0360651F
Digital Topography From SAR Interferometry:
Determination of and Correction for
Vegetation Height
Kamal Sarabandi
September 1998
RL996 = RL996
FINAL REPORT FOR NASA GRANT NAGW4555/ NAG54939
DIGITAL TOPOGRAPHY FROM SAR
INTERFEROMETRY: DETERMINATION OF AND
CORRECTION FOR VEGETATION HEIGHT
Submitted to:
Office of Mission to Planet Earth
NASA Headquarters
300 E. Street SW
Washington D.C. 20546
Attention: Dr. Diane Wickland
Kamal Sarabandi,
Radiation Laboratory
Department of Electrical Engineering and Computer Science
The University of Michigan
Ann Arbor, Ml 481092122
Tel: (313) 7640500, Fax: (313) 7472106
Project Duration: March 15, 1995 to September 15, 1998
1
Contents
1 Background and Objectives 1
2 Summary of Accomplished Results 2
2.1 Theoretical Model Development.......................... 2
2.1.1 Ak Radar Equivalence of an INSAR.................... 2
2.1.2 Statistical Analysis............................. 3
2.1.3 Vegetation Model............................. 3
2.2 Development of a Monte Carlo Coherent Scattering Model for Tree Canopies
Based on Fractal Theory.............................. 4
2.3 INSAR Response to Short vegetation....................... 9
2.4 INSAR Response to Trees............................. 9
2.5 Inversion Algorithm Based on Multiincidence Angle and/or Multifrequency SAR/INSAR 10
2.6 Experim ental Activities............................... 12
3 Graduate Students 12
4 Publications 14
4.1 Journal Papers........................................ 14
4.2 Conference Papers..................................... 15
I AkRadar Equivalent of Interferometric SARs: A Theoretical Study for Determination of Vegetation Height 11
II Electromagnetic Scattering Model for a Tree Trunk Above a Ground Plane 111
III A Monte Carlo Coherent Scattering Model For Forest Canopies Using FractalGenerated Trees 1111
IV Simulation of Interferometric SAR Response for Characterization of Scattering
Phase Center Statistics of Forest Canopies IV1
V Electromagnetic Scattering from Short Branching Vegetation V1
VI Retrieval of Forest Parameters Using a FractalBased Coherent Scattering
Model and a Genetic Algorithm Vl1
VII An Evaluation of JPL TOPSAR for Extracting Tree Heights VI 11
VIII GPS Measurements for SIRC/XSAR and TOPSAR Forest Test Stands at
Raco, Michigan Site VI ll1
3
1 Background and Objectives
Accurate estimation of gross forest parameters such as total vegetation biomass, total leaf area
index, and tree height on a regional to global scale has long been an important goal within
the remote sensing community. Over the past two decades much effort has been devoted to the
development of scattering models [1, 2, 3] for understanding of the interaction of electromagnetic
waves with vegetation, and to the construction and development of advanced imaging radars
for acquiring test data and examining the feasibility of the remote sensing problem [4]. In
most practical situations the number of vegetation parameters influencing the radar response
usually exceeds the number of radar observation parameters. For this reason the application of
multifrequency and multipolarization radar systems was proposed and such a system was flown
aboard the Shuttle Endeavor in April and October 1994 [4]. Preliminary results indicate that the
classification and retrieval of vegetation biophysical parameters indeed require many simultaneous
radar channels, however, freeflight of such systems is not practical due to the exorbitant power
requirements.
Characterization of the spatial organization of particles in a vegetation canopy is of great
importance for determining many ecosystem processes including energy and chemical exchanges.
Traditional remote sensing instruments provide twodimensional spatial information of the target
which may contain, depending on the instrument, some information on the vertical particle
arrangement in a convoluted fashion. Recent advancements in the field of radar interferometry
have opened a new door on radar remote sensing of vegetation. In addition to the backscattering
coefficient of a distributed target, radar interferometers provide two additional parameters that
contain information about the target. These parameters are the correlation coefficient and the
interferogram phase [5, 6]. To interpret these parameters and to characterize their dependence
on the physical parameters of the target, a thorough understanding of the coherent interaction of
electromagnetic waves with vegetation particles is required. The premise of this investigation with
regard to retrieving vegetation parameters from INSAR is that the location of the scattering phase
center of a target is a strong function of the target structure. For example the scattering phase
centers of nonvegetated terrain are located at or slightly below the surface depending upon the
wavelength and the dielectric properties of the surface media. Whereas for vegetated terrain, these
scattering phase centers lie at or above the surface depending upon the wavelength of the SAR
and the vegetation attributes. Another important feature of interferometric SARs with regard to
estimation of forest parameters is its sensitivity to biom ass. Radar backscattering coefficients are
found to increase with increasing biomass until saturation at biomass values that depend on the
radar frequency. For example, at Lband the backscattering coefficients reach a saturation level for
aboveground biomass values around 100150 tons/ha. Our preliminary investigations show that
the scattering phase center height reaches a saturation level at biomass levels significantly higher
than biomass values at which the backscattering coefficients reach their saturation levels. It also
must be recognized that the vegetation cover in many interferometric SAR applications where
the vegetation itself is not the primary target, such as geological field mapping or surface change
monitoring, acts as interference. In these cases it is also important to identify and characterize
the effect of vegetation on the topographic information obtained from the interferometric SAR.
In order to utilize the information gathered by INSARs, forward and inverse models have to be
developed and their accuracies be examined. Extensive modeling efforts were devoted to achieve
reliable models. Using these models in conjunction with careful experimentations we were able
1
to demonstrate the applicability and importance of INSAR data in retrieval of tree parameters.
This report gives a brief summary of our activities. The appendices are also provided here to give
the detailed description of methodologies procedures for the interested readers.
2 Summary of Accomplished Results
In March, 1995, the University of Michigan, in collaboration with the Radar Science Group of
Jet Propulsion Laboratory, was awarded a threeyear grant by the Terrestrial Ecology Program at
NASA Headquarters to characterize and quantify the role of vegetation attributes in determining
the scattering phase centers as observed by interferometric SARs. The objectives of the study
were to:
1. Quantify the role of vegetation attributes in determining the location of the scattering phase
centers as measured by SAR interferometry using a coherent electromagnetic: scattering
model for vegetation.
2. Map vegetation height through the combined use of SAR interferometry in conjunction
with available standard digital elevation data (derived largely from optical techniques).
3. Correct SAR interferometry for vegetation effects through use of an inversion algorithm
based upon vegetation type and biomass. The end product is surface elevation.
4. Estimate crown layer vegetation attributes (such as thickness) using multifrequency SAR
interferometry.
5. Integrate the products derived from SAR interferometry into ecophysiological classifications
and forest biophysical parameter estimations.
For this purpose analytical, numerical, and experimental aspects of electromagnetic scattering
from forest canopies have been under investigation. A summary of accomplishments realized to
date is given next. The details are provided in the attached appendices.
2.1 Theoretical Model Development
2.1.1 Ak Radar Equivalence of an INSAR
A fundamental relationship between INSAR and Ak radar is established. This relationship is
the cornerstone of analytical and numerical analysis of the problem at hand. Understanding
the relationship between the tree height and the corresponding location of the scattering phase
centers requires numerical simulations (Monte Carlo simulation of a fractal generated forest
stand) or controlled experiments using scatterometers. The scattering phase center of a target
can also be obtained using a Akradar assuming that the incidence angle is known. Evaluation
of the scattering phase centers using frequency shift can easily be accomplished in a numerical
simulation or in a controlled experiment using a wideband scatterometer. Basically, by requiring
that the backscatter phase differences, one obtained from a small change in the aspect angle and
2
the other one obtained from a small change in the frequency of operation, be identical for both
approaches we established that
B
A/f =o 2 sin(O ao) (1)
where Af is the frequency shift of the equivalent Ak radar, fo is the operating frequency, B and
oa are, respectively, the baseline distance and angle, r is the slant range, and 0 is the look angle.
It is mathematically proven that this equivalence relationship is valid for multiple scattering among
particles and the scattering interaction between particles and the ground plane. The details are
reported in Appendix I [7].
2.1.2 Statistical Analysis
In estimating the height of the scattering phase center of a distributed target, random fluctuations
of the calculated/measured phase due to fading was investigated. An analytical form for the p.d.f.
of the interferogram phase was obtained in terms of two independent parameters: (1)(: mean
phase and (2)a: degree of correlation, which is given by
I a2cos2(
27w [1 a2 COS2(o 2)
f acos(bC) 7r _ cos()Q 1 (2)
1 &ccos2(4) t2 an 1a2cos2(G()b l
( is proportional to the mean scattering phase center height and a is inversely proportional to the
uncertainty with which ( can be estimated. It is shown that a is directly related to the frequency
correlation function (FCF) of the distributed target given by
< E12 >(3)
Using this pdf the uncertainty in estimation of (, or equivalently the mean height, from a single
pixel can be evaluated. Figure 1 shows the phase uncertainty range for 80% and 90% confidence
criteria [7]. Statistical analysis shows that the uncertainty in the height estimation of a distributed
target is a function of the equivalent frequency decorrelation bandwidth and is independent of
the baseline distance.
2.1.3 Vegetation Model
Theoretical vegetation models capable of predicting backscattering coefficients and location of
scattering phase center for simple canopy structures (homogeneous particle distribution) were
developed [7, 8]. It is also shown that for a uniform closed canopy the extinction and the physical
height of the canopy top can be estimated provided that the correlation coefficient (a) can
be measured very accurately. For example for a dense canopy it is found that the extinction
coefficient can be directly obtained from a. Also the location of the scattering phase center
(from the canopy top) is given by the following simple relationship:
A d cos0 04)
A/d .2 (4)
2jr~
3
40.
30. .
20.
10.
~s I. L" X X ... I......  —. 9
0.990 0.992 0.994 0.996 0.998 1.000
Degree of Correlation, aX
Figure 1: The interferogram phase uncertainty for 80% and 90% error probability criteria as a
function of the Degree of Correlations, a. A high degree of correlation, near 1, gives a small error
in the interferometric phase.
However, for finite canopies, estimation of extinction and scattering phase center is not straightforward.
Using the model developed in [8], the estimation of tree height and surface topography was
attempted. It was shown that measurements of interferometric phase and amplitude were not
enough to estimate the three relevant parameters, which are the tree height, groundsurface altitude, and extinction coefficient, if only volume scattering (from the leafbranchtrunk canopy) is
considered. The first demonstration was therefore supplemented with in situ extinction coefficient
measurements and the dualbaseline estimates were based on INSAR data alone [11].
2.2 Development of a Monte Carlo Coherent Scattering Model for Tree
Canopies Based on Fractal Theory
Although there are a number of EM scattering models for vegetation canopies [1, 2], they are
of little use with regard to INSAR applications due to the their inability to predict the absolute
phase of the scattered field. The absolute phase of the scattered field is the fundamental quantity
from which the interferogram images are constructed. As mentioned earlier in order to simulate
the response of an INSAR system a coherent scattering model capable of preserving the absolute
phase of the scattered field is needed. Traditional scattering models for forest canopy such as
radiative transfer and the distorted Born approximation are incapable of providing the phase of
the backscatter and do not preserve the effect of coherence caused by the relative position of
scatterers within a tree.
We have completed the task of [9, 10]. The details of these models can be obtained in
Appendices 11 and Ill. In this model random generation of tree architectures is implemented by
4
/
H 0.0 0.1 0.2 0.3! ! Extinction Coeff. (Np/m)
(a) Stand 31 (b) Fractal Tree (c) Extinction Profile
Figure 2: The generated fractal tree (b), based on forest Stand 31 (a), and the calculated
extinction profile (c).
employing the Lindenmayer systems (Lsystems). An Lsystem is a convenient tool for creating
fractal patterns of botanical structures. After generating a tree structure, the electromagnetic
scattering problem is then solved by invoking the single scattering theory. In this solution scattering from individual tree components when illuminated by the mean field is computed and then
added coherently. This model was examined thoroughly and its validity was tested using SIRC
data. We used our test site (Hiawatha National Forest) in Michigan's Upper peninsula for which
we collected extensive groundtruth data during the SIRC overflight. Figure 2 shows a photo of
a red maple stand, computer simulated tree structure of the same stand, and the exact extinction
profile derived from the Monte Carlo simulation. Figures 3a and 3b show the comparison between the model prediction and SIRC polarimetric backscattering coefficients at L and Cband
respectively. The three angular measurement points correspond to three different orbits of the
October 94 mission. To our knowledge this model is the most accurate and sophisticated scattering model for forest canopies to date. The model preserves the exact structure of the trees,
it can simulate a forest over a hilly terrain, it can simulate both coniferous and deciduous trees,
it can also incorporate a radially inhomogeneous dielectric profile for the branches and the tree
trunk. The details of this model and all related references are reported in [10].
We have also used the Monte Carlo coherent model in simulating the location of the scattering
phase center of different forest stands [12]. As mentioned in the summary of the theoretical
activities, the equivalence relationship can be invoked to find the location of the scattering phase
5
Lband Cband
~D vh 3 C  5 Is=VX
0 B
u vh 1C.
15 15 h
m 20 20 
o
COD
1 20 20
U
o10 20 30 40 50 60 70 10 20 30 40 50 60 70
Incidence Angle (degrees) Incidence Angle (degrees)
(a) (b)
Figure 3: Comparison between the model predictions (lines) and SIRC data (symbols) at (a)
Lband and (b) Cband.
center of a tree. This is basically done by evaluating the backscatter from a forest stand at
two slightly different frequencies and calculating the phase difference (for details see Appendix
IV). The difference in frequency is directly proportional to the baseline distance and is also a
function of the center frequency and the incidence angle. In April 1995 JPL TOPSAR flew over
one of our test sites in the Michigan's Upper peninsula. For this site extensive ground truth
data for vegetation including tree heights, type, number density, dielectric constant and for the
ground surface including soil moisture and surface elevation were collected. Starting from a
relatively poor TOPSAR data we were able to compare the result of our model with the actual
measurement of TOPSAR at Cband after a calibration process (see the measurement section
for more details). Figure 4 shows a photo of a red pine stand, and a computer generated red
pine. Figures 5 and 6 respectively show the TOPSAR image of the test stand and the measured
(at two incidence angles) and estimated height of the scattering phase centers of this stand.
Finally Fig. 7 shows the measured and calculated backscattering coefficients. In Figs. 6 and 7
excellent agreements between the measured and calculated results are shown. The details of this
simulation and some sensitivity analysis can be found in [12]. Figure 6 shows the measured (at
two incidence angles) and estimated height of the scattering phase centers of this stand. Figure
6 show excellent agreement between the measured and calculated results. This shows that we
can reliably estimate the height of a tree stand whose class we know using a simple model of the
phase center height variation with local incidence angle. The estimated tree height is within 1
meter of the known 9 meter height. The details of this simulation and some sensitivity analysis
can be found in [12].
6
I
(a) Stand 22 (b) Fractal Tree
Figure 4: The red pine forest stand (a), the generated fractal tree (b).
Runway
Stand 22
Figure 5: Cband image (a,) of Stand 22 in Raco, Michigan.
7
10..............................
0
I I. I 1.!
I ' ' I' ' ' ' I...
4)
a,
c3
el3
E
8
6
4
2
n
TOPSAR
 Model
*
I....I.... I. I....... I....
~~~ll... I.... I..! i
10 20 30 40
Incidence Angle
Figure 6: The estimated height of scattering phase
interferometric data from JPL TOPSAR.
50 60
0i (Degrees)
center of Stand
70
22, compared with the
8
0. l.. I. I I I. I I I I I I
4 10 E       A —  
0
U 20  * TOPSAR
 Model (total)
30   Component a
m Component a gb a
40
10 20 30 40 50 60 70
Incidence Angle Oi (Degrees)
Figure 7: The simulated backscattering coefficient of Stand 22, compared with the measured
data from JPL TOPSAR.
2.3 INSAR Response to Short vegetation
Classification of SAR images using Cband and higher frequency SAR faces a difficulty in separating short vegetation from tall trees. However, using INSAR the location of scattering phase
center and correlation coefficient (coherence) can be used. We have conducted experiments with
TOPSAR and the polarimetric wideband scatterometers at KBS site. We have also developed a
very sophisticated and comprehensive scattering model for short vegetation [13]. This is the first
complete second order scattering model for vegetation that accounts for multiple scattering in
dense vegetation media. The result of this model was verified experimentally using polarimetric
scatterometers and the JPL AIRSAR. This model was also successfully used to retrieve parameters
of soybean fields. The details on this model can be found in Appendix V.
2.4 INSAR Response to Trees
Because the radar backscatter is wellknown to saturate in response to highbiomass forests there
is some concern that INSAR will suffer from the same trouble. Consequently, we performed
simulations with the MonteCarlo model for an increasingly taller red pine forest as shown in Fig.
8(a). The biomasses far exceeded those that saturate the radar power responses (which is about
200 tons/ha), yet the interferometric phase continued to track the increase in height. Figure 8(b)
and (c) shows the simulated scattering coefficients and scattering phase center (SPC) at L band
as a function of dry biomass and tree height, respectively. It is obvious that there is no saturation
problem when using the interferometric phase even for relatively large values of biomass (600
tons/ha), and so this technique could be applied to oldgrowth forests, such as in the Amazon
and other areas around the world.
The Lband interferometric phase is also sensitive to the tree density. In Figure 8 for a 12
meter red pine stand, the estimated phase center height is shown with increasing tree density.
As expected, the denser the forest, the higher the phase center height, due to the progressively
increasing importance of the branch scattering over the groundtrunk scattering.
9
9m 15m 22m
130 kg 900 kg 3000 kg
6,,. v
8
 10
1 12
0
t 16
I 18
O 20
 HH
 VH
V;
/ Red Pine, height and dbh varied
/ Volumetric soil moisture = 0.18 cm3/ cm3
Frequency = 1.25 GHz! Incidence angle = 45 degrees
(a)
16
14
10 K
6 VH o o
i 4 f';'/: H HH~0 100 200 300 400 500 600
Biomass (tons/ ha)
(c).I.
(/
22 I
0 100 200 300 400 500 600
Biomass (tons/ ha)
(b)
14
12 '
10 "
8 o
6
4
2
0 5 10 15 20 25 30
Tree Height (m)
(d)
Figure 8: Lband SAR/INSAR simulation of red pine as a function of biomass. The progression
of fractal trees used is shown in (a). The saturation of the backscattered powers is demonstrated
in (b). The scattering phase center is shown in (c) where the HHpolarized term is still showing
sensitivity out to about 500 tons/ha. The plot in (d) shows the difference in the scattering phase
center between the hvpolarized and hhpolarized responses. The striking linearity of the response
extends up to at least 25metertall trees.
2.5 Inversion Algorithm Based on Multiincidence Angle and/or Multifrequency SAR/INSAR
An obtain canopy parameters from an available set of SAR and INSAR data, a robust and
comprehensive inversion algorithm is needed so that any combination of multifrequency, multiincidence angle, and/or multipolarization SAR and/or INSAR data set can be used as the input
to the algorithm. A sensitivity analysis was carried out for determining the most influential canopy
parameters on the SAR/INSAR responses using the Monte Carlo coherent model. The result of
this analysis was used to identify the most sensitive SAR/INSAR channels to the changes in
the canopy parameters. Since the Monte Carlo coherent model is computationally intensive, its
direct application would cause the inversion process to be significantly slower. To rectify this
deficiency while maintaining the high fidelity of the model, simple empirical models based on the
10
Htw
Htvh
Hthh
wg sig5 v s 3 W
0_4 1 0 0 0
c2 / C
2
0 2 4 6 8 2 4 6 0 2 4 6
Simplified Model Simplified Model Simplified Model
sigwvv sigvh sighh
8 2
14
0 0 a r 4
56
E12 E 16 E
~20
1 s
20 15 10 22 20 18 16 14 0
Simplified Model Simplified Model Simplified Model
Figure 9: A comparison between an empirical spcatterin del and the Coherent Monte Carlo
model for a red pine stand.
Monte Carlo model for different tree types was developed first. Since the quantities of interest are
terms of canopy parameters. For example for a given frequency and polarization, a Taylor series
expansion can be used to relate radar measured quantities to the canopy parameters at a specific
incidence angle. Then by repeating this process for many incidence angles, the Taylor expansion
coefficients can be fit to an algebraic equation in terms of incidence angle.
This process was demonstrated successfully [20] and the details are provided in Appendix VI.
For a red pine stand Figure 9 shows a comparison between the empirical model and the Monte
Carlo model at Cband over a wide range of parameters including the incidence angle range
250  70~, and 40% variation on trunk diameter (dbh), tree height, tree density, branch angle,
branch moisture, and soil moisture. The top three graphs show the height of the scattering phase
center at the three principal polarizations and the lower three graphs show the backscattering
Once a comprehensive (multifrequency and multipolarization) easilycalculable scattering
and interferometric models for all tree types of interest are developed, inversion for any available
combination of INSAR and/or SAR data can be attempted by searching for an optimum set
11
of canopy parameters which would minimize the difference between the model prediction and
measured quantities. It is expected that the objective function will be highly nonlinear and
complex containing many local minima. In these situations traditional gradientbased (TGB)
optimization methods usually converge to a weak local minimum. Stochastic algorithms such as
simulated annealing [17] and genetic algorithms [18, 19] offer an alternative for the traditional
gradientbased optimization methods where the dimension of the parameter space is large and/or
the objective function is nondifferentiable. Applying this algorithm the parameters of Stand 22
was obtained from the JPL TOPSAR.
2.6 Experimental Activities
Our experimental activities were focused over two wellcharacterized sites: 1) Hiawatha National
Forest (HNF) in Michigan's Upper peninsula, and 2) the Kellogg Biological Station (KBS) near
Kalamazoo, Michigan. Nearly 25 different forest stands were chosen in the NHF test site which
included varieties of tree types, tree height and density, and surface topography. For these stands,
extensive ground truth data were collected. The ground truth for vegetation includes tree heights,
type and structure, number density, and dielectric constant and for the ground surface includes soil
moisture and surface elevation (see Appendix VIII for detailed experimental procedures and the
data). In April 1995 JPL TOPSAR flew over this site and interferometric images were collected
at two incidence angles. Figure 10 shows the map of HNF site and the location of some of the
forest test stands. The grey level indicates the surface elevation as measured by TOPSAR at
incidence angle 31~. An important and most difficulttocharacterized ground truth parameter
was the forest floor surface elevation data which is required to extract the scattering phase center
height from INSAR images. To accomplish this, differential GPS was used to characterize the
elevation map of the forest floor of each stand with a vertical resolution of the order of ~5 cm
(see Appendix VIII). Figure 11 shows a typical surface elevation map of a stand generated from
the differential GPS measurements.
In using TOPSAR data we noticed problems in quality of the DEM data. After comparing
sets of DEM obtained from the same area with USGS DEM, height discrepancies as high as 50
m were observed. Then we developed a correction model to correct for the aircraft residual roll
angle error and multipath. The details of this procedure is given in Appendix VII.
We also conducted an experiment at the KBS site mainly to characterize the role of short
vegetation on the phase and amplitude of interferograms. TOPSAR and polarimetric L and Cband AIRSAR data were collected for this site. Different test fields with different vegetation type
including wheat, alfalfa, corn, and native grass were considered. Ground truth data for each test
field were also collected. We have also conducted an extensive polarimetric wideband backscatter
measurements of these fields using The University of Michigan L and Cband scatterometers. We
used the KBS data to verify our short vegetation model and to demonstrate vegetation parameter
estimation..3 Graduate Students
This NASA contract supported the following Ph.D. and M.S. students.
Ph.D. Students:
12
Figure 10: The surface elevation map (measured by TOPSAR) and road map of HNF site and
the location of some of the forest test stands.
1. James M. Stiles, "A Coherent, Polarimetric Microwave Scattering Model for Grassland
Structures and Canopies," The University of Michigan, 1996. (partially supported by this
project)
2. YiCheng Lin, "A FractalBased Coherent Scattering and Propagation Model for Forest
Canopies," The University of Michigan, 1997. (fully supported by this project)
3. TsenChieh Chiu, "Electromagnetic Scattering from Rough Surfaces Covered with Short
Branching Vegetation," The University of Michigan, 1998. (partially supported by this
project)
M.S. Students:
13
GPS Height for Stand 67
280.5
280
~,279.5
Z 279
 278.5
278
277.5
84.81
46.3915
84.8095 46.391
84.809 \...... 46.3905
84.8085 46.39
West Longitude, degrees North Latitude, degrees
Figure 11: Surface elevation map of Stand 67 at HNF as measured by differential GPS.
1. Yutaka Koboyashi, "Assessment of TOSAR DEM Data Quality for Extracting Tree Heights,"
19961998. (partially supported by this project)
2. Criag Wilsen, "Sensitivity of INSAR Response to Biomass Saturation," 1998 Present.
(fully supported by this project)
4 Publications
A significant number of scientific papers were produced during the course of this project. The
articles are grouped into reviewed articles which appeared in scientific journal and conference
papers.
4.1 Journal Papers
1. Lin, Y.C., and K. Sarabandi, "Electromagnetic scattering model for a tree trunk above a
ground plane," IEEE Trans. Geosci. Remote Sensing., vol. 33, no. 4, pp. 10631070, July
1995.
2. Stiles, J.M., and K. Sarabandi, "A scattering model for thin dielectric cylinders of arbitrary
crosssection and electrical length," IEEE Trans. Antennas Propagat., vol. 44, no.2,260 266, Feb. 1996.
3. R. N. Treuhaft, J. J. van Zyl, and K. Sarabandi, "Extracting Vegetation and Surface Characteristics from Multibaseline Interferometric SAR," EOS Transactions, American Geophysical
Union, 76, November 1995.
4. Sarabandi,K., "AkRadar equivalent of Interferometric SARs: A Theoretical Study for
determination of vegetation height," IEEE Trans. Geosc. Remote Sensing., vol. 35, no. 5,
Sept. 1997.
14
5. Chiu, T.C., and K. Sarabandi, "Electromagnetic Scattering from Short Branching Vegetation," IEEE Trans. Geosci. Remote Sensing., submitted for publication (Jan. 98).
6. Lin, Y.C., and K. Sarabandi, "A Monte Carlo Coherent Scattering Model For Forest
Canopies Using FractalGenerated Trees," IEEE Trans. Geosci. Remote Sensing., vol.
37, no. 1, pp. 440451, Jan. 1999.
7. Lin, Y.C., and K. Sarabandi, "'Retrieval of forest parameters using a fractalbased coherent
scattering model and a genetic algorithm," IEEE Trans. Geosci. Remote Sensing., accepted
for publication.
8. Chiu, T.C., and K. Sarabandi, "Electromagnetic scattering interaction between a dielectric
cylinder and a slightly rough surface," IEEE Trans. Antennas Propagat., accepted for
publication.
9. Sarabandi, K., and Y.C. Lin, "Simulation of Interferometric SAR Response for Characterization of Scattering Phase Center Statistics of Forest Canopies," IEEE Trans. Geosci.
Remote Sensing., accepted for publication (Jan. 99).
10. Y. Kobayashi, K. Sarabandi, L. Pierce, M.C. Dobson, "An Evaluation of JPL TOPSAR for
Extracting Tree Heights," IEEE Trans. Geosci. Remote Sensing, accepted for publication,
(Feb. 1999).
4.2 Conference Papers
1. R. N. Treuhaft, J. J. van Zyl, and K. Sarabandi, "Extracting Vegetation and Surface Characteristics from Multibaseline Interferometric SAR," EOS Transactions, American Geophysical
Union, 76, November 1995.
2. Sarabandi, K., "Determination Of Vegetation Height From SAR Interferometry: A Theoretical Study," Proc. IEEE Trans. Geosci. Remote Sensing Symp., Lincoln, Nebraska, May
1996.
3. Lin, Y.C., and K. Sarabandi, "A coherent scattering model for forest canopies based on
monte carlo simulation of fractal generated trees," Proc. IEEE Trans. Geosci. Remote
Sensing Symp., Lincoln, Nebraska, May 1996.
4. Stiles, J.M., and K. Sarabandi, "Scattering from cultural grass canopies: a phase coherent
model," Proc. IEEE Trans. Geosci. Remote Sensing Symp., Lincoln, Nebraska, May 1996.
5. Treuhaft, R., M. Moghaddam, J. van Zyl, and K. Sarabandi, "Estimating vegetation and
surface topographic parameters from multibaseline radar interferometry," Proc. IEEE Trans.
Geosci. Remote Sensing Symp., Lincoln, Nebraska, May 1996.
6. Sarabandi, K., "Characterization of canopy parameters using interferometric SARs," American Geophysical Union, Spring meeting, Baltimore, May 1996.
15
7. Sarabandi, K., and Y.C. Lin, "Characterization of Scattering Phase Center Statistics of Forest Canopies Using a Monte Carlo Coherent Scattering Model Based on Fractal Generated
Trees," URSI General Assembly, Lille, France, August 1996 (invited).
8. Treuhaft, R.N., E. Rodriguez, M. Moghaddam, J.J. van Zyl, and K. Sarabandi, "Estimating vegetation and surface characteristics with multifrequency SAR interferometry," URSI
General Assembly, Lille, France, August 1996 (invited).
9. Sarabandi, K., and Y.C. Lin, " Simulation of Interferometric SAR Response to Deciduous and Coniferous Forest Stands," Proc. IEEE Trans. Geosci. Remote Sensing Symp.,
Singapore, 1997.
10. Chiu, T.C., and K. Sarabandi, "Electromagnetic scattering interaction between a dielectric
cylinder and a slightly rough surface," Proc. IEEE Trans. Geosci. Remote Sensing Symp.,
Singapore, 1997.
11. Y.C. Lin, and K. Sarabandi, "Coherent scattering and propagation model for coniferous and
deciduous tree canopies," Proc. IEEE Trans. Antennas Propagat.& URSI Symp., Montreal,
Canada, July 1997.
12. Chiu, T.C., and K. Sarabandi, "Electromagnetic scattering from targets above rough surfaces,"Proc. IEEE Trans. Antennas Propagat.& URSI Symp., Montreal, Canada, July
1997.
13. Y.C. Lin, and K. Sarabandi, "Tree parameter estimation from interferometric radar responses," Proc. IEEE Trans. Geosci. Remote Sensing Symp., Seattle, 1998.
14. T. Chu and K. Sarabandi, "A coherent secondorder scattering model for short vegetation,"
Proc. IEEE Trans. Geosci. Remote Sensing Symp., Seattle, 1998.
15. C.B. Wilsen, K. Sarabandi, Y.C. Lin "The Effect of Tree Architecture on the Polarimetric
and Interferometric Radar Responses," Proc. IEEE Trans. Geosci. Remote Sensing Symp.,
Seattle, 1998.
16. Y. Kobayashi, K. Sarabandi, L. Pierce, M.C. Dobson, "Extracting Tree Heights using JPL
TOPSAR DEM data," Proc. IEEE Trans. Geosci. Remote Sensing Symp., Seattle, 1998.
17. Sarabandi, K., C.G. Brown, and L. Pierce, "Tree height estimation from the polarimetric
and interferometric radar response," Proc. IEEE Trans. Geosci. Remote Sensing Symp.,
Hamburg, Germany, 1999.
18. Wilsen, C.B., and K. Sarabandi, "Modeling of INSAR response to forest biomass variation," Proc. IEEE Trans. Geosci. Remote Sensing Symp., Hamburg, Germany, 1999.
16
References
[1] F. T. Ulaby, K. Sarabandi, K. MacDonald, M. Whitt, and M. C. Dobson, " Michigan
Microwave Canopy Scattering Model", Int. J. Remote Sensing, Vol. 11, No. 7, pp. 1223 1253, 1990.
[2] M. A. Karam, A. K. Fung, R. H. Lang, and N. H. Chauhan, "A microwave scattering model
for layered vegetation," IEEE Trans. Geosci. Remote Sensing., vol. 30, no. 4, pp. 767784,
July 1992.
[3] K. Sarabandi, Electromagnetic Scattering from Vegetation Canopies, Ph.D. Dissertation,
University of Michigan, 1989.
[4] R. L. Jordan, B. L. Huneycutt, and M. Werner, "The SIRC/XSAR synthetic aperture radar
system," IEEE Trans. Geosci. Remote Sensing., vol. 33, pp. 829839, July 1996.
[5] Zebker, H/A., S. N. Madsen, J. Martin, K. B. Wheeler, T. Miller, Y. Lou, G. Alberti, S.
Vetrella, and A. Cucci, " The TOPSAR interferometric radar topographic mapping instrument," IEEE Trans. Geosci. Remote Sensing., vol.30, No.5, pp.933940, 1992.
[6] Rodriguez, E., and J.M. Martin, "Theory and design of interferometric synthetic aperture
radars," IEE Proceedings, vol. F139, no. 2, pp. 147159, 1992.
[7] Sarabandi,K., "AkRadar equivalent of Interferometric SARs: A Theoretical Study for determination of vegetation height,"IEEE Trans. Geosci. Remote Sensing., Vol. 35, No. 5, Sept.
1997.
[8] R. N. Treuhaft, M. Moghaddam, and J. J. van Zyl, "Inteferometric Remote Sensing of
Vegetation and Surface Topography," Radio Science, vol. 31, pp. 14491485.
[9] Lin, Y.C., and K. Sarabandi, "Electromagnetic scattering model for a tree trunk above a
tilted ground plane," IEEE Trans. Geosci. Remote Sensing., vol. 33, no. 4, pp. 10631070,
July 1995.
[10] Lin, Y.C., and K. Sarabandi, "A Monte Carlo Coherent Scattering Model For Forest Canopies
Using Fractal Generated Trees," IEEE Trans. Geosci. Remote Sensing., vol. 37, no. 1, pp.
440451, Jan. 1999.
[11] Treuhaft, R.N., E. Rodriguez, M. Moghaddam, J.J. van Zyl, and K. Sarabandi, "Estimating vegetation and surface characteristics with multifrequency SAR interferometry," URSI
General Assembly, Lille, France, August 1996 (invited).
[12] Sarabandi, K., and Y.C. Lin, "Simulation of Interferometric SAR Response for Characterization of Scattering Phase Center Statistics of Forest Canopies," IEEE Trans. Geosci. Remote
Sensing., accepted for publication.
[13] Chiu, T.C., and K. Sarabandi, "Electromagnetic scattering interaction between a dielectric cylinder and a slightly rough surface," IEEE Trans. Antennas Propagat., submitted for
publication (June 1997).
17
[14] Goldstein, R.M., H.A. Zebker, and C.L.Werner, "Satellite radar interferometry: Twodemensional phase unwrapping," Radio Sci., vol.23, no.4, pp. 713720, JulyAugust 1988.
[15] Gens, R., and J.L. van Genderen, "Review article: SAR interferometry issues,techniques,applications," Inter. J. of Remote Sensing, vol. 17, no. 10,pp. 18031835,
1996.
[16] Zebker, H.A., C. L. Werner, P.A. Rosen, S. Hensley, "Accuracy of Topographic Maps Derived
from ERS1 Interferometric Radar," IEEE Trans. Geosci. Remote Sensing., vol. 32,no.4, pp.
823836, July 1994.
[17] Kirkpatrick, S., J.C.D. Gelatt, and M.P. Vecchi, "Optimization by simulated annealing,"
Sci., vol. 220, pp. 671680, 1983.
[18] Holland, J.H., "Genetic Algorithms," Scientific American, pp. 6672, July 1992.
[19] DeJong, K.A.,"An Analysis of the behavior of a class of genetic adaptive systems," Ph.D.
dissertation, The University of Michigan, Ann Arbor, 1975.
[20] Lin, Y.C., and K. Sarabandi, "'Retrieval of forest parameters using a fractalbased coherent
scattering model and a genetic algorithm," IEEE Trans. Geosci. Remote Sensing., accepted
for publication.
18
Appendix I
AkRadar Equivalent of Interferometric SARs: A
Theoretical Study for Determination of Vegetation Height
19
AkRadar Equivalent of Interferometric SARs: A
Theoretical Study For Determination Of
Vegetation Height
Kamal Sarabandi
Radiation Laboratory
Department of Electrical Engineering and Computer Science
The University of Michigan, Ann Arbor, MI 481092122
Tel:(313) 9361575, Fax:(313) 7472106
email: saraband@eecs.umich.edu
In this paper the theoretical aspects of estimating vegetation parameters from SAR
interferometry is presented. In conventional applications of interferometric SAR
(INSAR), the phase of the interferogram is used to retrieve the location of the scattering phase center of the target. Although the location of scattering phase center
for point targets can be determined very accurately, for a distributed target such
as a forest canopy this is not the case. For distributed targets the phase of the
interferogram is a random variable which in general is a function of the system and
target attributes. To relate the statistics of the interferogram phase to the target
attributes, first an equivalence relationship between the twoantenna interferometer
system and an equivalent Ak radar system is established. This equivalence relationship provides a general tool to related the frequency correlation function (FCF)
of distributed targets, which can conveniently be obtained experimentally, analytically, or numerically, to the phase statistics of the interferogram. An analytical form
for the p.d.f. of the interferogram phase is obtained in terms of two independent
parameters: (1)(: mean phase and (2)a: degree of correlation. C is proportional to
the scattering phase center and a is inversely proportional to the uncertainty with
which ( can be estimated. It is shown that a is directly related to the FCF of the
distributed target which in turn is a function of scattering mechanisms and system
parameters. It is also shown that for a uniform closed canopy the extinction and the
physical height of the canopy top can be estimated very accurately. Some analytical
and numerical simulations are demonstrated.
1 Introduction
Vegetation cover on the earth's surface is an important factor in the study of global
changes. The total vegetation biomass is the most influential input to models for
terrestrial ecosystems and atmospheric chemistry. Monitoring parameters such as
1
the total vegetation biomass, total leaf area index, and rate of deforestation is vital
to keep our planet capable of supporting life. Microwave remote sensing techniques
offer a unique opportunity to probe vegetation canopies at different depths. Since a
forest stand is a very complicated random medium with many attributes that influence the forest radar response, accurate estimation of the forest physical parameters
requires a large number of independent radar observations (multifrequency and
multipolarization backscatter) in conjunction with some a priori information about
the forest stand [1, 2, 3, 4]. The use of polarimetric synthetic aperture radars as
active sensors to survey forested areas has reached a level of maturity. Despite considerable advancement in retrieving the canopy parameters from multipolarization
and multifrequency backscatter data, an unsupervised reliable inversion algorithm
has not yet been developed. With the recent advances in the development of interferometric SARs [5][10], another set of independent radar observation has become
available for the estimation of vegetation biophysical parameters.
The interferometric technique relies on a coherent imaging process to find the
range or distance to the scattering phase center of the scatterers in the radar image. Based on this principle, there are two standard approaches for extracting
topographical information using synthetic aperture radars. In one approach, SAR
systems equipped with two separate antennas mounted on the SAR platform are
used to generate two complex coregistered images from two slightly different aspect
angles. The phase difference calculated from the cross product of the two complex
images, referred to as an interferogram [6], is processed to estimate the height information. In the second approach the interferogram is formed using two successive
images taken by a single SAR with almost the same viewing geometry [7, 8]. It is
shown that the phase of the interferogram is proportional to the wavelength, slant
range, look angle, distance between the antennas (baseline distance), orientation of
the antennas with respect to each other, and the height of the scattering phase center
above a reference line [5, 9]. For nonvegetated terrain, the scattering phase centers
are located at or slightly below the surface depending upon the wavelength of the
SAR and the dielectric properties of the surface media. Whereas for vegetated terrain, these phase centers lie at or above the surface depending upon the wavelength
of the SAR and the vegetation attributes. Although it is expected that for vegetated
surfaces the temporal decorrelation would hamper repeatpass interferometry from
producing the location of scattering phase center, experimental investigations has
shown that even after 18 days the correlation associated with forested area can be
as high as 0.5 [11, 12].
The significant vegetation attributes are: (1) the type of vegetation, (2) the
quantity or biomass of the vegetation and (3) the dielectric properties of the vegetation. As pertains to SAR interferometry, the type of vegetation refers to the
structural attributes of vegetation elements and includes the shapes and sizes of
foliage and woody stems relative to wavelength and their threedimensional organizational structure. The biomass refers to attributes such as the height of the
2
vegetation, the thickness and density of the crown layer that contains foliage and
stems, and the number of plants per unit area. The dielectric properties of the vegetation elements determine scattering and propagation through the media; these may
vary with time due to seasonal changes in plant physiology and the phase of water
(liquid or frozen) or due to the presence of water films resulting from intercepted
precipitation or dew.
The main objective of this paper is to establish a thorough understanding of
the relationship between the INSAR parameters and the vegetation attributes and
the accuracy with which the vegetation scattering phase center can be measured.
To accomplish these goals an equivalence between INSAR and Akradar techniques
is established which facilitates numerical simulations and controlled experiments
using scatterometers. Monte Carlo simulation of a forest canopy which preserves the
absolute phase of the radar backscatter allows for quantifying the role of vegetation
attributes in determining the location of the scattering phase centers as measured
by SAR interferometry.
2 AkRadar Equivalent of an INSAR
In this section an equivalence relationship between an interferometric SAR and a
Akradar is obtained. As will be shown later the statistics of the phase of the
interferogram or equivalently the location of the scattering phase center and its
statistics is a very strong function of the location and number density of the forest
constituent particles and their dielectric and scattering properties. Understanding
the relationship between the tree height and the corresponding location of the scattering phase centers requires numerical simulations (Monte Carlo simulation of a
fractal generated forest stand) or controlled experiments using scatterometers. The
scattering phase center of a target can also be obtained using a Akradar assuming that the incidence angle is known. Evaluation of the scattering phase centers
using frequency shift can easily be accomplished in a numerical simulation or in a
controlled experiment using a wideband scatterometer.
To demonstrate the equivalence between an INSAR and a Akradar consider a
twoantenna interferometer as shown in Fig. 1. In this scheme one of the antennas
is used as the transmitter and receiver and the other one is used only as the receiver,
the phase of the interferogram (4) is related to the difference in path lengths from
the antennas to the scattering phase center (6) by
27rQ (1)
27r
where Ao = c/fo is the wavelength (in repeatpass interferometry the 27r factor in
(1) must be replaced by 47r). Having calculated 6 from (1) and knowing the baseline
3
distance B and baseline angle a, the look angle 0 can be computed from
sin(0  a) (2)
Referring to Fig. 1 it can easily be shown that the height of the scattering phase
center, with respect to an arbitrary reference level, is given by
h = H  r[cos(a) cos(O  a)  sin(a) sin(O  a)]. (3)
The accuracy in height estimation using this method is directly proportional to the
accuracy in the measurement of the interferogram phase. The uncertainty in phase
measurements is caused by two factors: (1) systematic errors, and (2) indeterministic
errors. The sources of systematic errors are image misregisteration and lack of
maintaining the geometry of the interferometer. The source of indeterministic error
is fading. Basically the backscatter signal from a distributed target including many
scatterers decorrelates as the incidence angle changes.
Now let us consider a radar capable of measuring the backscatter at two slightly
different frequencies fi = fo and f2 = fo + Af. Denoting the phase difference
between the two backscatter measurements by b, it can be shown that
( = 2AAkr = 47rAf r/c (4)
where c is the speed of light and r is the radar distance to the target scattering
phase center. Comparing (4) with (1) and (2) the desired relationship between the
Akradar and INSAR can be obtained. Basically by requiring the backscatter phase
differences, once obtained from a small change in the aspect angle and the other one
obtained from a small change in the frequency of operation, be identical for both
approaches we have
Af = fo sin(0a) (5)
Noting that r = H/cos(9), it can easily be shown that Af is rather insensitive
to variations in incidence angle over the angular range 30~  60~. For example, a
Cband (5.3 GHz) interferometer with a horizontal baseline distance 2.4 m at an
altitude 6 Km is equivalent to a Cband Akradar with Af = 530KHz.
The equivalence relation given by (5) is derived based on a single target. In
regard to this relationship there are two subtle issues that require clarification. In
almost all practical situations the scatterers are located above a ground plane which
give rise to three significant scattering terms besides the direct backscatter. These
include the bistatic scattering from the target reflected from the ground plane, the
bistatic scattering from the target when illuminated by the reflected wave, and the
backscatter reflected by the ground plane when the target is illuminated by the
reflected wave. The last term can be regarded as the direct backscatter of the
incident wave from the image target and therefore the equivalent Akradar can
4
accurately predict the interferometric phase associated with this term. However, for
the other two scattering terms (singlebounce terms), the validity of the equivalence
relationship is not obvious. Suppose a twoantenna interferometer, as shown in Fig.
2, is illuminating a target at point C above the ground plane. For the equivalent
Akradar located at A1, the interferometric phases of the two singlebounce terms
(qb) are identical and are given by:
Ob= Ak(A1Bl + B1C + CA1) = 2AkA10. (6)
Equation (6) indicates that the location of the scattering phase center for the groundbounce terms appears at the ground interface for the Akradar. The interferometric
phase of the two singlebounce terms for the twoantenna system can be obtained
from:
4/ = 2eik(AlC+CBl+B1lA)  (eik(AlC+CB2+B2A2) + eik(AiBi+BlC+CA2))
Noting that B1C = B1C', B2C = B2C', and after some simple algebraic manipulation, it can be shown that
k
= 2 [(A1C + A1C')  (A2C + A2C')].
Referring to Fig.2, it can easily be shown that C'C" = 200' and therefore A2C +
A2C' = 2A20. Similarly, it can be shown that (AiC + AiC') = 2A1O, thus
Ob = k(A10  A20).
which indicates that the location of scattering phase center for the two singlebounce
terms is at 0. Therefore the equivalence relation (5) guarantees that Ob = 4b.
The second issue pertains to the validity of the equivalence relation in regard
to multiple scattering terms. As mentioned earlier the equivalence relationship is
derived based on a single target and therefore it would be valid for a random medium,
if the overall backscatter is dominated by the firstorder scattering mechanisms. To
demonstrate that the equivalent Akradar provides the location of the scattering
phase center accurately even in the presence of multiple scattering, consider two
scatterers located at two arbitrary points C and D within a resolution cell. For an
INSAR whose antennas are at points A1 and A2, the interferometric phase associated
with the second order scattering terms is calculated from:
(S(2) _ / 2eik(A1C+CD+DA1)  z(eik(AC+CD+DA2) _ eik(AlD+CD+CA2))
INSAR = —e  e ) e
In derivation of the above equation, the reciprocity theorem is used which indicates
that the secondorder scattering amplitude obtained from the interaction between
particle C and particle D is equal to that obtained from the interaction between
particle C and particle D. As before it can easily be shown that
INSAR = [(AiC + A1D)  (A2C + A2D)]
5
Let us define M as point in the middle of CD line. Since the distance between the
antennas and the scatterers are much larger than the distance between the scatterers,
we have
(N)SAR = k(A1M  A2M)
which indicates that the phase center of the second order term apperas at the midpoint between the two scatterers. For a Akradar at A1 the same second order phase
term is given by:
k = Ak(AiC + CD + DAi)
Noting that A1C + A1D w A1M and CD << A1M, the above expression reduces to,) = 2Ak A1M (7)
Equation (7) shows that the location of scattering phase center measured by a Ak
radar is at M as well.
What remains to be shown is the algorithm by which the target height can be
extracted from an equivalent Akradar. Let us consider a random collection of
scatterers within a range and azimuth resolution cell illuminated by a plane wave
as shown in Fig. 3. The height of the scattering phase center for this collection can
be considered to be the algebraic sum of the physical height of the pixel center and
a residual apparent height of the scatterers which is a complex function of particles
and radar attributes. Suppose there are M scatterers within a resolution cell. Let
Sn denote the scattering amplitude of the nth scattering component of the ensemble
which can represent the direct backscattering from a particle, a multiple scattering
term between a number of the scatterers in the ensemble, or a bistatic scattering
term reflected from the ground plane. Without loss of generality let us assume that
the phase reference is on the reference plane just below the pixel center (see Fig. 3).
The total backscattered field is the coherent sum of all the scattering components
which can be obtained from:
eikor N
Es = e S ei2kOr (8)
r n=1l
where r is the distance from the origin to the observation point, rn is the total round
trip path length difference between a ray traveled to the origin and the ray corresponding to the nth scattering component. Note that a time convention of eiwt has
been assumed and suppressed. The equivalent problem is to replace the collection of
the random particles and the underlying ground plane with an equivalent scatterer
placed at the scattering phase center whose backscattering amplitude is denoted by
Se = Se I exp(i oe). In this case the backscattered field is given by
ikor
s Se e2iko h cos(e)
r
6
Computing the phase of the backscattered field (5) from (8) and noting that the
phase calculation is modulo 27r, the height of the scattering phase center can be
obtained from
2koh cos(0) + >e = 2mTr + A (9)
However, in computation of h from (9) two important parameters, namely m and
<&e are missing. This problem could be rectified, if a radar measurement from the
same collection of particles and the same viewing angle but at a slightly different
frequency were available. Suppose the change in frequency is small enough so that
the change in the phase of the scattering amplitudes is negligible. In this case the
change in the phase of the scattered field ( V =  9) due to the change in the
wavenumber (Ak = k2 k1) is basically dominated by the path length differences
and it can easily be shown that
h= 2c() Ak (10)
Equation (10) is the fundamental basis for extraction of height information from a
twofrequency radar. It should be emphasized that in this process the incidence angle
must be known which is the case in a numerical simulation or in a measurement
using a narrow beam scatterometer system. Since the shift in frequency is very
small (less than 0.1% of center frequency), the scattering amplitude terms Sn do not
change when the frequency is changed from fi to f2 and therefore they need not
be computed twice in a numerical simulation. However, the phase terms associated
with the path length differences must be modified by replacing ko with ko + Ak.
Expressing the measured phase in degrees, the difference in slant range (Ar =
h cos(0)) in meters, and the difference in frequency (Af) in MHz, (8) can be rewritten as
q$=2.4ArAf. (11)
Therefore if the uncertainty in the phase calculation/measurement is 1~ and a distance resolution of Im is required, a minimum frequency shift of 416.66 KHz is
needed assuming that the uncertainty in phase calculation/measurement is independent of frequency shift (a wrong assumption). Using this frequency shift the
unambiguous range of 360m can be achieved noting that the phase is measured
modulo 360~. The uncertainties in height estimation using a Akradar can easily be
obtained as the relationship between h and 0 is explicitly expressed by (10). It can
easily be shown that the uncertainty in height due to the lack of accuracy in the
knowledge of the incidence angle is given by:
6h =h tan(0)60
For uncertainties in incidence angle as high as 3~, the error in height is 5% of h at
0 = 45~.
7
Through the combination of two or more frequency shifts, an unambiguous height
profile with fine resolution can be achieved. The resolution in height estimation using
Akradar is characterized by the frequency correlation function of the target as will
be discussed next. Equation (10) indicates that accuracy in the height measurement
increases as the frequency shift increases. On the other hand as the frequency shift
(baseline distance) increases the phase shift caused by the path length differences
will change in a nonlinear and random fashion which causes an uncertainty in the
measurement of distance (height). Hence there may exist a critical frequency shift
for which the finest height resolution for a given distributed target can be achieved.
This critical frequency shift is the counterpart of a critical baseline distance in an
interferometer for which the finest height resolution for the same distributed target
is achievable.
3 Statistical Analysis
In estimating the height of the scattering phase center of a distributed target using (11), random fluctuations of the calculated/measured phase as a function of
frequency due to fading must be considered. In this section the effect of random
position of the scatterers on the height estimation is studied. Also a procedure for
calculation of the critical frequency shift (baseline distance) in terms the statistical properties of the distributed target is outlined. Phase statistics of polarimetric
backscatter response of distributed targets for single and multilook can be found
in literature [14, 15, 16]. The statistical analysis of interferometric phase given here
parallels the method given in [14]. For a random collection of particles the scattered
field given by (8) is a complex random variable. Since the location of the scatterers
in the illuminated volume is random, the process describing the scattered field is a
Wiener process [13]. If the number of scattering components M is large, the central
limit theorem mandates that the process is Gaussian. Let us denote the scattered
field at f/ and f2 by E1' = X1 + iX2 and E3 = X3 + iX4, respectively, where Xj denotes the real or imaginary part of the scattered fields. These quantities are jointly
Gaussian and can be represented by a fourcomponent random vector X. The joint
probability density function (pdf) of the random vector can be fully characterized
from a 4 x 4 symmetric positive definite matrix known as the covariance matrix A
whose entries are given by
tj = i =< XiX > ij E {1,*...*,4}
It has been shown that the entries of the covariance matrix for the Wiener process
satisfy the following conditions [14]:
A = 22 =< X2 >=< X2 >, (12)
A12 =< X1X2 >= 0, (13)
8
A33 = >44 =< X >=< X2 >, (14)
A34 =< X3X4 >= 0, (15)
A13 = A24 =< XlX3 >=< X2X4 >, (16)
A14 = 23 =< XX4 >=  < X2X3 >. (17)
In the same paper [14] it is also shown that the pdf for the difference between phases
of E2 and Es (for a singlelook case) is related to the elements of the covariance
matrix and is given by:
1 a2
=> 27r [1  a2 COS2(  ()]
a QCOS(  C) 7 _ a QCOS(O ) 1
* a 1+ cos( + tan cos() i
1 a2 cos2(4sC) 2 (1  cos2Qk J
(18)
where
/13 + 14 a1 14
a = XI, C=tan 
lV A1133 A13
The parameter a is known as the degree of correlation and can vary from 0 to 1.
When the scattered fields are completely correlated a = 1 and the pdf of 0 is a
delta function. In this case the calculation of the height from (10) has no error in
principle when the effect of thermal noise is ignored. The parameter ( is known as
the coherent phase difference and can vary from r to 7r. For ~b = C the pdf assumes
its maximum and this point corresponds to the average height of the scattering phase
center for a uniform distributed target over a flat ground plane.
In this analysis the objective is to establish a relationship between a desired
height resolution and the corresponding required frequency shift for a given error probability criterion. The Wiener processes considered in this problem satisfy
one more condition beyond those given by (12)(17). This condition can be derived by noting that the required frequency shift for the height estimation is much
smaller than the operating center frequency of the radar, therefore it is expected
that backscattered power carried by the two processes be equal. This requirement
renders the following condition:
A = A33. (19)
Let us define the normalized correlation function of the process by
R(Af) = < r2 (20)
<1IEl 12>
which is also known as the frequency correlation function [17]. Using (16), (17), and
(19), it can easily be shown that
R(Af) = a. (21)
9
It is interesting to note that the maximum of the normalized frequency correlation
function occurs at Af = 0 ( AkAf=o = 0), hence a = 1 to the first order in Af. In
other words for small variation of frequency the pdf of the phase difference is very
narrow which ensures accurate estimation of the height. As expected, when Af
increases, a = R(Af) approaches zero which corresponds to a uniform distribution
for the phase difference. In this case the probability of error in the height estimation
is close to unity.
