 51.
Figure
Attenuation recording of soybeans at C-band, VV
polarization and 16° incidence angle........................................... 123
52. Wheat attenuation measurements on Date 135................................ 127
iv
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Figure 53.
Wheat attenuation measurements on Date 158.............................. 129
Figure 54.
A comparison of wheat attenuation on Dates 135 and
158 at 56° incidence angle.............................................................. 130
Figure 55.
Soybean attenuation measurements on Date 181.......................... 132
Figure 56.
Soybean attenuation measurements on Date 188.......................... 133
Figure 57.
Recording of soybean defoliation experiment at
X-band, HH polarization and 52° incidence angle..................... 139
v
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LIST OF TABLES
Page
Table 1.
Sources of Dry Weight and Protein Intake on
Worldwide Basis (adapted from Evans, 1975)............
4
Table
2. Ground Truth Parameters.................................................... 19
Table
3. MAS 8-18/35 System Specifications................................. 20
Table
4. Sensor Combinations............................................................ 21
Table
5. 1979 Microwave Data Acquired........................................... 23
Table
6. Summary of Regression Analysis for 1980 Corn
Table
7. Summary of Regression Analysis for 1980 Sorghum... 68
Table
8. Model
A Constants for 1980 Corn................................... 80
Table
9. Model
A Correlation Coefficients for 1980C o rn .... 82
Table
10. Model
A RMS Errors for 1980 Corn................................. 83
Table
11. Model
A Constants for 1980 Sorghum.............................. 89
Table
12. Model
A Correlation Coefficients for 1980
68
Sorghum............................................................................... 90
Table
13. Model
A RMS Errors for 1980 Sorghum........................... 91
Table
14. Model
A Constants for 1980 Corn.................................... 97
Table
15. Model
A Correlation Coefficients for 1980 Corn
at 17.0 GHz, HH Polarization...................................... 97
Table
16. Model A RMS Errors for 1980 Com at 17.0 GHz,
HH Polarization............................................................... 97
Table
17. Comparison of the Volume, Interaction, and Soil
(Surface) Terms at 17.0 GHz, W P o la riz a tio n .... 98
Table
18. Contribution to Optical Depth by Leaf Scattering,
Leaf Absorption and Stalk Absorption, Total
Optical Depth and Albedo for Corn Field C3
on Date 204 Using Model A.............................................100
Table
19. Contribution to Optical Depth by Leaf
Scattering, Leaf Absorption and Stalk Absorption,
Total Optical Depth and Albedo for Sorghum Field SI
on Date 204 Using Model A
...............................103
Table
20. Model B Constants for 1980 Corn..................................... 105
Table
21. Model B Correlation Coefficients, and RMS Error for
a ll Fields Combined for i960 Corn.............................106
vi
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Table
22. Model C Constants for 1980 Corn..................................... 107
Table
23. Model C Correlation Coefficients, and RMS Error
fo r a ll Fields Combined for 1980 Corn.....................108
Table
24. Model D Constants for 1980 Corn..................................... 110
Table
25. Model D Correlation Coefficients, and RMS Error
for a ll Fields Combined for 1980 Corn.....................I l l
Table
26. A Comparison of the Average Correlation and RMS Error
for the Four Models Studied........................................ 112
Table
27. Comparison of Two-Way Canopy Attenuation for
Corn Field C3 on Date 204 Calculated from
Models A, B, C, and D....................................................114
Table
28. Summary of Wheat Attenuation Measurements at
Site W1............................................................................... 126
Table
29. Summary of Soybean Attenuation Measurements at
Site S I............................................................................... 131
Table
30. Summary of Cross-Polarized Measurements on Wheat and
Corresponding Like-Polarized Measurements............. 136
Table
31. Wheat Decapitation Experiment Data...............................137
Table
32. Soybean Decapitation Experiment Data........................... 140
Table
33. Summary of Wheat Stalk and Leaf Moisture Data..........151
Table
34. Summary of Estimated Wheat Leaf and Stalk
D ielectric Constants......................................................152
Table
35. Predicted Versus Observed Attenuation Data for
Wheat on Date 135............................................................153
Table
36. Predicted Versus Observed Attenuation Data for
Wheat on Date 150............................................................154
Table
37. Predicted Versus Observed Attenuation Data for
Wheat on Date 158............................................................155
Table
38. Summary of Soybean Primary Stem Moisture Data..........157
Table
39. Summary of Soybean Secondary Stem Moisture
Data..................................................................................... 157
Table
40. Summary of Soybean Leaf Moisture Data......................... 157
Table
41. Summary of Estimated Soybean Primary Stem Dielectric
Constants........................................................................... 159
Table
42. Summary of Estimated Soybean Secondary Stem
D ielectric Constants......................................................159
vi i
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Table 43.
Summary of Estimated Soybean Leaf D ielectric
Constants............................................................................159
Table 44.
Predicted Versus Observed Attenuation Data for
Soybeans on Date 181...................................................... 160
Table 45.
Predicted Versus Observed Attenuation Data
for Soybeans on Date
VI
188............................................. 161
'
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NOMENCLATURE
SYMBOL
UNITS
DESCRIPTION
A
—
empirical constant
B
—
empirical constant
C
—
empirical constant
C1,C2,C3
—
designation for com fie ld s 1,
2, and 3, respectively
c
—
factor obtained from t-d is trib u tio n
for confidence interval calculations
C (f,9 )
—
empirical constant which is a
function of frequency and angle of
incidence
D
dz
—
m
empirical constant
incremental path length through
canopy
E
--
empirical constant
e
dB
rms error
el» e2,e 3
dB
nns err or Tor field s 1,
2, and 3,
respectively
f
GHz
frequency
h
m
canopy height
HH
—
horizontal transmit, horizontal
recei ve
HV
—
horizontal transmit, vertical receive
j
—
symbol used to designate imaginary
part of a complex number
k
m-1
kc
—
wave number (2ir/X)
confidence interval lim it
L
m
correlation length
L^
dB
loss from model A
Las t (6,h)
dB
stalk absorption loss as afunction
of incidence angle for horizontal
polarization
ix
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LaSt ( e»v)
dB
stalk absorption loss as a function
of incidence angle for vertical
polarization
LAI
Lc( f , 9 )
m2/m2
leaf area index
dB
loss from model B
dB
loss from model C
dB
two-way canopy loss as a function
of frequency and incidence angle
LD
L123
dB
MPHLEAF
kg/m2
canopy le a f water content
MPHPLANT
kg/m2
canopy whole plant water content
MPHSTALK
kg/m2
canopy stalk water content
MSVOL
gm/cm3
volumetric soil moisture
Hly
loss from model D
layers 1, 2, and 3 combined
plant or plant part volume fraction
of water
•"w
N
plant or plant part moisture
n
number of samples
nQ
complex index of refraction for
number of leaves per plant
extraordinary wave
real part of ng
imaginary part of ng
complex index of refraction for
ordinary wave
real part of nQ
imaginary part of nQ
imaginary part of complex index of
refraction for v e rtic a lly polarized
wave
P
empirical constant
0
empirical constant
R
empirical constant
r
correlation coefficient
<hh
Fresnel reflection coefficient for
horizontal polarization
x
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
r l» r2, r 3
■"
correlation coefficient for fields 1,
2, and 3, respectively
S
—
empirical constant
s
—
sample standard deviation
S17VV50
—
radar backscatter coefficien t (o°)
at 17 GHz, VV polarization and 50°
S1,S2,S3
—
designation for sorghum or soybean
fie ld s 1, 2, and 3, respectively
t£
mm
leaf thickness
v£
—
volume fraction of leaves in canopy
VH
—
vertical transm it, horizontal receive
vs.j.
—
volume fraction of stalks in canopy
VV
—
vertical transm it, vertical receive
W1,W2
—
designation for wheat field s 1 and 2,
respectively
A
x
—
unit vector in x-direction
y
—
unit vector in y-direction
z
—
unit vector in z-direction
A
z^,Z2
E
m
end points of path through canopy
--
d ie le c tric constant vector
—
real part of canopy d ie le c tric
constant
—
imaginary part of canopy d ie le c tric
constant
ee
--
extraordinary wave d ie le c tric
COPiS c a n i
E£
--
leaf d ie le c tric constant
e£
--
real part of e£
—
imaginary part of e£
r
e£
y
ez
~
leaf d ie le c tric constant at l-Band
--
leaf d ie le c tric constant at C-Band
—
le a f d ie le c tric constant at X-Band
£0
—
ordinary wave d ie le c tric constant
EpS t
--
Drimary stem d ie le c tric constant at
primary
L-band
xi
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primary stem d ie le c tric constant at
pst
C-band
eX
pst
primary stem d ie le c tric constant at
X-band
er£
random leaves d ie le c tric constant
Er £
real part of epi
Er l
real part of
Ers
random stalk d ie le c tric constant
Ers
real part of eps
e"
imaginary part of ep$
el
secondary stem d ie le c tric constant at
rs
sst
L-band
secondary stem d ie le c tric constant at
sst
C-band
secondary stem d ie le c tric constant at
"SSt
X-band
Est
stalk
d ie le c tric constant at
L-band
■St
stalk
d ielectric constant at
C-band
EX
st
stalk
d ie le c tric constant at
X-band
Est
stalk
d ielectric constant
Est
real part of est
Est
imaginary part of e$t
x-component of d ie le c tric constant
vector
y-component of d ie le c tric constant
vector
z-component of d ie le c tric constant
vector
nepers/m
absorption coefficient
nepers/m
extinction coefficient
nepers/m
scattering coefficient
dB/m
canopy attenuation coefficient
dB/m
leaf attenuation coefficient
pst
dB/m
primary stem attenuation coefficient
""sst
dB/m
secondary stem attenuation
coefficient
xi i
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St
dB/m
stalk attenuation coefficient
aibedo
m
wavelength
m
free space wavelength
kg/m3
vegetation density
m
surface standard deviation
dB or
backscatter coefficient
m2/m2
T
Tis
dB
observed backscatter coefficient
dB
predicted backscatter coefficient
nepers
optical depth
nepers
optical depth component due to
le a f scattering
Tia
nepers
optical depth component due to
leaf absorption
Tsa
nepers
optical depth component due to stalk
absorption
degrees
incidence angle from nadir
xi i i
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ABSTRACT
The two major objectives
satisfied
in
this
investigation
include the development of an improved semi-empirical model for
microwave backscatter from vegetation and the acquisition
of a
complete set of canopy attenuation measurements as a function of
frequency, incidence angle and polarizatio n .
model
was tested
range.
The semi-empirical
on corn and sorghum data over the 8-35 GHz
The model generally provided an excellent f i t to the data
as measured by the correlation and rms error between observed and
predicted data.
The model also predicted reasonable values of
canopy attenuation.
The attenuation data was acquired over the
1.6 - 10.2 GHz range for the lin e ar polarizations at approximately
20°
and
50°
incidence
angles
for
wheat
and
soybeans.
An
attenuation model was proposed which provided reasonable agreement
with the measured data.
xiv
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1.0
INTRODUCTION
As the twentieth century draws to a close, we find that the
affluence enjoyed by the industrial
seriously
shortages.
threatened
by
a
nations around the world is
seemingly
never-ending
series
of
Shortfalls in food, water, and energy are perhaps the
most serious threats to our current lif e s t y le —and perhaps our
very existence.
The growing "third-world" countries w ill
only
accentuate the problems to be faced in the last decade of this
century and beyond.
Resource management on a global basis is essential i f we are
to maintain a reasonable standard of liv in g .
science of
decision-making,
however,
Management is the
and in te llig e n t
making requires accurate and timely information.
information
required
unfortunately,
d ig ita l
is
for
management
staggering.
It
of
our
decision-
The quantity of
global
resources,
is only with the aid of the
computer that resource managers can hope to process the
necessary data into
forms that can be interpreted and used as
decision-making inputs.
The acquisition
of data for resource management is also a
very significant problem area and needs as much or more attention
than does the processing phase.
Remote sensing techniques hold
great promise for solution of this data acquisition problem.
A l i t t l e over a century ago, mankind had to rely upon d ire c t,
on-the-ground
such
observations
management
photography
has
was
proved
for
resource
extremely
to
be
lim ited
extremely
management;
in
obviously,
scope.
valuable
to
Aerial
resource
managers in the f ir s t eighty years of this century and, of course,
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
is s t m
a
s a te llite s
legitim ate form of remote sensing.
with
visib le
and infrared
The launching of
sensors in
the
1970's,
however, has revolutionized the science of remote sensing.
These
spaceborne sensors have provided high-resolution imagery of even
the most remote parts of the Earth.
Any image, however, contains
an extremely large quantity of information.
d ig ita l
computer
technology
and
Therefore advances in
associated
d ig ita l
have been necessary and
image
processing
techniques
have encouraged
u tiliz a tio n
of this information by resource managers. Research is
continuing in this v ita l area which appears to hold great promise
for resource management.
Unfortunately infrared , and especially visible sensors, do
have serious
lim ita tio n s .
useless
severely
and
devices.
Cloud cover renders visible sensors
degrades
the
performance
of
infrared
In addition, visib le sensors can operate only during the
daylight hours
and are
affected
by tee
sun-angle.
For this
reason, much research is currently directed toward the development
of microwave remote sensing systems, bott- active and passive, to
supplement
data
provided
by
v is ib le
and
infrared
sensors.
Microwave systems may be operated day or night under clear-sky or
cloudy conditions over a very wide range of frequencies.
This
study is devoted to increasing the understanding of the response
of such systems—s p e cifically active microwave or radar systems to
vegetation.
sensing
Increased understanding w ill
find
production,
application
but
also
in
not
only
in
water-resource
help microwave remote
agriculture
management
and
as well
food
as
energy u tiliz a tio n , conservation and production.
2
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1.1
Agricultural Applications
Throughout man's history, he has used nearly 300 plants for
food and approximately 200 of these have been domesticated over
the years.
Today, however, only a few crops provide most of man's
food protein and dry-weight.
Table 1 (Evans, 1975), illu s tra te s
that a surprising portion of our protein and dry-weight intake is
supplied by plants, and in fa c t, by a very few plants.
Two crops,
wheat and ric e , are the primary sources of food for over one-half
of the World's population.
Despite sta b iliza tio n of the population in the more developed
countries, World population continues to increase at an alarming
ra te .
Perhaps
improved medical
technology, communications and
educational programs w ill help to slow this growth in the future,
but u ntil
that day comes, the demand for food w ill
increase at a near-exponential rate.
continue to
Increases in wheat and rice
production have generally kept pace with population growth over
the last five hundred years.
Improvements have been due primarily
to increases in yield per unit area in the developed countries,
while in the developing nations, over one-half of the progress is
due to increases in the area under c u ltiva tio n .
In these less-
developed nations, only a small portion of the total land area is
currently under cultivation and considerable increases are s t i l l
possible.
In addition
to these traditional
approaches toward
increasing food production, a significant amount of research has
been directed toward the development of alternative sources of
food—the so-called synthetic foods.
Synthesis of these products,
3
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TABLE 1. Sources of Dry Weight and Protein Intake
on a Worldwide Basis (Adapted from Evans, 1975)
Dry Matter (%)
Wheat
Rice
Corn
Barley
Sorghum and M ille t
Other Cereal Grains
Protein (%)
18.2
17.7
15.5
7.6
5.5
5.1
17.5
12.3
13.1
6.2
3.9
0.6
Potato
Sweet Potato and Yams
Cassava
4.4
2.6
2.3
3.2
1.5
0.4
Sugar Cane
Sugar Beet
2.9
2.0
0.0
0.0
Soybean
Peanuts
Peas
Beans
2.8
1.1
0.9
1.0
8.9
2.5
1.9
2.9
Vegetables
1.9
4.2
F ru it
1.7
0.7
Milk
Meat
Eggs
Fish
3.5
1.9
0.3
1.1
7.7
6.7
1.3
4.5
100.0%
100.0%
4
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however, requires significant amounts of energy—a resource that
is
in
short
supply
it s e lf .
Thus
it
appears that
for
the
foreseeable future our dependence upon major crops for food is
unlikely to decrease.
A re la tiv e ly recent development is the large-scale production
of alcohol from grain to be used as a fuel add itive.
I f this use
of grain continues, which seems lik e ly in lig h t of long-term oil
supply problems
nations,
our
and p o litic a l in s ta b ility
dependence
on
management may increase in
in the
oil-producing
effe c tiv e agricultural
the futu re,
even i f
resource
the population
stabi1i zes.
Agricultural
tasks.
The
resource
fir s t
task
management
involves
consists
the
of
two
major
discrimination
and
classifica tio n of crop species, ultim ately providing an estimate
of the acreage planted with each type of crop.
concerned
with
monitoring
crop
growth
and
The second task is
vigor
which,
in
conjunction with acreage estimates, allows forecasts of y ie ld .
The
discrimination
and
classifica tio n
problem
has
been
studied extensively using radar alone (Bush, 1976a) and combining
radar data with Landsat data (Eyton, 1979; L i, 1980).
The results of these investigations indicate that radar and
Landsat data are complementary in nature and that classification
accuracies of the order of 95% appear to be feasible, i f m ulti­
date information is obtained.
The second task, that is the monitoring of crop growth and
vigor and the estimation of y ie ld , is not well-understood.
understanding
can be enhanced,
however,
This
by the development of
5
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improved mathematical
models relating the microwave response to
plant physiological changes.
Models may range from simple lin ear
regression analysis on microwave and ground-truth data to complex
theoretical models based upon Maxwell's equations.
A middle-of-
the-road approach is the semi-empirical model which is hased upon
electromagnetic
theory,
but
is
generally
simple
and
u tiliz e s
easily measured ground truth parameters.
Electromagnetic
models
may
be
used
in
conjunction
with
evapotranspiration models developed by agronomists (Hodges, 1977;
Kanemasu,
1977)
to
predict
y ie ld .
In
addition,
microwave
measurements and models may provide data on crop disease or stress
and could provide valuable inputs to hydrological models used in
water resource management.
1.2
Advantages of Microwave Sensors
The
a b ility
to
penetrate
cloud
cover
and
to
operate
independently of solar radiation distinguishes microwave sensors
from th e ir
visib le
and infrared
counterparts.
In addition
these advantages, microwave sensors can e ffe c tiv e ly control
to
the
"roughness" of the target under study by a change in wavelength;
this
property
allows
studies
of
target
structure that
possible in the visible and infrared regions.
are not
In addition, active
microwave sensors have the a b ility to control the polarization of
the illum ination and to make cross-polarized measurements which
often provide information not available in like-po larized data.
The Earth's atmosphere and ionosphere are not transparent to
electromagnetic radiation of a ll wavelengths.
An “optical-window"
6
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extends from approximately 5 THz to 800 THz and a "radio-window"
extends
from about
30 MHz to
300 GHz.
The remainder of
the
spectrum is essentially useless for satellite-based remote sensing
purposes.
Even the "windows" are not to ta lly clear as the optical
window contains
many gaseous
absorption
lin e s ,
and the
radio
spectrum is obstructed by a few oxygen and water vapor lines near
the upper end.
Much of the interest in microwave sensors results from th e ir
a b ility to penetrate cloud cover.
On the average, a very large
percentage of the Earth experiences 50% or greater cloud cover
during
the year.
Since
visible
and
penetrate this cloud-cover, temporal
d iff ic u lt to obtain.
infrared
sensors
cannot
data on crops is extremely
This problem is c r itic a l
since plants may
undergo some rather dramatic physiological changes over the short
period of a few days.
Rainfall
but,
of
optical
problem
can degrade the performance of microwave sensors
course,
the associated
cloud
and infrared sensors useless.
in
that
precipitation
rates
cover would also
Rainfall
high
render
is not a major
enough
to
produce
significant attenuation occur only a small fraction of the time
available for observation of the vegetation.
In addition to the a b ility of microwave sensors to operate
effe ctive ly day or night under most weather conditions, they have
the
unique a b ility
d ie le c tric constant.
to
sense changes
in
target
roughness and
I t is this capability that provides the most
promise in monitoring the growth and vigor of agricultural crops.
7
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1.3
Prior Research
Some of the e a rlie s t
scattering experiments on vegetation
were conducted at the Ohio State University in the late 1950's and
1960's (Cosgriff, 1960; Peake, 1971).
Data were collected from a
wide variety of agricultural and cultural targets with a truckmounted doppler radar.
The radar was capable of operation in the
X (10 GHz), Ku (15.5 GHz), and Ka (35 GHz) bands and could measure
backscatter
angle.
from
0°
incidence
angle
(nadir)
to
80°
incidence
The absolute calibration of this early Ohio State data is
somewhat suspect when compared to more recent measurements (Bush,
1976b), but its precision is s t i l l
estimated to be about + 1 dB.
Unfortunately, this series of experiments lacked adequate ground
truth and in addition, was temporally incomplete for the purposes
of monitoring crop development over a growing season.
Despite
these lim itatio n s, the Ohio State experiments are significant in
that they launched the study of vegetation with microwaves and
provided the basis for additional, more detailed investigations.
In
1968,
a
program
designed
to
investigate
the
radar
backscatter from vegetation, crops and soils was in itia te d in the
Netherlands (deLoor, 1974).
In it ia l measurements used a 75 meter
television tower as a platform for an X-band pulse radar system.
Because of
fields
of
(> 8 0°).
some
the tower height
in te re s t,
insight
may
of the agricultural
data was lim ited to high
incidence angles
Despite these lim ita tio n s , these experiments provided
agricultural
crops
and location
into
the
s ta tis tic s
of
crops and more importantly
undergo
significant
changes
radar
backscatter
from
provided evidence that
in
th e ir
backscatter
8
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response over a growing season.
In 1973, the group constructed a
short-range FM-CW radar system that could be moved along a series
of test plots on r a ils .
This system was capable of taking data
over an incidence angle range of 20° to 75° with HH, HV, and VV
polarization.
This system has been used to acquire a considerable
amount of data on crops (deLoor, 1982).
The Dutch have also been
active in vegetation d ie le c tric constant investigations
(deLoor,
1983) and modeling (Hoekman, 1982).
In 1974 and 1975, a group from the Soviet Union conducted
experiments
on
vegetation
(Basharinov, 1976).
adequate
ground
using
a
K-band
imaging
radar
This series of experiments, although lacking
tru th ,
backscatter coefficien t
noted
sig n ifican t
changes
in
the
over a growing season and sp e cifically
noted a large increase in the backscatter coefficient of winter
wheat
at
approximately
the
"heading"
stage
of
growth.
The
experimenters also reported an inverse relationship between the
backscatter
coefficient
and the
“productivity
of
green mass."
Productivity of green mass is apparently the wet biomass of the
vegetation, measured in kilograms per square meter.
The Soviets
have also reported backscatter data acquired over the 0.8 cm to
30 cm range of wavelengths, as well as laboratory measurements of
microwave
absorption
and
scattering
of
isolated
vegetative
elements (Shutko, 1981).
A study conducted by the Agricultural Engineering Department
at the Ohio State University (Story, 1968; Story, 1970), unrelated
to
the
concluded
previously
that
the
discussed
backscatter
attenuation
by wheat
measurement
heads
is
program,
many times
9
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greater
than
magnetic
attenuation
(VV)
by
attenuation
the stalks
is
more
transverse e le c tric (HH) attenuation.
the
wheat
head
should
be
and
than
that
twice
as
transverse
great
as
These results suggest that
considered
individually
as
a
scattering/absorption element in detailed modeling studies.
Measurements
of
the
temporal response of
rice
have been
completed in India at the Communications Area Space Applications
Centre,
located
in Ahmedabad
(C alla,
1979).
The Indian
u tiliz e d a fixed X-band (9.4 GHz) CW radar system.
group
This study is
sig nificant because rice is one of the World's two most important
crops and l i t t l e ,
if
any, data is available onits
backscatter
response.
There is no information available on the precision of
this
which
data
is
of
concern, since
averaging was apparently not used; i t
spatial
or
frequency
is lik e ly , however, that
fading was reduced somewhat in this data set by time-averaging.
In addition, some of the data is also questionable because the
cross-polarized data is at times much greater in magnitude than
the like-polarized data.
There
has been considerable
interest
in
microwave
sensing of vegetation in Canada in recent years.
remote
This a c tiv ity
has been concentrated at the University of Guelph and the Canada
Centre for Remote Sensing in Ottawa (CCRS).
A major interest has
been the use of synthetic aperture radar (SAR) imagery for crop
discrimination
purposes
(Brisco,
1978;
1979;
1980).
A jo in t
experiment was conducted in M elfort, Saskatchewan by CCRS and the
University of Kansas in 1983.
was
to
calibrate
SAR
A major objective of the experiment
imagery
with
ground-based
backscatter
10
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measurements.
There is an intense interest in microwave remote sensing of
vegetation
in
West Germany.
The German
Aerospace
Research
Establishment (DFVLR) has conducted vegetation studies using both
ground-based
systems (Sieber,
1979; Graf,
aperture airborne systems (Sieber, 1983).
truth
data
q u a lity .
acquired by this
group is
1978)
and
synthetic
The radar and ground
extensive
and
of
high
The West Germans have also been deeply involved with the
Space!ab mission (Schlude, 1978) in which an X-band imaging radar
system
was
Although
f lig h t ,
It
carried aboard
a malfunction
future flig h ts
the
STS-9
prevented
space
acquisition
shuttle
of
data
f lig h t .
on this
should provide valuable vegetation data.
should be noted that the West Germans and the University of
Kansas worked jo in tly on a project to calibrate the X-band imagery
with
ground data
and active
calibrators,
but
of course,
the
Space!ab radar malfunction prevented successful completion of this
e ffo r t.
There has also been significant a c tiv ity in microwave remote
sensing in France (Lopez, 1979; LeToan, 1982).
recently
completed
characteristics
of
an
wheat
The French have
in-depth
study
of
the
backscatter
(Huet,
1983)
and
the
attenuation
properties of wheat (Lopes, 1983).
The backscatter study covered
the years 1980, 1981, and 1982 and included both winter wheat and
spring wheat.
The attenuation measurements presented are quite
significant in that are the f ir s t reliab le data on the attenuation
of
wheat
and
attenuation.
illu s tr a te
the
importance
The measurements,
however,
of
polarization
were conducted
in
on
a
11
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laboratory settin g , were limited to one frequency, and were only
conducted at an incidence angle of 90°.
