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Variability of microwave backscatter from loblolly pine forest and the implications for forest biomass estimation with imaging radar

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UNIVERSITY OF C A LIFO R N IA
Santa Barbara
Variability o f Microwave Backscatter from Loblolly Pine Forest and
the Implications for Forest Biomass Estimation with Imaging Radar
A D issertation submitted in partial satisfaction
o f the requirements for the degree o f
Doctor of Philosophy
in
Geography
by
John Lawrence Day
Committee in charge:
Professor Frank W . Davis, Chairperson
Professor John M . M elack
Professor D ar A . Roberts
D r. Jack F. Paris
June 1999
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UMI Num ber 9956149
___
A
UMI
UMI Microform9956149
Copyright 2000 by Bell & Howell Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
Bell & Howell Information and Learning Company
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P.O. Box 1346
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T he dissertation o f John Law rence Day is approved
C om m ittee Chairperson
A pril 1999
ii
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April 2, 1999
Copyright by
John Law rence Day
1999
iii
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Acknowledgements
First and foremost, I am grateful to my advisor, Frank Davis, for his patient support
and helpful prodding, and to all of my committee for their many valuable suggestions
over the five years of my doctoral studies. I also acknowledge Dave Simonett, and
though he died before I completed my M.A. degree, he was the magnet that drew me to
U.C.S.B. and into the Geography Department graduate program. I have benefited greatly
from an extended, and sometimes intensive, collaboration with Yong Wang (now at East
Carolina University). His help with the Chapter 4 modeling work is deeply appreciated.
I am grateful to Laura Hess for support and valuable discussions; on many occasions her
feet were on the ground when mine were not. I wish to thank Eric Kasischke, Pete Har­
rell, and Laura Bourgeau-Chavez for their help with field logistics, stand data, and
laboratory support for work in Duke Forest. Many thanks to Jose-Luis Saleta for his
unflagging assistance in Duke Forest, to Jim Wallace who has kindly given permission to
use his excellent photos (Chapter 3), and to volunteers from Riverside High School for
their enthusistic field support. Thanks also to Chris Pyke for assistance registering digital
stand maps, Mike Colee for help with DEMs, and J.C. Shi, Tom Albright and Tom
Painter for sharing their methods for SAR rectification. Many other colleagues and staff
at U.C.S.B., J.P.L., and elsewhere have facilitated this work and accommodated me in
various ways, and their help is appreciated. I would like to thank Landmark Education
for their Forum seminar program, which enabled me to see the possibility of carrying the
dissertation through to completion. Finally, thank you, Ann-Marie for your encourage­
ment, involvement, and support on many levels. This research was funded in large part
by the NASA SIR-C/X-SAR project through JPL under contract # 958468.
iv
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Dedication
I dedicate this work to Ann-M arie,
my dear companion and soon-to-be wife,
champion o f the psyche,
nurturer o f dreams,
purveyor o f poetry and beauty,
wellspring o f wisdom,
w ho has shown me previously unim agined ways
o f seeing, understanding and being.
I love you.
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VITA
June 10, 1948
Bom— Oakland, California
1976
B. S., Conservation o f Natural Resources, University of California,
Berkeley
1988-93
Teaching Assistant and Research Assistant, Dept, o f Geography,
University o f California, Santa Barbara
1993
M. A., Geography, University o f California, Santa Barbara
1994-99
Research Assistant, Institute for Computational Earth System Science,
University of California, Santa Barbara
PUBLICATIONS
Day, J. L., and F. W . Davis, 1992, SAR backscatter from coniferous forest gaps, Third
Annual JPL Airborne Geoscience Workshop, June, 1992, Pasadena, Calif.
Wang, Y., J. L. Day, and G. Sun, 1993, Santa Barbara microwave backscattering model
for woodlands, Int. J. Remote Sens., vol. 14, no. 8, pp. 1477-1493.
Wang, Y., J. L. Day, F. W. Davis, and J. M. Melack, 1993, Modeling L-band radar
backscatter of Alaskan Boreal forest, IEEE Trans, on Geosci. Remote Sens., vol. 31,
no. 6, pp. 1146-1154.
Day, J. L., 1993, Imaging coniferous forest gaps with synthetic aperture radar, M_A.
thesis, University of California, Santa Barbara.
Day, J. L., and F. W . Davis, 1996, Variations in SIR-C backscatter in Duke Forest, SIRCfX-SAR Science Team Meetings, Santa Barbara, Feb. 13-15, 1996.
Wang, Y., J. L. Day, and F. W. Davis, 1996, Sensitivity of Modeled C-band Backscatter
from Loblolly Pine Forests to Surface Soil Roughness and Moisture, Proceedings o f
IGARSS, Lawrence Kansas.
Wang, Y., J. L. Day, and F. W. Davis, 1998, Sensitivity o f modeled C- and L-band radar
backscatter to ground surface parameters in loblolly pine forest, Remote Sens.
Environ., vol. 66, pp. 331-342.
FIELD o f STUDY
Remote sensing of vegetation, with emphasis on radar sensing of forest.
Professors: David S. Simonett, Frank W. Davis and Jack F. Paris
PROFESSIONAL AFFILIATIONS
Institute of Electrical and Electronics Engineers (IEEE), Student Member since 1990
VI
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Abstract
Variability o f Microwave Backscatter from Loblolly Pine Forest and
the Implications for Forest Biomass Estimation with Imaging Radar
by
John Lawrence Day
The microwave backscatter coefficient (sigma-O) of forest, as measured by imaging
radar, varies depending on forest structure and biomass. It may, therefore, be possible to
estimate forest biomass and other biophysical properties from radar data. Sigma-0 also
varies in response to other forest and radar variables, including ground surface roughness
and moisture, forest phenology and radar calibration.
These extraneous sources of
sigma-0 variation can interfere with biomass estimation. In this dissertation, I examine
variability of sigma-0 for loblolly pine stands in Duke Forest, North Carolina, and assess
the impact of variability on accuracy o f biomass estimation.
A microwave canopy backscatter model was used to study how sigma-0 of a forest
changes as forest floor properties vary. L- and C-band backscatter was simulated at 3
polarizations and 3 radar incidence angles for pine stands at 3 biomass levels, while 5
ground surface parameters were varied over a range of realistic values, as determined
from field data. The surface parameters are litter depth and moisture content, soil RMS
height and correlation length, and soil moisture content. For incidence angles of 20-40
deg., L-HH varied by 5.3-9.6 dB as the surface parameters varied over their range,
whereas L - W varied by 3.7-4.5 dB. C-HH and C-VV were sensitive to the surface only
at steep incidence (20-30 deg.) for the lowest biomass stand studied. L-HV and C-HV
were relatively insensitive to the surface.
Variation of actual, measured sigma-0 was examined for C- and L-band backscatter
acquired over 21 loblolly stands in the biomass range of 3.5-44.5 kg/m2 during 10 passes
of NASA’s Shuttle Imaging Radar in April and October, 1994. Within any radar bandvii
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polarization combination and data take, the maximum sigma-0 range among the stands
was 3.6 dB; in most cases it was 2-3 dB. RMS variation of mean forest sigma-0 for the
10 data takes (after correcting for incidence angle) was 0.4-0.7 dB, which is comparable
to the standard deviation of sigma-0 among the 21 stands. Sigma-0 increased =1 dB
when the canopy was wet, but variation o f sigma-0 with surface moisture was not separ­
able from other factors. Biomass to sigma-0 correlations were affected by radar look
direction and appear unrelated to incidence angle or soil moisture. Multiple linear regres­
sions of biomass versus sigma-0 (adjusted to equalize mean forest sigma-0 among data
takes), yielded adjusted R-squared values up to 0.57. The regression models varied, the
best model for each data take requiring a different combination of SIR-C bands. RMS
error of biomass estimation decreased with the number of bands included in the model
for estimates based on the regression data, but increased with the number o f bands
included for estimates made from data acquired in different shuttle passes. Analysis of
the propagation of sigma-0 variance through the linear regression models confirms that
estimation error increases with model size and sigma-0 variability.
viii
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Table o f Contents
Chapter I: Introduction and background literature review -------------------------------------------
I
1. Introduction ______________________________________________________________
I
2. Problem statement: research questions--------------------------------------------------------------
4
3. Overview of dissertation ____________________________________________________
5
4. Definitions _______________________________________________________________
6
5. Background______________________________________________________________
8
5.1. Estimation of biomass and other forest properties from backscatter -------------------
8
5.2. Variation and fluctuation in microwave backscatter from forest -----------------------
13
6. References ___
22
Chapter 2: An overview of the Duke Forest loblolly pine stands
and estimation of stand characteristics -----------------------------------------------------
29
1. Introduction and background ________________________________________________
29
2. Uncertainty in estimates of stand biom ass---------------------------------------------------------
31
3. Grouping stands by age and biom ass---------------------------------------------------------------
32
4. Duke Forest fieldwork during the first SIR-C m ission------------------------------------------
34
4.1. Overview ____________________________________________________________
34
4.2. Litter depth and volumetric moisture ---------------------------------------------------
35
4 3 . Soil moisture _________________________________________________________
36
4.4. L-band soil dielectric constant ------------------------------------------------------------------
36
4.5. L-band soil dielectric constant versus volumetric soil moisture ..............
37
4.6. Tree dielectric constant at L-band -------------------------------------------------------------
37
5. Summary of key forest attributes and results ------------
38
6. References _____________________________________________________
39
Chapter 3: Forest floor surface roughness measurements in a loblolly pine forest ------------
50
1. Introduction ____________________________________
50
2. M ethodology_____________________________________________________________
51
ix
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2.1. Study Site Description ----------------------------------------------------------------------------
51
2.2. Defining Forest Floor Surface Roughness ----------------------------------------------------
52
23. Surface Roughness Gauge Design and U s e _________________________________
54
2.4. Field Measurements ____________________________________________________
57
23. Estimation of RMS Height and Correlation Length __________________________
57
3. Results ___________________________________________________________________
58
4. Conclusions _______________________________________________________________
59
5. References _________________________________________________________
59
Chapter 4: Sensitivity o f modeled C- and L-band microwave backscatter
to ground surface parameters in loblolly pine forest ________________________
69
1. Introduction _______________________________________________________________
70
2. Study area and m ethods_____________________________________________________
73
2.1. Ground d a ta ___________________________________________________________
73
2.2. Backscatter modeling o f loblolly forest--------------------------------------------------
76
23. Modeling the scattering from forest floor litter______________________________
77
2.4. Model simulations and modeled sensitivity ---------------------------------------------------
78
3. Results ___________________________________________________________________
80
3.1. Modeled sensitivity of C- and L-band backscatter to soil surface
and litter conditions ____________________________________________________
80
33. Comparative sensitivity o f modeled backscatter to individual soil surface
and litter parameters ____________________________________________________
81
4. Discussion________________________________________________________________
83
4.1. Patterns of sensitivity observed-----------------------------------------------------------------
83
43. Significance and limitations ---------------------------------------------------------------------
84
4.3. Relation o f backscatter-biomass correlation to surface moisture sensitivity ----------
86
5. Concluding remarks ________________________________________________________
89
6. References ______________________________________________
90
Chapter 5: Microwave backscatter from Duke Forest loblolly pines:
An analysis of the SIR-C data and its use in forest biomass estimation ------------
104
1. Introduction _______________________________________________________________
105
2. Study area and m ethods_____________________________________________________
109
2.1. Loblolly forest stand d a ta ..........................................
x
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109
2.2. SIR-C Data and Processing --------------------------------------------------------------------
111
23. Methods of Analysis ____________________________________________________
117
3. Results ___________________________________________________________________
127
3.1. Overview of backscatter characteristics-------------------------------------------------------
127
33. Correlation of SAR data to estimated forest characteristics____________________
128
33. Differences in O0 due to incidence angle ----------------------------------------------------
129
3.4. Differences in o° due to moisture and phenologic changes ----------------------------
130
33. Biomass - <J° regression re su lts -----------------------------------------------------------------
132
3.6. Error propagation in the regression m odels------------------------------------------------
135
4. D iscussion________________________________________________________________
137
4.1. Variability of <J°_______________________________________________________
137
4.2. Biomass estimation e rr o r ________________________________________________
138
4.3. Which biomass-c0 regression model? --------------------------------------------------------
140
5. Conclusions _______________________________
141
6. References ___ :____________________________________________________________
143
Chapter 6: Concluding remarks ----------------------------------------------------------------------------
178
Appendix I:
Mean and coefficient of variation of SIR-C o° for 21 pinesta n d s---------------
182
Appendix II:
Median and lower quartile of SIR-C <J° for 21 pine stands-----------------------
202
Appendix III: Decomposition of backscatter for 21 loblolly stan d s.........................................
222
Appendix IV: Correlation between backscatter and loblolly forest measures ------------------
240
xi
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List o f Tables
Chapter 2
Table I. Litter Depth and Volumetric Moisture, by S ta n d -------------------------------------------
41
Table 2. Litter Volumetric Moisture, by D a te ----------------------------------------------------------
41
Table 3. Litter Moisture Summary Statistics ------------------------------------------------------------
41
Table 4. Soil Moisture Measured for Moist and Wet Conditions ______________________
42
Table 5. L-band Dielectric Constant for Moist and Wet Soil__________________________
42
Table 6. Summary of L-band Dielectric Constants for 12 Trees _______________________
42
Chapter 3
Table 1. Loblolly pine stand d a ta _________________________________________________
63
Table 2. RMS height and correlation length summary statistics ___________________
63
Chapter 4
Table I. Characteristics of 3 loblolly pine stands, Duke Forest, NC ____________________
93
Table 2. Measured soil volumetric moisture content (%) for 6 loblolly pine stands ----------
94
Table 3. Measured soil surface roughness parameters for 6 loblolly pine stands --------------
95
Table 4. Measured vol. moisture content (%) of litter layer for 6 loblolly pine stands
96
Table 5. Measured litter layer depths (cm) for 6 loblolly pine stands .....................................
97
Table 6. Simulated maximum range o f C- and L-band total backscatter (dB)
over the modeled 5-D surface parameter sp ace ---------------------------------------------
98
Table 1. Simulated maximum range o f C-HH and C - W total backscatter (dB)
for each soil surface and litter parameter over the modeled region --------------------
99
Table 8. Simulated maximum range o f L-HH and L - W total backscatter (dB)
for each soil surface and litter parameter over the modeled region --------------------
100
Table 9. Simulated maximum range o f L-HV total backscatter (dB)
for each soil surface and litter parameter over the modeled region ......