To quantify the accuracy of the height estimation for a given distributed target,
let us assume that the normalized frequency correlation function of the target is
known. In this case only the coherent phase difference (C) is missing to fully characterize the pdf of the phase difference. The objective is to estimate ( from which
the mean height can be obtained from
h =  (22)
2.4A\fcos(0) (22)
However, the difficulty in calculation of h is that only one measurement of the phase
for each pixel is available. Suppose 6q =  ( represents the deviation in the phase
measurement which corresponds to an error in height measurement given by
Sh= (23)
2.4Af cos 0
where 8h is in meters, 6q is in degrees, and Af is in MHz. The uncertainty in the
estimation of height can be quantified according to a prescribed error probability
criterion. For example, 6S can be chosen such that the probability of measuring the
phase within the 6S neighborhood of the coherent phase difference to be 90%, that
is
P( E [C C, + a]) = 0.9
Hence, using this criterion the estimate of the height is
h = h ~ h
with a probability of 0.9.
The uncertainty in the height measurement defined by this criterion is a complex
function of Af noting that 6S is a function of a which is related to Af through
the correlation function. Referring to (23), it seems that the height uncertainty
decreases when Af is increased; however, it should also be noted that 68 increases
when Af is increased. This behavior suggests that there may exist a frequency
shift Af for which 8h is minimized. This particular frequency shift will be referred
to as the critical frequency shift. In order to investigate the possibility of finding
the critical frequency shift, the relationship between the height uncertainty and
the frequency shift must be obtained. The relationship between 8q and a can be
directly obtained from the cumulative distribution function (cdf) of AqS =  C.
10
Unfortunately, a close form for the cdf of Az/ does not exist and the relationship
between 6$o and a must be obtained numerically. Figure 4 shows the cdf of AX
for different values of a and the corresponding 6; for the 90% probability criterion.
Note that for most practical cases a > 0.95 (baseline distance or equivalently the
frequency shift is rather small). The relationship between 64 and a is shown in Fig.
5 for the 80% and 90% probability criteria.
Assuming a Gaussian form for the normalized frequency correlation function
the uncertainty in height estimation can easily be related to the frequency shift.
Suppose the normalized frequency decorrelation function is given by
R(Af) = e^fFd)2
where Fd is the decorrelation bandwidth defined as the frequency shift for which
R(Af) = e1. Using (21) the frequency shift can be related to the degree of correlation through
Af = na
Fd
For values of a close to unity the righthand side of the above equation is approximately equal to 1  a. Referring to Fig. 5, it can also be observed that
8q C 1 a
where C is a constant proportional to the probability criterion. Therefore &qis
linearly proportional to Af where upon substituting in (23) it can be shown that
the height uncertainty is independent of the frequency shift and the critical frequency
shift is not well defined. This result may be generalized to all frequency correlation
functions because for small values frequency shift, the frequency correlation function
of all targets can be approximated by
R(A f) ^ 1  (A/Fd)2 (24)
where Fd is a free parameter equal to the frequency decorrelation bandwidth of
an equivalent Gaussian correlation function. Figure 6 shows the product of the
height uncertainty and the equivalent decorrelation bandwidth versus frequency
shift normalized to the decorrelation bandwidth for both the 80% and 90% criteria.
Thus the uncertainty in height measurement for a distributed target with known
equivalent decorrelation bandwidth is independent of frequency shift or equivalently
the baseline distance. In other words, the frequency decorrelation bandwidth of the
target is the determining factor in the height measurement error.
4 Frequency Correlation Function of Distributed
Targets
As was shown in the previous section the frequency correlation function of a distributed target is the most important parameter in estimating its scattering phase
11
center height. The literature concerning the frequency correlation function of distributed targets is rather scarce. Analytical expressions for the frequency correlation
function of simple targets such as uniform independent scatterers and rough surfaces
using Kirchhoff approximation have been obtained for simple uniform plane wave
illuminations [18, 19]. For the uniform distribution of scatterers illuminated by a
uniform plane wave the frequency correlation function is given by
R(Af)  sin(7rp Af / 150)
7fPrZ f/150
where Pr is the slant range in meters and Af is in MHz. The corresponding Gaussian equivalent decorrelation bandwidth for this function is Fd = 117/pr MHz. Since
product of 6h and Fd is independent of Af/Fd, the uncertainty in height measurement can be improved by decreasing the slant range resolution.
In a recent study [17] it was shown that the frequency correlation function, in
general, depends on two sets of parameters: (1) radar parameters such as incidence
angle, frequency, polarization, and footprint size, and (2) target parameters such
as penetration depth and albedo. It is also shown that when the scattering is
localized, that is, the field correlation distance in the random media is relatively
small, the frequency correlation function can be expressed in terms of product of
two expressions, one depending only on the radar parameters and the second one
depending only on the target attributes. For example an expression for the frequency
cross correlation of backscatter from a homogeneous layer of random particles such
as leaves and stems above a smooth ground plane is found to be [17]
< Epp(f2)Epp(f2) >= fJf 4 ( [G(x, y)2dxdy. 4dRp 2W e2(iakcos~sec)d
+Wb ( 1 + R l42(iAk cos 0sec O)d) 1e2(ik cos ^ sec O)d }
PPP PI 1p2(K sec i k cos) J
(25)
where 0 is the incident angle, d is the layer thickness, and Rp is the Fresnel reflection
coefficient for ppolarized incident wave (p E v,h). The first term in (25) is the
system dependent component in which G is the antenna gain or the SAR pointtarget response (ambiguity function), r is the radar distance, and the limits of the
integrals represents the antenna footprint or the pixel area. The curly bracket in
equation (25) represents the target dependent component in which i denotes the
layer extinction and Wpppp and Wpppp are the copolarized components of the phase
matrix in the backscatter and specular (with respect to the vertical axis) directions
which are defined by
=b lim ppvh
where ASpp represents a scattering matrix element of a small volume AV of the random medium. In the expression given by (25) the reference phase plane is assumed
12
to be at the top of the layer, i.e., the ground plane is assumed to be at z = d as
shown in Fig. 7.
The decorrelation caused by the system dependent component for an imaging
radar is directly proportional to the system slant range resolution. Also for conventional radars the decorrelation caused by the system component is inversely proportional to antenna beamwidth and directly proportional to range and incidence
angle. In most existing INSAR systems the measured decorrelation is dominated
by the system component. As discussed before the uncertainty in height estimation increases as the correlation bandwidth increases. Fortunately the decorrelation
caused by the system parameters can be calibrated out since its effect appears as a
simple multiplicative factor. If the system ambiguity function or the antenna pattern is known, the system component of frequency correlation function can easily
be computed and removed from the measured data. In cases where the ambiguity
function or the antenna pattern is not well characterized the correlation over a rough
surface (a distributed target with no vertical extent) approximately represents the
system component of the decorrelation and can be used for calibration. Once the
target dependent component of the correlation function is obtained, the equivalent
frequency decorrelation bandwidth can be computed from which the uncertainty in
height estimation can be evaluated. As shown in the simple model described by (25)
the target decorrelation contains information about its physical parameters.
Figure 8 shows the frequency correlation function of a uniform random layer
of flat leaves with average area 50cm2, thickness 1.3 mm, and dielectric constant
= 19 + i6.3 above a ground plane with dielectric constant sg = 15 + j2.0 at 5.3
GHz and incidence angle 0 = 300. In this simulation the layer thickness was chosen
to be d = 2 m and leaf number density No was varied as a parameter. It is shown
that as the leaf number density, and as a direct result the extinction, increases
the frequency decorrelation bandwidth increases. Scattering contributions from the
ground bounce mechanisms are manifested in terms of oscillations on the frequency
correlation function due to constructive and destructive interferences among the
different scattering mechanisms. Existence of contribution from ground bounce
scattering mechanisms significantly reduce the frequency decorrelation bandwidth.
For interferometric SARs the equivalent frequency shift is rather small (< 1 MHz)
and the approximate form of the frequency correlation function given by (24) seems
to be adequate for all cases. Figure 9 shows Fd of the layer as a function of depth
for different values of particle number density. As the vegetation depth decreases
Fd should approach infinity and when the vegetation depth increases Fd reaches its
asymptotic value for the corresponding to a semiinfinite medium.
The theoretical expression for the frequency cross correlation function given by
(25) can be used to calculate the height of the scattering phase center above the
ground plane. Substituting the phase of the target dependent term of (25) in (22),
the mean height of the scattering phase center of the medium can be computed.
Figures 10a and 10b show the height of the scattering phase center of the uniform
13
medium as a function of layer thickness and extinction for 30~ and 600 incidence angles respectively. It is shown that depending on the layer thickness, extinction, and
incidence angle the scattering phase center may appear below or above the ground
plane, but always below the canopy top. Note that when the doublebounce scattering mechanism (groundtargetground) is dominant, the scattering phase center
appears below the ground plane. Other numerical simulations showed that particle orientation distribution can significantly influence the location of the scattering
phase center as well. This is due to the fact that the relative contribution of the
direct backscatter mechanism with respect to that of the doublebounce scattering
mechanism is a function of particle orientation distribution.
To illustrate the ability of INSAR in retrieving vegetation parameters, let us
consider a simple case of semiinfinite uniform medium. Vegetation canopy can be
regarded as a semiinfinite medium, when canopy transmissivity is below 0.1. In
this case an analytical expression for frequency correlation function and the phase
of the frequency cross correlation (mean phase) can be obtained directly from (25)
by setting K sec(9) = Cx. The expression for the frequency correlation function and
the mean phase are, respectively, given by
R(Af) = 1 2 1  ( f )2, (26)
1 a k cos 2 Ak cos2a (27)
=tan'(7
Using (26) the extinction coefficient of a thick vegetation layer can be obtained as
follows. For a system with a known baseline distance the equivalent Af can be calculated from (5) which together with the measured decorrelation can be substituted
in (26) to calculate i,. Having found Ks, (27) can be substituted in (22) to calculate
the location of the scattering phase center from the canopy top Ad which is given
by
Ad = Cos 0 (28)
It should be noted that for forest stands where particle size orientation and
distribution are highly nonuniform the simple uniform and homogeneous model
described above may not provide satisfactory results. More accurate models that
preserve the effect of tree structure are needed for this purpose. A coherent scattering model based on Monte Carlo simulation of fractal generated trees is under
development which allows efficient and accurate computation of frequency cross
correlation statistics.
5 Conclusions
In this paper theoretical and statistical relationships between the measured parameters obtained from an interferometric SAR, namely the phase and correlation
14
coefficient of interferogram, and target parameters are obtained. First an equivalent
relationship between an INSAR and a Ak radar is established. It is shown that the
knowledge of the frequency correlation behavior of radar backscatter is sufficient
to derive the desired statistics of height estimation using an interferometric SAR.
The equivalence relationship allows for conducting controlled experiments, using a
scatterometer, to characterize the response of a distributed target when imaged by
an INSAR. Similarly efficient numerical codes can be developed to simulate the results. Statistical analysis shows that the uncertainty in the height estimation of a
distributed target is a function of equivalent frequency decorrelation bandwidth and
is independent of the baseline distance. It was also shown that how the INSAR
measured parameters can be used to evaluate the extinction, the physical height,
and the height of the scattering phase center of a closed and uniform semiinfinite
canopy.
15
References
[1] K., Sarabandi, "Electromagnetic Scattering From Vegetation Canopies," Ph.D.
Thesis, The University of Michigan, 1989.
[2] F.T. Ulaby, K. Sarabandi, K. McDonald, M. Whitt, M.C. Dobson, "Michigan
Microwave Canopy Scattering Model", Int. J. Remote Sensing, vol. 11,no. 7,
12231253, July 1990.
[3] M.C. Dobson, F.T. Ulaby, L.E. Pirece, T.L. Sharik, K.M. Bergen, J. Kellndorfer, J.R. Kendra, E. Li, Y.C. Lin, A. Nashashibi, K. Sarabandi, and P. Siqueira,
"Estimation of Forest Biomass," IEEE Trans. Geosci. Remote Sensing., vol. 33,
no. 4, pp. 887895, July 1995.
[4] K.J. Ranson, S. Saatchi, and G. Sun, "Boreal forest ecosystem characterization
with SIRC/X SAR," IEEE Trans. Geosci. Remote Sensing., vol. 33, no. 4, pp.
867876, July 1995.
[5] H.A. Zebker, S.N. Madsen, J. Martin, K.B. Wheeler, T. Miller, Y. Lou, G.
Alberti, S. Vetrella, and A. Cucci, "The TOPSAR interferometric radar topographic mapping instrument," IEEE Trans. Geosci. Remote Sensing, vol. 30,
no. 5, pp. 933940, 1992.
[6] F.K. Li, and R.M. Goldstein, "Study of multibaseline spaceborne interferometric synthetic aperture radars," IEEE Trans. Geosci. Remote Sensing, vol. 28,
no. 1, pp. 8897, Jan. 1990.
[7] A.L. Gray and P.J. FarrisManning, "Repeatpass interferometry with airborne
synthetic aperture radar,"IEEE Trans. Geosci. Remote Sensing, vol. 31, no. 1,
pp. 180191, Jan. 1993.
[8] A.K. Gabriel and R.M. Goldstein, "Crossed orbit interferometry: Theory and
experimental results from SIRB," Int. J. Remote Sensing, vol. 9, no. 5, pp.
857872, 1988.
[9] S.N. Madsen, H.A. Zebker, and J. Martin, "Topographic mapping using radar
interferometry: Processing techniques," IEEE Trans. Geosci. Remote Sensing,
vol. 31, no. 1, pp. 246256, Jan. 1993.
[10] E. Rodriguez and J.M. Martin, "Theory and design of interferometric synthetic
aperture radars," IEE Proceedings, vol. F139, no. 2, pp.147159, 1992.
[11] H.A. Zebker and J. Villasenor, "Decorrelation in Interferometric Radar
Echoes," IEEE Trans. Geosci. Remote Sensing, vol. 30, no. 5, pp. 950959,
Sept. 1992.
16
[12] J.O. Hagberg, L.M.H. Ulander, and J. Askne, "Repeatpass SAR interferometry
over forested terrain," IEEE Trans. Geosci. Remote Sensing, vol. 33, no. 2, pp.
331340, March 1995.
[13] W.B. Davenport, Probability and random processes, New York: McGrawHill,
1970.
[14] K. Sarabandi, "Derivation of phase statistics of distributed targets from the
Mueller matrix," Radio Sci., vol. 27, no. 5, pp 553560, 1992.
[15] I.R. Joughin, D.P. Winebrenner, and D.B. Percival, "Probability density functions for multilook polarization signatures," Trans. Geosci. Remote Sensing, vol.
32, no. 3, pp. 562574, May 1994.
[16] J. Lee, K.W. Hoppel, S.A. Mango, A.R. Miller, "Intensity and phase statistics
of multilook polarimetric and interferometric SAR imagery," Trans. Geosci.
Remote Sensing, vol. 32, no. 5, pp. 10171028, Sept. 1994.
[17] K. Sarabandi and A. Nashashibi, "Analysis and applications of backscattered
frequency correlation function,"IEEE Trans. Geosci. Remote Sensing, to be
submitted for pulication.
[18] W.P. Brikemeier and N.D. Wallace, "Radar tracking accuracy improvement by
means of pulse to pulse frequency modulation," IEEE Trans. Commu. Electron., no. 1, pp. 571575, Jan. 1963.
[19] A.A. Monakov, J. Vivekanandan, A.S. Stjernman, and A.K. Nystrom, " Spatial
and frequency averaging techniques for a polarimetric scatterometer system,"
Trans. Geosci. Remote Sensing, vol. 32, no. 1, pp. 187196, Jan. 1994.
17
B
A1,,C.
r+ = r 2 + B 2 _ 2rB sin (0a)
r+6
r
HI
h
Figure 1: Geometry of a twoantenna interferometer.
A1
00' = C C"
2
C'
c
C'
Figure 2: Ray path configuration of the singlebounce groundtarget scattering
mechanism for a twoantenna interferometer.
18
0
oo 0
@0
h h
z z..............................................................,.......................... L I1....................................
X X
Figure 3: A random collection of M scatterers above a ground plane and its equivalent scatterer.
1 n.
1.0................................. 
o 0.9
= 0.8 .
0.7 ' /
6 — 0.69
Fgr: C a di...u.. fu0.9o:
0.5
~:  a=0.95
0.4:  a(x=0.90
1 0.3..'3  a=O.85
180. 135. 90. 45. 0. 45. 90. 135. 180.
Figure 4: Cumulative distribution function of the phase error for different values of
a~.
19
40.
30.
zg 20. 
10.
0.
0.990
0.992 0.994 0.996 0.998
1.000
a
Figure 5: The phase uncertainty for 80% and 90% percent error probability criteria
as a function of a.
20
150.
IlI[. ~ I v I I, I I I I
N
E
o
u
100.
50. L
O.C
— A
I
I
I  I ~ ~ I [! ~ I.... Ia I....
)
0.01 0.02 0.03 0.04 0.05 0.06
~ li ~
0.07
Af/Fd
Figure 6: Product of the height uncertainty and decorrelation bandwidth versus
frequency shift normalized to the decorrelation bandwidth for a Gaussian correlation
function.
Radar
I
I
I
h I
I
I
z
x
d
Figure 7: Geometry of a homogeneous
plane.
layer of random particles above a ground
21
1.00  I
~ % " ' .
0.80 \ \
U 0.60 \ ',a 0.40\ /
Z
0.20
0.00. I...
0 100 200 300 400
Af in MHz
N =500/m3
 N =1000/m3
 N =1500 /m3
 N =2000/m3
 N =5000/m3
Figure 8: Frequency correlation function of a 2mthick random layer of flat leaves
with average area 50cm2, thickness 1.3 mm, and dielectric constant t 19 + i6.3
above a ground plane with %g = 15 + j2 at 5.3 GHz and 0 = 30 (note for INSAR
case Af < 1MHz).
22
400
350
300
250
200
150
Nt
a
S
r 
v ..J......l....... lL.' ' X'*. 3
N=200/m3, K = 0.59 Np/m
N=500/m3,K = 1.48 Np/m
N=1000/m3, K = 2.95 Np/m
N=2000/m3, K = 5.91 Np/m
/


\,......,,,. 
100
50
0
0
2
4
6
8 10
d (m)
Figure 9: Gaussian equivalent decorrelation bandwidth of the layer as a function of
depth for different values of particle number density at f = 5.3GHz and 0 = 30~.
23
10
8
7
6
5
4
3
2
1
0
1
10
9
8
7
6
5
4
3
2
1
0
1
2
I
i
45~ line
 N=200/m3, K = 0.59 Np/m
 N=500/m3, K= 1.48 Np/m..  N=1000/m3, K = 2.95 Np/m
    N=2000/m3, K =5.91 Np/m.I
0 2 4 6 8 10
d (m)
I
0 2 4 6 8 10
d (m)
Figure 10: Height of the scattering phase center of the layer above the ground as
a function of layer thickness for different values of particle density at f = 5.3GHz
and 0 = 30~ (a) and 0 = 60~ (b).
24
Appendix I I
Electromagnetic Scattering Model for a Tree Trunk Above
a Ground Plane
Electromagnetic Scattering Model For A
Tree Trunk Above A Ground Plane
YiCheng Lin and Kamal Sarabandi
Radiation Laboratory
Department of Electrical Engineering and Computer Science
The University of Michigan
Ann Arbor, MI 481092122
ABSTRACT
An efficient and realistic electromagnetic scattering model for a tree trunk
above a ground plane is presented in this paper. The trunk is modeled as a
finitelength stratified dielectric cylinder with a corrugated bark layer. the
ground is considered to be a smooth homogeneous dielectric with an arbitrary slope. The bistatic scattering response of the cylinder is obtained by
invoking two approximations. In the microwave region, the height of the tree
trunks are usually much larger than the wavelength. Therefore the interior
fields in a, finite length cylinder representing a tree trunk can be approximated
with those of an infinite cylinder with the same physical and electrical radial
characteristics. Also an approximate image theory is used to account for the
presence of the dielectric ground plane which simply introduces an image excitation wave and an image scattered field. An asymptotic solution based on
the physical optics approximation is derived which provides a fast algorithm
with excellent accuracy when the radii of the tree trunks are large compared to
the wavelength. The effect of a bark layer is also taken into account by simply
replacing the bark layer with an anisotropic layer. It is shown that the corrugated layer acts as an impedance transformer which may significantly decrease
the backscattering radar cross section depending on the corrugation parameters. It is also shown that for a tilted ground plane a significant crosspolarized
backscattered signal is generated while the copolarized backscattered signal
is reduced.
1
1 Introduction
Because of the important role of the earth's vegetation cover on climatic
changes, characterization of physical parameters of the vegetation cover remotely and globally is of great importance. In recent years, considerable effort
has been devoted to the development of electromagnetic scattering models for
forest canopy [13]. In these models the forest canopy is considered to be
composed of simple geometrical particles having different sizes, shapes, and
dielectric constants. Using vector radiative transfer theory, it has been shown
that the backscattering from a typical forest stand can be decomposed into
four scattering components: (1) direct backscattering from the crown layer,
(2) bistatic scattering from the crown layer reflected from the ground plane, (3)
bistatic scattering from the trunk layer reflected from the ground plane, (4)
direct backscattering from the ground plane [1]. In lower microwave frequency
and/or when the crown layer is tenuous the backscattering is dominated by
the groundtrunk interaction. Therefore the accuracy of the scattering model
in such cases is directly proportional to the accuracy of the scattering model
for tree trunks above a ground plane.
In the mentioned models of forest stands, a tree trunk is simply modeled
by a vertical, homogeneous, finitelength dielectric cylinder. The scattering solutions for a finitelength cylinder, reported in the literature, are either based
on the eigenfunction expansion solution for an infinite cylinder [15], or low
frequency approximation where all dimensions of the cylinder are small compared to the wavelength [6]. When the cylinder radius is large compared to
the wavelength the eigenfunction solution becomes, numerically, inefficient
due to the poor rate of convergence of the series involved in the solution. This
is the case in microwave region where the radius of tree trunks in a forest
stand can be significantly larger than the wavelength. An inefficient solution
for the calculation of scattering properties of a canopy constituent particles
makes the canopy model numerically intractable because the scattering solution for individual particles must be evaluated many times to account for the
particle variability in size and orientation. Moreover, in modeling a tree trunk
with a dielectric cylinder, an important feature of the tree trunk, the bark
layer, has been overlooked. For many trees the bark layer is rough and can
be represented by longitudinal grooves on the surface of a dielectric cylinder
having possibly a different dielectric constant. The effect of the bark layer on
the RCS of a tree trunk was demonstrated recently by representing the bark
2
layer with a corrugated dielectric layer [7]. Using a hybrid scattering model
based on the method of moments and physical optics it was shown that the
RCS of a tree trunk is significantly reduced when the effect of the bark layer
is taken into account. However this model is not numerically efficient enough
to be used in conjunction with the scattering model for a forest canopy.
In this paper a realistic and efficient scattering model for a tree trunk above
a ground plane is developed. In this model the effect of the radial inhomogeneity as well as the rough bark layer are taken into consideration. Relying on
the fact that the dielectric constants of tree trunks are highly lossy, the phlysical optics (PO) approximation is used at high frequencies where the radius
of curvature is large compared to the wavelength. For finitelength cylinders
having radii comparable to the wavelength, the eigenfunction expansion in
conjunction with the field equivalence principle is used. The bark layer is
represented by a periodic corrugated layer and equivalently replaced by an
anisotropic layer as suggested in [9]. The ground plane is considered to be a
homogeneous medium having a smooth interface and both the cylinder and
the ground plane are allowed to have arbitrary orientation with respect to the
global coordinate system. Numerical simulations are demonstrated in section
7 where the region of validity of the PO approximation and the effect of a bark
layer and a tilted ground plane are investigated.
2 Global Coordinate System
In this paper, the problem of scattering from a cylinder above a ground plane in
most general configuration is considered as shown in Fig.1. A global coordinate
system (X, Y, Z) is constructed to describe the directional vector u,
A 010 AA
u0,q) = Xsin0cosq+Ysin0sin0+ Zcos0 (1)
representing the unit vector along the incidence direction k(O, ( i), the scattering direction ks(0s, qOs), the orientation direction of the cylinder z(^ c, X), or
the unit normal to the ground plane ing(0g, qfg). In this coordinate system,
the horizontal and vertical polarization of the incident and the scattered waves
are defined by
A A A A A
hp = Z x kp/IZ x kpl (2)
Vp = hp x kp (3)
3
where subscript p can be i or s. In this paper, the forward scatter alignment
convention [6] will be used. The components of the scattered field Es and the
incident field E' in the global coordinate system can be related to each other
by the scattering matrix S, i.e.,
Eh ) r Shv Shh ) E )
The ground is assumed to be smooth having an arbitrary slope in the global
coordinate system. It can be shown [8] that when the observation point is away
from the ground plane interface and in the far field region of the scatterer, the
effect of the ground plane on scattering can simply be taken into account by
including the mirror image contributions. Hence the scattering matrix consists
only of four components,
S St + Sgt + Stg + Sgtg (5)
where
St = S~(ks,ki) (6)
Sgt = eir(, n, Lksg) S~(ksgki) (7)
Stg = tS~(s, kgi). r(ki, ( g, k) (8)
Sgtg = ei(T+TS)r(is,,g). S~(k, ki) r(g~, jg, k). (9)
In the above expressions, the optical lengths Ti and T account for the extra
path lengths of the image excitation and the image scattered waves respectively. S~(kski) is the scattering matrix of the isolated target in free space,
and F(kr, ig, ki) is the reflection matrix which accounts for the specular reflection and polarization transformation due to the tilted ground plane. In order
to provide a physical insight for each term in (6)(9), subscripts t and g are
added to represent the scattering from the trunk and the reflection from the
ground plane respectively. The order of the subscripts indicates the sequence
of scattering in the first order solution. The unit vectors indicating the direction of incident, scattered, and reflected waves, as shown in Fig.1, are also
expressed in the arguments of S~ and F in the same order. In most cases the
total backscattered signal is dominated by the specular terms Sgt and Stg.
In the following sections, a general reflection matrix F for a tilted ground
plane with arbitrary slope is first obtained, and then the bistatic expressions
for the scattering matrix S~ of a stratified finite cylinder in free space based
on the eigenfunction expansion and the PO approximation are derived.
4
3 Reflection Coefficient Matrix For A Tilted
Ground Plane
The existing models for forest stands assume a flat horizontal ground plane
with no local slope. In this configuration the tree trunks are positioned normal
to the ground plane with possibly a narrow angular distribution around the
normal direction. In reality the ground plane may not be horizontal while the
tree trunks are still vertically oriented such as forest stands in mountainous
areas. The local slope has two significant effects on the backscatterer: (1)
depending on the slope angle and the trunk height, the groundtrunk term
in the backscattering direction reduces, and (2) a significant crosspolarized
component is generated through the reflection from the slanted ground plane
which enhances the crosspolarized backscattering coefficient.
Using a simple coordinate transformation the reflection coefficient matrix
of the ground plane can be easily computed. Consider a smooth ground plane
with a unit normal nig(Og, qg) that is illuminated by a plane wave propagating
in ki direction. The direction of the reflected wave is given by
kr ki  2ng(ng ki) (10)
which is normal to Er having Er and E~ as its vertical and horizontal components in the global coordinate system. Defining the reflection coefficient
matrix F by
Er  r(^ k) E ( 11)
the objective is to express the elements of F in terms of the Fresnel reflection
coefficients of the ground plane. In the local coordinate of the ground plane,
the vertical and horizontal polarization of a wave are defined by
hp = rg x kpl lg x kp[ (12)
v = hp x kp ('13)
where the subscript p can be i or r. By representing both the incident and
reflected field vectors in the local coordinate system (Vp, hp, kp) and noting that
( Eh' ( 0 ( Eh'
5
the elements of the reflection coefficient matrix can be obtained from
pq = (Pr rv)rFvq ( i) + (Pr hr)h(h qi) (15)
where p and q can be v or h, and Fv/ and Fh/ are, respectively, the vertical
and horizontal Fresnel reflection coefficients of the ground plane. The inner
products in the above expression in terms of the global coordinate parameters
are given by
A h 9..  h 7(k?  =( ' gkj)
V h h v.k,\x,
3 3 3 j\ngXkj\kZI
where j can be i or r.
4 A SemiExact Solution
Scattered fields of an infinite stratified cylinder can be obtained by the standard eigenfunction expansion method [10]. However, for finitelength cylinders, no exact solution exists. In the microwave region where the length of a
tree trunk is much larger than the wavelength and the dielectric constant has
a significant imaginary part, the effect of the longitudinal traveling waves on a
finite cylinder can be ignored. Therefore, the internal fields of a finite cylinder
may be approximated by those of an infinite cylinder having the same radial
characteristics. In this paper the scattered fields of a finite cylinder is obtained
by invoking the field equivalence principle. That is the dielectric cylinder is
replaced by fictitious electric and magnetic surface currents J and M given by
J =n x H (16)
M = nxE (17)
where H and E are the total (incident plus scattered) magnetic and electric
fields on the surface of the cylinder, and n is the unit vector outward normal
to the cylinder surface. These fields are approximated by those of the infinite
cylinder, and their tangential components on the surface of the cylinder are
given by
Ez (p a, q5, z') = E ze'(k (18)
n
6
ZoHz(p= a, ', z) = E HUei(ki;z''+n+') (19)
n
E0(p' =a,', z' = E0el( E;'z'+n') (20)
n
ZoH(p' = a, (', z') = H,,ei(ki.Z;tz'+n') (21)
n
where Zo is the intrinsic impedance of the free space and Ezn, Hzn, Eon, and
Hon are the Fourier components of electric and magnetic field which can be
found in a recursive fashion for a stratified cylinder as shown in [11]. In (18)(21), (p', q', z') define a local coordinate system in which the cylinder axis Zc
is along z' and ' = (ki x.')/ k Z x z'[. Using the fictitious current sources, the
electric and magnetic Hertz vector potentials can be evaluated from:
Ho 7 ~ikor rb/2 ]27r
I() = 47k r Jb/ J(z', ')eko ''ad'dz' (22)
47k0 r Jb/2Jo
)i ko r/2 p2ir tk k,
(I) 47ko r J/2 M(z', )eikoksf''ado'dz' (23)
where b is the height of the cylinder. The scattered field in the radiation zone
(far field region) of the cylinder can be obtained from
Es = ko2[k X (k, X He) + ks x (Zolm)]. (24)
After some algebraic manipulation as shown in [13], the elements of the scattering matrix for the finitelength cylinder in free space are found to be
sv = V ^ [(5 z)Ib) + ( h.z)K()] (25)
Sh  jlab sinV
Sv4h = ^ [( z) ( ')K(J)+ ) (26)
SO lab sin V
Sh= 4rk [(hs z')I (i) ( z')K()] (27)
 l ab sin V
Shh k0=  [(hs. ')I(h)  (v. z')K(h1)] (28)
where
I{HonUln i+ k (sin HznU2n  cos OHznUln) (29)
n B
7
sin ( cos
 EznU3n  Es znu2n
B B
K = {Enuln + B (sin 4Eznu2  cos (qEznu3n) (30)
n
sin cos
— H znU3n  B Hzn2n}
with
V Aob
V=  z (31)
2 (
Ul = 27(i)nJn(yo)ei
U2n = 27r(i) {icos qJ'(yo) + sin Jn(yo)}
Yo
u3n = 27r(i)n{i sinn J(yo)  cos nn (yo))}ei
Yo
B = /(.') + ((. y'()2
q = tan1 AS AYo = koaB.
Here Jn and Jn are, respectively, the Bessel function of first kind and its
derivative. It should be noted that I and K as given by (6) and (7) are
functions of the polarization of the incident wave.
5 Physical Optics Approximation
The semiexact solution described in the previous section becomes inefficient
at high frequencies where the radius of the cylinder is large compared to the
wavelength and fails when the cross section of the cylinder is not circular.
These deficiencies can be removed at high frequencies by employing the PO
approximation. This approximation is valid when the radius of curvature of
the cylinder is large compared to the wavelength and the permittivity of the
cylinder has a relatively large imaginary part so that the effect of the glory rays
and the creeping waves could be ignored. As before, the cylinder is replaced
by fictitious electric and magnetic currents, however in this case, the currents
8
are approximated by those of the local tangential plane which are proportional
to the sum of the incident and reflected waves.
To simplify the integration of the currents over the lit surface, the stationary phase (SP) approximation may be used. This approximation is valid
so long as the stationary point falls over the lit region. For convenience, a
local coordinate (n, t, ) is established at the SP point. The local tangential
directions are defined by
t = n x ki/ n x ki (32)
I = xt (33)
where n is a unit vector normal to the cylinder surface at the SP point. For the
general case of an anisotropic medium (the bark layer may exhibit anisotropic
properties) a dyadic reflection coefficient R is introduced to relate the polarization coupling between the incident and reflected waves, i.e.
ET = R. ET (34)
Combining the incident and reflected fields, the total fields E(= Er + E') and
H( H' + Hi) on the surface of the cylinder can be obtained from
( E ( 1 + Rv Rvh (E (35)
Et Rhv I + Rhh Eti
and
(Ht ( Rvh 1  R H (36)
Applying the stationary phase approximation, it can be shown that the Hertz
vector potentials are given by
i*o eikor
Te izoikoQJ (37)
I Im= ikor QM. (38)
ko r
where J and M are the fictitious currents evaluated from the total fields E
and H at the SP point (X' = q), and
ik0o b/2 r/2 ikOaBcos('q)e iko(kks).z ad'dz (39)
47 ]b/2 I7r/2
9
ib sinV ikoBa kaF Ik+Ba ( [ koBa ( 
27r 2B 2 2 J +F 2
with
B = {[(ks  ki) x']2 + [(ks  k ]] }/2
(k k ).k'
~ = tanl( A i)
and F(.) is the Fresnel Integral. This approximation is valid provided koaB >>
1 and q is away from the shadow boundary.
Using a similar procedure as in the previous section, the scattering matrix
elements are found to be
S~ = Q[(i,)ZJl (t. is)ZoJtv + ( )ZOt hs)Mlv + (t hs)Mtv] (40a)
Svh = Q[(i Vs)ZoJlh + (t *s)ZoJth + (1. hl)Mih + (t. h,)Mth] (40b)
S = Q[(. hs)Zo0JI + (t. h )ZoJ (  ( t. M)( M] (40c)
Shh = Q[(. hs)ZoJlh + (t hs)ZoJth  (l 's)Mlh (t. vS)Mth] (40d)
where Jpq and Mpq are the currents along p direction induced by a q polarized
incident wave (p can be t or I and q can be v or h ). The inner products of
the vectors in the above expressions can easily be calculated in terms of the
global coordinates.
The above results fail in the case of forward scattering for which B = 0.
However, in directions close to the forward direction, an alternative approximation for the scattered field is possible and is given by [13]
S 2iab ^ sin V sin W eik~r (4
Eo V W (41)
where W = koa(ks y') and V is given in (31).
6 Modeling of A Corrugated Bark Layer
For some tree species, the bark layer is corrugated with grooves along the
longitudinal direction. In this paper, the bark is simply modeled as a periodic
10
corrugated layer with period L and width d as shown in Fig.2a. It is shown
in [9] that,when L < Ao/2 (single Bragg mode), the corrugated layer can
be equivalently replaced by an anisotropic layer (see Fig.2b) with the same
thickness whose permittivity tensor is given by
(/ l 0 0
= 0 622 0. (42)
0 0 633
The entries of the tensor in terms of the permittivity, period, and width of the
corrugated layer, when L < 0.2Ao, are approximated by
611 (  d/L) d/L (43)
c22 = 633 1 + (r l)d/L. (44)
Assuming that the radius of the cylinder is much larger than the wavelength,
the permittivity of the bark layer can be represented by e(/, z, n) where eq =
E11 and zz = Cnn = 622.
To employ the PO approximation, a coordinate transformation from the
local (, z, n) to (t,, n) at SP point is needed. The resultant permittivity
tensor in coordinate (t, 1, n) is
etzz sin2 z + o 6 cos2 gz (e  eZ) sin z cos O 0
C = (E ,zz) sin oz cos Oz ezz cos2 qz + 6eo sin2 cz 0 (45)
0 0 C nn
where
0z = Cosl( ) (46)
The reflected fields from a stratified anisotropic dielectric half space is computed using the method described in [12].
7 Numerical Results
In this section a number of numerical examples for the scattering from a finite
cylinder above a ground plane are presented. In all the considered examples
11
the normalized RCS, defined by
47Spq42
pq kab2 ' (47)
are displayed for a twolayered cylinder with height b, exterior radius a, and
interior radius a2. The permittivity of the exterior and interior layers are
chosen to be: 61 = 4 + il and C2 = 10 + i5 respectively. Also the cylinder is
positioned vertically (0O = 0) on a tilted ground with permittivity cg = 10 + i5.
First, the validity region of the PO approximation in backscatter direction
is examined. Figure 3 compares av, and chh using the PO and semiexact solutions. It is found that the PO solution agrees well with the semiexact solution
when k0a > 10. For small values of k0a the resonance behavior of backscatter is shown by the semiexact solution. Figures 46 show the monostatic and
bistatic scattering patterns which are simulated for a twolayered cylinder with
and without a corrugation. The thickness of the corrugated layer and its filling factor are respectively chosen to be t = O.lAo and d/L = 0.7 (see Fig.2).
Figure 4 shows the backscattering pattern as a function of incidence angle.
At small angles of incidence, the PO approximation differs slightly from the
semiexact solution because the radial component of the propagation constant
(kp = ko sin 0) is small in this region and the condition kpa > 10 is not satisfied. The vvpolarized backscattering RCS has two minima corresponding to
the two Brewster angles one occurring on the surface of the cylinder (0  25~)
and the other occurring on the ground plane (0 c 75~). The backscattering
RCS vanishes at 0 = 0~ and 90~ since the four components contributing to the
backscattering RCS interfere destructively. The ripples on the curves are due
to the components St and Sgtg (see equation (1)), which become significant
for angles of incidence close to 90~; and the oscillation rate is proportional to
the cylinder length. This figure also shows the effect of the bark layer on the
backscattering RCS. Depending on the incidence angle the RCS of the cylinder
may be reduced as high as 10 dB. The reduction in the RCS is a function of
the cylinder length and the corrugation parameters. Basically the corrugated
layer behaves as an impedance transformer between the air and the vegetation material. Figure 5 shows the bistatic scattering pattern as a function of
elevation angle when O = 120~, i = 180~ and the observation point is moving
in the XZplane. Figure 6 shows the bistatic scattering pattern as a function
of azimuth angle (q$) with 0, = 120~, X =1800, and 0, = 60~. The discontinuities found on the PO solution near the forward directions are because of
12
switching the expression for scattering from (9) to (10).
Figures 79 show the effect of the tilted ground plane on the backscattering RCS. All the parameters in Fig.7 are the same as those given in Fig.4
except for the tilt angle of the ground,0g = 20~ and qg = 90~. Comparing
Fig.4 with Fig.7, it can be seen that a significant crosspolarized backscattered
signal is generated due to the slope of the ground plane. Figure 8 shows the
variation of backscattering RCS as a function of the ground azimuth angle fg
where 0, = 135~, h = 180~ and 0g = 20~. One can observe that the peak
of the backscattering RCS occurs at qg = 70~(=  Og). Figure 9 shows
the backscattering RCS as a function of the ground elevation angle 0( where
0i = 135~, i = 180~ and qg = 0~ and 180~. The regions in the positive and the
negative 0g represent the ascending and the descending sides of a mountain
respectively. In this case no crosspolarized signal is generated because the
cylinder is in the principal plane (XZ plane). Note that there are two maxima occuring at 0g = 0~ and 0g =22.5~. The first maximum corresponds to
the dihedrallike ground trunk interaction. The second maximum corresponds
to a reflection from the ground plane which illuminates the cylinder at normal
incidence. The backscatter from the cylinder bounce off from the ground plane
and returns toward the radar (see Fig.10). This strong backscatter component
can be observed where k q, g and Zc are in the same plane and 0i = 20g + /2.
8 Conclusions
An efficient and realistic electromagnetic scattering model for a tree trunk
above a ground plane is presented in this paper. The trunk is modeled as a
finitelength stratified dielectric cylinder with a corrugated bark layer. The
ground is considered to be a smooth homogeneous dielectric with an arbitrary
slope. An asymptotic solution based on the PO approximation for high frequencies is derived. This solution provides a fast algorithm with excellent
accuracy when the radii of tree trunks are large compared to the wavelength.
The effect of the bark layer is also taken into account by simply replacing the
bark layer with an anisotropic layer. It is shown that the corrugated layer acts
as an impedance transformer which may significantly decrease the backscattering RCS. The RCS reduction depends on the corrugation parameters. It is also
shown that for a tilted ground plane a significant crosspolarized backscattered
signal is generated while the copolarized backscattered signal is reduced.
13
References
[1] F. T. Ulaby, K. Sarabandi, K. MacDonald, M. Whitt, and M. C. Dobson,
"Michigan Microwave Canopy Scattering Model", Int. J. Remote Sensing, Vol. 11, NO. 7, pp. 12231253, 1990
[2] L. Tsang, C. H. Chan, J. A. Kong, and J. Joseph, " Polarimetric signature
of a canopy of dielectric cylinders based on first and second order vector
radiative transfer theory," J. Electromag. Waves and Appli. Vol. 1, No.
1, pp. 1951, 1992.
[3] S. L. Durden, J. J. van Zyl, and H. A. Zebker,"Modeling and observation
of the radar polarization signature of forested areas", IEEE Trans. Geosci.
Remote Sensing, Vol. 27, No. 3, pp. 290301, 1989.
[4] S. S. Seker and A. Schneider, "Electromagnetic scattering from a dielectric
cylinder of finite length", IEEE Trans. Antenna Propagat., Vol. 36, No.
2, pp. 303307, 1988
[5] M. A. Karam and A. K. Fung, " Electromagnetic scattering from a layer
of finitelength, randomly oriented dielectric circular cylinder over a rough
interface with application to vegetation", Int. J. Remote Sensing, Vol. 9,
No. 6, pp. 11091134, 1988
[6] F. T. Ulaby and C. Elachi,Radar Polarimetry for Geoscience Applications,
Artech House, 1990.
[7] K. Sarabandi and F. T. Ulaby, "High frequebcy scattering from corrugated
stratified cylinders", IEEE Trans. Antennas Propag., Vol. 39, No. 4, pp.
512520, 1991.
[8] K. Sarabandi, "Scattering from dielectric structures above impedance surfaces and resistive sheets," IEEE Trans. Antennas Propag., Vol. 40, No.
1, pp. 6778, Jan. 1992.
[9] K. Sarabandi, " Simulation of a periodic dielectric corrugation with an
equivalent anisotropic layer," International Journal of Infrared and Millimeter Waves, Vol. 11, pp. 13031321, 1990
14
[10] G. T. Ruck, D. E. Barrick, W. D. Staurt, and C. K. Krichbaum, Radar
Cross Section Handbook, pp. 259263 and pp. 479484, New York: Plenum
Press, 1970.
[11] M. O. Kolawole," Scattering from dielectric cylinders having radially layered permittivity, " J. Electromag. Waves and Appli., Vol. 16, No. 2, pp.
235259, 1992
[12] M. A. Morgan, "Electromagnetic Scattering by Stratified Inhomogeneous
Anisotropic Media," IEEE Trans. Antennas Propag., Vol. 35, pp. 191197,
1987
[13] K. Sarabandi, Electromagnetic Scattering from Vegetation Canopies,
Ph.D. Dissertation, pp. 224, eq. 7.40, University of Michigan, 1989.
15
z
A
As
A
A
zc
A
A 'J1O
vi I \\
VI
4 —
O s
Vs
/ 4oi
Y
1%
11%
1%
x
Figure 1: Global coordinlate system
16
d
e3
L
(a)
e3
(b)
Figure 2: A corrugated layer and its equivalent anisotropic layer.
17
0
5
10 
CL )
U
15
N
C 20
2  v, (SemiExact)
  —. ohh (SemiExact)
25
(P.O. Approx.)
30..
0 5 10 15 20 25 30 35 40
koa
Figure 3: Comparison of the PO approximation with the semiexact solution.
The ratio of the interior radius a2 and the exterior radius al(= a) is kept
constant (a2/al = 0.9). Other parameters are: b = 20Ao, c = 4 + il, C2
eg = 10 + i5, 0i = 120~, 5i = 180~, 0, = 60~, Os = 0~, 0= 0 = 0~.
18
0
 X h / /\B h (SemiExact)
\ /' ';   hh ~ )
20 , r, Ghh (SemiExact)
1........ thh (P.O.), ~ ov (SemiExact)
30 
vv (P.O.)
   Corrugated, ahh
    Corrugated, vv
40
40.I, I, I, I.I EI, I,
0 10 20 30 40 50 60 70 80 90
Incidence Angle 70i (Degrees)
Figure 4: The normalized backscattering RCS as a function of the incidence
angle 0 = w  0i for a two layered cylinder with and without the corrugation.
Other parameters are: b = 20Ao,a1 = 2Ao,a2 = 1.8A,t = 0.1Aod/L =
0.7, 4 = 180~, Os = 0~, 0= 0 = 0~.
19
(a)
10
I o SemiExact
0  P.O.
corrugated
10
liI I I
iii i^^ 11 L
501: ',, i, ':,,
scattering elevation angle 0s in XZplane (0s > 0 when 0, = 0~;0s < 0 when
05 = 180~). The backscattered and the specular directions are shown at s =
60~ and 0s = 60~ respectively. Other parameters are: = 120~, q =
80~ 0~, b = 1 = = 1
180~ 0 09 lb = t0o al = 2oa2 = 1.Ao.
20
(b)
20
10
0
10
J!. 20 4
30
40
50 
90
60 30 0 30 60
Scattering Elevation Angle Os (Degrees)
90
21
(a)
10
5
 SemiExact
0  P.O.
   —. Corrugated
5
25 ' I
30
0 30 60 90 120 150 180
Scattering Azimuth Angle 4s (Degrees)
Figure 6: The normalized bistatic cr~ (a) and chh (b) as a function of the
scattering azimuth angle s. The backscattered and forwardscattered direction are shown at q, = 0~ and (s = 180~ respectively. Other parameters are:
0i = 120~, i = 1800, s = 60~, 0g = = 0~, b = 20Ao, al = 4Ao, a = 3.6Ao.
22
4
(b)
20
SemiExact
—. P.O.
10 
 Corrugated
10
o *11; X
20
30
0 30 60 90 120 150 180
Scattering Azimuth Angle 0s (Degrees)
23
0
10  vv
 10 20 30 40 50 60 70 80 90
vh
Incidence Elevation Angle 70j (Degrees)
Figure 7: The normalized backscattering RCS as a function of the incidence
angle T  O. for a two layered cylinder above a tilted ground plane. Other
20
parameters are: g = 20~, g = 90, = 0~, = 180, s = 0~, = i b =
20Ao, a = 2Ao,a2 = 1.8Ao.
~,;.~,',..,
50~~~~~~ 'x,,,~.)iL,.,,t,,l,.... I
parmetr s ar g2~ g  9 ~ I0,~ 8~ 5 ~ ~~i
24
0,vv
10 v
   vh
~, 20
t 30
IIt
40 It
50I i
0 30 60 90 120 150 180
Ground Azimuth angle g (Degrees)
Figure 8: The normalized backscattering RCS as a function of the ground
azimuth angle g. Other parameters are 0g 20~0 0~i  1350~,
180, 0 = 45~, s 0~, b 20Ao, a = 2Ao, a2 1.8Ao.
25
0
10 ,, 
20
50 40 30 20 10 0 10 20 30 40 50
Ground Elevation Angle 0g (Degrees)
Figure 9: The normalized backscattering RCS as a function of the ground
elevation angle 0g (0g > 0 when fg =0 0~;0g < 0 when g = 180~). Other
parameters are: 0 = 135~, i 180~,, = 45~, 0~, b = 0Ao, al =
2Aoa2 = 1.8Ao.
50I
' i 11
A
60..... ' \ '
50 4 3 20 10 0 102 005
Grun Eeaion An gl 0g I(
II (Degrees)
Figure 9'Tenraie akcteig safnto ftegon
elevatio angl 0g II (0g > 0 whe &g  0~0 < 0 wh e qI  10~). Oher
paamtr s I are'O 3~4/10,~4~q ~b 0oa
2~o a2 18o
26
A
ng
Figure 10: The geometry of the scattering configurations for a cylinder over a
tilted ground where a strong backscatter can be observed.
27
Appendix Il
A Monte Carlo Coherent Scattering Model For Forest
Canopies Using FractalGenerated Trees
21
A Monte Carlo Coherent Scattering Model For
Forest Canopies Using FractalGenerated Trees
YiCheng Lin and Kamal Sarabandi
Radiation Laboratory
Department of Electrical Engineering and Computer Science
The University of Michigan
Ann Arbor, MI 481092122
ABSTRACT
A coherent scattering model for tree canopies based on a Monte Carlo simulation
of scattering from fractalgenerated trees is developed and verified in this paper. In
contrast to incoherent models, the present model calculates the coherent backscatter
from forest canopies composed of realistic tree structures where the relative phase
information from individual scatterers is preserved. Computer generation of tree
architectures faithful to the real stand is achieved by employing fractal concepts
and Lindenmayer systems as well as incorporating the insitu measured data. The
electromagnetic scattering problem is treated by considering the tree structure as a
cluster of scatterers composed of cylinders (trunks and branches) and disks (leaves)
above an arbitrary tilted plane (ground). Using the single scattering approximation,
the total scattered field is obtained from the coherent addition of the individual
scattering from each scatterer illuminated by a mean field. Foldy's approximation is
invoked to calculate the mean field within the forest canopy which is modeled as a
multilayer inhomogeneous medium. Backscatter statistics are acquired via a Monte
Carlo simulation over a large number of realizations. The accuracy of the model is
verified using the measured data acquired by a multifrequency and multipolarization
SAR (SIRC) from a maple stand at many incidence angles. A sensitivity analysis
shows that the ground tilt angle and the tree structure may significantly affect the
polarimetric radar response, especially at lower frequencies.
1
1 Introduction
Microwave radar remote sensing has been accepted as a viable instrument for monitoring and assessing significant parameters of forest ecosystems such as LAI and
vegetation biomass [1]. Over the past decade much effort has been devoted to the
development of scattering models for vegetation canopies as a step towards retrieving
the forest biophysical parameters from a set of radar measurements [2].
Radiative transfer (RT) theory [3] is the most widely used model for characterization of scattering from a forest canopy [4]. When the medium consists of sparse
scatterers that are small compared to the field correlation length within the random
medium, RT theory can accurately predict the second moments of the radar backscatter statistics. However, no information regarding the absolute phase, an important
quantity required for investigating the response of a forest to an interferometric SAR,
can be extracted from a RT model. The other shortcoming of RT theory is its inability to account for the coherent effects that may exist between different scatterers or
scattering mechanisms. Recent investigations on scattering behavior of tree canopies
have shown that both backscattering and attenuation are significantly influenced by
tree architecture [5]. Therefore, development of a coherent scattering model that accounts for tree architecture is crucial for the accurate estimation of radar behavior of
forest canopies.
Modeling vegetation using coherent approaches has attained prominence over the
past decades. The distorted Born approximation has been known as one of the
basic approaches used for coherent modeling of vegetation [6], where each scatterer
is illuminated by a mean field and the backscattered fields are added coherently. For
short vegetation Yueh et al. [7] considered the effect of the soybean plant structure
on radar backscatter using a twoscale branching model. Similarly, a coherent model
for cultural grass canopies, where the dimensions of the vegetation particles such as
grass blades and stems are comparable to the medium height dimension, has also been
developed [8]. It was shown that at low microwave frequencies the relative positions
of scatterers and plants with respect to each other affect the polarimetric backscatter
response of vegetation canopies. In these models the structure of the vegetation is
considered from a statistical point of view and therefore only the second moments of
the scattered fields are provided, that is, the absolute phase information is lost.
Further investigations have explored the coherent scattering from a 3D tree structure. In [9] the radar backscatter was simulated for various deciduous tree types using
fractal theory [10] for the tree structure. In a more recent paper [11] Lindenmayer Systems (Lsystems) [12], useful tools for implementation of fractal patterns or structures,
were employed to develop simple 3D tree structures of the order of few wavelengths
to examine the importance of coherent and multiple scattering. A straightforward
approach in constructing the tree structure was carried out in [13] where an accurate
description of particle positions was characterized for a red pine tree using surveying
tools. In this model the tree structure is divided into cylinders whose backscattered
fields are added coherently via the distorted Born approximation.
The purpose of this paper is to develop and validate a comprehensive coherent
scattering model for forest canopies, which can account for the coherent effect due to
2
the tree structure and provide information about the absolute phase of the backscattered field. The proposed model is comprised of three major components: (1) accurate generation of tree structures based on few physical parameters, (2) evaluation
of scattered fields, and (3) Monte Carlo simulation. In the tree structure modeling,
fractalbased Lsystems are employed to construct a realistic tree structure incorporating the ground truth data of the desired stand. As will be shown, the spatial and
angular distribution of branches strongly influences the behavior of radar backscatter,
indicating the importance of the treegenerating code in constructing the fine features
of tree structures. In the scattering model, individual tree components located above
a tilted dielectric plane are illuminated by the mean field, and the scattered fields are
computed and then added coherently. The branches and tree trunks are modeled by
stratified dielectric cylinders and leaves are modeled by dielectric disks and needles
of arbitrary cross sections. The mean field at a given point within the tree structure,
which accounts for the phase change and the attenuation due to the scattering and
absorption losses of vegetation particles, is calculated using Foldy's approximation [3].
Finally, a Monte Carlo simulation is performed on a large number of fractal generated
trees to characterize the statistics of the backscattered signals. Another feature of the
proposed coherent model is its capability in accounting for the effect of a nonuniform
extinction profile within a forest canopy. The accuracy of the model is compared
with the backscatter measurements acquired by SIRC from a forest test site in Raco,
Michigan.
In what follows, we first describe the procedure for generation of tree structures
using stochastic Lsystems. Next the construction of the coherent scattering model
and the Monte Carlo simulation is explained. Then, the validity of the model is examined against L and Cband backscatter measurements of a well characterized forest
stand. A sensitivity study is also carried out to examine the degree of dependency of
polarimetric backscatter on forest parameters.
2 Fractal 1Model for Generation of Tree Structures
2.1 Fractal Theory and Lindenmayer Systems
Tree structures in nature are complex and their mathematical description seems to require a large number of independent parameters. Contrary to this observation, it has
been shown that geometrical features of most botanical structures can be explained
using fractal theory where only a few parameters are required to specify the vegetation
structure. The mathematical concept of fractals was originated by Mandelbrot [10] in
the early seventies. Currently fractal theory is the most popular mathematical model
used for relating natural structures to abstract geometries. Mandelbrot defined a
fractal as a set whose HausdorffBesicovitch dimension strictly exceeded the topological dimension. In other words, the notion of fractal is defined only in the limit.
However, in order to apply the fractal concept to practical problems, a finite curve is
usually considered as an approximation of an infinite fractal so long as the significant
properties of both are closely related. A distinctive feature of a finite fractal is the
3
selfsimilarity which is kept through the derivation process.