The French work is very
high quality and includes extensive data on seasonal v a ria b ility
of ground truth parameters.
Undoubtedly, the most extensive measurement program on the
radar backscatter response of vegetation has been conducted in the
United States at the University of Kansas (Ulaby, 1981).
late
1960's,
studies
were
directed
toward
In the
demonstrating
that
panchromatic techniques were useful in the reduction of fading and
that additional information could be obtained by measuring over an
octave bandwidth (Waite,
1970).
The radar system used in this
series of measurements was a pulse-type system with the c arrier
frequency continuously varied from pulse to pulse.
were averaged a fte r
detection
to
reduce fading.
The pulses
This program
stimulated interest in the development of a ground-based, mobile
system with angular,
f i r s t such system was
frequency, and polarization
constructed in 1971 (Moe,
to collect agricultural
range.
The system's
a g ilit y .
The
1974) and was used
data near Eudora, Kansas in the 4-8 GHz
calibration was suspect, unfortunately,
3 ll dsts had to be reported with
and
respect to a fie ld of corn•
In
1972, the system was redesigned and calibrated against a Luneberg
lens rather than against a m etallic sphere.
much-improved calibration
The lens provided a
technique because of
its
large
radar
cross-section and its relative in s e n s itiv ity to orientation.
Data
was again acquired in the Eudora region during the 1972 growing
season with this improved system.
Analysis of this data revealed the significant result that
12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the moisture
in
the
soil
underlying
the
various
crops
had a
significant influence on the backscatter response, especially at
lower frequencies and angles of incidence (Ulaby, 1975a).
result
was the
f ir s t
indication
that
This
crop monitoring studies
should be conducted at higher frequencies and angles of incidence
to eliminate the effect of soil moisture variations.
In 1973, the
4-8 GHz system was redesigned to allow 2-8 GHz operation and an 818
GHz FM-CW radar
system was
constructed.
Some data
was
collected in 1973 (Ulaby, 1975b), but i t was in the 1974 growing
season that
the
fir s t
sets
of
temporally
complete data were
acquired on a wide variety of crops (corn, wheat, milo, soybeans,
and a lf a lf a ) .
Also in 1974, diurnal experiments were conducted in
the 2-8 GHz range.
One major conclusion reached from the 1974
experiments was that diurnal effects are minimized at frequencies
above 8 GHz and that
frequencies
moisture.
incidence
angles
of
40°
or
higher
and
of 8 GHz or greater minimize any response to soil
The temporal data acquired (Bush, 1975c; Bush, 1975d;
Ulaby, 1975c) revealed that the two economically important crops,
corn and wheat, exhibited substantial changes in the backscatter
c o e ffic ie n t, a0, over a growing season and thus held promise for
monitoring applications.
Among the other crops studied, a lfa lfa
displayed significant changes in o° over the growing season, but
milo (sorghum) and soybeans did not.
A large number of technical
reports and papers have resulted from analysis of this data (Bush,
1975a;
1975b,
1975c;
1975d;
Ulaby,
1975c;
1976).
Agricultural
data was again acquired in the 8-18 GHz range during the 1975 and
1976 growing seasons.
Acquisition of this data greatly enlarged
13
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the
available
database
on
agricultural
crops
which
allowed
enhanced s ta tis tic a l (Ulaby, 1979a), row-direction (Ulaby, 1979b),
and classifica tio n (Eyton, 1979) studies to be performed.
In 1977
and 1978, the emphasis in radar data acquisition shifted toward
snow and soil moisture applications, while analysis continued on
the available agricultural database.
In 1979 and 1980, the University of Kansas conducted jo in t
vegetation
experiments
Evapotranspiration
Department.
The
with
Laboratory,
Kansas
development
of
hydrological
applications
Kansas
State
associated
with
group has
been active
State
evapotranspiration
models
and crop yield
to
University's
its
be
forecasting
1974; 1976; 1977; Brun, 1972; Hodges, 1977).
Agronomy
in
the
used
in
(Kanemasu,
Kansas State had
used Landsat data for input to the evapotranspirati on models, but
had experienced considerable d iffic u lty
data
over
a
growing
season.
in obtaining cloud-free
The group
therefore
was
quite
interested in the potential of microwave remote sensing, which led
to the jo in t experiments.
The data was acquired over the 8-35 GHz
range on a number of test plots of corn and sorghum and on two
commercial wheat fields (Eger, 1982; Wilson, 1984).
During
the
period
1981-1983,
the
radar systems were
re­
designed to make them more mobile so that an increased number of
data sets
could be acquired on a given day.
The systems were
lim ited to L through X-band to correspond to operational systems
planned for the late
1980's and early 1990's.
radiometer system was constructed to
data.
In addition, a
acquire passive microwave
During this period data was acquired on a number of crops
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
near Lawrence, Kansas and in 1983, the jo in t experiment with the
Canadians
was
conducted.
A number
of
including flooding, screening, defoliation
also conducted during this period.
was
acquired
on a number of
special
experiments
and attenuation were
In 1984, L, C, and X band data
test
plots
of small
grains
and
attenuation measurements were conducted on wheat and soybeans.
As
this
review
indicates,
interest
in
microwave
remote
sensing of vegetation is global and has been increasing rapidly in
recent years.
The a v a ila b ility
imaging radars w ill
certainly
of the Space Shuttle to carry
vastly increase our knowledge in
th is area, but w ill not eliminate the requirement for additional,
detailed, ground studies such as those described in this review.
1.4
Objectives of Investigation
The investigation repoi'ted herein has two major objectives.
The f ir s t objective is to develop an improved semi-empirical model
(or
models)
to
vegetation in
describe
the
observed
backscatter
response of
terms of easily measured ground truth parameters.
The second objective, closely related to the f ir s t , is to obtain
data on the attenuation experienced by a microwave signal as i t
propagates
through
a vegetation
canopy
as
a function
of
its
frequency, polarization and angle of incidence.
The semi-empirical model w ill be based upon high quality data
acquired near Manhattan, Kansas on corn and sorghum.
is
characterized
by
backscatter
data
with
The data set
extensive
spatial
averaging to reduce fading, accurate calibration and frequent
15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
observations over the growing season.
high q u ality.
and
The ground truth is also of
In addition, the ground truth was carefully edited
"smoothed"
with
a polynomial
c u rv e -fittin g
routine.
The
objective is to postulate a model which provides a good f i t to the
data as measured by the correlation coefficien t between observed
and predicted data as well as a small root mean square (rms) error
between observed and predicted data
model
must
provide
a
reasonable
points.
estimate
In addition, the
of
the
attenuation
through the vegetation canopy.
The objective of the attenuation measurements is to obtain an
understanding
of
vegetation
attenuation
as
a
function
of
frequency, polarization and incidence angle fo r its own s c ie n tific
value as well as to provide data fo r testing semi-empirical and
theoretical
models.
Although
some
lim ited
attenuation
measurements have been made in the past, this w ill be the f ir s t
data set which demonstrates frequency, polarization, and angular
dependence.
Success
significant
in
meeting
contribution
these
two
objectives
w ill
provide
a
to the understanding of the microwave
propagation and backscatter characteristics of vegetation and to
the fie ld of microwave remote sensing.
16
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2.0
EXPERIMENT DESCRIPTION
The backscatter
data
to
be analyzed and modeled
in
this
investigation was acquired in 1979 and 1980 in a jo in t experiment
conducted by the University of Kansas and Kansas State University
near
Manhattan,
Kansas.
The
available in a technical
1979 and 1980 data
is
complete
set
memorandum (Wilson,
available
of
1979
data
in
1984) and selected
in a technical
report
format
(Eger, 1982; Ulaby, 1983).
The attenuation
data
to
investigation was acquired in
be analyzed and modeled
in
this
1984 at a s ite east of Lawrence,
Kansas by the University of Kansas.
2.1
1979 Backscatter Measurements
The
Kansas
1979
backscatter
State
measurements
University agronomy
were
conducted
research
field s
at
the
located
approximately 14 km south of Manhattan in a small community called
Ashland.
and
University-owned research plots were used to study corn
sorghum while
two
privately-owned
field s
adjacent
to
the
research plots were used to study wheat.
The
tv/e!y s
test
plots,
ssch spprcxiiristely
900 m2, were planted with varying
(six
each).
The two wheat field s
15 m x 60 m or
densities of corn and sorghum
used were several
acres in
extent, although only a lim ited area of each was used for data
collection.
The spring and summer growing season was unusually wet for
Central
Kansas
and thus
all
crops were generally
healthy
and
vigorous.
17
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Ground truth data for this experiment was acquired by Kansas
State
University.
radar
data.
Ground truth
Table 2 summarizes
was taken simultaneously with
the
ground
truth
parameters
measured.
The active microwave system used to acquire data for this
study
was the
system.
University
of
Kansas MAS 8-18/35
scatterometer
The MAS 8-18/35 was a low-power microcomputer-based FM-CW
radar,
capable
35.6 GHz.
over the
8-18 GHz range
and at
This truck-mountedsystemwas
mobile and had
its
source of
of
operation
e le c tric a l
own
power. Data acquired was recorded on a
standard data cartridge fo r subsequent transfer to larger computer
systems.
study
for
The system (Ulaby,1979c) was
single
(Wilson, 1980).
antenna
operation
modified prior
over
the
8-18
to this
GHz range
The accuracy and precision of the MAS 8-18/35 has
been investigated and reported previously (S tile s , 1979).
The key
system specifications are given in Table 3.
The choice of sensor combinations for this study was greatly
influenced by prior work at the University of Kansas.
the
response to
soil
moisture
variations,
angles
To minimize
of
incidence
greater than 30° and frequencies greater than 8 GHz were chosen.
This choice of system parameters also minimized any response to
crop row direction e ffe c ts .
polarizations.
Data was taken using the three linear
Table 4 summarizes the sensor combinations used in
the experiment.
Fifteen independent spatial samples were taken at 30° and 50°
while ten samples proved more than adequate at 70°.
18
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TABLE 2 .
Ground Truth Parameters
Leaf Area Index
Plant Wet Weight
Plant Dry Weight
Plant Density
Plant Height
Plant Growth Stage
Leaf Water Potential
Yield
Soil Moisture
Solar Radiation
Temperature
Precipitation
Wind Speed
Spectral Reflectance
19
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TABLE 3 .
MAS 8 -1 8 /3 5 System S p e c ific a tio n s
Radar Type
FM-CW
Modulating Waveform
Triangular
Frequency Range
8-18 and 35.6 GHz
FM Sweep
800 MHz
Transmitter Power
10 dBm
Intermediate Frequency
100 KHz
IF Bandwidth
10 KHz
Antennas
Maximum Height
Above Ground
20 m
8-18 GHz Feed
4-18 GHz Quadridged
Horn
8-18 GHz Reflector
45.7 cm Diameter
35.6
Scalar Horn
GHz
Polarization
HH, HV, VV, RR, RL, LL
Incidence Angle Range
0° (Nadir) to 80°
Calibration
Internal
Delay Line
External
Luneberg Lens
20
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TABLE 4 .
Sensor Combinations
FREQUENCY
8.6
13.0
17.0
35.6
GHz
GHz
GHz
GHz
POLARIZATION
KH
HV
VV
INCIDENCE ANGLE
30°
50°
70°
21
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A "standard"
data
independent spatial
each polarization.
set
consisted
of
the
above number of
samples at each of the four frequencies for
Thus, 180 data points were obtained at 30° and
50° with 120 data points at 70° for a total of 480 data points per
standard data set.
A "diurnal" data set consisted of fifte e n independent spatial
samples
at
50°
at
the
above
combinations or 180 data points.
frequency
and
polarization
A diurnal data set was repeated
periodically throughout the day from pre-dawn to post-dusk.
Table 5
summarizes
the
microwave
data
acquired
in
this
experiment.
2.2
1980 Backscatter Measurements
The 1980 backscatter measurements were also conducted at the
Kansas State University research fie ld s .
In 1980, however, data
was only acquired on corn and sorghum.
The 1980 test plots were increased in size to approximately
30 m x 60 m or 1800 m2.
Three plots were planted with corn and
three were planted with sorghum.
As in 1979, planting densities
va ned between piot s.
The summer growing season in 1980 was a sharp contrast to
1979
in
that
it
was dry
and one of
the
hottest
on record;
irrig a tio n was required to maintain the crops.
Ground
University.
tru th
data
was
again
acquired
by
Kansas
State
In 1980, sampling techniques were improved and the
data was expanded to include plant parameters by layer and by
22
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TABLE 5 .
1979 Microwave Data Acquired
WHEAT
24 Standard Data Sets
32 Diurnal Data Sets
CORN
40 Standard Data Sets
20 Diurnal Data Sets
SORGHUM
40 Standard Data Sets
20 Diurnal Data Sets
TOTAL DATA POINTS - 74,880
23
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parts.
In addition, the ground truth data was "smoothed" by a
polynomial curve f ittin g routine.
A significant improvement over 1979 was the increase in data
sets per f ie ld .
angles,
Because of the large number of fie ld s , incidence
and frequencies in
1979, only about six data sets per
fie ld were acquired for com and sorghum.
In 1980, the number of
fie ld s was reduced and angular data was lim ited to 50°, so that
approximately 25 data sets per fie ld were obtained.
In 1980, improvements were also made in the microwave data
collection e ffo r t.
The number of spatial samples in 1979 was set
at 15 because of the lim ited test plot width and because of the
time lim ita tio n s .
In 1980, since the size of the plots had been
increased and the only angle of incidence used was 50°, the number
of spatial
samples was increased to
measurement uncertainty.
25 to
further
reduce the
Also in 1980, external calibration was
performed on the system on a ll but five of the measurement days.
These changes sig n ifican tly improved the calibration and precision
of the 1980 backscatter measurements as compared to 1979.
2.3
1984 Attenuation Measurements
The
1984
University
attenuation
of
Kansas
measurements
on
were conducted
privately-owned
field s
by the
located
approximately 6 km east of Lawrence, Kansas.
Two crops were studied,
spring
and
early
summer
winter wheat,
growing
season
resulted in healthy and vigorous crops.
and soybeans.
was
quite
wet
The
which
Ground truth for this
24
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experiment was acquired both by layer and by part.
The ground
truth measurements are tabulated in Appendix 8.
The system used for data acquisition consisted of L, C, and X
band radars (1.55 GHz, 4.75 GHz, 10.2 GHz) mounted on a boom truck
(used only as a tra n sm itter),
mounted on a "sled".
synchronism with
the
and a receiver at
ground level
The sled was designed to be pulled in
boom truck
system of ropes and pulleys.
over fiberglass
ra ils
with
Figure 1 illu s tra te s the setup.
a
The
receiving antennas consisted of an L-band microstrip patch antenna
and a 4-18 GHz quad-ridged horn for C and X-band.
The C and X-
band antennas were followed by battery-powered am plifiers with
approximately 25 dB of gain.
The detector was a wide dynamic
range power meter whose output drove a chart recorder.
The r a ils , each approximately 6 meters long, were placed in
the vegetation canopy at locations corresponding to approximately
24°
and
56°
soybeans.
incidence
angle
for
wheat
and
16°
and
52°
Vegetation was cleared at each end of the test strip so
the free-space power could be measured and used as a reference.
wheat
for
head
experiment
decapitation
were
experiment
conducted
in
and a soybean
addition
to
A
defoliation
these
"standard"
experiments.
Attenuation measurements were made at the indicated angles;
at L, C, and X-band; and for HH and VV polarization.
data was acquired for HV and VH polarization.
Some lim ited
The recordings were
digitized and a mean attenuation was calculated (re la tiv e to free
space)
along
with
its
associated
99%
confidence
in te rv a l.
Repeatability tests were conducted for all sensor combinations and
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 1.
Configuration used to measure canopy attenuation.
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
it
was
within
found
1 dB
that
and
the measurements were generally
in
most
cases,
a
fraction
of
repeatable
a dB.
The
attenuation data is tabulated in Appendix B.
3.0
BACKSCATTER DATA ANALYSIS
The 1979 backscatter experiment was significant in that i t
provided the f ir s t 35 GHz data on vegetation over a growing season
and provided the basis for an analysis of a number of overall
vegetation backscatter characteristics.
I t was also valuable in
that i t was the f ir s t data set to include both active microwave
data and leaf area index.
The 1979 data set was, however, of
lim ited value in modeling because of the small number of data sets
per fie ld .
The 1980 backscatter experiment was designed to correct the
shortcomings of the 1979 experiment and to provide a very high
quality
data
set
on corn
and
sorghum,
suitable
for
modeling
studies.
A preliminary analysis of the 1979 and 1980 data sets has
already been completed (Eger, 1982) which includes temporal data
for both years, so this information w ill not be repeated in this
report.
The emphasis here w ill be to present results which have
not yet been published.
The s ta tis tic a l analysis was accomplished with the aid of the
1979 versions of the Biomedical Computer Programs, P-series (BMDP79).
These
programs
were
developed
at
the
Health
Sciences
Computing F a c ility at the University of California at Los Angeles
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(Dixon,
1979).
The
Health
Sciences
Computing
F a c ility
was
sponsored by NIH special resources grant RR-3.
The BMDP routines
used to
examine the
s ta tis tic s
microwave data were BMDP-2D, BMDP-5D, and BMDP-6D.
of the
RMDP-2D counts
and lis ts d istin c t values of each variable in the analysis.
computes
univariate
s ta tis tic s
including
the
standard deviation, skewness, and kurtosis.
mean,
median,
BMDP-2D also plots a
histogram for
each variable.
histograms in
a format which was much improved over that
BMDP-2D.
BMDP-6D
scatter p lo t.
lin e a r
It
BMDP-5D was u tiliz e d
displays one variable
to provide
in
against another in
a
I t computes and prints the equations of the simple
regression
relating each
variable
to
the
other,
and
indicates the intersections of the regression lines with the frame
of the p lo t.
BMDP-AR, a non-linear regression routine, was used
in the modeling studies.
In addition to BMDP, a number of FORTRAN routines were used
to
calculate
other
s ta tis tic s
and
provide
special
plots
not
available with BMDP.
3.1
Calibration, Accuracy, and Precision
The MAS 8-18/35 system used in these experiments u tilize d
both
internal
and
external
calibration
techniques.
Internal
calibration was achieved by periodically switching a coaxial delay
lin e in place of the antenna(s).
lin e
mode were
session
and
taken
were
every
used
Power measurements in the delay
few minutes
to remove
during
short-term
a measurement
fluctuations
in
o s c illa to r power or other component variations.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
External
from
a
calibration
Luneberg
lens
was achieved by measuring the return
of
known
cross-section
throughout the measurement period (Ulaby, 1979c).
sets" were taken
periodically
In 1979, "lens
approximately once per week; in 1980,lens sets
were taken on the day of each data set—except for five
dates.
After each lens set, a "sky-noise" measurement was taken to
determine the system noise flo o r.
Noise floo r data was used to
ensure that all data points used in the analysis had an adequate
signal-to-noise ra tio .
Previous
studies
(S tile s ,
1979)
have
concluded
that
the
number
of
accuracy of the MAS 8-18/35 was of the order of ± 2.6 dB.
Measurement
precision
is
a
function
independent samples obtained (S tile s , 1979).
of the
In the MAS 8-18/35,
independent samples are obtained by frequency averaging as well as
by spatial averaging.
The total number of independent samples is
determined by the product of these two terms.
The number of
independent samples may also be calculated empirically from the
data.
I t is estimated that the 90% confidence interval for the
1979 data is approximately + 1.0 dB, while for the 1980 data i t is
± 0.5 dB.
3.2
1979 Backscatter Data
The complete analysis of the 1979 data included consideration
of
each
plot
or
fie ld
individu ally,
fie ld s/p lo ts
of the same crop and a ll
these
were
cases
analyzed
at
a ll
of
polarization, and angular combinations.
various
combinations
crops combined.
the
various
All
of
of
frequency,
Since the 1979 data w ill
29
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not
be used for modeling in
preliminary
analysis
this
investigation
has been previously
Brakke, 1981), the emphasis here w ill
and because a
reported
(Eger,
be on overall
1982;
vegetation
characteristics.
Figure 2 is a histogram for a ll 1979 crops combined at 35.6
GHz, VV, 30° expressed in dB.
normal as expected.
expressed
in
This distribution is approximately
Figure 3 is a histogram of the same data
real
units (m2/m2) .
This
approximately log-normal, again as expected.
distribution
is
These distributions
are sim ilar to those observed on the much larger agricultural data
base maintained at the University of Kansas (Ulaby, 1979a).
Dynamic range is an important consideration in the design of
an operational
active microwave remote sensing system.
microwave response to
changes
system
and/or errors,
fluctuations
acquiring meaningful data.
range of a ll
in plant
If
the
parameters can be maskedby
there
is
little
hope
of
Figure 4 illu s tra te s that the dynamic
1979 crops combined increases as the frequency is
increased, especially for VV polarization.
I t is possible that an operational microwave remote sensing
system could be designed with multi-frequency cap ab ility .
multi-frequency
vegetation i f
capability
additional
frequencies.
To
could
be
useful
for
This
monitoring
information can be gained by additional
investigate
this
consideration,
frequency
decorrelation plots were produced for each linear polarization.
Figures
5,
6,
and
7
illu s tr a te
that
significant
additional
information may be obtained by operating at two or more
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2 .
Histogram fo r a l l
30° (d B ).
1979 crops combined at 35.6 GHz VV
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.
Histogram fo r a l l
30° ( r e a l ) .
1979 crops combined at 35.6 GHz VV
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
le of Incidence (Degrees); 50
— HV
_
25.0
20.0
a
i5.o
1&0
5.0
Frequency (GHz)
Figure 4.
1979 dynamic range versus frequency.
33
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Figure 5.
1979 frequency decorrelation fo r HH polarization.
34
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1979 frequency decorrelation fo r HV polarization.
35
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0,40901 00
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01
0.15001 02
M I I I I K I
Figure 7.
0.MO9I 02
( l i t )
1979 frequency decorrelation for VV polarization.
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
frequencies for HV and VV polarization, but that there would be
l i t t l e advantage to such an arrangement for HH polarization.
Another
possible
design
system would be m ulti-angle
consideration
c a p ab ility .
for
an operational
Aside from possible
advantages in remotely sensing soil moisture, Figures 8, 9, and 10
illu s tr a te that l i t t l e
additional information on vegetation would
be obtained from such an arrangement.
I f a microwave system is to be a day/night sensor, then i t is
important
to
investigate
any
possible
diurnal
response
of
vegetation which could corrupt acquired data or at least require a
correction.
Figure
experiment on wheat.
11
illu s tra te s
the
results
of
a diurnal
Figure 12 is a sim ilar plot for corn and
Figure 13 is for sorghum.
(The corn and sorghum experiments were
conducted over a three day period due to system problems.)
plots
indicate
diurnal
that
response.
the three
crops studied exhibited
These
minimal
These plots are typical of the complete data
set.
3.3
1980 Backscatter Data
The emphasis in the 1980 data analysis reported here w ill be
the relationship between the various ground truth parameters and
the relationship between the ground truth and selected backscatter
data.
All data used in this analysis is available in Appendix A.
Figures
14 and 15 illu s tr a te
that
the whole plant water
content expressed in kg/m2 is highly correlated with stalk water
content expressed in kg/m2.
The correlation coefficient for corn
is 0.94 and for sorghum i t is 0.97.
37
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Figure 8.
1979 angular decorrelation of 30° versus 50
38
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Figure 9.
1979 angular decorrelation of 30° versus 70
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1979 angular decorrelation of 50° versus 70°.
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
raroet: Wheat
le ta T l
requency (GHz): 17.0
kngle oMncidence (Degrees): 50
W
-15
-20
-25
1600
1800
2000
2200
Time
Figure 11.
1979 diurnal response of wheat at 17.0 GHz.
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
*—
w
HV
OB
Frequency (GHzk 13.0
Angle of incidence (Degrees): §0
Dates: 7/23/79
7/26/79
7/27/79
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-7/23/ 79- —7/26/ 79——
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Figure 12.
1979 diurnal response of corn.
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Tar^et^ Sorghum (Milo)
Frequency (GHzfe 8.6
Angle of Incidence (Degrees): 50
Dates: 7/23/79
7/26/79
7/27/79
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Figure 13.
1979 diurnal response of sorghum.
43
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Whole plant water (kg/m2) versus stalk water (kg/m2)
for 1980 corn.
44
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Whole plant water (kg/m2) versus stalk water (kg/m2)
for 1980 sorghum.
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figures 16 and 17 illu s tra te reasonable correlation between
leaf water content
(kg/m2) and stalk water content (kg/m2) but
note the "spread" at low values of water content for corn and for
intermediate values on sorghum.
The correlation coefficient for
corn is 0.86 and for sorghum i t is 0.84.
Figures 18 and 19 demonstrate reasonable correlation between
leaf area index (m2/m2) and stalk water (kg/m2) , but there is a
s ignificant "spread" at the lower end for com and at intermediate
values for sorghum.
The correlation coefficients are 0.80 for
com and 0.94 for sorghum.
The plots in Figures 20 and 21 indicate that the correlation
between leaf water (kg/m2) and whole plant water (kg/m2) are 0.83
for corn and 0.89 for sorghum.
clusters
Note, however,
of data points for corn for the lower
the two distinct
half of the plot;
this effect is not evident on the sorghum plot.
Figures 22 and 23 illu s tr a te leaf area index (m2/m2) versus
whole plant water (kg/m2) .
for
sorghum i t
is
0.94.
For corn the correlation is 0.79 and
The two d istin ct clusters are again
evident on the corn p lo t.
Leaf
area index
(m2/m2)
and
le a f
water
content
(kg/m2)
correlate at a level
of 0.93 for com (Figure 24) and 0.90 for
sorghum (Figure 25).
The "spread" appears greater for corn than
for
sorghum but note
that the scales on the plots d iffe r and
therefore i t is sim ilar for both crops.
Figures 26 and 27 plot the radar backscatter in real units
(m2/m2) at 17.0 GHz, VV polarization and 50° incidence angle
46
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Leaf water content (kg/m2) versus stalk water content
(kg/m2) for 1980 corn.