101
Chapter 5
Table 1. Measured loblolly stand biophysical characteristics
.......................................
149
Table 2. Summary of SIR-C data acquisitions for Duke Forest, North Carolina --------------
150
Table 3. Processed SIR-C data output bands _______________________________________
151
Table 4. a 0 range (dB) for 21 Duke Forest loblolly stands-----------------------------------------
152
Table 5. Median o° (dB) for 21 Duke Forest loblolly stands---------------------------------------
152
Table 6. Correlations (r) of mean a 0 vs. biomass ..........
153
xii
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Table 7. Models of o° to incidence relation ------------------------------------------------------------
154
Table 8. RMS deviation from cosine law (10 DT’s), compared to standard deviation of
o° stands in each DT, averaged over the 10 the DT’s ________________________
154
Table 9. Modeled o° difference (April-October) for three representative stands __________
155
Table 10. SIR-C a 0 difference (April-October) for three age/biomass g ro u p s____________
155
Table 11. Best weighted least squares regressions of biomass vs. o°
for the 10 Duke SIR-C data takes, based on maximum adjusted R2 -----------------
156
Table 12. Adjusted R2 for weighted regressions of biomass vs. <r° -------------------------------
157
xiii
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List of Figures
C h ap ter 2
Fig. 1 Duke
Forest Stand 68 (8 years old, total biomass =3.6 kg/m2) -------------------------
43
Fig. 2 Duke
Forest Stand 51 (=20 years old, biomass n/a) _________________________
44
Fig. 3 Duke
Forest Stand 44 (60 years old, total biomass =31.8 kg/m2) ---------------------
45
Fig. 4 Duke
Forest Stand 43 (=90 years old, biomass n/a) --------------------------------------
46
Fig. 5 Cumulative total biomass of Ioblloly pine stands vs. dbh -----------------------------------
47
Fig. 6 Cumulative crown biomass o f Ioblloly pine stands vs. d b h ---------------------------------
48
Fig. 7 L-band diel. const, vs. soil moisture showing linear and empirical models ------------
49
C h ap ter 3
Fig. 1 Removing forest litter along a surface roughness transect-----------------------------------
64
Fig. 2 Recording a surface profile using the surface roughness gauge ----------------------------
65
Fig. 3 Resetting the SRG pins ------------------------------------------------------------------------------
66
Fig. 4
Autocorrelation function as a function of surface displacem ent---------------------------
67
Fig. 5
RMS height vs. correlation length of 4 loblolly pine age groups -------------------------
68
C h ap ter 4
Fig. 1 Santa Barbara microwave canopy backscatter m odel-----------------------------------------
102
Fig. 2 A close-up view of modeled surface scattering_________________:---------------------
103
C h ap ter 5
Fig. I Digital orthophoto of Duke Forest Durham Division showing stand outlines ----------
158
Fig. 2
Color composite SIR-C image (DT# 113a) of Duke Forest Durham D ivision...........
159
K g. 3
Color composite SIR-C image (DT# 49o) of Duke Forest Durham D ivision
.....
160
Fig. 4a C-band Sigma-0, mean (+/- 1 sd) o f 21 Duke Stands --------------------------------------
161
Fig. 4b L-band Sigma-0, mean (+/- I sd) o f 21 Duke Stands --------------------------------------
162
Fig. 5 Sigma-O-biomass correlations vs. 0O, April and October data takes identified----------
163
Fig. 6 Sigma-O-biomass correlations vs. So, N- and S-looking data takes identified ----------
164
Fig. 7 Examples of Sigma-0 vs. Biomass, with least squares lin e s ---------------------------------
165
Eng. 8a
October Mean Sigma-0 with cosine law fitted curves, C -band ---------------------------
166
Fig. 8b
October Mean Sigma-0 with cosine law fitted curves, L -b an d ---------------------------
167
Eng. 9a C-band Sigma-0 for 10 data takes,
with Oct. cos law c u rv e s---------------------
168
Fig. 9b L-band Sigma-0 for 10 data takes,
with Oct. cos law curves ---------------------
169
Eng. 10 Regression-estimated vs. field-measured biomass .......
xiv
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170
Fig. 11 Effect o f model size on biomass estimation e rro r -------------------------------------------
171
Fig. 12 Effects of model size on biomass estimation for subsets
o f data takes -------------
172
Fig. 13 Mean error in predicted biomass propagated________________________________
173
Fig. 14 Distribution of propagated biomass error among 10 dt’s ----------------------------------
174
Fig. 15 Propagated
error for Lowland ConiferModel ------------------------------------------
175
Fig. 16 Propagated
error for Jack Pine M odel__________________________________
176
Fig. 17 Propagated
error for Red Pine Model-----------------------------------------------------
177
xv
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1
Chapter 1:
Introduction and background literature review
1. Introduction
The possibility of using spacebome imaging radar to estimate forest biomass at
regional to global scales has been with us since the mid 1980s, when researchers began
to observe correlations between radar backscattering coefficient (a0) and forest biomass
(Wu, 1987; Sader, 1987; Westman and Paris, 1987; Simonett et al., 1987a).
In many respects, SAR is well-suited to the task. The capability of microwaves to
penetrate cloud cover give SAR an advantage over other sensors, especially in equatorial
and high latitude regions, and SAR’s independence from solar illumination is useful at
high latitudes. Radar responds to water content and geometrical form, and consequently,
is sensitive to forest architecture and to woody and foliar forest components. The ability
of longer wavelengths (L- and P-bands) to penetrate through the canopy partially over­
comes signal saturation which limits forest sensing at optical wavelengths. Canopy pene­
tration allows the microwaves to interact with large branches and trunks that constitute
the bulk of aboveground biomass.
Different radar wavelengths, polarizations, and
incidence angles create different interactions of the microwaves with the forest and
ground, depending on the size, shape, orientation and roughness of tree components and
forest floor. Given so many dimensions of information, it might be possible to decipher
the forest signature and retrieve considerable detail on forest composition, structure, and
biomass distribution, information that is invaluable not only for biomass appraisal, but as
input to ecosystem models and climate models. In addition, because SAR data is pro­
cessed into 2-dimensional images, it has a natural extension to mapping. Several alterna­
tive sensing systems (e.g., airborne lasers and radar profilers) produce transects.
While
these systems have local and regional applications and could be valuable as part o f a
multi-scale sampling strategy, they would be impractical for global forest survey.
At the beginning of NASA’s Shuttle Imaging Radar C (SIR-C) program, enough
evidence had emerged from scatterometry studies and microwave backscatter modeling
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work then in progress for some researchers to envision direct inversion o f forest back­
scatter models to estimate forest characteristics (Zoughi et al., 1986; Hoekman, 1987;
Westman and Paris, 1987; Pitts et al., 1988; Richards et al., 1987; Simonett et al., 1987a;
and Ulaby et al., 1988). For example, one objective o f the SIR-C proposal that has par­
tially funded this dissertation work was to "Develop and Evaluate an inversion procedure
through which the above-ground forest biomass, partitioning, patchiness, and spatial and
height distributions within a stand can be estimated from multi-wavelength, multi­
polarization, multi-incidence angle and multi-date SAR images,..." (Simonett et al.,
1987b). Other SIR-C proposals sought to "... develop model inversion strategies for
selected ecosystem model input parameters" (Ranson, et al., 1989), and "... evaluate the
performance of retrieval techniques derived from inversions of the MIMICS model”
(Ulaby et al., 1989).
To retrieve forest properties by inverting physically based
microwave scattering models is an appealing approach, because, unlike empirical descrip­
tions, physical explanations explicitly characterize the linkages between forest parameters
and SAR-based estimates of them.
As of 1997, the biomass retrieval story has changed. The possibility o f direct inver­
sion appears to have faded. As one review explained, "Because of their complexity,
however, these models cannot be inverted to estimate surface and canopy characteristics
needed to study specific ecological features or processes. The value of these models lies
in their utility to better understand the dependence o f microwave scattering on system and
imaging parameters..." (Kasischke et al., 1997). This statement is hardly premature.
During the past decade, almost ail SAR-based estimation of actual forest properties has
utilized regression or neural network techniques. Backscatter model inversions have been
carried out, but only on highly simplified model-generated forest data, not real forests
(Polatin et al., 1994).
The reasons for the shift of methodology are readily understood. The forest
microwave scattering problem is extremely complicated even for an idealized forest, mak­
ing inversion technically difficult or intractable. Perhaps more importantly, in real forest,
the biotic complexity is too extreme to get all the details right, unless a great deal is
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3
known about the forest and its state. Conceivably, backscatter could be modeled with
high accuracy in very well studied test sites, but one does not find in the literature any
modeling studies in which backscatter predictions approach the < 0.5 dB level o f accu­
racy that may be necessary for biomass estimation (see Chapter 5). To solve the inverse
problem o f extracting the desired forest properties in the presence o f large variation is not
feasible. In a discussion of "reasons for indeterminacy in biology," Ernst Mayr quotes
physicist Elasser, "[An] outstanding feature of all organisms is their well-nigh unlimited
structure and dynamical complexity" (Mayr, 1988). The retreat of modelers toward
empiricism attests to this complexity.
hi the realm o f measurements, microwave backscatter from forest must be classified
as indirect. It condenses the many dimensioned forest variability into a few channels.
Forest properties that can be directly measured on the ground (such as tree height), as
well as more abstract ones (such as biomass), bear some complex relationship to back­
scatter that is conditioned by many factors that may be incidental to our study. Some
examples of these factors are soil surface roughness, thickness of the litter layer, moisture
on the leaves, water distribution in bunks, branches, leaves, etc. Thus, backscatter is a
response to an ensemble o f interrelated factors and not a measurement o f them, p e r se.
Contrast SAR imaging with near-nadir looking airborne profiling radar. The latter sam­
ples a transect, registering reflections off the ground surface and tree tops, the difference
in distance being an estimate of tree height. Not many forest or environmental factors can
interfere with this direct measurement, hi the case o f SAR, however, any number o f fac­
tors condition the backscatter, leading to potentially large and unknown uncertainty in
estimates of a 0 and derived forest properties.
As I view the current situation in SAR forest research, there are a large number of
variables that may influence forest backscatter and few of them are well quantified (see
§5.2, below). While much is known from sensitivity studies about backscatter trends in
response to certain forest parameters, far less is known about the ramifications o f actual
forest variations and fluctuations for the practical estimation of biomass and other forest
properties.
There is a gulf between the study of forest microwave backscatter and
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4
practical applications.
2. Problem statement: research questions
As will become apparent in the background presented below, estimating forest
biophysical attributes from SAR data entails extracting a < 3 dB signal in the presence of
numerous sources of variability that may lead to o° uncertainty in excess o f 3 dB. At
stake is development o f practical methods for SAR biomass retrieval at regional to global
scales. Methods that require intensive "ground tmthing" worldwide will not serve the
purpose. The ideal method would minimize the need for field survey and maximize
robustness to sources of variability. Even if calibration uncertainty o f future SARs is
reduced well below 0.5 dB, and even if large numbers of data takes can be acquired,
registered, and combined (as is being done with multitemporal AVHRR imagery), the
problem of multiple sources of variability will persist. There is a need for studies that
seek to identify radar bands, models and methods that are minimally sensitive to extrane­
ous variables.
Having offered this rationale, my generalized research questions are clear:
1)
Which SAR bands are least sensitive to variations and fluctuations that mask the
response of forest biophysical attributes of interest?
2)
How large are the forest variations and how large are the resulting o° variations
(for different radar bands, incidence angles, and forest biomass levels)?
3)
How accurate are biomass predictions by regression models when the models are
applied to data takes other than the one used to generate the model?
4)
How does the model itself affect propagation of forest variability into uncertainty
of forest attribute estimation?
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5
3. Overview of dissertation
Acknowledging that these questions arise in the context of an ongoing inquiry in an
evolving field, and recognizing that they are not going to be answered by a single indivi­
dual, I have focused on several sub-problems for this dissertation.
In Chapter 2, I describe the Duke Forest loblolly pine stands that are used
throughout the dissertation. I describe the forest survey data provided by researchers at
Duke University and outline the field measurements made in the loblolly stands, con­
current with the SIR-C mission in April, 1994. In this field trip, I characterized soil
moisture and roughness, and litter layer attributes, for the purpose o f modeling the
influence of their variability on backscatter. In Chapter 3, I describe the soil surface
roughness study in detail.
Chapter 4 represents the recently published results o f my 3-year collaboration with
Yong Wang (of East Carolina University, Greenville, N.C.). In this study, w e model
backscatter from loblolly stands at three levels of biomass and analyze variation in back­
scatter that results from varying volumetric soil moisture, litter moisture and depth, soil
surface RMS height and correlation length over their ranges of probable values, as deter­
mined from the field survey. The sensitivity of backscatter to these parameters (taken
individually and together) is determined at C- and L-bands, 3 polarizations, and over a
range of incidence angles.
Chapter 5 is an analysis of the 10 SIR-C data takes acquired over Duke Forest in
April and October, 1994. I examine o° variability in relation to incidence angle and
moisture using graphical and statistical analyses, and model comparisons. Correlation and
linear multiple regression analyses are done to determine which forest parameters and
SAR bands yield the best biomass estimates. Then, to test how robust the regression
models are, each regression model is used to estimate biomass from data takes other than
the one that generated it. Finally, I examine the error propagation properties o f the linear
regression models and compare propagated error to three other models.
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Following brief concluding remarks in the final chapter, I include appendices con­
taining a complete summary o f the SIR-C data for 21 loblolly stands, upon which
Chapter 5 is based. Also included are tables of correlation of several backscatter meas­
ures to the available forest biophysical measures.
4. Definitions
It is useful at this point to define and clarify some of the more important terms used
throughout the dissertation.
Though several distinct types o f active microwave sensors (radars) are in use, this
dissertation is concerned mainly with synthetic aperture radar (SAR). SARs are airborne
or spacebome, side-looking, coherent imaging systems. NASA’s Shuttle Imaging Radar
systems (eg., SIR-C) are o f this type.
Radars operate at different microwave frequencies or wavelengths in conventionally
designated bands. The most commonly used bands for forest sensing applications are
summarized below (from Liliesand and Kiefer, 1987):
Table 1.
R ad ar bands for forest applications
Band designation
X
c
L
P
Wavelength (cm)
2.4 - 3.75
3.75 - 7.5
1 5 -3 0
3 0 - 100
Frequency (GHz)
12.5 - 8.0
8.0 - 4.0
2.0 - 1.0
1.0 - 0 3
Microwave penetration through forest canopy increases with wavelength, so that in a con­
tinuous canopy, X-band microwaves interact primarily with upper canopy elements (e.g.,
leaves, needles, and twigs), while L- and P-band microwaves may pass through the upper
canopy (with some attenuation) and interact with larger structures (branches, trunks, and
ground surface).