To implement fractal theory, Lsystems have been wellknown tools for the construction of fractal patterns or structures where the selfsimilarity is preserved through
a socalled rewriting process [12]. Lsystems were originally proposed by Lindenmayer [14], who applied it to the development of lower forms of plant life, such as
red algae. Lsystems, also called developmental systems, have since been applied in
many fields, including formal language theory and biomathematics. The features of
Lsystems consist of the structural grammar rules and recursive processes which can
easily be implemented by modern computers.
In Lsystems, a tree structure G is specified by three components: (1) a set of edge
labels V, (2) an initiator w, called axiom, with labels from V, and (3) a set of tree
growth productions P. In compact notation this treegrowing process is symbolized
by G =< V, w, P >. Given a tree structure G, a tree T2 is directly derived from a
tree T1 (T1 => T2) if T2 is obtained from T1 by simultaneously replacing each edge in
T1 by its successor according to the production set P. A tree T is generated by G
in a derivation of length n if there exists a sequence of trees To, T1,..., Tn such that
To = w, and To =~ T1 =X... => Tn = T. Figure 1 shows an example of a simple twodimensional fractal tree of length 4, where the selfsimilarity can be easily observed
through each successive process.
2.2 Botanical Modeling
In order to simulate realistic tree structures, botanical properties must be incorporated into the tree generation. In this section, several botanical features such as
branch dimension rules, leaf attachment, and tree type development are described.
The cross section and the length of younger branches decrease as the branching
process progresses. At a node where a branch splits into two or more branches, a
common practice for determining the relationship between the radius of the originating branch (ra) and the radius of the younger branches (rb and r,) is the application
of the conservation law of the cross sectional area, given by:
a= r +r2. (1)
The relationship between the radius of the new branches (i.e. rb and r,) is specific to
the tree type, and should be specified according to the ground truth measurements.
Another parameter to be specified is the relationship between the length of the new
and old branches (la and lb, respectively). Defining g as the growth rate parameter,
we have
lb = la/9. (2)
For a threedimensional branching structure, two branching angles, the tilt angle 0
and rotation angle 4, must be specified to characterize the relationship between the
orientation of the new and the old branches.
Most leaves are attached to the end of the final branches noting that the term leaf
here refers to a general composite leaf which may be comprised of many leaflets. The
4
number of leaves surrounding a branch is a function of many factors including the
tree species, tree density, and the local environment. The tree generation algorithm
developed in this paper allows the user to specify the number of leaves per final
branch as well as a local orientation distribution for the leaves. The orientation of
a leaf, defined by the unit normal to the leaf surface, is mostly characterized by
the associated position and orientation of the end branch with respect to the global
coordinate system. However some relatively narrow distribution function is added to
allow for natural variations of leaf orientations.
Based on the architectural characteristics, tree structures can be categorized into
three primary classes: columnar, decurrent, and excurrent, which may be represented
by coconut, maple, and pine trees respectively [15]. In the majority of deciduous
trees, the lateral branches grow as fast as, or faster than, the terminal shoot, giving
rise to the deliquescent growth habit where the central stem eventually disappears
from repeated forking to form a large spreading crown. This branching pattern is
termed decurrent. On the other hand, most coniferous species belong to the excurrent
class, where the main stem outgrows the lateral branches giving rise to coneshaped
crowns and a clearly defined bole. In this study, a library of typical tree structures is
constructed that can easily be finetuned to simulate the desired tree stands. Figure
2 shows two fractal trees of decurrent and excurrent types generated by the developed
treegenerating algorithms of this study.
2.3 Computer Implementation
The computer work in the development of the tree structure consists of three main
components: the encoding, decoding, and visualization. In Lsystems, the encoding
is accomplished by iterating the labels with prescribed productions and length. A
long label string, like DNA in biology, is obtained at the end of the processes, holding
embedded information about the tree structure. Then this long label string is decoded
(or translated) into a tree structure through a so called turtle graph interpreter [12].
Numerical calculation is performed in this stage to quantify the geometries of the
entire tree structure.
Once the fractal tree is created, the tree data file usually contains a large number
of tree components and it is difficult to examine the accuracy by manual inspection of
the numerical data. Visual inspection of the tree image is a better way at this point.
In addition, realtime visualization of the tree structure during the developing stage
can also assist the user in learning the sensitivity of the fractal parameters to the tree
structure. In this study, a visualization program is developed using the PostScript
language where realtime display and printout can be easily performed without any
extra software. This program is capable of projecting a 3D fractal tree structure into
a 2D image with the functions of arbitrary scaling and perspective view. The red
pine shown in Figure 2(b) is viewed at 200 measured from the horizontal plane.
5
3 Coherent Scattering from Forest Canopies
In this section, a coherent scattering model is developed to calculate the polarimetric
radar response of the fractalgenerated trees. Once a tree is created, it is treated as a
cluster of scatterers composed of cylinders (trunks and branches) and disks (leaves)
with specific position, orientation, and geometric shape and size, as shown in Figure
3. It is assumed that the entire tree is illuminated by a plane wave, whose direction
of propagation is denoted by a unit vector ki and is given by
E'(r) = E eiki. (3)
The scattered field in the far zone is next calculated for individual trees. Since the
uncertainty in the relative position of trees with respect to each other is usually of
the order of many wavelengths, the total scattered power can simply be determined
by the incoherent addition of scattered power from individual trees. To the first order
of approximation, the scattering from a tree is approximated by the superposition of
the scattered field from each scatterer within the tree structure. Hence, neglecting
the effect of multiple scattering among the scatterers, the total scattered field from a
single tree can be evaluated from
eikr N
Es  E inSn.Eo, (4)
r n=1
where N is the total number of the scatterers within a tree structure, Sn is the
scattering matrix of the nth scatterer above a dielectric plane and On is a phase
compensation term accounting for the shift of the phase reference from the local
coordinate system of the nth scatterer to the global coordinate phase reference.
Denoting the position of the nth scatterer in the global coordinate system by rn, OEn
is given by
On = (k  ks) rn, (5)
where ks is the unit vector representing the propagation direction of the scattered
field.
In order to compute the local scattering matrix Sn let us consider a single scatterer
above a dielectric plane, as shown in Figure 4. Neglecting the multiple scattering
between the scatterer and its mirror image, each scatterer mainly contributes four
scattering components, denoted by: (1) direct scattering denoted by S', (2) groundscatterer scattering denoted by S9, (3) scattererground scattering denoted by Snt,
and (4) groundscattererground scattering denoted by Sgtg, as shown in Figure 4.
The scattering matrix Sn in terms of its components can be written as
Sn = S + St + St + Sfn, (6)
where
Sn = S~(ks k.), (7)
Sgt  eiksR(ksgs) S~(kgs, ki), (8)
Sng  ei iS(k5: kgi) R(kij, ki), (9)
S St e i( +s )R(,5 kgs) Sn(kg, kgi) R(kgi, i ), (10)
6
and
kgi = ki 2ig( n ki), (11)
A A A
kgs =ks 2nng(g* ks), (12)
i = 2ko(rn n )ng ki), (13)
s = 2ko(rn n')ng ks). (14)
In the expressions given by (7)(10), So is the bistatic scattering matrix of the nth
scatterer in free space. The direction of incidence and scattering are denoted by unit
vectors in the argument of So. In the above expressions, nig is the unit vector normal
to the tilted ground surface. The phase terms rT and 7S account for the extra path
lengths of the image excitation and the image scattered waves respectively. R is the
reflection matrix of the dielectric plane whose elements are derived in terms of the
Fresnel reflection coefficients and the polarization transformation due to the ground
tilt angle. The explicit expressions of the reflection matrix of a tilted dielectric plane
(R) with an arbitrary slope and the expressions for the bistatic scattering matrices
(Sn) of large scatterers like trunks and primary branches are given in [16], where
the semiexact solution together with the physical optics approximation are derived
for the calculation of scattering from a stratified dielectric cylinder above a tilted
dielectric plane. The formulae for the scattering matrices of small scatterers like
twigs and leaves are constructed based on the expressions given in [17,18].
The above analysis is not quite complete since in the calculation of scattering from
the nth scatterer the other scatterers are assumed to be transparent. The second
or higherorder analysis, which takes into account the multiple scattering among the
tree structures, is fairly complicated and is beyond the scope of this paper. However,
the effect of attenuation and phase change of the coherent wave propagating in the
random media can be readily modeled by calculating the mean field within the random
medium.
Consider a coherent radar wave propagating in a statistically uniform random
medium. Based on Foldy's approximation [3], the variation of the mean field E with
respect to the distance s along the direction k is generally governed by
dE= iK E, (15)
ds
where
ko + Mvv Mvh j (16
K [ jMvv o +k Mhh (16)
and
Mp= 2W~o< oS(kk) > (17)
Here ko is the wave number of free space; no is the volume density of the scatterer;
and < S~ (k, k) > is the ensemble average of the forward scattering matrix, (p and q
can be v or h). Using the standard eigenanalysis, the differential equation (15) can
easily be solved and the solution is given by
E(s) = eikosT(s, k). E, (18)
7
where E~ is the field at s = 0 and T is the transmissivity matrix accounting for the
extinction due to scattering and absorption. In most natural structures, azimuthal
symmetry can be assumed where Msh = Mhv = 0 and the transmissivity matrix is
reduced to
T [ 0 eiMhhs ] (19)
Note that the transmissivity matrix defined in (18) excludes the phase terms due
to free space path lengths, and merely accounts for the perturbation in propagation
caused by the vegetation.
To include the effect of wave extinction in the scattering model, consider a situation when the entire tree structure is embedded in an effective medium with an effective propagation constant given by (16). Under the aforementioned approximations
the expressions for the components of the nth scattering matrix in the backscatter
direction should be modified as follows:
St = T. S~(ki K ki) TT, (20)
St = eirnTt. R.T S~(k k) T:, (21)
Sg = in Tt S~(k  k T R. Tt, (22)
Sg = ei2nTt.. T. S~(krkr). T R.T', (23)
with
kr = ki  2ng(ng ki), (24)
n = 2ko(rn n ig)( kr), (25)
where T, T, and Tt are the transmissivity matrices, respectively, for the direct,
reflected, and total traveling path as shown in Figure 5. In the derivation of (20)(23)
the reciprocal property of wave propagation, is employed, i.e., T(s, k) = T(s,k),
which results in the expected reciprocal scattering relation S9t  (S9)t. Here the
superscript (.)t denotes the operation of matrix transposition followed by negation of
the crosspolarized elements in order to be consistent with the the forward scattering
alignment convention [1].
Distributions of vegetation particle type and size is nonuniform along the vertical extent of most forest stands unlike what has been assumed in the aforementioned
existing scattering models mostly for the lack of knowledge of such distributions. In
the proposed model where the exact description of particle distributions are available, propagation and scattering of the mean field within the forest medium can be
characterized rather accurately. To account for the vertical inhomogeneity, consider
an Mlayered random media above a tilted ground surface illuminated by a plane
wave. Each layer, with thickness dm(m = 1,2,...,M), is assumed to be parallel to
the ground surface. It is also assumed that the boundaries between the layers are
diffuse where no reflection or refraction can take place. Suppose the nth scatterer is
located in the mth layer, then the objective is to calculate the transmissivity matrices
TT r and Tt.
8
In the backscatter case, only the incident directions ~ki and the reflected directions ~kr are of interest. Therefore for each scatterer the forward scattering matrix
should be calculated for both ki and kr directions. Then for each layer (say the mth
layer), the layered transmissivity matrix is computed by
0,/ e ^ (26)
where Lm = dm/(ig kr) is the path length, and
Mi 27r DtE S(,/ ) (27)
nm
is the effective propagation constant for the mth layer. In the above expression Dt
is the tree density (number/mrn2) and Nm is the number of particles of a single tree in
the mth layer. The final expressions for the transmissivity matrices can be written
as
Tt = T1(L,)T2(L2)...T' (LM), (28)
T = Ti( Lmn)WTm (L(.1 )...TM(LM), (29)
Tn  TM(Lrn)T ,_(Lm1)...T (L1i), (30)
where Ln and Lm are the path length from the nth scatter to the top and bottom
of the mth layer boundary along the ki and kr directions, respectively, as shown in
Figure 5. These distances are given by L n = (Hm  rn n)/(ig kr) and L =
(rig  Hm)/(ng. kr) where Hm = k=l dk represents the height of the upper
interface of the mth layer.
For distributed targets, the radar backscattering coefficients and phase difference
statistics, instead of the scattering matrix, are usually the quantities of interest. These
quantities can be derived from the second moments of the backscattered field components [19]. The statistics of the scattered field are approximated from a Monte Carlo
simulation where a large number of tree structures are generated using stochastic
Lsystems and then the scattering matrix of all generated trees are computed. Computation of the scattering matrices is accomplished in the following manner. First
the canopy height is discretized into M layers and the extinction coefficient of each
layer and the integrated transmissivity matrices are computed as outlined previously.
Then these quantities are used in (20)(23) for calculating the scattering matrix of
individual trees.
The computation involved in the calculation of the scattering matrices of individual leaves for many trees is too excessive to be carried out even with the fastest
available computers. To solve this problem, the 47t solid angle covering the entire
vector space representing the orientation direction of a leaf is discretized into a finite
number and a lookup table for scattering matrices of a leaf oriented along all the
discrete directions is generated for the three principal backscattering (SO(ki, ki) and
S~(kr, kr)), forward scattering (S~(k, k:) and S~(kr, kr)), and bistatic scattering
9
(S~(kr, ki) and S(ki, kr)) directions. The number of discrete orientation directions is determined from the ratio of a typical leaf dimension to the wavelength (a/A).
According to this scheme the number of the discrete points should increase with increasing a/A. A similar scheme may be used for branches, however, we found that
this may unnecessarily increase the CPU time due to a large variability in diameter
and length of the branches.
In order to calculate the desired backscatter statistics, the differential covariance matrix of the backscattered field must be evaluated. As described earlier, the
backscattered fields of adjacent trees in a forest are uncorrelated at microwave frequencies and above. Therefore the backscattered power from individual trees can be
added and the covariance matrix elements are proportional to the tree density Dt and
are given by
WOt = Dt < SpqS >, (31)
where p, q,s, t G {v, h}. According to this definition for the differential covariance
matrix, the backscattering coefficient can be obtained from
pq = 47W q. (32)
4 Model Verification
In this section, the accuracy and validity of the developed model is examined using a
set of measured data acquired by the Spaceshuttle Imaging RadarC/XBand Synthetic Aperture Radar (SIRC/XSAR). The collected ground truth and the radar
parameters, such as frequency and incidence angle, are used as model input. In
this section we also present some examples to demonstrate the sensitivity of radar
backscatter to some important forest parameters.
4.1 SIRC/XSAR
The SIRC/XSAR radar system [22] was flown aboard the shuttle Endeavor in the
spring (SRL1) and fall (SRL2) of 1994. This mission was the first of its kind where a
beamsteerable, multifrequency, and multipolarization spaceborne synthetic aperture radar was deployed. The SIRC/XSAR system operated at L (1.25 GHz), C(5.3 GHz), and Xband (9.6 GHz). The L and Cband SARs were configured to
collect polarimetric data whereas the Xband SAR was a single channel radar and
collected the backscatter data at vv polarization. The look angle of the system was
varied from 15~ to 600. In this study, the polarimetric SIRC data (L and Cband)
during the SRL2 is selected for comparison with the results predicted by the model
developed in this paper.
4.2 Ground Truth
Raco, located in the eastern part of Michigan's Upper Peninsula, was designated by
NASA as a calibration and ecological Supersite and has been a test site for our radar
10
Tree Density: 1700/Hectare
Tree Height 16.8 m
Trunk Diameter (DBH) 14 cm
Leaf Density 382 #/m3
Leaf Area: 50 cm2/#
Leaf Thickness: 0.2 mm
Leaf Moisture (mg): 0.51
Wood Moisture (mg): 0.60
Soil Moisture (my): 0.18
Table 1: Ground Truth of Stand 31
Lband Cband
Leaf 17.9 + i6.0 14.7 + i4.7
Wood 32.1 + i10.O 27.7 + i8.4
Soil 9.7 + il.6 9.4 + IL.5
Table 2: Dielectric properties of Stand 31
remote sensing activities since 1991 [20,21]. Great efforts have been devoted towards
characterizing ground inventories and the site has been imaged by ERS1, JERS1, SIRC/XSAR, and JPL AIRSAR. The main research objective at this site has
been relating the measured SAR backscatter data to the forest ecological/biophysical
parameters, which are essential input parameters for the ecological models used for
the study of land and atmosphere processes.
The Raco Supersite contains most boreal forest species and many of the temperate
species. The SIRC/XSAR overflight occurred in the fall, a time of some seasonal
change where trees begin to dry and the deciduous leaves begin to undergo their
fall color change. During the SIRC overflight (October 1994), the leaves were still
predominantly green. Color change happened towards the end of the mission.
In this study, a deciduous forest stand, denoted in the existing report [20] as Stand
31, is selected as a test stand. This stand consists of a large number of red maple as
well as a few sugar maple, uniformly covering an area about 300 m by 300 m on flat
terrain. The ground truth of this stand has been collected since 1991, and a summary
of its pertinent parameters is reported in Table 1. The vegetation and soil dielectric
constants during the SIRC overflights are reported in Table 2, and are derived from
the measured moisture values using the empirical models described in [23,24].
4.3 Simulation Results
The first step in obtaining the model prediction is to generate fractal trees faithful to the real tree structure of the desired forest stand. There are two phases for
determining the input parameters for the tree generating code. The first phase is
to characterize the coarse parameters such as the branching nature of the trees, the
growth factors, and the finite fractal order. In the second phase, some of the fine input
11
parameters, such as the branch tilt angle and its distribution, are slightly tuned in
order to minimize the difference between the simulated and measured backscattering
coefficients co. In general accomplishing the second phase is much more difficult than
the first phase because there is no apparent rule for adjusting the parameters. To
establish a set of rules of thumb for finetuning the parameters of tree structures,
we performed a sensitivity analysis. The gradient of the desired radar backscatter
parameters with respect to the desired tree structure parameters was determined and
used for determining the fine tuning procedure. In this procedure, we allowed the fine
tree parameters to be adjusted to within 10% of the measured ground truth parameter to account for the uncertainty in the ground truth measurements. It is assumed
that the model (including tree generation and coherent scattering) is verified if the
simulation results can simultaneously match the polarimetric SIRC data for both
frequencies and different incidence angles.
Figure 6 shows a photo of Stand 31 (taken in April, 1994), the fractal tree structure
generated by the model, and its corresponding extinction coefficient (imaginary part
of Mm in (17)) profile. It is noted that the wave attenuation at Cband is much greater
than Lband, and the extinction coefficient for vertical polarization is slightly greater
than that for horizontal polarization at both frequencies. This extinction coefficient
profile is shaped according to the tree architecture and composition, which plays an
important role in radar backscatter parameters including the position of the scattering
phase center [25]. In this example, the entire tree canopy is divided into eleven layers,
and the extinction coefficient is calculated as described in the previous section. It
should be pointed out that the number of layers can be determined by imposing a
step discontinuity threshold. Basically the algorithm starts with a moderate number
of layers, calculates the extinction coefficient for each layer, and examines the step
discontinuity. If the discontinuity between any two layers is larger than the prescribed
threshold, these layers are divided into finer layers.
In performing Monte Carlo simulations, one should be careful of the convergence
properties of the simulation. In all simulation results reported in this paper convergence was achieved to within ~0.5 dB of the estimated mean values for less than 100
tree realizations. Figures 7(a) and 7(b) show, respectively, the convergence behavior
of the backscattering coefficients at L and Cband for forest Stand 31.
Figure 8 shows the comparison between the model prediction and the measured
backscattering coefficients for three consecutive SIRC overflights as a function of
incidence angle at L and Cband respectively. It is shown that an excellent agreement
is achieved for all incidence angles and polarizations except for the Cband crosspolarized backscattering coefficient. The lack of accuracy for this polarization can be
attributed to the effect of multiple scattering between branches or branches and leaves
in the canopy crown. It shows that the measured Cband data is consistently higher
than the simulated results by 1.3 dB which can be attributed to the overestimation
of radiometric calibration constants. The computation time for each incidence angle
point is about 35 minutes at Lband and 65 minutes at Cband on a Sun Sparc 20
workstation.
As mentioned in section 3, the total backscatter is comprised of different scattering components. Simulation results show that in all cases except for Lband hh
12
polarization the backscattering coefficients are dominated by the direct backscatter
component (cr~). The hhpolarized backscattering coefficient ghh at Lband, depending on the incidence angle, is mostly dominated by the direct backscatter or the
ground bounce term (ogt). The double ground bounce component ( tg) is negligible for all cases because of the low transmissivity for this canopy (see Figure 12 for
LAI=12). Figure 9 shows the scattering components of hC as a function of incidence
angle. The analysis for characterizing the contribution of each scattering component
is essential in determining the position of the scattering phase center of the forest.
It is also important to examine the effect of the inhomogeneity of the extinction
profile (see Figure 6(d) on the backscattering coefficient. Figure 10 compares the
copolarized backscattering coefficients of Stand 31 where the forest is both modeled
by a 2layer medium and by an 11layer medium. In the 2layer model the tree
canopy is composed of a trunk layer extending from 05 m and a crown layer which
extends from 517 m. It can be observed that the 2layer model overestimates the
backscatter at lower incidence angles and underestimates at higher incidence angles.
The discrepancy in this example is as high as 2.5 dB, and can be even higher for
stands with higher leaf density. It is also found that the discrepancy increases with
increasing frequency. For example, the discrepancy at Lband is only less than 0.3
dB. It should be mentioned that the CPU time for calculation of the backscattering
coefficient for a 2layer and an 11layer forest is almost the same, because the mean
field profile of the canopy is calculated before the Monte Carlo simulation is carried
out.
The statistical behavior of the backscatter can also be obtained from the present
model. Through the Monte Carlo simulations the desired histograms can be constructed by recording the backscatter results for each realization. Figure 11 shows
the estimated probability density function (pdf) of backscattering coefficients in dB
at incidence angle 43.6~. The pdf can provide additional information about the distributed target if the backscatter statistics are nonGaussian. For instance, although
the mean values of chh and a, at Lband are nearly identical, their pdfs are somewhat
different from each other.
The transmissivity is another quantity with which to characterize a stand. Based
on the extinction profile of the forest canopies, the transmissivity can be computed
by integrating the attenuation of each layer. In Figure 12, the oneway transmissivity
(from top to bottom) is calculated as a function of leaf area index (LAI), defined as
the total leaf area (single side) per unit area of forest. It is shown that the horizontally
polarized wave can more easily penetrate the canopies than the vertically polarized
wave. This phenomenon results from the fact that the tree trunk and branches are
oriented mostly along the vertical direction.
To demonstrate the effect of tree structures on the radar backscatter, two examples
are considered in this study. In the first example, denoted as Case 1, we change the
branching angle AO from 22~ ~5~ (used in Stand 31) to 150 ~30 while keeping the other
parameters the same. Figure 13 compares the orientation distribution of the branches
for Stand 31 and Case 1 example. The pdfs of branch orientation are obtained by
counting the number of branches in small increments of orientation angle for all the
branch segments of a fractal tree, which included about 7500 branch segments in
13
Tree Lband Cband
Structures c'vv (dB) (vh (dB)  hh (dB) oOv (dB) Cvh (dB) rh (dB)
Stand 31 8.8 14.6 8.2 9.3 16.4 10.1
Case 1 8.4 16.1 7.1 7.9 16.2 8.7
Case 2 13.2 19.6 9.1 11.4 21.6 10.3
Table 3: Effect of tree structures on backscattering coefficients, simulated at Oi =
43.6~.
more than 20 classes of diameters and lengths. In the second example referred to as
Case 2, we changed the tree height and trunk diameter while keeping the dry biomass
unchanged (14.4 kg/m2). A tree structure of Case 2 having height 8.6 m and trunk
diameter 17cm is shown in Figure 2(a). The backscattering coefficients calculated for
these three tree structures are given in Table 3, which indicates a significant variability
in the backscattering coefficients among the three simulated forest stands of different
geometrical structures having identical biomass.
The effect of the ground tilt angle on the radar backscatter from the forest canopy
is also investigated in this study. Using the same parameters of Stand 31 except
for changing the ground tilt angle 0g from 0~ to 10~, the backscattering coefficients
are computed as a function of the azimuthal look angle X for incidence angle Oi at
25.4~. As expected, simulation results show that the radar backscatter is not sensitive
to the tilt plane at Cband since most of the backscattered field emanates from the
crown layer. However, at Lband the radar backscatters, especially Th and Vh, show
sensitivity to the ground tilt angle (see Figure 14(a)). Near the azimuthal look angle
i = 70~, there are noticeable increases in o5h and C~h which can be attributed to a
groundtrunk interaction. To illustrate this point, consider a single cylinder oriented
along the Zc direction standing on a tilted ground surface with a unit normal ng, as
shown in Figure 14(b). The groundtrunk scattered ray is parallel to the incident ray
when the following relationship is satisfied:. Zc = (ki. ng)(fg z ). (33)
Assuming Zc is along the vertical direction Z (most trees grow vertically in spite of the
tilted ground), the above equation can be readily reduced to an explicit expression
given by
Cos 2 sin2 0g
cos4>i  tansn2. (34)
tan Oi sin 20g
Using this expression a maximum backscatter is expected at A =68~ when 0g = 10~
and 0i = 25.4~. For this particular look angle significant hhpolarized and crosspolarized backscatters are generated, as shown in Figure 14(c) which has a very good
coincidence with Figure 14(a). The radar cross section in Figure 14(c) is simulated
from a cylinder of radius a = 7.2cm, length b = 7.2m, and dielectric constant e =
32.1 + i10.0 vertically standing on a tilted dielectric plane with Og = 10~ and cg =
9.7 + ilZ.6 illuminated by a plane wave with incidence angle Oi = 25.4~.
14
5 Conclusions
A coherent scattering model for forest canopies based on a Monte Carlo simulation of
fractalgenerated trees is developed in this paper. A coherent model offers three major
advantages over the existing incoherent scattering models: (1) the model preserves
the effect of architectural structure of the trees which manifest itself in the extinction
and scattering profiles, (2) the model provides complete statistics of the scattered
field instead of just its second moments, and (3) the model is capable of simulating
the scattering from forest canopies on a tilted ground surface. In general the coherent
scattering model is comprised of two main components: (1) a tree structure generating
model which is developed based on stochastic Lsystems, (2) a firstorder scattering
model which can handle radially stratified cylinders and dielectric disks and needles
of arbitrary cross section.
The validity and accuracy of the model was demonstrated by comparing the results based on the model simulation with the backscattering coefficients measured
by polarimetric L and Cband SIRC at three different incidence angles. A very
good agreement between the measured quantities and the model predictions is obtained with the exception of ao for Cband which is believed due to the existence
of multiple scattering in the crown layer. A sensitivity study was also carried out
to demonstrate the effects of tilted ground surfaces and tree structures on the radar
backscattering coefficients.
6 Acknowledgment
This investigation was supported by NASA Office of Mission to Planet Earth under
contract NAGW 4555. The authors are thankful to Dr. L. Pierce for helping in
extracting the SIRC data used in this paper.
15
Appendix
The parameters for Lsystems for generating the maple tree used in this paper
is given below. Note that some userdefined symbols other than those used by Lsystems [12] are rendered to account for the sophisticated features of the tree structures. For example, the branch tapering symbols (),[], and {} are used to denote
small, medium, and large branch tapering respectively.
* Fractal Coding Parameters:
Length (number of iteration) n: 4
Axiom/initiator w:
FFF!(+A){!FF(+A FF(~~A)!F( {!F(+B)!(++B){F!(+A)!(++A) [!F[++B]![++B]![+B]]}}}}
Production pi:
A: ~ ff(+A)!f(+A){!(++A){!f[+A]!f[+B]}}}
Production p2:
B:  f(+A)[!f(++B)[!f[++B]!f[+B] [B]]]
Production p3:
F:  FF
Production p4:
f: ff
where F and f are respectively vertical and horizontal forward steps.
* Geometrical parameters include tree diameter at breast height (DBH), branching angle (0b) and rotation angle (1b), trunk tilt angle (0t), leaf orientation angle (01),
number of leaflet (Nleaflet), leaf radius (al), leaf thickness (ti), stem radius (a,), and
stem length (1s).
mean(DBH), std(DBH), mean(F), std(F), mean(f), std(f) (cm)
14. 3. 9. 1. 7.5 1.
mean(Ob), std(Ob), mean(Ob),std(Ob) (deg)
22. 5. 137.5 10.
mean(Ot), std(0t), mean(0), std(0l) (deg)
0. 3. 5. 10.
Nleaflet, aI, tl, as, Is, (cm)
5 4.0 0.02 0.1 8.
where mean(.) and std(.) refers to the statistical mean and the standard deviation of
the parameters respectively.
* Display postscript parameters
Xstart, Ystart, Zstart, Oview, 7vi
300 300 80 90 0
ew, Scale
25
16
References
[1] F. T. Ulaby and C. Elachi, Radar Polarimetry for Geoscience Applications,
Artech House, 1990.
[2] M. C. Dobson, F. T. Ulaby, T. Le Toan, A. Beaudoin, and E. S. Kasischke, "Dependence of radar backscatter on conifer forest biomass," IEEE Trans. Geosci.
Remote Sensing, vol. 30, pp. 402415, 1992.
[3] L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing,
New York: Wiley Interscience, 1985.
[4] F. T. Ulaby, K. Sarabandi, K. MacDonald, M. Whitt, and M. C. Dobson, "
Michigan Microwave Canopy Scattering Model", Int. J. Remote Sensing, Vol.
11, NO. 7, pp. 12231253, 1990.
[5] M. L. Imhoff, "A theoretical analysis of the effect of forest structure on SAR
backscatter and the remote sensing of biomass", IEEE Trans. Geosci. Remote
Sensing, Vol. 33, No. 2, pp. 341352, 1995.
[6] N. S. Chauhan, R. H. Lang, and K. J. Ranson, "Radar Modeling of a Boreal
Forest" IEEE Trans. Geosci. Remote Sensing, Vol. 29, No. 4, pp. 627638, 1991.
[7] S. H. Yueh, J. A. Kong, J. K. Jao, R. T. Shin, and T. L. Toan, "Branching
model for vegetation," IEEE Trans. Geosci. Remote Sensing, Vol. 30, No. 2, pp.
390402, 1992.
[8] J. M. Stiles and K. Sarabandi, "Scattering from cultural grass canopies: a phase
coherent model," Proceedings of IGARSS'96 held in Lincoln, pp. 720722, 1996.
[9] C. C. Borel and R. E. McIntosh, "A backscattering model for various foliated
decidous tree types at millimeter wavelengths," Proceedings of IGARSS'86 held
in Zurich, pp. 867872, 1986
[10] B. Mandelbrot, Fractal Geometry of Nature, New York, W. H. Freeman Company, 1983.
[11] G. Zhang, L. Tsang, and Z. Chen, "Collective scattering effects of trees generated
by stochastic Lindenmayer systems," Microwave and Optical Technology Letters, vol. 11, no. 2, pp. 107111, 1996.
[12] P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, SpringVerlag, New York, 1990.
[13] R. H. Lang, R. Landry, 0. Kavakhioglu and J. C. Deguise,"Simulation of microwave backscatter from a red pine stand," in Multispectral and Microwave
Sensing of Forestry, Hydrology, and Natural Reources, SPIE, Rome, Italy, vol.
2314, pp. 538548, 1994.
17
[14] A. Lindenmayer, "Developmental algorithms for multicellular organisms: a survey of Lsystems", Journal of theoretical biology, Vol. 54, pp. 322, 1975.
[15] M. H. Zimmermann and C. L. Brown, Tree Structures and Function, SpringerVerlag, New York, 1971.
[16] Y. C. Lin and K. Sarabandi, "Eletromagnetic scattering model for a tree trunk
above a tilted ground plane", IEEE Trans. Geosci. Remote Sensing, Vol. 33. No.
4, pp.10631070, 1995.
[17] K. Sarabandi and T. B. A. Senior, "Lowfrequency scattering from cylindrical
strutures at oblique incidence," IEEE Trans. Geosci. Remote Sensing, Vol. 28,
No. 5, pp. 879885, 1990.
[18] M. A. Karam, A. K. Fung, and Y. M. M. Antar, "Electromagnetic wave scattering
from some vegetation samples," IEEE Trans. Geosci. Remote Sensing, vol. 26,
no. 6, pp. 799808, 1988.
[19] K. Sarabandi, "Derivation of phase statistics from the Mueller matrix", Radio
Science, Vol. 27, No. 5, pp. 553560, 1992.
[20] K. M. Bergen, M. C. Dobson, T. L. Sharik, and I. Brodie, "Structure, Composition, and aboveground biomass of SIRC/XSAR and ERS1 forest test stands
19911994, Raco Michigan Site ", Rep. 0265117T, The University of Michigan
Radiation Laboratory, Oct., 1995
[21] K. M. Bergen, M. C. Dobson, L. E. Pierce, J. Kellndorfer, and P. Siqueira,
"October 1994 SIRC/XSAR Mission: Ancilary data report, Raco Michigan
Site ", Rep. 0265116T, The University of Michigan Radiation Laboratory, Oct.,
1995
[22] R. L. Jordan, B. L. Huneycutt, and M. Werner, "The SIRC/XSAR synthetic
aperture radar system," IEEE Trans. Geosci. Remote Sensing, vol. 33, pp. 829 839, July 1996.
[23] M. T. Hallikainen, F. T. Ulaby, M. C. Dobson, M. A. ElRayes, and L.K. Wu,
"Microwave dielectric behavior of wet soil  Part I: empirical models and experimental observations," IEEE Trans. Geosci. Remote Sensing, vol. GE23, pp.
2534, 1985.
[24] F. T. Ulaby and M. A. Elrayes, "Microwave dielectric spectrum of vegetation,
Part II: Dualdispersion model," IEEE Trans. Geosci. Remote Sensing, vol. GE25, pp. 550557, 1987.
[25] K. Sarabandi, "AkRadar equivalent of interferometric SARs: a theoretical study
for determination of vegetation height," IEEE Trans. Geosci. Remote Sensing,
vol. 35, no. 5, pp. 12671276, 1997.
18
1A n=4
1.n
I
Figure 1: The growing process of a fractal tree.
(a) Decurrent (b) Excurrent
Figure 2: Two fractal trees simulated for (a) decurrent and (b) excurrent types.
19
Es
Ei
Yx
Figure 3: Scattering from a cluster of scatterers above a tilted ground surface.
t
SA^' n
01
stg
n
I.~
sgt
n
W 9iA
A A A
k k
Figure 4: Four scattering components from an object above a tilted dielectric plane.
20
Figure 5: Extinction of a coherent wave in random media.
21
0.00 0.10 0.20 0.30
 I Extinction Coefficient (Np/m )
(a) Stand 31 (b) Fractal Tree (c) Fractal Tree (d) Extinction Profile
Figure 6: Visual verificatiin of the fractal model: photograph of the test maple stand (a), the generated fractal tree without (b)
and with leaves (c), and the calculated extinction profile (d).
0
m
o
A
C)
o
V
5
Lband
hh,'  ~' vh
I I
10
15
20
25
OfrI
0
5
10
15
20
25
30
Cband
hh
 vh
_( I.~ I
0
50
Realization Number
100 0
50
Realization Number
100
(a)
(b)
Figure 7: Convergence behavior of the Monte Carlo simulation for Stand 31 at Lband(a) and Cband (b) at incidence angle 0i = 30~.
Lband..................
11
CP
U
o
0.o.u
0
0
0
c
0
5
10 
i i I.... I....I '
hh
 
v  
vh E E E
[]
i ii
10 F
0
5
Cband
I... I... I... I..I.
A A
hh
E 0
* vh
I  I —.......
15 
15 F
20 
20 F
25
c;
25.. I. I... I... 1........ I ' '
10 20 30 40 50
Incidence Angle (degrees)
(a)
60 70 10 20 30 40 50
Incidence Angle (degrees)
(b)
60
70
Figure 8: Comparison between the model predictions (lines) and SIRC data (symbols) at (a) Lband and (b) Cband.
23
PQ
C3
~o
O
*4 r.
'3
u
O
~i
0
ca
Cm
4
cn
0
5
10
15
20
25
o
o '
t
 gt
* total
'... I.... I....I.... I.... I...
10
20 30 40 50 60 70
Incidence Angle (degrees)
Figure 9: Contribution of different scattering components (uodirect and aO groundtrunk) to the overall backscattering coefficient (Ct~otal) as a function of incidence angle.
5.. I I I I... I... I... I I I
5
0t
Q
0
U
a)
ct
10 
E.
S.__
— D 
 11layer (Chh)
— E  2layer (Chh)
Ict
C)
0
U
Ct
Cm
C.
pan
I I.. I I. I I I I I I.I I. I..
E1  —
 11layer (Cv)
VV),El
10 1
 2layer (CVV). 
I. I... I
15 ' ' ' '
10 20 30 40 50..........
V1.................
  
60 70
80
10 20 30 40 50 60 70
80
Incidence Angle 9O (Degrees)
Incidence Angle Oi (Degrees)
(a)
(b)
Figure 10: Comparison of the 11layer and 2layer extinction models simulated at
Cband for hh polarization (a) and vv polarization (b).
24
0
U6
0
LL
ci O.C
DL
0
UL:
6i 0.(c
Lband.1
wpol
)5
 n In_ n
40 20 0 20
). 1
vhpol
5 I40 20 0 20
hhpol
O5
)n
O.
0.c
1
I I
r
wpol
)5 2
m
Cband
I
v
40 20
0 20..
0.
I
1 vhpol,.
I
4
0 20 0 2
0
0.1
hhpol
0.05
(IM A__
0 20
40 20
0 20 40 20 0
C 0 (dB) O~ (dB)
20
Figure 11: Histogram of the backscattering coefficients for Stand 31 at i0 = 43.6~.
5
oF
1\
>^.,cn
Ct
~,.
10
15
— E =    
'E....
— L — — hh
 C Lvv.
— e  C,..
vv
— ^ — Gvv.... ~.... I I.... I
20
25
0.0
5.0 10.0
15.0
20.0
LAI
Figure 12: Oneway transmissivity as a function of leaf area index (LAI).
25
0.02,0.015
0.01
(' 0.01
u.ul I,,, I.....
0.02._0.015
0.01
0.005
 (b)
jlln
r
1.
ID
I
I
I I
II
I
Case 1
nnL;P
0o I I 1 " 1 " 11 11 1"" 11 11 " In I 1 X
0 10 20 30
40 50 60 70 80 90
Figure 13: Histogram of branch orientation resulting from two branching angles: (a)
AOb = 22~ ~ 50 (Stand 31); (b)AOb = 15~ ~ 3~ (Case 1). The tree structure of (b) is
also shown on the right.
26
1 C.ca.,
o
L>.bl
c~
ca
o
0
5... I..... I.. . 
(a)
I,,,
7
10 
hh
A .  A     ' .
w
vh  
Er __ )s .
15 
20.. I.. I..... I...
20 40 60 80 100
Azimuthal Look Angle, (i (Degrees)
120
z
(b)
A
ki
i,Y!
/ y,.......
 i* E c *
  ':.X..1.:.':.:..:.S..::~ Ss..:.::.s.s:i..
). r::w..... s.1::.....
000 —;fC000 —00f — s
E
cr
0
I,
u
o.cn
cn
cn
0
o
Cd
Ct
20
10
0
10
20 '
20
40 60 80 100 120
Azimuthal Look Angle, o. (Degrees)
Figure 14: The effect of the ground tilt angle on radar backscatter: (a) backscattering
coefficients for Stand 31 over a tilted ground with 0g = 10~ simulated at Lband with
incidence angle Qo = 25.4~, (b) a vertical cylinder on a tilted dielectric plane and the
associated coordinates, (c) RCS simulation for (b).
27
Appendix IV
Simulation of Interferometric SAR Response for
Characterization of Scattering Phase Center Statistics of
Forest Canopies
22
Simulation of Interferometric SAR Response for
Characterizing the Scattering Phase Center
Statistics of Forest Canopies
Kamal Sarabandi and YiCheng Lin
Radiation Laboratory
Department of Electrical Engineering and Computer Science
The University of Michigan
Ann Arbor, MI 481092122
Abstract
A coherent scattering model for tree canopies is employed in order to characterize the
sensitivity of an interferometric SAR (INSAR) response to the physical parameters of
forest stands. The concept of an equivalent scatterer for a collection of scatterers within
a pixel, representing the vegetation particles of tree structures, is used for identifying the
scattering phase center of the pixel whose height is measured by an INSAR. Combining
the recently developed coherent scattering model for tree canopies and the INSAR Akradar equivalence algorithm, for the first time accurate statistics of the scattering phase
center location of forest stands are obtained numerically. The scattering model is based
on a Monte Carlo simulation of scattering from fractal generated tree structures, and
therefore is capable of preserving the absolute phase of the backscatter. The model can
also account for coherent effects due to the relative position of individual scatterers and
the inhomogeneous extinction experienced by a coherent wave propagating through the
random collection of vegetation particles. The location of the scattering phase center
and the correlation coefficient are computed using the Akradar equivalence, simply by
simulating the backscatter response at two slightly different frequencies. The model
is successfully validated using the measured data acquired by JPL TOPSAR over a
selected pine stand in Raco, Michigan. A sensitivity analysis is performed to characterize
the response of coniferous and deciduous forest stands to a multifrequency and multipolarization INSAR in order to determine an optimum system configuration for remote
sensing of forest parameters.
1
1 Introduction
Accurate estimation of gross forest parameters such as total vegetation biomass, total
leaf area index, and tree height in global scale has long been an important goal within
the remote sensing community. Over the past two decades much effort has been devoted to the development of scattering models [16] for understanding the interaction
of electromagnetic waves with vegetation, and to the construction and development of
advanced imaging radars for acquiring test data and examining the feasibility of the
remote sensing problem [7,8]. In most practical situations the number of vegetation parameters influencing the radar response usually exceeds the number of radar observation
parameters. For this reason the application of a multifrequency and multipolarization
radar system was proposed and such a system was flown aboard the Shuttle Endeavor
in April and October 1994 [8]. Preliminary results indicate that the classification and
retrieval of vegetation biophysical parameters indeed require many simultaneous radar
channels; however, freeflight of such systems is not practical due to the exorbitant power
requirements.
Recent advancements in the field of radar interferometry have opened a new door
to the radar remote sensing of vegetation. In addition to the backscattering coefficient,
radar interferometers measure two additional quantities that contain target information [9]. These quantities are the correlation coefficient and the interferogram phase.
To interpret these quantities and to characterize their dependency on the physical parameters of the target, a thorough understanding of the coherent interaction of electromagnetic waves with vegetation particles is required. The premise of this investigation
with regard to retrieving vegetation parameters from INSAR data stems from the fact
that the location of the scattering phase center of a target is a strong function of the
target structure. For example the scattering phase centers of nonvegetated terrain are
located at or slightly below the surface depending upon the wavelength and the dielectric properties of the surface media, whereas for vegetated terrain, these scattering phase
centers lie at or above the surface depending upon the wavelength of the SAR and the
vegetation attributes. It also must be recognized that the vegetation cover adds noise
in many interferometric SAR applications where the vegetation itself is not the primary
target, such as geological field mapping or surface change monitoring. In these cases it
is also important to identify and characterize the effect of vegetation on the topographic
information obtained from the interferometric SAR.
In recent years some experimental and theoretical studies have been carried out
to demonstrate the potential INSARs in retrieving forest parameters. For example
in [10,11] and [12] experimental data using ERS1 SAR repeatpass and DOSAR singlepass are employed to show the applications of SAR interferometry for classification of
forest types and retrieval of tree heights. Also theoretical models have been developed
to establish relationships between the interferogram phase and correlation coefficient to
the physical parameters of vegetation and the underlying soil surface [1315]. Although
these models give qualitative explanation for the measured data and provide a basic
understanding of the problem, due to the oversimplified assumptions in the description
2
of vegetation structure, they are not accurate enough for most practical applications. For
example the shape, size, number density, and orientation distributions of vegetation in
forest stands are nonuniform along the vertical direction. The nonuniform distributions
of physical parameters of vegetation particles (such as leaves, and branches) give rise
to inhomogeneous scattering and extinction which significantly affects the correlation
coefficient and the location of the vegetation scattering phase center.
The purpose of this investigation is to develop a robust scattering model for forest
canopies capable of predicting the response of INSARs. Although there are a number of
EM scattering models available for vegetation canopies [13,5,6], they are of little use
with regard to INSAR applications due to their inability to predict the absolute phase of
the scattered field. The absolute phase of the scattered field is the fundamental quantity
from which the interferogram images are constructed. The proposed model described in
Section 2 is basically composed of two recently developed algorithms: 1) a fully coherent
scattering model for tree canopies based on a Monte Carlo simulation of scattering
from fractal generated trees [16], and 2) extraction of the scattering phase center based
on a Akradar equivalence relationship with INSAR [13]. In Section 3 the validity of
the model in predicting the backscatter coefficients and the location of the scattering
phase center of forest canopies is demonstrated by comparing the simulated results with
those measured by JPL TOPSAR [17]. Finally a sensitivity study is conducted to
demonstrate the variations of the scattering phase center of a forest stand in terms of
target parameters such as tree density, soil moisture, tree type, and ground tilt angle,
as well as INSAR parameters such as polarization, frequency and incidence angle.
2 Model Description
In this section an overview is given of the approaches which are employed to extract
statistics of the scattering phase center of forest canopies. Three tasks must be undertaken for the calculation of the correlation coefficient and the location of the scattering
phase center. These include: 1) accurate simulation of tree structures, 2) development of
the scattering model, and 3) development of an algorithm for evaluation of the location
of the scattering phase center.
2.1 Fractal Model
It will be shown that the location of the scattering phase center of a tree is a strong
function of the tree structure. For an accurate estimation of the scattering phase center
and the backscattering coefficients, the algorithm for generating desired tree structures
must be capable of producing realistic tree structures and yet be as simple as possible. It has been shown that geometrical features of most botanical structures can be
described by only a few parameters using fractal theory [18,19]. A distinctive feature of
fractal patterns is the selfsimilarity which is kept through the derivation process. To
generate fractal patterns we use Lindenmayer systems [20] which are versatile tools for
3
implementing the selfsimilarity throughout a socalled rewriting process. For a treelike structure, some essential botanical features must be added to the fractal process,
including branch tapering in length and cross section, leaf placement, and randomizing
the fractal parameters according to some prescribed probability density functions. The
botanical features and the probability density functions must be characterized according
to insitu measurements of a given stand.
Although there are many computer graphics available for generating treelike structures, most are not appropriate for the purpose of scientific modeling. At microwave
frequencies, the radar return and its statistics strongly depend on tree structures, which
necessitates the application of a realistic model for generating accurate tree structures.
Therefore, the final and most important step in the fractal model is to incorporate the
information about the tree structure and its statistics obtained from the insitu measurements of the ground truth. Figures 1 and 2 compare the simulated trees produced
by the fractal model developed in this paper with the photographs of the actual forest
stands. These simulated structures are generated according to insitu measurements collected from two test sites denoted by Stand 22 (red pine) and Stand 31 (red maple) in
Raco, Michigan. The fractal pine shown in Figure 1(b) consists of 792 branch segments,
391 end needle clusters, and 747 needlecovered stems. The fractal maple in Figure
2(b) comprises 7494 branch segments and 14818 leaves consistent with the ground truth
data [16]. To visualize the generated 3D tree structure, the fractal model is equipped
with a fast algorithm which displays the realtime projected tree image with arbitrary
scaling and perspective view.
2.2 Scattering Model
In contrast to the existing scattering models for tree canopies, the coherent model used
in this investigation is capable of preserving the absolute phase of the backscatter as
well as the relative phases of individual scatterers which give rise to coherent effects.
Once a tree structure is generated, the scattered field is computed by considering the
tree structure as a cluster of scatterers composed of cylinders (trunks and branches) and
disks/needles (leaves) with specified position, orientation, and size. The attenuation
and phase shift due to the scattering and absorption losses of vegetation particles within
the tree canopy are taken into account in the computation of the scattered field from
individual particles. To the first order of scattering approximation, the backscatter from
the entire tree is calculated from the coherent addition of the individual scattering terms.
Hence, neglecting the multiple scattering among the scatterers, the total scattered field
can be written as
Z6kr N
Es e, E (1)
n=1
where N is the total number of the scatterers, Sn is the individual scattering matrix of
the nth scatterer which may be a tree trunk [21] or a vegetation needle [22], and 4n is
the phase compensation accounting for the shifting of the phase reference from the local
4
to the global phase reference, given by  = ko(ki  k)  rn, where rn is the position
vector of the nth scatterer in the global coordinate system.
In order to compute the scattering matrix of the nth particle S~, consider a single
particle above a ground plane. Ignoring the multiple scattering between the scatterer
and its mirror image, the scattering matrix is composed of four components: 1) direct
component St, 2) groundscatterer component Sf9, 3) scattererground component St,
and 4) groundscattererground component Sgtg. Therefore, the individual scattering
matrix Sn can be written as
Sn = St + Sg + Stg + S5, (2)
where
St = TI Sk k) T: (3)
sgt ei"Tt R. RST( kI T (4)
Sg = "TT S~(ki kr). TRT (5)
tg = enTt R. T S~( k.T R Tt (6)
with kr = ki  2ng(n k) andn = 2ko(rn fig)(g kr). In the above expressions, ig is
the unit vector normal to the ground plane, which in general is tilted with respect to the
horizontal plane of the global coordinate system. The optical length Tn accounts for the
extra path length experienced by the groundscatterer or the scattererground scattering
components compared to the direct scattering component. So is the scattering matrix
of the nth scatterer isolated in free space. R is the reflection matrix of the ground plane
which includes the surface reflection coefficient and the polarization transformation due
to the tilted ground plane. T/ and Tr are transmissivity matrices accounting for the
attenuation and phase change of the meanfield from the canopy top and the ground to
the scatterer respectively, and Tt is the total canopy transmissivity (see Figure 3).
A forest stand with a closed canopy can be regarded as a multilayered random
medium where the properties of each layer can be characterized according to the particle distribution along the vertical extent of the forest canopy. The particle size, shape,
position, and orientation distributions are obtained directly from the fractal model. A
continuous multilayer random medium is not an accurate representation for the discontinuous canopies such as coniferous forest stands. In these cases, the mean field within
the canopy is a function of both the vertical and horizontal positions as shown in Figure
4. The scattering model developed for this study has the ability to keep track of the
attenuation and phase shift of the incident and reflected rays as they traverse through
the discontinuous canopies. This is accomplished by defining an envelope obtained from
the fractal model for the tree canopy. Depending on the incidence angle, the incident
or reflected rays may traverse through the neighboring trees [23]. In the Monte Carlo
siimulation the position of the neighboring trees are chosen randomly according to the
tree density and plantation.
5
2.3 Algorithms for Evaluating the Location of the Scattering
Phase Center
As mentioned earlier, the overall objective of this investigation is to study the relationship between the phase and correlation coefficient of an INSAR interferogram and
the physical parameters of a forest stand. An INSAR system measures the backscatter of a scene at two slightly different look angles, and the phase difference between
the two backscattered fields is used to derive the elevation information. In a recent
study [13] it has been established that similar information can be obtained by measuring the backscatter of the scene at two slightly different frequencies provided that the
look angle is known. For an INSAR system with known baseline distance (B) and angle
a operating at frequency fo, the frequency shift (Af) of an equivalent Akradar is given
by
Af = foB sin(ac 0) (7)
mr
where 0 is the looking angle, m = 1,2 for repeatpass, and twoantenna INSAR configurations respectively, and r is the distance between the antenna and the scatterer. This
equivalence relationship is specifically useful for numerical simulations and controlled experiments using steppedfrequency scatterometer systems. In Monte Carlo simulations,
once the tree structure and the scattering configuration are determined, the backscatter signals are calculated twice at two slightly different frequencies. The backscatter at
fi = Jo and f2 = fo + Af are represented by E1 and E2 respectively, which are computed
from
N
E = 3 e2ikokirn S(ko) E, (8)
n=1
N
E2 = E 62i(ko+~l k)k rnS (0k + Ak) ~ E'. (9)
n=l
It is also shown that the height of the equivalent scatterer above the xy plane of the
global coordinate system can be determined from
At
ze 2Akcos ' (10)
where Ak = 27rAf/c, and Ad = Z(EE2) represents the phase difference between E1
and E2. Note that the equivalent frequency shift for most practical INSAR configurations
is only a small fraction of the center frequency (Af/fo < 0.1%) and therefore the far
field amplitudes of individual isolated scatterers (S6) do not change when the frequency
is changed from to to fo+Af, that is, Sno(ko)  SO(ko+Ak). This approximation speeds
up the Monte Carlo simulation without compromising the overall accuracy of scattering
phase center height estimation.
For a random medium like a forest stand, the scattering phase center height (Ze) is a
random variable whose statistics are of interest. Usually the mean value and the second
6
moment of this random variable are sought. Based on a rigorous statistical analysis [13]
it is shown that the statistics of A<4 can be obtained from the frequency correlation
function of the target by computing
aet( < = (11)
WA EEz2 >< El
where a is the correlation coefficient, and ( is the coherent phase difference. In (11) < >
denotes the ensemble averaging which is evaluated approximately using a sufficiently
large number of realizations through the Monte Carlo simulation. When the backscatter
statistics are Gaussian, a and ( provide a complete description of the statistics of A/.
The apparent height of the scattering phase center of a forest stand is proportional to (
and can be obtained from
ze = 2Awos (12)
2Ak cos O
Note that ( is not the statistical mean of AD, but rather the phase value at which the
probability density function of AD assumes its maximum. In fact, using the mean value
may result in a significant error for calculating the apparent height Ze. To demonstrate
this, two cases may be considered where in one case ( = 0 and in the other case ( = 180~
(see [?] for plots of AO pdf). In both cases the mean value of A1D is zero whereas the
apparent heights calculated from (12) are obviously different.
In order to develop some intuition about the scattering phase center and to examine
the validity of the above equivalence algorithms, let us consider a simple case where
the target is a single scatterer above a ground plane. Through this illustrative case
the relationship between the location of the scattering phase center and the scattering
mechanisms can be demonstrated. Consider a dielectric cylinder of radius a = 5cm,
length b = 3m, dielectric constant ct = 22 + ilO, which is located at height h = 6m
above a ground plane having a complex permittivity Cg = 9.7 + il.6. Suppose the target
is illuminated by a plane wave whose direction of propagation is determined by the
incident angles 0 = 30~, i 180~, as shown in Figure 5. As mentioned previously, the
backscattered field is mainly composed of four scattering components with different path
lengths. In general it is quite difficult to characterize the location of the scattering phase
center of a scatterer analytically when multipath scattering mechanisms are involved.
However, in cases where a single scattering mechanism is dominant it is found that
the location of the scattering center is strongly dependent upon the path length of the
dominant scattering component.