47
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PAG?
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N
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fe
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Leaf water content (kg/m2) versus stalk water content
(kg/m2) for 1980 sorghum.
48
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P*CF 12 RB1>P*n *C»TTE9 »1.0TS
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Figure 18.
Leaf area index (m2/m2) versus stalk water (kg/m2) for
1980 corn.
49
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Leaf area index (m2/m2) versus stalk water (kg/m2) for
1980 sorghum.
50
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MCe
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Leaf water (kg/m2) versus vrfiole plant water (kg/m2)
for 1980 corn.
51
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2 .2 5
#
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1.50
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Leaf water (kg/m2) versus whole plant water (kg/m2)
for 1980 sorghum.
52
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MCE
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Leaf area index (m2/m2) versus whole plant water
(kg/m2) for 1980 corn.
53
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Leaf area index (m2/m2) versus whole plant water
(kg/m2) for 1980 sorghum.
54
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we
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1980 corn.
55
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M et
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Leaf area index (m2/m2) versus leaf water (kg/m2) for
1980 sorghum.
56
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MS€
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Backscatter (17 GHz, VV, 50°) versus leaf area index
(m2/m2) for 1980 corn.
57
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Backscatter (17 GHz, VV, 50°) versus leaf area index
(m2/m2) for 1980 sorghum.
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
versus leaf area index (m2/m2) .
The correlation is 0.69 for corn
and 0.70 for sorghum.
Leaf water (kg/m2) versus the radar backscatter (m2/m2) at
17.0
GHz, VV,
50°
is
illu s tra te d
in
Figures
28 and 29.
The
correlation is a modest 0.58 for corn and 0.70 fo r sorghum.
Figures
30 and 31 provide plots of the radar backscatter
(m2/m2) at 17.0 GHz, VV, 50° versus whole plant water (kg/m2).
The correlations are 0.41 for com and 0.75 for sorghum.
The correlation of stalk water (kg/m2) with radar backscatter
(m2/m2) at 17.0 GHz, VV, 50° is given in Figures 32 and 33.
Corn
correlates at a level of 0.37 while sorghum is at 0.67.
Figures
34 and 35 illu s tr a te
the correlation
between the
radar backscatter (m2/m2) at 17.0 GHz, VV, 50° and the volumetric
soil
moisture (gm/cm3) .
Corn shows l i t t l e
correlation at -0.06
and sorghum shows a slig ht negative correlation at -0.4 6.
Tables
6 and 7 summarize the
results
of this
regression
analysis.
To summarize this analysis on the 1980 backscatter and ground
truth data, i t is evident that a ll plant parameters are correlated
with each other.
This would indicate that a simple model using
any one of these parameters should provide reasonable results.
The results of the regressions against backscatter data seem to
indicate,
however,
that
depending on the crop.
certain
parameters
The best overall
perform
better,
single parameter for a
model covering both crops appears to be leaf area index.
Although the plant parameters are correlated with each other,
i t is reasonable to use more than one parameter in a more complex
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
RACE
k
RBOBkO SCATTER BLOTS
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Backscatter (17 GHz, VV, 50°) versus leaf water
(kg/m2) for 1980 corn.
60
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VFOSIIS V » » I*B L E
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Backscatter (17 GHz, VV, 50°) versus leaf water
(kg/m2) for 1980 sorghum.
61
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Backscatter (17 GHz, VV, 50°) versus vrfiole plant water
(kg/m2) for 1980 corn.
62
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a
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plots
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Backscatter (17 GHz, VV, 50°) versus whole plant water
(kg/m2) for 1980 sorghum.
63
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Backscatter (17 GHz, VV, 50°) versus stalk water
(kg/m2) fo r 1980 corn.
64
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315
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Backscatter (17 GHz, W , 50°) versus stalk water
(kg/m2) for 1980 sorghum.
65
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p»CC
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Backscatter (17 GHz, VV, 50°) versus volumetric soil
moisture (gm/cm3) for 1980 corn.
66
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.
♦
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Backscatter (17 GHz, VV, 50°) versus volumetric soil
moisture (gm/cm3) for 1980 sorghum.
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 6.
Summary of Regression Analysis fo r 1980 Com
MPHPLANT
MPHLEAF
MPHSTALK
LAI
MSVOL
S17VV50
MPHPLANT
—
0.83
0.94
0.79
—
0.41
MPHLEAF
0.83
—
0.86
0.93
—
0.58
MPHSTALK
0.94
0.86
—
0.80
—
0.37
LAI
0.79
0.93
0.80
—
—
0.69
MSVOL
—
—
—
—
—
-0.06
S17VV50
0.41
0.58
0.37
0.69
-0.06
TABLE 7.
Sunnary of Regression Analysis fo r 1980 Sorghum
MPHPLANT
MPHLEAF
MPHSTALK
LAI
MSVOL
S17VV50
MPHPLANT
—
0.89
0.97
0.94
—
0.75
MPHLEAF
0.89
—
0.84
0.90
—
0.70
MPHSTALK
0.97
0.84
—
0.94
—
0.67
LAI
0.94
0.90
0.94
—
—
0.70
MSVOL
—
—
—
—
—
-0.46
S17VV50
0.75
0.70
0.67
0.70
-0.46
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
model,
since
information,
each
which
additional
should
description of the process.
result
parameter
in
adds
additional
an improved mathematical
In addition, although soil moisture
showed l i t t l e or even a slig h t negative correlation with the radar
data,
it
too should be included in the modeling e ffo r t.
This
analysis indicates that soil moisture is not important over most
of the growing season, but other studies have shown that i t can be
quite significant very early in the season or very late because of
low canopy attenuation during these periods.
4 .0
BACKSCATTER RESPONSE MODELING
The microwave response to vegetation may be modeled using
various
levels
of
mathematical
sophistication.
The
most
elementary approach is via simple lin ear regression; a s lig h tly
more complex method is to use m ultiple linear regression.
These
methods are to ta lly empirical and thus require no knowledge of the
details of the target-sensor interaction.
Empirical models are
often developed by users of remote sensing data.
The advantage of
empirical models is that they are simple and provide a s traig h t­
forward relationship between the observed microwave response and a
ground truth parameter.
that
they
provide
little
The disadvantage of empirical models is
understanding
of
the
nature
of
the
target-sensor interaction and in addition, often do not provide
good f it s to the observed data.
At the other end of the modeling spectrum, one may u t iliz e
electromagnetic scattering theory, based upon Maxwell's equations,
to develop a rigorous solution to the targat-ssnscr interaction
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
problem (Ulaby, 1984a; Fung, 1977, Fung, 1979).
models for
scattering
from a vegetation
The theoretical
volume are
complex mathematically and require ground truth
d iff ic u lt
(and
expensive)
to
obtain.
re la tiv e ly
inputs that are
Theoretical
models
contribute greatly to the understanding of the physical processes
involved in vegetation scattering, but they are of lim ited value
to users of remote sensing data.
A middle-of-the-road approach to vegetation modeling is the
semi-empirical
model.
A semi-empirical
model
is
based
upon
macroscopic physical principles and commonly measured ground truth
parameters.
Such a model is developed with one or more constants
whose value is determined by f it t in g the model expression to the
observed
microwave
and
regression techniques.
ground
truth
data
using
non-linear
Semi-empirical models provide insight into
the nature of the target-sensor interaction and are of value to
users of microwave remote sensing data, since they are based upon
easily
measured
ground
truth
parameters.
The
semi-empirical
approach to modeling is the basis for the material
presented in
this section.
4.1
Review of Previous Approaches
One of the f ir s t effo rts to model the backscatter response of
vegetation
1959).
was conducted at the Ohio State University
(Peake,
Wheat and grass were modeled as a collection of lossy
d ie le c tric cylinders.
The in it ia l approach at the University of Kansas was to model
the
vegetation
canopy as a homogeneous d ie le c tric
slab.
The
70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
d ie le c tric
constant
of
the
slab was calculated
from a mixing
formula for a ir and vegetation.
An improved semi-empirical model was subsequently developed
at the University of Kansas by treating the vegetation as a water
cloud (Attema, 1978).
The water cloud was ju s tifie d by the fact
that dry vegetation's d ie le c tric constant (Carlson, 1967) d iffers
little
from that
of
a ir
(1.5
vs.
1 .0 ),
while the
constant of free water is considerably higher.
vegetation
canopy is
that
identical
the
cloud
water
In this model, the
modeled by a cloud characterized
volumetric water content.
are
d ie le c tric
by its
The assumptions inherent in this model
representing
particles
the
uniformly
vegetation
distributed
consists
of
throughout the
space according to a Poisson process, that only single scattering
needs to be considered, and that the only significant variables
are cloud height and cloud density.
be proportional
Cloud density is assumed to
to the volumetric water content of the canopy.
The cloud model has been tested on numerous data sets including
the
1979 and 1980 data
1982;
Ulaby,
1983)
acquired near Manhattan,
Kansas (Eger,
and has demonstrated satisfactory,
but
not
spectacular results.
The Dutch have extended the basic cloud model to a m ultilayer
approach (Hoekman, 1982) and have generated improved results.
The
Dutch model was tested on a wide variety of crops including beets,
potatoes, peas, winter wheat, summer wheat, barley, and oats.
A recent
primarily
models
for
for
approach
soil
surface
to
moisture
semi-empirical
applications,
scattering
and
the
modeling,
developed
uses the theoretical
cloud
model
for
the
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
vegetative cover (Mo, 1984).
Work
has continued
empirical
at
the
University
of Kansas on semi-
modeling and alternate approaches have been developed
which give reasonable f it s
to the observed data (Ulaby,
1984b;
Allen, 1984).
The obvious question which arises in this review is "which
model
is
best?"
and "by what
c r ite r ia
should
such models be
compared?"
As illu s tra te d
in Section 3.3, plant parameters are highly
correlated with each other, so i t is possible to generate a number
of
d iffe re n t
semi-empirical
models
using
basically
sim ilar
physical reasoning.
I t is common to judge such models by c r ite ria
such as correlation
between observed and predicted data and ms
error between observed and predicted values.
not
s u ffic ie n t,
however.
canopy attention
An essential
calculated
These c rite ria are
c riterio n
from the model
is
that
the
must be r e a lis tic .
Since few independent canopy attenuation measurements have been
reported to date, a major objective of this investigation is to
greatly expand the knowledge in this area.
This attenuation data
is presented in Chapter 5.
4.2
A Semi-Empirical Vegetation Model
This
section
w ill
present
an alternate
approach to
semi-
empirical
modeling of a vegetation canopy which bridges the gap
between
the
approach.
semi-empirical
approach
and
the
theoretical
The model is derived from recent work at the University
of Kansas.
72
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A theoretical model for scattering by a lossy volume over a
surface via the radiative transfer approach is available in the
lite ra tu re (Ulaby, 1984a).
volume is
treated
In the case of a vegetation canopy the
as having no definable upper surface.
The
result is in the form of a rather complex matrix equation which is
too complex for most users of remote sensing data including many
individuals whose interest is in semi-empirical modeling.
Althou^i the model is mathematically complex, i t consists of
three basic components as follows:
o
_ o
to ta l ” surface
o
volume
o
interaction*
In general, the surface term is a function of its d ie le c tric
constant and its surface roughness characterized by surface height
standard deviation,
three theoretical
upon surface
a, and surface correlation length, L.
models used for surface scattering
roughness) are the Small
Perturbation
The
(depending
Model, the
Kirchhoff-Scalar Approximation Model or the Kirchhoff-Stationary
Phase Approximation Model.
Because the surface term is negligible
over the majority of the growing season in most vegetation canopy
situations, we may avoid the theoretical models and use a simple
relationship for Csurf ace:
Surface = C<f ’ 9> * LC<f ’ 9) * MSV0L
where C is a constant which is a function of frequency, f ,
incidence angle,
6; and
and
is the two-way canopy loss which is
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
also a function of frequency and incidence angle and MSVOL is the
volumetric soil moisture.
The volume term can be sim plified greatly by assuming that
losses due to scatter and absorption are polarization independent,
that a ll scattering within the volume behaves in a Rayleigh phase
manner, and that only single scatter is considered.
Under these
conditions, the model sim plifies to:
°VV = °HH =
where w is
depth.
" exP(~^T sece)] cose
the single
scattering albedo and x is the optical
This is exactly equivalent to the cloud model discussed
previously.
A s lig h tly more complex and accurate model may be obtained by
continuing to assume that the volume may be characterized by its
albedo and optical depth, but including products and higher powers
of a) and x.
The model is of the form:
°VV = °HH = P
+ ° “T +
*
( l - exp(-S x secQ)) cos 0
where P, Q, R, and S are constants.
fu ll
theoretical
model
This model was f i t to the
for the single scatter case using non­
linear regression to obtain the following result (Allen, 1984):
J^
V y y
-—
-0
W j_ ||_ |
_
—
n
W
-j/io
./T 6
..fi
UW ^ J.
.
-P
r\
coc
ULl l
“
<1
oo"7
U .L O / \
/ U. —
\ 2 ^J
Ul j
.
-
(l - exp(-2.119 x sec©)) cos0
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
rms error
associated with this
correlation coefficient was 0.999.
fit
was 0.174 dB and the
The lim its on this model are
8.4° < 8 < 84.5°; 0.1 < x < 2.2; 0.01 < u < 0 .5 .
The
interaction
term turns
out
to
be
negligible
for
VV
polarization with the above lim its and of some significance for HH
polarization.
Using
techniques
sim ilar
to
those
used
in
developing the volume term, the interaction term becomes (Allen,
1984):
o?
= 1.924 « [l + 0.924
ut
+ 0.398(<ut) 2] •
HH
[l - exp(-1.925
t
sece)] [exp(-1.372 t 1*12 sece)] •
exp[-0 .8 3 6 (ka)2 coss] |
|
2 cos 0
where k = Zn/Xy a is the surface standard deviation and Rhh is the
Fresnel Reflection Coefficient for horizontal
rms
error
associated
with
this
correlation coefficient was 0.999.
fit
was
p o larization.
0.233
dB
and
The
the
The lim its on this model are
8.4° < 0 < 62.7°; 0.1 < t < 2.2; 0.01 < u < 0.5; 0.1 < ko < 0.9.
Although these models are of theoretical in te re s t, they s t i l l
do not include ground truth parameters which are easily measured
in the
f ie ld .
The semi-empi rical
models to
be used in this
75
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investigation w ill be derived by postulating relationships between
the
albedo,
w and
the
optical
depth,
t
and
ground
truth
parameters.
Optical depth is defined as (Ulaby, 1982):
Z2
T =
/
K
dZ
Z1
where <e is the extinction coe ffic ien t and dz is an increment of
path length through the vegetation canopy.
Extinction in a volume
is the result of scattering and absorption.
Sources of extinction
in a vegetation canopy include the leaves, fr u it and s ta lk .
purposes
of
significant
absorption
this
model,
sources
it
w ill
of extinction
by leaves,
be
are
and absorption
assumed
that
scattering
by stalks.
the
from
It
For
only
leaves,
w ill
be
further assumed that the leaf scattering is proportional to le a f
area index, leaf absorption is proportional to leaf water content
and
stalk
absorption
These assumptions
depth,
lead
is
proportional
to
the
to
following
stalk
water
form for
content.
the optical
t:
t
= A • LAI + B • MPHLEAF + D • MPHSTALK
where A, B, and D are constants, LAI is leaf area index (m2/m2) ,
MPHLEAF is leaf water content (kg/m2) and MPHSTALK is stalk water
content (kg/m2) .
The albedo is defined as (Ulaby, 1982):
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where
<s is
the
scattering
c o e ffic ie n t.
Based on the above
assumptions for optical depth, the albedo is :
0, =
A • LAI
_
.
The albedo and optical
depth are each a function of frequency.
The two-way canopy loss required in the surface term as a function
of optical depth is:
Lc = exp(-2 t sece) .
The surface term becomes:
°surface = C ’ MSV0L * ^exp^‘ 2 T sec6)]-
The model, to be referred to as Model A, is summarized as follows
for VV polarization:
T
= A • LAI + B • MPHLEAF + D • MPHSTALK
-»■ - A ■ LAI
T
a j v = 0 .7 4 2
0,(1 + 0 . 5 3 6
ujt - 0 . 2 3 7 ( o n ) 2 ) •
( l - exp(-2.119 r sece)) cose +
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C • MSVOL • e x p ( - 2 . 0
t
s e c 8 ).
For HH polarization, the following assumptions were made:
x = A ♦ LAI + B • MPHLEAF (no stalk term)
Q) =
A, • LAI
T
(ka) 2 = C
i Rhh i 2 = D * m s v o l
The stalk absorption term is not sp e cifically included in this
version
to
keep
the
number
of
constants
reasonable
addition, i t should be negligible for HH polarization,
and
in
(ko) 2 is
assumed to be a constant because i t depends upon surface roughness
(which is essentially
constant for the test data).
|
! 2 is
assumed to be proportional to soil moisture since i t is a function
of
d ie le c tric
constant
and d ie le c tric
constant
increases
with
increasing soil moisture.
Model A for HH polarization becomes:
oJH = 0.742 w[l + 0.536 orr - 0 .2 3 7 ( ut ) 2 ] •
[ l - exp(-2.119 t sece)] cos 8 +
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 .9 2 4 u [ l + 0 .9 2 4 urr + 0 .3 9 8 (u r r)2 ]
[l - exp(-1.925
sece)] •
t
[exp(-1.372
sece]] •
[exp(-0.836 • C • cose]] •
D • MSVOL • cose +
E • MSVOL • exp(-2
t
sece).
Model A was tested extensively using VV polarization on the
1980 data set
described previously.
using HH polarization
at
17.0 GHz.
backscatter and ground truth
The
The model was f i t
values
f ie ld .
These
by calculating
predicted
and
Additionally,
generated.
the
observeddata
plots
of
the
The constants in the model were
corn field s
or a ll
sorghumfie ld s .
model was then used to generate predicted o° values
individual
to
data using the BMDP-AR non-linear
regression routine (Dixon, 1979).
determined by combining a ll
The model was also tested
a0 values
well
predicted
each
were compared to observed
correlation
as
for
coefficien t
as
the
(r)
between
rms error
andobserved
data
(e ).
were
All relevant data for this analysis is available in
Appendix A.
Table 8 summarizes the Model A constants at 8.6 GHz, 13.0
GHz, 17.0 GHz, and 35.6 GHz for corn.
In addition, constant
79
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TABLE 8.
CROP
FREQUENCY (GHz)
Model A Constants fo r 1980 Com
POLARIZATION
Corn
8.6
VV
0.09
0.83
1.05
0.09
Corn
13.0
VV
0.14
1.35
1.32
0.03
Corn
17.0
VV
0.15
1.26
0.97
0.03
Corn
35.6
VV
0.14
0.50
0.88
0.14
Corn
10.2
VV
0.11
1.02
1.15
0.07
(interpolated)
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
values were obtained by interpolation for 10.2 GHz for use in a
la te r section (4.5) on model attenuation.
The correlation
between observed and model
predicted corn
data is summarized in Table 9.
Table
10
presents
the
rms
errors
in dB for each
corn
field/frequency combination.
Figures 36, 37, 38, and 39 are plots of a° predicted versus
o° observed
fo r
a selected
corn
fie ld
at each of
the
four
frequencies u tiliz e d in the study.
Figure 40 illu s tra te s
the importance of the soil
moisture
term as compared to the vegetation term for a selected com fie ld
at 8.6 GHz.
This term is of some importance early in the growing
season, of minor importance throughout most of the season, and
quite important at the very end of the measurement period.
should be noted that 1980 was a very hot anddry
year and
moisture values were generally quite low (Appendix A).
It
soil
A wetter
growing season would have increased the contribution of the soil
moisture term.
Table 11 summarizes the Model A constants obtained for 1980
sorghum.
Table 12 illu s tra te s the correlation co efficien ts, and
the rms errors are tabulated in Table 13.
Figures
41,
42,
43,
and
44
graphically
illu s tr a te
the
observed versus predicted backscatter response for 1980 sorghum.
In general, the model provided a s lig h tly in fe rio r f i t for sorghum
as compared to corn.
Model
A fo r
interaction term.
HH polarization
includes
the
soil-vegetation
This term is negligible for VV polarization,
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 9 .
Model A C o rre la tio n C o e ffic ie n ts fo r 1980 Corn
CROP FREOUENCY (GHz)
POLARIZATION
rj
r2
r3
Corn
8.6
VV
0.87
0.87
0.86
Corn
13.0
VV
0.93
0.69
0.92
Corn
17.0
VV
0.93
0.78
0.94
Corn
35.6
VV
0.96
0.82
0.95
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 1 0 .
CROP
FREQUENCY (GHz)
Model A RMS E rro rs fo r 1980 Com
POLARIZATION
e^dB)
e2(dB)
e3(dB)
Corn
8.6
VV
0.66
0.78
0.93
Corn
13.0
VV
0.45
0.92
0.69
Corn
17.0
VV
0.66
0.96
0.69
Corn
35.6
VV
0.63
0.88
0.58
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Com (Cl)
o° observed
o° predicted
-2
ca
12
-
160
170
180
190
200
210
220
230
240
250
260
Julian Date
Figure 36.
Observed versus predicted seasonal response for 1980
com at 8.6 GHz, VV polarizatio n , 50°; correlation is
0.87 and rms error is 0.66 dB.
84
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Corn (Cl)
s° observed
o° predicted
-2
<aP)o°
-6
160
170
180
190
200
2 10
220
2 30
2 40
250
260
Julian Date
Figure 37.
Observed versus predicted seasonal response fo r 1980
corn at 13.0 GHz, W polarization, 50°; correlation is
0.93 and rms error is 0.45 dB.
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Com O
-2
+ ------- o° observed
o ------- o° predicted
-4
-B
-8
-1 0
-12
-1 4
-1 6
160
j—
i—
170
i—
160
i—
i—
190
.—
i—
2 00
i____ i
210
____ '
220
•
i
230
.
i
2 40
■
i
260
260
JulWn Date
Figure 38.
Observed versus predicted seasonal response for 1980
com at 17.0 GHz, VV polarization, 50s; correlation is
0.94 and rms error is 0.69 dB.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Com O
0
-2
-4
-B
(9P) o°
-8
-10
-1 2
160
170
190
200
210
220
2 30
2 40
250
260
Julian Date
Figure 39.
Observed versus predicted seasonal response for 1980
corn at 35.6 GHz, VV p o larization, 50°; correlation is
0.95 and rns error is 0.58 dB.
87
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Corn (Cl)
o
i — o° Vegetation
o—•—o° Soti
-5
o° Total
a
-1 0
0°(dB)
-1 5
-2 0
-2 5
-3 0
-3 5
160
j
170
i
i
i
i
180
190
200
.
i
i
i
210
2 20
230
•
i
240
.
i
2 50
260
Julian Date
Figure 40.
Comparison of model soil moisture term to model
vegetation term and to ta l predicted o° for 1980 corn
(C l) at 8.6 GHz, W p o larization, 50°.
88
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 1 1 .
CROP
rfodel A Constants fo r 1980 Sorghum
FREQUENCY (GHz)
POLARIZATION
A
B
C
D
Sorghum
8.6
VV
0.13
1.61
0.00
0.14
Sorghum
13.0
VV
0.15
1.45
0.00
0.15
Sorghum
17.0
VV
0.14
1.02
0.00
0.21
Sorghum
35.6
VV
0.11
0.33
0.32
0.40
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 12.
CROP
Model A C orrelation C oefficients fo r 1980 Sorghum
FREQUENCY (GHz)
POLARIZATION
rx
r2
r3
Sorghum
8.6
VV
0.95
0.47
0.54
Sorghum
13.0
VV
0.91
0.65
0.80
Sorghum
17.0
VV
0.95
0.61
0.78
Sorghum
35.6
VV
0.88
0.72
0.90
90
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 13.
CROP
Model A RMS Errors fo r 1980 Sorghum
FREQUENCY (GHz) POLARIZATION
e^dB)
e2(dB)
e3(dB)
Sorghum
8.6
VV
1.10
1.36
1.08
Sorghum
13.0
VV
1.07
1.19
0.78
Sorghum
17.0
VV
0.95
1.40
0.90
Sorghum
35.6
VV
1.16
1.26
0.63
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Sorghum (SI)
o
o° observed
-2
o
o° predicted
-4
-6
<aP)o<>
o e -M —
-8
e
-1 0
-1 2
•14
160
J
I
I
I
I
170
180
190
2 00
210
1------ 1------ 1------ 1------ 1------ 1------ ;------ L
220
2 30
240
250
260
Julian Date
Figure 41.
Observed versus predicted seasonal response for 1980
sorghum at 8.6 GHz, VV p o larizatio n , 50°; correlation
is 0.95 and rms error is 1.10 dB.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Sorghum (SI)
o
— o° observed
— o° predicted
-2
-4
o° MB)
-6
____ _________ ________
-8
-10
•12
-1 4
160
170
180
190
200
210
220
2 30
240
250
260
Julian Date
Figure 42.
Observed versus predicted seasonal response for 1980
sorghum at 13.0 GHz, VV polarization, 50°; correlation
is 0.91 and rms error is 1.14 dB.
93
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Sorghum (SI)
0
+ ------- 8° observed
-2
o------- o° predicted
-4
-S
<8P)oO
...
>
©-
©-—o-
-8
-10
•12
-1 4
160
J
170
i
I
I
I
180
190
200
I
I
210
I
I
220
:_____I____ i____ I_____ ______L
230
240
250
260
Julian Date
Figure 43.
Observed versus predicted seasonal response for 1980
sorghum at 17.0 GHz, W polarization, 50°; correlation
is 0.95 and rms error is 0.95 dB.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Sorghum (S3)
o
o° observed
-2
— o° predicted
-4
(fm)
-6
--e
■ © --
-o
-1 0
-12
160
170
180
190
2 00
2 10
2 20
2 30
2 40
2 50
2 60
Julian Date
Figure 44.
Observed versus predicted seasonal response for 1980
sorghum at 35.6 GHz, VV polarization, 50°; correlation
is 0.90 and rms error is 0.63 dB.
95
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
but is normally of some significance for HH polarization, so i t
was included in the model.
for
VV polarization
specifically
in
included.