Radars are also characterized by polarization configuration. Radars in common use
transmit horizontally (H) or vertically-polarized (V) microwaves and receive either
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7
polarization, resulting in four possible linear polarizations o f backscatter HH and VV
(co-polarized), and HV and VH (cross-polarized). Because HV and VH are theoretically
equal (by "reciprocity"), they are often forced to be equal in the processing.
Backscatter is measured as radar "cross-section” in square meters. This scattering
"area" is equivalent to actual area only for a perfectly reflecting isotropic target. As a
result of forward scattering and absorption, most natural targets have cross-sections
smaller than their physical area, but in some cases the scattering geometry focuses energy
back toward the antenna, causing very bright returns. The backscatter coefficient (o°), is
backscatter cross-section normalized by actual horizontal pixel area. It is a fraction
describing the backscattered power compared to that of the incident field (Henderson and
Lewis, 1998). Units are m2/ m2, usually reported as unitless. The backscatter coefficient,
which is unity for a perfectly reflecting isotropic surface, can vary by many orders o f
magnitude depending on radar wavelength, polarization, and incidence angle, as well as
on the size, orientation, and dielectric properties of the target. For this reason o° is usu­
ally reported in decibels (dB), i.e., 10Iog10[a ° ]. In dB units, G° is zero for an isotropic
reflecting surface and negative for most natural targets, bare or vegetated. Strictly speak­
ing, o° is an attribute of the imaged scene, similar to reflectivity. In practice, however, it
commonly refers to the quantity measured with a radar and is more accurately termed
"measured cr°". Several other loosely worded phrases in common usage could lead to
some confusion. These include "radar backscatter," "forest backscatter," "ground surface
backscatter," and so forth. Where I use such terms in this dissertation as a convenient
short hand, the reader should understand that it is microwaves that are scattered, not the
radar, forest or ground (Jack Paris, pets, comm., 1999).
Microwave backscatter from forest, is composed of scattered and reflected waves
generated via various scattering mechanisms. The most commonly discussed mechan­
isms are direct scattering from the ground surface, volume scattering from the canopy,
and double-bounce specular reflections from antenna to ground to tree trunk and back to
the antenna. Thus, forest <y° is a composite quantity.
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Incidence angle (0O) (sometimes tenned "incident angle" to be grammatically pre­
cise), is the angle between a vertical line through the radar antenna and a ray drawn from
the antenna to a point imaged on the ground. Local incidence angle is the angle between
that ray and a normal drawn to the tangent plane o f the ground surface within the imaged
pixel. A "small" incidence angle (e.g., 20°) is one that is more vertical than a "large”
incidence angle (e.g. 65°). Because the terms "small" and "large" can leave the reader in
doubt as to the meaning, the visually descriptive terms "steep" and "shallow" may be
preferable.
The term biomass as used in this dissertation refers to total aboveground oven-dry
forest biomass, or more precisely average areal biomass density, unless otherwise stated.
The units are kg/ m2.
5. Background
5.1. Estimation of biomass and other forest properties from backscatter
Through the late 1980s and into the middle 1990s a number of empirical studies,
many of which were supported by backscatter modeling, confirmed that o° does depend
on biomass (see Kasischke et al., 1997, for a brief review). These studies also found, in
general, 1) o° increases with biomass, leading to "saturation" at relatively low biomass
levels (typically <15 kg/m2),
2) sensitivity is higher, and the saturation threshold also
higher, for longer wavelengths than shorter ones (P-band > L-band > C-band), and 3)
sensitivity varies with polarization, with HV most sensitive and W
least. In order to
reduce complications from variation in forest structure, many of these studies have been
carried out in uniform, monospecies, managed forests. To reduce complications from
fluctuations in forest state or SAR calibration, most studies are based on single radar
images.
Some highlights of this work are as follows:
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9
1)
P-HV stands out as the most useful single band for forest biomass retrieval (Dobson
et al., 1992; LeToan et al., 1992; Beaudoin et al., 1994; Ranson and Sun, 1994; Rignot et al., 1994). P-HV has been demonstrated to predict biomass accurately for
biomass levels below about 20 kg/m2 in coniferous forest and 10 kg/m2 in broadleaf
evergreen forest (Imhoff, 1995b); higher levels may be possible (Kasischke et al.,
1995; Rignot et al., 1995). Although, orbital P-band SARs might become feasible at
a future date (Rignot et al., 1995), none are planned a t present.
2)
In most studies, L-HV backscatter is moderately correlated to forest biomass, mean
tree height, and basal area (Sader, 1987; Wu, 1987; Hussin et al., 1991; Dobson et
al., 1992; LeToan et al., 1992; Beaudoin et al., 1994; Ranson and Sun, 1994; Rignot
et al., 1994; Kasischke et al., 1995; Wang et al., 1995a; Ranson et al., 1995). This
is not invariably the case (San Miguel-Ayanz, 1996).
In general, increases in
biomass are accompanied by increases in <Jl_hv f°r l°w biomass forest- Judging
from published scatter plots of (Xl-hv versus biomass, for most homogeneous coni­
ferous forests the signal saturates (in the sense that it ceases to have practical predic­
tive value) above biomass levels of about 4-10 kg/m2. In evergreen broadleaf
forests, saturation may occur at lower biomass levels (Imhoff, 1995b).
It is
estimated that saturation of c° limits the useful biomass sensing range at L-band to
perhaps as little as 7% of the total world vegetated area (or 19% based on a 10
kg/m2 saturation threshold) (Imhoff, 1995b).
3)
There is evidence that the cross-pol ratio
(Tl - h v ^ ° c -
hv
correlates more strongly to
biomass than does L-HV, resulting in somewhat higher saturation thresholds (Ranson
and Sun, 1994; Ranson et al., 1995). Regressions in log space, multiple regressions
using several or all of the available SAR bands, and multi-band indices may also
lead to better fits to the biophysical data than linear L-HV regressions (Wu, 1987;
Kasischke et al., 1995; San Miguel-Ayanz, 1996; Harrell et al., 1997), but do not
overcome the biomass saturation problem.
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10
4)
SAR response varies according to forest structural type. Dobson et al. (1992)
observed, "Radar scattering models of forests show backscatter to be dependent not
only on the quantity of biomass but also on the three-dimensional architecture o f the
forest (size, shape, and orientation distributions o f trunks, branches and foliage). As
a consequence, it is to be expected that inverse formulations seeking to retrieve esti­
mates of aboveground phytomass will be dependent on tree and/or forest structure."
Imhoff (1995a) demonstrated structural dependence by modeling forests that had
equivalent biomass, but represented a wide range o f structure types. He showed that
biomass does not map one-to-one into backscatter except within a structural type,
and therefore, unless one controls for structure, biomass cannot be unambiguously
determined from backscatter. Prediction o f biomass and other biophysical properties
improves when regressions are confined to forests that have homogeneous structure
and composition; the purer the forest, the stronger the regression (Dobson et al.,
1995b). Stronger biomass regressions have been obtained for even-aged plantations
and homogeneous forests than for less homogeneous ones.
5)
SAR responds to the geometric structure o f a forest as well as total biomass. Dobson
et al. (1995a), point out that linear correlation of o° to biomass is ill-posed because
biomass is not the true independent variable, but "a summation o f mass over the dis­
tribution of structural variates." Furthermore, "The structural properties are nonindependent and they are non-Iinearly related to o°." Within a given structural type,
trunk biomass is proportional to the product of stem density (s), the square o f dbh
(d), and height (h), that is, sd2h, whereas o° is proportional to s d h 2 (Dobson et
al., 1995b). It follows that "ambiguity can be reduced by direct inversion for the
primary structural attributes themselves."
It was argued, convincingly, that
"apparent” saturation of backscatter is attributable in part to the failure to estimate
the true independent variables (i.e., structural properties) and failure to control for
forest structure or account for it in the (linear) regressions. Empirical support for
these ideas comes from a neural network study o f backscatter from Duke forest lob­
lolly stands (Pierce et al., 1994). Estimates o f mean trunk diameter, tree height, and
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11
stem density of the stands were obtained using a neural network that, having been
trained on one NASA AirSAR data take, was then tested on another data take. Esti­
mation errors were low (2-12% on average), which may indicate that the relation o f
o° to forest structural parameters can be well captured in a non-linear representation.
Indirect biomass retrieval, in which structural properties are estimated from o°, and
biomass estimated alio metrically from those estimates, has been fairly successful in
several studies. Hussin et al. (1991) developed second-order regressions to predict basal
area and height from L-HV backscatter from slash pine plantations. Total above-ground
dry biomass was then derived from basal area and height using allometric relations.
Kasischke et al. (1995) used multiple linear regressions to predict total branch biomass
from C-, L-, and P-band quad-pol backscatter from loblolly pine stands. Total above­
ground dry biomass was estimated from branch biomass using allometric relations.
Dobson’s ideas on non-linearity and structural control o f backscatter were fully incor­
porated in a study to estimate Michigan hardwood and conifer forest biomass from SIR-C
backscatter (Dobson et al., 1995b). The method comprises three steps: 1) segment the
image into structurally homogeneous classes (may be done with SAR), 2) perform regres­
sions on each class separately, using non-linear models to estimate forest structural
parameters (tree height, basal area, and crown biomass), and 3) estimate biomass
allometrically from the structural parameter estimates. In this study, estimation accuracies
of structural parameters and biomass were higher when the image was segmented into
narrowly defined forest structural types, as compared to a broadly classified types. RMS
error for predicting the field-based allometric biomass estimates of stands ranging up to
=25 kg/m2 was 1.4 kg/m2. (This reported error appears low, considering that uncertainty
in field estimates of diameter, basal area, and density are given as 14%, 16%, and 21%.)
An interesting and useful aspect o f this approach is that the same allometry are used in
both field and SAR biomass estimates, and therefore, this source of error is factored out
of the biomass estimates.
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12
If this approach proves itself in other forests, then saturation may be overcome and
accurate SAR-based estimates o f biomass up to 25 kg/m2 might be realizable. However,
as noted by Dobson, "lateral and temporal extensibility" could be a problem. If it is
necessary to tailor the regression to a narrowly defined stand class in order to obtain
accurate biomass estimates, the regressions may fail to make good predictions in slightly
different forest, terrain, moisture conditions, SAR parameters, etc. The regressions that
generated the estimates o f structural parameters were obtained by "brute force", trying
[all possible combinations of] "single-channel and two-channel ratios (differences in dB)
using either a linear model, log-linear model, exponential, or Iog-Iog form" (Dobson,
pers. comm, 1995). Thus, there is no assurance the models are direcdy linked to the
structural parameters; rather, they reflect the entire ensemble of backscatter conditioning
factors, which may differ in the adjoining watershed. It is unsettling that the regression
models for height of three conifer types in Dobson et al. (1995b) are as different as the
following:
lowland conifers:
H = 1.162(<y°LVV—<y0cHV)-f-12.012
jack pine:
H =26.423 * l0-°-l92(a " "
red pine:
H =4.669 <J°LVV+ 71.53
The refinement of classification that was found necessary to estimate biomass accurately
in this study suggests that the ground-truthing to obtain the required forest parameters
and derive allometric relations may be too costly for practical applications, but this
depends to some degree on how extensible the method proves to be.
In a study of loblolly pine stands in Duke Forest (Harrell et al., 1997) accuracies of
biomass predictions obtained using the Kasischke method, the Dobson method, and direct
biomass to L-HV regression were found comparable to each other for October, 1994,
SIR-C data. Regression of biomass versus the L-HV/C-HV ratio regression led to lower
accuracy than the other 3 methods for biomass < 20 kg/m2 and higher accuracy than the
other methods for biomass > 20 kg/m2. Using April, 1994 SIR-C data, direct L-HV
regression yielded biomass estimation errors equal to or lower than the other methods.
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13
Judging from the scatter plots, none o f the methods accurately predict biomass above
about 10 kg/m2. The implementation o f Dobson’s method in this study did not include
non-linear regression models as used by Dobson. Thus, at this writing, it is an open
question whether the Dobson method is applicable to diverse forest types and data sets,
and whether or not it performs better in general than simpler regression methods.
5.2. Variation and fluctuation In microwave backscatter from forest
If the biomass signal embedded in backscatter were a strong one, small a 0 varia­
tions might be of little concern for biomass estimation. In the range o f 0-5 kg/m2 dry
biomass, strong o°-biomass relations have indeed been reported and may lead to valuable
applications in the study o f forest regeneration (eg., Luckman et al., 1997). In the Duke
Forest data set that I study in this dissertation, loblolly pine biomass ranges from nil to
upwards of 50 kg/m2; most 10 year old loblolly stands exceed 5 kg/m2. It is estimated
that globally over 80% of terrestrial biomass is in forests having >10 kg/m2 and only
about 7% is in vegetation with <4 kg/m2 dry biomass (Imhoff, 1995b). It is the >4
kg/m2 forests that are of interest to me in this dissertation. For these forests, the biomass
signal can be a weak one. A simple example (from Chapter 5, this dissertation) will
illustrate. In the SIR-C data from Duke forest, the highest correlations of o° to loblolly
pine biomass (or any of the forest structural attributes tested) are at L-HV (0O=22-33°)
and C-HH (0O=54°). Single-band regressions o f o° versus biomass yield slopes o f 0.037
and 0.042 in these two examples, so that the full range of forest biomass surveyed (3.544.5 kg/m2) corresponds to a 0 ranges of only 1.7 dB and 1.5 dB respectively. (The
range of mean o° for all stands is 2-3 dB, including scatter in the data). Thus, if o°
uncertainty from all causes combined were greater than, say, ±0.5 dB for a given stand,
biomass estimates based on these single SAR bands will be poor. Many other studies
have reported similarly low biomass sensitivities. Dobson e t al. (1992) gives particularly
clear illustrations showing the fall-off of sensitivity with saturation.