Here we illustrate this fact through an experimental study where the orientation of
the cylinder is properly arranged in four configurations, as shown in (a)(d) of Figure 5,
such that the total backscatter is dominated by (a) St, (b) Sgb, (c) S9tg, and (d)St + Sg9b
respectively. Note that Sb is the combination of the reciprocal pair Sgt and Stg. The
simulation results at Jo =1.25 GHz are shown in Table 1, which includes the scattering
phase center height normalized to the physical height Ze/h, the ratio of the amplitude
of individual scattering components to the total backscattered field S()/S, and the
overall radar cross section (RCS) of the target for each orientation configuration and for
7
both polarizations. It is obvious from the results reported in Table 1 that in scattering
configuration (a) where the backscatter is dominated by the direct component (St/S =
0.99) the location of the scattering phase center appears at the physical location of
the scatterer above the ground (ze/h  1). Similarly in scattering configurations (b)
and (c) where the backscatter is dominated, respectively, by the single ground bounce
component and the double ground bounce component, the locations of the scattering
phase center appear on the ground surface and at the mirror image point as shown
in Figure 5. In scattering configuration (d), the direct and the single ground bounce
components of the backscatter are comparable in magnitude and as shown in Table 1
the location of the scattering phase center in this case appears at a point between the
physical location of the scatterer and the ground surface. When the number of scatterers
is large the location of the scattering phase center is a convoluted function of physical
locations of the constituent scatterers and the relative magnitudes and phases of the
scattering components. Note that \Ze/hl and \S)/S\ in Table 1 may exceed 1 since the
total backscattered field S is the superposition of four scattering components which are
not necessarily in phase.
3 Comparison with Measured Data and Sensitivity
Study
In this section full simulations of forest stands are carried out. As a first step, the model
predictions are compared with the JPL TOPSAR measurements over a selected pine
stand, denoted as Stand 22. Then a sensitivity study is conducted to characterize the
variations of the scattering phase center height and correlation coefficient as a function
of both forest and INSAR parameters.
Stand 22 is a statistically uniform red pine forest located within Raco Airport, Raco,
Michigan. This scene was selected for this study because the stand is over a large flat
terrain which reduces the errors in the measured tree height due to possible surface
topographic effects. In addition, the nearby runway provides a reference target at the
ground level. Ground truth data for this stand have been collected since 1991 [24]
and careful insitu measurements were conducted by the authors during the overflights
of TOPSAR in late April, 1995. The relevant physical parameters of this stand are
summarized in Table 2. The vegetation and soil dielectric constants are derived from
the measured moisture contents using the empirical models described in [25,26].
The JPL TOPSAR is an airborne twoantenna interferometer, operating at Cband
(5.3 GHz) with vv polarization configuration [17]. During this experiment, Stand 22 was
imaged twice at two different incidence angles 39~ and 53~. Figure 6 shows a portion of
the 39~ radar image which includes the test stand. Each side of the dark triangle in this
image is a runway of about 2 miles long. The measured height of the stand is obtained
from the elevation difference between the stand and the nearby runway. Using the
ground truth reported in Table 2, the backscattering coefficient and the location of the
scattering phase center as a function of the incidence angle were simulated at 5.3 GHz.
8
As shown in Figures 7 and 8, excellent agreement between the model predictions and
TOPSAR measurements is achieved. The simulated height of the scattering phase center
of the same forest for an hhpolarized INSAR having the same antenna configuration
and operating at the same frequency is also shown in Figure 7. It is shown that the
estimated height at the hhpolarization configuration is lower than that obtained from
the vvpolarization configuration. This result is usually true for most forest stands
since the groundtrunk backscatter for hhpolarization is much higher than that for vvpolarization. Also noting that the location of the scattering phase center for a groundtrunk backscatter component is at the airground interface, the location of the scattering
phase center of trees for hhpolarization is lower than that for vvpolarization.
The comparison between the simulated ao and the measured cov acquired by TOPSAR as a function of the incidence angle is shown in Figure 8. Also shown in this figure is
the contribution of each scattering component (the direct backscatter a' and the groundbounce backscatter u75 ) to the overall backscattering coefficient. It was found that the
contribution of the double groundbounce component (T9t was relatively small and for
most practical cases can be ignored. In this case, at low incidence angles (0 < 30~) the
groundbounce backscatter is the dominant component. whereas at higher incidence angles the direct backscatter becomes the dominant factor. This trend is the cause for the
increasing behavior of the scattering phase center height as a function of the incidence
angle found in Figure 7. It is worth mentioning that the contribution of pine needles to
the overall backscattering coefficient was found to be negligible compared to the contribution from the branches and tree trunks. However, inclusion of the needles in the
scattering simulation was necessary because of their significant effect on the extinction.
With some confidence in the scattering model and the algorithm for evaluation of the
scattering phase center height, further simulation can be performed to characterize the
dependence of the scattering phase center height of a forest stand on the system parameters such as frequency, polarization, and incidence angle, and the forest parameters such
as tree density, soil moisture, and tree types. In addition, we demonstrate the capability
of the present model as a tool for determining an optimum system configuration for
retrieving physical parameters of forest canopies. Figure 9 shows the estimated height
of Stand 22 for two principal polarizations at Cband (5.3 GHz) and Lband (1.25 GHz)
as a function of the ground soil moisture, simulated at Oi = 45~. As the soil moisture
increases, the ground plane reflection will also increase, which in turn causes the ground
bounce scattering component to increase. As a result of this phenomenon, the scattering
phase center height decreases with soil moisture as shown in Figure 9. This effect is more
pronounced for Lband vvpolarization than other INSAR configurations, suggesting a
practical method for monitoring the soil moisture using the apparent height of the forest
stand. This high sensitivity at Lvv is achieved because of the existence of competitive
scattering components. Basically, at low soil moisture the direct backscatter component
is comparable with the ground bounce component and the scattering phase center lies
amidst the canopy. As the soil moisture increases, the ground bounce scattering component becomes more dominant, which results in lowering the apparent height of the stand.
On the other hand, the least sensitive configuration is Lhh since the dominant scattering
9
component, independent of the soil moisture, is the ground bounce component.
Figure 10 shows the effect of the tree density on the estimated height of a red pine
stand having a similar structure as that of Stand 22 at 0, = 45~. As the tree density
increases, the extinction within the canopy increases, which reduces the groundbounce
component. Increasing the tree density would also increase the direct backscatter component. As a result of these two processes, the apparent height of the canopy increases
with increasing tree density as demonstrated in Figure 10. As before, the apparent
height for Lhh configuration does not show any sensitivity to the tree density indicating
that the ground bounce component remains dominant over the entire simulation range
of 7001200 trees/Hectare. This lack of sensitivity to the apparent height of coniferous
stands for Lhh suggests that this configuration is most suitable for mapping the surface
height of coniferous forest stands.
Now let us examine the response of INSAR when mapping deciduous forest stands.
For this study a red maple stand, denoted by Stand 31, is selected whose structure
and scatterers are different from the previous example. A fractal generated red maple
tree and a picture of the stand are shown in Figure 2. This stand was selected as a
test stand to validate the previously developed coherent scattering model [16], using
the SIRC data. The average tree height and tree number density were measured to
be 16.8m and 1700 trees/Hectare respectively. Table 3 provides the detailed ground
truth data from Stand 31. The simulations for estimating the scattering phase center
height are performed fullypolarimetrically at Lband and Cband. Figure 11 shows the
variation of the apparent height of Stand 31 as a function of the incidence angles for coand crosspolarized L and Cband INSAR configurations. Simulation results at Cband
show that except at very low angles of incidence, the scattering phase center is near the
top of the canopy. In this case the backscatter in all three polarizations is dominated by
the direct backscatter components of particles near the canopy top. The same is true
for Lt, and Lsh configurations; however, since penetration depth at Lband is higher
than Cband, the location of the scattering phase center appears about 13 m below the
apparent height at Cband. The scattering phase center height for Lhh configuration,
on the other hand, is a strong function of the incidence angle where it appears near the
ground surface at low incidence angles and increases to a saturation point near grazing
angles. At low incidence angles the groundtrunk interaction is the dominant scattering
mechanism for hh polarization and since the location of the scattering phase for all
single ground bounce terms is on the ground, the overall scattering phase center height
appears close to the ground. Close examination of this figure indicates that a pair of
Cvv and Lhh INSAR data at low incidence angles can be used to estimate the tree height
of deciduous forest stands with closed canopies. A Cband foliated canopy behaves as a
semiinfinite medium and as shown in [13] the knowledge of extinction would reveal the
distance between the location of the scattering phase center and the canopy top (Ad)
using Ad = cosO/(2K). If an average extinction coefficient (}M) of 0.2N./m is used in
the above equation, a distance Ad 1.77m is obtained at 0 = 45~. However, a simple
relation for evaluating the apparent height for Lhh does not exist yet.
Figure 12 shows the effect of the ground tilt angle on the estimated scattering phase
10
center height. This simulation is obtained by setting a ground tilt angle 9g = 10~ for a
forest stand similar to Stand 31 and calculating the estimated scattering phase center
height as a function of the azimuthal incidence angle (<j at O = 25.4~. As mentioned
in [16], there is a strong groundtrunk backscatter around i = 70~, particularly for Lhh
and Lsh This accounts for the dip in the apparent height simulations for Lhh and Lvh
configurations at i = 70~ shown in Figure 12.
So far only the behavior of the mean value of the scattering phase center height
has been investigated; however, the model has the ability to provide an approximate
probability distribution function of the scattering phase center height. The histograms
of the scattering phase center height can be constructed by recording the simulated
results for each scattering simulation. Figure 13 shows the simulated probability density
function (PDF) of the scattering phase center height of Stand 22 at 0 = 45~ for the three
principal polarizations and for both L and Cband. At Lband the scattering phase
center height has a narrow distribution for hhpolarization, indicating that a relatively
small number of independent samples are sufficient for estimating the apparent height.
At Cband the scattering phase center height of the crosspolarized backscatter exhibits
a narrower PDF.
As mentioned earlier, the correlation coefficient (ac) is an independent parameter
provided by INSARs which, in principle, may be used for inversion and classification
processes. The measured correlation coefficient is a function of INSAR parameters such
as look angle, baseline distance and angle, radar range to target and target parameters.
To examine the behavior of a as a function of target parameters, the Akradar equivalence relationship given by (7) is used where the dependence on INSAR parameters are
lumped into one parameter, namely, the frequency shift. Figure 14 shows the calculated
correlation coefficients (a) as a function of the normalized frequency shift (Af//fo) (corresponding to the baseline distance in an INSAR), simulated for Stand 22 and Stand 31
at Oi = 45~. As shown in [13] the correlation coefficient is inversely proportional to the
width of the PDF, that is, a high value of a indicates a narrow distribution. A comparison between the histograms shown in Figure 13 and the values of a shown in Figure
14(a) demonstrates this relationship. It is interesting to note that simulated a for Stand
31 at Lhh is significantly smaller than the correlation coefficients at other polarizations
(see Figure 14(b)). This behavior is a result of the fact that the direct backscatter and
groundbounce backscatter components are comparable.
It is shown that for the same baseline to distance ratio (B/r) which corresponds to a
constant Af/fo, a at Cband is smaller than a at Lband independent of polarization. It
should be mentioned here that for most practical situations Af/fo is of the order of 104
or smaller which renders a value for a near unity (a > 0.99). That is, for practical INSAR
configurations, the effect of forest parameters on the correlation coefficient appears on
the third digit after the decimal point. It can be shown that the measured correlation
coefficient is a product of three factors: 1) target decorrelation which is a function of
target parameters only and is proportional to B/r, 2) system decorrelation which is a
function system slant range resolution and B/r, and 3) temporal decorrelation which a
function of target change between the two backscatter measurements. Unfortunately the
11
decorrelation caused by the target is far less than those caused by the other two factors.
This puts a serious limitation on the applicability of ae for inversion and classification
algorithms, since accurate measurement of a with three significant digits is not practical
even with two antenna INSARs. For repeatpass interferometry, the a values reported
for forest stands is below 0.7 which is caused mostly by the temporal decorrelation of
the target. Therefore, it does not seem logical to use a as a parameter for classifying
forest types. The TOPSAR measured as for Stand 22 at incidence angles 390 and 530
are, respectively, 0.935 and 0.943 which are below the calculated values of 0.998 and
0.999. This discrepancy can be attributed to processing errors and thermal noise.
4 Conclusions
In this paper a scattering model capable of predicting the response of interferometric
SARs when mapping forest stands is described. The model is constructed by combining
a firstorder scattering model applied to fractal generated tree structures and a recently
developed equivalence relation between an INSAR and a Akradar. Using this model,
for the first time accurate statistics of the scattering phase center height and the correlation coefficient of forest stands are calculated numerically. The validity and accuracy of
the model are demonstrated by comparing the measured backscattering coefficient and
the scattering phase center height of a test stand with those calculated by the model.
Then an extensive sensitivity analysis is carried out to characterize the dependence of
the scattering phase center height on forest physical parameters, such as soil moisture,
tree density, and tree types, and INSAR parameters such as frequency, polarization, and
incidence angle. The ability of the model to predict the PDF of the scattering phase
center height and the correlation coefficient is also demonstrated. It is shown that for
practical INSAR configurations, the correlation coefficient of forest stands is near unity,
much larger than what can be measured by existing INSAR systems.
Acknowledgments:
This investigation was supported by NASA under contract NAG54939. The authors
appreciate the help of the JPL Radar Science group in providing the TOPSAR image
data used in this study.
12
References
[1] F. T. Ulaby, K. Sarabandi, K. MacDonald, M. Whitt, and M. C. Dobson, " Michigan
Microwave Canopy Scattering Model", Int. J. Remote Sensing, Vol. 11, No. 7, pp.
12231253, 1990.
[2] L. Tsang, C. H. Chan, J. A. Kong, and J. Joseph, " Polarimetric signature of
a canopy of dielectric cylinders based on first and second order vector radiative
transfer theory," J. Electromag. Waves and Appli. Vol. 6, No. 1, pp. 1951, 1992.
[3] M. A. Karam, A. K. Fung, R. H. Lang, and N. H. Chauhan, " A microwave scattering model for layered vegetation," IEEE Trans. Geosci. Remote Sensing, Vol. 30,
No. 4, pp. 767784, July 1992.
[4] K. Sarabandi, Electromagnetic Scattering from Vegetation Canopies, Ph.D. Dissertation, University of Michigan, 1989.
[5] G. Sun, and K.J. Ranson, "A threedimensional radar backscatter model of forest
canopies," IEEE Trans. Geosci. Remote Sensing, Vol. 33, No. 2, 1995.
[6] K.C. McDonald and F.T. Ulaby, "Radiative transfer modeling of discontinuous tree
canopies at microwave frequencies," Int. J. Remote Sensing, Vol. 14, No. 11, 1993.
[7] J. B. Cimino, C. Elachi, and M. Settle, "SIRB the second shuttle image radar
experiment," IEEE Trans. Geosci. Remote Sensing, vol. 24, pp. 445452, July 1986.
[8] R. L. Jordan, B. L. Huneycutt, and M. Werner, "The SIRC/XSAR synthetic
aperture radar system," IEEE Trans. Geosci. Remote Sensing, vol. 33, pp. 829839,
July 1996.
[9] E. Rodriguez and J.M. Martin, "Theory and design of interferometric synthetic
aperture radars," IEE Proceedings, vol. F139, no. 2, pp. 147159, 1992.
[10] J. O. Hagberg, L. M. H. Ulander, and J. Askne, "Repeatpass SAR Interferometry
over forested terrain," IEEE Trans. Geosci. Remote Sensing, Vol. 33, pp. 331340,
March, 1995.
[11] U. Wegmuller and C. L. Werner, "SAR Interferometry Signature of Forest," IEEE
Trans. Geosci. Remote Sensing, vol. 33, pp. 11531161, Sep. 1995.
[12] N.P. Faller and E.H. Meier, "First results with the airborne singlepass DOSAR
interferometer," 1EEE Trans. Geosci. Remote Sensing, vol. 33, No. 5, Sep. 1995.
[13] K. Sarabandi, "AfkRadar equivalent of interferometric SARs: a theoretical study
for determination of vegetation height," IEEE Trans. Geosci. Remote Sensing, vol.
35, no. 5, Sept. 1997.
13
[14] R. N. Treuhaft, S. N. Madsen, M. Moghaddam, and J. J. van Zyl, "Vegetation characteristics and underlying topography from interferometric radar," Radio Science,
Vol. 31, No. 6, pp. 14491485, 1996.
[15] J.I.H. Asken, P.B.G. Dammert, L.M.H. Ulander, and G. Smith, "Cband repeartpass interferometric SAR observations of the forest," IEEE Trans. Geosci. Remote
Sensing, Vol. 35, No.1, 1997.
[16] Y. C. Lin and K. Sarabandi, "A Monte Carlo Coherent Scattering Model For Forest
Canopies Using Fractal Generated Trees,"IEEE Trans. Geosci. Remote Sensing,
accepted for publication.
[17] H. A. Zebker, S. N. Madsen, J. Martin, K. B. Wheeler, T. Miller, Y. Lou, G. Alberti,
S. Vetrella, and A. Cucci, " The TOPSAR interferometric radar topographic mapping instrument," IEEE Trans. Geosci. Remote Sensing, Vol.30, No.5, pp.933940,
1992.
[18] B. Mandelbrot, Fractal Geometry of Nature, New York, W. H. Freeman Company,
1983.
[19] C. C. Borel and R. E. McIntosh, "A backscattering model for various foliated deciduous tree types at millimeter wavelengths," Proceedings of IGARSS'86 held in
Zurich, pp. 867872, 1986
[20] P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, SpringVerlag, New York, 1990.
[21] Y. C. Lin and K. Sarabandi, "Electromagnetic scattering model for a tree trunk
above a tilted ground plane", IEEE Trans. Geosci. Remote Sensing, Vol. 33. No. 4,
pp.10631070, 1995.
[22] K. Sarabandi and T. B. A. Senior, "Lowfrequency scattering from cylindrical structures at oblique incidence," IEEE Trans. Geosci. Remote Sensing, Vol. 28, No. 5,
pp. 879885, 1990.
[23] Y. C. Lin, "A fractalbased coherent microwave scattering model for forest
canopies," Ph.D. Dissertation, The University of Michigan, 1997.
[24] K. M. Bergen, M. C. Dobson, T. L. Sharik, and I. Brodie, "Structure, Composition,
and aboveground biomass of SIRC/XSAR and ERS1 forest test stands 1991 1994, Raco Michigan Site ", Rep. 0265117T, The University of Michigan Radiation
Laboratory, Oct., 1995
[25] M. T. Hallikainen, F. T. Ulaby, M. C. Dobson, M. A. ElRayes, and L.K. Wu, "Microwave dielectric behavior of wet soil  Part I: empirical models and experimental
observations," IEEE Trans. Geosci. Remote Sensing, vol. GE23, pp. 2534, 1985.
14
[26] F. T. Ulaby and M. A. Elrayes, "Microwave dielectric spectrum of vegetation, Part
II: Dualdispersion model," IEEE Trans. Geosci. Remote Sensing, vol. GE25, pp.
550557, 1987.
15
Configuration (a) (b) (c) (d)
Polarization vv hh vv hh vv hh vv hh
ze/h 1.00 0.99 0.01 0.01 1.06 0.96 0.49 0.43
IS'SI 0.99 0.97 0.02 0.01 0.05 0.05 0.62 0.42
Isg/SI5 0.03 0.02 0.99 1.01 0.13 0.08 0.62 0.59
iS9tg/Si 0.00 0.00 0.01 0.00 1.10 1.03 0.00 0.00
RCS (dBsm) 8.06 5.19 0.46 6.16 6.05 5.23 17.2 15.1
Table 1: The normalized height of the scattering phase center, the normalized scattering
components, and the radar cross section for four different scattering configurations as
shown in Figure 5.
Tree Density: 1142#/Hectare
Tree Height: 8.9 m
Trunk Diameter (DBH): 14.6 cm
Dry Biomass: 53 (tons/ha)
Needle Length: 10 cm
Needle Diameter: 1.2 mm
Needle Moisture (mg): 0.62
Wood Moisture (mg): 0.42
Soil Moisture (mv): 0.18
Table 2: Ground truth data of Stand 22
Tree Density: 1700/Hectare
Tree Height: 16.8 m
Trunk Diameter (DBH): 14 cm
Dry Biomass: 140 (tons/ha)
Leaf Density: 382 #/m3
Leaf Area: 50 cm2/#
Leaf Thickness: 0.2 mm
Leaf Moisture (mg): 0.51
Wood Moisture (ma): 0.60
Soil Moisture (mv): 0.18
Table 3: Ground Truth of Stand 31
16
(a) Stand 22 (b) Fractal Pine
Figure 1: The photograph of a red pine stand (Stand 22), and the simulated tree structure using the fractal model.
(a) Stand 31 (b) Fractal Maple
Figure 2: The photograph of a red maple stand (Stand 31), and the simulated tree
structure using the fractal model.
distructure using the fractal model.
17
A /
k/
0.3
Extinction Coeff. (Np/m)
(a)
(b)
Figure 3: Propagation of a coherent wave in a continuous canopy (a),
of extinction profile calculated for Stand 31 (b).
and an example
0
A
k
0
c/3.I
E
CA
E
5
10
15
(a)
Figure 4: The position dependence of the
shadow effect caused by neighboring trees.
0 10 20 30 40 50 60 70 80 90
0 (deg)
(b)
transmissivity for coniferous trees and the
18
(a)
Z St
OcII
h Ze I
B I
z
(b)
Sgb
A
h
X
(C) Z
S ts
h I
_____ ^ 1 \ s/
(d) Z St+ Sgb
I /
h \/x
I I V x
Figure 5: Four configurations for a cylinder above a ground plane with orientation
angles: (a) 0, = 60~,0 = 180~, (b) O, = 0~, c = 0~, (c) O, = 60~,  = 0~, (d)
0C = 450, (c = 1500, and their principal scattering mechanisms respectively. The center
of the scatterer is denoted by (e) and equivalent scattering phase center by (l).
Runway
Stand 22
Figure 6: A portion of a TOPSAR Cband image (ar,), indicating Stand 22 at an airport
near Raco, Michigan.
19
E
N.c:
*4 (t
';
10
8
6
4
2
0
10 20 30 40 50 60 70
Incidence Angle Oi (Degrees)
Figure 7: The estimated height of scattering phase center of Stand
the data extracted from two TOPSAR images of the same stand.
22
0
U
bC)
C)
ct
m
09
uY
ct
0
10
20
E.
 * TOPSAR " .
— o Model (total) \
   Component ( \
\Componentgb
— o  Component Ogb \x&.... I.... I.... I.... I.... I........ I... I.... I........ I ~ I ~,
2, compared with
'0
30
40...........................
10 20 30 40 50 60
7
Incidence Angle 0i (Degrees)
Figure 8: The simulated backscattering coefficient of Stand 22, compared with the
measured oa, extracted from two TOPSAR images of the same stand.
20
EE
(1)
N
C,
a)
4i
E
4)
Qn
wL
6
5
4
3 
2 
O 
00
0.0
A
'  I
,..........
E 'X NA.
'Q —  ,
El  — E
   .. 
—. 7    7   
I. I. I. I * 1

0 C —
vv
  Chh
 L
— v Lhh
I..........
0.1 0.2 0.3 0.4
Soil Moisture, mv
0.5
0.6
Figure 9: The estimated scattering phase center height of Stand 22 as a function of soil
moisture, simulated at Oi = 45~.
0
N
tb
* 14:3
cz)
o~~
mr
qC,,
6
5
4
3
2
1
( 
  ,,,  — E.a  —   ....... V .. V.. .V —.V

— 00
   1  
300
C
cvv
Chh
Lvv
Lhh
II. I. I. I. I i
600 700 800 900 1000 1100 1200
Tree Density, (#/Hectare)
Figure 10: The estimated scattering phase center height of
tree density, simulated at 0i = 45~.
12
Stand 22 as a function of
21
20............
~z 10 ~ LhS) 15 (.e=:# i =::t — f 1
N
'S, — A^ L
J^ A ]..
5  vh
1 0 .. ~"' ~ —, —
C vh
e  Chh
0....
10 20 30 40 50 60 70
Incidence Angle Oi (Degrees)
Figure 11: The estimated scattering phase center height of Stand 31 as a function of
incidence angle, with fullypolarimetric L and Cand response.
E 15 t p — v L
10~  A —   L vh
A — A —a\ /' C hh
N ''
0.. hh
20 40 60 80 100 120
Azimuthal Look Angle, 0i (Degrees)
Figure 12: The estimated scattering phase center height of Stand 31 over a tilted ground
with tilt angle 0g = 10~, at 0 = 25.4~.
— < —' Cv
c. ~F~
22
0c
aCL
aa.
Lband
).2 
0.  n ~JM liL, hii o
10 0 1 0 24
).2. 1 
Q. o1 nEk
1 0 0 1 0 24
).2 
).i 
n nA  — n.
.0
aD
10
a0 O
C0.a
Cband.2 .1
10 0 1 0 2C.2.1 
0 ~.nr
10 0 10 2
10
aC0
Ca
a0
Aa
a
10 0 10 20 10 0 10 20
Ze (in)
Ze (in)
Figure 13: PDF of the scattering pha
function of frequency and polarization.
iLse center height of Stand 22 at Oi 450 as a
23
Stand 22
1.0,:. —4
^ \\ — ^: —! 
0.4 
0.2    C.)  Cvv
0.,....
 Chh
0.0 '. ' ' '. ' ' ' ' ' ' ' ' ' ' ' ' '
0.0 2.0 4.0 6.0 8.0 10.0
Frequency Shift Af/fo (x 103)
(a)
Stand 31
1.0 I    . Lh
0.8 
Lvv
~6 —... Lvh
0.4 hh,, ~ — a Cvv
0.2 —<> Cvh
— 4 — Chh
0.0,,
0.0 2.0 4.0 6.0 8.0 10.0
Frequency Shift Af/fo (x 103 )
(b)
Figure 14: The correlation coefficient as a function of the frequency shift, simulated
from (a) Stand 22 and (b) Stand 31.
24
Appendix V
Electromagnetic Scattering from Short Branching
Vegetation
23
Electromagnetic Scattering from Short Branching Vegetation
Tsenchieh Chiu and Kamal Sarabandi
Department of Electrical Engineering and Computer Science
The University of Michigan, Ann Arbor, MI 481092122
Tel:(313) 9361575, Fax:(313) 7472106
Email: tcchiu@eecs.umich.edu
Abstract  A polarimetric coherent electromagnetic scattering model for short branching vegetation is developed in this paper. With the realistic structures which reasonably describe
the relative positions of the particles, this model is able to consider the coherent effect due to
the phase difference between the scattered fields from different particles, and account for the
secondorder nearfield interaction between particles to which the relative positions and orientation of the particles are essential. The model validation with measurements is also presented,
and excellent agreement is obtained. The polarimetric radar backscatter measurements for soybean plants using truckmounted scatterometers were conducted at Lband and Cband under
different soilmoisture conditions. Through an extensive ground truth, the important plant and
rough surface parameters, such as the soil moisture and surface roughness, vegetation dielectric constant, and geometry of the soybean plants, were characterized for model verification.
It is found that the secondorder nearfield scattering is significant at Cband for fullygrown
soybeans due to the high vegetation particle density, and at Lband the contribution from the
secondorder near field is negligible. The coherence effect is shown to be important at Lband
and to a much lower extent at Cband. This model is then used to demonstrate its ability for
estimating the physical parameters of a soybean field including soil moisture from a polarimetric
set of AIRSAR images.
1
1 Introduction
Microwave remote sensing has evolved into an important tool for monitoring the atmosphere and surface of the earth. Electromagnetic waves at microwave frequencies are able to
penetrate more deeply into vegetation, and, therefore, retrieving parameters of vegetation and
underlying ground surfaces has become one of the major applications of microwave remote sensing. With the advent of polarimetric synthetic aperture radars (SAR) and the development of
radar polarimetric techniques, microwave remote sensing has attained significant prominence.
While a large amount of data can be collected very efficiently, there are still difficulties in accurately predicting the physical parameters of the targets from the collected radar information.
To accomplish this task, a necessary step is to construct a highfidelity scattering model by
which the relationship between all targets' physical parameters to the radar backscatter can be
established.
In the early vegetation scattering models, the vegetation medium was simplified in terms
of a homogeneous random medium and the single scattering theory was applied to account for
the scattering and propagation in the random medium [1, 2, 3]. For example, in [1] a forest
stand is represented in terms of a twolayer random medium including a crown layer composed
of randomly oriented cylinders and disks representing branches and leaves and a trunk layer
containing nearly vertical cylinders representing tree trunks below the crown layer. Although
these models are capable of predicting the scattering behavior of vegetation qualitatively, they
are incapable of predicting the scattering behavior quantitatively due to their simplifying assumptions. An important feature of a high fidelity scattering model is to preserve the structure
of vegetation as different species of vegetation have their own unique structures, which are
expected to exhibit their own scattering behaviors. An important effect of the vegetation structure is the coherence effect caused by the relative position of the vegetation particles which
produce certain interference pattern. It is shown that the coherence effects caused by the
vegetation structure become more significant at lower frequencies [4]. In the remote sensing
of vegetationcovered terrain where the underlying soil surface is the target of interest, low
microwave frequencies are recommended and therefore the coherence effects must be carefully
accounted for. The model developed by Yueh et al. [5] may be among the first to address the
coherence effects caused by the vegetation structure. In their scattering model for soybeans, a
twoscale branching vegetation structure was constructed, and the scattered fields from particles were added coherently. Lin et al. [6] also proposed a coherent scattering model for forest
canopies in which rather realistic treelike structures are constructed using the fractal theory.
In both models, the scattering solutions are formulated using the single scattering theory.
Another important issue in modeling the scattering from vegetation is the effect of the
multiple scattering among vegetation particles. Vegetation particles are usually arranged in
clusters within a single plant, such as leaves around end branches and branches around main
stems and trunks. Therefore, a vegetation medium may be appropriately considered as locally
dense. In such cases, the nearfield multiple scattering is strong and may significantly affect
the overall response. To accurately evaluate the nearfield interaction, the realistic description
of the relative positions and orientations of the vegetation particles and accurate and efficient
scattering formulations are required. In recent years, some advanced scattering solutions that
account for the nearfield interaction between scatterers have been presented [7, 8]. However,
vegetation scattering models which can handle the nearfield interaction with realistic vegetation
structures have not been developed yet. The evaluation of the nearfield interaction is usually
numerically intensive, considering the huge number of particles in the medium.
In this paper, a scattering model for soybeans is presented which incorporates realistic
2
computergenerated vegetation structures and accounts for the secondorder nearfield scattering interaction. Soybeans are erect branching plants composed of components which can
be often found in many vegetation: stems, branches, leaves and fruits (pods) arranged in a
very welldefined manner. Hence it is very appropriate for studying the effect of the vegetation structure on the radar backscatter. Also because of its moderate number of particles,
the computation of the secondorder nearfield interaction is not formidable. Also from the
experimental point of view, the dimensions of soybean plants are small enough to allow for
conducting controlled experiments using truckmounted scatterometers. Due to the uniformity
of the plants and underlying soil surface, gathering the ground truth data is rather simple. The
paper is organized as follows: Section 2 gives the theoretical description of the model, including
the vegetation structure modeling and the scattering solution. In Section 3 the experimental
procedures using the University of Michigan truckmounted scatterometer and AIRSAR are
discussed. Finally in Section 4 model validation using the measured data and a sensitivity
analysis are presented.
2 Theoretical Analysis
Consider a global coordinate system with xy plane parallel to a horizontal ground plane
and zaxis along the vertical direction, as shown in Fig. 1. Suppose a plane wave given by
E'(r) = Eeikok. (1)
is illuminating the ground plane from the upper halfspace, where ki is the unit vector along
the propagation direction given by
ki = sin 0i cos 0 + y sin 9i sin X z cos i. (2)
The vector Eo in (1) is expressed in terms of a local coordinate system (Qihk) where hi =
ki x z/jki x zl and vi = hi X ki denote the horizontal and vertical unit vectors, respectively.
Representing the direction of the observation point by Aks, the polarization of the scattered field
can also be expressed in terms of a local coordinated system (vshsks) where
kS = x sin 9s cos OS + y sin 0s sin >s + z cos s, (3)
and Vs and hs can be obtained using similar expressions as those given for vi and h, respectively.
2.1 Vegetation Structure Modeling
To make the proposed scattering solution tractable, simple geometries are chosen to represent vegetation particles. Leaves are represented by elliptical thin dielectric disks. The other
particles, which include stems, branches, and pods, are modeled using circular cylinders. Analytical scattering solutions are available for both geometries and will be introduced in the next
section.
The orientation and dimension of each particle are described by four parameters, as shown
in Fig. 2. The values of these parameters are determined by random number generators during
the simulation with predescribed probability distribution functions (pdf). The orientation parameters of the particles are described by two angles: 3(elevation angle) and y(azimuth angle).
Azimuthal symmetry is assumed for 7, and its pdf is given by
( 1 ^[0,2r).
1E [O,2w). (4)
2wr
3
However, for A, a bellshaped pdf is chosen:
e((Im)/3s)2
P fO) fe_((03I/M)/03)2 dO/" E [0,G ]. (5)
For leaves, the axis ratio (b/a) assumed constant and the thickness and major axis (a) are given
Gaussian pdfs. Three types of cylinders are considered for main stems, branches, and pods. For
these cylinders, Gaussian pdfs are chosen to describe the statistics of their radii and lengths.
The branching structure of soybeans is rather simple and can be developed using the following algorithm:
1. All parameters of main stem are determined using random number generators. The main
stem is then divided into subsections, whose lengths are again decided by Gaussian random
number generator.
2. At each node (connecting point of two subsections of the stem), a branch is placed whose
orientation is obtained from (4) and (5). Depending on the growth stage, pods may be
added at each node.
3. To each branch end a leaf is attached. In this paper, the number of leaflets at each branch
end is three (this may be different for other soybean species). Azimuthal orientation angle
of leaves is determined from the orientation angle of the branches they are connected to.
Figure 9 shows a typical computergenerated soybean structures according to the aforementioned algorithm.
2.2 Scattering Mechanism and Scattering Formulations for the Vegetation
Particles and Rough Surfaces
Several scattering mechanisms are considered for the scattering model. Figure 3 depicts
6 different mechanisms including: (1) direct backscatter from the underlying rough surface,
(2) direct backscatter from vegetation particles, (3) single ground bounce, (4) double ground
bounce, (5) secondorder scattering interaction among vegetation particles, and (6) scattering
interaction between main stem and the rough surface. The first four mechanisms are included in
almost all existing vegetation scattering models. Mechanism #5 is a secondorder solution which
accounts for the nearfield interaction within a single plant. Mechanism #6 is only considered for
predicting the crosspolarized scattering at Lband according to a study reported in [10] where it
is shown that the copolarized scattering of mechanism #6 at Lband is weak compared to that
of Mechanism #2. Mechanism #6 is also ignored at Cband, because of attenuation experienced
by the wave propagating through the vegetation layer. In what follows, the scattering solutions
for each mechanism is briefly described.
1. Mechanism #1:
There exist many roughsurface scattering models available in the literature. In this paper,
a secondorder small perturbation model(SPM) [17] and a physical optic (PO) model [18]
are incorporated to handle the backscatter from the rough surface.
2. Mechanisms #2,#4:
These mechanisms are often referred to as the single scattering solutions in which only
the scattering solutions for the isolated vegetation particles are considered. The effect of
4
the ground surface in mechanisms #3 and #4 are considered by introducing the ground
reflection coefficients. If the SPM is used in mechanism #1, the Fresnel reflection coefficients are used directly. If the PO is needed according to the surface roughness condition,
the reflection coefficients are modified by e2(kscos^) to account for the reduction in the
surface reflectivity [11]. The single scattering solutions for dielectric disks and cylinders
are obtained from the following formulations:
(a) Elliptical disk:
The thickness of the soybean leaves (a 0.2  0.3mm) is usually small compared to
the wavelength in microwave region and the ratio of the thickness to the diameter
of the leaves is much less than unity. Also by noting that the dielectric constant of
vegetation is lossy, the RayleighGans formulation [12] can be applied to derive the
scattering solution for the elliptical disks representing the vegetation leaves. For an
elliptical disk, the scattering matrix elements are found to be
Sd d 2 j P,Alv/~7 ^
pq =p (Pd q) 2A J (aA) + (bB )2) (6)
where Ad, a and b are the area, major axis, and minor axis of the disk respectively.
= =1 =0 = = 0
In (6), Pd = Uj PdUd, where Pd is the disk's polarizability tensor which can be
found in [12, 13], and Ud is the matrix of coordinate transformation which transfers
the global coordinate system to a local coordinate system defined by the major axis,
minor axis, and the normal of the disk respectively. The explicit expression for Ud
can be obtained from [14]. Also A and B are given by
A=ko [Ud (kiks)] x
B=ko[Ud (kiks)]'. (7)
(b) Circular cylinder:
Exact scattering solution does not exist for cylinders of finite length, but an approximated solution, which assumes the internal field induced within the finite cylinder
is the same as that of the infinite cylinder with the same cross section and dielectric
constant, can be used [15]. Generally, this solution is valid when the ratio of the
length to the diameter is large.
3. Mechanism #5:
The secondorder scattered field between two particles is formulated using an efficient
algorithm based on the reciprocity theorem [7]. For two adjacent particles we have
P E21 =J Ee2 J1 dv. (8)
where Ee2 is the scattered field from particle #2 illuminated by an infinitesimal current
source at the observation point in the absence of particle #1, and J1 is the induced
polarization current of particle #1 illuminated by the incidence field in the absence of
particle #2. E12 can be obtained using the reciprocity theorem. Hence the secondorder
scattered field are conveniently obtained from the plane wave solution of the induced
polarization current and near field of individual particles. These quantities for disks and
cylinders are given by:
5
(a) Disk: The induced polarization current is obtained from RayleighGans approximation and is given by
Jl(r) ikoYoPd Eoekkir, (9)
where Pd is the polarizability tensor. The exact nearfield scattered field must be
numerically evaluated from
Ee2(r) ikZ o (Pd ) G(k, R)eik~(k'r'+R) ds'
E(47r)2 ro PdP Gk e(10)
where
(IoR)=  1+ ( — oRIR^, (11)
and R is a unit vector defined by R = (r  r')/lr  r'j.
(b) Cylinder: The formulation for finite finite cylinders is used again to calculate the
induced polarization current and the nearfield scattered field. The formulation of
the scattered field in the vicinity of the cylinder is given by [7]
Ee2(r) ikZi F(b  ) ()H 1)(ko sin Osp)ekocosz. (12)
Equation (12) is derived using the stationary phase approximation along the axial
direction of the cylinder axis. This solution has been verified by the method of
moments [7, 16], and the region of validity is given by
p > 2d2/A, (13)
where dc is the diameter of the cylinder, and p is the radial distance between the
observation point and the cylinder axis. For the main stem of soybeans, the radius
is usually less than 5mm. Applying (13) it is found that p > 3.5mm at Cband (5.3
GHz). Therefore, (12) is appropriate for calculating the nearfield interaction.
4. Mechanism #6:
The incoherent interaction between the main stems and rough surface is formulated using
the reciprocity technique introduced in [7]. The details and lengthy formulation for the
cylinderrough surface scattering interaction can be found in [19]. This model is only
applied to calculate the scattering interaction between the main stem and underlying
rough surface. The reason for this is that for a titled cylinder with large elevation angle (/3)
such as branches, the crosspolarized scattering from mechanisms #2 and #3 is dominant.
However, main stems often grow nearly vertically and its interaction with the ground
becomes a important source of the crosspolarized scattering, noting that the mechanisms
#2 and #3 of nearly vertical cylinders do not produce significant crosspolarized scattering
field. As will be shown later, the crosspolarized scattering at Lband is mainly dominated
by two scattering mechanisms #2 and #6.
6
2.3 Propagation in a Lossy Layered Media
2.3.1 Foldy's Approximation
The scattering solutions provided in the previous section are for targets in free space. However, for vegetation canopies the targets are within a lossy random medium. Thus, a particle
is illuminated by not only the incident plane wave, but also by the scattered fields from other
particles. To calculate the total scattered field from a particle, it is usually assumed that the
particle is embedded in homogeneous lossy medium, as shown in Fig. 4(a). The vegetation
layer can be divided into many sublayers which contain different types and number density of
vegetation particles, and thus each layer exhibits different equivalent propagation constants.
Foldy's approximation [14] has been widely used in many vegetation scattering models to
account for the attenuation experienced by the wave traveling through the vegetation medium.
According to the Foldy's approximation the vertical and horizontal components of the mean
electric field in a sparse random medium satisfy
dEh =i (ko + Mhh) Eh + iMhvEv
ds
d = iMvhEh + i (ko + Mvv)Ey, (14)
ds
where s is the length along the propagation path within the medium and
Mpq = k(Spq(k,k)) I pq C {h,v} (15)
ko
Here no is the number density of the scatterers within the medium, and (Spq(k, k)) is the
averaged forward scattering matrix element of the scatterers. Since the vegetation structure
exhibits statistical azimuthal symmetry, there is no coupling between horizontal and vertical
components of the coherent field and therefore Mhv = Mvh = 0. From (14), the effective
propagation constants for both polarizations are given by
k =ko + Mhh
k'=ko+MMv. (16)
As mentioned previously, the secondorder nearfield interaction is incorporated in this
model, and it will only be calculated for the scatterers within a single plant. It is reasonable to assume that no extinction should be considered for the calculation of the nearfield
interaction. However, since both particle are still embedded in the vegetation layer, extinction
is considered for the incident wave and secondary scattered fields. As shown in Fig. 4(b), the
space between two scatterers is considered as free space, and Foldy's approximation is still used
on paths #1 and #2.
2.3.2 Propagation Paths
In this section, the phase difference and extinction caused by the wave propagating in the
vegetation layer will be formulated using the method presented in [20]. To build a coherent
scattering model, the phase of each scattering mechanism has to be calculated with respect to
a phase reference point. Figure 5(a) shows the propagation geometry for the direct path. The
reference phase point is taken to be the origin of the coordinate system. Using ray optics, the
propagation from the equiphase plane (shown in Fig. 5(a)) directly to the scatterer is given by
V(ko, r',p) = kor,. ko + ke(r'  r) ke, (17)
7
where r1 denotes the location where the ray intersects the interface between the vegetation layer
and freespace. Here the effect of refraction is ignored assuming a diffuse boundary between
the vegetation layer and freespace (ke = ko) and p denotes the polarization of the wave.
Substituting (16) into (17), it is found that
(ko, r', p) = kor' ko + Mpp(r'  r) ko (18)
The first term on the righthand side of (18) is the freespace propagation term and will be
included in the scattering matrix elements of the scatterer. The secondterm on the righthand side is the extra phase difference and extinction caused by the propagation in the lossy
vegetation media, and will be denoted as (d(ko, r', p). The free spacevegetation interface is set
to be the xy plane, so it is found that
ZI
(r' ri). ko. (19)
ko.
Therefore, 4d(r', p) can be written as
ZI
d(fo, r', p) = Mpp. (20)
ko pz
The groundbounce path, as shown in Fig. 5(b), includes a reflection from the ground plane.
In Fig. 5(b), the image position is given by
rlimage = x'x + y'y  (z' + 2d), (21)
where d is the thickness of the layer. Using (20), it is found that (I(kCo, r',p), which only
accounts for the extra phase difference and extinction caused by the propagation in the lossy
vegetation media, can be written as
(~g(cor',p) =Mpp, o   (22)
' + 2d
2.4 Scattering from Soybean Fields and MonteCarlo Simulation
Consider an area of soybean field with Np soybean plants per unit area. For a given
computergenerated soybean plant (the kth plant with Ns particles), the total scattering amplitude can be written as
N, Ns Ns
s d + Sg,g2 k
Spq I,. + L s2nd (23)
[ i pqki pqki + Spq,i] + / pqkij erk
i=1 j
where rk is the location of the plant. In (23) each term includes the attenuation and phase
shift due to the propagation:
direct: Ski = Spq,ki(ks, ki)ei d(k,'rks p)ei>d(ik'rki'q),roundplant: Spki= Spqki(ks, kI)Rpeig(ks'rki'p)eiq)d(ki'rki'q)
groundplant: S = Spq,k(ks f CO
plantground:,ki q,i(ks, ki)Rqi4d(kS 'rki'P)eiI g(ki 'rki'q)
groundground: Spg Spq,ki(kl k) RqRqeg( rkiP)ig(irkiq)
nearfield 2ndorder: = Sndk k )ei s r), (24)
8
where k$ = ki  2(ki  z)4 and k' = k,  2(k, z)z. Note that all scattering mechanisms are
added coherently to capture the coherence effect caused by the vegetation structure.
The scattering coefficient of the soybean field is then computed by incoherent addition of
the scattered powers from vegetation, rough surface, and main stemrough surface interaction.
Hence
Ua"pq = uqpq(vegetationugh sure) + (rough(sterough surface), (25)
where
Np 2
poqpq(vegetation) = 41r ( S k (26)
k=l
0 O
upq,,(rough surface) = opq,, ledd(kdzip)eibd(ki,dzq)2 (27)
pqpq(stemrough surface) =47rNp Srqe s pei 05 q)
+ Spqrei d(kt,dz,P) iId(ks,(d+.5lc)zq). (28)
In calculation of the contribution from the direct rough surface and the stemrough surface, the
propagation attenuation through vegetation layer is also included. Spg and Sp are, respectively,
the rough surfacecylinder and cylinderrough surface scattering amplitudes. The ensemble
averaging in (28) is carried out analytically using the SPM formulation, and the details are
reported in [10]. As mentioned earlier, the contribution from this term is only significant at
Lband for the crosspolarized term.
The ensemble averaging in (26) is carried out using a MonteCarlo simulation. For each
realization in the MonteCarlo simulation, a group of computergenerated soybean plants are
generated and distributed on a square area of 1 m2, and then the scattered fields are computed.
This procedure will be repeated until a convergence is reached. To examine the coherence effect,
the scattered power from the vegetation is also calculated incoherently from
uq (vegetation) =47rK{ [Sd + SS qj + Sg 2 + Spq 2]
'p"qpq pq pq,ki pq
i=1 j=l
j~i
3 Experimental Results
In this section, the experimental procedure and the multifrequency multipolarization
backscatter measurements using polarimetric scatterometer systems and JPL AIRSAR are presented.
3.1 Measurement Using the University of Michigan's POLARSCAT
In August of 1995, a series of polarimetric measurements were conducted on a soybean field
near Ann Arbor, MI. These measurement were conducted using the University of Michigan polarimetric scatterometer systems (POLARSCAT) [21]. The polarimetric backscatter data were
9
collected at two different frequencies (Lband and Cband) over a wide range of incidence angles
(from 200 to 700 at 100 increment). The overall goal of these experiments was to investigate the
feasibility of soilmoisture retrieval of vegetationcovered terrain from radar backscatter data.
Experiments were designed to observe the radarbackscatter variations due to the change in
soil moisture while the vegetation parameters were almost the same. Two sets of data were
collected. In one measurement the angular polarimetric data were collected on August 14 when
the underlying soil surface was dry, and in another a similar data was collected right after a
heavy rain on August 18. At the time of experiments the soybean plants were fully grown with
significant number of pods. In fact the vegetation biomass was at its maximum. Since the
separation between the time of experiments were only about 4 days, no significant change in
the vegetation parameters were observed.
The vegetation structural parameters and moisture in addition to the soil surface roughness
and moisture were carefully characterized. The dielectric constant of the soil surface was measured by using a Cband fieldportable dielectric probe [22]. The measured relative dielectric
constant (Er) was used to estimate the moisture contents (my) by inverting a semiempirical
model [23] which give or in terms of me. The mean mt, which is shown in Table 1, is then used
to estimate Er at Lband.
Two dielectric measurement techniques [24, 25] were used to measure the dielectric constant
of leaves and stems. These measurement were performed at Cband using WR187 waveguide
sample holder, and the results are shown in Fig. 6. The corresponding dielectric constants
at Lband was then calculated using the empirical model provided in [26]. The gravimetric
moisture content (mg) of the vegetation was also measured on the day of radar measurement to
monitor the variation of the biomass. As shown in Table 1, the vegetation moisture remained
almost the same on both dates of the experiments.
The dimensions and orientations of vegetation particles were also recorded. Table 2 shows
the means and standard deviations of vegetation parameters. Unlike most cultivated fields
where the plants are planted in row structures, the soybean plants of this field were distributed
in a rather random pattern, as shown in Fig. 7. This picture shows the topview at the end
of the season where all the leaves were fallen. The surface roughness parameters were also
measured and reported in Table 1.
3.2 Measurement Using AIRSAR
JPL Airborne Synthetic Aperture Radar (AIRSAR) [27] was deployed to conduct backscatter measurements on a number of cultivated fields. Although AIRSAR is capable of measuring
polarimetric backscatter at three microwave frequencies (P,L, and Cband), only Lband and
Cband data were collected. The backscatter data were collected by AIRSAR during its flight
over the Kellogg Biological Station near Kalamazoo, Michigan, on July 12, 1995. Also these
data sets were collected at three different incidence angles: 30, 40, 45 degree. Unfortunately
the soybean fields were not within the research site of the station and the ground truth data
was rather limited. The only available informations are that the soybean were about a month
old and the volumetric soil moisture content was less than 0.1. Figure 8 shows the composite
Lband and Cband SAR image at 450 incidence angle.
4 Data Simulation and Analysis
The vegetation scattering model is first validated using the data collected by POLARSCAT.
Guided by the ground truth data, many soybean plant structures were generated in order to
10
carry on the data simulation (see Fig. 9(a)). The computergenerated plants were uniformly
distributed using a random number generator. The MonteCarlo simulations are performed at
incidence angles ranging from 20~ to 70~ at 5~ increment. Figures 10(a) and ll(a) show the
simulated and measured backscattering coefficients versus incidence angle at Lband and Cband, respectively. Good agreement is achieved by allowing the dielectric constants of vegetation
particles vary within the confidence region shown in Fig. 6. In figures 10(b), (c), and (d),
the contributions from individual scattering mechanisms are plotted as functions of incidence
angle at Lband. The cross products of among different mechanisms, which account for the
coherence effect, are not presented in these figures. It is quite obvious that the contribution from
the secondorder nearfield interaction at Lband is negligible for both co and crosspolarized
terms. It is also shown that for copolarized backscattering coefficient the direct backscatter
from soybean, direct backscatter from rough surface, and single groundbounce are sufficient to
characterize the scattering behavior. For crosspolarization, however, the two most significant
mechanisms are the direct backscatter from vegetation and the incoherent rough surfacestem
interaction. The later mechanism contains information regarding the underlying soil surface
including the soil moisture. Figures 11(b), (c), and (d) show scattering contributions from
different mechanisms versus incidence angle at Cband. The direct backscatter form vegetation
and the secondorder nearfield interaction are the dominant scattering mechanisms at Cband.
Because of larger nearfield region, the nearfield interaction is stronger at Cband than at
Lband. Also the secondorder nearfield interaction has more profound effect on the vv and
crosspolarization, because the orientation of the main stems is nearly vertical. The other
mechanisms, which include the soil moisture information, are not significant for two reasons:
(1) high extinction through the vegetation layer, and (2) surface roughness which decreases the
reflectivity of the ground surface.
From these analysis it is found that the backscatter at Cband or higher frequencies are
mainly sensitive to vegetation parameters for sufficiently high vegetation biomass (in this case,
biomass = 1.97 kg/m2). At Lband or lower frequencies, it is possible to sense the soil moisture
for surfaces covered with short vegetation and relatively high biomass. Figures 12(a), (b), and
(c) demonstrate the sensitivity of the backscatter to soil moisture as a function of incidence
angle for the soybean field. The simulations are performed under four different soilmoisture
conditions: mr = 0.1, 0.2, 0.3 and 0.4 at Lband. The backscatter data collected on August 14
and August 18 are also plotted in these figures for comparison. These results suggest that the
appropriate range of incidence angle for the the purpose of soilmoisture retrieval is Q0 < 500
where there is about 6dB of dynamic range. At incidence angles larger than 500, the sensitivity
to soil moisture decreases due to the high extinction caused by the vegetation. To retrieve the
soil moisture accurately, vegetation parameters must be estimated as accurately as possible.
It seems a combination of high and low frequency backscatter data is needed to estimate the
vegetation and soil moistures accurately.
Due to the limited groundtruth data, the AIRSAR data set is used for estimating the
vegetation and surface roughness parameters. Although the retrieval algorithm presented here
is based on trial and error, it indicates the feasibility of estimating vegetation parameters and
soil moisture from image radars. The procedure for estimating these parameters is described
below:
1. Based on a series of trial simulations, it is found that the secondorder nearfield interaction can be ignored at L and Cband for the onemonth old soybeans. In this case the
soybean plants are still young with shorter branches and stems and much fewer number
of vegetation particles. Also there are no pods on the plants whose interaction with the
11
main stem is the major source of the nearfield interaction.
2. Judging from the measured values of the copolarized scattering coefficients reported
in Fig. 13(a), it is inferred that the vegetation biomass is rather low. In this case,
depending on the surface roughness, the surface scattering mechanism can be dominant
at low incidence angles. If the surface scattering is dominant entirely, it is expected that
Va be larger than Uhh. However, this is not observed from the measured data at 300.
Hence, there is at least a comparable backscattering contribution from the vegetation.
Under this condition, a significant contribution to the backscatter at Cband comes from
the vegetation.
3. At relatively low biomass, it is found that crosspolarized scattering coefficient is dominated by the direct backscatter from the soybean at both frequency bands. The size of
the main stems for onemonthold soybean is small, so the rough surfacestem interaction
is not significant. Also at Cband the direct backscatter from the rough surface is weak
due to the small rms height and extinction through the vegetation layer. Therefore, the
dimension, the number density, and the dielectric constant of the soybean can be estimated by matching the crosspolarized backscatter at Cband. This is done by confining
the range of the vegetation dielectric constants to those reported in Fig. 6. The elevation
angles of all vegetation particles can be estimated by matching the copolarized scattering
coefficient ratio rav/(Jh and crosspolarized scattering coefficient. The vegetation parameters as a first iteration is decided by matching the data at Cband. Then, by matching
the data at Lband with the same vegetation structure, the parameters of the rough surface is estimated. The simulation is then iterated between Lband and Cband until the
simulated and measured data match at both frequency bands.
After matching the backscatter data at both L and Cband, the final estimated target
parameters are shown in Tables 3 and 4. A typical corresponding computergenerated soybean
plant is shown in Fig. 9(b). Figures 13(a) and 14(a) show the simulated and measured scattering
coefficients versus incidence angle at L and Cband, respectively. MonteCarlo simulation are
performed at 5 degree increments. Figures 13(b), (c), and (d) show scattering contributions from
different mechanisms versus incidence angle at Lband. As predicted, the scattering between
stems and rough surface is not significant due to the shorter and slimmer main stems and smaller
surface roughness. Figures 13(b), (c), and (d) show scattering contributions from different
mechanisms versus incidence angle at Cband. As predicted, the secondorder scattering can
be neglected.