The model also d iffers from the form
that
a stalk
absorption
term was not
This term was eliminated to reduce the
number of constants in the model and can be ju s tifie d on the basis
that a horizontally polarized wave should suffer l i t t l e absorption
by a vertically-oriented s ta lk .
Table 14 summarizes the Model A constants for HH polarization
at the one frequency studied, 17.0 GHz.
Table 15 tabulates the
correlation coefficients and Table 16 lis ts the rms errors.
The
only crop considered at HH polarization was corn.
Table 17 compares the magnitude of the volume, interaction
and soil
(surface) terms for 17.0 GHz, HH polarization.
I t is
noted that both the soil and the interaction terms are 15-20 dB
below the level of the vegetation terms which indicates that they
are of minimal significance.
I t should be noted, however, that
1980 was a very hot and dry year and these levels are depressed
from more moist
conditions.
Additionally,
the
soil
term is
important very early in the growing season when there is minimal
biomass and late in the season a fte r the vegetation has dried.
Figure
45
illu s tra te s
the
seasonal
response
of
observed
versus predicted backscatter data at 17.0 GHz, HH polarization.
The
fit
on
this
data
is
sim ilar
to
that
obtained
for
VV
polarization.
Table
18 summarizes
the
individual
contributions
to
the
optical depth term by leaf scattering, leaf absorption and stalk
absorption as well as total optical depth and albedo for a
96
i
>
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 14. Model A Constants fo r 1980 Com
at 17.0 GHz, HH Polarization
CROP
FREQUENCY (GHz)
Corn
17.0
POLARIZATION
A
B
0.11 1.24
HH
C
D
E
0.00
0.86
0.86
TABLE 15. Model A Correlation C oefficients fo r
1980 Com at 17.0 GHz, HH P olarization
CROP
Corn
FREQUENCY (GHz)
17.0
TABLE 16.
POLARIZATION
HH
rl
r2
r3
0.87
0.78
0.93
Model A RMS Errors fo r 1980 Com at
17.0 GHz, HH P olarization
CROP
FREQUENCY (GHz)
Corn
17.0
POLARIZATION
HH
e1(dB)
e2(dB)
e3(dB)
0.76
0.93
0.64
97
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 17. Comparison of the Volume, In te ra ctio n ,
and Soil (Surface) Terms at 17.0 GHz,
W Polarization
DATE CROP
FREQUENCY
(GHz)
POLARIZATION
o°ol (dB)
o ? t (dB)
o°o i1 (dB)
170
Corn
17.0
HH
-8 .9
-25.7
-23.6
204
Corn
17.0
HH
-7 .5
-24.8
-27.7
98
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Com (C3)
-2
+------- r observed
-4
o--------o* predicted
o°(dB)
-6
-8
-10
-1 2
-1 4
-1 6
160
170
J
------ 1------
180
190
1------1____:------.____i____
200
2 10
220
i
230
■
i
240
■
i
250
260
Julian Date
Figure 45.
Observed versus predicted seasonal response for 1980
corn at 17.0 GHz, HH polarization, 50°; correlation is
0.93 and rms error is 0.64 dB.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 18. Contribution to Optical Depth by Leaf
Scattering, Leaf Absorption and Stalk Absorption,
Total Optical Depth and Albedo fo r Corn Field C3
on Date 204 Using Model A
CROP
FREQUENCY
(GHz)
Corn
8.6
VV
0.39
0.71
0.28
1.38
0.28
Corn
13.0
VV
0.59
1.17
0.09
1.85
0.32
Corn
17.0
VV
0.63
1.09
0.09
1.81
0.35
Corn
35.6
VV
0.60
0.42
0.44
l.Afi
0.41
POLARIZATION
t £s
Tga
t
u
100
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
selected fie ld of 1980 corn at mid-season (date 204).
Figure 46
is a plot of the seasonal variation of optical depth and albedo
for a d ifferen t 1980 corn f ie ld .
Note the "plateau" region for
the optical depth and the fact that the albedo remains constant at
approximately 0.3 until the end of the growing season.
All data
is for VV polarization.
Table 19 provides a tabulation identical to Table 18 except
i t is for sorghum on the same mid-season date (204).
This data is
also VV polarization.
4.3
Additional Semi-Empirical Models
Although
Model
A is
a ttra c tiv e
because
it
can
be tied
directly back to a theoretical model based upon electromagnetic
scattering theory, other semi-empirical approaches can yield good
f it s .
The following model, developed at the University of Kansas
(Allen, 1984), w ill be referred to as Model B:
a°= A[l - exp(-B • LA I/h)] [l - exp(-2 • E • LAI sece)] cose +
C ♦ MSVOL[exp(-2 • E • LAI sece)] +
D • MPHSTALK[exp(-2 • E • LAI sece)]
where h is the canopy height.
This model was tested on the 1980 corn data and produced a
good f i t
as measured by the
correlation
coefficients
and rms
101
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Com (Cl)
1.4
Optica! Depth
Albedo, Optical Depth
Albedo
0.8
0.6
0 .4
0.2
0.0
160
170
180
190
200
2 10
2 20
230
240
250
260
Julian Date
Figure 46.
Seasonal variation of albedo and optical depth for
1980 com (Cl) at 8.6 GHz, VV p o larization, 50°.
102
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TABLE 19.
Contribution to Optical Depth by Leaf
S cattering, Leaf Absorption and Stalk Absorption,
Total Optical Depth and Albedo fo r Sorghum Field SI
on Date 204 Using Model A
CROP
FREQUENCY
(GHz)
Sorghum
8.6
VV
0.67
1.64
0.25
2.56
0.26
Sorghum
13.0
VV
0.78
1.73
0.27
2.51
0.31
Sorghum
17.0
VV
0.72
1.41
0.37
2.13
0.34
Sorghum
35.6
VV
0.56
1.05
0.71
1.61
0.35
POLARIZATION
t
4s
T$a
t
u
103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
error.
Table
tabulates
the
20 summarizes the model
correlation
fields combined.
Note that
area index although a stalk
coefficients,
constants and Table 21
and rms error for a ll
this model is prim arily driven
by leaf
term is included.
A model developed at NASA/JPL (Paris, 1984) was also tested
on the 1980 com data.
This model introduces a new variable, N,
the number of leaves per plant into the model expressions.
N is
determined from the growth stage of the crop and is tabulated in
Appendix A along with the other corn ground tru th .
Model C is:
g
o°=---- L j J M — Li!
[i . exp(-2 • C • MPHLEAF • sece)] +
2 • MPHLEAF • sec 6
[D + E • MSVOL] • [exp(-2 • C • MPHLEAF • sece)].
Table 22 summarizes the constants obtained by f it t in g
the
model to the 1980 corn data and Table 23 gives the correlation
coefficients, and rms error
for a ll fields combined. Again,
model provides a good f i t to
the 1980 data.
the
In an e ffo rt to improve Model C, a stalk term was added to
the expression which w ill be referred to as Model D:
g
a0 = ■ A -* VAI— 1J L _ [ i . exp(-2 • C • MPHLEAF • sece)] +
2 • MPHLEAF sec0
D • MSVOL • [exp(-2 • C • MPHLEAF • sec6)] +
E ♦ MPHSTALJC • [exp(-2 • C * MPHLEAF • sec 6 )].
104
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TABLE 2 0 .
CROP
FREQUENCY
(GHz)
Corn
8.6
Corn
Model B Constants fo r 1980 Com
POLARIZATION
A
B
C
D
E
VV
0.23
2.05
0.19
0.03
0.45
13.0
VV
0.28
2.09
0.18
0.04
0.47
Corn
17.0
VV
0.31
2.36
0.23
0.03
0.41
Corn
35.6
VV
0.40
1.35
0.10
0.04
0.43
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 2 1 .
Model B C o rre la tio n C o e ffic ie n ts ,
and RMS E rro r fo r a l l F ie ld s Combined fo r 1980 Com
CROP
FREQUENCY
(GHz)
Corn
8.6
POLARIZATION
rx
r2
r3
e(dB)
VV
0.85
0.94
0.89
0.71
Corn
13.0
VV
0.93
0.89
0.94
0.68
Corn
17.0
VV
0.91
0.88
0.91
0.73
Com
35.6
VV
0.94
0.91
0.93
0.61
106
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TABLE 2 2 .
Model C Constants fo r 1980 Com
CROP
FREQUENCY
(GHz)
Corn
8.6
VV
0.11
1.03
0.68
0.07
0.04
Corn
13.0
VV
0.11
0.94
1.10
0.07
0.00
Corn
17.0
VV
0.18
1.25
2.17
0.01
0.23
Com
35.6
VV
0.17
1.08
1.17
0.07
0.00
POLARIZATION
A
B
C
D
107
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TABLE 2 3 .
Model C C o rre la tio n C o e ffic ie n ts ,
and RMS E rro r fo r a ll F ie ld s Combined fo r 1980 Com
CROP
FREQUENCY
(GHz)
Corn
8.6
POLARIZATION
rx
r2
r3
e(dB)
VV
0.81
0.86
0.83
0.81
Com
13.0
VV
0.89
0.82
0.90
0.85
Corn
17.0
VV
0.93
0.86
0.94
0.89
Com
35.6
VV
0.93
0.87
0.91
0.73
108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Note also that the soil moisture term has been simplified in this
model to reduce the number of constants.
Table 24 illu s tra te s
the constants derived by f it tin g this
model to the 1980 com data and Table 25 gives the correlation
coefficien ts, and rms error for a ll field s combined.
A comparison
of Tables 21 and 23 indicates that the addition of the stalk term
improves an already good f i t to the data.
4.4
Model Comparisons
Table 26 provides a comparison of the average correlation for
a ll
fields
field s
there
and frequencies
and frequencies
are
slight
and the average
for the four models studied.
differences
nearly id e n tic a l.
rms error
in
performance,
the
for a ll
Although
results
are
As previously indicated, this is a result of
the high correlation between the various ground truth parameters
used in these models.
The four models must be compared on the basis of the canopy
attenuation they predict, however, before they can be considered
v alid.
4.5
Canopy attenuation is the subject of the next section.
Canopy Attenuation from Model
The four models discussed in this section each have a two-way
canopy attenuation of the form:
= exp(-2
t
secQ)
1
Art
l\jy
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 2 4 .
Model D Constants fo r 1980 Com
CROP
FREQUENCY
(GHz)
POLARIZATION
Corn
8.5
Com
A
B
C
D
VV
0.10
1.05
1.49
0.26
0.06
13.0
VV
0.11
0.97
1.67
0.24
0.07
Corn
17.0
VV
0.12
1.00
1.59
0.31
0.07
Com
35.6
VV
0.17
1.11
1.79
0.16
0.08
110
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.
TABLE 75
Model D C o rre la tio n C o e ffic ie n ts ,
and RMS E rro r fo r a l l F ie ld s Combined fo r 1980 Com
FREQUENCY
CROP(GHz)
POLARIZATION
rx
r2
r3
e(dB)
Corn
8.6
VV
0.83
0.90
0.85
0.76
Com
13.0
VV
0.91
0.85
0.85
0.91
Corn
17.0
VV
0.93
0.86
0.91
0.69
Corn
35.6
VV
0.94
0.92
0.92
0.67
111
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TABLE 26.
A Comparison of the Average Correlation
and RHS Error fo r the Four Models Studied
MODEL A
MODEL B
MODEL C
MODEL D
Correlation (r )
0.88
0.91
0.88
0.89
RMS Error (e)
0.74 dB
0.68 dB
0.82 dB
0.76 dB
112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
or in dB:
Lc (dB) = 4.343 (2 t sece).
The
models d iffe r in th e ir expressions for the optical depth,
t
,
however:
Model A:
t
= A • LAI + B • MPHLEAF + D • MPHSTALK
Model
B: t = E • LAI
Model
C:
t
= C • MPHLEAF
Model
D:
t
= C • MPHLEAF .
Theconstants are derived from f it tin g the models to the
thus the values for "C" in Models C and
Table
27
provides
a
comparison
data and
D d iff e r .
of
the two-way
canopy
attenuation calculated from the four models for a selected 1980
corn fie ld on a mid-season date (204).
Note that Models A, B, and
D are in reasonable agreement with respect to the general level of
attenuation over the frequency range considered, but that Model C
predicts a much lower attenuation except at 17.0 GHz where i t is
sim ilar to the others.
The only way the appropriateness
which provides a good f i t
of these models, each
of
to the data, can be judged is with a
comparison to direct canopy attenuation data.
Although canopy
113
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TABLE 2 7 .
Comparison o f Two-Way Canopy A tten u atio n fo r
Corn F ie ld C3 on Date 204 C alcu lated from
Models A, B, C, and D
FREQUENCY
LA(dB)
LB(dB)
Lc(dB)
LD(dB;
VV
18.6
25.8
7.8
17.3
13.0
VV
25.0
26.9
12.8
19.5
Corn
17.0
VV
24.4
23.5
25.3
18.2
Com
35.6
VV
19.7
24.6
13.6
20.8
CROP
(GHz)
Corn
8.6
Corn
POLARIZATION
114
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
attenuation data is extremely lim ited , data on corn at 10.2 GHz,
VV polarization is available (Ulaby, 1984c).
The 10.2 GHz data
year, so the comparison
to ta lly appropriate.
in
1980,
so model
was taken in 1982 which was
to 1980 which was
a very wet
a very dryyear is not
In addition, data was not taken at 10.2 GHz
constants
had to
be interpolated.
difference between 1980 and 1982 was canopy height.
Another
The 1982 corn
was t a lle r due to the more favorable moisture conditions.
Figure
47
provides
a
plot
of
the
canopy
attenuation
calculated from Model A on a selected fie ld of 1980 com over the
growing season.
The attenuation values have been normalized to
dB/meter by dividing by the canopy height.
The plot also includes
the direct attenuation measurements from 1982 again normalized to
dB/meter by dividing by the canopy height.
The agreement between these two curves is quite reasonable
during the early part of the growing season considering that they
were
d iffe re n t
fie ld s
d ifferen t environmental
during
d iffe re n t years
conditions.
and
subject to
The attenuation difference
during the last part of the growing season, while not excessive is
most lik e ly due to the fact that the 1982 corn remained green (and
thus more moist) while the 1980 corn "browned-out" due to the hot,
dry summer.
This comparison would seem to indicate that Models A, B, and
D,
which
exhibit
sim ilar
attenuation
while Model C is not, because i t
behavior
are
reasonable,
predicts an u n re a lis tic a lly low
value of canopy attenuation.
115
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 Com <C3)
14
- 1980 fttadei Two-Way Attenuation (dB/m)
- 1982 Measured Two-Way Attenuation (dB/m)
12
Two-Way Attenuation (dB/m)
10
160
170
180
190
200
2 10
220
230
2 40
2 50
260
Julian Date
Figure 47.
A comparison of corn canopy attenuation calculated
from Model A (1980 corn, C3) and canopy attenuation on
corn measured d ire c tly at 10.2 GHz, VV polarization,
50°.
116
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Comparing the four models, Model C is the only model without
a stalk
poor
attenuation term, which may account for its
performance
essentially
withrespect
to
attenuation.
re la tiv e ly
Model
D is
the same asModel C with the addition of a stalk term
and i t performs w ell.
The ideal verificatio n for this set of models would be direct
attenuation
defoliation
data at the four frequencies of interest with a leaf
experiment to
check
the various
components
of
attenuation suggested by Model A.
A complete
function
of
set
of
frequency,
canopy
attenuation
polarization
and
measurements
incidence
as
angle
a
fo r
various crops and various growth stages (and moistures) would be
an extremely
valuable
tool
fo r
individuals
interested
in
the
development of semi-empirical and theoretical vegetation models.
Such a data set would also aid greatly in understanding the nature
of microwave propagation and backscatter in vegetation.
Although
i t may take several years to accumulate a ll of the desired data,
the remainder of this report documents and attempts to model the
f ir s t complete set of attenuation measurements as a function of
frequency, angle and polarization.
117
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5.0
ATTENUATION DATA ANALYSIS
As previously discussed in this report, the only vegetation
attenuation
scope.
measurements
to
date
have
been
very
lim ited
in
Data on vegetation attenuation is essential to validate
semi-empirical
and theoretical
understanding
of
microwave
measurements
reported
here
models and to provide increased
propagation
are
the
and backscatter.
f ir s t
complete
set
The
of
attenuation measurements on vegetation as a function of frequency,
polarization and incidence angle.
The crops chosen for the study
were the two economically important crops, wheat and soybeans.
addition to th e ir
s c ie n tific
In
economic importance, these two crops are of
interest
because
of
th e ir
contrasting
structures.
Wheat is dominated by its vertical stalk and the soybean plant is
dominated by its leafy structure.
the study was dictated
The frequency range chosen for
by the microwave remote sensing systems
planned for orbit in the late 1980's and early 1990's; thus L, C,
and X band were chosen.
were the
two
linear
The polarizations chosen for the study
polarizations,
HH and
VV,
although
some
limited measurements were made at HV and VH polarization.
The
angles of incidence chosen for the study were a low angle (16° or
24°), because of soil moisture monitoring applications as well as
for its
s c ie n tific
interest and a higher angle (52° or 56°) to
correspond to lik e ly vegetation monitoring applications and also
for its s c ie n tific in terest.
also somewhat dictated
The angles of incidence chosen were
by the
physical
conditions at the test
sites.
118
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The attenuation data presented here consists of a number of
“standard" data sets,
cross-polarized
as well
attenuation
as "special" data sets including
measurements,
a wheat
experiment and a soybean defoliation experiment.
decapitation
The attenuation
data w ill be modeled in Chapter 6.
5.1
Calibration, Accuracy, and Precision
As previously discussed, theattenuation data was acquired by
pulling
a
receiver on a sled
mounted transm itters.
in
synchronism
with boom-truck
The data was captured ona chart recorder
and la te r digitized and averaged.
traces of actual recordings.
Figures 48, 49, 50, and 51 are
These figures include data on both
crops, wheat and soybeans, and provide samples of data at each of
the frequencies, polarization and angles used.
These recordings
were selected as a representative sample, the remaining ones were
sim ilar
in nature.
The figures
even at maximum
attenuation,
the
noise flo o r.
While this "noise-margin" is ty p ic a l, in a few cases
it
dropped
to
received signal
indicate that
approximately
was 10 dB to 20 dB above the
5 dB.
None of
the
recordings
indicated attenuation "saturation" due to receiver noise.
The attenuation measurements were calibrated by the simple
procedure of referencing a ll
attenuation to the power measured
under free-space conditions.
Free-space conditions were created
by clearing vegetation at each end of the canopy s trip .
Sources
of error in this experimental procedure include in it ia l boresight
error from transm itter to receiver, d r if t
o ff boresight during
horizontal tra v e l, short-term transm itter power fluctuations, and
119
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Wheat Date 158
L W 56°
120
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4^
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121
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10 dB above noise floor
«>
£
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c
<
TJ
.Q •
I (V
X »
—
9
<0
40 C
40
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122
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Soybeans Date 188
C VV 16°
- 20 dB above noise floor
ro
CO
Free Space
Free Space
Vegetation
Figure 51.
Attenuation recording of soybeans at C-band, VV
polarization and 16° Incidence angle.
variations in connector loss due to vibration.
is associated with d ig itiza tio n
space reference lin e .
In addition, error
and determination of the free-
I t is estimated that the accuracy of these
measurements is approximately 10%.
The
attenuation
recordings
were
d ig itized
corresponding to approximately 14 cm in
at
length.
intervals
This interval
resulted in approximately 45 samples for the 6 meter canopy strip
length.
In many instances, 90 or more samples were obtained by
repeating the measurement.
The sampling interval was in excess of
the "Nyquist rate" necessary to accurately reproduce the somewhat
"periodic" waveforms.
a mean attenuation
interval
The attenuation data in Appendix B includes
value and the lim its
about that mean.
for the 99% confidence
The confidence interval
lim its were
calculated from:
where ± kc are the confidence interval
standard
deviation
constant
obtained
confidence
and n is
from the
level
chosen.
the
lim its , s is the sample
number of
t-d is trib u tio n ,
This
samples.
depending
procedure
is
c is
a
upon the
valid
for
distributions which are normal with unknown variance or for other
distributions
number
of
with
samples.
approximately normal
unknown variance with
In
this
and even i f
case
a s u ffic ie n tly
the
distributions
they were not,
large
are
the number of
samples is large enough to ensure the v a lid ity of the procedure.
124
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The 99% confidence interval lim its ranged from + 0.1 dB, usually
at L-band to + 2.4 dB for some X-band measurements.
In summary, the experimental procedure used to acquire this
attenuation
data
produced
reasonable
accuracy
and
precision,
comparable to the accuracy and precision of published backscatter
data.
5.2
Angular, Polarization and Frequency Response of Wheat Data
The wheat measurements were conducted at two widely-separated
sites on the same privately-owned wheat f ie ld .
Site W1 was used
for the frequency, angular and polarization studies, while Site W2
was used for the special decapitation experiment which is reported
in Section 5.4.
All wheat attenuation data and associated ground
truth is available in Appendix R.
Table 28 provides a summary of wheat attenuation measurements
at Site W1 on date 135 and date 158.
The attenuation values are
expressed in dB per meter to allow valid comparisons between the
two sets of angular data, as well as comparisons between data on
dates with d ifferen t
canopy heights.
The path length used in
these computations is simply the si ant-1ength through the canopy
and is tabulated in Appendix B.
Figure 52 is a plot of the attenuation data in dB per meter
as measured on date 135.
Noteworthy are the values of attenuation
at 56° versus those at 24°.
The difference is not due to a path
length difference since the data has been normalized to dB per
meter.
125
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TABLE 28.
Sumnary of liie a t Attenuation Measurements
at S ite tfl
ONE-WAY CANOPY LOSS (dB/m)
FREQUENCY (GHz)
POLARIZATION
ANGLE (°)
DATE 135
DATE 158
1.55
1.55
VV
HH
24
24
2.0
2.5
1.1
1.1
4.75
4.75
VV
HH
24
24
2.3
3.3
4.7
3.2
10.20
10.20
VV
HH
24
24
9.4
7.0
9.4
8.1
1.55
1.55
VV
HH
56
56
6.6
2.1
3.7
1.4
4.75
4.75
VV
HH
56
56
24.3
8.3
9.4
3.2
10.20
10.20
VV
HH
56
56
31.9
28.8
19.0
14.1
126
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
o W
□ HH
AW
+ HH
30
24°
24*
56*
56*
Date 135
Date 135
Date 135
Date 135
Mean Canopy Loss (dB/m)
25
20
15
10
1
2
3
4
5
6
7
8
g
10
Frequency (GHz)
Figure 52.
Wheat attenuation measurements on Date 135.
127
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Also noteworthy is the large difference between HH and VV
polarization- at 56°.
and C band,
attenuation
but almost equal
remains
L-band to C-band.
date 158.
The difference is roughly three tines at L
at
re la tiv e ly
X-band.
" fla t"
Note also that the
at
24°,
especially
from
Figure 53 illu s tra te s identical measurements on
By date 158, the wheat plants had dried as compared to
date 135 and the leaf area index was less than one-half of its
value on date
135.
The
comparable on both dates,
24°
attenuation
values
were
roughly
but the 56° values on date 158 were
depressed considerably from those on date 135.
Figure 54 compares
the 56° data on these two dates.
5.3
Angular, P olarization, and Frequency Response of Soybean Data
The soybean measurements were conducted at a single site on a
privately-owned f ie ld .
and
polarization
defoliation
Site SI was used for frequency, angular
studies
and was
experiment which is
also
reported
used
in
for
the
special
Section 5.4.
All
soybean attenuation data and associated ground truth is available
in Appendix B.
Table
29
provides
a
summary
of
soybean
measurements at Site SI on date 181 and date 188.
attenuation
As with wheat,
the attenuation values are expressed in dB per meter.
Path length
used in the computations is available in Appendix B.
Figure 55 is a plot of the soybean attenuation data on date
181 while
Figure
56 plots
identical
measurements on date 188.
Both plots present attenuation data in dB per meter.
The data
taken on date 181 illu s tra te s increasing attenuation with
128
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
«
□
£
+
Mean Canopy Loss (dB/m)
30
W
HH
W
HH
24* Data 158
24* Data 158
56° Oats 158
56° Data 158
25
20
15
10
1
2
3
4
5
6
7
8
9
10
11
Frequency (GHz)
Figure 53.
Wheat attenuation measurements on Date 158.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Wheat
35
o
□
W
HH
a W
+ HH
Mean Canopy Loss (dB/m)
30
56°
56°
56°
56°
Date 135
Date 135
Date 158
Date 158
25
20
15
10
1
2
3
4
5
6
7
8
9
10
11
Frequency (GHz)
F ig u re
54.
A c o m p a riso n o f w heat a tte n u a tio n
a t 56° in c id e n c e a n g le .
on D ates 135 and 158
130
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 29.
Sumary of Soybean Attenuation Measurements
at Site SI
ONE-WAY CANOPY LOSS (dB/m)
FREQUENCY (GHz)
POLARIZATION
ANGLE (°)
DATE 181
DATE 188
1.55
1.55
VV
HH
16
16
3.3
1.1
4.8
1.5
4.75
4.75
VV
HH
16
16
5.8
4.4
7.0
6.7
10.20
10.20
VV
HH
16
16
9.6
10.2
14.4
20.2
1.55
1.55
VV
HH
52
52
2.7
0.7
3.3
0.9
4.75
4.75
VV
HH
52
52
14.3
5.7
12.7
4.0
10.20
10.20
VV
HH
52
52
19.7
13.3
16.0
15.5
131
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Soybeans
35
W
HH
W
HH
Mean Canopy Loss (dB/m)
30
W#
16°
52°
52°
Data 181
Date 181
Date 181
Date 181
3
4
25
20
15
10
5 -
1
2
5
6
7
e
9
10
11
Frequency <GHz)
Figure 55.
Soybean attenuation measurements on Date 181.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Soybeans
35
o W 16°
□ HH 16°
a W 52°
+ HH 52°
Mean Canopy Loss (dB/m)
30
Date 188
Date 188
Date 188
Date 188
25
20
15
10
1
2
3
4
5
6
7
0
9
10
11
Frequency (GHz)
Figure 56.