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14
Regression models that have higher sensitivity to biomass or the underlying struc­
tural attributes might have lower sensitivity to extraneous factors, but this depends on the
model in at least three ways. First, if the model is closely connected to the structural
attributes, it might be insensitive to variation in moisture and other incidental factors (but
not to variation in structure). However, if the model is dependent on the whole universe
of scattering factors associated with a given forest, forest state, and imaging particulars o f
a given data take, it could be sensitive to the incidental factors. Second, some SAR
bands respond strongly to certain extraneous factors. If these bands are included in a
model, the model inherits that sensitivity. For example, in one scatterometry experiment,
o °lh h decreased 2 dB with decreasing soil moisture in a walnut orchard, which was
twice the decrease of a ° LHV o r ° ° l w (McDonald et al., 1990). Hence, inclusion of LHH in a model increases its vulnerability to soil moisture change. Third, model form has
a bearing on sensitivity of estimated forest attributes to variation in backscatter due to
extraneous factors and calibration. Error propagation properties o f different models can
have a large effect on sensitivity to the input variability (see Chapter 5). In short, high
sensitivity of a model to forest structural properties or biomass and accurate prediction of
biomass for a given site and data take do not assure that a model can be successfully
applied in the presence o f forest and SAR variation. This state o f affairs is unavoidable
because, as was asserted before, backscatter is a response to an ensemble of interrelated
factors and not a direct measurement o f them.
5.2.1. Scene-related sources of o° variation
Sources of variation or fluctuation that probably affect <5° in most forests include
tree dielectric constant, forest floor moisture, roughness and litter layer, water on the
canopy surface, forest phenology, and topography. These sources will be discussed
below. In certain environments, flooding is an important factor that can strongly enhance
forest backscatter; the largest effect is observed at L-HH and P-HH bands, and probably
results from strong comer-reflection from trunks and the smooth water surface. (Hess et
al., 1990; Wang et al., 1995b). Other environmental variables demonstrated or believed
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15
to affect forest backscatter include presence/absence o f snow on trees and ground (and
snow liquid water content), ice, temperature (especially freezing of trees and ground), and
wind (Henderson and Lewis, 1998). Other forest variables include presence/absence o f a
shrub layer (and its state), and leaf orientation. Forest composition, structure and spatial
pattern can vary continuously across a landscape and are not necessarily compatible with
stand classification. These variations form a spatial overlay on other primarily spatial
variables such as topography.
a) Canopy water distribution and dielectric constant
Canopy and trunk water content are known to vary diumally and seasonally as a
function of both water availability and tree physiology. (Gates, 1991, gives an excellent
review.) Patterns o f change vary with species, tree age and site, and are not well docu­
mented. Dielectric constant, the moisture-related parameter that theoretically governs
microwave reflection and scattering, increases with water content, and is also a function
of solute concentration and temperature in plant tissue (Ulaby and El-Rayes, 1987). In
several studies, bole dielectric constant is partially correlated to leaf water potential,
though results are inconsistent; dielectric constant may lag water potential in conifers
(Weber and Ustin, 1991; McDonald et al., 1992; Dobson et al., 1991a; Salas et al.,
1994). Most tree dielectric constant measurements have been made in the bole, and reli­
able estimates of canopy dielectric constant are scarce.
Some reported diumal variations for the real part of the dielectric constant are =12
to =24 for hemlocks at C-band (Salas et al., 1994), <5 to >50 in walnut trees at L-band
(McDonald et al., 1990), roughly 8 to 15 at C-band for Siberian fir (Ranson et al., 1992),
and <15 to >40 at L-band and <10 to >35 at C-band for Duke forest loblolly pines (Dob­
son et al., 1991a). Dielectric fluctuations occur with the passage of clouds (Salas et al.,
1994). Dielectric constant may vary from the sunlit to shaded side of trees, and there is
evidence that it varies with height in the tree in a pattern that changes diumally (Dobson
et al., 1991a). Recent measurements of small fir and spruce trees show appreciable
differences in trunk, branch, and needle dielectric constants; new fir needles had
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16
dielectric constants approx 50% higher than old needles. In walnut orchard, the diumal
fluctuations in canopy dielectric constant led to fluctuations in o° o f about 1.5 dB at LHV and <1 dB at HH and W polarizations. Superimposed on these fluctuations was a
a 0 decrease (most evident at L-HH) over the course of three days that coincided with a
decrease in soil moisture and dielectric constant. Model simulations indicate diumal
fluctuations in white spruce backscatter may exceed 3 dB (McDonald et al., 1992). To
summarize, o° varies in response to diumal and seasonal changes in dielectric constant,
modified by effects of sunlight, soil moisture, and other factors. The dielectric constant
changes are different in different parts of the tree and for different species (and probably
site conditions). o° variations on the order of 1.5-3 dB have been observed- b) Soil
moisture, roughness and litter layer
An extensive literature exists on effects of soil moisture, surface roughness, and
composition on radar backscattermg coefficient. Most studies are agriculturally oriented,
as soil moisture estimation is a commercially important application. The general pattern
is well understood (Ulaby et al., 1978; Ulaby et al., 1979; Ulaby et al., 1982; Hallikainen
et al., 1985; Dobson et al., 1985). o° increases with soil dielectric constant, which
depends on soil moisture content and other soil properties (and can be approximated
using empirical models with volumetric soil moisture and soil texture as the inputs), a 0
also increases with decreasing 00, that is, <r° is higher at steeper radar incidence angles.
The slope of the o° versus 0O relation decreases as surface roughness increases (where
roughness is relative to the radar wavelength). Many models, from theoretical to empiri­
cal, have been published to estimate soil backscatter; I will not review them here. There
are no published field studies o f the effects o f the litter layer and forest floor debris on
backscatter. One laboratory study examined bistatic scattering of aspen and pine litter,
and found that its presence reduced specular reflectivity of the ground surface and
increased scattering in other directions (De Roo et al., 1991).
Surface scattering in forest is considerably more complicated than it is for bare soil.
Forest backscatter comprises canopy backscatter, direct surface backscatter, and double­
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17
bounce scattering that follows a "comer reflector” trajectory from the radar antenna to
tree trunks (or canopy), then to the ground, then back to the antenna (Richards et al.,
1987; Ulaby et al., 1990; Wang et al., 1993). The surface and double-bounce pathways
are modified by canopy extinction, which is incidence-dependent; the ground surface
interactions of these pathways depend in different ways on soil moisture and roughness,
litter moisture and density, and incidence. All o f these interactions vary greatly with
radar wavelength and polarization.
The influence of soil moisture on ERS-1 backscatter (C -W ) is well documented.
For young loblolly forest, wet soil conditions was observed to boost o° of nearly bare
soil by up to ~5 dB, the increase falling off with increasing biomass up to =5 kg/m2
(Wang et al., 1994). A similar effect was observed and modeled by others (Dobson et
al., 1995a; Pulliainen et al., 1994; Pulliainen et al., 1996). hi the latter study it was
observed that biomass-backscatter correlations were poor for wet soil conditions. Back­
scatter model simulations at L-band (0o=2O°) for closed canopy white spruce forest sug­
gest that at this longer wavelength and steep incidence, o° may vary by as much as >8
dB at HH and >5 dB at W over the maximum range o f soil moisture (McDonald and
Ulaby, 1993). In Amazonian forest, soil moisture had little effect on modeled C- and Lband backscatter, because canopy penetration was low and canopy scattering high at these
wavelengths. At P-band, forest backscatter consisted mainly of trunk-ground scattering,
and was therefore sensitive to soil moisture (Wang et al., 1995b).
In Chapter 4 of this dissertation, the response of forest o° to variation of forest floor
parameters is taken up again with the modeling of loblolly pine stands. In Chapter 5, I
revisit the topic by examining variation in SIR-C backscatter.
c) Water on surface o f the canopy
Water on the surface of trees from rain has been reported to increase o°. Dobson et
al. (1991b) found the o° increase following rain showers to be 2-3 dB at C-band, 1-2 dB
at L-band, and no increase at P-Band. They noted that the increase was largely masked
by extinction in the wet crown layer. Modeled backscatter from spruce and walnut
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18
canopies increased by 3 and 6 dB when the dielectric constant was increased so as to
simulate the effect o f decreased xylem flow observed following the spraying o f a tree
with water (McDonald et al., 1992). That is, water on leaves may boost backscatter by
increasing tree dielectric constant (through reduced transpiration) and by increasing sur­
face microwave reflection from the leaves or needles. In a scatterometry study o f pygmy
conifer forest, Westman and Paris (1987) found increases in o° at C-band of <1 to >4 dB
associated with fog. They demonstrated that the increase accompanied a large increase o f
internal moisture content of leaves and branches. In one of the SIR-C data takes from
April, 1994, acquired when the loblolly canopy was wet, o° was elevated about 1 dB
above the expected values at both C- and L-bands (Chapter 5)
d) Forest phenology
Anecdotal evidence abounds regarding seasonal changes in forest microwave back­
scatter. In many studies changes in phenology, moisture, and other factors are convolved
and may be difficult to unscramble. For instance, as reported in.Ulaby et al. (1986),
Hoekman (1984) measured o° variations (X-HH, 90 = 65°) o f >3 dB between March and
September for several deciduous and coniferous species. Pulliainen et al. (1996) found
variations of up to 4 dB in ERS-l backscatter from three boreal sites from June, 1993 to
March, 1994. Some unknown fraction of this variation is due to phenologic change.
Dobson et al. (1991b) report that in a study in northern Michigan using airborne SAR,
jack pine and red pine backscatter decreased between April 1 and July 10 by 1-2 dB at
L-band and by 1 dB at C-band. The changes are attributed to increases in foliar and
stem biomass in the crown region and changes in vegetation dielectric properties. The
authors hypothesize that the changes in the crown layer enhance scattering at the shorter
wavelength, while increasing extinction at the longer wavelengths. In deciduous species,
foliation and associated changes in trunk and branch dielectric constant caused a decrease
in g ° at all wavelengths, with the largest change (2-4 dB) at P-band and the smallest at
C-band (0-2 dB). At shorter wavelengths (X-band to K-band) backscatter from leaf-on
trees in the spring was 2-8 dB greater than leaf-off trees in autumn, depending on
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19
incidence angle (Ulaby et al., 1986).
C-band scatterometry that monitored backscatter of high-density aspen canopies
through a growing season showed roughly a doubling o f the backscatter coefficient at HH
and W polarizations that coincided with leafing-out; at HV the increase was smaller and
preceded the leafing out. Following senescence, backscatter in all polarizations dropped
to well below initial (before leafing out) levels, a strong indication that other factors in
addition to leaves drive seasonal backscatter variation (Pitts et al., 1988). Modeling o f an
aspen canopy indicates o° may be up to 10 dB higher for leaf-on than for leaf-off condi­
tions at HH and VV in all bands; at HV, o° may increase with leaf-on only slightly at Pand L-bands and decrease >5 dB at C- and X-bands (Henderson and Lewis, 1998, Fig.
9.12, provided by G. Sun). In another C-band study in which trees were systematically
defoliated, Zoughi et al. (1989) found that removal o f leaves enhanced HV backscatter
for sugar maple and pin oak (by as much as 6.6 dB for pin oak at 0o=5O°). Whether
branches or leaves dominated co-polarized backscatter depended on species and
incidence. For pines, needles dominated backscatter, and cones were also significant
scatterers. At L-band, Paris and Ustin (1990) found that removal of vertical stems and
leaves at the top of an almond crown increased backscatter by 1.16 dB at HH, 0.70 dB at
HV, and decreased it 0.44 dB at W , though the amount of material removed was small
(0.30 kg/m2 fresh weight).
Although the understanding o f phenologic control of forest backscatter is fragmen­
tary, several points are clear. First, c° variation depends on species, site conditions,
incidence, wavelength and polarization. Phenologic change can induce o° variation
amounting to at least several dB with no obvious visible signs of change in the forest.
Leaf-on/Ieaf-off may result in changes in excess of 10 dB. Further long-term, accurately
calibrated scatterometry studies are needed to better characterize the effects of phenology
on backscatter.
e) Topography
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20
Surface topography can have large effects on backscatter. Warner et al. (1996)
found that at X- and C-bands, the local Incidence angle influenced o° more than did
forest composition for both deciduous and coniferous forests. Beaudoin et al. (1994)
modeled P-band backscatter at 0O=45° for maritime pines in the 0-14 kg/m2 biomass
range, varying surface slope from 0-30° (inclined toward the radar). o° varied by up to
>10 dB at P-HH for all biomass levels, 3-4 dB at P-VV for low biomass forest (<3
kg/m2) and <1 dB at P - W for biomass >5 kg/m2, and <1 dB at P-HV for all biomass
levels. Bayer et al. (1991) estimated that variance related to surface relief in L-HH
(SEASAT) data amounts to 40% of backscatter variance. Comparing empirical models to
correct o° for effects of topography, they found the best models reduced image variance
in forest by about 12% (i.e., =30% o f the topographic fraction of total variance). Hinse
et al. (1988) studied cosine law-based models for reducing topographic effects at C-HH,
and obtained variance reductions o f 9.5% for deciduous and 7.4% for coniferous forest.
It is safe to generalize that, except where canopy scattering is strongly dominant (eg.,
dense canopy or HV polarization), topographic variation may cause non-negligible o°
variation.
Where present, topographically-related variation in forest o° is complex; it depends
on the relative intensity of canopy, surface and double-bounce backscatter, on ground sur­
face properties, and on slope angle and orientation in relation to radar incidence and
azimuth. The relative scales of topographic variation, canopy roughness, and pixel size
may also be involved. As shown in the studies cited above, partial correction can be
made using empirical or semi-empirical models, with or without digital elevation models.
The contribution of topography to registration and rectification error may also be a
factor in biomass estimation error, insofar as accurate registration is needed for image
segmentation, topographic correction, test site location, and other image processing steps
(see Kellndorfer et al., 1998).
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21
5.2.2. SAR-related sources of variation in measured c°
Absolute calibration uncertainties for SIR-C data are estimated to be ±2.3 dB and
±2.2 dB at C- and L-bands for the April, 1994, mission, and ±2.0 dB and ±3.2 dB for
the October, 1994, mission (Freeman et al., 1995). Pass-to-pass calibration is 1.0 dB
better than the above. H H -W amplitude imbalance is ±0.6-0.7 dB, and cross swath
uncertainty is ±1.0 dB. Freeman et al. (1992) suggested that for vegetation
mapping/monitoring purposes, uncertainty of <±0.5 dB is required. He indicated that,
while to achieve ±0.5 dB represents a challenge, current progress in calibration methods
make this goal achievable (Freeman, 1992). Calibration for the ERS-1 and JERS-1
single-band orbiting SARs is reportedly on the order o f ±0.5 dB (Kellndorfer et al.,
1998). Whether ±0.5 dB is accurate enough for forest classification or biomass retrieval
remains to be seen.