Finally, Figs. 15 and 16 show the coherence effect of the vegetation structure. The scattering
coefficients do not include the contribution from the main stemsrough surface scattering and the
direct backscatter from the rough surface. In these figures the coefficients denoted as "coherent"
are calculated using (26), while those which are denoted as "incoherent" are calculated using
(29). It is shown that for a fully grown soybean, the coherence effect is significant at Lband
for copolarized components, while the effect is not observable at Cband. However, for low
biomass condition (AIRSAR data), it is found that the coherent effect is also significant at
Cband. This can be explained noting that a fullygrown soybean plant has more complex
structure with more particles than a onemonthold plant. Nevertheless, it should be noted
that the secondorder nearfield interaction is significant for POLARSCAT data at Cband,
and can be evaluated only when the relative distance and orientation of particles are given.
Therefore, to some extent, the coherence effect of structure embedded in this mechanism is also
12
important at Cband. For the crosspolarized scattering, the coherence effect is less significant
in both low and high biomass conditions at both frequencies.
5 Conclusions
In this paper, an electromagnetic scattering model for short branching vegetation is presented. The vegetation particles are modeled as simple geometries such as cylinders and disks
for which analytical scattering solutions are available. With the realistic structures which reasonably describe the relative positions of the particles, this model is is constructed so that
the coherence effect due to the phase difference between the scattered fields from different
particles and the secondorder nearfield interaction among particles are accounted for. Also
the interaction between the main stems and underlying rough surface is incorporated into this
model which is shown to be important only at low frequencies (Lband) and for crosspolarized
backscattering coefficient.
The model accuracy is verified using polarimetric radar backscatter measurements of a soybean field obtained from truckmounted scatterometers. Through an extensive groundtruth
data collection, target parameters such as the soil and vegetation moisture contents, geometry
of the soybean plants, and surface roughness were characterized. MonteCarlo simulations were
carried out simulating the statistical properties of the backscatter at different incidence angles. Good agreement is obtained between the model prediction and measured backscattering
coefficients. From a sensitivity analysis, it is found that: (1) the secondorder nearfield interaction is more significant at Cband than at Lband, (2) the interaction between the main stems
and rough surfaces could be significant for crosspolarized scattering at Lband, (3) the double
groundbounce mechanism is generally not important, and (4) highfrequency data (C(band
or higher) can be used to probe the vegetation, and lowfrequency data (Lband or lower) is
needed to probe the soil moisture through vegetation.
The model was also used to estimate the parameters of a soybean field using the AIRSAR
data, and reasonable results which agree with the limited groundtruth data was obtained. The
coherence effect was also examined using the model simulation.
Acknowledgment: This research was supported by NASA under contract NAGW4180 and
JPL under contract JPL958749.
13
References
[1] Ulaby, F.T., K. Sarabandi, K. McDonald, M. Whitt, and M.C. Dobson, "Michigan microwave canopy scattering model," Int. J. Remote Sensing, vol. 11, no. 7, pp. 20972128,
1990.
[2] Karam, M.A. and A.K. Fung,"Electromagnetic scattering from a layer of finite length,
randomly oriented, dielectric circular cylinders over a rough interface with application to
vegetation," Int. J. Remote Sensing, vol. 9, pp. 11091134, 1988.
[3] Lang, R.H. and J.S. Sidhu,"Electromagnetic backscattering from a layer of vegetation: a
discrete approach," IEEE Trans. Geosci. Remote Sensing, vol. 21, pp. 6271, 1983.
[4] Zhang G., L. Tsang, and Z. Chen, "Collective scattering effects of trees generated by
stochastic Lindenmayer systems," Microwave and Optical Technology Letters, vol 11, no.
2, pp. 107111, Feb. 1995.
[5] Yueh, S.H., J.A. Kong, J.K. Jao, R.T. Shin, and T.L. Toan, "Branching model for vegetation," IEEE Trans. Geosci. Remote Sensing, vol. 30, no. 2, pp. 390402, March 1992.
[6] Lin, Y.C. and K. Sarabandi, "A Monte Carlo Coherent Scattering model for forest canopies
using fractal generated trees," to be submitted to IEEE Trans. Geosci. Remote Sensing.
[7] Sarabandi, K. and P.F. Polatin, "Electromagnetic scattering from two adjacent objects,"
IEEE Trans. Antennas Propagat., vol. 42, no. 4, pp. 510517, 1994.
[8] Tsang L., K. Ding, G. Zhang, C.C. Hsu, and J.A. Kong, "Backscattering enhancement
and Clustering effects of randomly distributed dielectric cylinders overlying a dielectric
half space based on MonteCarlo simulations," IEEE Trans. Antennas Propagat., vol. 43,
no. 5, pp. 488499, May 1995.
[9] Raven, P.H., R.F. Evert, and S.E. Eichhorn, Biology of Plants, Worth Publishers, INC.,
New York, NY, 1986.
[10] Chiu, T. and K. Sarabandi, "Electromagnetic scattering interaction between a dielectric
cylinder and a slightly rough surface," submitted to IEEE Trans. Antennas Propagat..
[11] Ishimaru A. Wave Propagation and Scattering in Random media, vol. 2, New York: Academic, 1978.
[12] Schiffer, R. and K.O. Thielheim, "Light Scattering by Dielectric Needles and Disks," J.
Appl. Phys., 50(4), April 1979.
[13] Sarabandi, K. and T.B.A. Senior, "Lowfrequency Scattering from Cylindrical Structures
at Oblique Incidence," IEEE Trans. Geosci. Remote Sensing, vol. 28, no. 5, pp. 879885,
1990.
[14] Tsang, L., J. Kong, and R.T. Shin, Theory of Microwave Remote Sensing, John Wiley and
Sons, New York, 1985.
[15] Seker S.S. and A. Schneider, "Electromagnetic Scattering from a dielectric cylinder of finite
length," IEEE Trans. Antennas Propagat., vol. 36, no. 2, pp. 303307, Feb. 1988.
14
[16] Polatin P.F., K. Sarabandi, and F.T. Ulaby, "MonteCarlo simulation of electromagnetic
scattering from a heterogeneous twocomponent medium," IEEE Trans. Antennas Propagat., vol. 43, no. 10, pp. 10481057, Oct. 1995.
[17] Sarabandi K. and T. Chiu, "Electromagnetic scattering from slightly rough surface with
inhomogeneous dielectric profiles," IEEE Trans. Antennas Propagat., vol. 45, no. 9, pp.
14191430, Sep. 1997.
[18] Ulaby F.T., R.K. More, and A.K. Fung, Microwave Remote Sensing: Active and Passive,
vol. 2, Artech House, Norwood, MA., 1982.
[19] Chiu T. and K. Sarabandi, "Electromagnetic scattering interaction between a dielectric
cylinder and a slightly rough surface," submitted to IEEE Trans. Antennas Propagat..
[20] Stiles J., A coherent polarimetric microwave scattering models for grassland structures and
canopies, Ph.D. dissertation, the University of Michigan, Ann Arbor, 1996.
[21] Tassoudji M.A., K. Sarabandi, and F.T. Ulaby, "Design consideration and implementation of the LCX polarimetric scatterometer (POLARSCAT)," Rep. 022486T2, Radiation
Laboratory, The University of Michigan, June 1989.
[22] Brunfeldt D.R., "Theory and design of a fieldportable dielectric measurement system,"
IEEE Int. Geosci. Remote Sensing Symp. (IGARSS) Digest, vol. 1, pp. 55956 3, 1987.
[23] Hallikainen M.T., F.T. Ulaby, M.C. Dobson, M.A. ElRayes, and L. Wu, "Microwave
dielectric behavior of wet soil  Part I: Empirical models and experimental observations,"
IEEE Trans. Geosci. Remote Sensing, vol. GE23, pp. 2534, 1985.
[24] Sarabandi K. and F.T. Ulaby, "Technique for measuring the dielectric constant of thin
materials," IEEE Trans. Instrum. Meas, vol. 37, no. 4, pp. 631636, Dec. 1988.
[25] Sarabandi K., "A technique for dielectric measurement of cylindrical objects in a rectangular waveguide," IEEE Trans. Instrum. Meas, vol. 43, no. 6, pp. 793798, Dec. 1994.
[26] Ulaby F.T. and M.A. ElRayes, "Microwave dielectric spectrum of vegetation, part II:
Dualdispersion model," IEEE Trans. Geosci. Remote Sensing, vol. GE25, pp. 550557,
1987.
[27] http://www.jpl.nasa.gov/mip/airsar.html
15
Aug. 14 Aug. 18
soil (m,) 0.06 0.17
rms height(s) 0.0115m
correlation length(l) 0.0879m
vegetation (mg) 0.769 0.767
number density of plant 34 ~ 13 plants/m2
biomass 1.97 kg/m2
Table 1: Measured ground truth for the POLARSCAT data set.
3m, Ps (degree) radius (cm) length or thickness (cm)
stem 5, 5 0.3 ~ 0.09 73.0 t 3.4
node 5, 5 0.3 i 0.09 5.4 1.4
branch 45.8, 25.6 0.12 i 0.031 20.7 ~ 6.5
pod 135.5, 30.8 0.35 ~ 0.03 3.7 ~ 0.48
leaf 45.6, 30.1 3.8 ~ 0.07(0.576) 0.022~0.002
Table 2: Measured vegetation parameters of soybeans for the POLARSCAT data set.
soil (my) 0.05
rms height(s) 0.0038 m
correlation length(l) 0.038 m
number density of plant 19 plants/m2
biomass 0.22 kg/m2
Table 3: Estimated ground truth for the AIRSAR data set.
f3m, 3P (degree) radius (cm) length or thickness (cm)
stem 7.5, 5 0.18 ~ 0.05 30.2 i 3.4
node 7.5, 5 0.18 ~ 0.05 5.0 ~ 1.0
branch 60.8, 25.6 0.12 ~ 0.031 14.7 ~ 4.5
leaf 47.0, 30.0 3.7 ~ 0.08(0.6) 0.02~0.001
Table 4: Estimated vegetation parameters of soybeans for the AIRSAR data set.
16
Figure 1: Definition of the incident and scattering angles.
17
z
7! P
/; of —
@/ // i
x:Cl — E
2ac/ i
_Jc,~ j..^ ' 'l/ ''xr Y
2ac'
z
XA,2 Y
(a)
(b)
Figure 2: Denotation of the dimensional and orientational parameters for (a) a cylinder and
(b) a disk.
(aL)
(1) directbackscatter
(2) 1ground bounce
(3) 2ground bounce
(1)
(2)\ 7i
(b) 3)
(b)
(c)
(d)
Figure 3: Scattering mechanisms. (a) direct backscatter from rough surface, (b) direct backscatter from vegetation, single groundbounce, and double groundbounce, (c) secondorder nearfield interaction, and (d) incoherent main stemrough surface interaction.
18
(a) (b)
Figure 4: Vegetation particles embedded in the lossy medium. (a) Stratified structure for the
calculation of the equivalent propagation constant. (b) Free space is assumed in the calculation
of the secondorder nearfield interaction.
L
'," equiphase
rpo, plane
rpa
rL
I:
I equiphase
plane
Al
(a) (b)
Figure 5: Propagation paths in the vegetation layer. (a) direct and (b) ground bounce.
19
40.
0
ct
4 —
rA
0
u
a1
o,..
30.
b ~....... .....
..!
f  — t 
c3
0
o
CD
*!
40.
30.
20....................
  — i —..
20.
10.
10.
0.
0. '
4.
5.
6.
4.
5.
6.
Frequency (GHz)
Frequency (GHz)
(a)
(b)
Figure 6 Measured dielectric constants for (a) branches and
Cband using the procedure outlined in [24, 25].
main stems, and (b) leaves at
Figure 7: Picture of the soybean plant distribution for POLARSCAT data set. It was taken
from the top of the field when plants were dry. Unlike the row structure which is often seen in
many cultivated field, the distribution pattern is rather random.
20
Figure 8: AIRSAR image of the Kellogg Biological Station in July of 1995. This image combined
the Lband and Cband backscatter data at 45 degree of incidence angle. Two soybean field is
on the left side of the image with dark color.
(a)
(b)
Figure 9: Computergenerated soybean plants for (a) POLARSCAT data set and (b) AIRSAR
data set.
21
.
10. p
"0
U
0
lr:,
U
C)
u.,..
u
=1
20. F
1 I I I I I
V
* ~
vv, simulation
  hh, simulation
 xx, simluation
v vv, measurement
< hh, measurement
* vh, measurement
* hv, measurement
m
"0
0
Izd
10.
20.
30.
40.
50.
60.
70.
80.
90.
30. 
40. F
50. L
10.. ~~........
20. 30. 40. 50.
60. 70.
100. ' I ' ' ' '
10. 20. 30. 40. 50. 60. 70.
80.
80.
Incidence Angle (degree)
Incidence Angle (degree)
(a)
(b).0
10.
20.
30.
40.
50.
60.
70.  
80.
10.
e —, —, dr — c —t —
\
 total
 direct
 1ground
 2ground
< 2ndorder
 rough surface
x
o
10
Iz..
20.
30.
40.
50.
60.
70.
80.
90.
 A.
'  <y —
o total ^.
',,
   direct
  1ground Y,
    2ground
 >  2ndorder
—. rough surface
 *  stemrough surface
I mI I I m
I An I
20.. I.. *.....
30. 40. 50. 60. 70.
IU. '.
10. 20.
80.
30. 40. 50.
'.......
60. 70.
80.
Incidence Angle (degree)
Incidence Angle (degree)
(c)
(d)
Figure 10: Scattering coefficients versus incidence angle at Lband for August 14 POLARSCAT
data set: (a) model validation, and (b)(c)(d) scattering mechanism analysis for vv, hh, and
crosspolarizations, respectively.
22
0.
I I I I I I I

o
c
c()
u
4 
10.
20. F
 I " —.
vv, simulation
  hh, simulation
xx, simluation
v vv, measurement
O hh, measurement
* vh, measurement
* hv, measurement
0
0
10.
30.
50.
70.
90.
110.
' I I I ' I:": — a': ' —~:~  :~ 
 SA,
n'A
u,
' \
C)
V V <
' —v. '
— O — total
— o — direct ',
   1ground \
    2ground
— < — 2ndorder
 rough surface v
30. F
40. F
50.
10
I.......I I I I.
I
130.
10
I I.I.I I. I,
20. 30. 40. 50. 60. 70.
Incidence Angle (degree)
80.
I.
20. 30. 40. 50. 60. 70.
Incidence Angle (degree)
80.
(a)
(b)............
10.
30.
0
C)
to
50......
"a0.
 — O total
    direct
  1ground
     2ground
* < — 2ndorder
— * rough surface
10.
111
0
0
30.
50.
I I I i ' "!
~40,. ,....
4C) V'v,
   total
   direct
  1ground
     2ground
  . 2ndorder,. I...,. I.
70.
90.
70.
90.
110. 2.
10. 20.
I.. i. I I I.
110. L
1C
30. 40. 50. 60. 70.
80.
).
Incidence Angle (degree)
(c)
20. 30. 40. 50. 60. 70.
Incidence Angle (degree)
(d)
80.
Figure 11: Scattering coefficients versus incidence angle at Cband for August 14 POLARSCAT
data set: (a) model validation, and (b)(c)(d) scattering mechanism analysis for vv, hh, and
crosspolarizations, respectively.
23
..... I  ~
2.
1.
I 1 I I I I I
m  =O.1
 m =0.2
 m =0.3
 m =0.4
0 mv=O.17(Aug. 18)
\\* m (Aug. 14)
I\ '~ m —0.06 (Aug. 14)
4.
1.
2.
5.
8.
Io
U..
4.
7.
o
1ZI
mv=O.1
m — =0.2
 m=0.3
 m m=0.4
^ 0 m =0.17(Aug. 18)
* m=0.06 (Aug. 14),,\ ' \,\  \ 
\^>
10. 
13.
16.
11.
14.
0
19. 
10..
20. 30. 40. 50. 60. 70.
Incidence Angle (degree)
80.
17. L
10.
20. 30. 40. 50. 60............!
70. 80.
Incidence Angle (degree)
(a)
(b)........ I
11.
14. F
17. F
m — 0.1
 m=0.2
 =0.3
 m =0.4
O mv=O0.17 (Aug. 18)
  * mv=0.06 (Aug. 14),  \
*
;?,..,., *.,.,
20. 
23. F
26. L
10.
20. 30. 40. 50. 60. 70.
80.
Incidence Angle (degree)
(c)
Figure 12: Analysis of sensitivity to the variation of the soil moisture for the POLARSCAT
data set at Lband.(a) vvpolarization, (b) hhpolarization, and (c) crosspolarization.
24
~ ~ ~ ~
20.
u.,..
u
to
Cld
ccn
r  
~~. " ~  ~ _
30. F
I I

I I
I..
40. F
"3
U
20.30.
40.
50.
60.
70.
80.
90.
100.
I If,
.,  —.g  
    direct '
\
  ground
 2ndorder
 totalugh surface
—... direct
 1ground
   2ground
 <  ~2ndorder
— e — rough surface
50. 
V
I
vv, simulation
hh, simulation
xx, simulation
vv, AIRSAR
hh, AIRSAR
xx, AIRSAR
~ I. I
60. L
10


20. 30. 40. 50. 60.
Incidence Angle (degree)
(a)
70.
11U.
1(
0. 20. 30. 40. 50. 60. 70
Incidence Angle (degree)
(b), *. *.., r. *
0
c..0
20.
30.
40.
50.
60.
70.
80.
90.
100.
110.
1(
I....., ... 

 '
v v
< —  ,.       Q o
  total
— 3i  direct
— A  1ground
  '  2ground
 > ~ 2ndorder
*  — rough surface
~ I...., i _. i
"0
x
x
JV.
40.
50.
60.
70.
80.
90.
100.
110.
120. 
10.
_2n
  '

r  total
— 0 .
  V  
  
  
I I I
direct
1ground
2ground
2ndorder
rough surface
stemrough surface
i i 
0. 20..............!
30. 40. 50. 60.
70.
20. 30. 40. 50. 60. 70.
Incidence Angle (degree)
Incidence Angle (degree)
(c)
(d)
Figure 13: Scattering coefficients versus incidence angle at Lband for AIRSAR data set:
(a) model validation, and (b)(c)(d) scattering mechanism analysis for vv, hh, and crosspolarizations, respectively.
25
I I I I I
10.
"0
CC
V
4:
a
q)
0
U
O
'C
to
20.
30. 
, __*
vv, simulation
—.  hh, simulation
 xx, simulation
v vv, AIRSAR
0 hh, AIRSAR
* xx, AIRSAR
_ i I I _ i _ I
0
0
10.
20.
30.
40.
50.
60.
70.
80.
{
— a
* — A
  I
 0
* —~
^v E l, \,
s \
 total ',
—. direct
 ground
 2ground
 2ndorder 
 rough surface. I. I.!. I
40. r
50.
 1
10.
I
0. 20. 30. 40. 50. 60. 70
Incidence Angle (degree)
(a). j... . I
90.
Kt
D..
20. 30. 40. 50. 60.
Incidence Angle (degree)
(b)
70.
20.
30.
0
I:
40. I
. 
*s
M S < ov —^~ — '~ —. o _ <,_ 0.~
— o  total
— a  direct
— A  1ground
  v   2ground
  <. 2ndorder
 * — rough surface
40.
30.
x
U
20.
I 1 " 1 I
""A A'
  O — 8   7  ~
V— A  1ground
   2ground
 >  2ndorder
~ I. I. I, I.
50.
50.
60.
60.
70.
70.
on L
Su. 
10....... I...
20. 30. 40. 50. 60.
Incidence Angle (degree)
80. L
lC
70..
20. 30. 40. 50. 60.
Incidence Angle (degree).
70.
(c)
(d)
Figure 14: Scattering coefficients versus incidence angle at Cband for AIRSAR data set:
(a) model validation, and (b)(c)(d) scattering mechanism analysis for vv, hh, and crosspolarizations, respectively.
26
.......
0.
10.
r.
(U
0
0
bju
I C:
(1)
0
U
4i
4i
ct
u
20. F
[...'' ' '[ ] I] tQ..
E ' vv, coherent
— ea  hh, coherent
  xx, coherent
  e   vv, incoherent
 <  hh, incoherent
  xx, incoherent
~ I,!, I, I,
* —l
C)
i:.k
V)
0
biU
'C
10.
A.
 vv, coherent
— e . hh, coherent
  xx, coherent
    vv, incoherent
   hh, incoherent
 xx, incoherent
~ I. I I I I A,
30. 
20.
40.
50. 
10.
30.
20. 30. 40. 50. 60. 70.
Incidence Angle (degree)
80.
10. 20. 30. 40. 50. 60. 70.
80.
Incidence Angle (degree)
(a)
(b)
Figure 15: Demonstration of the coherence effect caused by the soybean plant structure for a
fully grown soybean field at (a) Lband and (b) Cband.
25.

u
4 —
o
e0
~.
r.')
0
u
cn
30.
35.
40.
45.
D   [.
 ~^  — E ^ 4E —
'  '  ' ' a  
A.. "
 vv, coherent
 — 43  hh, coherent
— I  xx, coherent
     vv, incoherent
 c  hh, incoherent
 xx, incoherent
*4>
0
o
bct
't::
0
'C
u
to
0
10.
20.
25.
30.
35.
15.
 vv, coherent
 — 4  hh, coherent
 xx, coherent
     vv, incoherent
 <0  hh, incoherent
— 0  xx, incoherent
50.
1I.......!
40.
I I I,..
20. 30. 40. 50. 60. 70.
10. 20. 30. 40. 50. 60.
70.
Incidence Angle (degree)
Incidence Angle (degree)
(a)
(b)
Figure 16: Demonstration of the coherence effect caused by the soybean plant structure for a
young soybean field at (a) Lband and (b) Cband.
27
Appendix VI
Retrieval of Forest Parameters Using a FractalBased
Coherent Scattering Model and a Genetic Algorithm
24
Submitted to IEEE Trans. Geosci. Remote Sensing (October 7, 1997)
Retrieval Of Forest Parameters Using A
FractalBased Coherent Scattering Model And A
Genetic Algorithm
YiCheng Lin and Kamal Sarabandi
Radiation Laboratory
Department of Electrical Engineering and Computer Science
The University of Michigan
Ann Arbor, MI 481092122
ABSTRACT
In this paper a procedure for retrieval of forest parameters is developed using the recently
developed fractalbased coherent scattering model (FCSM) and a stochastic optimization
algorithm. Since the fractal scattering model is computationally extensive, first a simplified
empirical model with high fidelity for a desired forest stand is constructed using FCSM.
Inputs to the empirical model are the influential structural and electrical parameters of the
forest stand such as the tree density, tree height, trunk diameter, branching angle, wood
moisture, and soil moisture. Other finer structural features are embedded in the fractal
model. The model outputs are the polarimetric and interferometric response of the forest
as a function of the incidence angle. In this study a genetic algorithm is employed as a global
search routine to characterize the input parameters of a forest stand from a set of measured
polarimetric/interferometric backscatter responses of the stand. The success of the inversion
algorithm is demonstrated using a set of measured singlepolarized interferometric SAR data
and several FCSM simulation results.
1
1 Introduction
Retrieval of gross biophysical parameters of forest stands, such as basal area, tree
height, and leaf area index (LAI), is of great importance in many environmental
research programs. Radar remote sensing at lower microwave frequencies has been
proposed as a sensitive instrument for such applications [1,2]. In support of programs
pertaining to radar remote sensing of vegetation, many advanced polarimetric (SIRC, AIRSAR) [3] and interferometric (TOPSAR) [4] radar instruments have been
developed.
The study of the inversion problems in geophysical science and engineering has
been of great importance from the onset of the remote sensing science [5, 6]. For
example, in microwave remote sensing of vegetation the inverse problem is defined
as the application of the measured quantities such as the polarimetric backscattering
coefficients (from a SAR) [7] and/or the scattering phase center heights (from an
interferometric SAR) [8,9] in an algorithm in order to retrieve forest parameters such
as tree type, tree density and height, and moisture content of vegetation and soil.
Over the past two decades significant effort has been devoted towards the development of scattering models for vegetation canopies [1015] as well as inversion
models to retrieve forest parameters from the measured data [1618]. So far the emphasis of the scattering model development has been on the construction of simplified
models with as few input parameters as possible so that the inversion problem becomes tractable. In this process the importance of structural features of the canopy
(particle arrangement), coherence effects, and multiple scattering were ignored. Even
with these simplifications, the inversion process is rather complex. In [16,18] neural
network approaches are suggested for the inversion process where extensive computer
simulations or experimental results are used to train a neural network in a reverse
order (the model outputs are fed as the input to the program). This method is computationally extensive and its success depends on the fidelity and the extent of the
training data. In [17] a gradientbased search routine is applied to a nested linearized
model. This model is computationally efficient; however, its applicability is limited
to models with small dimensionality and its success depends on the fidelity of the
forward model.
This paper describes the application of a high fidelity scattering model in an
inversion process based on a stochastic global search method. Basically, a recentlydeveloped coherent scattering model that preserves the structural features of tree
canopies using fractal models is employed to generate simplified empirical models
(for different tree species) that can predict the polarimetric and interferometric radar
response of a forest stand efficiently and accurately. The premise for the successful
2
development of such empirical models stems from the fact that the model outputs
are averaged quantities, such as backscattering coefficients or the mean height of the
scattering phase center, and therefore are very gentle functions of model inputs.
As demonstrated in [15], the fractalbased coherent scattering model (FCSM) offers two advantages over the traditional scattering models, namely, FCSM is more versatile and accurate. Basically, FCSM is a firstorder scattering model and is capable
of simulating the fully polarimetric (including the phase statistics) and polarimetricinterferometric (scattering phase centers and correlation coefficients for any polarization configuration [19]) radar responses of coniferous and deciduous forest stands.
High accuracy is achieved by FCSM through incorporating the coherent effects among
the individual scatterers and scattering components and by accounting for the accurate position of scatterers which is manifested in inhomogeneous scattering and
extinction profiles. However, this versatility and accuracy has been achieved at the
expense of the model complexity which demands extensive computational power. For
example, the number of input parameters needed to accurately characterize the tree
structures and the environment may easily exceed 30 (it should be noted that once
a tree type is chosen much fewer free parameters are needed to model the natural
variabilities). On the other hand, to obtain a solution with a reasonable accuracy in
the Monte Carlo simulation, a sufficiently large number (> 100) of realizations are
required. The required computational time for each simulation limits the model's
utility in inverse processes which may demand the calculation of the forward problem
many times.
To circumvent the aforementioned problem, development of empirical models
based on FCSM is proposed. Construction of an empirical model can be achieved
using a standard procedure such as curvefitting and regression method. Unlike physical models, empirical models are simple mathematical expressions formed from a set
of data acquired from measurements or a physical model prediction. Once empirical formulae are obtained, they are easy to use and require minimal computation
time. However, it should be noted that an empirical model is usually valid only for
a specific case within a certain range of the parameter space over which the model is
c onstructed.
For the development of the empirical model used in this study, first a sensitivity
analysis is conducted in order to determine the significant parameters, the number
of which determines the dimensionality of the input vector space. A red pine stand
is chosen in this paper and six parameters are selected as the input parameters.
Each selected parameter is allowed to have about 30% variation with respect to a
centroid. Using the Monte Carlo simulation results obtained from FCSM a database
is constructed by varying the individual parameters over a prescribed range of the
3
input vector space around the centroid. The parameters at the centroid are obtained
from the ground truth data of a red pine test stand (Stand 22) in Raco, Michigan.
For the inversion process, first a leastsquare estimator is used and is shown to
work properly when the number of measured channels is equal to or larger than the
dimension of the input vector space. But since this may not be the case in general
situations, a genetic algorithm (GA) [20] is developed and employed as a search
routine for the nonlinear optimization problem. GAs are known to be very successful
when the dimension of the input vector space is large and/or when the objective
function is nonlinear.
2 Empirical Model Development
In general, the output of the Monte Carlo coherent scattering model can be expressed
as
M = (f,p, 0; da, Ht, Dt, b, msmw), (1)
where L is a complex operator relating the input and output of the model and the
output M is a vector which may contain the backscattering coefficient (Os, aoh, ohh),
scattering matrix phase difference statistics, the scattering phase center height Ze, or
the interferogram correlation coefficient. The input parameters are divided into two
categories: 1) radar system parameters, and 2) target parameters. Radar parameters
include the radar frequency f, the polarization configuration p, and the incidence
angle 0. The number of target parameters can be very large, consisting of the tree
structural parameters and the dielectric properties of the constituent components.
However, the number of these parameters is reduced drastically once a tree type is
chosen. In this case only a few structural parameters are sufficient to allow for natural
variabilities observed for that type of tree. The rest of the structural parameters are
embedded in the fractal code of the tree. In this paper we demonstrate development
of an empirical model for a red pine tree where only six free parameters are sufficient
to describe the stand. These include the trunk diameter d,, tree height Ht, tree
density Dt, branching angle 6b, soil moisture m, and wood moisture mw. It should
be noted that these parameters themselves are statistical in the coherent model with
prescribed distribution functions and here we are referring to their mean value.
Multifrequency polarimetric SAR systems operate at discrete frequencies, usually
at P, L, C, and Xband, and the polarization configuration p are vv, vh, and hh.
In this study, we demonstrate a model with three fundamental backscattering coefficients and the associated mean scattering phase center height as the model output
and fix the frequency at Cband (5.3 GHz). The empirical model is developed to
4
operate over the angular range 25~ 70~. Therefore the output and input vectors M
and x are defined as:
Ze ~ da
e
Zvht
zhh Dt
e = and x =.
070M
^vh
010M
L hh m
As mentioned earlier since no resonance behavior is expected, the output vector M
is a gentle function of the input vector x and the incidence angle 0 which may be
related to each other via a simple empirical relationship
M = (0;x), (2)
where ~ is the simple empirical operator and M is the output of the empirical model.
It is expected that M be as close to M as possible.
In general, the output parameters are nonlinear functions of the incidence angle
and other input parameters. In order to establish these relationships the coherent
model must be run by varying the incidence angles and other input parameters.
Through an extensive sensitivity study it was found that over a finite domain of the
input vector space a logarithmic relationship between the backscattering coefficient
(linear in dB scale) and a linear relation between the scattering phase center height
and the input parameters exist. The dependence on the incidence angle was found to
be nonlinear.
The first step in the construction of the empirical model is to choose the domain
of the input vector space. In this investigation we chose the structural parameters
of a young red pine stand, a test forest stand in Raco Michigan (Stand 22), and the
seasonal average of soil and vegetation moisture as the centroid of the input domain.
These parameters and their range of variation used in the model development are
shown in Table 1. The range of parameter space is chosen so that the measured
parameters of a red pine test stand (see Table 2) is at the centroid of the parameter
space. The Monte Carlo simulation was then carried out for specific incidence angles
by varying the six free parameters within the prescribed ranges. The average scattering phase center heights (Ze) for each polarization configuration and backscattering
coefficients (C~ in dB) are shown in Figures 1 and 2 as a function of each parameter
respectively. These figures clearly demonstrate the linear relationship previously described. Hence the output vector can be readily approximated by the Taylor series
expansion of the exact model to the first order, and is given by
C(x)= (xo) + A.(xxo) (3)
5
where xo denotes the input vector at the centroid and A is the matrix of partial
derivatives whose ijth element is given by
aij =  lx=xo (4)
aij simply represents the derivative of the ith output channel 12 with respect to the
jth input parameter xj, evaluated at the centroid xo.
In this matrix, each element was evaluated by calculating the slope of a fitting
line over 5 sample points based on a least square method. In Figures 1 and 2 the
symbols (*) are the simulation results and the lines are the best linear estimation. It
should be pointed out that each point in each figure represents an ensemble average
of 200 realizations of the Monte Carlo simulation. This indicates that the initial task
of generating a matrix of coefficients is very tedious and timeconsuming. However,
once the empirical model is obtained, it can provide a highly accurate solution to an
arbitrary input in almost realtime. This property of the empirical model is especially
important in the inversion processes.
Results in Figures 1 and 2 are for a fixed incidence angle 0 = 25~. However, the
simulations at other incidence angles show that the general form of (3) is valid for all
incidence angles with the exception that C(xo) and A are functions of the incidence
angle, i.e.,
L(0; x) = Lo~(0) + A(0). (x  xo). (5)
It is found that L0(0) and A(0) are nonlinear, but gentle, functions of the incidence
angle 0 over the range of interest (25~ to 70~). In order to obtain the functional
form of 12 and A on 0, the aforementioned Monte Carlo simulation was repeated
at several different incidence angles, and the corresponding values 1~ and A were
evaluated. Polynomial functions are used to capture the angular variations of L~ and
A. It was found that C~ and A can be accurately expressed by
1~(0) = 4o +,10 + C202 + C303, (6)
and
A(O) = Ao + A10 + A202 + A303 + A404, (7)
where Li and Ai are 6 x 1 and 6 x 6 matrices whose values are reported in the
Appendix. Figure 3 compares the results of the empirical model given by (5) with
those of the Monte Carlo simulation at the centroid (x = xo). It should be noted
that the choice of the output parameters are arbitrary and depends on the available
set of input data. For example, an empirical model for a twofrequency system with
three backscattering coefficients could be developed using the same procedure.
6
Equation (5) represents the overall empirical model whose accuracy can be evaluated through a comparison with the Monte Carlo simulations. For this comparison
a large number Monte Carlo simulations with independent input vectors were carried
out. Figures 4, 5, and 6 show the comparison between the results of the empirical
model and those of the Monte Carlo coherent model using 200 independent input data
sets randomly selected within the aforementioned domain of the empirical model. The
figures show excellent agreement between the empirical model and the Monte Carlo
coherent model, noting that the convergence criteria for the Monte Carlo model is
~0.5 dB. Having confidence on a fast and accurate empirical model, the inversion
processes can be attempted which is the subject of the next section.
3 Inversion Algorithms
Consider a physical system whose inputoutput relation is expressed by M L Z(x)
where in general M and x are multidimensional vectors of arbitrary length. The
inverse problem is mathematically defined as x = C1 (M) subject to certain physical
constraints. Although the inverse problem may be welldefined mathematically, in
practice the inverse solution may not exist for two reasons: 1) mathematical construction of the model may not be exact, and 2) the measured vector M may not be
exact because of measurement errors. Hence, instead of casting the problem in terms
of an inverse problem, the problem of finding x is usually cast in terms of a constraint
minimization problem.
Suppose there exists a set of measurements M, the problem is defined as characterization of x so that the objective function (or error function), defined by
E(x) = 112(x)M 112. (8)
is minimized over a predefined domain for x. Here, H denotes the norm of the
argument. As mentioned earlier there are a number of inversion processes available
in the literature; however, in this paper by constructing a simple empirical model a
traditional leastsquare minimization approach and a stochastic global minimization
method are examined.
3.1 LeastSquare Approach
As it was shown in Section 2, the scattering problem can be cast in terms of a linear
system of equations of the form C(u) = Au where A is an m x n matrix and u is an
ndimensional vector in D, D c R'. For a given mdimensional vector G, (8) can be
7
expanded as
m n
= (E ai g)2. (9)
i=1 j=l
A solution that minimizes S must satisfy
=0, j= 1,2,...,n (10)
and is referred to as the leastsquare solution. It is shown that the solution of (10)
(Um) can be obtained from the solution of the following matrix equation [21]:
(A*A) ~ um = A* ~ G. (11)
Here, A* is the transpose of A. It is also demonstrated that the solution U =
(A*A)1A*G exists if rank(A) = n. This requirement states that the number of
independent equations should exceed the number of unknowns.
To apply (11) to our empirical model using (3), it is noted that
(x)  ~~ =A  (x  xo), (12)
thus we use the substitution u = x  xo and G = M . Here ~~ and A are
evaluated from (6) and the solution is given by
Xm = xo + (A*A)1A*(M  ~C). (13)
The leastsquare solution may not be suitable for the inverse problem at hand
for two reasons. First, the number of output channels m is usually less than that of
unknown parameters n. In this case, rank(A) < n, and A*A is not invertible. Even
when the number of channels is larger than the unknowns, the solution provided by
(13) may not be accurate. This happens when A*A is illconditioned. Basically, some
elements of (A*A)1 become very large which amplify the errors in M [22].
3.2 Genetic Algorithms
In recent years, applications of genetic algorithms to a variety of optimization problems in electromagnetics have been successfully demonstrated [24, 25]. The fundamental concept of genetic algorithms (GAs) is based on the concept of natural selection in the evolutionary process which is accomplished by genetic recombination
and mutation. The algorithms are based on a number of ad hoc steps including:
1) discretization of the parameter space, 2) development of an arbitrary encoding
algorithm to establish a onetoone relationship between each code and the discrete
8
points of the parameter space, 3) random generation of a trial set known as the initial
population, 4) selection of high performance parameters according to the objective
function known as natural selection, 5) mating and mutation, 6) recursion of steps 4
and 5 until a convergence is reached. Figure 7 shows the flow chart of GAs. Note
that the population size is provided by the user and an initial population of the given
size is generated randomly.
In this study, since we have as many as six input ground truth parameters and
six output channels, it is expected that the objective function is complex and highly
nonlinear containing many local minima. In this case, the traditional gradientbased
optimization methods usually converge to a local minimum and fail to locate the
inverted data. One interesting feature of GAs is that the method would provide a list
of optimal solutions instead of a solution. This is important in a sense that a solution
that best meets the physical constraints (not included in the objective function) may
be selected from the list of optimal solutions.
For this problem, each of the input parameters was discretized and encoded into
a 4bit binary code, creating a discrete input vector space with 224 members. A
population of 240 members was used for each generation and the objective function
was defined by
~(x) = w C[M  A (x  xo)] 2, (14)
where w is a userdefined weighting function assigned to individual output channels.
To examine the performance of this GAbased inversion algorithm, many arbitrary
points within the domain of the input vector space were selected and then the Monte
Carlo simulation was used to evaluate the polarimetric backscattering coefficients and
the scattering phase center heights at 5.3 GHz. The output of FCSM for these simulations were used as a synthetic measured data set M for the inversion algorithm.
Figures 8(a)8(f) show the performance of the inversion algorithm through comparisons of the input parameters x and the inverted parameters x'. Also shown in each
of the figures is the calculated average error r7, defined by
NAx (15)
where N is the number of points (N=10 in this case), and Ax is the range of validity
of the parameter according to the empirical model. It should be noted here that the
quantization error for 4bit quantization (~3%) is also included in the results. To
examine the importance of the quantization error and the stochastic nature of the
solution in the inversion process, the inversion process was applied to another set
of synthetic measurement data generated by the empirical model. Figures 9(a) —9(f)
show the comparison between the actual input x and the inverted solution x'. It is
9
noticed that the error in Figures 9(a)9(f) are slightly smaller than those obtained
from Figures 8(a)8(f). This indicates that the quantization error and the stochastic
nature of the solution are considerable factors on the overall error. Increasing the
quantization level to 5 bits increases the members of the input vector space by factor of
26. This slows down the inversion process since the population in each generation must
also be increased. However, this does not improve the overall accuracy drastically as
the errors inherent in the empirical model and those caused by the stochastic nature
of the GA solution are independent of quantization error.
At last, the developed inversion algorithm is tested using the real measured data
acquired by the JPL TOPSAR over a test stand of red pine forest in Raco, Michigan.
Although only four data points (Cband vvpolarized backscattering coefficients and
scattering phase center heights at incidence angles 0 = 39~ and 53~) are available, the
inversion algorithm can be easily modified via the objective function of the GA. In
this case, the objective function is given by
S(x) = 6(x)+ ~2(x), (16)
where
~1(x) = w [M1  A1 (xx0)] 2, (17)
2(x) = w. [M2 A1.(xxo)] 2. (18)
Here the subscript 1 and 2 denotes, respectively, the case for the incidence angle
0 = 39~ and 53~. Note that the weighting function and the measured vectors in this
case are written as
w = 0 0 1 0 0 1, (19)
M1 =0 [zv(o=390) 0 0, (0=39~) 0 Of (20)
M2 = [Z(0=530) 0 0 a(= 530) 0 0 ]. (21)
The simulation results are compared with ground truth data [2] in Table 2 where a
very good agreement is shown.
4 Conclusions
In this paper, a simplified empirical model was developed using a high fidelity Monte
Carlo coherent scattering model to be incorporated in an efficient inversion algorithm.
The empirical model was specifically developed for a red pine forest stand which provides simple expressions for the polarimetric backscattering coefficients and scattering
10
phase center heights at Cband as a function of the incidence angle. The accuracy of
the empirical model was examined by comparing its output with that of the Monte
Carlo fractalbased coherent scattering model. The empirical model in conjunction
with a stochastic search algorithm (genetic algorithm) were used to construct an inversion algorithm. The accuracy of the inversion algorithm was demonstrated by first
using synthetic measured data generated from the empirical model and the Monte
Carlo FCSM. It was shown that the inversion algorithm can accurately estimate the
input parameters where synthetic data were used. Next we applied the inversion
algorithm to an actual data set, obtained from TOPSAR, composed of vvpolarized
backscattering coefficient and scattering phase center height at Cband and at two
incidence angles. Excellent agreement was obtained between the ground truth data
and the output of the inversion algorithm.
5 Acknowledgment
This investigation was supported by NASA Office of Earth Science Enterprise under
contract NAG5 4939. and the Jet Propulsion Laboratory under contract JPL 958749.
11
Appendix
In this appendix, the values of coefficient matrices LC and Ai used in (6) and (7)
are reported for the red pine stand investigated in this study.
[,o 0 1 C2
3.1051
3.6061
3.6264
12.2843
50.1483
3.5502
0.2642
0.0659
0.3188
0.2713
2.1623
0.3062
0.0020
0.0029
0.0094
0.0079
0.0431
0.0005
0.0000
0.0000
0.0001
0.0000
0.0003
0.0000
7
and
Ao
1.5294
0.6424
7.1314
13.5348
1.0359
4.7396
 0.1943
0.0581
0.7710
1.3292
0.0508
0.6771
0.0086
0.0019
0.0297
0.0469
0.0010
0.0305
0.0002
0.0000
0.0005
0.0007
0.0000
0.0005
0.2244
0.2687
0.1875
1.8434
1.0341
2.3518
0.0320
0.0244
0.0071
0.1763
0.1137
0.1919
0.0013
0.0010
0.0002
0.0057
0.0040
0.0052
0.0000
0.0000
0.0000
0.0001
0.0001
0.0001
49.0879
0.5762
10.3344
45.9425
22.6264
224.1260
4.2781 I
0.0609 I
0.5252
3.9880 
2.1445 I
19.5566
0.1302
0.0025
0.0005 I
0.1266
0.0673
0.6039 I
0.0017 i
0.0000 i
0.0002
0.0017 i
0.0009 i
0.0079
10.8663
0.7727
7.0854
16.2122
5.2748
6.9444
0.9772 
0.0693
0.6810
1.3883
0.2531 
0.7884
0.0316
0.0029 
0.0233 
0.0433 
0.0035
0.0325 
0.0004 
0.0001
0.0003
0.0006
0.0000 
0.0006
5.22i
2.42(
3.654
2.22(
6.66'
4.89!
0.7657
0.1572
0.3879
0.3188
0.5110
0.9928
0.0312
0.0038
0.0161
0.0218
0.0144
0.0354
0.0005
0.0000
0.0003
0.0004
0.0002
0.0005
89 59.6487
09 7.0918
40 2.5728
69 108.8944
77 73.7306
94 114.7993
5.5036
0.5872
0.3659
11.9278
6.0220
10.1014
0.1844
0.0198
0.0121
0.4499
0.1697
0.3303
0.0027
0.0003
0.0001
0.0072
0.0021
0.0047
A3 =
12
0.0097 0.0013 0.0795 0.0222 0.0306 0.1417
0.0014 0.0009 0.0025 0.0033 0.0016 0.0148
0.0278 0.0008 0.0218 0.0176 0.0142 0.0044
0.0390 0.0038 0.0831 0.0302 0.0284 0.4111
0.0003 0.0033 0.0469 0.0002 0.0079 0.0906
0.0339 0.0023 0.3794 0.0357 0.0218 0.2407
13
References
[1] M. C. Dobson, F. T. Ulaby, T. L. Toan, A. Beaudoin, and E. S. Kasischke, "Dependence of radar backscatter on conifer forest biomass," IEEE Trans. Geosci.
Remote Sensing, vol. 30, pp. 402415, 1992.
[2] M. C. Dobson, F. T. Ulaby, L. E. Pierce, T. L. Sharik, K. M. Bergen, J. Kellndorfer, E. L. J. R. Kendra, Y. C. Lin, A. Nashashibi, K. Sarabandi, and P. Siqueira,
"Estimation of forest biophysical characteristics in Northern Michigan with SIRC/XSAR," IEEE Trans. Geosci. Remote Sensing, vol. 33, pp. 877895, 1995.
[3] R. L. Jordan, B. L. Huneycutt, and M. Werner, "The SIRC/XSAR synthetic
aperture radar system," IEEE Trans. Geosci. Remote Sensing, vol. 33, pp. 829 839, 1996.
[4] H. A. Zebker, S. N. Madsen, J. Martin, K. B. Wheeler, T. Miller, Y. Lou, G. Alberti, S. Vetrella, and A. Cucci, "The topsar interferometric radar topographic
mapping instrument," IEEE Trans. Geosci. Remote Sensing, vol. 30, pp. 933 940, 1992.
[5] V. Dimri, Deconvolution and Inverse Theory: application to geophysical problems. Elsevier, 1992.
[6] M. K. Sen, Global Optimization Methods in Geophysical Inversion. Elsevier,
1995.
[7] F. T. Ulaby and C. Elachi, Radar Polarimetry for Geoscience Applications.
Artech House, 1990.
[8] K. Sarabandi, "AkRadar equivalent of interferometric SARs: a theoretical study
for determination of vegetation height," IEEE Trans. Geosci. Remote Sensing,
vol. 35, no. 5, pp. 12671276, 1997.
[9] R. N. Treuhaft, S. N. Madsen, M. Moghaddam, and J. J. van Zyl, "Vegetation
characteristics and underlying topography from interferometric radar," Radio
Science, vol. 31, pp. 14491485, 1996.
[10] K. Sarabandi, Electromagnetic Scattering from Vegetation Canopies. PhD thesis,
University of Michigan, 1989.
[11] F. T. Ulaby, K. Sarabandi, K. MacDonald, M. Whitt, and M. C. Dobson,
"Michigan microwave canopy scattering model," Int. J. Remote Sensing, vol. 11,
pp. 12231253, 1990.
[12] L. Tsang, C. H. Chan, J. A. Kong, and J. Joseph, "Polarimetric signature of
a canopy of dielectric cylinders based on first and second order vector radiative
transfer theory," J. Electromag. Waves and Appli., vol. 6, pp. 1951, 1992.
14
[13] M. A. Karam, A. K. Fung, R. H. Lang, and N. H. Chauhan, "A microwave
scattering model for layered vegetation," IEEE Trans. Geosci. Remote Sensing,
vol. 30, pp. 767784, 1992.
[14] N. S. Chauhan, R. H. Lang, and K. J. Ranson, "Radar modeling of a boreal
forest," IEEE Trans. Geosci. Remote Sensing, vol. 29, pp. 627638, 1991.
[15] Y. C. Lin and K. Sarabandi, "A Monte Carlo coherent scattering model for forest
canopies using fractalgenerated trees," revised for IEEE Trans. Geosci. Remote
Sensing, September 1997.
[16] L. Pierce, K. Sarabandi, and F. Ulaby, "Application of an artificial neural network in canopy scattering inversion," Int. J. Remote Sensing, vol. 15, pp. 3263 3270, 1994.
[17] P. F. Polatin, K. Sarabandi, and F. T. Ulaby, "An iterative inversion algorithm
with application to the polarimetric radar response of vegetation canopies," IEEE
Trans. Geosci. Remote Sensing, vol. 32, pp. 6271, 1994.
[18] F. Amar, M. S. Dawson, and A. K. Fung, "Inversion of the relevant forest and
vegetation parameters using neural networks," in Proc. of Progress in Electromagnetic Research Symposium (PIERS), 1993.
[19] K. Sarabandi and Y. C. Lin, "Simulation of interferometric SAR response for
characterizing the scattering phase center statistics of forest canopies," IEEE
Trans. Geosci. Remote Sensing, submitted March 1997.
[20] D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning. AddisonWesley, 1989.
[21] S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra. Prentice Hall,
Inc., 1979.
122] A. Ishimaru, Wave propagation and scattering in random media, Section 224,
Vol. II. Academic Press, 1978.
[23] J. Bosworth, "Comparison of genetic algorithms with conjugate gradient methods: technical report," Tech. Rep. UMR0554, The University of Michigan, Computer and Communication Sciences Dept., 1972.
[24] K. Sarabandi and E. S. Li, "Characterization of optimum polarization for multiple target discrimination using genetic algorithms," IEEE Trans. Antennas
Propag., accepted for publication, 1997.
[25] R. L. Haupt, "An introduction to genetic algorithms for electromagnetics," IEEE
Ant. and Propagat. Magazine, vol. 37, pp. 715, 1995.
15
Parameter Range Variation
Trunk Diameter 10.9  14.9(cm) 31 %
Tree Height 8.0  9.9(m) 21 %
Tree Density 807  1027 (trees/Hectare) 24 %
Branching Angle 13.8 ~ 15.8 (deg) 14 %
Soil Moisture 0.36  0.56 (g/g) 43 %
Wood Moisture 0.28 ~ 0.48 (g/g) 52 %
Table 1: The ranges of the selected ground truth parameters and the corresponding
percentage variations to the centroid.
Measured Zv(O = 39~) = 3.6m oaV( = 390)= 10.26 dB
Channels M Z (0 = 53~) = 6.1m = 530)= 13.07 dB
Parameters d (cm) Ht(m) Dt(#/Hectare) Ob mw
Ground truthx 12.9 9.00 907 14.8~ 0.46 0.38
Inverted x' 12.4 9.37 945 13.9~ 0.44 0.37
Table 2: The inversion results using the interferometric TOPSAR data as the measured channels M. Here x is the actual ground truth data and x' is the output of the
inversion process.
16
5
4
3
3
(a)
VH
  *    ~* 3
6
5
4
(b)
. 4
j
_   * "
'* "* "^ —.
(c)
4
3
 * *     +
E
N
2 * *VV
E
N 2
1

N)
N
2,,* * *
1
1
* ..* H  H
0 HH
0
1
1
1
I.
11 12 13 14
dbh (cm)
8 8.5 9 9.5
Ht (m)
0.085 0.09 0.095 0.1
Dt (m2)
(d)
(e)
(f)
M
5
I —
a)
N
4
3
Ei
N
1
0
1
p *  *  .* : * * * 4(
14 14.5 15 15.5 0.4 0.45 0.5 0.55
0b (deg) ms (g/g)
0.3 0.35 0.4 0.45
m (g/g)
W
Figure 1: The sensitivity analysis of the Cband polarimetric scattering phase center
height as a function of the physical parameters: (a) trunk diameter, (b) tree height, (c)
tree density, (d) branching angle, (e) soil moisture, and (f) wood moisture, simulated
at incidence angle 0 = 25~.
17
(a)
. _ —*. —  "HH
(b)
5
C ' *
t
(c)
  
o
V
m 
O
I.~0,*,* *  m10 vv 0
 U
m'10
10
15
15
15
20
  VH
11 12 13 14
dbh (cm)
20  "
K
20       ~  9
20
0.085 0.09 0.095 0.1
D (m2)
8 8.5 9 9.5
Ht (m)
(d)
(e)
(f),,.
~ * —     f
  . .*    i
5 ' *.
5
co 
I3
1O
10^
15
     ~14 14.5 15 15.5
0b (deg)
c 1
0 10
L* * * 
15
10
o l0
a
0
15
20
5
*  t IC —
20~
20
 *   *  * 
I — *   *  *   *
I. I
0.4 0.45 0.5 0.5E
ms (g/g)
0.3 0.35 0.4 0.45
m (g/g)
w
Figure 2: The sensitivity analysis of the Cband polarimetric backscattering coefficient
as a function of the physical parameters: (a) trunk diameter, (b) tree height, (c) tree
density, (d) branching angle, (e) soil moisture, and (f) wood moisture, simulated at
incidence angle 0 = 25~.
18
8
I I
7
6
5
E
,4
N
3
~(5
.4
+ t
2
1
I I
30 40 50.
r L
20
30 40 50
0 (degrees)
(a)
60 70
I I
VV
 VH
 HH
IE
5
10
 
'0
vl
1
15p
_3 J 5 I
20 30 40 50
0 (degrees)
(b)
60 70
Figure 3: The angular dependence of the polarimetric backscatter in terms of: (a)
the scattering phase center height Ze and (b) the backscattering coefficient cr. The
simulation results are fitted with polynomials of degree 3.
19
(a)
(b)
4 6 8 20 18 16 14 12 1(
Empirical Model (m) Empirical Model (dB)
Figure 4: A comparison between the empirical model and the Monte Carlo coherent
scattering model for a red pine stand at vv polarization configuration.
(a)
(b)
1 2 3 4 5 6 7
Empirical Model (m)
Empirical Model (dB)
Figure 5: A comparison between the empirical model and the Monte Carlo coherent
scattering model for a red pine stand at vh polarization configuration.
(a)
(b)
c
cm
Io
I
_!
6
 5
4
3
2
1)
5 0
1
2 4 6 15 10 5
Empirical Model (m) Empirical Model (dB)
Figure 6: A comparison between the empirical model and the Monte Carlo coherent
scattering model for a red pine stand at hh polarization configuration.
20
Discretization of
Parameter Space and
Binary Transformation Population Size
IF. LI,
Decoding of Genes Initialization of
— l Decoding of Genes* Population
Random Number
Generator
Evaluation Noo 
t Funtion of Convergence Check  Natural Selection
___ _ ____ —. 1 
Yes
__ Mating
Stop
Decoding of Genes Mutation
Figure 7: A flow chart of a genetic algorithm.
21
14
0
 13
'D
c 12
m:
IU)
U)
12 14
Input da (cm)
16
(a)
(b)
II 1 I.I.....
0.1, 0.095
0 0.09
a)
> 0.085
0.08
r = 6.2%
~ /
00
0.. nlr,,'
0.075 0.08 0.085 0.09 0.995 0.1
Input Dt (m )
(c)
(d)
0.55
Co 0.5
0
) 0.45
c 0.4
0.35
0.35 0.4 0.45 0.5 0.55
Input ms
0.3 0.35 0.4 0.45 0.5
Input mw
(e)
(f)
Figure 8: Comparison of the input parameters (x) and the output of the inversion
algorithm (x') using the ined from the Monte Carlo simulation,
for (a) trunk diameter da, (b) tree height Ht, (c) tree density Dt, (d) branching angle
Ob, (e) soil moisture mn, and (f) vegetation moisture mw. Here 7r is a measure of the
average error in the inversion process defined by equation(15).