Soybean attenuation measurements on Date 188.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
frequency
and minimal
angular difference
between 16° and 52°,
except for VV data at C-band and X-band.
Note again that the
difference in path length is not reflected in these plots since
they are in dB per meter.
The data illu s tra te d in Figure 56 is
generally sim ilar to that in Figure 55, except for X-band, HH, 16°
which is nearly twice the value measured approximately one week
e a r lie r.
This
data
point
should
be considered
questionable,
although no errors were apparent in the measurement process or in
d ig itiz a tio n .
The ground truth
as tabulated in Appendix B is
sim ilar for both dates.
5.4
Special Attenuation Experiments
In addition to the primary objective of obtaining data on the
frequency, polarization and angular attenuation characteristics of
vegetation, a number of special experiments were conducted at the
two
test
site s.
These
experiments
included
cross-polarized
attenuation measurements, a wheat decapitation experiment and a
soybean defoliation experiment.
Cross-polarized data was taken on wheat on three dates.
date
135,
VH data
was taken
at
C-band,
56°
at
site
Wl;
On
on
date 150, VH and HV data was taken at C-band, 56° at site W2; and
on date 158,
X-band HV data was taken at 56° at site Wl.
In
referring to cross-polarized measurements, the f ir s t le tte r refers
to the transmit polarization, while the second le tte r refers to
receive
polarization.
horizontally-polarized
with
a
HV
polarization
therefore
means
a
EM wave was transmitted and was received
vertic ally-p o larize d
antenna.
The
cross-polarized
134
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measurements are tabulated in Table 30.
presented
in
dB per meter.
The data
The data in Table 30 is
shows the
interesting
characteristic that cross-polarized attenuation is less than the
attenuation measured for either lik e polarization in a ll cases.
This characteristic is most lik e ly the result of depolarization by
the canopy p a rtia lly compensating for attenuation by the canopy.
Although this data is of theoretical in te re st, i t is not apparent
that i t is of practical value.
A special wheat head decapitation experiment was conducted at
Site W2.
This experiment, conducted at 56° angle of incidence,
consisted
of
attenuation
measurements
at
each
frequency
and
polarization for a normal strip of wheat and for the same strip
with the heads sheared-off (to obtain a uniform height, some stalk
below the head was also removed).
tabulated
in Table
reduced attenuation
showed a slight
31.
in
The data for this experiment is
The data indicates
a ll
increase).
that
decapitation
but the case of L-band,
The decapitation
VV (which
process
however
reduced the average canopy height from 1.11 meters to 0.70 meters
and the path length from 1.59 meters to 0.86 meters.
Table 31
also gives
When the
attenuation
expressed
in
dB per meter.
attenuation is expressed in this fashion, an increase is observed
after decapitation.
fir s t,
examination
Although this
of
a wheat
result may seem puzzling at
canopy
reveals
that
the
upper
portion containing the head is less dense than the lower portion
containing leaves at the growth stage of this experiment.
of the
less
dense head portion
Removal
of the canopy leaves a lower
section which provides greater attenuation when expressed on a per
135
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TABLE 30. Summary of Cross-Polarized Measurements
on Wheat and Corresponding Like-Polarized
Measurements
FREQUENCY
(GHz)
ONE-WAY CANOPY LOSS (dB/m)
POLARIZATION
ANGLE (°)
4.75
4.75
4.75
4.75
VV
HH
HV
VH
56
56
56
56
10.20
10.20
10.20
VV
HH
HV
56
56
56
DATE 135
DATE 150
DATE 158
24.3
8.3
11.3
1.9
0.3
0.8
-----
—
4.5
---
- -
--
19.n
14.1
10.4
136
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 31.
FREQUENCY
(GHz)
POLARIZATION
Uheat Decapitation Experiment Data
NON-DECAPITATED
DECAPITATED
NON-DECAPITATED
CANOPY LOSS (dB)
CANOPY LOSS (dB)
CANOPY LOSS (dB/m)
DECAPITATED
CANOPY LOSS (dB/m)
1.55
1.55
VV
HH
3.2
1.3
3.9
0.9
2.0
0.8
4.5
1.1
4.75
4.75
VV
HH
17.9
3.0
13.1
2.9
11.3
1.9
15.2
3.4
10.20
10.20
VV
HH
31.2
14.1
21.4
8.4
19.6
8.9
24.9
9.8
meter
basis.
It
should
be
noted
that
this
experiment
conducted at a growth stage when the head was s t i l l
was
quite moist
(82.2% H2O) and that d ifferen t results might be obtained a fte r the
head dried and hardened.
A special
site S I.
soybean defoliation
experiment was conducted at
This experiment, conducted at 52° angle of incidence
consisted of a "standard" set of attenuation measurements for the
non-defoliated canopy strip and a second set of measurements with
a ll
leaves removed from approximately one-half of the length of
the canopy s trip .
Figure 57 is a recording of the p a rtia lly
defoliated s trip at X-band, HH polarization.
Note the dramatic
decrease in attenuation for the defoliated section.
tabulation of the soybean defoliation
data.
Table 32 is a
Note that
for VV
polarization, removal of the leaves made almost no difference in
the attenuation value measured, thus indicating that they are of
minor
importance.
At
X-band,
VV,
however,
the
leaves
contribute to the attenuation as the data illu s tr a te s .
polarization,
the
leaves
appear
to
be
a
very
do
For HH
significant
contributor to attenuation at all frequencies, but especially at
X-band.
The results of this experiment can be explained by the
predominately horizontal
predominately
vertical
orientation
orientation
of soybean leaves and the
of
the
primary
stem.
secondary stems tend to be oriented approximately randomly.
results
of
this
experiment
are
quite
significant
in
that
The
The
it
demonstrates that leaf and stem characteristics may be separated
with microwave measurements.
138
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
15 dB above noise floor
Soybeans Date 188
X HH 52°
Defoliation Experiment
C
XQ
»
C
Hh
6m
Free Space
Defoliated Soybeans
Figure 57.
Non-Defollated Soybeans
Recording of soybean d efoliation experiment at X-band,
HH polarization and 52° Incidence angle.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 32.
FREQUENCY
(GHz)
POLARIZATION
Soybean Defoliation Experiment Data
NON-DEFOLIATED
DEFOLIATED
NON-DEFOLIATED
CANOPY LOSS (dB)
CANOPY LOSS (dB)
CANOPY LOSS (dB/m)
DEFOLIATED
CANOPY LOSS (dB/m)
1.55
1.55
VV
HH
2.6
0.7
2.4
0.4
3.3
0.9
3.6
0.6
4.75
4.75
VV
HH
9.9
3.1
8.8
1.7
12.7
4.0
13.1
2.5
10.20
10.20
VV
HH
12.5
12.1
8.3
3.7
16.0
15.5
12.4
5.5
6.0
ATTENUATION MODELING
The
Chapter
attenuation
help
to
measurements
fill
measurements w ill
a
void
presented
in
in
experimental
the
previous
data.
These
assist those involved in modeling backscatter
response in the development and validation of semi-empirical and
theoretical
models.
These measurements can also contribute to
the understanding of the nature of microwave propagation through
a vegetation canopy.
understanding
is
The most effective means of gaining this
to
postulate
mathematical
models
th eir output against the measured attenuation data.
agreement
between
indication
that
observed
the
and
model
predicted
describes
the
data
and
check
Reasonable
is
a
physical
good
process
adequately.
The results
approximations,
presented in this Chapter w ill
not
only
because
of
only be rough
experimental
erro r,
or
possible in a p p lic a b ility of models, but also because there is a
lack of d ie le c tric data on the two crops studied.
data on other vegetation
recently (Ulaby,
properties
of
has,
however,
D ielectric
been greatly expanded
1984c) and useful estimates of the d ie le c tric
wheat
and soybeans
may be derived
from these
measurements.
6.1
D ielectric Properties of Vegetation
A vegetation canopy is a d ie le c tric mixture consisting of
discrete
etc.
d ie le c tric
distributed
d ielectric
in
inclusions
such as leaves,
a host material
stalk,
such as a ir .
f r u it ,
Since the
inclusions are often comparable to a wavelength in
141
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the
microwave
portion
of
inhomogeneous anisotropic
the
spectrum,
medium.
the
canopy
is
an
Propagation through such a
medium is subject to absorption and scattering loss.
Absorption,
often
co e ffic ie n t,
scattering
incidence
described
and scattering,
c o e ffic ie n t,
angle,
d ie le c tric
a
volume
absorption
usually described by a volume
are
ks
by
a
function
constant,
of
volume
polarization,
fraction
and
geometry of the canopy.
The d ie le c tric
measured d ire c tly ,
constant of a vegetation canopy cannot be
so the usual approach to estimation of its
d ie le c tric properties involves d ie le c tric mixing models (Ulaby,
1984a).
All of the d ie le c tric mixing models assume d ie le c tric
inclusions
much smaller
than
a wavelength
in
a host medium.
Since this condition is often violated at microwave frequencies,
the
result
is
only an approximation.
Many d ie le c tric
mixing
models assume a geometry (needles, disks, e tc .) which may not
accurately
describe the
vegetative
inclusions.
In addition,
mixing models require the volume fraction of the inclusion which
is
d if f ic u lt
lim itatio n s,
to
it
estimate
accurately.
Despite
a ll
of
these
is possible to compute a reasonable value for
canopy d ie le c tric
constant
and estimate the volume absorption
c o e ffic ie n t, <a from:
<
3
2 IT e“
2 k e"
= _____£ a_______c
X /e ‘
0
C
X
0
Simple models for calculating the volume scattering coefficient
of a vegetation canopy have not been developed, but this is not
142
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a serious drawback in this analysis, since at the frequencies of
interest loss w ill prim arily be due to absorption.
The d ie le c tric
properties
of a canopy element such as a
leaf or stalk are governed by the d ie le c tric properties of the
dry vegetative material
flu id .
The
d ie le c tric
d iffe rs l i t t l e
constant
of
dry
of the
vegetative
vegetative
material
is dominated by the properties of its
Vegetative flu id has properties sim ilar to water with an
equivalent NaCl
The
properties
from that of a ir , so the d ie le c tric constant of
any vegetative material
f lu id .
and the
s a lin ity of approximately 10 °/oo to 15 °/oo.
d ie le c tric
constant
of
th is
flu id
and
therefore
the
d ie le c tric constant of the vegetative part w ill be a function of
its
flu id
s a lin ity
temperature,
fraction
the
(especially
fraction
of
at
“bound"
(mv) is
and the
its
volume
The volume fraction of
related to its
content (n^) by the vegetation density,
frequencies),
water,
of water in the plant part.
water in a plant
Empirical
lower
gravimetric moisture
pv:
formulas which may be used to estimate
pv
have been
recently reported (Ulaby, 1984c):
Corn Stalks:
py = 0.75
+ 0.25
Corn Leaves:
py = 0.64
+ 0.17
Wheat Stalks:
pv
= 0.76
+ 0.20
Wheat Leaves:
p„ = 0.76
+ 0.20
143
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The recently
available data on vegetative d ie le c tric
constant
(Ulaby, 1984c) is presented as plots of the real and imaginary
parts of the d ie le c tric
fraction of water, my.
constant as a function of the volume
Data is available on wheat heads, leaves
and stalks from 7.6 GHz to 8.4 GHz and on corn leaves and stalks
over
the
following
3.5 GHz to
6.5
frequency
GHz,
ranges:
and 7.6
1.1
GHz to
GHz to 8.4 GHz.
1.9
All
GHz,
reported
measurements were made with a sweep oscillator-waveguide-network
analyzer system.
For purposes of this
report, the d ie le c tric properties of
wheat at the frequencies of interest w ill
be extrapolated from
the
X-band
reported
measurements
on wheat
for
and w ill
be
estimated from reported measurements on com for L-band and Cband.
For soybeans, d ie le c tric data w ill be estimated from corn
data for a ll frequencies.
6.2 Vertical Stalk Absorption Loss Model
The
vertical
model
stalks
to
be
of
used
to
vegetation
estimate
is
a
absorption
uniaxial
crystal
developed at the University of Kansas (Ulaby, 1984a).
applies to a canopy of thin vertical
loss
in
the
stalk
A pplicability
material
model
The model
stalks whose diameter is
much smaller than the wavelength X, where X = X0//e ^
wavelength
of
with
re lative
is
the
p erm ittiv ity
of this model therefore depends upon the
stalk diameter, the water content of the stalk and the signal
wavelength
XQ.
Although
the
model
w ill
not
be
s tr ic tly
144
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
applicable at the higher frequencies used in this study, i t w ill
be used to provide an estimate of stalk absorption loss.
The
uniaxial
containing thin
crystal
parallel
model
assumes
a
d ie le c tric
slab
cylinders oriented along the z-axis.
The slab is therefore an anisotropic d ie le c tric medium with:
« = x ex + y ey + z *2.
Because
of
azimuthal
components
symmetry
ey
*
=
e .
The
y
d ie le c tric
and ez may be related to the d ie le c tric constants
of the inclusions by d ie le c tric mixing formulas.
since ex and
In addition,
are associated with the propagation of a so-
called "ordinary wave" and ez is associated with the propagation
of
an
"extraordinary
wave"
in
the
d ie le c tric
slab,
convenient to use the notation e = e = e and e = e .
x
y
o
z
e
Polder-Van
Santen/deLoor
d ie le c tric
mixing
formula
it
is
The
(Ulaby,
1984a) for needles (stalks) oriented along the z-axis in a ir is
an appropriate mixing formula:
2 v_
£* = £ * = £
=1 +
(e
^
- 1)
St
( 's t * »
' Z = 'e * 1 * vs t ( 's t - U ■
The real and imaginary parts of these expressions are:
. (e*
- 1) (e ‘ + 1) + (e“ )2
e‘ = 1 + 2 v . -------51------------- —---------------- —— ]
St
+
145
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In these expressions the stalk d ie le c tric constant is
- je “t and vst is the volume fraction of stalks in the
canopy.
The uniaxial
crystal
model
is
normally developed in
terms of the complex indices of refraction:
n = n' - j n"
o
o
o
n = n’ - j n”
e
e
J e
The model requires:
= Un»keo}|
ne
For
= l Itni/ee}l
a
•
v e rtic a lly
polarized
wave
propagating
in
a
uniaxial
crystal, the index of refraction is:
nv = no cos2e + ne sin2e*
The stalk absorption loss for this v e rtic a lly polarized wave is:
146
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where h is the canopy height and 0 is the angle of incidence.
For horizontal polarization the stalk absorption loss is:
4 * n" h secB
o
Expressed in dB, the model becomes:
Lfte.v) =
4.343 (4ir) n" h sec8
v
X
o
4.343 ( 4ir)
L f (e,h)
6.3
h sec0
=
Random Leaf Absorption Loss Model
A reasonable
approximation
to
use
in
deriving
a
leaf
absorption loss model is to assume that the leaves are randomly
distributed
within
the
leaves can be ignored.
canopy
and that
interactions
between
Under these conditions, the Polder-Van
Santen/deLoor d ie le c tric mixing formula for thin circu lar disks
(leaves)
in
a ir
may be used to
obtain
a complex d ie le c tric
constant (er £) of the equivalent isotropic medium:
6r t ' 1
(2
- 1 ♦
7
147
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The l e a f a b s o r p t i o n
c o e ffic ie n t,
<a i s :
The leaf absorption loss is:
1.5(0) « exp(ic h sec6) = exp(O
C
In terms of leaf area index the expression becomes:
4it e"g t g sec 6 LAI
L*(0) - exp(-
)
where t A is the mean leaf thickness and LAI is the leaf area
index.
g
6.4
In dB the expression is:
4.343 (4ir)
t^ sec6 LAI
Random Stalk Absorption Loss Model
Some vegetation
canopies
include
a primary
stalk which is approximately randomly oriented.
coefficient
and absorption
loss
for
or secondary
The absorption
such a situation
may be
derived in a sim ilar fashion to that for random leaves.
Polder-Van
Santen/deLoor
mixing
formula
for
random
The
needles
(stalks) in a ir gives the following complex d ie le c tric constant
(erJl) of the equivalent isotropic medium:
»
rs
rs
-I
J rs *
148
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The random s t a l k
a b s o rp tio n
c o e ffic ie n t,
<a i s :
2ir e"
rs
x
o
K
a
The random stalk absorption loss is:
2* e"
l / s (e) - exp(*
a
This
a
expression
absorption
h secQ) = exp(-
h sec 6
X
o
is
equivalent
to
the
expression
loss of random leaves except that
simple expression for e"s in terms of
as accurate.
for
in this
the
case a
is possible, but not
The expression in dB is:
4.343 ( 2ir)
h sec6
X
o
6.5
Wheat Attenuation Model
Wheat
leaves.
w ill
The
interaction
be modeled
assumption
between stalks
as
w ill
vertical
stalks
be
that
made
with
there
random
is
no
and leaves so that the attenuation
for each may be calculated separately and summed to obtain the
total
canopy
attenuation.
Based
upon
the
wheat
head
decapitation experiment reported in Section 5.4, the head w ill
be considered as part of the stalk and the total canopy height
w ill
be used in a ll
computations.
This approximation is valid
for this set of measurements where the head is quite moist, but
may not be valid for situations when the head has dried and loss
149
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
due to scattering increases.
Accurate modeling of the dry wheat
head may require development of a scattering loss model.
Table
content
33
summarizes
(m^,), density
stalk
(py) ,
and
le a f
gravimetric
and volume fraction of water (my)
for the three dates data is available on wheat.
A complete set
of
ground truth data is available in Appendix A.
in
Section 6.1, d ie le c tric data is
the volume fraction
wheat
(Ulaby,
of water,
1984c).
water
Table
As discussed
available as a function of
my and frequency for corn and
34 provides
a summary of the
estimated d ie le c tric constants for wheat stalks and leaves which
was derived from this published data.
The subscript on the e's
in the table heading indicates stalk (s t) or leaves ( i ) and the
superscript indicates the microwave band (L,C ,X).
Additional
ground
truth
and
includes
plant
density
requires
le a f
thickness
necessary
stalk
and
leaf
for
the
diameter.
area
stalk
model
The leaf
model
index.
Both models
require wavelength, angle of incidence and canopy height.
All
necessary data is available in Appendix B.
The output of the models is compared to measured data in
Tables 35 to 37.
Attenuation data is presented in dB per meter
for both calculated and measured values.
k' s
refer to stalks ( s t ) , leaves {&)
The uncertainty
(+) associated
The subscripts on the
and canopy ( c ).
with each model
calculated
attenuation value was determined by assuming that in the worst
case the stalk diameter and the leaf thickness
determined
within
+
20% and
that
the
could only be
density,
d ie le c tric
constant and leaf area index could be determined within + 10%.
150
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 33.
DATE
STALK
Strasary of Wheat Stalk and Leaf
Moisture Data
STALK Pv
STALK m,,
LEAF
LEAF py
LEAF mv
135
0.85
0.84
0.71
0.80
0.81
0.65
150
0.67
0.71
0.47
0.55
0.62
0.34
158
0.76
0.78
0.59
0.64
0.69
0.44
151
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 34.
Summary of Estimated Wheat Leaf and
Stalk D ielectric Constants
ec
st
ex
st
34-j 4
4 0 -jl5
30-jl5
42—j 15
30-j 10
23-3*13
150
16-j 2
21-j 5
18—
j9
20-j 7
12-j 3
9—j 4
158
27-j 3
30-j 10
2 4 -j11
27-jlO
17-35
14-j 7
DATE
est
135
EC
A
H
EX
H
152
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 35.
Predicted Versus Observed Attenuation Data
for Uheat on Date 135
FREOUENCY
(GHz)
ANGLE
POLARIZATION
(°)
MODEL
Ks t(dB/m)
MODEL
MODEL
MEASURED
K*(dR/m)
Kc(dR/m)
*cc(dB/m)
1.55
1.55
VV
HH
24
24
0.5 ±
0.0 ±
0.3
0.0
2.7 ± 1.2
2.7 ± 1.2
3.2 ±
2.7 t
1.5
1.2
2.0 ± 0.5
2.5 t 0.5
4.75
4.75
VV
HH
24
24
5.2 i
0.1 ±
3.4
0.1
5.5 ± 2.5
5.5 ± 2.5
10.7 i
5.6 ±
5.9
2.6
2.3 ± 0.7*
3.3 i 0.5
10.20
10.20
VV
HH
24
24
11.6 i
0.3 t
7.7
0.2
15.3 i 6.9
15.3 ± 6.9
26.9 ± 14.6
15.6 ± 7.1
9.4 i 2.3*
7.0 ± 2.0
1.55
1.55
VV
HH
56
56
1.9 i
0.0 t
1.3
0.0
2.7 ± 1.2
2.7 ± 1.2
4.75
4.75
VV
HH
56
56
21.6 ± 14.3
0.1 t 0.1
10.20
10.20
VV
HH
56
56
47.4 i 31.3
0.3 t 0.2
* Model and measured bands n o n -o v e rla p p in g .
4.6 ±
2.7 t
2.5
1.2
6.6 ± 1.0
2.1 ± 0.5
5.5 ± 2.5
5.5 ± 2.5
27.1 i 16.8
5.6 ± 2.6
24.3 t 2.9
8.3 1 1.8
15.3 ± 6.9
15.3 ± 6.9
62.7 ± 3B.2
15.6 ± 7.1
31.9 ± 3.8
28.8 ± 3.3*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 36.
FREQUENCY
(GHz)
ANGLE
POLARIZATION
(°)
Predicted Versus Observed Attenuation Data
for Wheat on Date 150
MODEL
Ks t (dB/m)
MODEL
MODEL
MEASURED
tc*(dB/m)
Kc (dB/m)
^(dP/m)
1.55
1.55
VV
HH
56
56
0.6 ±
0.0 ±
0.4
0.0
0.4
0.2
0.4 ± 0.2
1.0 ±
0.4 ±
0.6
0.2
2.0 ± 0.8
0.8 ± 0.4
4.75
4.75
VV
HH
56
56
4.7 ±
0.1 ±
3.1
0.1
0.5 i 0.2
0.5 ± 0.2
5.2 i
0.6 i
3.3
0.3
11.3 ± 1.8*
1.9 ± 0.7*
10.20
10.20
VV
HH
56
56
18.1 ± 12.0
0.2 ± 0.2
1.5 i 0.7
1.5 ± 0.7
19.6 i 12.7
1.7 ± 0.9
19.6 ± 3.9
8.9 ± 3.1*
* Model and measured bands non-overlapping.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 37.
FREOIJENCY
(GHz)
ANGLE
POLARIZATION
(°)
Predicted Versus Observed Attenuation Data
for Wheat on Date 158
MODEL
Ks t(dR/m)
MODEL
MODEL
MEASURED
tc*(dB/m)
»cc (dB/m)
icc(dR/m)
1.55
1.55
VV
HH
24
24
0.4 ±
0.0 ±
0.3
0.0
0.5 t 0.2
0.5 ± 0.2
0.9 t
0.5 ±
0.5
0.2
1.1 i 0.2
1.1 t 0.3*
4.75
4.75
VV
HH
24
24
3.6 i
0.1 ±
2.4
0.1
0.8 i 0.4
0.8 t 0.4
4.4 i
0.9 t
2.8
0.5
4.7 i 1.1
3.2 ± 0.7*
10.20
10.20
VV
HH
24
24
8.7 ±
0.3 ±
5.7
0.2
2.5 ± 1.1
2.5 ± 1.1
11.2 ±
2.8 ±
6.8
1.3
9.4 ± 2.6
8.1 i 1.9*
1.55
1.55
VV
HH
56
56
1.5 ±
0.0 ±
1.0
0.0
0.5 i 0.2
0.5 ± 0.2
2.0 ±
0.5 ±
1.2
0.2
3.7 ± 1.0
1.4 ± 0.7
4.75
4.75
VV
HH
56
56
14.7 i
0.1 t
9.7
0.1
0.8 t 0.4
0.8 ± 0.4
15.5 ± 10.1
0.9 ± 0.5
9.4 ± 1.2
3.2 ± 0.9
10.20
10.20
VV
HH
56
56
35.4 t 23.4
0.3 + 0.2
2.5 ± 1.1
2.5 + 1.1
37.9 ± 24.5
2.8 + 1.3
19.0 ± 2.9
14.1 + 2.7*
*Model and measured hands n o n -o v e rla p p in g .
The worst-case uncertainty
associated with the measured value
includes the ± 10% estimated accuracy error plus the precision
estimate.
Examination of the data reveals overlap between observed
and predicted values in most instances.
values do not overlap,
uncertainty
For the cases where
sources of error not
calculations may be responsible.
included in the
These potential
errors include the canopy height measurement and the condition
that the inclusions in the mixing models must be small compared
to a wavelength (which was vio late d ).
6.6
Soybean Attenuation Model
The
soybean
canopy
w ill
be modeled
as
vertical
stalks
representing the primary stems, random stalks representing the
secondary
stems
assumption w ill
and
random
leaves.
As
with
wheat,
be made that there is no interaction
parts so that attenuation
the
between
values may be calculated separately
and summed to obtain the total canopy attenuation.
Table
content
38
summarizes
(m^,), density
( pv )
the
primary
stem gravimetric
and volume fraction of water
water
(m v ) .
Tables 39 and 40 provide identical information for the secondary
stems and leaves.
empirical
since
an
available.
The density values were computed from the
relationship developed for corn given in Section 6.1
equivalent
relationship
for
soybeans
is
not
A complete set of ground truth data is available in
156
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TABLE 38.
Summary of Soybean Primary
Stem Moisture Data
DATE
PRIMARY STEM
PRIMARY STEM
PRIMARY STEM mv
pv
181
0.88
0.91
0.80
188
0.79
0.84
0.66
TABLE 39.
Sumary of Soybean Secondary
Stem Moisture Data
DATE
SECONDARY STEM
SECONDARY STEM py
SECONDARY STEM my
181
0.91
0.93
0.85
188
0.82
0.87
0.71
TABLE 40.
DATE
Sumary of Soybean Leaf Moisture Data
LEAF
LEAF Py
LEAF my
181
0.78
0.67
0.52
188
0.72
0.63
0.45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix B.
The estimated
d ie le c tric
constants tabulated
in
Tables 41, 42, and 43 were derived from the published data for
corn.