Radar incidence angle has a large effect on c°, up to >4 dB in my study (Chapter
5). a 0 defined with respect to a unit area on the horizontal ground plane. Forest back­
scatter is reported as a 0, but consists largely of canopy volume scattering, with some
admixture of direct ground surface backscatter and other surface-related scattering (eg.,
trunk-ground, double-bounce) (Richards et al., 1987; Ulaby et al., 1990; Wang et al.,
1993). All of these scattering mechanisms are separately dependent on radar incidence
angle, wavelength, and polarization. The proportion of the total backscatter that is direct
surface backscatter depends on the properties of the forest floor, canopy transmissivity,
and the intensity o f backscatter from the other mechanisms; all o f these factors vary
among forests and forest conditions, with topography, etc. Thus, it is difficult to model
the incidence angle dependence of o°; the problem is far more complicated than nominal
incidence correction, as described by VanZyl et al (1993). Empirically-fit cosine-law
models have been used in a number of studies (see Chapter 5). Truly "correcting" o° for
incidence may only be possible over small incidence increments, because the microwave
interactions are sensitive to the orientation of canopy elements and other scene elements,
and respond non-linearly to changes in incidence.
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22
Radar track direction (azimuth) may significantly affect backscatter if the scene is
anisotropic or asymmetrical. The most obvious example is topographic relief. Even in
gently sloping terrain, the backscattering geometry for a forested slope inclined toward
the SAR may be very unlike that o f an identical forest inclined away from it. Other
types of asymmetry may occur due to soils, drainage patterns, etc. As discussed above,
there is some evidence that the sunlit leaves can have different canopy dielectric constant
than shaded leaves (W eber and Ustin, 1991), implying that o° could vary depending on
the relation of solar azimuth and radar track angle.
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29
Chapter 2:
An overview o f the Duke Forest loblolly pine stands
and estimation o f stand characteristics
1. Introduction and background
Duke Forest is a research forest that covers 3400 ha extending westward from the
Duke University campus in Durham* NC. Approximately 1/3 of the forest consists o f
stands of loblolly pines (Pinus taeda L.) with less than 10% admixture o f hardwoods in
the more mature stands and even fewer hardwoods in the young stands (Harrell et al.,
1997). A large amount of information is available on the loblolly forest, detailing its suecessional pattern (Christensen and Peet, 1984; Kasischke and Christensen, 1990),
geometric properties and biomass distribution (Kasischke et al., 1994a), and the relation
of radar backscatter to biomass and other biophysical characteristics (Kasischke et al.,
1994b; Kasischke et al., 1995; Harrell et al., 1997). Estimates o f allometric relations
among tree components (small and large branches, needles, bole, crown-bole, etc) are
available owing in part to Kasischke’s surveys and analysis, and in part to the rich litera­
ture on loblolly pine that exists because of this species’ commercial value.
The successional chronosequence of loblolly forest that follows field abandonment
or clearing, as described in the above references, may be generalized as follows: The
sequence begins with colonization o f an abandoned field by pines. During the establish­
ment phase of a stand, pine density increases rapidly (in roughly 10 years) from nil to the
site-dependent maximum. Leaf area index (LAI) also increases to its maximum. Follow­
ing establishment, at stand age of about 15 years, the thinning phase begins and continues
for about 50 years. During this period, pine tree size increases and density declines, LAI
holds constant, and total biomass steadily increases to its maximum. Hardwoods gradu­
ally develop in the understory. The transition phase to hardwood forest follows thinning.
The pines die and are replaced by hardwoods as the principal canopy trees. LAI and
total biomass fall below their peak pine forest levels. Some 150 years after initial estab­
lishment the stand may achieve a steady state as a hardwood forest containing few pines.
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30
To illustrate the structural changes that occur during the lifetime o f a loblolly stand, pho­
tographs of four stands, aged 8, 20, 60, and 90 years, are included (Figs. 1-4).
The 21 stands used in this dissertation are a subset o f those surveyed by Eric
Kasischke and his colleagues at Duke University. The stands are located in the Durham,
Blackwood, and Eno divisions o f the forest. Within the study area the topography is
gentle, though the elevation varies by some 200 m and some stands slope noticeably
(=0-10%, as estimated from topographic maps). The stands range in age from 7 to 84
years (median 26 years) and in size from 3 to 28 hectares (median 10 ha). The youngest
stands are densely stocked and are almost pure loblolly pine, whereas the more mature
ones have partially closed canopies and an hardwood understory. The estimates of
biophysical properties adopted for this dissertation are summarized in Table 1 o f Chapter
5.
The estimates are those published by Harrell et al. (1997), based on methods
described in Kasischke et al. (1994a-b). Dense, young stands were surveyed with the
point-quarter method, with >20 sample points on 2-4 transects. The more mature stands
were sampled with 10 to >20 plots, each 100-200 m2, located randomly along 2-4 tran­
sects. Biomass of aboveground component tree parts and total aboveground dry biomass
were computed from the dbh and stem density data using allometric relations developed
and validated in Duke Forest by Kasischke et al. (1994a).
The raw held data from which the biomass estimates are derived, together with
forest stand maps showing stand locations and borders, and ancillary information were
provided by Harrell (pers. comm., 1994-7). The raw data was used in several ways: first,
to generate histograms of stand dbh and to estimate stem density for modeling purposes
(Chapter 4); second, to examine stand structure as a preliminary to grouping the 21
stands into meaningful age/biomass groups; and third, to compute stand biomass for both
modeling and empirical studies (Chapters 4-5). (These stand biomass estimates have
been supplanted by Harrell’s estimates, as discussed below.) Digital stand maps were pro­
vided as Arc/Info coverages by Laura Bourgeau-Chavez of ERIM (pers. comm., 1995). I
revised these coverages to conform to U.S.G.S. digital orthophotos (Chapter 5).
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31
2. Uncertainty in estimates of stand biomass
The uncertainty in estimates o f biomass and other forest measures has direct bearing
on evaluation of errors of SAR-based biomass estimates, as studied in Kasischke et al.
(1995), Harrell et al. (1997), and Chapter 5 (this dissertation). Error o f allometric
biomass estimation of young Ioblollys is reported to be ±1.5 Kg (Kasischke et al.,
1994b). Apparently, however, there is no published analysis of field sampling error as it
impacts biomass estimates.
My own biomass computations for the 21 stands deviate from Harrell's estimates,
with a mean absolute deviation of 4.1 kg/m2 (Wang and Day, unpublished data). My
estimates of mean dbh and stem density also differ from Harrell’s. There are many pos­
sible causes for the lack of agreement. I may not have received exactly the same data as
were used by Harrell et. al. (1997) since I received it in four batches between 1994 and
1997. My tree inclusion rules ( i.e., minimum tree size cut-off, whether to include all
species and/or dead trees, etc.) may be different. Interpretation and handling o f question­
able data entries surely differ. The methods o f estimating density from point-quarter data
also differ. (I use the method suggested by Pollard, 1971, for obtaining unbiased density
estimates, and avoid underestimation that can result from a clumped spatial distribution of
trees. See Bonham, 1989). Finally, how Harrell and I apply the allometric formulas may
differ, particularly since I was not involved in their formulation. To permit comparison
of my results to those of Harrell et al. (1997), and recognizing that the Duke group is
more intimately familiar with the field data than I am, I have elected to use their esti­
mates of biomass and other forest measures in Chapter 5.
Because I did not participate in the forest surveys or the development o f the
allometric relations, it would would be a poor idea to attempt to analyze the uncertainty
in the raw dbh and density data or in Harrell’s estimates of biomass and other forest
characteristics. However, I have examined the plot-to-plot variation in some o f the stands
using a calculation that circumvents some the data processing uncertainties described
above. I give two examples here. First is Stand 41, 4.7 ha in area, 29 years old, with
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32
estimated total biomass of 25.1 kg/m2 (Chapter 5, Table 1). The stand was surveyed
with twelve 100 m2 plots. Assuming biomass o f each tree is roughly proportional to dbh2
(Kasischke et al., 1994a), plot-to-plot variability o f total basal area provides an indication
of variability in biomass. I summed dbh2 for all trees in each plot, computed the stan­
dard error o f the mean, and compared it to the mean. Thus, the mean basal area o f the 12
plots is 3635 cm2/plot, with s.d. of 2071 cm2. Standard error o f the mean is 598 cm2,
which is 16.4% o f the mean. Thus, biomass estimation error should be roughly 16% o f
the mean biomass estimate of 25.1 kg/m2, or 4.1 kg/m2. Second, Stand 105 is 13.7 ha in
area, 55 years old, has estimated total biomass o f 26.4 kg/m2, and was surveyed with 6
plots. By the above, biomass estimation error should be about 3.9 kg/m2. Stands younger
than about 15 years of age that were sampled primarily with the point-quarter method
may have lower uncertainties, hi some cases, plot data for the same stands is available,
therefore, it should be possible to check the accuracy of the point-quarter estimates. This
is not intended to be a rigorous analysis, only an indication that uncertainty in stand
biomass estimates (resulting from sampling error) may be as large as ±4 kg/m2, as com­
pared to uncertainty in tree biomass estimates (resulting from allometric estimation), that
are reported to be ±1.5 kg/m2.
3. Grouping stands by age and biomass
Because the maturation of a loblolly is a continuous process, grouping stands into
age or biomass classes is arbitrary. There are many categorizing criteria that could be
imposed on the data depending on ones aims or insights. Recognizing the lack of
inherent existence of stand classes, I use them with restraint in this dissertation, hi
studying backscatter as a function of biomass and backscatter fluctuations in response to
surface conditions (Chapter 5), it is useful to group stands into classes. Doing so aver­
ages out stand-specific variations and emphasizes the overall trends.
To group the 21 stands into "age/biomass groups” that have relevance to both forest
description and microwave backscattering, I examined the relations of cumulative total
biomass to dbh and cumulative crown biomass to dbh (Figs. 5-6). The biomass data
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33
used for these plots was estimated by Wang and Day (unpublished data). As dbh
increases, the more mature stands progress to greater total biomass along roughly similar
trajectories. The younger stands show higher biomass accumulation in small trees, as seen
in the hump in the trajectories at 15-40 cm dbh (Fig. 5). The stands form three distinct
groups, with stands 38, 78, and 93 being transitional. This plot has most relevance for
L-band, which responds to the large branches and boles that constitute most o f the total
biomass. On the other hand, as dbh increases, crown biomass follows quite different tra­
jectories for relatively young stands as compared to more mature ones that are in
advanced stages of thinning (Fig. 6). In this figure too, three stand groups are dis­
tinguished. They are 1) small trees and partially developed canopy, 2) slightly larger
trees and fully developed canopy, and 3) large trees and fully developed canopy. Stands
25, 38, and 107 are on the hinges. This view is relevant at L-band but also at C-band,
as the shorter wavelength is sensitive to the small scale elements o f the canopy. Thus,
16 stands are situated solidly within the three groups and 5 stands are borderline.
In Harrell’s biomass data (Chapter 5, Table 1), the groups are not as clearly
separated as in Figs. 5-6. I resolved the differences by forming the groups in the follow­
ing way. I defined the young/low-biomass group as stands with total biomass (Harrell’s
estimate) <9.0 kg/m2 and the mature/high-biomass group as >26.0 kg/m2. With this
definition, all the stand assignments agreed with the natural groupings evident in Figs. 56 (except for #112, which is on the border o f the medium and high-biomass groups in
Harrell’s data). The three groups defined by these criteria have mean ages of 11, 29, and
58 years, and mean total biomass of 5 3 , 18.4, and 33.3 kg/m2. The groups correspond
to mid-late establishment, early thinning, and late thinning-transitional phases. That about
1/3 of the stands are borderline between groups will weaken inter-group comparisons to
some degree.
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34
4. Duke Forest fieldwork during the first S1R-C mission
To observe conditions and acquire "ground truth” in conjunction with the first SIRC mission (SRL-1, 10-20 April, 1994), I made a field trip to Duke Forest, accompanied
by Jose Saleta. The principal objective was to estimate ground surface parameters
needed to model loblolly backscatter, in order to enrich our interpretation o f the SIR-C
data (see Chapter 4). With extensive support from Eric Kasischke and Pete Harrell, (and
many enthusiastic volunteers from Riverside High School), the two o f us sampled forest
floor properties and made limited measurements of loblolly pine dielectric constant.
Forest floor measurements comprised litter layer thickness and density, soil moisture, soil
dielectric constant, and soil surface roughness. The surface roughness experiment is
treated separately (Chapter 3). The the other measurements are briefly summarized here.
The details of field schedule, methods, calibration, analysis, photos, etc., are thoroughly
documented in a report prepared following the SRL-1 mission (Day, 1994). The SIR-C
missions are discussed more fully in Chapter 5.
4.1. Overview
During the 10 day mission, we sampled 28 plots in 6 stands representing 4 age
classes. The stands are #7, 14, 43, 44, 51, and 68, four of which are included in the
Chapter 5 study. A total of 86 volumetric soil samples, 86 litter samples, 258 soil dielec­
tric profiles, 56 surface roughness transects, and 12 tree dielectric profiles were taken.
The litter and soil samples were dried and weighed under Pete Harrell’s supervision and
used to augment the soil moisture data he collected concurrently. During the experiment,
there were two major rain storms and subsequent dry-down periods.
On most days we succeeded in measuring plots in at least three stands so as to
document forest floor conditions during the SIR-C overflights. The moisture samples
were collected in the morning, as early as possible, because the Shuttle passes over North
Carolina were in the early morning hours (4 to 7 AM). Three to six randomly located
plots were measured in a stand on any given day. In each plot, the litter was sampled at
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35
a random location, a soil sample was collected at a second location, and a cluster o f three
soil dielectric profiles were measured near it. At a different time, 2 surface roughness
transects were measured adjacent to the moisture plots. Tree dielectric constant was sam­
pled outside the plots in early morning on a non-flight day.
4.2. Litter depth and volumetric moisture
Depending on thickness, composition, and moisture content, forest litter has a
potential to modify the backscattermg and forward scattering characteristics o f the under­
lying surface. Pine litter may be modeled as a loosely packed blanket o f needles oriented
randomly in air or as a water cloud, overlaying the rough soil surface (see Chapter 4). It
is impractical with a field dielectric probe to measure dielectric constant o f the litter
because it consists of a loose mixture o f organic debris and air. Its roughness is likewise
difficult to measure, and ill-defined as well.