22
1 14
o 13
a)
a)
12
_ 12
16
(a) (b)
X n,,,I
15.5
a,
15
0
a,
1 14.5
a)
>
14
11= =6.4% /
o
/0
/0
1'J _q i & i
13.5 14 14.5 15 15.5
Input 0b (deg)
16
(c)
(d)
0.55
Et 0.5
a, 0.45
0.4
' 0.4
0.35
0.35 0.4 0.45 0.5 0.55
Input ms
0.3 0.35 0.4 0.45 0.5
Input mw
(e)
(f)
Figure 9: Comparison of the input parameters (x) and the output of the inversion
algorithm (x') using the synthetic data obtained from the empirical model, for (a)
trunk diameter da, (b) tree height Ht, (c) tree density Dt, (d) branching angle Ob, (e)
soil moisture m, and (f) vegetation moisture m,. Here 77 is a measure of the average
error in the inversion process defined by equation (15).
23
Appendix VII
An Evaluation of JPL TOPSAR for Extracting Tree Heights
25
An Evaluation of the JPL TOPSAR for Extracting
Tree Heights
Yutaka Kobayashi, Kamal Sarabandi, Leland Pierce, and M. Craig Dobson
Radiation Laboratory
Department of Electrical Engineering and Computer Science
The University of Michigan
Ann Arbor, MI 481092122
Phone: (734) 9361575 FAX: (734) 6472106
Email: saraband@eecs.umich.edu
ABSTRACT
In this paper the accuracy of the Digital Elevation Model (DEM) generated by the JPL
TOPSAR for extracting canopy height is evaluated. For this purpose an experiment using
Cband TOPSAR at the Michigan Forest Test Site (MFTS) in Michigan's Upper peninsula
was conducted. Nearly 25 forest stands were chosen in MFTS which included a variety of
tree types, tree heights and densities. For these stands, extensive ground data were also
collected. The most important and difficulttocharacterize ground truth parameter was the
forest ground level data which is required for extracting the height of the scattering phase
center from the interferometric SAR(INSAR) IDEM. To accomplish this, differential GPS
(Global Positioning System) measurements were done to accurately (~ 5 cm) characterize
the elevation of (1) a grid of points over the forest floor of each stand, and (2) numerous
ground control points ((CPs) over unvegetated areas.
Significant discrepancies between GPS and TOPSAR DEMs and between the two TOPSAR DEMs of the same area were observed. The discrepancies are attributed to uncompensated aircraft roll and multipath. An algorithm is developed to remove the residual errors in
roll angle using elevation data from (1) 100meter resolution U.S. Geological Survey DEM
and (2) the GPSmeasured GCPs. With this algorithm the uncertainties are reduced to
within 3 m. Still, comparison between the corrected TOPSAR DEMs shows an average periodic height discrepancy along the crosstrack direction of about ~5 m. Simulation results
show that this might have been caused by multipath from an object near one of the INSAR
antennas. Careful examination of the coherence image and the backscatter image also show
such periodic patterns. Recommendations are provided for the extraction of the best estimate of the scattering phase center height and a model is provided to estimate actual tree
height. It is accurate to within 1 meter or 10% for the red pine test stands used here.
1
1 Introduction
One of the most critical biophysical parameters that is needed for accurate Global Climate
Model (GCM) predictions is biomass. Radar has been used extensively in attempts to
estimate this parameter, especially for trees. Previous work of ours has used the strategy
of accurately classifying the trees to several structural categories followed by classspecific
inversion models for various biomassrelated terms [4,5]. One of the most important of
these parameters is the height of the tree canopy. Because a Synthetic Aperture Radar
(SAR) records both amplitude and phase of the target reflections, two such observations
from different locations can be used to infer the elevation of the target. This is called
interferometric SAR, or INSAR.
Besides the backscattering coefficient image, interferometric SARs provide two additional
images that are sensitive to the target parameters. These are the magnitude and phase of the
backscatterer cross correlation between the signals received by the two antennas of INSAR.
The phase of the interferogram is the quantity from which the height of the pixel (with
respect to a reference) is retrieved. The magnitude of the cross correlation, or simply the
correlation coefficient, characterizes the uncertainty with which the height can be measured
[18]. For random media in which the radar signal can penetrate to some extent, such as a
vegetation canopy, the measured height is somewhere within the random volume depending
on the location and relative strengths of the scatterers comprising the medium. The measured
height is the location of the scattering phase center for each pixel which of course is a random
variable. The statistics of this scattering phase center height is a function of size, orientation,
spatial distribution and the vertical extent of the random medium. Therefore the measured
scattering phase center height can be used as an independent and sensitive parameter for
remote sensing of vegetation.
The coherence was used in an attempt to obtain tree height from repeatpass ERS1 data
[1,7]. In those studies a model was used to predict tree height from the time variation of
the coherence. Another study [3] used polarimetric phase differences to obtain images of
the phase difference due to the presence of trees, but made no attempt to model the actual
height, as there was no ground truth.
In an attempt to establish the relationship between the canopy parameters and the INSAR parameters (phase of interferogram and correlation coefficient) simplified theoretical
models based on the distorted Born approximation have been developed [17,18]. These models are first order and are capable of explaining the phenomenology of the problem rather
accurately. However, due to their underlying simplifying assumptions they are not capable
of producing very accurate quantitative results. To rectify this deficiency, a sophisticated
scattering model based on Monte Carlo simulation of fractalgenerated trees was developed
recently [14,15].
For verifying these models and eventually developing an inversion algorithm experimental
data are needed. Since the height of most forest stands range from 10 m to 60 m, accuracy
in height measurement of the order of ~ 0.5 m is needed. Initially we excluded INSAR data
generated by repeatpepass interferometry as the temporal decorrelation and problems with
baseline estimation hamper height evaluation with such required accuracy. Twoantenna
2
systems such as the JPL TOPSAR are potentially capable of height measurements of the
required accuracy.
To examine the feasibility of using INSAR data for estimating tree height, we conducted
a set of experiments with JPL TOPSAR over a wellcharacterized forest test site. The test
stands at the Michigan Test Site (MFTS) are chosen to include different tree species at
different growth stages and densities. The wealth of data collected at this site over the past
several years makes this an ideal area to use: species composition, diameter, height, and
stand densities have been meticulously measured with groundbased tools [2]. Also, much of
our previous classification work was done at this test site [6,8], and so we are very familiar
with the types and distribution of the vegetation.
This paper is organized as follows: section two describes the test site and the groundbased measurements. Section three presents the two height estimation algorithms and Sec —
tion four gives the conclusions.
2 Ground Measurements
2.1 Tree height measurements
The MFTS is located in the eastern part of Michigan's Upper Peninsula. The surveyed
forest stands cover an area of approximately 20 Km x 20 Km centered at Raco. The species
composition, diameters, heights and number densities were measured over a period of several
years ending in 1994 [2]. In some cases heights of trees were measured with calibrated height
poles, in others heights were estimated based on their diameters and species using equations
appropriate to that species under similar growing conditions. Because over 70,000 individual
trees were measured in 70 different stands we feel that the dataset is one of the best available
for testing algorithms for tree height estimation.
To supplement this dataset we wanted closelyspaced and accurate measurements of
ground elevation. The data available from the USGS (U.S. Geological Survey) was neither
accurate enough nor dense enough (100 m spacing), and so we used differential GPS (Global
Positioning System) measurements to obtain our own elevation data.
2.2 GPS Measurements
GPS consists of many satellites in known orbits that are constantly sending signals to receivers on the ground. The ground receiver uses the known orbits and the time it takes
for each message to propagate from the satellite to triangulate its own position in three
dimensions. The accuracy of the measured position increases with more satellites and more
messages.
We used the Trimble Site Surveyor GPS receiver in order to obtain accuracies on the order
of 2 cm. This involves the use of a fixed base station and any number of rovers. The base
station is a GPS receiver set up over a surveyed benchmark with known threedimensional
3
coordinates. It broadcasts its own signal to the rovers to supplement the satellite signals
and a difference vector is calculated that relates the rover to the base station.
The benchmarks we used were surveyed by the U.S. National Geodetic Survey and are
brass plates set in concrete pilings in the ground. The coordinates of these benchmarks can
be obtained from NGS at their web site. Note that the coordinates given are referenced to
various earth models called ellipsoids. There are many of these, and it is best to convert
from those given to one named WGS84, as that is the one the GPS receivers use internally.
A good review of the ellipsoids used throughout the world is given in Schreier [9].
A typical rover measurement involves: (1) setting the antenna on a measured height pole
with a level bubble; (2) finding a clear view of the satellites through the trees (the Lband
signal is significantly attenuated by even a few branches); (3) initializing so the satellites
are tracked and the position fix is within a meter; and lastly (4) taking a data point by
keeping the pole very still and level, waiting for about 10 seconds for the averaging process
to converge to a given error tolerance, usually 2 cm.
There were two kinds of measurements we needed to take with the GPS receivers: (1)
Ground Control Points, (2) Forest Stand Floor. The ground control points were specially
chosen areas on the ground that we could identify in the SAR images. This usually meant
road intersections. These points were needed in order to assure ourselves of the accuracy of
the USGS and TOPSAR DEMs. The forest stand floor was measured in order to be able to
calculate tree heights above the ground using a simple difference with the TOPSAR DEM.
In order to deal with ground height variability in a stand a grid of points was used. This was
the same grid of points used to measure the tree heights originally and consisted of 40 points
per 200 m x 200 m forest stand. The tree stands chosen for this study were monocultures
all planted at the same time, resulting in a very uniform height distribution. It took between
1 and 3 hours to measure a stand, depending on how often we had to reinitialize because
of lost signal from the overlying canopy. In some large, dense stands it was impossible to
use the GPS receivers at all, and we contented ourselves with measurements along the stand
periphery and field notes about the approximate elevation variation within the stand.
Of course, the USGS and GPS data did not agree exactly, however the errors were within
the expected range given the large (lOOm) horizontal spacing of the USGS data.
3 Tree Height Estimation
3.1 INSAR Overview
In singlepass INSAR the platform has two antennas as shown in Figure 1. One antenna
transmits and both receive. The pathlength differences (8) between the two signals results
in a phase difference (0) given by:
27 (1)
O8
where A is the carrier wavelength. Since the geometry of the two antennas is known the
baseline length (B) and the baseline angle (a) can be used to determine the look angle (0):
4
(r+ 8) 2B2
sin(a  0) = B (2)
where r is the range of the target from the transmitting antenna. Using the height of the
radar platforms (H) as an arbitrary reference, the target elevation is given by:
h= Hrcos0. (3)
The height h is really the height of the scattering phase center for a given pixel. In the
case of trees the height is somewhere below the height of the top of the canopy. The pertinent
parameters for the JPL TOPSAR are given in Table 1, while the details concerning the data
are given in Table 2.
The raw data was processed by JPL into three standard products: (1) Cvv power, (2)
DEM, (3) coherence. It is these standard products that are used in this study. Note that the
TOPSAR flights occurred in April of 1995 and that the most recent height measurements
were taken in the fall of 1994. Since the growing season had not yet started in April, we
believe that there was no significant change in the height of the trees during this time.
3.2 Uncompensated Aircraft Roll Correction
Since the TOPSAR platform [10] is an aircraft, significant effort is expended in measuring
and compensating for the deviation of the airplane from smooth level flight. This is called
motion compensation and has been successfully applied in the AirSAR data which uses the
same platform but different antennas. Motion compensation must correct for variations
from steady, level flight, which includes variations in: height, heading, pitch, and roll. As
mentioned in [16] the compensation of the roll angle variability is very important, and for
TOPSAR the accuracy of this correction is approximately 0.01~.
In comparing the TOPSAR DEMs of the same area from two different TOPSAR images
we noticed that there was serious disagreement between them. This prompted us to examine
the data more carefully. Eventually we came up with a way of explaining much of the
discrepancy with an uncompensated roll angle error of less than 0.3~.
First, we attempted to match the USGS DEM to the TOPSAR DEM which has an
expected heighterror of about 2 m [11]. This involved converting the USGS DEM into
height over the NAD27 ellipsoid, and then manually warping it to the TOPSAR image
geometry. Residual errors in aircraft altitude and roll angle are lumped into one parameter,
namely roll angle error, which is a good approximation for very small values of residual
altitude and roll angle errors. The roads and other sparselyvegetated areas were compared
as seen in Figure 2. Apart from a constant difference between the USGS DEM and the
TOPSAR DEM, Fig. 2c shows a significant variation in the height difference (about 50 im)
as a function of alongtrack distance. This variation far exceeds the expected uncertainties
in the TOPSAR and USGS DEMs. We interpreted this as a height error caused by the
residual errors in the roll angle. The error in roll angle is directly proportional to the error
in the look angle, which is used to calculate the height. Equation 3 can be used to obtain
what the height error due to an incorrect look angle would be:
5
dh/dO = rsin = x (4)
where x is ground range. This shows that the height error is x A0, and so will increase
with range and with lookangle error. This is shown in Fig. 2b from a given cut along the
crosstrack direction (about 13 m for 900 pixels). The look angle error can be caused by
an uncompensated roll angle error. Unfortunately a constant roll angle error does not work
well for the entire image as can be seen from Fig. 2c. Hence, we used an azimuthdependent
error model. For each azimuth line, j, we can write:
Ahj = xA0j + hoffset, (5)
where hoffset is some constant height error that can be used to adjust the offset between
the TOPSAR and USGS reference planes. In order to use the USGS DEM to correct the
TOPSAR DEM we used only areas in the TOPSAR DEM that were bare spaces or short
vegetation. Hence we classified the images using the C,, power to three classes: bare, short
vegetation, and trees. Because we only had one channel the approach was based on simple
thresholds with trees being greater than 15 dB, and bare less than 20 dB.
The error model given by (5) is used in a statistical sense over the entire image. This is
done to minimize the error between the USGS and TOPSAR DEMs as the USGS DEM is
coarse and has a height uncertainty of approximately ~ 35 m. Determination of the best
value for hoffset requires the minimization of the following equation:
M N
s = E E (Ahj  xAj hoffset)2 (6)
i=1 j=1
where i and j refer to the range and azimuth (alongtrack) coordinates, respectively, and
Ah = hTOPSAR  hUSGS For estimation of hoffset (a constant over the entire image) we did
not use every azimuth line in the image because the resultant matrix equation was too large;
instead we subsampled in azimuth, using about 100 lines.
The minimization is carried out by finding a stationary point:
= 0 and =0, for all j. (7)
Ohoffset (0j
This results in the following set of equations:
N M \ M N
hoffsetMN + z x AOj = EZ Ahj (8)
j=l i=1 i=1 j=l
M \ M M
hoffset + xiq + j x2 = E i/hij, for all j,
i=l i1 i=l
which can be solved for the A0O's and hoffset. This hoffset is then used for each azimuth line
to get AO0 using a linear leastsquares fit to equation 5. The resulting roll angle error is a
6
continuous function of azimuth, which makes this believable as an error mechanism since the
airplane cannot have a very high frequency roll angle change. Figure 3 shows the calculated
roll angle error for the two TOPSAR scenes. Note that the error is quite small, less than
0.3~ in all cases.
Finally the calculated height error is compensated for in the TOPSAR DEM pixelb)ypixel. To assess how well we did, we used the ground control points (GCPs) that were
collected using GPS. The GCP locations are shown in Figure 4, and the height errors before
and after the roll angle correction are shown in Table 3. This shows that the height error has
been reduced to an average of about 2 meters, although there are still a few points where
the error is much worse.
Note that in calculating the TOPSAR DEMI height for a given point involves averaging
over at least 4 x 4 pixels in the neighborhood of that point. This is because the phase noise
standard deviation is large, and averaging will result in a decreased height error, which in
this case is about 35 meters, comparable to the USGS DEM height errors. This allows
comparisons using these heights to be meaningful.
3.3 Multipath
Despite our efforts in correcting for the roll angle error there still appears to be some residual
errors left. This is most apparent when looking at the Cm, power images, as seen in Figure 5,
where a quasiperiodic sinusoid is apparent with the crests parallel to the azimuth direction.
The spacing of these crests increases from about 60 pixels in the near range to about 130 in
the far range. The same pattern is seen in the DEM data. The magnitude of those errors
is approximately 8 dB and 10 meters peaktopeak, in the power and elevation images,
respectively. This is a significant effect that must be dealt with in order to estimate tree
heights accurately. In all fairness, these errors are not present at all with some of the
TOPSAR data we have. Unfortunately, for this application this is the only data we could
use.
This problem may be due to multipath [12,13] where an object near the antennas is
reflecting the returned pulse into the antennas. The coherent addition of the direct return
and the multipath return could cause such a pattern. Assume that the multipath object
only reflects into the upper of the two antennas. Also assume that the object is near the
upper antenna. These assumptions are made according to the arrangement of the TOPSAR
and other AirSAR antennas. As shown in Figure 6, we can then model the fields at each
antenna as:
rA1 E eik2AlT (9)
A2 = E[eik(A1T+A2T) + dezk(A1T+TC+CA2)]
where k = 27r/A is the wave number, the terms A] T, A2T, TC, and CA2 are the path lengths,
and d is a diffraction coefficient. If we represent the additional path length due to the
multipath object as AL == TC + A2C  A2T we can write the amplitude error as:
7
I A21 2 Es12
21 s = d2 + 2dcos(kAL)  2dcos(kAL). (10)
It can easily be shown that (TC  TA2) increases with increasing range in a nonlinear
fashion which gives rise to a sinusoid whose period increases with range. We can also derive
an expression for the phase difference that this would induce in the interferogram phase.
Representing this error in phase by terror and noting that d <K 1 it can be shown that,error  L[eik(A2TAT) + deik(TC+CAAT)]  Leik(A2TAT) dsin(kAL). (11)
Equations (10) and (11) indicate that the phase and power errors are in phase quadrature.
These equations were used to calculate the expected multipath error which was compared
to the known error. First, the period of the oscillation as a function of range was used to
narrow in on the best position for a single scatterer, then the peaktopeak variation was
used to get the best diffraction coefficient. Unfortunately, the best we could do with a single
scatterer did not match the rangevarying period exactly and so there remained residual
errors. The result was unsatisfactory.
This led us to try another approach. Apparently the TOPSAR processing involves a step
where a measured phase screen is applied to the data in order to remove any multipath that
is repeatable. This phase screen is calculated by JPL at the beginning of each deployment
season, and depends on a very accurate DEM that is compared with the TOPSAR data to
produce the phase error as a function of the look angle. We obtained a copy of this phase
screen and used it as in the multipath equations above in order to correct both the DEM
and power data from TOPSAR. Unfortunately the variations due to this correction still did
not exactly cancel the variations in the data we had, and so this method did not work either.
Consequently, we gave up in our attempt to correct for the multipath error. Unfortunately
this limited the number of forest test stands we could use, since only a few had bare spots
near them that were unaffected by the multipath errors.
3.4 Tree Height Estimation
The corrected DEM is now as consistent with the USGS DEM and the GCP's collected
with GPS as was possible. The determination of the height of the trees is next. While the
Cband, vvpolarized signal scatters significantly from branches and needles or leaves in the
crown, the scattering phase center is rarely at the top of the trees, so we need a model that
relates it to the true height. Such a model has been developed using fractalgenerated trees
by Lin and Sarabandi [14,15].
Using cylinders, disks, and needles a fullwave Monte Carlo simulation was used to estimate powers and scattering phase center heights for several different tree stands, at several
incidence angles. The major lessons are that the height of the scattering phase center varies
with incidence angle and with the extinction distribution in the tree canopy. Typically the
height was higher for large incidence angles and for large total extinctions. However, the
calculated phase center height never achieved the true tree height, and often was significantly
8
less, down to onetenth or less of the true height. This means that some kind of model must
be used in order to obtain tree heights from a TOPSAR DEM, even after we estimate the
phase center height.
An heuristic model for tree height of red pine stands given the phase center height,
incidence angle, and extinction [or correlation] is now developed. Figure 7 shows the results
for the fractal model described above as applied to one stand at the MFTS. Recall that the
tree stands chosen for this study were monocultures all planted at the same time, resulting
in a very uniform height distribution. The sigmoidal shape can be modeled with
1 + (0/0c,)(
where hph is the phase center height, ho is the true height, 0 is the incidence angle, 00 is
a free parameter that corresponds to the incidence angle where the curve has an inflection
point, and the power n is also a free parameter, but could depend on extinction, with higher
n corresponding to higher extinction. The bestfit curve to the C~, data is also shown in
Fig. 7. For that data a simple leastsquares fit gives n = 2.7 and 0o = 45~. As a first
approximation, for all the other data in this study we will assume that only ho changes.
This gives us a family of curves that we can use to easily estimate ho given hph and 0. This
is crude, and probably only works for red pine trees at this test site, but further refinements
must await more simulations with the fractal model.
There are two ways of determining the height of the scattering phase center, hph, for
use in height estimation. First, if the TOPSAR DEM is correct in an absolute sense then a
simple subtraction of the known DEM of the area from the USGS data is sufficient. However,
as seen previously, generating correct TOPSAR. DEM data is laborious. An alternative is
to use the good relative heights. In this scheme there MUST be a bare and flat area near
the tree stand of interest in order to be able to have confidence that the subtraction gives
meaningful results. Since we were able to find appropriate areas in the images, we used
both methods. Table 4 shows the results of the phase center height estimation and the
tree height estimation for several stands. Only two stands were used for several reasons:
(1) limited to monoculture pine stands so could use model, (2) the stand must appear in
both TOPSAR images in order to have data for two different incidence angles, and (3) an
adjacent bare, flat surface at the same range for subtraction within the DEM while avoiding
multipath errors. For each tree stand, we used the GPS data for the subtraction as well
as the TOPSAR DEM. As you can see both methods yield similar results which compare
well with the groundbased measurements of the tree height. The comparison with any
independentlymeasured elevation still suffers due to the residual multipath errors, with an
error as high as 2.65 meters, or 30% for stand 22. The worstcase error when using a nearby
flat area for reference is 1 meter, or 11%. It is hoped that removal of the multipath errors will
allow comparison with groundbased measurements to yield accurate tree height estimations.
9
4 Conclusions
While the data from the TOPSAR has problems with roll angle errors and multipath it
appears that these can either be fixed, or judiciously avoided. A nicer method to deal with
the roll angle error would not require a known DEM.
Tree height determination seems feasible, but we need more sophisticated models in order
for it to work for a greater variety of trees. This work is in progress.
Another method of tree height determination could use more frequencies and polarizations so that a reference height is unneeded.
Acknowledgments
The authors appreciate the help of the JPL Radar Science group in providing the TOPSAR
image data used in this study, and specially Dr. Y. Kim for corresponding with us related
to this study.
References
[1] Askne, Jan I. H., Patrick B. G. Dammert, Lars M. H. Ulander, Gary Smith, " CBand
RepeatPass Interferometric SAR Observations of the Forest," IEEE Trans. Geosci.
Remote Sensing, Vol. 35, No. 1, pp. 2535, Jan. 1997.
[2] Bergen, K.M., Dobson, M.C., Sharik, T.L., Brodie, I., Structure, Composition, and
Aboveground Biomass of SIRC/XSAR and ERS1 Forest Test Stands 19911994,
Raco Michigan Site, University of Michigan, Report 0265117T, Oct. 1995.
[3] Cloude, Shane R., Kostas P. Papathanassiou, "Polarimetric SAR Interferometry," IEEE
Trans. Geosci. Remote Sensing, Vol. 36, No. 5, pp. 15511565, Sept. 1998.
[4] Dobson, M. Craig, Fawwaz T. Ulaby, and Leland Pierce, "LandCover Classification and
Estimation of Terrain Attributes using Synthetic Aperture Radara," Remote Sensing
of Environment, Vol. 51, No. 1, pp. 199214, Jan. 1995.
[5] Dobson, M. Craig, Fawwaz T. Ulaby, Leland Pierce, Terry L. Sharik, Kathleen M.
Bergen, Josef M. Kellndorfer, Jogn R. Kendra, Eric Li, YiCheng Lin, Adib Nashashibi,
Kamal Sarabandi and Paul Siqueira, "Estimation of Forest Biophysical Characteristics
in Northern Michigan with SIRC/XSAR," IEEE Trans. Geosci. Remote Sensing, Vol.
33, No. 4, pp. 877895, July 1995.
[6] Dobson, M. Craig, Leland E. Pierce, Fawwaz T. Ulaby, "KnowledgeBased LandCover
Classification using ERS1/JERS1 SAR Composites," IEEE Transactions on Geosciences and Remote Sensing, Vol. 33, No. 1, pp. 8399, Jan. 1996.
10
[7] Hagberg, Jan O., Lars M. H. Ulander, Jan I. H. Askne, "RepeatPass SAR Interferometry
over Forested Terrain," IEEE Trans. Geosci. Remote Sensing, Vol. 33, No. 2, pp. 331 —
340, March 1995.
[8] Pierce, Leland E., Ulaby, Fawwaz T., Sarabandi, Kamal, Dobson, M. Craig, KnowledgeBased Classification of Polarimetric SAR Images, IEEE Transactions on Geosciences
and Remote Sensing, Vol. 32, No. 5, pp. 10811086, Sept. 1994
[9] Schreier, G. (editor), SAR Geocoding: Data and Systems, Wichmann, Germany, 1993.
[10] Zebker, H.A., Madsen, S.N., Martin, J., Wheeler, K.B., Miller, T., Lou, Y., Alberti, G.,
Vetralls, S., and Cucci, A., The TOPSAR Interferometric Radar Topographic Mapping
Instrument, IEEE Transactions Geosciences and Remote Sensing, Vol. 30, No. 5, pp.
933940, 1992.
[11] Madsen, S.N., Zebker, H.A., and Martin, J., Topographic Mapping Using Radar Interferometry: Processing Techniques, IEEE Trans. Geoscience and Remote Sensing, Vol.
31, No. 1, pp. 246256, 1993.
[12] Madsen, S.N., and Zebker, H.A., Automated Absolute Phase Retrieval in Acrosstrack
Interferometry, IGARSS '92: Proceedings of the 1992 International Geosciences and
Remote Sensing Symposium, Houston, Texas, USA, Vol. 2, pp. 15821584.
[13] Y.J. Kim, Personal communication.
[14] Lin, Y.C., and Sarabandi, K., A., " Monte Carlo Coherent Scattering Model for Forest Canopies Using Fractal Generated Trees, " IEEE Trans. Geoscience and Remote
Sensing, Vol. 37, No. 1, pp. 440451, 1998.
[15] Sarabandi, K., and Lin, Y.C., Simulation of Interferometric SAR Response for Characterizing the Scattering Phase Center Statistics of Forest Canopies, submitted to IEEE
Transactions Geosciences and Remote Sensing, (March 1997).
[16] Kim, Y., et al., NASA/JPL Airborne ThreeFrequency Polarimetric/Interferometric
SAR System, 1996 Intl. Geosci. and Remote Sensing Symp., pp. 16121614, 1996.
[17]Treuhaft, R. N., S. N. Madsen, M. Moghaddam, and J. J. van Zyl, Inteferometric
Remote Sensing of Vegetation and Surface Topography, Radio Science, vol. 31, pp.
14491485.
[18] Sarabandi,K., AkRadar equivalent of Interferometric SARs: A Theoretical Study for
determination of vegetation height, IEEE Trans. Geosci. Remote Sensing, vol. 35, no.
5, Sept. 1997.
11
Table 1: TOPSAR interferometric parameters
Parameter TOPSAR value
Baseline length(B) 2.58meter
Baseline angle(a) 62.77degree
Radar platform height(H) around 7470meter
Wavelength of carrier frequency(A) 5.67cm
Table 2: Description of test site and DEM data from the TOPSAR and USGS.
Michigan Forests Test Located in the eastern part of Michigan's Upper Peninsula. The
Site(MFTS) region is approximately 20 Km square. According to U.S.Geological
Survey, the elevation difference in the whole area of MFTS is less
than 60 m, which means MFTS is relatively flat area.
TOPSAR DEM Both ground range and azimuth pixel spacing are 10 m. The following data are used.
CCTID:TS0149(Acquired 26April1995)
CCTID:TS0171(Acquired 26April1995)
Some regions are covered by both of these two data, but are illuminated at different incidence angles.
USGS DEM Original pixel spacing is 100 m in both NorthSouth direction and
EastWest direction. It is interpolated into 10 m spacing. Elevation
is based on NAD27 ellipsoid.
12
Table 3: Assessment of roll angle error compensation using GCPs. The compensation improves the agreement between the differential GPS measured data and TOPSAR DEM. Both
the mean and standard deviation of height difference are improved.
(a) TOPSAR DEM(CCTID:TS0171, referenced DEM: USGS DEM)
GCP hTOPSAR  hGP hTOPSAR  hGps
No. Before compensation After compensation
1 54.3 2.0
2 43.7 2.2
3 50.1 2.7
4 47.7 1.8
5 43.9 0.3
6 58.7 3.2
7 44.8 1.7
8 68.6 6.3
Mean 51.5 1.5
Standard deviation 8.72 2.82
(b) TOPSAR DEM(CCTID:TS0149, referenced DEM: corrected TS0171 DEM)
GCP hTOPSAR  hGPs hTOPSAR  hGPs
No. Before compensation After compensation
1 46.7 1.4
2 44.5 0.5
3 44.9 1.7
4 48.0 0.6
5 44.0 2.0
6 36.4 1.3
7 41.9 1.8
8 44.0 2.4
Mean 43.8 1.5
Standard deviation 3.5 0.64
13
Table 4: Results of extracted tree height from TOPSAR DEM. Height extracted by method
(2) fits in the trend that the height of scattering phase center will increase as the incidence
angle increases and it always appear below the canopy top, whereas height extracted by
method (1) doesn't always fit this trend.
(a) Extracted by using DGPS data. (Method (1))
Stand phase center height phase center height Modeled Actual tree
No. (CCTID:TS0149) (CCTID:TS0171) Tree ht height
[meters] [meters] [meters] [meters]
22 3.8 7.0 9.0, 11.4 8.7
(incidence angle) (40~) (53~)_
68 8.0 5.5 14.2, 8.0 13.8
(incidence angle) (490) (59~) _____
(b) Extracted by using elevation difference between
the forest stand and the nearby flat area. (Method (2))
Stand phase center height phase center height Modeled Actual tree
No. (CCTID:TS0149) (CCTID:TS0171) Tree ht height
[meters] [meters] [meters] [meters]
22 3.0 6.0 7.0, 9.7 8.7
(incidence angle) (40~) (53~) ___ _
68 7.7 9.0 13.6, 13.1 13.8
(incidence angle) (490) (59~) ___
Remark:
1) Source of actual tree height and species are from [2].
14
Radar platform
A2
B
A1
(Al
H
r+6
r
( Target i
Location of scattering
phase center
h
I
x
(Ground range direction)
Figure 1: Geometry of singlepass interferoretric SAR(INSAR)
15
Range direction
(Crosstrack direction)
TOPSAR image
(CCTID: TS0149)
Flighttrack direction
(Azimuth direction) (a) TOPSAR image
(a) TOPSAR image
a)
I
0)
'0
n
300.00
280.00
260.00
240.00
220.00
200.00
 USGS NAD27 DEM..TOPS.AR DEM....I....I....IJ..I..
a)
a)
E3
20. 120. 220. 320. 420. 520. 620. 720.
Range Pixel No.
(b1) Profile of TOPSAR DEM and
USGS NAD27 DEM
20. 120. 220. 320. 420. 520. 620. 720.
Range Pixel No.
(b2) Difference between TOPSAR
and USGS NAD27 DEMs
(b) Profile by cutting plane No.1
/ USGS NAD27 DEM
310.00
290.00...... I4......
1(
LL~
a)
a1)
E
r
c,)
a)
I
270.001
TOPSAR DEM "'
^WAv^/\^
' 30.00
a)
EE 50.00
0 70.00
250.00
230.00
210.00
90.00 L —
120.
120. 320. 520. 720. 920.
Azimuth Line No.
(c1) Profile of TOPSAR DEM and
USGS NAD27 DEM
320. 520. 720.
Azimuth Line No.
920.
(c2) Difference between TOPSAR
and USGS NAD27 DEMs
(c) Profile by cutting plane No.2
Figure 2: Comparison between TOPSAR DEM and USGS NAD27 DEM
16
0.30
O
r(U
I
I r .
ti
ct
0.20
0.10
3 .... I.... I.... I.... I.... I 1.... I.... I.... I........ I.... I...... I.... I.... I.... I.... I.... I....
A A\n~ I
u.uu 
332........................
403. 474.
545. 616. 687. 758. 829. 900. 971.
1042.
Azimuth line No.
(a) Estimated roll angle error (CCTID: TS0171)
(Reference DEM: USGS DEM)
r "
0 o
t)
ct,,
~
0.00
0.10
0.20
0.30
....i.... *... I........ I.... I... I.......
28. 98. 167. 237. 306. 376. 446.
515. 585. 654.
724.
Azimuth line No.
(b) Estimated roll angle error (CCTID: TS0149)
(Reference DEM: corrected TS0171 DEM)
Figure 3: Estimated roll angle error for two TOPSAR DEMs based on leastsquare minimization between TOPSAR and USGS data.
17
Range direction
 (Crosstrack direction)
ir
Flighttrack direction
(Azimuth direction)
a/: GCP locations
Figure 4: Corrected TOPSAR DEM(TS0171) showing both the location of the GCPs and
the two test forest stands (22 and 68). The DEM image is shown in greyscale such that low
to high elevation is shown varying from black to white.
18
Range direction
 (Crosstrack direction)
Cutting
plane '
Flighttrack + + I
direction Location of quasiperiodic patterns
(Azimuth direction)
(a) Location of quasiperiodic patterns in TOPSAR DEM(CCTID:TS0171)
10.00
20.00
30.00
50.00
0. 100. 200. 300. 400. 500. 600.
Range Pixel No.
(b) Profile of TOPSAR power image
by cutting plane as shown in Figure 5(a)
Figure 5: Location of quasiperiodic patterns in TOPSAR power image
19
A2 (Receive only)
AIC Q —q
 \
Diffraction
object
A1
(Transmit
and Receive)
AIT
TA2
( Target
AT
Location of scattering. —. phase center
Figure 6: Multipath problem
Figure 6: Multipath problem
20
10.............................................. &. o MonteCarlo Simulation
8 Curvefit (eqn. 12)
c ~ TOPSAR estimates
) 6~
*~ 4  j. O..........~......
2
0
10 20 30 40 50 60 70
Incidence Angle Oi (degrees)
Figure 7: The estimated height of the scattering phase center of Stand 22, compared with
the height extracted from two TOPSAR images of the same stand. This figure was adapted
from a similar figure in [12].
21
Appendix VIII
GPS Measurements for SIRC/XSAR and TOPSAR Forest
Test Stands at Raco, Michigan Site
26
RL945
GPS Measurements for SIRC/XSAR
and TOPSAR Forest Test Stands
at Raco, Michigan Site
Yutaka Kobayashi
Kamal Sarabandi
M. Craig Dobson
Leland Pierce
Taeyeoul Yun
July 30, 1997
Table of Contents
1. Purpose.............................................................. 1
2. M ethodology.............................. 1
21. Differential GPS
22. Application to Forest Environments
3. Equipment..................................... 4
4. Results.............................. 4
5. Appendices........................................ 5
A. Daily Log
B. Data of Each Stand
C. Description of Stands
D. Data of Ground Control Point(=GCP) Location
E. NGS Data Sheet
(i)
1. Purpose
This report presents the GPS measurement of ground level at SIRC/XSAR
and TOPSAR forest test stands. In order to extract the trees' height
information from images of SIRC/XSAR and TOPSAR, the ground level
of each stands should be measured in high accuracy. To fulfill this purpose,
differential GPS measurement has been done in May 18  24,1997.
At the same time, in order to create the Interferometric SAR(=IFSAR)
images, the location of Ground Control Points(=GCPs) is needed in high
accuracy for registeration of two images. To fulfill this purpose, differential
GPS measurement has been done.
2. Methodology
21. Differential GPS
24 GPS satellites orbit the earth twice per day. GPS receivers on the ground
calculate their positions by making distance measurement to four or more
satellites.
If two GPS receivers are located within several miles and one of the their
locations is the point whose coordinates are already known in high accuracy,
differential GPS is applied for higher accurate measurement.
Figure 1 shows the concept of differential GPS. The GPS receiver
A(known point) transmits the information of calculated location to GPS
receiver B(unknown point) through radio link. This enables the GPS receiver
B to calculate its own location in high accuracy. To calculate the location in
high accuracy, the following things are required.
(a) The location of known point(GPS receiver A) should be known in
high accuracy in advance.
(b) GPS receiver B analyzes the time it takes for radio signal to travel
from GPS receiver A to GPS receiver B. So the farther the distance
is, the more chances of multipath will occur. To avoid the multipath,
the distance between the two GPS receivers should be within several
miles.
To satisfy the condition (a), NGS data sheets of Benchmark are used in this
measurement.(See Appendix E)
1
0
0
0
p
(,:: Ground Pos'ition ny Sare//i te s)
Ra di, 241/(
I~lknJ/ Ro,07rt
( CPy Re ceiver A )
Figure 1 Differential GPS
(nk410n?07,0rt
(GA' S ARe Ce Ve r 6' _
2
22. Application to Forest Environments
To apply differential GPS to forest environments, 10meter pole is used.
If the GPS antenna is installed at the top of the pole, GPS signal will be
received even in the high forests. Figure 2 shows the installation.
X ofpfh jPae re'
Figure 2
10meter pole and GPS antenna
3
3. Equipment
Table 1 shows the equipment which were used in the measurement and its
accuracy.
Table 1
Equipment used in the measurement
GPS Receiver "Site Surveyor SSi 4000" [Trimble Navigation Co.]
Horizontal +_(lcm +2ppm)
accuracy +_(0.03ft.+2ppm*baseline length)
Vertical +_(2cm +2ppm)
accuracy +_(0.07ft.+2ppm*baseline length)
If the radio link is established, the calculation of location is done in
realtime.This measurement is called "Realtime Kinematic(=RTK) mode".
In case that the radio link is unable to be established, postprocessing is
possible by running the software at the personal computer. This measurement
is called "Postprocess infill(=PP infill) mode".
4. Results
Table 2 shows the results of the measurement. The detail results are shown
in the appendices.
Table 2 The results of the measurement
Number of measured stands 23
Number of points in measured stands 408
Number of locations of Ground Control Points(=GCPs) 29
4
Appendix A: Daily Log
A1
Table A1 shows the daily record. The measurement was done by two
rovers(groups). The detail data record is shown afterwards.
All the data are expressed on WGS coordinate.
Including the cover sheet, appendix A is totally 20 pages.
A2
Table A1
GPS measurement daily record (1 of 2)
Day Rover 1 Rover 2
May 18 [LelandJennis,Taeyeoul,Yutaka]
(Sun) GCP in Rudyard area
10001016(PP infill)
valid points: 5
__invalid points: 2
May 19 [Leland,Yutaka] [Dennis,Taeyeoul]
(Mon) Stand 67 Stand 22
10011040(PP infill) 20022007(RTK)
valid points: 40 valid points: 5
invalid points: 0 invalid points: 1
May 20 [Leland,Dennis] [Taeyeoul,Yutaka]
(Tue) GCP in Raco area GCP in Mc Nearney Lake area
R14,R15,R16,R17,R8 R22
10001005(RTK) 10001005(PP infill)
valid points: 6 valid points: 6
invalid points: 0 invalid points: 0
Stand 59 Stand 58
10061045(RTK) 10091029(RTK)
valid points: 40 valid points: 21
invalid points: 0 invalid points: 0
Stand 56
10471085(RTK)
valid points: 39
invalid points: 0
May 21 [Leland,Dennis,YiCheng] [Kamal,Taeyeoul,Yutaka]
(Wed) GCP in Raco area Stand 61
R9??? 20002012(RTK)
1000(RTK) valid points: 13
valid points: 1 invalid points: 0
invalid points: 0 Stand 68
Stand 54 20142032(RTK)
10011043(RTK) valid points: 19
valid points: 43 invalid points: 0
invalid points: 0
Stand 38
10441085(RTK)
valid points: 42
invalid points: 0
Stand 80
10861101 (RTK)
valid points: 16
invalid points: 0
RTK: Data are acquired by realtime kinematic mode.
PP infill: Data are acquired by postprocess infill mode
A3
Table A1
GPS measurement daily record (2 of 2)
Day Rover 1 Rover 2
May 22 [Dennis,YiCheng] [Kamal,Taeyeoul,Yutaka]
(Thu) GCP in Raco area Stand 71
R8 20012012(RTK)
1000,1001(RTK) valid points: 12
valid points: 2 invalid points: 0
invalid points: 0 Stand 72
Stand 66 20132024(RTK)
10021029(RTK) valid points: 12
valid points: 28 invalid points: 0
invalid points: 0 Stand 40
Stand 55 20252039(RTK)
10301046(RTK) valid points: 15
valid points: 17 invalid points: 0
invalid points: 0 GCP in Raco area
Stand 69 R18,R19,R20
10471053(PP infill) 20402064(PP infill)
valid points: 3 valid points: 25
invalid points: 4 invalid points: 15
May 23 [Dennis,YiCheng] [Kamal,Taeyeoul,Yutaka]
(Fri) Stand 45 Stand 31
10001016(PP infill) 20002003(PP infill)
valid points: 17 valid points: 4
invalid points: 0 invalid points: 0
Stand 34 Stand 49
10171022(PP infill) 20042026(PP infill)
valid points: 4 valid points: 22
invalid points: 2 invalid points: 1
May 24 [Dennis,YiCheng] [Kamal,Taeyeoul,Yutaka]
(Sat) Stand 33 Stand 50
10001006(RTK) 20002007(RTK)
valid points: 7 valid points: 8
invalid points: 0 invalid points: 0
Stand 85 GCP in Mc Nearney Lake area
1007(PP infill) 20082018(PP infill)
valid points: 1 valid points: 10
invalid points: 0 invalid points: 1
GCP in RACO area GCP in RACO area
R18,R19,R20,R31 20192025(RTK)
10081019(PP infill) valid points: 7
valid points: 12 invalid points: 0
invalid points: 0
GCP in Rudyard area
R33,R34
10201027(RTK)
valid points: 6
invalid points: 2
RTK: Data are acquired by realtime kinematic mode.
PP infill: Data are acquired by postprocess infill mode
A4
Jun 2 16:55 1997 rudyard.rep Page 1
GCP measurement
May 18(Sunday) Rudyard area Day #1
The data are WGS coordinate.
Base Station
Pnt # Latitude Longitude Height Code
3001,46.1872884000,84.5622481306,204.000,RJ1102 BM "RJ1102"
/*N RTI= ====== Rover No.l ============================*
No RTK mode measurement was done.
/
PP infill mode
Pnt # Latitude Longitude Height Code
1000,46.1870756889,84.5716812758,203.182,R51
1001,46.1871502019,84.5715828700,202.900,R52
1002,46.1870113742,84.5715860187,203.053,R53
1003,46.1870087821,84.5717947099,202.910,R54
1004,46.1871423580,84.5717901641,202.922,R55
1005,46.2159930864,84.5716630728,207.031,R21
1006,46.2160548285,84.5715898442,206.907,R22
1007,46.2159567158,84.5715958889,206.842,R23
1008,46.2159595341,84.5717193246,206.875,R24
1009,46.2160450130,84.5717210675,206.933,R25
1010,46.2451467360,84.5924850466,211.120,R41
1011,46.2451885535,84.5924081648,210.922,R42
1012,46.2450965072,84.5924086203,210.933,R43
1013,46.2450922316,84.5925334188,211.020,R44
1014,46.2451822000,84.5925362311,211.025,R45
1015,46.2319067712,84.5917093551,65.068,L413.4VBM
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
Not
"R5" No. 1
"R5" No.2
"R5" No.3
"R5" No.4
"R5" No. 5
"R2" No. 1
"R2" No.2
"R2" No.3
"R2" No.4
"R2" No.5
"R4" No. 1
"R4" No.2
"R4" No.3
"R4" No.4
"R4" No.5
Good. Memory
is full.
is full.
1016,46.1725819811,84.5719508663,214.580,L513.0VBM Not Good. Memory
A5
Jun 2 16:47 1997 racola.rep Page 1
GCP measurement
May 19(Mon) Raco area Day #1
Base Station
Pnt # Latitude Longitude Height Code
3002,46.3589376000,84.8456664300,280.746,RJ0241
2000,46.3563470300,84.8038236900,274.367,AIR001
/*..=.===.==.====. Rover No. ===============================*/
RTK mode
Pnt # Latitude Longitude Height Code
1000 46.382342331 84.801919850 276.485 R50 GCP "R50" See notebook.
PP infill mode
Pnt # Latitude Longitude Height Code
1001,46.3901153567,84.8102929206,278.472,R67122 Stand 67
1002,46.3903320207,84.8102212677,279.217,R67132
1003,46.3905563080,84.8101885853,279.238,R67142
1004,46.3907785626,84.8102541785,279.241,R67152
1005,46.3910944753,84.8103553184,279.696,R67162
1006,46.3913078929,84.8104376751,279.095,R67172
1007,46.3915762219,84.8104398255,279.219,R67182
1008,46.3917080041,84.8099755002,280.514,R67282
1009,46.3914887362,84.8099043301,279.745,R67272
1010,46.3912710794,84.8098207622,279.936,R67262
1011,46.3909702621, 84.8097178568,281.017, R67252
1012,46.3905140327,84.8098087827,279.603,R67242
1013,46.3902935312,84.8098721003,279.640,R67232
1014,46.3900423730,84.8098969017,279.033,R67222
1015,46.3898230162,84.8098215379,278.831,R67212
1016,46.3897977728, 84.8093393276,278.973,R67312
1017,46.3900217497,84.8093710389,279.341,R67322
1018,46.3902453046,84.8093827462,279.783,R67332
1019,46.3905503042,84.8093388985,280.496,R67342
1020,46.3907776197,84.8092989739,280.324,R67352
1021,46.3909922274,84.8092192219,279.618,R67362
1022,46.3912179216,84.8091899876,279.160,R67372
1023,46.3914723283,84.8091766301,279.449,R67382
1024,46.3914269833, 84.8086793304,279. 182,R67482
1025,46.3912050421,84.8087161767,278.690,R67472
1026,46.3909750806,84.8087802228,279.071,R67462
1027,46.3906693470,84.8087550522,280.309,R67452
1028,46.3903209758,84.8087292940,280.636, R67442
1029,46.3900917064, 84.8087105046,279.835, R67432
1030, 46.3898614454, 84.8086914054,280.072,R67422
1031,46.3900171706, 84.8082189129,280.365, R67512
1032,46.3901973896, 84.8082417540,280.423, R67522
1033,46.3904010544, 84.8082495966,280.007,R67532
1034,46.3905863191, 84.8082545052,279.435,R67542
1035,46.3908177930, 84.8082667713,278.632, R67552
1036,46.3910184144, 84.8082729834,278.514, R67562
1037,46.3911883484,84.8082880742,279.009,R67572
1038,46.3914748533, 84.8082972707,279.624, R67582
1039,46.3895566138,84.8081602981,278.969,R67ROAD5
1040,46.3895728339, 84.8102629235,277.436,R67ROAD1
RTK mode
A6
Jun 2 16:47 1997 racola.rep Page 2
1041 46.358937606 84.845666811 280.768 MORNINGBM just for checking
/1* ~~===~~~====== Rover No.2 — =================================*/
RTK mode
Pnt # Latitude
2000 46.356347028
2001 46.357666139
2002 46.355478178
2003 46.355351597
2004 46.354171394
2005 46.353626133
2006 46.354466206
2007 46.354800464
2008 46.357666106
Longitude
84.803823692
84.804970567
84.822579681
84.822109336
84.821035328
84.818556731
84.820438744
84.819968989
84.804970583
Height
274.367
274.405
275. 804
276.011
274.415
275.137
275.928
275.841
274.421
Code
AIR001
AIR002
S22B00
S2211
S2251
S2258
S2235
S2218
AIR002
measurement failed(Taeyeoul)
Stand 22
just for checking
No PP infill mode measured by Rover No.2
A7
Jun 2 16:54 1997 raco2a.rep Page 1
GCP measurement
]May 20(Tue) Raco area Day #2
The data are WGS coordinate.
Base Station
Pnt # Latitude Longitude Height Code
3005,46.3563470306,84.8038237000,274.367,AIR001
/*====  —== === Rover No.1
— ======~ —r —~  — *t I
RTK mode
Pnt # Latitude
1000 46.356880953
1001 46.356454694
1002 46.356454703
1003 46.350713006
1004 46.344839564
1005 46.375190372
1006
1007
1008
1009
1010
11011
1012
1013
1014
10(15
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
46.367859906
46.367592900
46.367382475
46.367132597
46.366978833
46.366830272
46.366711428
46.366592236
46.366569769
46.366266639
46.366438761
46.366399100
46.366451444
46.366455650
46.366452578
46.366460256
46.366428572
46.366591547
46.366652681
46.366637300
46.366679486
46.366727250
46.366768269
46.367554586
46.367380450
46.366949694
46.366742656
46.366595133
46.366392569
46.366227781
46.366012044
46.365798122
46.366019486
46.366252017
46.366452269
46.366642639
Longitude
84.804882997
84.824510278
84.824510278
84.819791794
84.814679747
84.801734792
84.805234450
84.805231686
84.805204844
84.805103519
84.804928961
84.804683567
84.804417706
84.804147569
84.803842072
84.804098531
84.804297275
84.804613814
84.804949319
84.805261608
84.805576981
84.805899608
84.806211783
84.806216175
84.806620786
84.806959483
84.807268811
84.807577419
84.807894933
84.807303108
84.806302281
84.806265497
84.806250047
84.806218267
84.806179744
84.806186386
84.806109253
84.806025161
84.804992633
84.805136383
84.805258064
84.805354239
Height
274.760
277.009
277.005
275.375
275.618
276.557
275.974
276.150
275.971
276.226
275.749
275.561
275.486
275.362
275.480
275.320
275.381
275.425
275.555
275.679
276.019
275.934
276.098
276.075
276.082
276.326
276.459
276.299
276.352
273.035
275.736
276.068
275.976
276.117
276.069
276.253
276.195
276.012
275.695
275.791
275.652
275.639
Code
R1 4
R15
R152
R1 6
R17
R8
GCP
GCP
GCP
GCP
GCP
GCP
at
at
at
at
at
at
RAC
RAC
RAC
RAC
RAC
roc
NO
NO
30
'O airport runway
'0 airport runway
id intersection
of 3364&3018
airport
airport
airport
runway
runway
runway
R59TEST
R59112
R59122
R59132
R59142
R59152
R59162
R59172
R59182
R59282
R59272
R59262
R59252
R59242
R59232
R59222
R59212
R59362
R59352
R59342
R59332
R59322
R59312
R59512
R59522
R59532
R59533
R59542
R59552
R59562
R59572
R59582
R59382
R59372
R59362
R59352
Stand 59
A8
Jun 2 16:54 1997
raco2a.rep Page 2
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1081
1082
1083
1084
1085
46.366894772
46.367089233
46.367307589
46.367514544
46.388173150
46.381754772
46.381727869
46.381775167
46.381774139
46.381820583
46.381824156
46.381817558
46.381453267
46.381447494
46.381444344
46.381487336
46.381418861
46.381402597
46.381390578
46.381399756
46.381040956
46.381069522
46.381117000
46.381095117
46.381101233
46.381084858
46.381106006
46.381110975
46.380703642
46.380688039
46.380718872
46.380698569
46.380678775
46.380660481
46.380692603
46.380716006
46.380301953
46.380306083
46.380284794
46.380322958
46.380300125
46.380268908
46.380265614
84.805420578
84.805370764
84.805331878
84.805241700
84.803176031
84.801591100
84.801276542
84.801019625
84.800695314
84.800283914
84.799756797
84.799516517
84.799394472
84.799661258
84.799979831
84.800279100
84.800599967
84.800885431
84.801252661
84.801471064
84.801323078
84.800996819
84.800802831
84.800336811
84.800076058
84.799773853
84.799424650
84.799053322
84.799381139
84.799826900
84.800131686
84.800529686
84.800708064
84.801010111
84.801297406
84.801567478
84.801541378
84.801314550
84.800649306
84.800381447
84.800170539
84.799888894
84.799541300
275.465
275.960
275.841
276.036
278.957
276.520
275.765
275.205
275.319
277.078
277.343
277.346
277.438
277.330
277.041
276.761
276.757
276.709
277.066
277.307
276.899
276.936
276.956
277.131
277.140
277.180
277.357
277.710
277.522
277.263
277.267
277.323
277.558
277.259
277.173
277.321
277.242
277.083
277.248
277.271
277.420
277.099
277.264
R59342
R59332
R59322
R59312
BASE10
R56112
R56122
R56132
R56142
R56152
R56172
R56182
R56128
R56272
R56262
R56252
R56242
R56232
R56222
R56212
R56312
R56322
R56332
R56342
R56352
R56362
R56372
R56382
R56482
R56472
R56462
R56452
R5642
R56422
R56422
R56412
R56512
R56522
R56542
R56552
R56562
R56572
R56582
Base candidate
No PP infill mode measured by Rover No.1
/*================ Rover No.2
RTK mode
Pnt # Latitude Longitude
1007 46.356341622 84.80383464
1009 46.373175500 84.7707935:
1010 46.373175528 84.7707935:
1011 46.373207139 84.7711163:
1012 46.373248633 84.7713998:
1013 46.373656881 84.7709147:
====* /
69
31
28
14
19
31
Height
274.304
275.514
275.495
275.252
275.353
275.952
Code
AIR001 Nearl just for checking
S58INIT POINTA Stand 58
S58INIT POINTB
S5802
S5803
S5821
A9
Jun 2 1 6: 54 1 997 rcoa ep ag 3
raco2a. rep Page 3
1 0 14
1 0 15
10 016
1 01 7
10ID18
1 0 19
1 02 0
1 021
1022
1 023
1 02 4
1025
1 C)26
1 C)27
1 02 8
1 02 9
1 030
1 031
1032
1033
1 034
1 035
1 036
46.373723114
4 6.37 38 1 1353
4 6. 373 955225
46.373891192
4 6.374 02 5064
4 6.37 41254 56
46.374254747
46.374341083
46.374405289
4 6. 374 537 864
46.374728978
4 6. 374 911622
46.375153150
46.375154547
46. 375147022
4 6. 37514 3825
46.375154703
46.375151878
4 6. 375287 639
4 6. 375421111
46.375418719
46.375284444
4 6. 375154 7 83
84.771218011
84.771512831
84.771633875
84.771819656
84.772070636
84.772357878
84.77262 6 692
84.770855900
84.771090567
84.771347869
84.771534067
84.771728556
84.771707106
84.771377011
84.771048308
84.770715694
84.770503836
84.770375394
84.770373375
84.770367964
84.770498033
84.770503714
84.770503872
2 75. 377
27 5. 507
275. 38 9
275. 171
27 4. 92 9
2 74. 152
273. 309
275. 193
275. 187
274. 912
274.194
273. 21 8
272. 882
273. 621
274. 621
274. 917
274. 736
274. 8 02
274. 8 97
275. 173
275. 033
274. 807
274. 74 3
S58 22
S5823
S5824
S58 24
S5825
S5826
S 5827
S5841
S5842
S5843
S5844
S5845
S58R5
S58R4
S 58 R3
S 58 R2
S58CORNER1
S58CORNER2
S58CORNER3
S58CORNER4
S58 CORNERS
S58CORNER6
S58CORNER7
GCP
GCP
GCP
GCP
GCP
GCP
GCP
"R42"
"R42"
I"R42"1
"R4 2"
"R4 2"
"R4 2"
"R4 2"
cornerl
corner2
corner3
corner4
cornerS
corner6
corner7
PP infill mode
Pnt # Latitude Longitude Height Code
1OOO,46.4297625588,84.90613645l7,266.469,BM NEAR ST45  > GCP "IR22"I Corner_1
lOOl,46.4298219199,84.906178018l,266.578,BM NEAR ST45  >BM N 2
lOO2,46.4297385741,84.9059882138,266.574,ROAD CORN ST45 — > GCP "R22"1 Corner_2
1003,46.4295992170,84.9059718765,266.597,ROAD CORN ST45 >GCP "IR22"1 Corner_3
1004,46.4296658391,84.9061221572,266.56lROAD~ CORN ST45> GCP "'R22" Corner_4
1005,f46.4296928091,84.9060537808,266.666fROPJ9 CORN ST45 >GCP "IR22"1 Center
1OO6,46.3576660391,84.8049707158,274.417,AIROO2 just for checking
A10
Jun 2 19:09 1997 raco3a.rep Page 1
GCP measurement
May 21(Wed) Raco area Day #3
The data are WGS coordinate.