The subscripts on the e's in the table headings indicate
primary
stem (p s t),
secondary
stem (sst)
or leaves
(4 );
the
superscript indicates the microwave band (L, C, X).
Additional
model
includes
ground
truth
plant density,
necessary
for
the
primary
stem
stem length and stem diameter.
The secondary stem model requires plant density, stem diameter,
mean number of stems per plant, and mean stem length.
model requires leaf thickness and le a f area index.
The leaf
All models
require wavelength, canopy height and angle of incidence.
All
necessary data is available in Appendix B.
The output of the models is compared to measured data in
Tables 44 and 45.
Attenuation data is presented in dB per meter
for both calculated and measured values.
k' s
The subscripts on the
refer to primary stems (p s t), secondary stems (s s t), leaves
(i ) and canopy (c ).
The uncertainty
(+) associated with each model calculated
attenuation value was determined by assuming that in the worst
case the
primary
and secondary
stem diameters
and the
leaf
thickness could only be determined within + 20% and that the
density,
d ie le c tric
constant,
secondary stem length,
area index could be determined within + 10%.
worst-case
includes
uncertainty
both
the
+
associated
10% estimated
with
and leaf
As with wheat, the
the
accuracy
measured
error
plus
value
the
precision estimate.
158
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TABLE 4 1 .
Sum ary o f Estim ated Soybean
Prim ary Stem D ie le c tr ic Constants
ex
epst
DATE
eL
pst
181
42- j 6
48-j 21
46—j 23
188
31-j 3
38-j 14
30—
j 15
cC
epst
TABLE 42. Sumary of Estimated Soybean
Secondary Stem D ie le c tric Constants
DATE
eL
esst
Esst
C
£X
sst
181
45-j 7
51-j24
50-j25
188
35-j 4
4 0 -jl5
35-j 18
TABLE 43. Summary of Estimated Soybean
Leaf D ie le c tric Constants
DATE
eL
zl
zi
EX
H
ec
181
32—j 12
22-j 7
20-j 9
188
2 7 -jl0
18-j 6
16-j 7
159
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 44.
FREQUENCY
(GHz)
POLARIZATION
Predicted Versus Observed Attenuation Data
for Soybeans on Date 181
ANGLE
MODEL
MODEL
MODEL
MODEL
MEASURED
(°)
KpSf. (dB/m)
Kssj.(dB/m)
KA(dB/m)
Kc (dB/m)
Kc(dB/m)
1.55
1.55
VV
HH
16
16
0.1 ± 0.1
0.0 ± 0.0
0.2 ± 0.2
0.2 ± 0.2
3.2 ± 1.4
3.2 ± 1.4
3.5 ± 1.7
3.4 ± 1.6
3.3 i 0.4
1.1 t 0.2*
4.75
4.75
VV
HH
16
16
1.0 ± 0.7
0.0 ± 0.0
2.1 ± 1.9
2.1 ± 1.9
5.6 ± 2.5
5.6 ± 2.5
8.7 ± 5.1
7.7 ± 4.4
5.8 ± 1.0
4.4 ± 0.7
10.20
10.20
VV
HH
16
16
2.4 ± 1.8
0.0 ± 0.0
4.7 ± 4.3
4.7 ± 4.3
15.5 ± 7.0
15.5 ± 7.0
22.6 ±13.1
20.2 ±11.3
9.6 ± 1.6
10.2 ± 1.6
1.55
1.55
VV
HH
52
52
0.8 ± 0.6
0.0 ± 0.0
0.2 ± 0.2
0.2 ± 0.2
3.7 ± 1.7
3.7 ± 1.7
4.7 ± 2.5
3.9 ± 1.9
4.75
4.75
VV
HH
52
52
8.0 ± 5.8
0.0 ± 0.0
2.3 ± 2.1
2.3 t 2.1
6.6 ± 3.0
6.6 t 3.0
16.9 ±10.9
8.9 ± 5.1
14.3 ± 2.2
5.7 ± 1.1
10.20
10.20
VV
HH
52
52
19.0 ±13.9
0.0 ± 0.0
5.2 ± 4.8
5.2 ± 4.8
18.1 ± 8.2
18.1 ± 8.2
42.3 ±26.9
23.3 ±13.0
19.7 ± 3.6
13.3 ± 2.2
*Model and measured bands non-overlapping.
2.7 ± 0.5
0.7 ± 0.2*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 45.
FREQUENCY
(GHz)
POLARIZATION
Predicted Versus Observed Attenuation Data
fo r Soybeans on Date 188
ANGLE
MODEL
MODEL
MODEL
MODEL
MEASURED
(°)
Kpst(dB/m)
Ks s t(dB/m)
^(dB/m)
Kc (dB/m)
Kc (dB/m)
1.55
1.55
VV
HH
16
16
0.0 ± 0.0
0.0 ± 0.0
0.1 ± 0.1
0.1 ± 0.1
2.0 ± 0.9
2.0 ± 0.9
2.1 ± 1.0
2.1 i 1.0
4.8 ± 0.7*
1.5 ± 0.4
4.75
4.75
VV
HH
16
16
0.6 ± 0.4
0.0 ± 0.0
1.2 i 1.1
1.2 ± 1.1
3.7 i 1.7
3.7 i 1.7
5.5 ± 3.2
4.9 ± 2.8
7.0 ± 1.5
6.7 ± 1.1
10.20
10.20
VV
HH
16
16
1.4 ± 1.0
0.1 + 0.1
3.1 ± 2.9
3.1 + 2.9
9.2 t 4.1
9.2 ± 4.1
13.7 ± 8.0
12.4 ± 7.1
14.4 + 2.8
20.2 ± 3.4
1.65
1.55
VV
HH
52
52
0.3 ± 0.2
0.0 ± 0.0
0.1 ± 0.1
0.1 ± 0.1
2.2 i 1.0
2.2 i 1.0
2.6 ± 1.3
2.3 ± 1.1
3.3 ± 0.6
0.9 ± 0.3
4.75
4.75
VV
HH
52
52
4.7 ± 3.4
0.0 ± 0.0
1.3 ± 1.2
1.3 ± 1.2
4.0 ± 1.8
4.0 ± 1.8
10.0
6.4
5.3 ± 3.0
12.7 ± 2.2
4.0 ± 0.7
10.20
10.20
VV
HH
52
52
10.8 ± 7.9
0.1 ± 0.0
3.3 ± 3.0
3.3 ± 3.0
9.9 ± 4.5
9.9 ± 4.5
24.0 ±15.4
13.3 i 7.5
16.0 ± 3.2
15.5 ± 2.7
*Model and measured hands non-overlapping.
Examination of the data reveals overlap between observed and
predicted values in a ll but three instances.
sources of potential
The unaccounted for
error are the same as those indicated for
wheat.
The model
defoliation
output
is
also
re la tiv e ly
consistent
with
the
experiment which demonstrated that the primary and
secondary stems were much more important for W polarization as
compared to HH polarization.
7 .0
CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK
The
develop
two
major
objectives
of
this
an improved semi-empirical
vegetation
and to
obtain
data
model
on the
investigation
for
were to
backscatter
frequency,
angular
from
and
polarization response of attenuation due to vegetation canopies.
Both of these major objectives were accomplished, as well
number of supporting objectives.
have contributed to the fie ld
as a
Although these accomplishments
of microwave remote sensing and
microwave propagation, they only point to the need for additional
work in this area.
This Chapter w ill provide a b rief summary of
the important conclusions that can be drawn from this work and
suggest directions for additional research e ffo rts .
7.1
Conclusions
The 1979 backscatter measurements were significant
in that
they were the f ir s t to include leaf area index as a ground truth
parameter and were the f ir s t backscatter measurements at 35 GHz
162
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
over a growing season.
suitable
for
detailed
drawback, several
The data
modeling
acquired,
e ffo rts .
however, was not
In
spite
of
this
key conclusions can be drawn from this data.
The data demonstrated that dynamic range increases with frequency
over the 8-35 GHz range and that dynamic range is greatest for VV
p olarization.
Another conclusion which may be drawn from this
data is that W and HV polarization decorrelates with frequency
much faster than HH polarization over the 8-35 GHz range.
The
data also showed that angular decorrelation is minimal from 30° to
70° over the 8-18 GHz range.
Diurnal experiments on the 1979 data
showed that such variations are not important for corn, sorghum
and
wheat
over
the
8-35
GHz
range.
The
most
important
contribution of the 1979 experiment, however, was to provide the
experience
which
necessary to design an improved experiment
would
produce
high-quality
of the
1980 data
data
suitable
for
in
1980
modeling
studies.
Analysis
provided valuable relationships
between key plant parameters over a growing season.
Especially
important was the fact that many of these parameters are highly
correlated with each other.
area
index was the
best
The study also demonstrated that le a f
single
parameter to
use in
modeling
studies, at least at 17 GHz.
The semi-empirical model developed in this study provides a
direct link to more complex theoretical models, but is re la tiv e ly
simple mathematically and u tiliz e s commonly measured ground truth
parameters.
The model also provides an estimate of the loss due
to leaf and stalk absorption and leaf scattering.
Because of the
163
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high
correlation
between
plant
parameters,
it
was shown that
alternate models could also provide good f it s to the data.
demonstrated, however, that a good f i t
I t was
is not the only criterio n
to be met in judging the performance of a model; equally important
is the prediction of a re a lis tic value for canopy attenuation.
Data
on
canopy
attenuation
as
incidence angle and polarization
modeling studies.
a
function
of
frequency,
has been the missing lin k
in
The 1984 attenuation experiment was a f ir s t
step toward f il l i n g
this
void.
soybean
w ill
not
attenuation
The data acquired on wheat and
only
provide
those who have an
interest in modeling with a check on the v a lid ity of th e ir models,
but w ill also contribute greatly to the understanding of microwave
propagation through a vegetation canopy.
The attenuation models
proposed in this study provided an output which was in reasonable
agreement with the measurements, so this is an indication that at
least
a
basic
understanding
of
the
processes
involved
is
available.
7.2
Recommendations for Future Work
As indicated
additional
previously,
there
is
a continuing
need
for
ground-based studies to complement data which may be
acquired by s a te llite systems.
In the area of backscatter modeling, the proposed model, as
well as the alternate models, need to be tested on a wide variety
of crops.
The data acquired must be of a quality comparable to
the 1980 data u tiliz e d in this study.
Work should also continue
on improving the performance of semi-empirical models.
A possible
164
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area for improvement would be to u tiliz e ground truth taken both
by layer and by part
in the proposed model and
the alternate
models.
Simultaneously with the backscatter data acquisition for the
modeling studies, attenuation data should be acquired on the same
fie ld s as a function of frequency, angle and polarization.
This
data would provide a direct validation for the backscatter models
developed and would enlarge the available attenuation data base
which
would
lead
to
increased understanding.
Also
to
aid
understanding of the propagation of microwaves through vegetation,
additional
data
vegetative
parts.
applicable for
needed
on
D ie lectric
vegetative
also be useful.
improved
is
Work
attenuation
the
d ie le c tric
mixing
models
parts
which
are
of
fu lly
at microwave frequencies would
should also
models,
properties
as
continue on
the
ones
thedevelopment of
u tiliz e d
in
this
investigation are only marginally applicable at the frequencies of
in te re s t.
In summary, much work remains to be done.
sensors
w ill
provide
additional data
suggest more detailed ground studies.
which
w ill
Satellite-based
most
lik e ly
The late 1980's and 19901s
w ill be an exciting and challenging period for researchers in this
f ie ld .
165
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REFERENCES
Allen, C. T. (1984), “Modeling the Temporal Behavior of the
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Dutch ROVE Program," IEEE Transactions on Geoscience and Remote
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Evans, L. T. (1975), Crop Physiology, Cambridge University Press.
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Eyton, R. J ., R. L i, and F. T. Ulaby (1979), "Combined Radar and
Landsat Multitemporal Crop C lassificatio n ," Remote Sensing
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Fung, A. K., and H. S. Fung (1977), "Application of First-Order
Renormalization Method to Scattering from a Vegetation-Like
Half-Space," IEEE Transactions on Geoscience Electronics, October.
Fung, A. K. (1979), "Scattering from a Vegetation Layer," IEEE
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Graf, G. (1978), "High Resolution Imaging of Radar Targets with
Microwaves," Proceedings of the M ilita ry Microwave Conference,
London, England, October.
Hodges, T. and E. T. Kanemasu (1977), "Modeling Daily Dry Matter
Production of Winter Wheat," Agronomy Journal, Vol. 69.
Hoekman, D. H., L. Krul, and E. P. W. Attema (1982), "A M ultilayer
Model for Radar Backscattering from Vegetation Canopies," Oigest
of the 2nd IEEE I n t l . Geoscience and Remote Sensing Symp., Munich,
West Germany, 1-4 June.
Huet, M. (1983), "Evolution des parametres de structure et de
biomass d'un couvert de ble. U tilis a tio n des techniques de
teledection micro-ondes," Ph.D. dissertation , L'Universite Paul
Sabatier de Toulouse, Toulouse, France, October.
Kanemasu, E. T. (1974), "Seasonal Canopy Reflectance Patterns of
Wheat, Sorghum, and Soybeans," Remote Sensing of Environment,
Vol. 3.
Kanemasu, E. T ., L. R. Stone, and W. L. Powers (1976),
“Evapotranspiration Model Tested for Soybeans and Sorghum,"
Agronomy Journal, Vol. 68.
Kanemasu, E. T. (1977), "An Evaluation of an Evapotranspiration
M
od^l
.
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• • •
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11 Anrrmr\rm/
9
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£0
•
LeToan, T. (1982), “Active Microwave Signature of Soil and Crops,"
Digest, 2nd Annual International Geoscience and Remote sensing
Symposium, Munich, West Germany. June.
L i, R. Y., F. T. Ulaby, and J. R. Eyton (1980), "Crop
C lassification with a Landsat/Radar Sensor Combination," presented
at the Sixth Purdue Symposium on Machine Processing of Remotely
Sensed Data, Purdue University, West Layfayette, Indiana, June.
Lopes, A. (1983), "Etude experimentale et theorique de
11attentuation et de la retrodiffusion des micro-ondes par un
couvert de ble. Application a la teledection," Ph.D.
dissertation, L'Universite Paul Sabatier de Toulouse, Toulouse,
France. October,
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Lopez, J. M. (1979), "RAMES: A Ground-Based Radar for Microwave
Remote Sensing Experiment," Proceedings of the EARSeL, Workshop
Report: Microwave Remote Sensing on Bare S o il, Paris, France,
A p ril.
Mo, T ., T. J. Schmugge, and T. J. Jackson (1984), "Calculations of
Radar Backscattering Coefficient of Vegetation-Covered S oils,"
Remote Sensing of Environment, Vol. 15, pp. 119-133.
Moe, R. D. (1974), “Spectral Characteristics of Cultivated Crops
at Microwave Frequencies," Ph.D. Dissertation, University of
Kansas, Lawrence, Kansas, A p ril.
Paris, J. (1984), "Effects of Vegetation Canopy Structure on
Microwave Scattering," NASA Technical Memorandum 86078, NASA
Goddard Space Flight Center, Greenbelt, Maryland, March.
Peake, W. H. (1959), “Interaction of Electromagnetic Waves with
Some Natural Surfaces," IRE Transactions on Antennas and
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Peake, W. H., and T. L. Oliver (1971), "The Response of
T errestrial Surfaces at Microwave Frequencies," OSURF Report
Number 2440-7, Electroscience Laboratory, Ohio State University,
Columbus, Ohio, May.
Schlude, F. (1978), "Analysis of Remote Sensing Payload for the
Spacelab D3 Mission," European Space Agency TT-482.
Shutko, A. M., and A. A. Chukhlantsev (1981), "Microwave Radiation
P e culiarities of Vegetative Covers," presented at URSI Meeting,
University of Kansas, Lawrence, Kansas, January.
Sieber, A. J. (1979), "Signatures of Vegetation and Bare Soil in a
High Resolution Radar Measurement Mode (8-18 GHz)," Proceedings of
the Symposium of Measurement Physics, DFVLR, Oberpfaffenhoffen,
West Germany, December.
Sieber, A. J ., and J. W. Trevett (1983), “Comparison of
Multi frequency Band Radars for Crop C lassification," IEEE
Transactions on Geoscience and Remote Sensing, July.
S tile s , W. H., D. Brunfeldt, and F. T. Ulaby (1979), "Performance
Analysis of the MAS (Microwave Active Spectrometer) Systems:
C alibration, Precision and Accuracy," Remote Sensing Laboratory
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In c ., Lawrence, Kansas, A p ril.
Story, A. G. (1968), "Scattering of Centimeter-Wavelength
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Ohio State University, Columbus, Ohio.
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Story, A. G., W. H. Johnson, and R. E. Stewart (1970), "Remote
Measurement of Concentration and Height of Heads of Standing Grain
with Microwave Energy," Transactions of the ASAE, Vol. 13, No. 1,
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Transactions on Antennas and Propagation, Vol. AP-23, No. 1,
pp. 36-45, January.
Ulaby, F. T ., T. F. Bush, and P. P. Batlivala (1975b), "Radar
Response to Vegetation I I : 8-18 GHz Band," IEEE Transactions on
Antennas and Propagation, Vol. AP-23, No. 5, pp. 608-618,
September.
Ulaby, F. T ., and T. F. Bush (1975c), "Corn Growth as Monitored by
Radar," Remote Sensing Laboratory Technical Report 177-57,
University of Kansas Center for Research, In c ., November.
Ulaby, F. T ., and T. F. Bush (1976), "Monitoring Wheat Growth with
Radar," Photogrammetric Engineering and Remote Sensing, Vol. 42,
No. 4, pp. 557-568, A p ril.
Ulaby, F. T ., and G. Burns (1979a), "S tatistical Properties of the
Radar Scattering Coefficient of Agricultural Crops," Remote
Sensing Laboratory Technical Report 360-2, University of Kansas
Center for Research, In c., Lawrence, Kansas, July.
Ulaby, F. T ., and J. E. Bare (1979b), "Look Direction Modulation
Function of the Radar Backscattering Coefficient of Agricultural
Fields," Photogrammetric Engineering and Remote Sensing, Vol. 45,
pp. 1495-1506, November.
Ulaby, F. T ., W. H. S tile s , D. R. Brunfeldt, and M. E. Lubben
(1979c), "MAS 8-18/35 Scatterometer," Remote Sensing Laboratory
Technical Report 360-5, University of Kansas Center for Research,
In c., Lawrence, Kansas, February.
Ulaby, F. T ., R. K. Moore, and A. K. Fung (1981), Microwave Remote
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Uocl ay P'jbl i S ftl
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Ulaby, F. T ., R. K. Moore, and A. K. Fung (1982), Microwave Remote
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A p ril.
Ulaby, F. T ., R. K. Moore, and A. K. Fung (1984a) Microwave Remote
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^ublisning Company, Menlo Park, C a lifo rn ia.
170
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Ulaby, F. T ., C. T. Allen, and G. Eger I I I (1984b), "Relating the
Microwave Backscattering Coefficient to Leaf Area Index," Remote
Sensing of Environment. Vol. 14, pp. 113-133.
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Wilson, E. A., D. R. Brunfeldt, F. T. Ulaby, and J. C. Holtzman
(1980), "Circularly Polarized Measurements of Radar Backscatter
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ETL-0201, February.
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Documentation," Remote Sensing Laboratory Technical Memorandum
360-2, University of Kansas Center for Research, In c ., Lawrence,
Kansas, June.
171
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX A
Model A Predicted and Observed Backscatter
Data and Associated Ground Truth
A1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.87
DATE
168
170
176
178
182
190
192
196
198
204
206
210
213
221
225
231
240
247
8.6 GHz
Model A
rms error = 0.66 dB A = 0 .09
®§(dB)
- 9.94
- 9.07
- 8.84
- 8.37
- 8.68
- 7.82
- 8.81
- 8.37
- 8.75
- 9.55
- 9.96
- 9.85
- 9.73
-10.04
-10.28
- 9.34
-12.50
-11.41
of(dB)
LAI
- 9.58
- 9.52
- 8.14
- 8.69
- 8.94
- 8.20
- 8.37
- 8.61
- 8.35
- 8.63
- 8.69
- 8.71
- 8.87
- 9.19
- 9.52
- 9.49
-12.90
-10.86
0.97
1.17
1.77
1.96
2.33
3.41
3.37
3.31
3.30
3.24
3.21
3.09
2.96
2.41
2.05
1.46
0.56
0.06
W
Cl
B = 0.83
MPHLEAF
0.18
0.24
0.40
0.44
0.51
0.61
0.62
0.64
0.65
0.65
0.65
0.63
0.62
0.56
0.53
0.47
0.35
0.22
C = 1.05
MSV0L
0.04
0.03
0.22
0.13
0.07
0.12
0.09
0.04
0.33
0.12
0.08
0.10
0.05
0.10
0.10
0.25
0.05
0.19
D = 0.09
MPHSTALK
N
0.24
0.33
1.03
1.28
1.79
2.58
2.71
2.87
2.91
2.90
2.87
2.76
2.66
2.34
2.17
6
6
7
1.92
1.56
1.31
8
11
13
14
15
16
16
16
16
16
16
16
16
16
16
A2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.87
DATE
168
170
176
178
182
190
192
196
198
204
206
210
213
217
221
225
231
240
247
8 .6 GHz
Node! A
rms error = 0.78 dB A = 0.09
®S(dB)
-10.36
- 8.82
- 7.88
- 8.01
- 8.12
- 7.53
- 8.27
- 7.61
- 7.69
- 8.20
- 9.06
- 8.63
- 8.15
- 8.63
- 9.34
- 9.67
- 9.15
-11.90
-11.10
°p°(dB)
LAI
- 9.73
- 9.95
- 8.40
- 9.12
- 9.40
- 8.40
- 8.57
- 8.72
- 8.56
- 8.74
- 8.85
- 9.02
- 9.23
- 9.11
- 9.38
- 9.80
- 9.39
-13.13
-10.52
0.84
1.00
1.51
1.68
1.99
3.05
3.02
3.01
2.99
2.83
2.75
2.56
2.42
2.29
2.01
1.70
1.18
0.44
0.03
W
C2
B = 0.83
MPHLEAF
0.17
0.23
0.38
0.42
0.49
0.57
0.58
0.59
0.60
0.59
0.58
0.56
0.54
0.51
0.48
0.44
0.38
0.28
0.18
C = 1.05
MSV0L
0.05
0.03
0.23
0.12
0.06
0.10
0.06
0.03
0.16
0.14
0.11
0.09
0.05
0.11
0.09
0.08
0.24
0.06
0.20
D = 0.09
MPHSTALK
0.29
0.36
1.04
1.28
1.72
2.36
2.46
2.57
2.60
2.57
2.54
2.44
2.36
2.24
2.11
1.98
1.80
1.56
1.40
N
6
6
7
8
11
13
14
15
16
16
16
16
16
16
16
16
16
16
16
A3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.86
)ATE
165
168
170
171
176
178
182
189
190
192
196
198
204
206
210
213
217
220
221
225
231
240
247
8 .6 GHz
Model A
rms error = 0.93 dB A = 0. 09
°°(dB)
-10.30
- 9.68
- 8.64
- 9.05
- 8.36
- 8.36
- 7.98
- 7.65
- 7.64
- 8.67
- 8.12
- 8.62
- 8.34
- 9.74
- 9.49
- 9.61
-10.09
- 9.74
-10.00
-10.24
- 9.70
-13.50
-10.92
«f(dB)
LAI
- 8.61
- 9.27
- 9.17
- 9.17
- 8.40
- 8.55
- 8.62
- 7.96
- 8.04
- 8.16
- 8.33
- 8.21
- 8.32
- 8.40
- 8.57
- 8.74
- 8.65
- 9.13
- 9.37
- 9.95
-10.24
-15.32
-11.08
0.94
1.35
1.63
1.78
2.49
2.77
3.27
4.46
4.45
4.42
4.36
4.33
4.24
4.14
3.86
3.57
3.14
2.75
2.62
2.06
1.23
0.26
0.08
W
C3
B = 0.83
MPHLEAF
0.18
0.31
0.39
0.43
0.59
0.64
0.73
0.83
0.84
0.86
0.87
0.88
0.86
0.85
0.82
0.80
0.75
0.72
0.71
0.65
0.56
0.40
0.25
C = 1.05
MSV0L
0.11
0.05
0.04
0.04
0.24
0.19
0.11
0.25
0.19
0.14
0.04
0.43
0.23
0.13
0.09
0.10
0.49
0.27
0.17
0.16
0.33
0.06
0.21
D = 0..09
MPHSTALK
0.42
0.44
0.63
0.74
1.40
1.67
2.20
2.88
2.95
3.05
3.17
3.20
3.15
3.10
2.98
2.88
2.73
2.61
2.56
2.40
2.16
1.80
1.54
N
5
6
6
6
7
8
11
11
13
14
15
16
16
16
16
16
16
16
16
16
16
16
16
A4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
168
170
176
178
182
190
192
196
198
204
206
210
213
221
225
231
240
247
- 8.64
- 8.28
- 7.33
- 7.34
- 7.75
- 7.01
- 7.11
- 7.22
- 7.38
- 8.01
- 7.83
- 8.05
- 8.53
- 8.98
- 9.19
- 8.48
-11.61
-10.73
CO
°o(dB)
Cl
)ATE
rms error = 0.45 dB A = 0. 14
rfo
r = 0.93
1 3 .0 S te
Model A
- 8.50
- 8.48
- 7.65
- 7.91
- 7.92
- 7.12
- 7.25
- 7.42
- 7.36
- 7.50
- 7.53
- 7.58
- 7.70
- 8.10
- 8.45
- 8.81
-11.80
-10.32
LAI
0.97
1.17
1.77
1.96
2.33
3.41
3.37
3.31
3.30
3.24
3.21
3.09
2.96
2.41
2.05
1.46
0.56
0.06
W
Cl
B = 1.35
MPHLEAF
0.18
0.24
0.40
0.44
0.51
0.61
0.62
0.64
0.65
0.65
0.65
0.63
0.62
0.56
0.53
0.47
0.35
0.22
C = 1.32
MSVOL
0.04
0.03
0.22
0.13
0.07
0.12
0.09
0.04
0.33
0.12
0.08
0.10
0.05
0.10
0.10
0.25
0.05
0.19
0 = 0 . 03
MPHSTALK
0.24
0.33
1.03
1.28
1.79
2.58
2.71
2.87
2.91
2.90
2.87
2.76
2.66
2.34
2.17
1.92
1.56
1.31
N
6
6
7
8
11
13
14
15
16
16
16
16
16
16
16
16
16
16
A5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.69
)ATE
168
170
176
178
182
190
192
196
198
204
206
210
213
217
221
225
231
240
247
*
-
-
•
-
-
*
1 3 .0 GHz
Model A
rms error = 0.92 dB A = 0. 14
°S(dB)
cf(dB)
LAI
9.51
7.54
6.74
7.31
7.04
6.28
6.63
6.71
7.00
7.69
7.73
7.69
8.09
8.53
8.73
8.70
9.00
9.42
9.75
- 8.71
- 8.90
- 7.95
- 8.32
- 8.35
- 7.32
- 7.44
- 7.53
- 7.49
- 7.66
- 7.74
- 7.89
- 8.03
- 8.00
- 8.26
- 8.64
- 8.67
-11.91
- 9.65
0.84
1.00
1.51
1.68
1.99
3.05
3.02
3.01
2.99
2.83
2.75
2.56
2.42
2.29
2.01
1.70
1.18
0.44
0.03
W
C2
B = 1.35
MPHLEAF
0.17
0.23
0.38
0.42
0.49
0.57
0.58
0.59
0.60
0.59
0.58
0.56
0.54
0.51
0.48
0.44
0.38
0.28
0.18
C = 1.32
MSVOL
0.05
0.03
0.23
0.12
0.06
0.10
0.06
0.03
0.16
0.14
0.11
0.09
0.05
0.11
0.09
0.08
0.24
0.06
0.20
0 = 0 . .03
MPHSTALK
0.29
0.36
1.04
1.28
1.72
2.36
2.46
2.57
2.60
2.57
2.54
2.44
2.36
2.24
2.11
1.98
1.80
1.56
1.40
N
6
6
7
8
11
13
14
15
16
16
16
16
16
16
16
16
16
16
16
A6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.92
)ATE
165
168
170
171
176
178
182
189
190
192
196
198
204
206
210
213
217
220
221
225
231
240
247
.