We sampled the litter as follows: A rectangular wooden flame (approx. 0.34 m2)
was placed on the ground. Knives and pruning shears were used to cut through the litter
around the inside edge of the frame. Then, using the fingers, the loose litter was removed
down to the surface of the soil or consolidated organic layer, where present. Litter depth
was estimated with a ruler. Samples were transported in plastic bags and oven-dried to
constant weight.
Estimated mean litter depth ranged from 2.1 to 6.5 cm among the stands and
appeared unrelated to stand age, except that the youngest (8 year old) stand had the thin­
nest (2.1 cm) layer (Table 1). Volumetric litter moisture ranged from 0.011 to 0.142
cm3/cm 3 (Tables 1-3). The highest value was for poorly drained Stand #14 under nearly
saturated soil conditions. Analysis o f the data led me to suggest the following general­
ized estimates of litter depth and moisture for purposes of modeling Duke forest stands
during this period: Litter depth is =2 cm for young stands (<10 years) and =4 cm for all
other stands. Volumetric moisture =0.04 cm3/cm 3 under moist conditions and =0.09
cm3/cm 3 for very wet conditions.
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36
4.3. Soil moisture
Following removal of the loose litter and duff, soil samples were collected with a
horticultural bulb planter. The cylindrical samples were 10.0 cm. deep and had a volume
of 269 cm3. They were removed in plastic bags and oven-dried. The 86 samples supple­
mented the more extensive data set collected by the Duke team, however, the main use of
the samples was to establish the relation o f dielectric constant to soil moisture for Duke
forest soils for use in backscatter modeling.
Estimated soil moisture varied among stands. However, due to two rain storms dur­
ing the April SIR-C mission, the day-to-day differences were more pronounced than
stand-to-stand ones. The volumetric and gravimetric soil moisture for two moist days
and two wet ones are summarized in Table 4. The values shown are derived from the
mean soil moisture for each stand sampled on each day.
4.4. L-band soil dielectric constant
An L-band portable dielectric probe with a #3 soil tip was used. This tip is designed
for a dielectric constant (real) range o f 1-30 (Applied Microwave, 1989). The probe was
allowed to warm up until readings stabilized, and was calibrated with reference to carbon
tetrachloride and methanol. Three soil dielectric profiles were taken in a cluster, i.e.,
within a circle approximately 30 cm in diameter around the soil moisture sample. Litter
and unconsolidated organic matter was removed, and measurements were taken at the
surface and at depths of approximately 5 cm and 10 cm. After making calibration adjust­
ments, the measurements from three depths and three sample points were averaged for
comparison to the soil moisture sample at the same approximate location. Dielectric con­
stant for two moist days and two wet ones are summarized in Table S. (This is directly
comparable to the soil moisture summary o f Table 4.)
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37
4.5. L-band soil dielectric constant versus volumetric soil moisture
Plots of real (RE) and imaginary (IM) parts of the dielectric constant versus
volumetric soil moisture (Mv) showed considerable scatter. Figure 7 shows RE vs. Mv.
(The IM vs. Mv plot is omitted.) Linear regression o f RE and IM versus yielded
R2=0.55 and 0.21 respectively. Slope and R2 of the regressions were found to decrease
with stand age: R2 for young, mid-aged, and mature stands were 0.85, 0.66, and 031.
After evaluating several available models to predict dielectric constant from Mv, we
resolved to use the semi-empirical model o f Ulaby et al. (1986), which fits the data well
(Fig. 7).
4.6. Tree dielectric constant at L-band
L-band tree dielectric measurements were taken between 4:20 and 7:20 AM, April
17. Dielectric profiles were made at = 1.5 m high on the trunks o f 9 loblolly pines and 3
hardwood trees in or adjacent to the stands in which our plots were located. A 5/32"
drill bit with the tip ground flat was used to drill into the trunks fo r insertion of the tree
tips (from Applied Microwave Corp.). Measurements were made at the active cambium,
and at 1 cm, 5 cm, and 10 cm depths below it. The probe was calibrated with reference
to carbon tetrachloride, methanol, and water.
The loblolly pine dielectric constants follow a now familiar pattern: a peak in the
cambium and lower values deeper in the bole. Young loblollys have higher cambium
dielectric constant than the more mature ones. Average dielectric constant for three Stand
68 loblollys (8-10 cm dbh) was 43 -jl2.1, as compared 273 -j83 for six more mature
loblollys (15-39 cm dbh). Dielectric constant of the hardwoods fell off sharply between
the cambium and I cm depth and increased toward the center of the tree. The dielectric
constants for all trees combined are summarized in Table 6.
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38
5. Summary of key forest attributes and results
This chapter provides background on the loblolly stand biomass measurements and
environmental parameters that are used in Chapters 4-5. The 21 stands studied range
from 7-84 years of age, 3.5-44.5 kg/m2 in biomass, and 3-28 ha in area (see Chapter 5,
Table 1). Estimates o f error in field-measured biomass are not available, but uncertainty
may be as large as 4 kg/m2. Three age/biomass stand groups are identified for a com­
parison of modeled and measured a 0 in Chapter 5. Their biomass ranges are 3.5 to <9.0,
9.0 to <26.0 and >26.0 kg/m2, corresponding to the mid-late establishment, early thin­
ning, and late thinning-transitional successional phases. One stand typifying each group
serves as the basis for modeling o° o f low, medium and high biomass stands (Chapter 4,
Table 1).
In connection, with the first SIR-C mission (April, 1994), I measured forest floor
properties in Duke Forest. Estimated mean litter depth ranged from 2.1 to 6.5 cm among
the stands and appeared unrelated to stand age, except that the youngest (8 year old)
stand had the thinnest litter layer (2.1 cm). For modeling purposes, reasonable values are
2 cm for young stands and 4 cm for all others. Volumetric moisture content of the pine
litter ranged from 0.011 to 0.142 cm3/cm 3, the highest value representing nearly
saturated soil. For modeling, 0.01, 0.04 and 0.09 cm3/cm 3 are appropriate values for
dry, moist and wet litter. Mean volumetric moisture of the top 10 cm o f soil in a stand
on a given day ranged from 0.15 to 0.43 cm3/cm3. Day-to-day variation was pro­
nounced, due to rain on April 16. Estimated average soil moisture on the days of the
SIR-C overpasses (April 12, 16, 17, and 18) is 25%, 34%, 31%, and 28%. Mean L-band
soil dielectric constant ranged from 11.3-j0.1 to 29.2-j2.7, averaging 14.6-j0.9 and 21.8jl.5 under moist and wet soil conditions. The relation of Mv and dielectric constant (RE)
fit a semi-empirical model, but with considerable scatter (R2=0.55). In limited sampling
of L-band dielectric constant profiles in tree boles, dielectric constant measured at the
cambium of three young loblollys (8-10 cm dbh) was 43 -jl2.1, as compared 27.3 -j8.3
for six more mature loblollys (15-39 cm dbh), suggesting a decrease o f dielectric constant
with tree age. Soil roughness measurements are discussed separately (Chapter 3).
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39
6. References
Applied Microwave Corp., 1989, Portable Dielectric Probe Instruction and Operating
Manual, 2500 W 6th St., Lawrence, KS 66049-2402.
Bonham, C. D., 1989, Measurements fo r Terrestrial Vegetation, Wiley, New York, pp.
159-164.
Christensen, Jr., N. L. and R. K. Peet, 1984, Secondary forest succession on the North
Carolina Piedmont, Forest Succession: Concepts and Applications (D. C. West, H.
H. Shugart, and D. B. Botkin, Ed), Springer-Verlag, New York, pp. 230-245.
Day, J. L., 1994, Final Report on UCSB Fieldwork in Duke University Forest April 5-20,
1994 fo r SIR-C/X-SAR internal report, September, 1994.
Harrell, P. A., E. S. Kasischke, L. L. Bourgeau-Chavez, and E. M. Haney, 1997, Evalua­
tion of approaches to estimating aboveground biomass in southern pine forest using
SIR-C data, Remote Sens. Environ., vol. 59, pp. 223-233.
Kasischke, E. S. and N. L. Christensen, Jr., 1990, Connecting forest ecosystem and
microwave backscatter models, Int. J. Remote Sens., vol. 11, pp. 1277-1298.
Kasischke, E. S., N. L. Christensen, Jr., and E. Haney, 1994a, Modeling o f geometric
properties of loblolly pine tree and stand characteristics for use in radar backscatter
models, IEEE Trans, on Geosci. Remote Sens., vol. 32, no. 4 pp. 800-822.
Kasischke, E. S., L. L. Bourgeau-Chavez, N. L. Christensen, Jr., and E. Haney, 1994b,
Observation on the sensitivity of ERS-1 SAR image intensity to changes in
aboveground biomass in young loblolly pine forests. Int. J. Remote Sens., vol. 15,
pp. 3-16.
Kasischke, E. S., N. L. Christensen, Jr., and L. L. Bourgeau-Chavez, 1995, Correlating
radar backscatter with components of biomass in loblolly pine forests, IEEE Trans,
on Geosci. Remote Sens., vol. 33, no. 3, pp. 643-659.
Pollard, J. H., 1971, On distance estimators o f density in randomly distributed forests.
Biometrics, vol. 27, pp. 991-1002.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
Ulaby, F. T., R. K. Moore, and A. K. Fung, 1986, Microwave Remote Sensing: active
and passive. Volume III: From theory to applications, Artech House, Dedham, MA.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1. Litter Depth and Volumetric Moisture, by Stand
stand
7
14
43
44
51
68
all
litter depth (cm)
mean
sd
n
3.7
4.8
3.2
6.5
3.9
2.1
4.0
1.2
1.0
0.6
1.6
1.2
0.9
1.9
15
11
3
15
18
18
80
vol. moisture (cm3/cm3)
mean
sd
n
.0507
.0867
.0380
.0648
.0372
.0588
.0540
.0199
.0373
.0131
.0323
.0171
.0168
.0277
13
7
3
11
18
9
61
Table 2. Litter Volumetric Moisture, by Date
date
mean
(cm3/cm3)
sd
n
4/10/94
4/11/94
4/12/94
4/16/94
4/17/94
4/19/94
all
.0477
.0495
.0501
.0930
.0465
.0339
.0540
.0263
.0144
.0245
.0286
.0124
.0118
.0277
11
13
14
10
4
9
61
-
Table 3. Litter Moisture Summary Statistics
for moist and wet conditions
min
mean
max
sd
Moist
(4/10/94,4/19/94)
Wet
(4/16/94,4/17/94)
0.011
0.042
0.085
0.022
0.033
0.080
0.142
0.033
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42
Table 4. Soil Moisture Measured for Moist and Wet Conditions
moist (4/10/94, 4/19/94)
minimum
mean
maximum
wet (4/16/94, 4/17/94)
(g/g)
by volume
(cm3/cm3)
by weight
(g/g)
0.149
0.215
0.264
0.284
0357
0.527
0.181
0393
0.433
by volume
(cm3/cm3)
by weight
0.204
0.253
0.302
Table 5. L-band Dielectric Constant for Moist and Wet Soil
moist (4/10/94, 4/19/94)
wet (4/16/94, 4/17/94)
11.3- j 0.1
14.6- j 0.9
18.5 - j 1.7
16.7- j 1.0
21.8 -j-1.5
29.2 -j 2.7
minimum
mean
maximum
Table 6.
Sum m ary
of L-band Dielectric Constants for 12 Trees
cambium
min
mean
max
18.9- j 5.7
29.5 - j 9.0
44.8—
j 12.4
1 cm
5.2 - j 0.9
9 .9 - j 3.4
16.3- j 6.3
5 cm
10 cm
5 .9 -J 2.4
12.2 - j 4.2
20.6 - j 6 5
10.8- j 3.3
16.4-j 4.8
25.6- j 6.2
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43
Fig. L
Duke Forest Stand 68 (8 years old, total biomass =3.6 kg/m2)
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44
Fig. 2
Duke Forest Stand 51 (=20 years old, biomass n/a)
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45
Fig. 3
Duke Forest Stand 44 (60 years old, total biomass =31.8 kg/m2)
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Fig. 4
Duke Forest Stand 43 (= 90 years old, biomass n/a)
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47
-1 0 6
Cumulative total dry-weight biomass (kg/m2)
108
3044
20-
.•14
10-
0
20
40
60
80
dbh (cm)
R g. 5. C um ulative total biom ass of ioblloly pine stan d s vs. dbh
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48
Cumulative crown dry-weight biomass ( kg/ nf )
3.0-
-14
.-78
2.5-
108
44
12
2 .0 -
1.5-
86/
1.0 -
0.5-
0 .0 -
0
20
40
dbh (cm)
60
80
Fig. 6 . Cumulative crown biom ass of loblloly pine stan d s vs. dbh
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49
U la b /s m odef
soil dielectric co n stan t (R E)
25-
'
linpaf
reg ressio n
••
20
-
• •
15-
10
-
0.1
0.2
0.3
0.4
Mv (cm 3/cm 3)
Fig. 7 L-band dielectric constant vs. soil moisture
showing linear and empirical m odels (Ulaby e ta l., 1986, p. 2102-3)
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50
Chapter 3:
Forest floor surface roughness
measurements in a loblolly pine forest
1. Introduction
Knowledge of soil surface microtopography is valuable in radar remote sensing stu­
dies of unvegetated ground because surface roughness (in combination with soil moisture)
has a major influence on surface backscatter. One practical consequence o f the depen­
dence of backscatter on surface roughness is that roughness must be taken into account in
developing radar-based methods for soil moisture estimation. Surface roughness, soil
moisture, and soil dielectric constant have been widely studied in relation to surface
scattering from agricultural fields. A number of theoretical and empirical models have
been developed for microwave scattering from bare and also crop-covered soil (Ulaby et
al., 1978, 1979, 1982; Hallikainen et al., 1985; Fung et al., 1992; Oh et aL, 1992, 1994;
Saatchi et al., 1994).
Surface roughness is also important in radar remote sensing of forests since
microwave scattering from the forest floor can contribute appreciably to the total back­
scatter from the forest. Modeling indicates that direct surface backscatter may be
significant for young or sparse forest stands and at steep radar incidence angles (Wang et
al., 1993a).
Direct surface backscatter is not expected to be important at shallow
incidence angles or for well developed forests due to microwave extinction in the canopy.
However, double-bounce trunk-ground scattering may be a major source o f backscatter
for a range of forest densities and incidence angles, at least at L-band HH polarization
(Ulaby et al., 1990; Sun et al., 1991; Wang et al., 1993b, 1994).