Base Station
Pnt # Latitude Longitude
3006 46.356347028 84.803823703
Height Code
274.367 AIR001
/*.==..======.===.I= Rover No.l
~~rri2I1 
RTK mode
Pnt # Latitude
1000 46.365141342
1001 46.385504494
1002 46.385503156
1003 46.385483736
1004 46.385526697
1005 46.385560511
1006 46.385534781
1007 46.385575900
1008 46.385581953
1009 46.385997086
1010 46.386000525
1011 46.385976581
1012 46.385971439
1013 46.385934336
1014 46.385912131
1015 46.385869464
1016 46.385879886
1017 46.385150022
1018 46.385150239
1019 46.385162486
1020 46.385143875
1021 46.385132667
1022 46.385140600
1023 46.385147783
1024 46.385159828
1025 46.386210422
1026 46.386239714
1027 46.386231797
1028 46.386296067
1029 46.386335042
1030 46.386369461
1031 46.386380383
1032 46.386368272
1033 46.386697239
1034 46.386705694
1035 46.386682714
1036 46.386645822
1037 46.386656178
1038 46.386621808
1039 46.386511114
1040 46.386552322
1041 46.386618967
1042 46.384820889
1043 46.384820964
Longitude
84.760581550
84.801439514
84.801135367
84.800846850
84.800592911
84.800309789
84.799935033
84.799604081
84.799320497
84.799440678
84.799716156
84.799984422
84.800298667
84.800598531
84.800856125
84.801166189
84.801516889
84.801507142
84.801249689
84.800947769
84.800654514
84.800303267
84.800032214
84.799744192
84.799412533
84.801457542
84.801160500
84.800875278
84.800557400
84.800209319
84.799964786
84.799609989
84.799263061
84.799445269
84.799765408
84.800045892
84.800314056
84.800673644
84.800960789
84.801369583
84.801523122
84.801911567
84.801858075
84.801858122
Height Code
263.327 R8
278.623 R54512 Stand 54
278.403 R54522
278.283 R54532
278.335 R54542
278.485 R54552
278.596 R54562
277.816 R54572
277.758 R54582
277.891 R54482
278.197 R54472
278.171 R54462
278.591 R54452
278.632 R54442
278.358 R54432
278.731 R54422
278.453 R54412
278.407 R54512
278.519 R54522
278.182 R54532
278.486 R54542
278.728 R54552
278.225 R54562
278.376 R54572
278.603 R54582
278.818 R54212
278.529 R54222
278.539 R54232
278.803 R54242
278.276 R54252
278.784 R54262
278.452 R54272
277.890 R54282
278.516 R54182
278.469 R54172
278.264 R54162
277.676 R54152
277.277 R54142
278.008 R54132
277.762 R54122
277.776 R54112
277.683 R54BLO
278.342 R54BL1
277.836 R54BL1
All
Jun 2 19:09 1997
raco3a.rep Page 2
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
10 65
1066
10 67
1068
1069
1070
1071
10172
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
10C97
1098
46.389788078
46.390036983
46.390183119
46.390329922
46.390522706
46.390733875
46.391069258
46.391287794
46.391128256
46.391361900
46.390920581
46.390713097
46.390516894
46.390290008
46.390077350
46.389861364
46.389812314
46.390006033
46.390254894
46.390464608
46.390685453
46.390851478
46.391086333
46.391277142
46.391362403
46.391135822
46.390932669
46.390706269
46.390521025
46.390293514
46.390076908
46.389862158
46.389802475
46.390001525
46.390213992
46.390409206
46.390643928
46.390850350
46.391071264
46.391262450
46.389658639
46.389653581
46.340864353
46.340898856
46.340901892
46.340962608
46.340600489
46.340570142
46.340560278
46.340523606
46.340255472
46.340279442
46.340322158
46.340348314
46.339919667
84.796109789
84.796109189
84.795913369
84.795816925
84.795733733
84.795668756
84.795546231
84.795465983
84.794847697
84.794786933
84.794960822
84.795088717
84.795221828
84.795272328
84.795438981
84.795520647
84.795140675
84.795022558
84.794928458
84.794827725
84.794720667
84.794634239
84.794524806
84.794463422
84.793874522
84.793959447
84.794045286
84.794187758
84.794271525
84.794358097
84.794472142
84.794580181
84.794059039
84.793913897
84.793801447
84.793743683
84.793591692
84.793438794
84.793350325
84.793248003
84.793659053
84.796257856
84.905768011
84.906358378
84.906962819
84.907612953
84.907754861
84.907307519
84.906891783
84.906372950
84.906200339
84.906699783
84.907171717
84.907703256
84.907718475
278.896 R38112 Stand 38
279.268 R38122
279.074 R38132
278.758 R38142
278.202 R38152
278.271 R38162
277.347 R38172
277.334 R38182
277.404 R38272
277.260 R38282
277.553 R38262
277.870 R38252
277.924 R38242
278.026 R38232
278.482 R38222
277.850 R38212
278.035 R38312
278.066 R38322
277.885 R38332
277.689 R38342
277.516 R38352
277.585 R38362
277.147 R38372
277.210 R38382
277.170 R38482
277.271 R38472
277.370 R38462
277.540 R38452
276.900 R38442
277.087 R38432
277.417 R38422
277.718 R38412
277.326 R38512
277.609 R38522
277.363 R38532
276.543 R38542
277.570 R38552
277.390 R38562
277.333 R38572
277.565 R38582
276.843 R38blO
279.639 R38bll
278.491 R8011 Stand 80
277.688 R8012
277.804 R8013
277.756 R8014
278.331 R8024
278.925 R8023
278.904 R8022
279.138 R8021
279.267 R8031
279.324 R8032
279.122 R8033
278.778 R8034
279.028 R8044
A12
Jun 2 19:09 1997 raco3a.rep Page 3
1099 46.339957861
1100 46.340021633
1101 46.340051022
84.907255611
84.906807128
84.906184628
279.110
279.471
279.336
R8043
R8042
R8041
No PP infill mode measured by Rover No.1
/ * ===.==.===..==== Rover No. 2 =======
/
RTK mode
Pnt # Latitude
2000 46.367813819
2001 46.367538775
2003 46.366957700
2004 46.366959606
2005 46.366164253
2006 46.366169942
2007 46.367847589
2008 46.367845217
2009 46.367859342
2010 46.367850494
2011 46.367411161
2012 46.367157322
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2025
2026
2027
2028
2029
2030
2031
2032
2033
46.367783572
46.367791731
46.367798503
46.367803117
46.367798425
46.368418719
46.368414850
46.369071008
46.369512683
46.369277558
46.369436500
46.369444392
46.369376408
46.368768047
46.368676894
46.368651675
46.368747019
46.368739253
46.356350897
Longitude
84.812976461
84.813256864
84.813403606
84.813406689
84.813711631
84.814388119
84.813896900
84.814411350
84.814802392
84.815340022
84.815059242
84.815114481
84.786611078
84.786089939
84.785581544
84.785068611
84.784539567
84.784632419
84.784629156
84.784691983
84.784717133
84.784869981
84.786126814
84.786620183
84.787182458
84.787050372
84.786991508
84.786410053
84.785859956
84.785120672
84.803821389
Height
276.940
277.033
277.028
277.034
277.565
277.213
277.483
277.629
277.833
278.125
277.611
277.333
273.305
273.340
273.161
273.929
273.677
274.303
273.282
273.143
274.117
272.761
273.654
273.580
274.931
275.052
272.730
273.519
272.979
273.047
274.302
Code
S61R1
S61Tll
S61T13
S61T13
S61T15
S61T15
S61R2
S61R3
S61R4
S61R5
S61T42
S61T52
S68R1
S68R2
S68R3
S68R4
S68R5
S68T51
S68T51
S68T52
S68T53
S68T54
S68T45
S68T35
S68T25
S68T32
S68T31
S68T21
S68T22
S68T23
AIR001
Stand 61
Stand 68
just for checking
No PP infill mode measured by Rover No.2
A13
Jun 2 16:54 1997 raco4a.rep Page 1
GCP measurement
May 22(Thursday) Raco area Day #4
The data are WGS coordinate.
Base Station
Pnt # Latitude Longitude Height Code
3002,46.3881731700, 84.8031762400,278. 946,BASE10A
/* =============== Rover No.l 1=========== — =====================*
RTK mode
Pnt # Latitude
1000 46.388173172
1001 46.388166236
1002 46.382977881
1003 46.382977933
1004 46.383351053
1005 46.383802664
1006 46.384324011
1007 46.384126281
1008 46.383911286
1009 46.383667886
1010 46.383421642
1011 46.383188706
1012 46.382978575
1013 46.382792661
1014 46.382948294
1015 46.383137072
1016 46.383347686
1017 46.383554844
1018 46.383751947
1019 46.383922425
1020 46.384081192
1021 46.384262981
1022 46.384116369
1023 46.383932647
1024 46.383778628
1025 46.383595239
1026 46.383386392
1027 46.383195089
1028 46.383026636
1029 46.382845403
Longitude
84.803176236
84.803181056
84.807120883
84.807120892
84.807208094
84.807285931
84.807254783
84.807694833
84.807682567
84.807757156
84.807834303
84.807929464
84.807938097
84.807895261
84.808358242
84.808178281
84.808017217
84.807833181
84.807661597
84.807499028
84.807387072
84.807244036
84.806909236
84.807043806
84.807175783
84.807294456
84.807483767
84.807615903
84.807744708
84.807836383
84.795589928
84.795176511
84.794775864
84.794534700
84.794845378
84.795316981
84.795645567
84.796099161
84.796416011
84.796112136
84.795581458
84.795213953
84.795537344
Height
278.946
278.938
273.131
273.635
274.095
273.528
273.886
273.190
272.555
272.101
272.387
272.695
273.046
272.503
272.113
272.584
272.193
272.358
272.549
273.542
274.037
273.978
274.901
274.192
273.538
273.327
273.329
273.154
272.986
272.552
281.691
281.377
281.526
280.996
280.100
280.923
281.301
281.420
281.740
281.217
281.090
279.879
280.331
Code
R8
R8CHECK
R6611
R66112
R6612
R6613
R6614
R6624
R6623
R6622.9
R6622.3
R6625
R6626
R6627
R6641
R6642
R6643
R6644
R6645
R6646
R6647
R6648
R6638
R6637
R6636
R6635
R6634
R6633
R6632
R6631
Stand 66
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
104:2
46.398455031
46.398676514
46.398904494
46.399215561
46.399607292
46.399377392
46.399239753
46.399109081
46.399294797
46.399468872
46.399741500
46.399909403
46.400113900
R5511 Stand 55
R5512
R5513
R5514
R5524
R5523
R5522
R5521
R5531
R5532
R5533
R5534
R5544
A14
Jun 2 16:54 1997 raco4a.rep Page 2
1043 46.399919100
1044 46.399730617
1045 46.399546383
1046 46.399702561
84.795876806
84.796282606
84.796595486
84.796989983
281.364 R5543
281.571 R5542
281.639 R5541
281.992 R5551
PP infill mode
Pnt # Latitude Longitude Height Code
1047,46.4048937315,84.7386432491,271.272,R6911 Stand 69
1048,46.4049365707,84.7383223638,271.287,R6912
1049,46.4047676075,84.7379993578,271.927,R6913
1050, 46.4055185944,84.7382674861,178.112,R6914 Not Good. Memory was full
1051,46.4049030472,84.7384378667,227.756,R6915 Not Good. Memory was full
1052,46.4054099000,84.7384945694,341.713,R6917 Not Good. Memory was full
1053,46.4057799194,84.7381197528,249.478,R6918 Not Good. Memory was full
/* ================ Rover No.2
*1~~ —~ ~~~i~~~ ~ 
RTK mode
Pnt # Latitude
2000 46.356348533
2001 46.390223167
2002 46.390194797
2003 46.390215258
2004 46.390183361
2005 46.390283386
2007 46.390746569
2008 46.390911217
2009 46.390762506
2010 46.391341567
2011 46.391439022
2012 46.391597147
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
46.389923261
46.389964342
46.389974114
46.390406753
46.390316242
46.390694903
46.391101447
46.391200369
46.391426872
46.391803644
46.392210481
46.392194483
46.391111836
46.390988736
46.391564658
46.391555519
46.391556806
46.391549497
46.391648186
46.391752728
46.391781081
46.391238889
46.390324272
Longitude
84.803822056
84.765548475
84.765147622
84.764702297
84.763911497
84.763241019
84.763620067
84.765158344
84.766047581
84.766071275
84.765572256
84.763916400
84.762884100
84.762104206
84.761145825
84.761218017
84.762203517
84.762436144
84.762864014
84.761974664
84.760631175
84.760716350
84.760845792
84.761957697
84.755114625
84.754577050
84.754977950
84.754448842
84.753937856
84.753373394
84.752932339
84.752380517
84.751774747
84.751523853
84.751265589
Height
274.356
274.429
272.827
272.162
272.069
273.058
272.409
272.135
275.468
274.738
272.299
272.245
273.479
273.053
272.680
275.077
274.749
274.913
272.734
272.160
273.924
271.040
272.423
272.435
274.096
274.374
272.450
272.871
272.918
272.982
273.744
274.171
274.685
274.721
274.390
Code
AIR001 just for checking
S71Tll Stand 71
S71T21
S71T31
S71T41
S71T51
S71T52
S71T22
S71T12
S71T13
S71T23
S71T53
S72Tll Stand 72
S72T31
S72T51
S72T52
S72T22
S72T23
S72T24
S72T34
S72T44
S72T45
S72T46
S72T26
S40Tll Stand 40
S40T21
S40T23
S40T33
S40T43
S40T53
S40T63
S40T73
S40T83
S40T82
S40T81
A15
Jun 2 16:54 1997 raco4a.rep Page 3
2036 46.390388747 84.751728369 273.930 S40T71
2037 46.390575847 84.752711903 273.748 S40T61
2038 46.390791981 84.753706117 274.284 S40T51
2039 46.390976528 84.754567169 274.471 S40T41
PP infill mode
Pnt # Latitude Longitude Height Code
2040,46.4042942552,84.7392223628,272.399,R21A GCP "R21" No.1
2041,46.4044018162,84.7392304077,272.365,R21B GCP "R21" No.2
2042,46.4043883303,84.7391176508,272.431,R21C GCP "R21" No.3
2043,46.4042878505,84.7391207019,272.440,R21D GCP "R21" No.4
2044,46.4041332027,84.7391172883,272.454,R21E GCP "R21" No.5
2045,46.4040676061,84.7391176308,272.468,R21F GCP "R21" No.6
2046,46.4040730130,84.7392110507,272.476,R21G GCP "R21" No.7
2047,46.4041331362,84.7392097999,272.479,R21H GCP "R21" No.8
2048,46.4040949452,84.7391640552,272.561,R21I GCP "R21" No.9
2049,46.4043478102,84.7391624788,272.504,R21J GCP "R21" No.10
2050,46.3696386596,84.7392186814,202.125,R18A Not Good. Memory was full
2051,46.3692960958,84.7388804146,199.837,R18B Not Good. Memory was full
2052,46.3692526867,84.7388282896,154.804,R18C Not Good. Memory was full
2053,46.3692066236,84.7391163874,174.292,R18D Not Good. Memory was full
2054,46.3753719534,84.7389104231,204.387,R19A Not Good. Memory was full
2055,46.3750873072,84.7388523601,196.343,R19E Not Good. Memory was full
2056,46.3751883760,84.7387607832,197.745,R19B Not Good. Memory was full
2057,46.3751714324,84.7390817597,268.893,R19C Not Good. Memory was full
2058,46.3750818698,84.7387220582,212.382,R19D Not Good. Memory was full
2059,46.3896185989,84.7391013943,263.278,R20E Not Good. Memory was full
2060,46.3898563539,84.7392369441,243.927,R20A Not Good. Memory was full
2061, 46.3898819871,84.7391537674,277.634,R20B Not Good. Memory was full
2062,46.3897391906,84.7391128107,291.512,R20C Not Good. Memory was full
2063,46.3896612350,84.7391497828,276.082,R20D Not Good. Memory was full
2064,46.3897006541,84.7390836882,242.232,R20D Not Good. Memory was full
A16
Jun 2 16:55 1997 raco5a.rep Page 1
GCP measurement
May 23(Friday) Raco area Day #5
The data are WGS coordinate.
Base Station
Pnt # North East Height Code
3001,46.3563470300, 84.8038237000,274.367,AIR001
/* ==inm~=in== Rover No. l ============ ==================*/
No RTK mode measurement was done by Rover No.2
PP infill mode
Pnt # Latitude Longitude Height Code
1000,46.4365839577,84.9187931110,255.337,R4511 Stand 45
1001,46.4366218777,84.9184608646,255.601,R4512
1002,46.4374355212,84.9176143379,255.150,R4513
1003,46.4372892501,84.9174154600,254.983,R4523
1004,46.4372894440,84.9174157271,255.543,R4523
1005,46.4369403120,84.9171518857,255.732,R4533
1006,46.4365483460,84.9170620612,255.869,R4532
1007,46.4365480911,84.9175889154,255.826,R4533
1008,46.4365978184,84.9180329024,255.833,R4534
1009,46.4366627572,84.9183520006,255.699,R4535
1010,46.4362817201,84.9184352662,255.268,R4541
1011,46.4360954328,84.9180471209,255.561,R4542
1012,46.4362133052,84.9175049734,255.493,R4543
1013,46.4362134354,84.9175049825,255.487,R4543
1014,46.4362293337,84.9169745528,255.944,R4544
1015,46.4360253642,84.9170291355,255.799,R4554
1016,46.4358002985,84.9173617144,256.713,R4553
1017,46.4297585419,84.9076556245,276.400,S3411 Stand 34
1018,46.4297583075,84.9076557435,268.706,S3411
1019,46.4283677891,84.9085358781,270.109,S3418
1020,46.4300459221,84.9096448955,269.077,S343
1021,46.4295527084,84.9100049274,197.634,S3454 Not Good. Memory was full
1022,46.4291308060,84.9102622806,242.284,S3454 Not Good. Memory was full
/*===  —— Rover No.2  —— *1
No RTK mode measurement was done by Rover No.2
PP infill mode
Pnt # Latitude Longitude Height Code
2000,46.4339206424,84.9060179304,256.163,S31R1 Stand 31
2001,46.4339082715,84.9050283954,256.342,S31T1
2002,46.4327372279,84.9046723278,256.645,S31T2
2003,46.4324554032,84.9060329670,257.515,S31R5
2004,46.4309067575,84.9012592083,257.559,S49BASE1 Stand 49
2005,46.4303569257,84.9017260754,259.287,S49BASE2
2006,46.4305381461,84.9011065354,259.541,S49T11
2007,46.4303660329,84.9010633171,258.197,S49T12
2008,46.4302623675,84.9005200489,205.246,S49T13
2009,46.4300308731,84.9009847520,259.731,S49T23
A17
Jun 2 16:55 19.97 racc5a.rep Page 2
2010,46.4298352713,84.9011805030,261.339,S49T24
2011,46.4297100957,84.9011904800,262.448,S49T25
2012,46.4296476971,84.9012287543,263.229,S49T35
2'013,46.4295384146,84.9013181699,263.618,S49T45
2014,46.4296505475,84.9014200266,263.711, S49T46
2015,46.4297327994,84.9013710273,262.966,S49T35
2016,46.4297933404,84.9014471757,262.133, S49T36
2017,46.4299891044,84.9016304519,261.663,S49T34
2018,46.4300136680,84.9017078434,261.811,S49T33
2019,46.4300791292,84.9017117465,260.945,S49T32
2020,46.4301459191,84.9017549974,260.450,S49T331
2021,46.4302067742,84.9017837576,260.139,S49T31
2022,46.4300712672,84.9020575414,261.314,S49T3ROAD
2023,46.4297600451,84.9022895670,263.478,S49T41
2024,46.4296037331,84.9022320765,263.931,S49T42
2025,46.4296432952,84.9019489311,263.854,S49T43
2026,46.4295179658,84.9017728642,263.967,S49T44
A18
Jun 2 16:55 1997 raco6a.rep Page 1
GCP measurement
May 24(Saturday) Raco area Day #6
The data are WGS coordinate.
Base Station
Pnt # Latitude Longitude
3001 46.429762561 84.906136458
5001 46.358937600 84.845666433
6001 46.187288400 84.562248133
Height
266.469
280.746
204.000
Code
R22ATCORNER located at Mc Nearney Lake
RJ0241 located at Raco
RJ1102 located at Rudyard
/*= ======= Rover No.l
=~ ~ * / ' 
RTK mode
Pnt # Latitude
1000 46.431094403
1001 46.431391442
1002 46.431715600
1003 46.431896214
1004 46.432338517
1005 46.431849892
1006 46.431998686
Longitude
84.910565575
84.911817011
84.912801706
84.912336172
84.912333939
84.911089378
84.910379150
Height
268.339
269.639
269.574
269.344
269.554
268.382
267.223
Code
R3311
R3331
R3351
R3353
R3358
R3334
R3318
Stand 33
1020
1021
1022
1023
1024
1025
1026
1027
46.230411150
46.230394158
46.230559117
46.230559069
46.230559042
46.230471825
46.230474958
46.230584964
84.571541517
84.571827400
84.571815422
84.571815319
84.571612122
84.550923908
84.550780092
84.550770667
210.555
210.142
210.235
210.620
210.558
209.141
209.158
209.170
IT331 (
IT332 I
IT333 I
IT3332
IT3342
IT341
IT342 (
IT343 (
GCP
Not
Not
GCP
GCP
"R33"
Good.
Good.? "R33'? "R33'
No.1 (Rudyard area)
(by YiCheng)
(by YiCheng)
" No.2 (Rudyard area)
" No.3 (Rudyard area)
GCP "R34"
GCP "R34"
GCP "R34"
No.1
No.2
No. 3
(Rudyard area)
(Rudyard area)
(Rudyard area)
PP infill mode
Pnt # Latitude Longitude Height Code
1007,46.3942790996,84.9706821837,278.604,R851
1008,46.3694893633,84.7388115976,259.044,IT1
1009,46.3694390760,84.7390001988,259.091, IT2
1010,46.3693180115,84.7388104672,258.946,IT3
1011,46.3732296627,84.7390470582,259.416, IT191
1012,46.3733355559,84.7390545540,259.473,IT192
1013,46.3733039973,84.7389944168,259.513,IT193
1014,46.3896860152,84.7390268249,266.384, IT201
1015,46.3896005033,84.7390261682,266.409,IT202
1016,46.3895905163,84.7391350773,266.300,IT203
1017,46.3751789172,84.7809876803,275.045,IT311
1018,46.3751902311,84.7808610433,274.628,IT312
1019,46.3752989637,84.7808818752,274.445,IT313
/1*=.====.========== Rover No.2 ================
RTK mode
Pnt # Latitude Longitude Height Code
2000 46.426453714 84.900390139 268.155 S50T1
2001 46.426775761 84.899897294 266.754 S50T1:
2002 46.427709986 84.898846422 264.892 S50T1
Stand 85
GCP "R18"
GCP "R18"
GCP "R18"
GCP "R19"
GCP "R19"
GCP "R19"
GCP "R20"
GCP "R20"
GCP "R20"
GCP "R31"
GCP "R31"
GCP "R31"
No.1
No.2
No.3
No.1
No.2
No.3
No. 1
No.2
No.3
No.1
No.2
No.3
I
================= 2/
r
2
3
Stand 50
A19
Jun 2 16:55 1997
raco6a. rep Page 2
2003
2004
2005
2006
2007
2019
2020
2021
2022
2023
2024
2025
46.427754147
46.425699444
46.425727914
46.425772539
46.425977581
46.358734100
46.375215489
46.356631278
46.358503917
46.367233003
46.367112186
46.351503847
84.898418281
84.898554119
84.899038236
84.899008414
84.899728903
84.829831186
84.833054431
84.893252253
84.893683442
84.893898458
84.893884428
84.905825956
264.534
268.047
268.416
268.635
267.909
278.615
283.468
282.384
281.662
277.844
276.955
275.119
S50T23
S50R4
S50R4A
S50R4B
S50R3
R10NEAR
R1OE
R30
R6
R78
R78E
R24
GCP "R1ONear"
Center of intersection "RO0"
GCP "R30"
GCP "R6"
GCP "R7" No.1
GCP "R7" No.2
GCP "R24"
PP infill mode
Pnt # Latitude Longitude Height Code
2008,46.4549477881,84.9058569749,205.738, RllF
2009,46.4549553575,84.9059144442,205.665, RlE
2010,46.4555509192, 84.9059012910,204.829, RllNEAR1
2011, 46.4569101202, 84.9058848591,205.425, R1lNEARHILL1
2012,46.4586133798, 84.9058626065,205.821, CRYDERMAN1
2013,46.4649589117, 84.9058862222,185.549, CORNERLAKE
2014,46.4730625042,84.9573431082,213.650,R12A
2015,46.4731295504,84.9569849900,214.061,R12B
2016,46.4729805411, 84.9566907434,214.475,R12C
2017,46.4865157492, 85.0394154128,211.261,R13A
2018,46.4865525296,85.0393407835,206.746,R13B No
GCP "Rll" No.1
GCP "Rll" No.2 (Ce
Near "Rll"
Near "Rll"
GCP "R40"
GCP "R41"
GCP "R12" No.1
GCP "R12" No.2
GCP "R12" No.3
GCP "R13" No.1
t Good. (by Yutaka)
nter)
A20
Appendix B: Data of Each Stand
B1
Table Bl shows the information on measured stands.
Figure B1 shows location of each stand.
The detail data record is shown afterwards.
All the data are expressed on WGS coordinate.
Including the cover sheet, appendix B is totally 28 pages.
B2
Table Bi GPS measurement results at each stand (1 of 2)
Raco Area
Stand Tree Tree Mode Measured Valid Invalid GPS measured Height
No. description Mean Date point point Average Minimun Maximum Std.dev.
Height (m) (m) (m) (m)
1) (m) 1) 
22 Red Pine 8.74 RTK 5/19 5 1 275.466 274.415 276.011 0.683
(sa) 2) (1994) 3) (Mon)
38 Jack 5 RTK 5/21 42 0 277.722 276543 279.639 0.658
Pine(sa) (Wed)_________________________
40 Red Pine 23 RTK 5/22 15 0 273.856 272.450 274.721 0.723
(seedling) (Thu) _____
54 Jack 5 RTK 5/21 43 0 278.292 277.277 278.818 0.364
Pine(sa) ____ (Wed)
55 Jack 5 RTK 5/22 17 0 281.186 279.879 281.992 0589
Pine(sa) ________hu)
56 Jack 2) 11 RTK 5/20 39 0 277.042 275.205 277.710 0540
Pine(ma) (Mon)
58 Jack 3 RTK 5/20 21 0 274.769 272.882 275.952 0.869
Pine(sa) (Mon)
59 Jack 6 RTK 5/20 40 0 275.884 275.320 276.459 0.311
Pine(sa) _____ (Mon) ___________________________
61 Jack 13 RTK 5/21 13 0 277.402 276.940 278.125 0.370
Pine(ma) (Wed)
66 Jack Pine RTK 5/22 28 0 273.146 272.101 274.901 0.724
(seedling) (Thu) ____
67 Jack 15 Infill 5/19 40 0 279.496 277.436 281.017 0.711
Pine(ma) 3) (Mon)
68 Red Pine 11 RTK 5/21 19 0 273.584 272.730 275.052 0.667
(pole) (Wed)__________________________
69 Aspen 6 Infill 5/22 3 4 271.495 271.272 271.927 0.374
(sa) (Thu) __________________
71 Red Pine 11 RTK 5/22 12 0 273.076 272.069 275.468 1.219
(pole) _______ (Thu)
72 Red Pine 14 RTK 5/22 12 0 273.222 271.040 275.077 1.239
(pole) (Thu)
80 Red Pine 23 RTK 5/21 16 0 278.780 277.688 279.471 0.592
(seedling) (Wed) . ....... t —. *r ~.   t:J
Remark 1) Tree description and tree mean height intormation are acquired irom
the following reference.
"Structure, Composition, and Aboveground Biomass of SIRC/X SAR and ERS1 Forest Test Stands 19911994, Raco Michigan
Site"
Kathleen M.Bergen, M.Craig Dobson, Terry L.Sharik, Ian Brodie
October 30,1995, Report 0265117T
Remark 2) The meanings of abbreviation are shown below.
(ma): mature
(sa): sapling
Remark 3) The meanings of abbreviation are shown below.
(RTK): realtime kinematic mode
(Infill): postprocessing infill mode
B3
Table BI
GPS measurement results at each stand (2 of 2)
Mc Nearney Lake area
Stand Tree Tree Mode Measured Valid Invalid GPS measured Height
No. description Mean Date point point Average Minimum Maximum Std.dev
Height (m) (m) (m)
1) (mi) 1)
31 Hardwood 18 Infill 5/23 4 0 256.666 256.163 257.515 0.600
(ma) 2) 3) (Fri)
33 Aspen(sa) 12 3)RT 5/24 7 0 268.865 267.223 269.639 0.914
2) K (Sat)_______.
34 Hardwood 20 Infill 5/23 4 2 271.073 268.706 276.400 3.601
(ma) (Fri)
45 Aspen(sa) 3 Infill 5/23 17 0 255.638 254.983 256.713 0.385
(Fri)
49 Aspen(sa) 6 Infill 5/23 22 1 261.605 257559 263.967 1.937
(Fri)
50 Red Pine 16 RTK 5/24 8 0 267.168 264.534 268.635 1.617
(ma) ______(Sat) ______________
85 Hardwood 15 Infill 5/24 1 0 278. 278. 604 278. 604 0.000
(ma) (Sat)
Remark 1) Tree description and tree mean height information are acquired from
the following reference.
"Structure, Composition, and Aboveground Biomass of SIRC/X SAR and ERS1 Forest Test Stands 19911994, Raco Michigan
Site"
Kathleen M.Bergen, M.Craig Dobson, Terry L.Sharik, Ian Brodie
October 30,1995, Report 0265117T
Remark 2) The meanings of abbreviation are shown below.
(ma): mature
(sa): sapling
Remark 3) The meanings of abbreviation are shown below.
(RTK): realtime kinematic mode
(Infill): postprocessing infill mode
B4
        
~ 2N
j ~, T1K
/: A
'7/1(
Al ~A
J L
toi.'
/1K N
~, 7 <it
J k
'4 f"ft2
C,~
I/
Jun 2 17:10 1997 stand22.dat Page 1
GCP measurement at Stand 22
May 19(Mon) Raco area Day #1
Pnt # Latitude Longitude Height Code
2003 46.355351597 84.822109336 276.011 S2211
2004 46.354171394 84.821035328 274.415 S2251
2005 46.353626133 84.818556731 275.137 S2258
2006 46.354466206 84.820438744 275.928 S2235
2007 46.354800464 84.819968989 275.841 S2218
B6
Jun 2 17:37 1997 stand31.dat Page 1
GCP measurement at Stand 31
May 23(Friday) Raco area Day #5
Pnt # Latitude Longitude Height Code
2000,46.4339206424,84.9060179304,256.163,S31R1
2001,46.4339082715,84.9050283954,256.342,S31T1
2002,46.4327372279,84.9046723278,256.645,S31T2
2003,46.4324554032,84.9060329670,257.515,S31R5
B7
Jun 2 17:40 1997 stand33.dat Page 1
GCP measurement at Stand 33
May 24(Saturday) Raco area Day #6
Pnt # Latitude Longitude
1000 46.431094403 84.910565575
1001 46.431391442 84.911817011
1002 46.431715600 84.912801706
1003 46.431896214 84.912336172
1004 46.432338517 84.912333939
1005 46.431849892 84.911089378
1006 46.431998686 84.910379150
Height
268.339
269.639
269.574
269.344
269.554
268.382
267.223
Code
R3311
R3331
R3351
R3353
R3358
R3334
R3318
B8
Jun 2 17:36 1997 stand34.dat Page 1
GCP measurement at Stand 34
May 23(Friday) Raco area Day #5
Pnt # Latitude Longitude Height Code
1017,46.4297585419,84.9076556245,276.400, 3411
1018,46.4297583075,84.9076557435,268.706,53411
1019,46.4283677891,84.9085358781,270.109, S3418
1020,46.4300459221,84.9096448955,269.077, 343
B9
Jun 2 17:18 1997 stand38.dat Page 1
GCP measurement at Stand 38
May 21 (Wed) Raco area Day #3
Pnt # Latitude Longitude
1044 46.389788078 84.796109789
1045 46.390036983 84.796109189
1046 46.390183119 84.795913369
1047 46.390329922 84.795816925
1048 46.390522706 84.795733733
1049 46.390733875 84.795668756
1050 46.391069258 84.795546231
1051 46.391287794 84.795465983
1052 46.391128256 84.794847697
1053 46.391361900 84.794786933
1054 46.390920581 84.794960822
1055 46.390713097 84.795088717
1056 46.390516894 84.795221828
1057 46.390290008 84.795272328
1058 46.390077350 84.795438981
1059 46.389861364 84.795520647
1060 46.389812314 84.795140675
1061 46.390006033 84.795022558
1062 46.390254894 84.794928458
1063 46.390464608 84.794827725
1064 46.390685453 84.794720667
1065 46.390851478 84.794634239
1066 46.391086333 84.794524806
1067 46.391277142 84.794463422
1068 46.391362403 84.793874522
1069 46.391135822 84.793959447
1070 46.390932669 84.794045286
1071 46.390706269 84.794187758
1072 46.390521025 84.794271525
1073 46.390293514 84.794358097
1074 46.390076908 84.794472142
10,75 46.389862158 84.794580181
1076 46.389802475 84.794059039
1077 46.390001525 84.793913897
1078 46.390213992 84.793801447
1079 46.390409206 84.793743683
1080 46.390643928 84.793591692
1081 46.390850350 84.793438794
1082 46.391071264 84.793350325
1083 46.391262450 84.793248003
1084 46.389658639 84.793659053
1085 46.389653581 84.796257856
Height Code
278.896 R38112
279.268 R38122
279.074 R38132
278.758 R38142
278.202 R38152
278.271 R38162
277.347 R38172
277.334 R38182
277.404 R38272
277.260 R38282
277.553 R38262
277.870 R38252
277.924 R38242
278.026 R38232
278.482 R38222
277.850 R38212
278.035 R38312
278.066 R38322
277.885 R38332
277.689 R38342
277.516 R38352
277.585 R38362
277.147 R38372
277.210 R38382
277.170 R38482
277.271 R38472
277.370 R38462
277.540 R38452
276.900 R38442
277.087 R38432
277.417 R38422
277.718 R38412
277.326 R38512
277.609 R38522
277.363 R38532
276.543 R38542
277.570 R38552
277.390 R38562
277.333 R38572
277.565 R38582
276.843 R38blO
279.639 R38bll
B10
Jun 2 17:33 1997 stand40.dat Page 1
GCP measurement at Stand 40
May 22(Thursday) Raco area Day #4
Pnt # Latitude
2025 46.391111836
2026 46.390988736
2027 46.391564658
2028 46.391555519
2029 46.391556806
2030 46.391549497
2031 46.391648186
2032 46.391752728
2033 46.391781081
2034 46.391238889
2035 46.390324272
2036 46.390388747
2037 46.390575847
2038 46.390791981
2039 46.390976528
Longitude
84.755114625
84.754577050
84.754977950
84.754448842
84.753937856
84.753373394
84.752932339
84.752380517
84.75177474
84.751523853
84.751265589
84.751728369
84.752711903
84.753706117
84.754567169
Height Code
274.096 S40Tll Stand 40
274.374 S40T21
272.450 S40T23
272.871 S40T33
272.918 S40T43
272.982 S40T53
273.744 S40T63
274.171 S40T73
274.685 S40T83
274.721 S40T82
274.390 S40T81
273.930 S40T71
273.748 S40T61
274.284 S40T51
274.471 S40T41
Bll
Jun 2 17:34 1997 stand45.dat Page 1
GCP measurement at Stand 45
May 23(Friday) Raco area Day #5
Pnt # Latitude Longitude Height Code
1000,46.4365839577,84.9187931110,255.337,R4511
1001,46.4366218777,84.9184608646,255.601, R4512
1002,46.4374355212,84.9176143379,255.150,R4513
1003,46.4372892501,84.9174154600,254.983, R4523
1004,46.4372894440,84.9174157271,255.543, R4523
1005,46.4369403120,84.9171518857,255.732,R4533
1006,46.4365483460, 84.9170620612,255.869,R4532
1007,46.4365480911,84.9175889154,255.826,R4533
1008,46.4365978184,84.9180329024,255.833,R4534
1009,46.4366627572,84.9183520006,255.699,R4535
1010,46.4362817201,84.9184352662,255.268,R4541
1011,46.4360954328,84.9180471209,255.561,R4542
1012,46.4362133052,84.9175049734,255.493,R4543
1013,46.4362134354,84.9175049825,255.487,R4543
1014,46.4362293337,84.9169745528,255.944,R4544
1015, 46.4360253642, 84.9170291355,255.799, R4554
1016, 46.4358002985, 84.9173617144,256.713, R4553
B12
Jun 3 10:52 1997 stand49.dat Page 1
GCP measurement at Stand 49
May 23(Friday) Raco area Day #5
Pnt # Latitude Longitude Height Code
2004,46.4309067575,84.9012592083,257.559,S49BASE1
2005,46.4303569257,84.9017260754,259.287,S49BASE2
2006,46.4305381461,84.9011065354,259.541,S49T11
2007,46.4303660329, 84. 9010633171,258.197, S49T12
2009,46.4300308731,84.9009847520,259.731,S49T23
2010,46.4298352713,84.9011805030,261.339,S49T24
2011,46.4297100957,84.9011904800,262.448,S49T25
2012,46.4296476971,84.9012287543,263.229,S49T35
2013,46.4295384146,84.9013181699,263.618,S49T45
2014,46.4296505475,84.9014200266,263.711,S49T46
2015,46.4297327994,84.9013710273,262.966,S49T35
2016,46.4297933404, 84.9014471757,262.133, S49T36
2017,46.4299891044,84.'9016304519,261.663,S49T34
2018,46.4300136680,84.9017078434,261.811,S49T33
2019,46.4300791292, 84.9017117465,260.945, S49T32
2020,46.4301459191,84.9017549974,260.450,S49T331
2021,46.4302067742,84.9017837576,260.139,S49T31
2022,46.4300712672,84.9020575414,261.314,S49T3ROAD
2023,46.4297600451,84.9022895670,263.478,S49T41
2024,46.4296037331,84.9022320765,263.931,S49T42
2025,46.4296432952,84.9019489311,263.854,S49T43
2026,46.4295179658, 84.9017728642,263. 967, S49T44
Remark) Point #2008 is excluded because of incorrect measurement.
B13
Jun 2 17:42 1997 stand50.dat Page 1
GCP measurement at Stand 50
May 24(Saturday) Raco area Day #6
Pnt # Latitude
2000 46.426453714
2001 46.426775761
2002 46.427709986
2003 46.427754147
2004 46.425699444
2005 46.425727914
2006 46.425772539
2007 46.425977581
Longitude
84.900390139
84.899897294
84.898846422
84.898418281
84.898554119
84.899038236
84.899008414
84.899728903
Height
268.155
266.754
264.892
264.534
268.047
268.416
268.635
267.909
Code
S50T1
S50T12
S50T13
S50T23
S50R4
S50R4A
S50R4B
S50R3
Stand 50
B14
Jun 2 19:10 1997 stand54.dat Page 1
GCP measurement at Stand 54
May 21(Wed) Raco area Day #3
Pnt # Latitude
1001 46.385504494
1002 46.385503156
1003 46.385483736
1004 46.385526697
1005 46.385560511
1006 46.385534781
1007 46.385575900
1008 46.385581953
1009 46.385997086
1010 46.386000525
1011 46.385976581
1012 46.385971439
1013 46.385934336
1014 46.385912131
1015 46.385869464
1016 46.385879886
1017 46.385150022
1018 46.385150239
1019 46.385162486
1020 46.385143875
1021 46.385132667
1022 46.385140600
1023 46.385147783
1024 46.385159828
1025 46.386210422
1026 46.386239714
1027 46.386231797
1028 46.386296067
1029 46.386335042
1030 46.386369461
1031 46.386380383
1032 46.386368272
1033 46.386697239
1034 46.386705694
1035 46.386682714
1036 46.386645822
1037 46.386656178
1038 46.386621808
1039 46.386511114
1040 46.386552322
1041 46.386618967
1042 46.384820889
1043 46.384820964
Longitude
84.801439514
84.801135367
84.800846850
84.800592911
84.800309789
84.799935033
84.799604081
84.799320497
84.799440678
84.799716156
84.799984422
84.800298667
84.800598531
84.800856125
84.801166189
84.801516889
84.801507142
84.801249689
84.800947769
84.800654514
84.800303267
84.800032214
84.799744192
84.799412533
84.801457542
84.801160500
84.800875278
84.800557400
84.800209319
84.799964786
84.799609989
84.799263061
84.799445269
84.799765408
84.800045892
84.800314056
84.800673644
84.800960789
84.801369583
84.801523122
84.801911567
84.801858075
84.801858122
Height
278.623
278.403
278.283
278.335
278.485
278.596
277.816
277.758
277.891
278.197
278.171
278.591
278.632
278.358
278.731
278.453
278.407
278.519
278.182
278.486
278.728
278.225
278.376
278.603
278.818
278.529
278.539
278.803
278.276
278.784
278.452
277.890
278.516
278.469
278.264
277.676
277.277
278.008
277.762
277.776
277.683
278.342
277.836
Code
R54512
R54522
R54532
R54542
R54552
R54562
R54572
R54582
R54482
R54472
R54462
R54452
R54442
R54432
R54422
R54412
R54512
R54522
R54532
R54542
R54552
R54562
R54572
R54582
R54212
R54222
R54232
R54242
R54252
R54262
R54272
R54282
R54182
R54172
R54162
R54152
R54142
R54132
R54122
R54112
R54BLO
R54BL1
R54BL1
B15
Jun 2 17:26 1997 stand55.dat Page 1
GCP measurement at Stand 55
May 22(Thursday) Raco area Day #4
Pnt # Latitude
1030 46.398455031
1.031 46.398676514
1032 46.398904494
1033 46.399215561
1034 46.399607292
1035 46.399377392
1036 46.399239753
1037 46.399109081
1038 46.399294797
1039 46.399468872
1040 46.399741500
1041 46.399909403
1042 46.400113900
1043 46.399919100
1044 46.399730617
1045 46.399546383
1046 46.399702561
Longitude
84.795589928
84.795176511
84.794775864
84.794534700
84.794845378
84.795316981
84.795645567
84.796099161
84.796416011
84.796112136
84.795581458
84.795213953
84.795537344
84.795876806
84.796282606
84.796595486
84.796989983
Height Code
281.691 R5511
281.377 R5512
281.526 R5513
280.996 R5514
280.100 R5524
280.923 R5523
281.301 R5522
281.420 R5521
281.740 R5531
281.217 R5532
281.090 R5533
279.879 R5534
280.331 R5544
281.364 R5543
281.571 R5542
281.639 R5541
281.992 R5551
B16
Jun 2 17:12 1997 stand56.dat Page 1
GCP measurement at Stand 56
May 20(Tue) Raco area Day #2
Pnt # Latitude
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1081
1082
1083
1084
1085
46.381754772
46.381727869
46.381775167
46.381774139
46.381820583
46.381824156
46.381817558
46.381453267
46.381447494
46.381444344
46.381487336
46.381418861
46.381402597
46.381390578
46.381399756
46.381040956
46.381069522
46.381117000
46.381095117
46.381101233
46.381084858
46.381106006
46.381110975
46.380703642
46.380688039
46.380718872
46.380698569
46.380678775
46.380660481
46.380692603
46.380716006
46.380301953
46.380306083
46.380284794
46.380322958
46.380300125
46.380268908
46.380265614
Longitude
84.801591100
84.801276542
84.801019625
84.800695314
84.800283914
84.799756797
84.799516517
84.799394472
84.799661258
84.799979831
84.800279100
84.800599967
84.800885431
84.801252661
84.801471064
84.801323078
84.800996819
84.800802831
84.800336811
84.800076058
84.799773853
84.799424650
84.799053322
84.799381139
84.799826900
84.800131686
84.800529686
84.800708064
84.801010111
84.801297406
84.801567478
84.801541378
84.801314550
84.800649306
84.800381447
84.800170539
84.799888894
84.799541300
Height
276.520
275.765
275.205
275.319
277.078
277.343
277.346
277.438
277.330
277.041
276.761
276.757
276.709
277.066
277.307
276.899
276.936
276.956
277.131
277.140
277.180
277.357
277.710
277.522
277.263
277.267
277.323
277.558
277.259
277.173
277.321
277.242
277.083
277.248
277.271
277.420
277.099
277.264
Code
R56112
R56122
R56132
R56142
R56152
R56172
R56182
R56128
R56272
R56262
R56252
R56242
R56232
R56222
R56212
R56312
R56322
R56332
R56342
R56352
R56362
R56372
R56382
R56482
R56472
R56462
R56452
R5642
R56422
R56422
R56412
R56512
R56522
R56542
R56552
R56562
R56572
R56582
B17
Jun 2 17:15 1997 stand58.dat Page 1
GCP measurement at Stand 58
May 20(Tue) Raco area Day #2
Pnt # Latitude
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1 )25
1026
1027
1028
1029
46.373175500
46.373175528
46.373207139
46.373248633
46.373656881
46.373723114
46.373811353
46.373955225
46.373891192
46.374025064
46.374125456
46.374254747
46.374341083
46.374405289
46.374537864
46.374728978
46.374911622
46.375153150
46.375154547
46.375147022
46.375143825
Longitude
84.770793531
84.770793528
84.771116314
84.771399819
84.770914731
84.771218011
84.771512831
84.771633875
84.771819656
84.772070636
84.772357878
84.772626692
84.770855900
84.771090567
84.771347869
84.771534067
84.771728556
84.771707106
84.771377011
84.771048308
84.770715694
Height
275.514
275.495
275.252
275.353
275.952
275.377
275.507
275.389
275.171
274.929
274.152
273.309
275.193
275.187
274.912
274.194
273.218
272.882
273.621
274.621
274.917
Code
S58INIT POINTA
S58INIT POINTB
S5802
S5803
S5821
S5822
S5823
S5824
S5824
S5825
S5826
S5827
S5841
S5842
S5843
S5844
S5845
S58R5
S58R4
S58R3
S58R2
B18
Jun 2 17:10 1997 stand59.dat Page 1
GCP measurement at Stand 59
May 20(Tue) Raco area Day #2
Pnt # Latitude Longitude Height Code
1006 46.367859906 84.805234450 275.974 R59TEST
1007 46.367592900 84.805231686 276.150 R59112
1008 46.367382475 84.805204844 275.971 R59122
1009 46.367132597 84.805103519 276.226 R59132
1010 46.366978833 84.804928961 275.749 R59142
1011 46.366830272 84.804683567 275.561 R59152
1012 46.366711428 84.804417706 275.486 R59162
1013 46.366592236 84.804147569 275.362 R59172
1014 46.366569769 84.803842072 275.480 R59182
1015 46.366266639 84.804098531 275.320 R59282
1016 46.366438761 84.804297275 275.381 R59272
1017 46.366399100 84.804613814 275.425 R59262
1018 46.366451444 84.804949319 275.555 R59252
1019 46.366455650 84.805261608 275.679 R59242
1020 46.366452578 84.805576981 276.019 R59232
1021 46.366460256 84.805899608 275.934 R59222
1022 46.366428572 84.806211783 276.098 R59212
1023 46.366591547 84.806216175 276.075 R59362
1024 46.366652681 84.806620786 276.082 R59352
1025 46.366637300 84.806959483 276.326 R59342
1026 46.366679486 84.807268811 276.459 R59332
1027 46.366727250 84.807577419 276.299 R59322
1028 46.366768269 84.807894933 276.352 R59312
1029 46.367554586 84.807303108 273.035 R59512
1030 46.367380450 84.806302281 275.736 R59522
1031 46.366949694 84.806265497 276.068 R59532
1032 46.366742656 84.806250047 275.976 R59533
1033 46.366595133 84.806218267 276.117 R59542
1034 46.366392569 84.806179744 276.069 R59552
1035 46.366227781 84.806186386 276.253 R59562
1036 46.366012044 84.806109253 276.195 R59572
1037 46.365798122 84.806025161 276.012 R59582
1038 46.366019486 84.804992633 275.695 R59382
1039 46.366252017 84.805136383 275.791 R59372
1040 46.366452269 84.805258064 275.652 R59362
1041 46.366642639 84.805354239 275.639 R59352
1042 46.366894772 84.805420578 275.465 R59342
1043 46.367089233 84.805370764 275.960 R59332
1044 46.367307589 84.805331878 275.841 R59322
1045 46.367514544 84.805241700 276.036 R59312
B19
Jun 2 17:21 1997 stand6l.dat Page 1
GCP measurement at Stand 61
May 21(Wed) Raco area Day #3
Pnt $ Latitude Longitude
2000 46.367813819 84.812976461
2001 46.367538775 84.813256864
2003 46.366957700 84.813403606
2004 46.366959606 84.813406689
2005 46.366164253 84.813711631
2006 46.366169942 84.814388119
2007 46.367847589 84.813896900
2008 46.367845217 84.814411350
2009 46.367859342 84.814802392
21010 46.367850494 84.815340022
2011 46.367411161 84.815059242
2012 46.367157322 84.815114481
Height
276.940
277.033
277.028
277.034
277.565
277.213
277.483
277.629
277.833
278.125
277.611
277.333
Code
S61R1
S61Tll
S61T13
S61T13
S61T15
S61T15
S61R2
S61R3
S61R4
S61R5
S61T42
S61T52
B20
Jun 2 17:24 1997 stand66.dat Page 1
GCP measurement at Stand 66
May 22(Thursday) Raco area Day #4
Pnt # Latitude
1002 46.382977881
1003 46.382977933
1004 46.383351053
1005 46.383802664
1006 46.384324011
1007 46.384126281
1008 46.383911286
1009 46.383667886
1010 46.383421642
1011 46.383188706
1012 46.382978575
1013 46.382792661
1014 46.382948294
1015 46.383137072
1016 46.383347686
1017 46.383554844
1018 46.383751947
1019 46.383922425
1020 46.384081192
1021 46.384262981
1022 46.384116369
1023 46.383932647
1024 46.383778628
1025 46.383595239
1026 46.383386392
1027 46.383195089
1028 46.383026636
1029 46.382845403
Longitude
84.807120883
84.807120892
84.807208094
84.807285931
84.807254783
84.807694833
84.807682567
84.807757156
84.807834303
84.807929464
84.807938097
84.807895261
84.808358242
84.808178281
84.808017217
84.807833181
84.807661597
84.807499028
84.807387072
84.807244036
84.806909236
84.807043806
84.807175783
84.807294456
84.807483767
84.807615903
84.807744708
84.807836383
Height
273.131
273.635
274.095
273.528
273.886
273.190
272.555
272.101
272.387
272.695
273.046
272.503
272.113
272.584
272.193
272.358
272.549
273.542
274.037
273.978
274.901
274.192
273.538
273.327
273.329
273.154
272.986
272.552
Code
R6611
R66112
R6612
R6613
R6614
R6624
R6623
R6622.9
R6622.3
R6625
R6626
R6627
R6641
R6642
R6643
R6644
R6645
R6646
R6647
R6648
R6638
R6637
R6636
R6635
R6634
R6633
R6632
R6631
B21
Jun 2 17:11 1997 stand67.dat Page 1
GCP measurement at Stand 67
May 19(Mon) Raco area Day #1
Pnt # Latitude Longitude Height Code
1001,46.3901153567,84.8102929206,278.472,R67122
1002,46.3903320207,84.8102212677,279.217,R67132
1003,46.3905563080,84.8101885853,279.238,R67142
1004,46.3907785626,84.8102541785,279.241,R67152
1005,46.3910944753,84.8103553184,279.696,R67162
1006,46.3913078929, 84.8104376751,279.095,R67172
1007, 46.3915762219,84.8104398255,279.219,R67182
1008,46.3917080041,84.8099755002,280.514,R67282
1009,46.3914887362,84.8099043301,279.745,R67272
1010,46.3912710794, 84.8098207622,279. 936, R67262
1011,46.3909702621, 84.8097178568,281.017, R67252
1012,46.3905140327,84.8098087827,279.603,R67242
1013, 46.3902935312, 84.8098721003,279.640, R67232
1014, 46.3900423730,84.8098969017,279.033,R67222
1015, 46.3898230162, 84.8098215379,278.831, R67212
1016,46.3897977728, 84.8093393276,278. 973,R67312
1017,46.3900217497,84.8093710389,279.341,R67322
1018,46.3902453046,84.8093827462,279.783,R67332
1019,46.3905503042,84.8093388985,280.496,R67342
1020,46.3907776197,84.8092989739,280.324,R67352
1021,46.3909922274,84.8092192219,279.618,R67362
1022,46.3912179216,84.8091899876,279.160, R67372
1023,46.3914723283,84.8091766301,279.449,R67382
1024,46.3914269833,84.8086793304,279.182,R67482
1025,46.3912050421, 84.8087161767,278.690, R67472
1026,46.3909750806, 84.8087802228,279.071, R67462
1027,46.3906693470, 84.8087550522,280.309, R67452
1028,46.3903209758, 84.8087292940,280.636, R67442
1029,46.3900917064,84.8087105046,279.835,R67432
1030,46.3898614454,84.8086914054,280.072,R67422
1031, 46.3900171706, 84.8082189129,280.365, R67512
1032,46.3901973896, 84.8082417540,280.423, R67522
1033,46.3904010544, 84.8082495966,280.007, R67532
1034,46.3905863191, 84.8082545052,279.435, R67542
1035,46.3908177930, 84.8082667713,278.632, R67552
1036,46.3910184144, 84.8082729834,278.514, R67562
1037,46.3911883484, 84.8082880742,279.009,R67572
1038,46.3914748533,84.8082972707,279.624,R67582
1039,46.3895566138, 84.8081602981,278.969,R67ROAD5
1040, 46.3895728339,84.8102629235,277.436,R67ROAD1
B22
Jun 3 10:42 1997 stand68.dat Page 1
GCP measurement at Stand 68
May 21(Wed) Raco area Day #3
Pnt # Latitude Longitude
2014 46.367783572 84.786611078
2015 46.367791731 84.786089939
2016 46.367798503 84.785581544
2017 46.367803117 84.785068611
2018 46.367798425 84.784539567
2019 46.368418719 84.784632419
2020 46.368414850 84.784629156
2021 46.369071008 84.784691983
2022 46.369512683 84.784717133
2023 46.369277558 84.784869981
2025 46.369436500 84.786126814
2026 46.369444392 84.786620183
2027 46.369376408 84.787182458
2028 46.368768047 84.787050372
2029 46.368676894 84.786991508
2030 46.368651675 84.786410053
2031 46.368747019 84.785859956
2032 46.368739253 84.785120672
Height Code
273.305 S68Rl
273.340 S68R2
273.161 S68R3
273.929 S68R4
273.677 S68R5
274.303 S68T51
273.282 S68T51
273.143 S68T52
274.117 S68T53
272.761 S68T54
273.654 S68T45
273.580 S68T35
274.931 S68T25
275.052 S68T32
272.730 S68T31
273.519 S68T21
272.979 S68T22
273.047 S68T23
B23
Jun 2 17:28 1997 stand69.dat Page 1
GCP measurement at Stand 69
May 22(Thursday) Raco area Day #4
Pnt # Latitude Longitude Height Code
1047,46.4048937315, 84.7386432491,271.272,R6911
1048,46.4049365707,84.7383223663,271.287,R6912
1049,46.4047676075,84.7379993578,271.927,R6913
B24
Jun 2 17:30 1997 stand71.dat Page 1
GCP measurement at Stand 71
May 22(Thursday) Raco area Day #4
Pnt # Latitude Longitude
2001 46.390223167 84.765548475
2002 46.390194797 84.765147622
2003 46.390215258 84.764702297
2004 46.390183361 84.763911497
2005 46.390283386 84.763241019
2007 46.390746569 84.763620067
2008 46.390911217 84.765158344
2009 46.390'762506 84.766047581
2010 46.391341567 84.766071275
2011 46.391439022 84.765572256
2012 46.391597147 84.763916400
Height
274.429
272.827
272.162
272.069
273.058
272.409
272.135
275.468
274.738
272.299
272.245
Code
S71Tll
S71T21
S71T31
S71T41
S71T51
S71T52
S71T22
S71T12
S71T13
S71T23
S71T53
B25
Jun 2 17:31 1997 stand72.dat Page I
GCP measurement at Stand 72
May 22(Thursday) Raco area Day #4
Pnt # Latitude
2013 46.389923261
2014 46.389964342
2015 46.389974114
2016 46.390406753
2017 46.390316242
2018 46.390694903
2019 46.391101447
2020 46.391200369
2021 46.391426872
2022 46.391803644
2023 46.392210481
2024 46.392194483
Longitude
84.762884100
84.762104206
84.761145825
84.761218017
84.762203517
84.762436144
84.762864014
84.761974664
84.760631175
84.760716350
84.760845792
84.761957697
Height
273.479
273.053
272.680
275.077
274.749
274.913
272.734
272.160
273.924
271.040
272.423
272.435
Code
S72Tll
S72T31
S72T51
S72T52
S72T22
S72T23
S72T24
S72T34
S72T44
S72T45
S72T46
S72T26
B26
Jun 2 17:20 1997 stand80.dat Page 1
GCP measurement at Stand 80
May 21(Wed) Raco area Day #3
Pnt # Latitude Longitude
1086 46.340864353 84.905768011
1087 46.340898856 84.906358378
1088 46.340901892 84.906962819
1089 46.340962608 84.907612953
1090 46.340600489 84.907754861
1091 46.340570142 84.907307519
1092 46.340560278 84.906891783
1093 46.340523606 84.906372950
1094 46.340255472 84.906200339
1095 46.340279442 84.906699783
1096 46.340322158 84.907171717
1097 46.340348314 84.907703256
1098 46.339919667 84.907718475
1099 46.339957861 84.907255611
1100 46.340021633 84.906807128
1101 46.340051022 84.906184628
Height
278.491
277.688
277.804
277.756
278.331
278.925
278.904
279.138
279.267
279.324
279.122
278.778
279.028
279.110
279.471
279.336
Code
R8011
R8012
R8013
R8014
R8024
R8023
R8022
R8021
R8031
R8032
R8033
R8034
R8044
R8043
R8042
R8041
B27
Jun 2 17:41 1997 stand85.dat Page 1
GCP measurement at Stand 85
May 24(Saturday) Raco area Day #6
Pnt # Latitude Longitude Height Code
1007, 46.3942790996, 84. 9706821837,278. 604, R851
B28
Appendix C: Brief Description of Stands
C1
Appendix C consists of three parts.