*
•
•
•
•
•
•
•
-
1 3 .0 GHz
Model A
rms error = 0.69 dB A = 0. 14
®S(dB)
c£(dB)
LAI
9.31
8.94
7.95
8.44
7.63
7.84
7.71
7.50
7.28
7.49
7.20
8.43
8.23
8.10
7.86
8.13
8.77
8.52
8.37
9.45
10.44
12.70
11.02
- 7.79
- 8.40
- 8.34
- 8.32
- 7.86
- 7.85
- 7.73
- 7.05
- 7.10
- 7.17
- 7.30
- 7.30
- 7.34
- 7.39
- 7.54
- 7.72
- 7.90
- 8.26
- 8.43
- 9.03
- 9.83
-14.54
-10.50
0.94
1.35
1.63
1.78
2.49
2.77
3.27
4.46
4.45
4.42
4.36
4.33
4.24
4.14
3.86
3.57
3.14
2.75
2.62
2.06
1.23
0.26
0.08
W
C3
B = 1.35
MPHLEAF
0.18
0.31
0.39
0.43
0.59
0.64
0.73
0.83
0.84
0.86
0.87
0.88
0.86
0.85
0.82
0.80
0.75
0.72
0.71
0.65
0.56
0.40
0.25
C = 1.32
MSV0L
0.11
0.05
0.04
0.04
0.24
0.19
0.11
0.25
0.19
0.14
0.04
0.43
0.23
0.13
0.09
0.10
0.49
0.27
0.17
0.16
0.33
0.06
0.21
D = 0..03
MPHSTALK
0.42
0.44
0.63
0.74
1.40
1.67
2.20
2.88
2.95
3.05
3.17
3.20
3.15
3.10
2.98
2.88
2.73
2.61
2.56
2.40
2.16
1.80
1.54
N
5
6
6
6
7
8
11
11
13
14
15
16
16
16
16
16
16
16
16
16
16
16
16
A7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.93
DATE
168
170
176
178
182
190
192
196
198
204
206
210
213
221
225
231
240
247
17.0 GHz
Model A
rms error = 0.66 dB A = 0.15
°§(dB)
- 9.54
- 7.76
- 7.90
- 6.83
- 6.91
- 6.65
- 6.87
- 6.71
- 7.10
- 6.98
- 7.37
- 8.25
- 7.96
- 8.68
- 9.09
- 8.39
-12.65
-11.27
<£(dB)
LAI
- 8.30
- 8.20
- 7.44
- 7.59
- 7.55
- 6.75
- 6.88
- 7.04
- 7.00
- 7.12
- 7.15
- 7.20
- 7.31
- 7.72
- 8.09
- 8.59
-11.59
-11.27
0.97
1.17
1.77
1.96
2.33
3.41
3.37
3.31
3.30
3.24
3.21
3.09
2.96
2.41
2.05
1.46
0.56
0.06
W
Cl
B = 1.26
MPHLEAF
0.18
0.24
0.40
0.44
0.51
0.61
0.62
0.64
0.65
0.65
0.65
0.63
0.62
0.56
0.53
0.47
0.35
0.22
C = 0.97
MSV0L
0.04
0.03
0.22
0.13
0.07
0.12
0.09
0.04
0.33
0.12
0.08
0.10
0.05
0.10
0.10
0.25
0.05
0.19
D = 0.03
MPHSTALK
0.24
0.33
1.03
1.28
1.79
2.58
2.71
2.87
2.91
2.90
2.87
2.76
2.66
2.34
2.17
1.92
1.56
1.31
N
6
6
7
8
11
13
14
15
16
16
16
16
16
16
16
16
16
16
A8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.78
3ATE
168
170
176
178
182
190
192
196
198
204
206
210
213
217
221
225
231
240
247
1 7 .0 GHz
Model A
rms error = 0.96 dB A = 0. 15
o?(dB)
8.39
_ 7.41
6.82
- 6.89
6.25
6.84
6.62
_ 6.37
_ 6.23
6.26
7.26
8.01
- 7.87
- 8.26
8.44
8.01
7.34
9.48
10.40
<£(dB)
LAI
- 8.59
- 8.65
- 7.78
- 8.02
- 7.98
- 6.95
- 7.06
- 7.15
- 7.13
- 7.29
- 7.37
- 7.52
- 7.65
- 7.65
- 7.91
- 8.31
- 8.58
-11.84
-10.72
0.84
1.00
1.51
1.68
1.99
3.05
3.02
3.01
2.99
2.83
2.75
2.56
2.42
2.29
2.01
1.70
1.18
0.44
0.03
W
C2
B = 1.26
MPHLEAF
0.17
0.23
0.38
0.42
0.49
0.57
0.58
0.59
0.60
0.59
0.58
0.56
0.54
0.51
0.48
0.44
0.38
0.28
0.18
C = 0.97
MSV0L
0.05
0.03
0.23
0.12
0.06
0.10
0.06
0.03
0.16
0.14
0.11
0.09
0.05
0.11
0.09
0.08
0.24
0.06
0.20
0 = 0 . .03
MPHSTALK
0.29
0.36
1.04
1.28
1.72
2.36
2.46
2.57
2.60
2.57
2.54
2.44
2.36
2.24
2.11
1.98
1.80
1.56
1.40
N
6
6
7
8
11
13
14
15
16
16
16
16
16
16
16
16
16
16
16
A9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.94
DATE
165
168
170
171
176
178
182
189
190
192
196
198
204
206
210
213
217
220
221
225
231
240
247
rms error = 0.69 dB A = 0.15
°°(dB)
- 8.97
- 8.91
- 7.96
- 8.05
- 7.07
- 6.86
- 6.78
- 6.22
- 6.53
- 7.19
- 7.08
- 7.15
- 7.63
- 7.90
- 8.29
- 8.49
- 8.64
- 8.75
- 8.12
- 8.68
- 8.81
-14.50
-12.42
W
17.0 GHz
Model A
°p(dB)
LAI
- 7.81
- 8.11
- 7.99
- 7.95
- 7.51
- 7.47
- 7.32
- 6.66
- 6.71
- 6.78
- 6.90
- 6.91
- 6.95
- 7.00
- 7.14
- 7.31
- 7.52
- 7.87
- 8.03
- 8.63
- 9.61
-14.48
-11.38
0.94
1.35
1.63
1.78
2.49
2.77
3.27
4.46
4.45
4.42
4.36
4.33
4.24
4.14
3.86
3.57
3.14
2.75
2.62
2.06
1.23
0.26
0.08
C3
B = 1.26
MPHLEAF
0.18
0.31
0.39
0.43
0.59
0.64
0.73
0.83
0.84
0.86
0.87
0.88
0.86
0.85
0.82
0.80
0.75
0.72
0.71
0.65
0.56
0.40
0.25
C = 0.97
MSV0L
0.11
0.05
0.04
0.04
0.24
0.19
0.11
0.25
0.19
0.14
0.04
0.43
0.23
0.13
0.09
0.10
0.49
0.27
0.17
0.16
0.33
0.06
0.21
D = 0.03
MPHSTALK
0.42
0.44
0.63
0.74
1.40
1.67
2.20
2.88
2.95
3.05
3.17
3.20
3.15
3.10
2.98
2.88
2.73
2.61
2.56
2.40
2.16
1.80
1.54
N
5
6
6
6
7
8
11
11
13
14
15
16
16
16
16
16
16
16
16
16
16
16
16
A10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.96
)ATE
168
170
176
178
190
192
196
198
204
206
210
213
221
225
231
240
247
rms error = 0.63 dB
< # dB)
_ 7.79
7.05
•
6.62
7.24
•
6.33
*
6.48
*
6.34
6.70
•
7.64
7.39
6.60
8.16
•
7.80
*
8.77
•
8.41
• 12.53
- 11.84
3 5 .6 GHz
Model A
A = 0. 14
Op°(dB)
LAI
- 7.82
- 7.56
- 6.59
- 6.88
- 6.36
- 6.51
- 6.70
- 6.62
- 6.76
- 6.79
- 6.82
- 6.92
- 7.28
- 7.63
- 8.03
-11.28
-11.34
0.97
1.17
1.77
1.96
3.41
3.37
3.31
3.30
3.24
3.21
3.09
2.96
2.41
2.05
1.46
0.56
0.06
W
Cl
B = 0.50
MPHLEAF
0.18
0.24
0.40
0.44
0.61
0.62
0.64
0.65
0.65
0.65
0.63
0.62
0.56
0.53
0.47
0.35
0.22
C = 0.88
MSV0L
0.04
0.03
0.22
0.13
0.12
0.09
0.04
0.33
0.12
0.08
0.10
0.05
0.10
0.10
0.25
0.05
0.19
0 = 0 . 14
MPHSTALK
0.24
0.33
1.03
1.28
2.58
2.71
2.87
2.91
2.90
2.87
2.76
2.66
2.34
2.17
1.92
1.56
1.31
N
6
6
7
8
13
14
15
16
16
16
16
16
16
16
16
16
16
A ll
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.82
)ATE
168
170
176
190
192
196
198
204
206
210
213
217
221
225
231
240
247
-
3 5 .6 GHz
Model A
W
C2
rms error = 0.88 dB A = 0. 14 B = 0.50
Ǥ(dB)
<£(dB)
LAI
9.24
8.35
6.65
6.57
6.24
6.34
6.70
7.12
7.00
7.41
7.40
7.60
6.72
7.13
7.76
8.78
11.12
- 8.15
- 8.04
- 6.94
- 6.54
- 6.67
- 6.78
- 6.74
- 6.90
- 6.99
- 7.14
- 7.29
- 7.27
- 7.56
- 7.98
- 8.23
-11.84
-11.32
0.84
1.00
1.51
3.05
3.02
3.01
2.99
2.83
2.75
2.56
2.42
2.29
2.01
1.70
1.18
0.44
0.03
MPHLEAF
0.17
0.23
0.38
0.57
0.58
0.59
0.60
0.59
0.58
0.56
0.54
0.51
0.48
0.44
0.38
0.28
0.18
C = 0.88
MSV0L
0.05
0.03
0.23
0.10
0.06
0.03
0.16
0.14
0.11
0.09
0.05
0.11
0.09
0.08
0.24
0.06
0.20
0 = 0. 14
MPHSTALK
0.29
0.36
1.04
2.36
2.46
2.57
2.60
2.57
2.54
2.44
2.36
2.24
2.11
1.98
1.80
1.56
1.40
N
6
6
7
13
14
15
16
16
16
16
16
16
16
16
16
16
16
A12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.95
DATE
165
168
170
171
176
178
189
190
192
196
198
204
206
210
213
217
220
221
225
231
240
247
rms error = 0.58 dB A = 0.14
°S(dB)
- 7.83
- 7.19
- 6.44
- 6.39
- 6.43
- 5.95
- 5.58
- 6.06
- 5.80
- 5.46
- 6.40
- 7.64
- 6.20
- 6.84
- 7.08
- 7.21
- 7.37
- 7.90
- 8.27
- 7.70
-13.00
-12.12
W
35.6 GHz
Model A
oj^dB)
LAI
- 7.40
- 7.28
- 7.06
- 7.01
- 6.46
- 6.52
- 6.01
- 6.07
- 6.16
- 6.30
- 6.27
- 6.33
- 6.39
- 6.53
- 6.69
- 6.80
- 7.18
- 7.36
- 7.95
- 8.76
-14.02
-11.54
0.94
1.35
1.63
1.78
2.49
2.77
4.46
4.45
4.42
4.36
4.33
4.24
4.14
3.86
3.57
3.14
2.75
2.62
2.06
1.23
0.26
0.08
C3
B = 0.50
MPHLEAF
0.18
0.31
0.39
0.43
0.59
0.64
0.83
0.84
0.86
0.87
0.88
0.86
0.85
0.82
0.80
0.75
0.72
0.71
0.65
0.56
0.40
0.25
C = 0.88
MSV0L
0.11
0.05
0.04
0.04
0.24
0.19
0.25
0.19
0.14
0.04
0.43
0.23
0.13
0.09
0.10
0.49
0.27
0.17
0.16
0.33
0.06
0.21
0 = 0.14
MPHSTALK
0.42
0.44
0.63
0.74
1.40
1.67
2.88
2.95
3.05
3.17
3.20
3.15
3.10
2.98
2.88
2.73
2.61
2.56
2.40
2.16
1.80
1.54
N
5
6
6
6
7
8
11
13
14
15
16
16
16
16
16
16
16
16
16
16
16
16
A13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0.95
8 .6 GHz
Model A
rms error = 1.10 dB A = 0. 13
DATE
o°0m
<£(dB)
LAI
168
170
176
178
182
190
192
196
198
204
206
210
213
221
225
231
240
-12.50
-11.50
-10.30
-10.10
- 9.34
- 9.30
- 8.63
- 9.40
- 9.65
- 9.18
- 9.54
- 9.42
- 8.89
- 9.86
- 9.68
- 9.46
- 9.11
-11.93
-10.39
- 8.97
- 8.89
- 8.41
- 8.17
- 8.14
- 8.11
- 8.10
- 8.14
- 8.17
- 8.21
- 8.27
- 8.44
- 8.52
- 8.61
- 8.53
0.38
0.66
1.49
1.72
2.46
3.65
3.92
4.41
4.62
5.12
5.23
5.38
5.42
5.21
4.96
4.42
3.40
W
SI
B = 1.61
MPHLEAF
0.05
0.11
0.28
0.34
0.45
0.68
0.74
0.84
0.89
1.02
1.05
1.11
1.14
1.15
1.11
0.99
0.68
C = 0.00
MSV0L
0.16
0.06
0.26
0.19
0.07
0.08
0.06
0.04
0.03
0.18
0.11
0.08
0.05
0.11
0.08
0.30
0.06
D = 0.14
MPHSTALK
0.01
0.10
0.45
0.58
0.84
1.30
1.40
1.56
1.63
1.78
1.82
1.87
1.88
1.87
1.84
1.76
1.58
A14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0.47
DATE
168
170
176
178
182
190
192
196
198
204
206
210
213
217
221
225
231
240
247
254
8 .6 GHz
Model A
rms error = 1.36 dB A = 0. 13
°°(dB)
-12.80
-11.30
-10.42
-10.40
-10.29
- 9.50
-10.20
- 9.50
- 9.36
- 8.87
- 9.82
- 8.87
- 9.29
- 9.69
-10.20
- 9.60
- 9.16
- 8.83
-10.53
- 9.69
cf(dB)
LAI
-12.45
-12.17
-10.87
-10.41
- 9.72
- 8.85
- 8.71
- 8.51
- 8.45
- 8.41
- 8.45
- 8.62
- 8.83
- 9.24
- 9.85
-10.70
-12.36
-12.18
-11.96
-11.68
0.32
0.44
1.07
1.36
1.94
2.96
3.15
3.44
3.52
3.55
3.48
3.24
2.98
2.54
2.04
1.54
0.90
0.74
0.65
0.58
W
S2
B = 1.61
MPHLEAF
0.03
0.12
0.36
0.43
0.54
0.68
0.70
0.73
0.74
0.74
0.73
0.70
0.68
0.63
0.59
0.53
0.45
0.32
0.23
0.15
C = 0.00
MSV0L
0.14
0.06
0.23
0.20
0.12
0.08
0.05
0.04
0.03
0.13
0.06
0.07
0.05
0.04
0.11
0.09
0.28
0.09
0.21
0.08
D = 0.14
MPHSTALK
0.05
0.11
0.50
0.60
0.76
0.99
1.02
1.06
1.08
1.09
1.08
1.06
1.05
1.01
0.98
0.94
0.87
0.77
0.67
0.56
A15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0.54
DATE
168
170
171
176
178
182
189
190
192
196
198
204
206
210
212
213
217
221
224
225
231
240
247
8 .6 GHz
Model A
rms error = 1.08 dB A = 0. 13
°2(dB)
-14.20
-10.37
-10.12
-10.40
- 9.57
-10.00
- 9.26
- 8.80
- 9.27
- 9.28
- 8.97
- 9.08
-10.22
-10.30
- 9.41
- 9.60
- 9.85
- 9.44
- 8.98
- 9.01
- 8.26
- 8.75
-10.02
< £ (« )
LAI
-11.59
-11.36
-11.25
-10.72
-10.51
-10.31
- 9.18
- 9.21
- 9.31
- 9.52
- 9.62
- 9.91
-10.01
-10.19
-10.27
-10.31
-10.45
-10.55
-10.60
-10.61
-10.56
-10.07
- 9.32
0.45
0.58
0.65
1.04
1.22
1.53
2.51
2.55
2.58
2.61
2.61
2.54
2.50
2.40
2.33
2.30
2.15
1.99
1.86
1.82
1.56
1.20
0.99
W
S3
B = 1.61
MPHLEAF
0.08
0.15
0.18
0.33
0.38
0.48
0.63
0.64
0.68
0.73
0.75
0.80
0.81
0.81
0.81
0.80
0.77
0.73
0.68
0.66
0.53
0.30
0.12
C = 0.00
MSV0L
0.17
0.08
0.07
0.26
0.14
0.08
0.10
0.09
0.06
0.03
0.03
0.16
0.09
0.09
0.08
0.07
0.04
0.08
0.13
0.11
0.29
0.07
0.21
D = 0.14
MPHSTALK
0.07
0.16
0.20
0.42
0.51
0.65
0.82
0.84
0.87
0.90
0.91
0.92
0.91
0.90
0.89
0.88
0.85
0.82
0.80
0.79
0.73
0.66
0.59
A16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0 .9 1
DATE
168
170
176
178
182
190
192
196
198
204
206
210
213
221
225
231
240
rms e r r o r = 1 .0 7 dB
a ° (d B )
-11.40
-10.19
- 9.83
- 9.17
- 8.19
- 8.50
- 8.50
- 7.83
- 8.56
- 8.20
- 8.46
- 8.12
- 8.37
- 8.70
- 9.20
- 7.90
- 8.25
1 3 .0 fflz
Model A
A = 0 .1 5
a ° (d B )
LAI
-11.11
- 9.55
- 8.09
- 8.00
- 7.51
- 7.26
- 7.23
- 7.20
- 7.19
- 7.22
- 7.25
- 7.30
- 7.35
- 7.50
- 7.58
- 7.67
- 7.62
0.38
0.66
1.49
1.72
2.46
3.65
3.92
4.41
4.62
5.12
5.23
5.38
5.42
5.21
4.96
4.42
3.40
W
SI
B = 1 .4 5
MPHLEAF
0.05
0.11
0.28
0.34
0.45
0.68
0.74
0.84
0.89
1.02
1.05
1.11
1.14
1.15
1.11
0.99
0.68
C = 0 .0 0
MSVOL
0.16
0.06
0.26
0.19
0.07
0.08
0.06
0.04
0.03
0.18
0.11
0.08
0.05
0.11
0.08
0.30
0.06
D = 0 .1 5
MPHSTALK
0.01
0.10
0.45
0.58
0.84
1.30
1.40
1.56
1.63
1.78
1.82
1.87
1.88
1.87
1.84
1.76
1.58
A17
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0.65
rms error = 1.19 dB A = 0. 15
DATE
168
170
176
178
182
190
192
196
198
204
206
210
213
217
221
225
231
240
247
254
1 3 .0 GHz
Model A
12.00
10.65
9.96
9.53
- 8.57
8.32
8.48
8.90
8.62
7.86
8.29
7.79
- 8.78
7.79
9.00
_ 8.44
8.70
8.50
8.99
9.52
<£(dB)
LAI
-11.66
-11.30
- 9.90
- 9.43
- 8.74
- 7.89
- 7.76
- 7.57
- 7.51
- 7.47
- 7.51
- 7.67
- 7.87
- 8.28
- 8.88
- 9.70
-11.35
-11.23
-11.06
-10.82
0.32
0.44
1.07
1.36
1.94
2.96
3.15
3.44
3.52
3.55
3.48
3.24
2.98
2.54
2.04
1.54
0.90
0.74
0.65
0.58
W
S2
B = 1.45
MPHLEAF
0.03
0.12
0.36
0.43
0.54
0.68
0.70
0.73
0.74
0.74
0.73
0.70
0.68
0.63
0.59
0.53
0.45
0.32
0.23
0.15
C = 0.00
MSV0L
0.14
0.06
0.23
0.20
0.12
0.08
0.05
0.04
0.03
0.13
0.06
0.07
0.05
0.04
0.11
0.09
0.28
0.09
0.21
0.08
D = 0.15
MPHSTALK
0.05
0.11
0.50
0.60
0.76
0.99
1.02
1.06
1.08
1.09
1.08
1.06
1.05
1.01
0.98
0.94
0.87
0.77
0.67
0.56
A18
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0.80
)ATE
168
170
171
176
178
182
189
190
192
196
198
204
206
210
212
213
217
221
224
225
231
240
247
•
-
•
•
•
-
1 3 .0 9 iz
Model A
rms error = 0.78 dB A = 0. 15
o°(dB)
c£(dB)
LAI
12.80
10.40
10.19
9.36
8.59
8.24
8.33
8.29
8.02
7.89
7.82
8.06
8.34
8.05
8.83
8.61
8.70
9.30
8.55
9.11
8.20
8.94
8.64
-10.76
-10.48
-10.35
- 9.76
- 9.54
- 9.32
- 8.21
- 8.24
- 8.33
- 8.52
- 8.61
- 8.89
- 8.98
- 9.15
- 9.23
- 9.27
- 9.40
- 9.51
- 9.56
- 9.57
- 9.55
- 9.16
- 8.53
0.45
0.58
0.65
1.04
1.22
1.53
2.51
2.55
2.58
2.61
2.61
2.54
2.50
2.40
2.33
2.30
2.15
1.99
1.86
1.82
1.56
1.20
0.99
W
S3
B = 1.45
MPHLEAF
0.08
0.15
0.18
0.33
0.38
0.48
0.63
0.64
0.68
0.73
0.75
0.80
0.81
0.81
0.81
0.80
0.77
0.73
0.68
0.66
0.53
0.30
0.12
C = 0.00
MSV0L
0.17
0.08
0.07
0.26
0.14
0.08
0.10
0.09
0.06
0.03
0.03
0.16
0.09
0.09
0.08
0.07
0.04
0.08
0.13
0.11
0.29
0.07
0.21
D =
MPHSTAL
0.07
0.16
0.20
0.42
0.51
0.65
0.82
0.84
0.87
0.90
0.91
0.92
0.91
0.90
0.89
0.88
0.85
0.82
0.80
0.79
0.73
0.66
0.59
A19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r
= 0 .9 5
DATE
168
170
176
178
182
190
192
196
198
204
206
210
213
221
225
231
240
rms e r r o r = 0 .9 5 dB
<J°(dB)
-11.60
- 9.62
- 9.22
- 8.63
- 8.43
- 8.26
- 7.70
- 7.83
- 7.94
- 7.29
- 8.10
- 8.30
- 7.96
- 8.26
- 8.20
- 7.98
- 7.94
1 7 .0 GHz
Model A
A = 0 .1 4
c £ (d B )
LAI
-11.30
- 9.61
- 7.93
- 7.80
- 7.27
- 6.98
- 6.94
- 6.89
- 6.88
- 6.88
- 6.90
- 6.94
- 6.98
- 7.12
- 7.20
- 7.32
- 7.39
0.38
0.66
1.49
1.72
2.46
3.65
3.92
4.41
4.62
5.12
5.23
5.38
5.42
5.21
4.96
4.42
3.40
W
SI
B = 1 .0 2
MPHLEAF
0.05
0.11
0.28
0.34
0.45
0.68
0.74
0.84
0.89
1.02
1.05
1.11
1.14
1.15
1.11
0.99
0.68
C = 0 .0 0
MS VOL
0.16
0.06
0.26
0.19
0.07
0.08
0.06
0.04
0.03
0.18
0.11
0.08
0.05
0.11
0.08
0.30
0.06
D = 0 .2 1
MPHSTALK
0.01
0.10
0.45
0.58
0.84
1.30
1.40
1.56
1.63
1.78
1.82
1.87
1.88
1.87
1.84
1.76
1.58
A20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0.61
DATE
168
170
176
178
182
190
192
196
198
204
206
210
213
217
221
225
231
240
247
254
rms error = 1.40 dB A = 0 .14
a°(dB)
. 13.00
•
•
•
•
-
1 7 .0 GHz
Model A
10.90
9.09
10.20
9.99
7.87
8.35
8.15
7.75
7.30
7.64
8.24
7.54
7.55
8.99
8.23
7.78
8.53
8.90
8.54
c£(dB)
LAI
-11.93
-11.33
- 9.62
- 9.12
- 8.38
- 7.51
- 7.38
- 7.19
- 7.13
- 7.10
- 7.14
- 7.30
- 7.51
- 7.92
- 8.53
- 9.38
-11.09
-11.12
-11.08
-10.97
0.32
0.44
1.07
1.36
1.94
2.96
3.15
3.44
3.52
3.55
3.48
3.24
2.98
2.54
2.04
1.54
0.90
0.74
0.65
0.58
W
S2
B = 1.02
MPHLEAF
0.03
0.12
0.36
0.43
0.54
0.68
0.70
0.73
0.74
0.74
0.73
0.70
0.68
0.63
0.59
0.53
0.45
0.32
0.23
0.15
C = 0.00
MSV0L
0.14
0.06
0.23
0.20
0.12
0.08
0.05
0.04
0.03
0.13
0.06
0.07
0.05
0.04
0.11
0.09
0.28
0.09
0.21
0.08
D = 0.21
MPHSTALK
0.05
0.11
0.50
0.60
0.76
0.99
1.02
1.06
1.08
1.09
1.08
1.06
1.05
1.01
0.98
0.94
0.87
0.77
0.67
0.56
A21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0 .7 8
DATE
168
170
171
176
178
182
189
190
192
196
198
204
206
210
212
213
217
221
224
225
231
240
247
rms e r r o r = 0 .9 0 dB
o °(d B )
12.50
11.68
- 10.22
8.84
8.04
9.07
8.40
8.43
8.46
_
7.70
7.37
_
7.53
7.70
_
7.72
7.63
_
7.64
7.91
7.95
7.85
8.11
7.91
_
8.72
9.18
1 7 .0 GHz
Model A
A = 0 .1 4
o £ (d B )
LAI
10.89
10.47
10.28
9.51
9.24
8.96
7.80
7.82
7.90
8.06
8.15
8.39
8.47
8.63
8.71
8.74
8.89
9.01
9.08
9.10
9.16
9.04
8.74
0.45
0.58
0.65
1.04
1.22
1.53
2.51
2.55
2.58
2.61
2.61
2.54
2.50
2.40
2.33
2.30
2.15
1.99
1.86
1.82
1.56
1.20
0.99
•
•
•
•
_
•
-
•
-
W
S3
B = 1 .0 2
MPHLEAF
0.08
0.15
0.18
0.33
0.38
0.48
0.63
0.64
0.68
0.73
0.75
0.80
0.81
0.81
0.81
0.80
0.77
0.73
0.68
0.66
0.53
0.30
0.12
C = 0 .0 0
MSVOL
0.17
0.08
0.07
0.26
0.14
0.08
0.10
0.09
0.06
0.03
0.03
0.16
0.09
0.09
0.08
0.07
0.04
0.08
0.13
0.11
0.29
0.07
0.21
D = 0 .2 1
MPHSTALK
0.07
0.16
0.20
0.42
0.51
0.65
0.82
0.84
0.87
0.90
0.91
0.92
0.91
0.90
0.89
0.88
0.85
0.82
0.80
0.79
0.73
0.66
0.59
A22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0 .8 8
DATE
168
170
176
178
190
192
196
198
204
206
210
213
221
225
231
240
rms e r r o r = 1 .1 6 dB
c® (d B )
-11.90
- 9.74
- 8.44
- 8.74
- 8.49
- 7.42
- 8.16
- 7.56
- 7.08
- 7.59
- 8.67
- 7.89
- 8.04
- 7.98
- 8.47
- 8.65
3 5 .6 GHz
Model A
A = 0 .1 1
Oj°(dB)
LAI
9.77
9.64
7.61
7.68
7.00
6.95
6.86
6.83
6.76
6.76
6.76
6.78
6.90
7.01
7.20
7.62
0.38
0.66
1.49
1.72
3.65
3.92
4.41
4.62
5.12
5.23
5.38
5.42
5.21
4.96
4.42
3.40
.