There is little published information on forest floor roughness and composition by
which to link radar scattering theory to models and imagery. In a laboratory study,
DeRoo et al. (1991) measured the X-band bistatic scattering response for samples of three
forest litter types placed on smooth sand. They found the presence of a litter layer
increased backscatter while reducing specular reflection. The effect was large for wet
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51
pine litter. To my knowledge, comparable measurements have not been made at C- or
L-band; it is at these longer wavelengths that canopy penetration, and hence forest floor
scattering, is expected. Working in Howland forest, Maine, Chauhan et al. (1991) meas­
ured surface roughness along 8 transects. They determined the standard deviation o f verti­
cal surface height to be 24.3 cm and correlation length to be 1.0 m, or 9.9 m computed
differently. The authors note that the ground was hummocky, giving rise a quasioscillatory correlation function that made it difficult to define correlation length. The
effect of the litter layer was not discussed. Apart from these two papers there appears to
be no published data to support the modeling of forest floor scattering.
This paper reports on forest floor roughness measurements made in April, 1994 in
Duke University Forest, North Carolina, in connection with the NASA Shuttle Imaging
Radar (SIR-C) mission. In this field study, pine litter thickness, volumetric moisture con­
tent of the litter, soil moisture and L-band dielectric constant, and soil surface roughness
were measured in loblolly pine stands ranging in age from 8 to approximately 100 years.
The objective was to generate a realistic set o f ground surface parameters for forest back­
scatter modeling, particularly for L-band (24 cm wavelength) at which canopy penetration
may permit a significant amount o f surface scattering to occur. M y purpose here is to
describe the design for the simple, inexpensive, and field-worthy surface roughness gauge
used in this experiment and to present our methodology and surface roughness data for
the loblolly forest floor.
2. Methodology
2.1. Study Site Description
The study area is within the Durham Division of Duke Forest, located just west of
Durham, North Carolina, adjacent to the Duke University campus. This forest contains
approximately 800 ha of loblolly pine QPinus taeda L.) stands. The loblolly stands,
which range from 1 to >100 years o f age, have been studied extensively as an example of
an "old-field" successional chronosequence (Christensen and Peet, 1981; Kasischke and
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52
Christensen, 1990). They have also been the focus o f research on sensitivity o f radar
backscatter to above-ground forest biomass (Kasischke et al., 1994a, 1994b, 1995; Dob­
son et al., 1992; Wang et al., 1995).
I measured surface roughness in 6 stands, the youngest o f which was 8 years old
and the oldest approximately 100 years (Table 1). Soil surface microtopography may
change over time due to animal burrowing, litter-fall, tree-fall, erosion, etc., all o f which
are influenced by forest composition and structure. Therefore, I expected that the forest
floor might evolve during the succession following clearing or cropland abandonment,
resulting in a forest floor chronosequence. The youngest stand measured is a dense
thicket, while the oldest is open and park-like. All 6 stands are predominantly loblolly,
but the oldest (#43) also contains shortleaf pine (P. echinata) and the three oldest (> 60
year) stands have hardwood understories. Mean tree diameter (dbh) ranges from 7 cm
(#68) up to 53 cm (#43). Stem density ranges from over 5000 per hectare (#68) down to
120 per hectare (#43).
The stands are on fairly level ground. However, stand #7 slopes noticeably and #43
contains some gullies. Stand #14 is not as well drained as the other stands. Some
shrubs are present, but nowhere do they constitute a dense layer. The mean litter thick­
ness ranges from 2.1 to 6.5 cm (Table 1). These estimates are based on limited sampling
(a total of 80 samples, each approximately 0.34 m2). There appears to be no direct rela­
tionship between litter thickness and either stand age or density, though the youngest
stand has the thinnest litter layer.
2.2. Defining Forest Floor Surface Roughness
For the purpose of modeling microwave scattering from bare soil, surface roughness
is commonly described by two parameters: RMS height (a) and correlation length (/). cr
is the standard deviation of surface height variation. / is the horizontal displacement
along the ground (xO at which the autocorrelation function p(xO = l/e (Ulaby et al.,
1982). The heights o f points on the ground separated by a distance greater than I are
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53
assumed to be statistically independent. Surface height variations over much smaller hor­
izontal distances than the radar wavelength have little effect on scattering. For measuring
surface profiles, Ulaby et al. (1982) suggest as a rule of thumb that sample points be
spaced at Ax<0.lA~ Based on this criterion, at L-band (A.= 2 4 cm) surface height should
be measured at intervals o f 2.4 cm or smaller. (Other measures o f surface roughness
such as radius of curvature are not considered here.)
These definitions make-good sense and the measurements are straightforward for
idealized bare soil. The forest floor, however, is generally not a simple surface, but con­
sists of composidonally distinct layers that increase in density with depth, hi a typical
mature Duke Forest loblolly stand the surface is covered with 3-6 cm of pine needles
packed in a tight thatch containing some twigs and cones (the O l horizon). Under this
diffuse upper layer the organic layer graduates by degrees over several centimeters to
layers of greater decomposition, consolidation, and density (the 0 2 horizon) until the true
soil (A l horizon) is reached. The actual scattering "surface" is not easily located because
there is no simple discrete surface.
In this study, I adopt a conceptual model in keeping with the slab model offered by
DeRoo et al. (1991). The litter layer, including any loose, Iow-density duff, is regarded
as a diffuse volume-scattering layer. Scattering from this layer adds to soil surface
scattering, while volume extinction in the litter layer reduces the intensity of microwaves
reaching the underlying soil surface, thereby diminishing soil surface scattering. The
overall effect is to reduce net surface scattering and alter the bistatic scattering response.
Litter composition, thickness, and water content should affect these changes, which
depend also on radar wavelength, polarization and incidence angle. Dry litter may
weakly attenuate the microwaves, whereas a deep, wet litter layer may strongly modify
the directional distribution of scattered waves, increasing backscatter and reducing for­
ward reflection (DeRoo et al., 1991). The air-litter interface appears smooth because the
random litter-fall blankets the surface and covers up small-scale irregularities, yet the
litter surface is quite diffuse. The litter layer might be modeled as a water cloud, a col­
lection of randomly oriented cylinders, or a dielectric slab. Existing surface scattering
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54
models can be applied, to the underlying soil surface.
As a practical matter, I found that the needle litter can be lifted off the
surface and
the loose duff gendy brushed away to reveal the surface o f the consolidated material
below. In some plots, this surface coincides with the top o f the A l horizon, hi other
plots in which the lower 0 2 horizon is dense and compact, the so-called "surface" is
located somewhere in the 0 2 horizon. In most cases the seemingly arbitrary demarcation
between the litter-duff layer and the surface was definite and identifiable. Therefore, for
all surface roughness profiles measured, the litter was carefully removed along with loose
small twigs and cones. Although this procedure has an element of subjectivity, different
field assistants appeared to clear the litter to nearly the same depth. There may be some
difference between the surface identified under wet as compared to dry litter, since wet
duff is more cohesive than dry duff.
2.3. Surface Roughness Gauge Design and Use
Surface roughness measuring devices in use range from tape measures to highly
precise 2-dimensional laser-ranging tables. The surface roughness gauge (SRG) we con­
structed falls between these extremes. It is simple, inexpensive, is designed for easy
assembly in the field, and can be carried through dense forest by a crew of two.With
the SRG, 4m transects can be measured efficiently with adequate precision.
The SRG is constructed from 15" x 3” x 15’ (3.8 cm x 7.6 cm x 4.6 m) rectangu­
lar aluminum tubing. (See photo, Figure 1). It is fabricated in two sections to facilitate
shipping. The frame is drilled with 210 holes for 5/16" (8 mm) pins on 3/4" (1.9 cm)
centers. (English units are used because of the dimensioning o f available materials and
limitations of the indexing drill press used.) The pin spacing meets the sampling cri­
terion for L-band (Ulaby et al., 1982). The holes are drilled slighdy larger than the nom­
inal dowel size (by trial and error) to enable the dowels to glide easily through them.
The joint between sections permits a slight amount o f vertical adjustment until the 8
machine screws connecting the sections are tightened. To verify alignment o f the
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55
sections, we placed an 8’ (2.4 m) length o f square aluminum tubing along the top o f the
frame. The pins are conventional hardwood furniture dowels, selected for straightness,
cut to 18.0" (45.7 cm), capped with a wooden plug, and spray-lacquered. The plugs keep
the dowels from falling through the frame and provide a flat surface against which to rest
a pencil. The lacquer reduces swelling and warping of the wooden pins due to moisture.
Pin supports consisting of lengths o f aluminum angle are secured to the bottom o f the
front face of the frame with nylon thumb-screws. They hold the pins in a raised position
until they are intentionally released. The two ends o f the frame are supported on capped
1/2" (1.3 cm) steel pipes that can be driven into the ground. The ends of the frame are
freely adjustable up and down the pipe until clamped at the desired height by tightening
the thumb-screws. Three 18” (45.7 cm) high sections o f "gator board," a rigid light­
weight foam-core art craft material, are screwed to the back of the frame to provide a
support for strips of chart paper.
The SRG is used as follows:
•
Position the SRG over a transect.
•
Drive the support pipes into the ground and clamp the frame about 15 cm above
the ground, approximately horizontal.
•
Mount a strip of white 40# butcher paper 15”x l4 ’ (38.1 cm x 4.27 m) on the
gator board support using spring clips.
•
Carefully remove loose forest litter from beneath the frame (photo, Figure 1).
•
Loosen the nylon thumb-screws on the pin supports, allowing the pins to drop.
•
Mark the positions of the tops of all 210 pins on the paper strip with a flat car­
penters’ pencil (photo, Figure 2).
•
Fold the paper strip up to 10.5"xl5" (27cmx38cm) and record plot information
on the outside.
•
Push the pins back to the starting position using the aluminum pin support as a
pusher (photo, Figure 3).
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56
The SRG proved to be light-weight, rugged, and field-worthy. It fits fully
assembled in a long cargo van, minimizing the need to reassemble it repeatedly.
We were able to carry it into dense young pine stands with reasonable effort and
care. The SRG can be handled by two workers, but a crew o f three o r four is
preferable.
It is easy to use; our volunteer helpers from a local high school
learned the routine in under an hour, fri open stands, the time required fo r a crew
o f four to m easure a transect was about 20 minutes, including walking into the
stand. In dense stands, a crew o f two required about an hour per transect. The
SRG dimensions are appropriate. Only one transect, which crossed a sm all gully,
exceeded the vertical travel limit o f the pins. In this case w e m easured the gap
beneath the pins w ith a ruler and recorded the additional height increm ent on the
paper strip. T he pin diameter is large enough that the pins stop falling at the soil
surface and rarely penetrate far. Since all the correlation lengths we recorded are
well under a m eter, the length of the SRG could be reduced for use in the Duke
Forest, but possibly not in other forests.
The pins are not perfectly straight,
resulting in a displacem ent along the surface o f up to about 0.5 cm in the worst
case. This is not considered serious; we replaced the most badly w arped dowels
with spares and rotated the dowels so that any visible warping was across rather
than along the transect. On the wettest day we experienced, the dowels swelled
and did not slide freely. For use in wet conditions, the wooden dowels, gator
board, and paper strips should be replaced w ith moisture-resistant materials.
Recording the surface profile on a paper strip m ay seem primitive, but it is
effective. Com plications o f electronic or photographic systems are avoided and
malfunctions resulting in lost data are unlikely. The paper strip provides a per­
manent field record. It can be digitized in three sections on a 60" (152 cm ) digi­
tizer. C om bined error from misalignment o f the sections and paper shrinkage
(across the 15" dimension) is negligible, <0.5 m m under our conditions. The
digital data record produced for each transect is a file o f 210 height values. Since
the horizontal increm ent is a constant =0.75" (1.9 cm ), horizontal positions need
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57
not be measured.
2.4. Field Measurements
Three to six plots were located in each o f the six stands u sin g a spatially
stratified random sampling scheme. In all, 28 plots were established. These plots
were used for volumetric soil m oisture sampling, soil dielectric m easurem ents and
litter samples, as well as surface profiles. A total o f 56 surface roughness tran­
sects were measured, two in each p lo t For each plot a pair o f perpendicular tran­
sects was laid out along compass bearings o f 50° and 140°, i.e., approxim ately
parallel and perpendicular to the SIR-C ground track. This was do n e in order to
detect anisotropic roughness patterns, if present. For each transect pair, the tran­
sect centers were located adjacent to each other at a random bearing from the plot
center and at a random distance between 4.0 and 9.0 meters from th e plot center
(so as to avoid the zone o f tram pling and disturbance caused by the soil and litter
sampling). Transects
falling on a tree were shifted slightly to th e side. The
litter was carefully moved aside following the method outlined above. The sur­
face profiles were recorded on paper strips.
The strips were digitized in the
laboratory at the conclusion o f the field trip.
2.5. Estimation o f RMS Height and Correlation Length
A least squares regression was run on the height data fo r each transect. The
distances x' along a transect consisted o f a sequence o f 210 points beginning at
zero and separated by 1.905 cm (i.e., 0.75 inches), a and I w ere calculated from
the regression residuals. This has the effect o f setting the mean h eig h t to zero
and removing the average slope.
The autocorrelation function p(x') was com ­
puted using the S-PLUS statistical package.
(The procedure is equivalent to
U laby et al., 1982, Eqn. 11.11.) An estimate for I was made by determ ining the
displacement distance for which p(xO = 1/e. A typical plot o f p(x') as a function
of
x' is shown in Figure 4.
F or most transects the autocorrelation function
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58
oscillated and in m ore than half o f them p(xO dropped below —1/e before return­
ing to zero. This oscillatory behavior is reminiscent o f the correlation functions
reported in (Chauhan et al., 1991), w hich the authors o f that study suggest may
reflect large-scale periodicity o f the forest floor. Excursions o f the autocorrelation
function below —1/e are ignored in th e estim ates o f I given in the follow ing section.
3. Results
RMS height and correlation length statistics for the 6 stands are sum marized
in Table 2. It can be seen that stand-to-stand differences in the m eans o f both
param eters are small compared to w ithin-stand variability.
T he sam e d ata are
shown in a scatterplot in Figure 5, w ith transects labeled according to stand age
group. T he large numerals indicate the age group means, and th e ellipses show
±1 standard deviation around the m eans. Contrary to my expectation, there is no
evidence that cr and I vary as a function o f stand age. A dditionally, estim ates o f
along-track and across-track means fo r I are nearly identical (28.5 and 28.6 cm).
A long-track and across-track <7 differ slightly (2.37 versus 1.95 cm ); how ever, the
null hypothesis that they represent the sam e population was not rejected at the
90% confidence level.