(1) The location and description of each stand
The information is based on the following reference...... Page C3  C7
Reference)
"Structure, Composition, and Aboveground Biomass of SIRC/XSAR
and ERS1 Forest Test Stands 19911994, Raco Michigan Site"
Kathleen M.Bergen, M.Craig Dobson, Terry L.Sharik, Ian Brodie
October 30,1995
Report 0265117T
(2) 3 dimensional plots of each stand......Page C8  C30
Each measured datum is plotted three dimensionally.
(3) The brief sketches of some stands......Page C31 C39
During the measurement, sketches were made in some stands, not all of
the stands.
C2
Stand 22 (D) —Red pine —sapling (C55S35)
Raco Airfield, NW corner. Entrance to airport is south off M28, 0.1 mi.
west of Rt. 3157. Baseline starts 30 m. down from NW corner of airfield and
runs along stand edge on azimuth of 155 deg. Transect #1 begins at m. 30 on
the baseline and runs on 110 deg. azimuth. Sample points begin a minimum of
20 m. from the baseline (plantation edge), except for transect #5 where the
minimum was 30 m. Location of the first sample point on the transects is 19, 23,
4, 6, and 9 m. beyond the minimum distance, respectively.
Stand 31 (Q) —Northern hardwoods —pole (C20S8)
W side of Rt. 3159, 0.2 mi. N of Rt. 3156. Baseline runs along stand
edge on az of 180 deg. Transect #1 starts at m. 19 along the baseline and runs
on az of 90 deg, with first sample point a min. of 30 m. from the edge. Location
of the first sample point on the transects is 1, 24, 3, 22, and 21 m. beyond the
minimum distance, respectively.
Stand 33 (S) —Aspen —sapling (C20S10)**
On Rt. 3156, 0.15 mi. W of intersection with Rt. 3159. Original baseline
ran along stand edge on az. of 115 deg for a distance of 320 m. Transect #1
started at m. 14 along baseline on an az. of 0 deg.; first sample point was a min.
of 20 m. from the edge. There were 8 transects with 5 sample points per
transect. Due to stand irregularities, transects 9 and 10 were added (with 4
points per transect) to the west of transect #1 to compensate for missing plots on
Transects 6, 7, and 8, which now contain 1, 2, and 4 points, respectively.
Transect #9 starts 33 m. W of a logging trail which runs on an az of 20 deg.
Location of the first sample point is 22,15,18,13, 20,19, 10, 16,17, and 1 m.
beyond the minimum distance for transects 110 respectively.
Stand 34 (T) —Aspen —mature (C19S24)**
On N side of Rd. opposite Stand S, starting 75 m. W of intersection with
Rt. 3161. Baseline runs along stand edge on az. of 295 deg. Transect #1 starts
at m. 39 on the baseline and runs on an az of 205 deg; first sample point is a
minimum of 30 m. from the edge. Transect #5 has only 5 points because of
space constraints. Location of the first sample point on the transects is 7, 13, 8,
16, and 6 m. beyond the minimum distance, respectively.
Stand 38 (X) —Jack pine —sapling (C31S50)
On Rt. 3036, 0.25 mi. E of junction with Rt. 3018. Baseline runs along
the N side of Rt. 3036, on az. of 90 deg.; m. 200 on the baseline is 61.8 m. W of
the E edge of the stand. Transect #1 starts at m. 5 along the baseline and runs
on an az. of 20 deg.; first sample point is min. of 10 m. from the baseline.
Location of first sample point on the transects is 5, 16, 3, 13, and 7 m. beyond
the minimum distance, respectively.
C3
Stand 40 (Z —Red Dine —sapling (C29R18)*
On Rt. 3366, 0.25 mi. E of junction with Rt. 3041. Baseline runs along
the N side of Rt. 3366 for a distance of 440 m, on az. of 120 deg.; baseline starts
38 m. E of W edge of stand, while m. 440 on baseline is 42 m. W of E end of
stand. There are 9 transects along the baseline, with a variable number of
sample points per transect to accommodate the irregular shape of the stand.
The number of points are 3, 2, 3, 3, 6, 7, 7, 6, and 3 respectively. Transect #1
starts at m. 38 along the baseline and runs on an az. of 30 deg.; first sample
point is a min. of 10 m. from the baseline. Location of first sample point on the
transects is 22, 11, 10, 21, 23, 1, 23, 6, 22, 9, and 22 m. beyond the minimum
distance, respectively.
Stand 45 (EE) —Aspen —sapling (C20R30)
Take Rt. 3156 0.9 mi. NW of junction with Rt. 3159, turn right (NE) onto
spur road for 75 m. to Wcentral edge of stand. Baseline starts 20 m. in from
spur road and runs along the edge of the stand on an az. of 152 deg. Transect
#1 begins at m. 9 on the baseline and runs on an az. of 36 deg.; first sample
point is a minimum of 30 m. from the baseline. Location of first sample point on
the transects is 15, 8, 7, 10, and 17 m. beyond the minimum distance,
respectively. Wire flags marking sample points are reversed, with yellow at the
upper stratum plot center and red at the middle stratum plot centers. Rebars
may be absent at the ends of the baseline. There are scattered individuals in
the overstory which have not been removed as of 101992 (ditto for 7/94).
Stand 49 (JJ) —Aspen —sapling (C21S9 & 10)**
On Rt 3640, 0.3 mi. NE of junction with Rt. 3156. Baseline starts 40 m.
from the NE corner of the stand and runs on an az. of approx. 230 deg. along
the NW edge of the stand. Transect #1 begins at m. 36 on the baseline and
runs on an az. of 100 deg.; first sample point is a minimum of 20 m. from the
baseline. Due to size limitations, only 38 sample points were established along
5 transects, with 5, 6, 8, 10, and 9 sample points, respectively. Location of first
sample point of the transects is 10, 4, 7 (17?), 3, and 9 m. beyond the minimum
distance, respectively. On transect #5 a truck trail passes between sample
points 3 and 4, thus moved point #4 20 m. down the transect.
Stand 50 (KK) —Red pine —mature (C21S8)**
On Rt. 3156, 0.33 mi. SE of junction with Rt. 3159. Baseline starts 40 m.
from W edge of stand and runs along N side of Rt. 3156, on an az. of 118 deg.
Transect #1 begins at m. 9 on the baseline and runs on an az. of 360 deg.; first
sample point is a min. of 20 m. from the baseline. Because of stand
irregularities, transect #5 was skipped and a sixth transect added. The number
of sample points per transect is 6, 8, 8, 9, and 9, respectively. Location of first
sample point on the transects is 11, 1, 12, 16, and 3, respectively.
C4
Stand 54 —Jack pine —sapling (C31S38)
On FS 3018, m. 0.0 is 0.3 mi. south of junction with FS 3036. Baseline
runs along the east side of 3018, on an az. of 180 deg. Transect #1 begins at
m. 7 on the baseline and runs on an az. of 87 deg. First sample point is a
minimum of 20 m. from the baseline. Location of first sample point on the
transects is 9, 159 12, 15, and 6 m. beyond the minimum distance, respectively.
Stand 55 —Jack pine —sapling (C31S52)
On north side of FS 3366, a reference point is 0.3 mi. east of junction with
FS 3018. From reference point, baseline m. 0.0 is 62.5 m. into the forest at an
az. of 18 deg. Transect #1 begins at m. 36 on the baseline and runs on an az.
of 288 deg. First sample point is a minimum of 0 m. from the baseline.
Location of first sample point on the transects is 6, 25, 11, 3, and 5 m,
respectively.
Stand 56 —Jack Pine —pole (C31S62)
On FS 3018, m. 0.0 is 40 m. south of junction with FS 3037. Baseline
runs along the east side of FS 3018, on and az. of 180 deg. Transect #1 begins
at m. 18 on the baseline and runs on an az. of 90 deg. First sample point is a
minimum of 20 m. from the baseline. Location of first sample point on the
transects is 3, 6, 22, 2, and 6 m. beyond the minimum distance, respectively.
Stand 58 —Jack pine —sapling (C49S33)
On FS 3040, m. 200 is 20 m. south of junction with FS 3364. Baseline
runs along the west side of FS 3040, on an az. of 0 deg. Transect #1 begins at
m. 11 on the baseline and runs on an az. of 270 deg. First sample point is a
minimum of 20 m. from the baseline. Location of first sample point on the
transects is 19, 24, 18, 9, and 18 m. beyond the minimum distance, respectively.
Stand 59 —Jack pine —sapling (C48S5)
On FS 3040, m. 200 is 0.2 mi. west of junction with FS 3018. Baseline
runs along the south side of FS 3040, on an az. of 269 deg. Transect #1 begins
at m. 30 on the baseline and runs on an az. of 180 deg. First sample point is a
minimum of 20 m. from the baseline. Location of first sample point on the
transects is 6, 20, 6, 17, and 22 m. beyond.the minimum distance, respectively.
Stand 61 —Jack pine —mature (C48S13)
On FS 3040, m. 0.0 is 50 m. west of junction with FS 3039. Baseline runs
along the south side of FS 3040, on an az. of 88 deg. Transect #1 begins at m.
24 on the baseline and runs on an az. of 180 deg. First sample point is a
minimum of 30 m. from the baseline. Location of first sample point on the
transects is 15, 6, 6, 22, and 2 m. beyond the minimum distance, respectively.
C5
Stand 66 —Jack pine —seedling (C32S21)
On FS 3037, m. 160 is 0.2 mi. west of junction with FS 3018. Baseline
runs along the north side of FS 3037, on an az. of 270 deg. Transect #1 begins
at m. 29 on the baseline and runs on an az. of 36 deg. (Road crosses baseline
at 50 m. mark.) First sample point is a minimum of 80 m. from the baseline.
Location of first sample point on the transects is 13, 14, 2, and 25 m. beyond the
minimum distance, respectively. The stand shape is irregular with 4 transects
having 10 plots each.
Stand 67 —Jack pine —mature (C32S22)
On FS 3036, m. 200 is 0.3 mi. west of junction with FS 3018. Baseline
runs along the north side of FS 3036, on an az. of 90 deg. Transect #1 begins
at m. 24 on the baseline and runs on an az. of 0 deg. First sample point is a
minimum of 30 m. from the baseline. Location of first sample point on the
transects is 4, 8, 14, 8, and 22 m. beyond the minimum distance, respectively.
Stand 68 —Red pine —ole (C49S9)
On FS 3040, m. 0.0 is 0.8 mi. east of junction with FS 3018. Baseline
runs along the north side of FS 3040, on an az. of 90 deg. Transect #1 begins
at m. 29 on the baseline and runs on an az. of 355 deg. First sample point is a
minimum of 50 m. from the baseline. Location of first sample point on the
transects is 19, 14, 17, 15, and 22 m. beyond the minimum distance,
respectively. A jack pine inclusion occurs at 125 m. on the baseline and goes in
approx. 60 m.
Stand 69 —Aspen (upland) —sapling (C23S23)
On FS 3154, m. 200 is 0.1 mi. north of junction with FS 3622. Baseline
runs along the east side of FS 3154, on an az. of 180 deg. Transect #1 begins
at m. 23 on the baseline and runs on an az. of 90 deg. First sample point is a
minimum of 20 m. from the baseline. Location of first sample point on the
transects is 18, 11, 21, 5, and 12 m. beyond the minimum distance, respectively.
15 plots were measured in 1993. (T1 plots 15, T2 plots 14, T3 plots 13, T4
plots 4 & 6, T5 plot 5). Later reconfigured for GPS survey to be 8 transects (320
m.) by 5 plots ea. deep.
Stand 71 —Red pine —pole (C30S52)
On FS 3036, m. 200 is 220 m. west of junction with FS 3041. Baseline
runs along the north side of FS 3036, on an az. of 90 deg. Transect #1 begins
at m. 3 on the baseline and runs on an az. of 0 deg. First sample point is a
minimum of 30 m. from the baseline. Location of first sample point on the
transects is 12, 21, 9, 19, and 11 m. beyond the minimum distance, respectively.
C6
Stand 72 —Red pine —pole (C30S52)
On FS 3036, m. 200 is 17.5 m. west of junction with FS 3041. Baseline
runs along the north side of FS 3036, on an az. of 90 deg. Transect #1 begins
at m. 9 on the baseline and runs on an az. of 0 deg. First sample point is a
minimum of 30 m. from the baseline. Location of first sample point on the
transects is 13, 15, 30, 4, and 2 m. beyond the minimum distance, respectively.
Stand 80 —Red pine —seedling (C58S39)
On FS 3139, m. 160 is 0.4 mi. south of junction with M28. Baseline runs
along the west side of FS 3139, on an az. of 0 deg. Transect #1 begins at m. 28
on the baseline and runs on an az. of 260 deg. First sample point is a minimum
of 65 m. from the baseline. Location of first sample point on the transects is 3,
259 24, and 5 m. beyond the minimum distance, respectively. The stand shape
is irregular having 4 transects with 10 plots each.
Stand 85 —Northern hardwoods —pole (C44S19)
On trail to Peck and Rye Lake, m. 0.0 is 0.3 mi. north of junction with FS
3162. Baseline runs along the west side of the trail to Peck and Rye lake, on an
az. of 360 deg. Transect #1 begins at m. 31 on the baseline and runs on an az.
of 270 deg. First sample point is a minimum of 20 m. from the baseline.
Location of first sample point on the transects is 14, 5, 12, 1, and 8 m. beyond
the minimum distance, respectively.
*AII baselines are 200 m. long with 5 transects situated along them and with 8
sample points per transect, unless otherwise indicated. Sample points on a
transect are at intervals of 25 m, with the first point located at a random distance
of 125 m. from the baseline or from the "minimum distance from the baseline",
depending on the stand. White wire flags mark locations of transects on the
baseline, while red and yellow flags mark the centers of the upper and middlestratum plot centers, respectively, unless otherwise noted. Magnetic
declination is 5 deg. W.
**Some irregularities in plot layout or homogeneity of vegetation, topography,
and/or soil conditions
C7
GPS Height for Stand 22
276
275.5
E 275.
274.5
I
274.
273.5
84.822
84.821
84.E
Longitude(*1) > East
46.355
32
46.3545
84.819
46.354
South < Latitude > North
C8
GPS Height for Stand 31
I I
o measured data
256.
257.4 X 1 
256.4
256.2
84.906
v 46.4338
46.4336
46.4334
46.4332
46.433
46.4328
46.4326
Longitude(*1) > East South < Latitude > North
C9
GPS Height for Stand 33
269.5 
269  \
E
268.5._Q)
I 268
267.5
84.9125 
84.912
84.9115
Longitude(*1) > East
84.911
84.9105
46.4314
46.4312
46.4322
46.432
46.4318
46.4316
South < Latitude > North
C10
GPS Height for Stand 34
0 measured data
270
E269.5.a)
r269
268.5
84.9095
46.43
46.4285
Longitude(*1) > East
South < Latitude > North
Cll
GPS Height for Stand 38
o measured data
279.5
279,278.5
E
$ —o
r.m 278
a)
I
277.5
277
84.796
84.7955
84.795
84.7945
Longitude(*1) > East
South < Latitude > North
C12
GPS Height for Stand 40
276
o measured data:. I
~,...
84.755
84.754
84.753
~  i~ ~ 46.3916
~:: 46.3914
~: — 46.3912: 46.391
\.; 46.3908
46.3906
46.3904
84.752
Longitude(*1) > East
South < Latitude > North
C13
GPS Height for Stand 45
o measured data
E,..
0)
I.
46.436
84.917
Longitude(*1) > East
South < Latitude > North
C14
GPS Height for Stand 49. o measured data
264
263
262
E 261
c*' 260
I
259
258. 46.4308
 ' 46.4306
46.4304
'.^.46.4302
46.43
46.4298
46.4296
Longitude(*1) > East 84.901
South < Latitude > North
C15
GPS Height for Stand 50
o measured data
268.5
268
267.5
E 267
& —
0t
,266.5.D
Q)
I 266
265.5
265
46.4275
84.8985
Longitude(*1) > East
South < Latitude > North
C16
GPS Height for Stand 54
o measured data
400
350
300
E
i 250
I 200
150
100
84.8015
84.801
84.8005
Longitude(*1) > East..
o..
*,..'.....'....'..
~......... —........ 46.~:::::
3865
46.386
84.8
84.7995
' ~ ~
46.3855
46.385
South < Latitude > North
C17
GPS Height for Stand 55
o measured data
~::.:
282.5
2824.7965.
_281.5.
E. 281
46.4
84.795 ~ 46.399
Longitude(*1) > East 46.3985
South < Latitude > North
C18
GPS Height for Stand 56
E 276.5.I 276 
275.5.
84.8015 m
84.801
84.8005
46.3815
84.8
46.381
84.7995
46.3805
Longitude(*1) > East
South < Latitude > North
C19
GPS Height for Stand 58
0 measured data
290
2851 ~280
275
270
265
4. 7725
84.7725
Longitude(*1) > East Rou~th < I atitutrlp :) Nnrth
8a
%A %.# %A L I I I  I.. " L I % " %A %W .0' 1 V %J I L I I
C20
GPS Height for Stand 59
a ~ ~ 
276.4
276.2
E 276..)
'a 275.8
I
275.6
275.4
0 measured data'.
46.3665
84.804 46.366
South < Latitude > North
Longitude(*1) > East
C21
GPS Height for Stand 61
277.8
E 277.6..'277.4
I
277.2
277
'
J
1<
84.815
84.8145
46.3675
84.814
46.367
84.8135
46.3665
84.813
Longitude(*1) > East
South < Latitude > North
C22
GPS Height for Stand 66.
0
measured data
I.a)
I 00)
 100
~92~ K..
0
84.808
46.384
84.8075
46.3835
84.807
46.383
Longitude(*1) > East
South < Latitude > North
C23
GPS Height for Stand 67
280.5.
280.,279.5.
E
C 279
2: 278.5
278
277.5
46.3915
84.8095
84.809
84.8085
Longitude(*l1) > East
46.3905
South <,Latitude > North
C24
GPS Height for Stand 68
46.3695
46.369
46.3685
South < Latitude > North
46.368
Longitude(*1) > East
C25
GPS Height for Stand 69
0 measured data
27 1.9
2r?7 1.8
2271.7
E
271)
i271.5
46.4048
Longitude(*1) >East 84.738 ~*A% M..I
1%
OU~ULI I <. LILILUUU > INIJI LI
C26
GPS Height for Stand 71: o measured data
E
' 274
'a)
I
* . 46.3914
 46.3912..* 46.391: 46.3908
46.3906
46.3904
46.3902
Longitude(*1) > East
South < Latitude > North
C27
GPS Height for Stand 72

I~
o measured data
*:....:.:
~.
*:
* *..
I,...~..
275
274.5
274
E 273.5
C) 273
I
272.5
272
271.5
84.7625
46.392
46.39
Longitude(*1) > East
South < Latitude > North
C28
GPS Height for Stand 80. I..
I  .~
measured data
I
279.51.
E
279.5...
46.3406.
84.90657. " 46.3408
A46.3406
84.906 463402
Longitude(*1) > East South < Latitd  North
% . O% — X. O — I. %00....
C29
0
e0
1.8..6.4.2
0>.*
1
0.8,.,,,%
GPS Height for Stand 85:: measured data
~..
~. ~~..,....,..o...,
~.,......
~Oo.. ~.:.o..
~..
~..
o...
~..
o.
~ o'...
~. ~.
~..
oo
~~~~.......
~~~....:..
0
1
U.O
0.e
1
u.o
0.2
0.4
0.2
Longitude(*1) > East
South < Latitude > North
C30
F
Stand 22  Red pine  not sapling( 10 m)
Measured by Dennis Taeyeoul on May 19(Mon.).
Species; All trees are red pine(99.9%).
Tree height; 10m
Ground surface; very flat
Tree density; Red pines were regularly planted following EastWest direction(see below figure)
Weather; a little rain, very windy, 8 oC, not good condition to get data.!,~K00 L,//.^\\\~_____^ /^ * a(
^ \ \ v <*; "'
 .11
g hco geld /:
V0 0 0 ~0V
0 0 0 
> 0 0 o
'\ I rC31
p OL'Iyl~
~j 4_ c, 'lt &r Vv —e
Stand 31  Maple  pole
Measured by Kamal, Yutaka, Taeyeoul on May 23(Fri.).
Species; Almost of all trees are Maples(> 90%).
Tree height; greater{5m
Ground surface; flat
Tree density; not dense, 1 tree/2m*2m
Weather; no rain, very small wind, 15 ~C, very good condition to get data.
4)o4A rw,k,,,,
'V
— I
(
I x
I
I
I
I
I
I
I
I
I
I
I
A L7
i~77R,lfA lvO.
SP 7T P o
gA&1 6 LDO&E.
P 5 Vl(veA 
CAer r5.ur E vJ of (1 * 4& () ~D OwC/leeyk"gij~
C32
Stand 40  Red Pine  sapling
Measured by Kamal, Yutaka, Taeyeoul on May 22(Thu.).
Species; Almost of all red pine trees are regularly planted(> 90%). randomly growing jack pine.
Tree height; greater than  2m
Ground surface; flat
Tree density; spacing of 2m by lm.
Weather; no rain, no wind, 15 ~C, very good condition to get data.
1 (1 3? O 1
a o X 1,(1
q rA,^ 5" IJ6x
tqqotw 
C33
Stand 49  Aspen  sapling
Measured by Kamal, Yutaka, Taeyeoul on May 23(Fri.).
Species; Almost of all trees are aspen(> 90%).
Tree height; 3  5m
Ground surface; Ground level is linearly slanted, i.e. increasing from Tl to T5.
Tree density; very dense, hard to move
Weather; no rain, very small wind, 15 ~C, very good condition to get data.
TT
T.e se ^ / / y ^ I ^ E
aI I —rl (DC,j/ / 54 H41
<( o f I
ScfLT PbAT ROfP
C34
Stand 50  Red Pine  mature
Measured by Kamal, Yutaka, Taeyeoul on May 24(Sat.).
Species; All tall trees are Maples(> 90%).
Tree height;  20m, branches come out from height of 10m.
Ground surface; flat
Tree density; not dense, 1 tree/2m*2m
Weather; no rain, very small wind, 15 ~C, very good condition to get data.
TN
`1
4./ I. stow S1 s rd
61 Ko LkA A4 15 ID0,
{ )u6t an 0 r
aiw ^0 L/hrr
C35
Stand 58  Jack Pine  sapling
Measured by Yutaka, Taeyeoul on May 20(Tue.).
Species; Almost of all trees are Jack pine(> 99.9%).
Tree height;  2m
Ground surface; flat
Tree density; Tree spacing is aoubt 2.5m by 2.5m, irregularly.
Weather; no rain, very small wind, 10 ~C, very good condition to get data.
I,  I
/(
H
f — I, I.
C36
Stand 61  Jack Pine  mature
Measured by Yutaka, Taeyeoul on May 21 (Wed.).
Species; All trees are Jack pine(> 99.9%).
Tree height;  15m
Ground surface; flat
Tree density; randomly located, tree spacing is 2.5m by 2.5m.
Weather; no rain, very small wind, 15 ~C, very good condition to get data.
T7
S 3o4o
I
C37
Stand 68  Red Pine  mature
Measured by Kamal, Yutaka, Taeyeoul on May 21(Wed.).
Species; All trees are Jack pine(> 99.9%).
Tree height; greater than  15m
Ground surface; some locations are higher, generally flat.
Tree density; regularly planted, tree spacing is 2.5m by 2.5m.
Weather; no rain, no wind, 15 ~C, very good condition to get data.
V'so I?
j
'4
a Aet;(X ^^
w.s 3ZL&Q
C38
Stand 71 and 72  Red Pine  pole
Measured by Kamal, Yutaka, Taeyeoul on May 22(Thu.).
Species; All trees are Red pine(> 99.9%).
Tree height; 10  15m
Ground surface; flat and 2 3 hills
Tree density; Almost of all red pine was already logged. There are several trees near hills.
Weather; no rain, no wind, 15 ~C, very good condition to get data.
/)
Zr
r 5 '3o I
A
a 51 i4/
PFSE —L te f
C39
Appendix D:
Data of Ground Control Point(=GCP) Location
D1
Table D1 shows the information on GCPs.
Figure D1 shows location of each GCP.
The detail data record is shown afterwards.
All the data are expressed on WGS coordinate.
Including the cover sheet, appendix D is totally 7 pages.
D2
Table D1
Ground Control Point(GCP) description (1 of 2)!
tv
I
GCP Description Area Measured by Measurec
NO. ldate
R2 Road intersection of Centerline Road & 20 Mile Road. Rudyard Leland,Dennis, May 18
__________Taeyeoul, Yutaka
R4  Road intersection of Tilson Road & 18 Mile Road. At the northwestern Rudyard the same as above May 18
corer, there is "Christian Reformed Church".
R5 Road intersection of Centerline Road & M48. ' Rudyard the same as above May 18
R6 Road intersection of USFS3161(Flatfoot Road) & 3367(snow mobile Raco kamal, Taeyeoul, May24
trail) Yutaka
R7 Cross point of USFS3161(Flatfoot Road) & Power line Raco the same as above May 24
The power line is the same power line which is extending along
USFS3364. l_
R8 Road intersection of USFS3364 & USFS3018. Raco Leland, Dennis May
USFS3364 is running from East to West and there is power line along
USFS3364. ll
R9 Road intersection of M28 & USFS3131 (Sullivan Creek T.T.) Raco. the same as above ay 2
R10NEAR Road intersection of M28 & USFS3157(Rexford Road) Raco Kamal, May 24
_______Taeyeoul,Yutaka
R10 Road intersection of USFS3364 & USFS3157(Rexford Road) Raco the same as above ay 24
R 1 Road intersection of USFS3159(Salt Point Road) & Wyckoff Road. Mc Nearney the same as above May 24
This GCP is located 620 meter south of the lakeshore of Lake
Superior.
Wyckoff Road is not shown in the map. ___
R12 Located West of Naomikong Point. This GCP is along the Me Nearney the same as above May 24
FH42(Curley Lewis Road) and is located at the cross point of FH42 &
Road to Naomikong pond(ball field).___
R13 Located 4miles West of Naomikong Point. This GCP is along the Me Nearney the same as above May 24
FH42(Curley Lewis Road) and is located at the cross point of FH42 &
North Country Trail.
R14 The Northeast corer of Raco airfield runway. IRaco Leland, Dennis May20
R15 The Northwest comer of Raco airfield runway. Raco the same as above May 20
d
Il
i=
Table D1
Ground Control Point(GCP) description
( 2 of 2)
tv
I
0r
GCP Description Area Measured by Measure
NO. date
NO.
R16 The middle point between R15 and R17. (Raco airfield runway.) Raco Leland, Dennis May
R17 The South comer of Raco airfield runway. Raco the same as above May 20
R18 Road intersection of M28 & USFS3154(Ranger Road) Raco Dennis, YiCheng May24
R19 Road intersection of USFS3364 & USFS3154(Ranger Road) Raco the same as above May 24
R20 Road intersection of USFS3581 & USFS154(Ranger Road) Raco the same as above ay2
R21 Road intersection of USFS3622 & USFS3154(Ranger Road) Raco Taeyeoul, Yutaka Ma22
R22 Road intersection of USFS3159(Salt Point Road) & Mc Nearney Taeyeoul, Yutaka May 20
USFS3156(Richardson Avery Grade)
R4 Road intersection of M28 & USFS3139(Dick Road) Raco Kamal, Taeyeoul, May 2
Yutaka
R30 Road intersection of M28 & USFS3161(Flatfoot Road) Raco the same as above May24
R31 Road intersection of USFS3605 & USFS3364 Raco Dennis, YiCheng May 24
R33 Road intersection of Centerline Road & M48. Rudyard the same as above May 24
34 Road intersection of Kallio Road & 19 Mile Road. Rudyard the same as above May 24
R40 This GCP is located at the entrance of Cryderman hill. This point is Mc Nearney Kamal, Taeyeoul, May 24
along USFS3159 (Salt Point Road). Yutaka
This GCP is located 410 meter south of the lakeshore of Lake
Superior.
R4 i Road intersection of USFS3159 (alt Point Road) & Ne ey amal, Taeyeoul, May 24
USFS3150(Curley Lewis Road). _Yutaka
42 Road intersection o USFS3364 & USFS3040. Raco Taeyeoul,Yutaka May 20
This GCP is located northeastern corer of Stand 58.
Remark)
1. The map shown below is very helpful to know the exact location of the GCPs.
"Eastern Upper Peninsula of Michigan" $3.95 ISBN 1564643549
Distributed by Universal Map, Inc. P.O. Box 15 795 Progress Court Williamston, MI. 48895 Phone (517)6555641
Stock No. MI206
d
=l
3t
I; (*
i
i.,,C
I
Jun 2 19:12 1997 gcp2.rep Page 1
GCP measurement of Ground Control Points(=GCPs)
Pnt # Latitude Longitude Height Code
1005,46.2159930864,84.5716630728,207.031, R21
1006,46.2160548285, 84.5715898442,206.907,R22
1007,46.2196159567158, 84.5715958889,206.842, R23
1008,46.2159595341,84.5717193246,206.875,R24
1009,46.2160450130, 84.5717210675,206.933, R25
1010,46.2451467360, 84.5924850466,211.120, R41
1011,46.2451885535,84.5924081648,210.922,R42
1012,46.2450965072,84.5924086203,210.933, R43
1013,46.2450922316,84.5925334188,211.020, R44
1014,46.2451822000,84.5925362311,211.025,R45
1000,46.1870756889,84.5716812758,203.182,R51
1001,46.1871502019,84.5715828700,202.900, R52
1002,46.1870113742,84.5715860187,203.053,R53
1003,46.1870087821, 84.5717947099,202.910, R54
1004,46.1871423580,84.5717901641,202.922,R55
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
"R2"
"R2 "
"R2"
"R2"
"R4"
"R4"
"R4"
"R4"
"R5"
"RS"
"R5"
"R5"
No.1
No.2
No.3
No.4
No. 5
No.1
No.2
No.3
No.4
No. 5
No.1
No.2
No.3
No.4
No.5
2022
2023
2024
46.358503917
46.367233003
46.367112186
84.893683442
84.893898458
84.893884428
281.662
277.844
276.955
R6
R78
R78E
GCP "R6"
GCP "R7" No.1
GCP "R7" No.2
1005 46.375190372 84.801734792 276.557 R8
1000
1001
1000
2020
2019
46.388173172
46.388166236
46.365141342
46.375215489
46.358734100
84.803176236
84.803181056
84.760581550
84.833054431
84.829831186
278.946
278.938
263.327
283.468
278.615
R8
R8 CHECK
R8
R1OE
R10NEAR
GCP at road intersection
of 3364&3018
Maybe wrong
Maybe wrong
Maybe GCP "R9"
GCP "R10" (Center)
GCP "R1ONear"
GCP "Rll" No.1
GCP "Rll" No.2 (Center)
2008,46.4549477881, 84.9058569749,205.738,RllF
2009,46.4549553575,84.9059144442,205.665, R11E
2014,46.4730625042, 84.9573431082,213.650,R12A
2015,46.4731295504, 84.9569849900,214.061,R12B
2016,46.4729805411,84.9566907434,214.475,R12C
2017,46.4865157492,85.0394154128,211.261,R13A
1000 46.356880953 84.804882997 274.760 R14
1001 46.356454694 84.824510278 277.009 R15
1002 46.356454703 84.824510278 277.005 R152
1003 46.350713006 84.819791794 275.375 R16
1004 46.344839564 84.814679747 275.618 R17
1008,46.3694893633,84.7388115976,259.044,IT1
1009,46.3694390760,84.7390001988,259.091,IT2
1010,46.3693180115,84.7388104672,258.946,IT3
1011,46.3732296627,84.7390470582,259.416,IT191
1012,46.3733355559,84.7390545540,259.473,IT192
1013,46.3733039973,84.7389944168,259.513,IT193
GCP "R12"
GCP "R12"
GCP "R12"
No.1
No.2
No.3
GCP
GCP
GCP
GCP
GCP
GCP
"R13" No.1
"R14"
"R15"
"R15"
"R16"
"R17"
GCP "R18"
GCP "R18"
GCP "R18"
GCP "R19"
GCP "R19"
GCP "R19"
No. 1
No.2
No.3
No.1
No.2
No.3
D6
Jun 2 19:12 1997 gcp2.rep Page 2
1014,46.3896860152,84.7390268249,266.384,IT201
1015,46.3896005033,84.7390261682,266.409,IT202
1016,46.3895905163, 84.7391350773,266.300, IT203
2040,46.4042942552,84.7392223628,272.399, R21A
2041,46.4044018162,84.7392304077,272.365, R21B
2042,46.4043883303, 84.7391176508,272.431, R21C
2043,46.4042878505, 84.7391207019,272.440, R21D
2044,46.4041332027,84.7391172883,272.454, R21E
2045,46.4040676061, 84.7391176308,272.468, R21F
2046,46.4040730130,84.7392110507,272.476, R21G
2047,46.4041331362,84.7392097999,272.479,R21H
2048,46.4040949452,84.7391640552,272.561, R21I
2049,46.4043478102,84.7391624788,272.504, R21J
GCP "R20"
GCP "R20"
GCP "R20"
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
GCP
"R21"
"R21"
" R21"
"R21"
"R21"
"R21"
"R21"
"R21"
"R21"
"R21"
No. 1
No.2
No.3
No.1
No.2
No.3
No.4
No.5
No.6
No.7
No.8
No.9
No.10
1000,46.4297625588,84.9061364517,266.469,BM NEAR ST45 — >GCP
1002,46.4297385741,84.9059882138,266.574,ROAD CORN ST45 >GCP
1003,46.4295992170,84.9059718765,266.597,ROAD CORN ST45 >GCP
1004,46.4296658391,84.9061221572,266.561,ROAD CORN ST45 >GCP
1005,46.4296928091,84.9060537808,266.666,ROAD CORN ST45 >GCP
"R22" Corner1_
"R22" Corner_2
"R22" Corner_3
"R22" Corner_4
"R22" Center
2025 46.351503847 84.905825956 275.119 R24
2021 46.356631278 84.893252253 282.384 R30
1017,46.3751789172,84.7809876803,275.045,IT311
1018,46.3751902311,84.7808610433,274.628,IT312
1019,46.3752989637,84.7808818752,274.445,IT313
GCP "R24"
GCP "R3 0"
GCP "R31"
GCP "R31"
GCP "R31"
No.1
No.2
No.3
1020
1023
1024
1025
1026
1027
46.230411150
46.230559069
46.230559042
46.230471825
46.230474958
46.230584964
84.571541517
84.571815319
84.571612122
84.550923908
84.550780092
84.550770667
210.555
210.620
210.558
209.141
209.158
209.170
IT331
IT3332
IT3342
IT341
IT342
IT343
GCP "R33"
GCP " R33"
GCP "R33"
GCP "R34"
GCP "R34"
GCP "R34"
GCP "R40"
GCP "R41"
No.1
No.2
No.3
No.1
No.2
No.3
2012,46.4586133798,84.9058626065,205.821,CRYDERMAN1
2013,46.4649589117,84.9058862222, 185.549, CORNERLAKE
1030
1031
1032
1033
1034
1035
1036
46.375154703
46.375151878
46.375287639
46.375421111
46.375418719
46.375284444
46.375154783
84.770503836
84.770375394
84.770373375
84.770367964
84.770498033
84.770503714
84.770503872
274.736
274.802
274.897
275.173
275.033
274.807
274.743
S58CORNER1
S58CORNER2
S58CORNER3
S58CORNER4
S58CORNER5
S58CORNER6
S58CORNER7
GCP
GCP
GCP
GCP
GCP
GCP
GCP
"R42"
"R42"
"R42"
"R42"
"R42"
"R42"
"R42"
cornerl
corner2
corner3
corner4
corner5
corner6
corner7
D7
Appendix E: NGS Data Sheet
E1
Two benchmarks are used in this measurement. Here are the orignal
sources of these two benchmarks.
Including the cover sheet, appendix E is totally 6 pages.
E2
The NGS Data Sheet
DATABASE = Sybase,PROGRAM = datasheet, VERSION = 5.21
Retrieval Date = MAY 8, 1997 Version = 5.21
Starting Datasheet Retrieval...
1 National Geodetic Survey, Retrieval Date = MAY 8, 1997
RJ1102 ************************************
RJ1102 DESIGNATION  OVERPASS
RJ1102 PID  RJ1102
RJ1102 STATE/COUNTY MI/CHIPPEWA
RJ1102 USGS QUAD  RUDYARD (1977)
RJ1102
RJ1102 *CURRENT SURVEY CONTROL
RJ1102
RJ1102* NAD 83(j99A) 4L11 14.238231N) V8&A 33. b.LJ9326(W) ADJUSTED
RJ1102* NAVD 88  204. (met,rs) 669. (feet) SCALED
RJ1102
RJ1102 LAPLACE rORR 3.49 (seconds) DEFLEC96
RJl102 GEOID HEIGHT 36.07 (me ers) GEOID96
RJ1102
RJ1102 HORZ ORDER  THIRD
RJ1102
RJ1102
RJ1102
RJ1102.The horizontal coordinates were established by classical geodetic methods
RJ1102.and adjusted by the National Geodetic Survey in February 1997.
RJ1102
RJ1102.The orthometric height was scaled from a topographic map.
RJ1102
RJ1102.The Laplace correction was computee from DEFLEC96 der'trea 0d^fl1i,;^cRJ1102
RJ1102.The geoid height was determined by GEOID96.
RJ1102
RJ1102; North East Units Scale Converg.
RJ1102;SPC MI N  158,934.365 8,188,150.489 MT 0.99990429 +1 45 43.1
RJ1102;UTM 16  5,117,745.562 688,120.601 MT 1.00003505 +1 45 34.6
RJ1102
RJ1102: Primary Azimuth Mark Grid Az
RJ1102:SPC MI N  OVERPASS AZ MK 265 03 18.2
RJ1102:UTM 16  OVERPASS AZ MK 265 03 26.7
RJ1102
RJ1102  —
RJ1102 PID Reference Object Distance Geod. Az
RJ1102 dddmmss.s
RJ1102 OVERPASS RM 1 29.329 METERS 12119
RJ11021 OVERPASS RM 2 16.923 METERS 20456
RJ11021 RJ1112 MAPLE HILL MICROWAVE MAST APPROX.17.4 KM 2584451.2
RJ1102 OVERPASS AZ MK 2664901.3
RJ1102 RJ1101 RUDYARD BELL TEL CO MICROWAVE APPROX. 6.1 KM 3483321.4
RJ1102 
RJ1102
RJ1102 SUPERSEDED SURVEY CONTROL
RJ1102
RJ1102 NAD 83(1986) 46 11 14.23079(N) 084 33 44.09122(W) ADJUSTED
RJ1102 NAD 27  46 11 14.16536(N) 084 33.43.92730(W) ADJUSTED
RJ1102
RJ1102.Superseded values are'not recommended for survey control.
RJ1102.NGS no longer adjusts projects co the NAD 27 or NGVD 29 datums.
RJ1102.See file format.dat to determine how the superseded data were derived.
RJ1102
E3
RJ1102 HISTORY  Date Condition Recov. By
RJ1102 HISTORY  1965 MONUMENTED CGS
RJ1102
RJ1102 STATION DESCRIPTION
RJ1102
RJ1102'DESCRIBED BY COAST AND GEODETIC SURVEY 1965 (LMC)
RJ1102'THE STATION IS LOCATED NEAR THE NORTHWEST CORNER OF A BRIDGE, WHERE
RJ1102'STATE HIGHWAY 48
RJ1102'CROSSES OVER INTERSTATE HIGHWAY 75, ABOUT 31/2 MILES
RJ1102'SOUTHEAST OF RUDYARD, 61/2 MILES
RJ1102'WESTSOUTHWEST OF KINROSS, AND ON
RJ1102'STATE OWNED PROPERTY.
RJ1102'
RJ1102'TO REACH THE STATION FROM THE POST OFFICE IN RUDYARD, GO EAST ON
RJ1102'MAIN STREET FOR
RJ1102'0.4 MILE TO A CROSSROAD. TURN RIGHT AND GO SOUTH ON
RJ1102'MACKINAC TRAIL AND STATE HIGHWAY
RJ1102'48 FOR 3 MILES TO A SIDE ROAD LEFT.
RJ1102'TURN LEFT AND GO EAST ON HIGHWAY 48 FOR 1.5 MILES
RJ1102'TO A CROSSROAD AND
RJ1102'THE AZIMUTH MARK ON THE RIGHT. CONTINUE EAST ON HIGHWAY 48 FOR 0.45
RJ1102'MILE TO THE
RJ1102'STATION ON THE LEFT NEAR THE NORTHWEST CORNER OF THE BRIDGE.
RJ1102'
RJ1102'STATION MARKS ARE STANDARD DISKS STAMPED OVERPASS 1965. THE
RJ1102'SURFACE DISK IS
RJ1102'SET IN A ROUND CONCRETE MONUMENT WHICH IS FLUSH WITH
RJ1102'WITH THE SURFACE OF THE GROUND.
RJ1102'TT IS 213 FEET WEST OF THE CENTER OF
RJ1102'THE SOUTH BOUND LANE OF INTERSTATE 75, 173 FEET
O.T 1 '9T' TIT.WF.cT.. OF A FENCE
RJ1102'CORNER, 133 FEET SOUTH OF A WIRE FENCE, AND 91 FEET NOKTHEAST OF
RJ1102'THE NORTHWEST
RJ1102'CORNER OF THE BRIDGE. THE UNDERGROUND DISK IS SET IN AN
RJ1102'IRREGULAR MASS OF CONCRETE
RJ1102'44 INCHES BELOW THE SURFACE OF THE GROUND.
RJ1102'
RJ1102'REFERENCE MARK NO. 1, A STANDARD DISK STAMPED OVERPASS NO 1 1965,
RJ1102'CEMENTED IN A
RJ1102'DRILLED HOLE IN THE NORTH END OF THE 3RD CONCRETE FOOTING
RJ1102'EAST OF THE WEST END OF THE
RJ1102'BRIDGE. THE FOOTING PROJECTS 30 INCHES.
RJ1102 '
RJ1102'REFERENCE MARK NO. 2, A STANDARD DISK STAMPED OVERPASS NO 2 1965,
RJ1102'CEMENTED IN A
RJ1102'DRILLED HOLE IN THE NORTH END OF THE 1ST CONCRETE FOOTING
RJ1102'EAST OF THE WEST END OF THE
RJ1102'BRIDGE. THE FOOTING PROJECTS 14 INCHES.
RJ1102 '
RJ1102'AZIMUTH MARK, A STANDARD DISK STAMPED OVERPASS 1965, IS SET IN A
RJ1102 'ROUND CONCRETE
RJ1102'MONUMENT WHICH PROJECTS 4 INCHES. IT IS 57 FEET SOUTH
RJ1102'OF THE CENTER OF STATE HIGHWAY
RJ1102'48, 32 FEET WEST OF THE CENTER OF A
RJ1102'GRAVELED ROAD, 3 FEET NORTH OF A TELEPHONE POLE,
RJ1102'AND 2 FEET SOUTH OF A
RJ1102'METAL WITNESS POST.
*** retrieval complete.
Elapsed Time = 00:00:02
E4
The NGS Data Sheet
DATABASE = Sybase,PROGRAM = datasheet, VERSION = 5.21
Retrieval Date = MAY 5, 1997 Version = 5.21
Starting Datasheet Retrieval...
1 National Geodetic Survey, Retrieval Date = MAY 5, 1997
RJ0241 ***********************************************************************
RJ0241 DESIGNATION 
RJ0241 PID
RJ0241 STATE/COUNTYRJ0241 USGS QUAD
RJ0241
RJ0241
RJ0241
RJ0241* NAD 83(1994)RJ0241* NAVD 88 
RJ0241
RJ0241 X
RJ0241 Y
RJ0241 Z
RJ0241 LAPLACE CORRRJ0241 ELLIP HEIGHTRJ0241 GEOID HEIGHTRJ0241 DYNAMIC HT 
RJ0241 MODELED GRAVRJ0241
RJ0241 HORZ ORDER 
RJ0241 VERT ORDER 
RJ0241 ELLP ORDER 
RJ0241
RJ0241
RJ0241
T 44
RJ0241
MI/CHIPPEWA
SULLIVAN CREEK (1978)
*CURRENT SURVEY CONTROL
46 21 32.17537(N) 084 50 44.39915(W) ADJUSTED
280.746 (meters) 921.08 (feet) ADJUSTED
396.162.391 (meters) COMP
4,391,871.074
4,593,049.896
5.88
244.86
35.89
280.758
980,650.3
(meters)
(meters)
(seconds)
(meters)
(meters)
(meters)
(mgal)
COMP
COMP
DEFLEC96
GPS OBS
GEOID96
921.12 (feet) COMP
NAVD 88
FIRST
FIRST
FOURTH
CLASS II
CLASS I
RJ0241.The horizontal coordinates were established by GPS observations
RJ0241.and adjusted by the National Geodetic Survey in February 1997.
RJ0241
RJ0241.The orthometric height was determined by differential leveling
RJ0241.and adjusted by the National Geodetic Survey in June 1991.
RJ0241
RJ0241.The X, Y, and Z were computed from the position and the ellipsoidal ht.
RJ0241
RJ0241.The Laplace correction was computed from DEFLEC96 derived deflections.
RJ0241
RJ0241.The ellipsoidal height was determined by GPS observations
RJ0241.and is referenced to NAD 83.
RJ0241
RJ0241.The geoid height was determined by GEOID96.
RJ0241
RJ0241.The dynamic height is computed by dividing the NAVD 88
RJ0241.geopotential number by the normal gravity value computed on the
RJ0241.Geodetic Reference System of 1980 (GRS 80) ellipsoid at 45
RJ0241.degrees latitude (G = 980.6199 gals.).
RJ0241
RJ0241.The modeled gravity was interpolated from observed gravity values.
RJ0241
RJ0241; North East Units Scale Converg.
RJ0241;SPC MI N  177,371.816 8,165,763.023 MT 0.99990366 +1 33 25.7
RJ0241;UTM 16  5,136,184.510 665,731.283 MT 0.99993764 +1 33 33.8
RJ0241
RJ0241 SUPERSEDED SURVEY CONTROL
RJ0241
ES5
RJ0241 NAD 83(1986) 46 21 32.16828(N) 084 50 44.39628(W) ADJUSTED
RJ0241 NGVD 29  280.702 (meters) 920.94 (feet) ADJ UNCH
RJ0241
RJ0241.Superseded values are not recommended for survey control.
RJ0241.NGS no longer adjusts projects to the NAD 27 or NGVD 29 datums.
RJ0241.See file format.dat to determine how the superseded data were derived.
RJ0241
RJ0241_MARKER: DB = BENCH MARK DISK
RJ0241_SETTING: 7 = SET IN TOP OF CONCRETE MONUMENT (ROUND)
RJ0241_STAMPING: T 44 1934
RJ0241_STABILITY: C = MAY HOLD, BUT OF TYPE COMMONLY SUBJECT TO
RJ0241+STABILITY: SURFACE MOTION
RJ0241_SATELLITE: THE SITE LOCATION WAS REPORTED AS SUITABLE FOR
RJ0241+SATELLITE: SATELLITE OBSERVATIONS  May 01, 1991
RJ0241
RJ0241 HISTORY  Date Condition Recov. By
RJ0241 HISTORY  1934 MONUMENTED CGS
RJ0241 HISTORY  1935 GOOD NGS
RJ0241 HISTORY  1988 GOOD USE.RC241 HISTORY  19910501 GOOD NOS
RJ0241
RJ0241 STATION DESCRIPTION
RJ0241
RJ0241'DESCRIBED BY NATIONAL GEODETIC SURVEY 1935
RJ0241'5.9 MI E FROM STRONGS.
RJ0241'5.9 MILES EAST ALONG THE DULUTH, SOUTH SHORE AND ATLANTIC
RJ0241'RAILWAY FROM STRONGS, CHIPPEWA COUNTY, 5 FEET SOUTH OF MILEPOST
RJ0241'26, AND 20 FEET NORTH OF THE TRACK. A STANDARD DISK, STAMPED
RJ0241'T 44 1934 AND SET IN THE TOP OF A CONCRETE POST.
RJ0241
RJ0241  STATION RECOVERY (1988)
RJ0241
RJ0241'RECOVERY NOTE BY US ENGINEERS 1988 (RAB)
RJ0241'THE STATION IS LOCATED ABOUT 5.9 MILE EAST OF STRONGS MICHIGAN.
RJ0241'
RJ0241'TO REACH THE STATION FROM STRONGS MICHIGAN, GO EAST FOR 9.5 KM
RJ0241'(5.9 MI) ALONG M28 TO STATION LOCATED 6 METERS (20 FEET) NORTH OF
RJ0241'ABANDONED RAILROAD GRADE WHICH IS ALONG NORTH SIDE OF HIGHWAY M28.
RJ0241
RJ0241 STATION RECOVERY (1991)
RJ0241
RJ0241'RECOVERY NOTE BY NATIONAL OCEAN SURVEY 1991
RJ0241'RECOVERED IN GOOD CONDITION.
*** retrieval complete.
Elapsed Time = 00:00:02