-
W
SI
B = 0 .3 3
MPHLEAF
0.05
0.11
0.28
0.34
0.68
0.74
0.84
0.89
1.02
1.05
1.11
1.14
1.15
1.11
0.99
0.68
C = 0 .3 2
MSVOL
0.16
0.06
0.26
0.19
0.08
0.06
0.04
0.03
0.18
0.11
0.08
0.05
0.11
0.08
0.30
0.06
D = 0 .4 0
MPHSTALK
0.01
0.10
0.45
0.58
1.30
1.40
1.56
1.63
1.78
1.82
1.87
1.88
1.87
1.84
1.76
1.58
A23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0 .7 2
DATE
168
170
176
190
192
196
198
204
206
210
213
217
221
225
231
240
247
254
rms e r r o r = 1 .2 6 dB
a °(d B )
-10.54
-11.10
- 7.88
- 7.77
- 7.34
- 7.91
- 6.81
- 7.43
- 7.29
- 7.87
- 7.64
- 7.35
- 8.07
- 7.33
- 8.12
- 7.85
-10.50
- 9.48
3 5 .6 GHz
Model A
A = 0 .1 1
c £ (d B )
LAI
-10.49
-11.01
- 8.97
- 7.26
- 7.13
- 6.96
- 6.88
- 6.84
- 6.90
- 7.09
- 7.32
- 7.78
- 8.40
- 9.30
-10.54
-11.24
-10.70
-11.30
0.32
0.44
1.07
2.96
3.15
3.44
3.52
3.55
3.48
3.24
2.98
2.54
2.04
1.54
0.90
0.74
0.65
0.58
W
S2
B = 0 .3 3
MPHLEAF
0.03
0.12
0.36
0.68
0.70
0.73
0.74
0.74
0.73
0.70
0.68
0.63
0.59
0.53
0.45
0.32
0.23
0.15
C = 0 .3 2
MSVOL
0.14
0.06
0.23
0.08
0.05
0.04
0.03
0.13
0.06
0.07
0.05
0.04
0.11
0.09
0.28
0.09
0.21
0.08
0 = 0 .4 0
MPHSTALK
0.05
0.11
0.50
0.99
1.02
1.06
1.08
1.09
1.08
1.06
1.05
1.01
0.98
0.94
0.87
0.77
0.67
0.56
A24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 SORGHUM
r = 0.90
DATE
168
170
171
176
178
189
190
192
196
198
204
206
210
212
213
217
221
224
225
231
240
247
3 5 .6 GHz
Model A
rms error = 0.63 dB A = 0. 11
°§(dB)
-10.36
- 9.99
- 9.98
- 8.08
- 8.24
- 6.86
- 6.39
- 7.08
- 6.66
- 6.79
- 7.53
- 7.53
- 8.07
- 8.27
- 7.15
- 7.53
- 8.83
- 9.11
- 8.14
- 7.88
- 8.52
- 9.59
cj?(dB)
LAI
- 9.60
-10.18
-10.12
- 8.71
- 8.84
- 7.46
- 7.47
- 7.53
- 7.64
- 7.69
- 7.80
- 7.89
- 8.02
- 8.10
- 8.14
- 8.31
- 8.44
- 8.52
- 8.58
- 8.58
- 9.26
- 8.98
0.45
0.58
0.65
1.04
1.22
2.51
2.55
2.58
2.61
2.61
2.54
2.50
2.40
2.33
2.30
2.15
1.99
1.86
1.82
1.56
1.20
0.99
W
S3
B = 0.33
MPHLEAF
0.08
0.15
0.18
0.33
0.38
0.63
0.64
0.68
0.73
0.75
0.80
0.81
0.81
0.81
0.80
0.77
0.73
0.68
0.66
0.53
0.30
0.12
C = 0.32
MSV0L
0.17
0.08
0.07
0.26
0.14
0.10
0.09
0.06
0.03
0.03
0.16
0.09
0.09
0.08
0.07
0.04
0.08
0.13
0.11
0.29
0.07
0.21
D = 0.40
MPHSTALK
0.07
0.16
0.20
0.42
0.51
0.82
0.84
0.87
0.90
0.91
0.92
0.91
0.90
0.89
0.88
0.85
0.82
0.80
0.79
0.73
0.66
0.59
A25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.87
)ATE
168
170
176
178
182
190
192
196
198
204
206
210
213
221
225
231
240
247
1 7 .0 GHz
Model A
rms error = 0.76 dB A = 0.11
E = 0.86
o°(dB)
-10.09
- 8.42
- 8.27
- 7.26
- 6.95
- 6.97
- 7.26
- 6.93
- 6.84
- 7.42
- 7.96
- 8.30
- 8.60
- 9.71
- 9.75
- 9.07
-12.08
-10.61
°p(dB)
LAI
- 8.92
- 8.87
- 7.51
- 7.92
- 8.02
- 7.12
- 7.28
- 7.50
- 7.15
- 7.49
- 7.57
- 7.60
- 7.78
- 8.11
- 8.45
- 8.53
-11.95
- 11.11
0.97
1.17
1.77
1.96
2.33
3.41
3.37
3.31
3.30
3.24
3.21
3.09
2.96
2.41
2.05
1.46
0.56
0.06
HH
Cl
B = 1,.24
MPHLEAF
0.18
0.24
0.40
0.44
0.51
0.61
0.62
0.64
0.65
0.65
0.65
0.63
0.62
0.56
0.53
0.47
0.35
0.22
C = 0.00
MSV0L
0.04
0.03
0.22
0.13
0.07
0.12
0.09
0.04
0.33
0.12
0.08
0.10
0.05
0.10
0.10
0.25
0.05
0.19
D = 0. 86
MPHSTALK
0.24
0.33
1.03
1.28
1.79
2.58
2.71
2.87
2.91
2.90
2.87
2.76
2.66
2.34
2.17
1.92
1.56
1.31
N
6
6
7
8
11
13
14
15
16
16
16
16
16
16
16
16
16
16
A26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.78
DATE
168
170
176
178
182
190
192
196
198
204
206
210
213
217
221
225
231
240
247
rms error = 0.93 dB A = 0.11
E = 0.86
<#dB)
- 9.79
- 8.45
- 6.60
- 7.24
- 6.50
- 7.26
- 6.78
- 6.99
- 6.25
- 6.48
- 7.75
- 8.30
- 7.75
- 8.86
- 8.51
- 8.57
- 7.96
- 9.96
-10.81
HH
17.0 GHz
Model A
°p°(dB)
LAI
- 9.12
- 9.30
- 7.79
- 8.34
- 8.47
- 7.35
- 7.50
- 7.63
- 7.43
- 7.61
- 7.73
- 7.90
- 8.11
- 7.98
- 8.25
- 8.65
- 8.37
-11.85
-10.55
0.84
1.00
1.51
1.68
1.99
3.05
3.02
3.01
2.99
2.83
2.75
2.56
2.42
2.29
2.01
1.70
1.18
0.44
0.03
C2
B = 1.24
MPHLEAF
0.17
0.23
0.38
0.42
0.49
0.57
0.58
0.59
0.60
0.59
0.58
0.56
0.54
0.51
0.48
0.44
0.38
0.28
0.18
C = 0.00
MSV0L
0.05
0.03
0.23
0.12
0.06
0.10
0.06
0.03
0.16
0.14
0.11
0.09
0.05
0.11
0.09
0.08
0.24
0.06
0.20
D = 0.86
MPHSTALK
0.29
0.36
1.04
1.28
1.72
2.36
2.46
2.57
2.60
2.57
2.54
2.44
2.36
2.24
2.11
1.98
1.80
1.56
1.40
N
6
6
7
8
11
13
14
15
16
16
16
16
16
16
16
16
16
16
16
A27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1980 CORN
r = 0.93
DATE
165
168
170
171
176
178
182
189
190
192
196
198
204
206
210
213
217
220
221
225
231
240
247
rms error = 0.64 dB A = 0.11
E = 0.86
®S(dB)
- 9.39
- 9.03
- 8.21
- 8.51
- 7.21
- 7.31
- 7.10
- 6.78
- 7.31
- 6.88
- 7.60
- 7.93
- 7.99
- 8.42
- 8.39
- 8.57
- 8.89
- 8.89
- 8.96
- 9.25
- 8.96
-14.69
-11.81
HH
17.0 GHz
Model A
Op°(dB)
LAI
- 8.03
- 8.71
- 8.62
- 8.60
- 7.82
- 7.88
- 7.84
- 7.09
- 7.16
- 7.26
- 7.42
- 7.26
- 7.38
- 7.47
- 7.64
- 7.81
- 7.69
- 8.18
- 8.42
- 8.99
- 9.47
-14.69
-11.12
0.94
1.35
1.63
1.78
2.49
2.77
3.27
4.46
4.45
4.42
4.36
4.33
4.24
4.14
3.86
3.57
3.14
2.75
2.62
2.06
1.23
0.26
0.08
C3
B = 1.24
MPHLEAF
0.18
0.31
0.39
0.43
0.59
0.64
0.73
0.83
0.84
0.86
0.87
0.88
0.86
0.85
0.82
0.80
0.75
0.72
0.71
0.65
0.56
0.40
0.25
C = 0.00
MSV0L
0.11
0.05
0.04
0.04
0.24
0.19
0.11
0.25
0.19
0.14
0.04
0.43
0.23
0.13
0.09
0.10
0.49
0.27
0.17
0.16
0.33
0.06
0.21
D = 0.86
MPHSTALK
0.42
0.44
0.63
0.74
1.40
1.67
2.20
2.88
2.95
3.05
3.17
3.20
3.15
3.10
2.98
2.88
2.73
2.61
2.56
2.40
2.16
1.80
1.54
N
5
6
6
6
7
8
11
11
13
14
15
16
16
16
16
16
16
16
16
16
16
16
16
A28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX B
Crop A tte n u a tio n Data and Associated Ground Truth
B1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Site
Julian Date
Low Angle (24°) PathLength (m)
High Angle (56°) PathLength (m)
FREOUENCY
Wheat
W1
135
0.69
1.13
ANGLE
MEAN ONE-WAY
99% CONFIDENCE
(GHZ)
POLARIZATION
(°)
CANOPY LOSS (dB)
INTERVAL LIMITS (dB)*
1.55
1.55
VV
HH
24
24
1.4
1.7
± 0.3
± 0.2
4.75
4.75
VV
HH
24
24
1.6
2.3
+ 0.5
± 0.2
10.20
10.20
VV
HH
24
24
6.5
4.8
i 1.4
+ 1.3
1.55
1.55
VV
HH
56
56
7.4
2.4
+ 0.3
± 0.3
4.75
4.75
4.75
VV
HH
VH
56
56
56
27.4
9.4
5.1
+ 0.5
+ 1.0
+ 0.2
10.20
10.20
VV
HH
56
56
36.0
32.5
+ 0.8
+ 0.4
♦Does not include estimated ± 10% accuracy error.
B2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Site
Julian Date
Low Angle (24°) Path Length (m)
High Angle (56°) Path Length (m)
FREQUENCY
Wheat
W2
150
1.59
ANGLE
fCAN ONE-WAY
99% CONFIDENCE
(GHZ)
POLARIZATION
(°)
CANOPY LOSS (dB)
INTERVAL LIMITS (dB)*
1.55
1.55
VV
HH
56
56
3.2
1.3
4.75
4.75
4.75
4.75
VV
HH
VH
HV
56
56
56
56
17.9
3.0
0.4
1.2
±
±
±
±
10.20
10.20
VV
HH
56
56
31.2
14.1
± 1.9
± 2.2
+ 0.6
± 0.3
0.7
0.5
0.1
0.5
* Does not include estimated ± 10% accuracy error.
B3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Site
Julian Date
Low Angle (24°) Path Length (m)
High Angle (56°) Path Length (m)
FREQUENCY
Wheat
W2
150
0.86 (decapitated)
ANGLE
MEAN ONE-WAY
99% CONFIDENCE
(GHZ)
POLARIZATION
(°)
CANOPY LOSS (dB)
INTERVAL LIMITS (dB)*
1.55
1.55
VV
HH
56
56
3.9
0.9
± 0.5
± 0.3
4.75
4.75
VV
HH
56
56
13.1
2.9
± 0.9
+ 0.7
10.20
10.20
VV
HH
56
56
21.4
8.4
+ 2.4
± 1.5
Does not include estimated1 ± 10% accuracy erro r.
B4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Site
Julian Date
Low Angle (24°) Path Length(m)
High Angle (56°) Path Length (m)
FREQUENCY
Wheat
W1
158
1.16
1.90
ANGLE
MEAN ONE-WAY
99% CONFIDENCE
(GHZ)
POLARIZATION
(° )
CANOPY LOSS (dB)
INTERVAL LIMITS (dB)*
1.55
1.55
VV
HH
24
24
1.3
1.3
+ 0.1
± 0.2
4.75
4.75
VV
HH
24
24
5.4
3.7
± 0.6
± 0.4
10.20
10.20
VV
HH
24
24
10.9
9.4
± 1.7
± 1.1
1.55
1.55
VV
HH
56
56
7.1
2.6
± 0.6
± 0.6
4.75
4.75
VV
HH
56
56
17.8
6.0
± 0.3
± 0.6
10.20
10.20
10.20
VV
HH
HV
56
56
56
36.1
26.7
19.8
± 1.0
± 1.3
± 0.8
* Does not include estimated ± 10% accuracy error.
B5
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
Crop
Site
Julian Date
Low Angle (16°) Path Length (m)
High Angle (52°) Path Length (m)
FREQUENCY
Soybeans
SI
181
0.45
0.60
ANGLE
MEAN ONE-WAY
CANOPY LOSS (dB)
99% CONFIDENCE
(GHZ)
POLARIZATION
(°)
1.55
1.55
VV
HH
16
16
1.5
0.5
± 0.1
± 0.1
4.75
4.75
VV
HH
16
16
2.6
2.0
± 0.4
± 0.3
10.20
10.20
VV
HH
16
16
4.3
4.6
± 0.6
+ 0.6
1.55
1.55
VV
HH
52
52
1.6
0.4
+ 0.2
+ 0.1
4.75
4.75
VV
HH
52
52
8.6
3.4
+ 0.8
± 0.5
10.20
10.20
VV
HH
52
52
11.8
8.0
± 1.6
± 0.9
INTERVAL LIMITS (dB)'
Does not include estimated + 10% accuracy erro r.
B6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Site
Julian Date
Low Angle (16°) Path Length(m)
High Angle (52°) Path Length (m)
FREQUENCY
Soybeans
SI
188
0.54
0.78
ANGLE
MEAN ONE-WAY
99% CONFIDENCE
(GHZ)
POLARIZATION
(°)
CANOPY LOSS (dB)
INTERVAL LIMITS (dB)*
1.55
1.55
VV
HH
16
16
2.6
0.8
+ 0.2
± 0.2
4.75
4.75
VV
HH
16
16
3.8
3.6
+ 0.8
+ 0.4
10.20
10.20
VV
HH
16
16
7.8
10.9
± 1.4
± 1.4
1.55
1.55
VV
HH
52
52
2.6
0.7
+ 0.3
+ 0.2
4.75
4.75
VV
HH
52
52
9.9
3.1
+ 0.9
± 0.3
10.20
10.20
VV
HH
52
52
12.5
12.1
± 1.6
± 1.1
* Does not include estimated ± 10% accuracy erro r.
B7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Site
Julian Date
Low Angle (16°) Path Length (m)
High Angle (52°) Path Length (m)
FREOUENCY
Soybeans
SI
188
(Defoliated)
0.67(Defoliated)
ANGLE
MEAN ONE-WAY
99% CONFIDENCE
(GHZ)
POLARIZATION
(°)
CANOPY LOSS (dB)
INTERVAL LIMITS (dB)*
1.55
1.55
VV
HH
52
52
2.4
0.4
± 0.5
± 0.4
4.75
4.75
VV
HH
52
52
8.8
1.7
± 1.9
± 0.9
10.20
10.20
VV
HH
52
52
8.3
3.7
+ 2.3
± 1.1
* Does not include estimated ± 10% accuracy error.
B8
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
Crop
Wheat
Site
W1
Julian Date
135
Mean Canopy Height (m)
0.73
Head Length (m)
0.15
Density (stems/m2)
1694
Top 1/3 Leaf H2O
80.0% (1.46 kg/m2)
Mid 1/3 Leaf H20
80.2% (0.71 kg/m2)
Low 1/3 Leaf H20
81.1% (0.11 kg/n2)
Top 1/3 Stalk H20
86.1% (1.19 kg/m2)
Mid 1/3 Stalk H20
84.1% (1.56 kg/m2)
Low 1/3 Stalk H20
t
C
O
O
O
Head H20
1
L123 Leaf H20
80.1% (2.28 kg/m2)
L123 Stalk H20
84.6% (4.21 kg/m2)
Whole Plant H20
82.9% (6.49 kg/m2)
Leaf Area Index
8.0
Growth Stage*
23 (Flag Leaf V isible)
Leaf Thickness (mm)
0.15
Stem Diameter (mm)
2.00
Look Direction
Perpendicular to Rows
Receiver Height (m)
0.10
&
Row Spacing (m)
(1.46 kg/m2)
1
* LACIE Crop Inventory System
B9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Wheat
Site
W2
Julian Date
150
Mean Canopy Height (m)
1.11 (0.70 Decapitated)
Head Length (m)
0.08
Row Spacing (m)
0.15
Density (stems/m2)
1027
Top 1/3 Leaf H2O
68.9% (0.18 kg/m2)
Mid 1/3 Leaf H20
52.1% (0.15 kg/m2)
Low 1/3 Leaf H20
8.3% (0.00 kg/m2)
Top 1/3 Stalk H20
65.8% (0.41 kg/m2)
Mid 1/3 Stalk H20
69.0% (0.75 kg/m2)
Low 1/3 Stalk H20
63.4% (0.43 kg/m2)
Head H20
82.2% (1.11 kg/m2)
L I23 Leaf H20
55.2% (0.33 kg/m2)
L123 Stalk H20
66.6% (1.59 kg/m2)
Whole Plant H20
69.9% (3.03 kg/m2)
Leaf Area Index
3.6
Growth Stage*
34 (Kernels Formed)
Leaf Thickness (mm)
0.15
Stem Diameter (mm)
2.00
Look Direction
Perpendicular to Rows
Receiver Height (m)
0 .2 2
* LACIE Crop Inventory System
B10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Wheat
Site
W1
Julian Date
158
Mean Canopy Height (m)
1.16
Head Length (m)
0.08
Row Spacing (m)
0.15
Density (stems/m2)
1694
**
L
G
•
C
M
Top 1/3 Leaf H2O
(0.46 kg/m2)
Mid 1/3 Leaf H20
53. 7% (0.15 kg/m2)
Low 1/3 Leaf H20
47. 8% (0.07 kg/m2)
Top 1/3 Stalk H20
75. 7% (0.87 kg/m2)
Mid 1/3 Stalk H20
78.2% (1.49 kg/m2)
Low 1/3 Stalk H20
72.9% (1.00 kg/m2)
Head H20
72.5% (1.13 kg/m2)
L123 Leaf H20
64.0% (0.69 kg/m2)
L123 Stalk H20
75.9% (3.36 kg/m2)
Whole Plant H20
73.3% (5.18 kg/m2)
Leaf Area Index
4.0
Growth Stage*
42 (Soft Dough)
Leaf Thickness (mm)
0.15
Stem Diameter (mm)
2.00
Look Direction
Perpendicular to Rows
Receiver Height (m)
0.10
* LACIE Crop Inventory System
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Soybeans
Site
SI
Julian Date
181
Mean Canopy Height (m) Low Angle (
0.56
Mean Canopy Height (m) High Angle
0.50
Row Spacing (m)
0.77
Row Width (m)
0.54
Density (plants/m2)
42.0
Leaf H2O
78.3**
(0.75 kg/m2)
Main Stem H2O
87.7**
(0.60 kg/m2)
Secondary Stem H2O
90.9**
(0.66 kg/m2)
Whole Plant H2O
84.8**
(2.00 kg/m2)
Leaf Area Index (m2/m2)
4.2
Mean Main Stem Length (m)
0.34
Mean Secondary Stem Length (m)
0.18
Mean Secondary Stems per Plant
11.1
Growth Stage**
31 (One Open 1rlower)
Leaf Thickness (mm)
0 .2
Main Stem Diameter (mm)
5.6
Secondary Stem Diameter (mm)
1.9
Look Direction
Perpendicular to Rows
Receiver Height (m)
0.13
(5 9 .9 )*
(6 .0 )*
* Vegetated portion of fie ld only (percent cover «70*)
* * LACIE Crop Inventory System
B12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Crop
Soybeans
Site
SI
Julian Date
188
Mean Canopy Height (m) - Low Angle (16°)
0.65
Mean Canopy Height (m) - High Angle (52°)
0.61 (0.54 Defoliated)
Row Spacing (m)
0.77
Row Width (m)
0.64
Density (plants/m2)
42.0 (5 1 .6 )*
Leaf H2O
72.1%* (0.62 kg/m2)*
Main Stem H2O
78.5%* (0.58 kg/m2)*
Secondary Stem H2O
81.7%* (0.60 kg/m2)*
Whole Plant H20
77.2%* (1.80 kg/m2)*
Leaf Area Index (m2/m2)
4.6
Mean Main Stem Length (m)
0.44
Mean Secondary Stem Length (m)
0.22
Mean Secondary Stems per plant
11.1
Growth Stage**
32 (Full Bloom)
Leaf Thickness (mm)
0 .2
Main Stem Diameter (mm)
5.6
Secondary Stem Diameter (mm)
1.9
Look Direction
Perpendicular to Rows
Receiver Height (m)
0.13
(5 .5 )*
* Vegetated portion of fie ld only (percent cover ■»83%)
* * LACIE Crop Inventory System
B13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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