These data provide a first cut a t characterizing <7 and I fo r the D uke Forest
loblolly stands. Despite the large w ithin-stand sampling variability (that is indica­
tive o f forest floor heterogeneity), the means and dispersion o f the d ata are
roughly sim ilar for all stands. This finding that the overall m ean values <7=2.2
cm and /= 2 9 cm may be used in backscatter modeling in this forest, without
ancillary data on stand age o r structure, a t least until additional studies become
available.
These <7 and I values m ay also have applicability fo r o th er similar
forests. The approximate ranges 0.8 cm < <7 < 5.7 cm and 7 cm < I < 57 cm can
be used as guides for surface roughness sensitivity analyses.
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59
M ost o f the individual measurements and the mean values o f both parame­
ters fall within the regions o f validity (at L-band) o f recently proposed theoretical
and empirical surface scattering models (O h et al., 1992, 1994; F ung e t al., 1992),
b u t they are wholly or partially outside the ranges o f the w ell-know n geometric
optics, physical optics, and sm all perturbation models. It is uncertain w hether or
no t the existing surface m odels, w ith the addition o f a diffuse surface layer, can
realistically describe forest floor scattering at the longer w avelengths (i.e., C-, L-,
and P-bands).
4. Conclusions
A simple surface roughness gauge and method fo r m easuring forest floor
surface roughness profiles have been described. The problem o f how to define
the surface under the litter layer is addressed in relation to practical field sam­
pling and modeling needs.
56 four-m eter transects w ere m easured in loblolly
pine stands ranging from 8 to about 100 years o f age in D uke F o rest
RMS
heights and correlation lengths derived from this data are sum m arized. Mean
RM S height and correlation length o f the soil surface are 2.2 cm and 29 cm
respectively. Despite large w ithin-stand variability, there is no evidence that sur­
face roughness varies as a function o f stand age or transect orientation. The data
can be used to param eterize forest floor surface scattering m odels fo r Duke Forest
and possibly other sim ilar forests.
5. References
Chauhan, N. S., R. H. Lang, and K. J. Ranson, 1991, R adar m odeling o f a boreal
forest, IEEE Trans. G eosci. R em ote Sens., vol. 29, no. 4, pp. 627-638.
Christensen, Jr., N . L. and Peet, R. K., 1981, Secondary forest succession on the
North Carolina Piedm ont, F orest Succession: C oncepts a n d A pplications (D.
C. West, H. H. Shugart, and D. B. Botkin, Ed), Springer-V erlag, New York,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
New York, pp. 230-245.
De Roo, R., Y. Kuga, M. C. Dobson, and F. T . Ulaby, 1991, Bistatic radar
scattering from organic debris o f a forest floor, Proceedings o f IGARSS, vol.
1, pp. 15-18.
Dobson, M. C., F. T. Ulaby, T. Le Toan, A. Beaudoin, E. S. Kasischke, and N.
Christensen, 1992, Dependence o f radar backscatter on coniferous forest
biomass, IE E E Trans. on GeoscL Rem ote Sens., vol. 30, no. 2, pp. 412-415.
Fung, A. K., Z. Li, and K. S. Chen, 1992, Backscattering from a randomly rough
dielectric surface, IE E E Trans, on Geosci. Remote- Sens., vol. 30, no. 2, pp.
356-369.
Hallikainen, M. T., F. T. Ulaby, M. C. Dobson, M . A. El-Rayes, and L. K . W u,
1985, M icrowave dielectric behavior o f w et soil— Part I: Empirical models
and experimental observations, IEEE Trans, on G eosci. and Rem ote Sens.
vol. GE-23, no. 1, pp. 25-34.
Kasischke, E. S. and N. L. Christensen, Jr., 1990, Connecting forest ecosystem
and microwave backscatter models, Int. J. Rem ote Sens., vol. 11, pp. 12771298.
Kasischke, E. S., L. L. Bourgeau-Chavez, N. L. Christensen, Jr., and E. Haney,
1994a, Observations on the sensitivity o f ERS-1 SA R image intensity to
changes in aboveground biomass in young loblolly pine forests, Int. J.
Rem ote Sens., vol. 15, pp. 3-16.
Kasischke, E. S., N . L. Christensen, Jr., and E. Haney, 1994b, M odeling o f
geometric properties o f loblolly pine tree and stand characteristics for use in
radar backscatter models, IEEE Trans, on G eosci. Rem ote Sens., vol. 32, no.
4 pp. 800-822.
Kasischke, E. S., N. L. Christensen, Jr., and L. L. Bourgeau-Chavez, 1995, Corre­
lating radar backscatter with components o f biomass in loblolly pine forests,
IEEE Trans, on G eosci. Remote Sens., vol. 33, no. 3, pp. 643-659.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Oh, Y, K. Sarabandi, a n d F. T . Ulaby, 1992, A n empirical model and an inver­
sion technique fo r radar scattering from bare soil surfaces, IE E E Trans. on
G eosci. Rem ote Sens., vol. 30, no. 2, pp. 370-381.
Oh, Y, K. Sarabandi, and F. T. Ulaby, 1994, A n inversion algorithm fo r retriev­
ing soil m oisture and surface roughness from polarimetric radar observation,
Proceedings o f IG A RSS, pp. 1582-1584.
Saatchi, S. S., D . M . L e Vine, and R. H . Lang, 1994, M icrowave backscattering
and em ission m odel for grass canopies, IE E E Trans, on G eosci. Rem ote
Sens., vol. 32, no. 1, pp. 177-186.
Sun, G., D. S. Sim onett, and A. H. Strahler, 1991, A radar backscatter m odel fo r
discontinuous coniferous forests, IEEE Trans, on G eosci. Rem ote Sens., vol.
29, no. 4, pp. 639-650.
Ulaby, F.T., Pi*. Batlivala, and M.C. Dobson, 1978, M icrowave backscatter
dependence on surface roughness, soil m oisture, and soil texture: Part I—
Bare Soil, IE E E Trans, on Geosci. and R em ote Sens. vol. GE-16, no. 4, pp.
286-295.
Ulaby, F.T., G.A. Bradley, and M .C. Dobson, 1979, M icrowave backscatter
dependence on surface roughness, soil m oisture, and soil texture: Part H—
Vegetation-covered soil, IEEE Trans, on G eosci. and Rem ote Sens.
vol.
GE-17, no. 2, pp. 33-40.
Ulaby, F. T., M oore, R. K., and Fung, A. K., 1982, M icrow ave Rem ote Sensing:
A ctive a n d P assive, vol. II, Addison-W esley Publishing Company, Reading,
Mass.
Ulaby, F. T., K. Sarabandi, K. McDonald, M. W hitt, and M . C. Dobson, 1990,
M ichigan m icrow ave canopy scattering m odel, Int. J. Rem ote Sens., vol. 11,
no. 7, pp. 1223-1253.
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62
W ang, Y., J. L. D ay, and G. Sun, 1993a, S an ta B arbara microwave backscattering
m odel for woodlands, Int. J. Rem ote Sens., vol. 14, no. 8, pp. 1477-1493.
W ang, Y., F. W . D avis, and J. M . M elack, 1993b, Simulated and observed back­
scatter at P-, L-, and C-bands from ponderosa pine stands, IE E E Trans, on
G eosci. Rem ote Sens., vol. 31, no. 4, pp. 871-879.
W ang, Y., E. S. Kasischke, J. M . M elack, F . W . Davis, and N . L. C hristensen,
Jr., 1994, T he effects o f changes in loblolly pine biomass and soil m oisture
variations on ERS-1 SA R backscatter, R em ote Sens. Environ., vol. 49, pp.
25-31.
W ang, Y., F. W . Davis, J. M. M elack, E . S. Kasischke, and N . L. C hristensen,
Jr., 1995, The effects o f changes in forest biom ass on radar backscatter from
tree canopies, Int. J. Rem ote Sens., vol. 16, no. 3, pp. 503-513.
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63
Table 2
Table 1
Loblolly pine stand data
stand #
stand age
(years)
litter depth
(cm)
7
14
43
44
51
68
62
23
= 100
=60
29
8
3.7
4.8
3.2
6.5
3.9
2.1
RMS height and correlation length summary statistics
RMS height (cm)
correlation length (cm)
m ean
s.d.
4.2
3.6
3.2
3.2
5.7
3.2
27.7
21.3
27.9
23.9
32.7
33.2
9.1
12.3
17.0
13.6
10.6
10.6
0.8 - 5.7
28.5
12.0
stand #
mean
s.d.
range
7
14
43
44
51
68
2.5
1.8
2.0
2.0
2.4
2.1
1.2
0.9
0.9
0.8
1.3
0.6
1.1
1.0
0.8
1.0
0.9
0.9
all
2.2
1.0
-
range
14.9
6.7
13.4
8.4
16.6
12.8
-
40.0
46.1
56.8
52.4
48.8
47.5
6.7 - 56.8
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64
Fig. L
Rem oving forest litter along a surface roughness transect
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 2
Recording a surface profile using the surface roughness gauge
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the SRC K G Pms
Per^ission
°fthe
c°Pyright
°Wrier,
FurtherrP„
Product;
Potior,
Pr°hibiteci
withoUt
Perrr>issi0n
67
o
Duke Forest, Stand 43
autocorrelation
IT)
o'
O
o'
U)
o'
I
-1/eI = .237 m.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
displacement (meters)
Fig. 4 Autocorrelation function as a function of surface displacement
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68
co -
RMS height (cm)
in -
1
2
3
-100 yrs60-62 yrs.
20-28 yrs.
4
8 yrs.
co cm
-
20
30
40
correlation length (cm)
Fig. 5 RMS height vs. correlation length of 4 loblolly pine age groups
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69
Chapter 4:
Sensitivity o f m odeled C - and L-band m icrowave backscatter
to ground surface param eters in loblolly pine forest
A bstract
Variations and fluctuations o f forest floor scattering properties can lead to variability
in radar backscatter from forest, thereby interfering with SAR backscatter-based estima­
tion of forest biophysical characteristics. Understanding how forest backscatter varies
over the range of probable surface conditions is important in the selection of appropriate
radar bands and incidence angles for forest sensing applications and for quantifying
uncertainty of the derived forest characteristics. Using a canopy backscatter model, we
examined the sensitivity o f modeled C- and L-band backscatter to five surface parameters
in three loblolly pine stands representing different stages of development in Duke Forest
(NC). The parameters were litter depth and moisture content, soil RMS height and corre­
lation length, and soil moisture content. O f the bands considered, L-HH backscatter had
the highest sensitivity to the surface parameters, followed by L - W . In the incidence
angle range of 20°—40°, L-HH varied by 5 3 —9.6 dB as the surface parameters changed
over their range, whereas L - W varied by 3.7—4.5 dB. At shallower incidence angles the
sensitivities were lower, but probably not negligible. C-HH and C - W were sensitive
only at steep incidence (0O = 20°—30°) for the lowest biomass stand studied. C-HH and
C - W sensitivity fell off with increasing incidence angle and stand maturity. L-HV
showed slight sensitivity for the low-biomass stand and at 0O = 20°—30°, but was other­
wise insensitive. C-HV was insensitive to the surface for all stands and angles. At Lband the most influential o f the 5 parameters was soil RMS height, whereas at C-band all
parameters were more equal in influence. The modeled sensitivities suggested that the
surface-related uncertainty in forest backscatter at L-HH and L -W , and at C-HH and CW at steep incidence angles, may be unacceptably large for many applications.
This paper has been published as:
Wang, Y., J. L. Day, and F. W. Davis, 1998, Sensitivity of modeled C - and L-band
radar backscatter to ground surface parameters in loblolly pine forest, Remote Sens.
Environ., vol. 66, pp. 331-342.
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70
1. Introduction
Many studies have explored the potential o f imaging radar for estimating forest
biophysical characteristics, especially biomass (e.g. Hussin et al., 1991; Dobson et al.,
1992; Kasischke et al., 1994a; Dobson et al., 1995; Harrell et al. 1997; Ranson and Sun,
1997). In reviewing ecological applications o f SAR backscatter, Kasischke et al. (1997),
while acknowledging that their opinion represents the optimistic side o f an ongoing
debate, state that radar appears to offer the greatest promise o f remote sensing techniques
for estimating the forest biomass. Indeed, the ability o f microwaves to penetrate through
cloud cover and respond to branches and trunks deep in the forest canopy gives SAR a
potential advantage over optical sensors such as LANDSAT TM. However, deep pene­
tration also carries with it a drawback; it ensures that forest backscatter is a complex mix­
ture of backscatter from several scattering mechanisms that vary in relative importance
depending on forest structure, moisture content and ground surface conditions. Whether
or not the many sources of variability in forest backscatter can be brought into tight
enough control to permit accurate synoptic biomass assessment is an important research
question.
Recent studies indicate that backscatter response to forest biomass depends on
stand-to-stand differences in stand structure (tree height, diameter, and stocking density)
and also on species-related differences in growth form and branching pattern (Dobson et
al., 1995; Imhoff, 1995). Lack o f control over these variables is one cause o f weak
backscatter-biomass regressions and apparent "saturation" of the regression curves at low
biomass levels. By segmenting a SAR backscatter image into structurally homogeneous
forest types (utilizing remotely sensed data or prior knowledge), it may be possible to
make accurate regression estimates of important forest parameters for each forest type, at
least for some forests (Dobson et al., 1995).
Another source of backscatter variability that complicates SAR estimation o f forest
biomass is the forest floor. Forest backscatter modeling studies have shown that, depend­
ing on the radar parameters and the scattering and attenuation properties o f canopy and
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71
ground, a significant fraction o f total forest backscatter may be surface-related (e.g.
McDonald et al., 1990; Chauhan et al., 1991; Pulliainen et al. 1994; Wang et al., 1994).
Surface-related backscatter, as we use the term, includes direct ground surface backscatter
and also double-bounce backscatter from trunk-ground and crown-ground interactions
(Fig. 1). Where the magnitude of surface-related backscatter approaches that of canopy
backscatter, variability in forest floor scattering will tend to weaken regressions and may
bias estimates of forest parameters. Stratifying the forest according to stand structure and
canopy geometry (Dobson et al., 1995) can be expected to control for some part of the
surface-related backscatter variability for two reasons. First, surface-related backscatter is
a function of branch and trunk scattering (in the double-bounce pathways) as well as
canopy attenuation. Second, the forest floor is not independent o f the overlying canopy,
being linked to it by climate, characteristics of litter, etc. Yet, even within a forest type,
variability of forest floor scattering can significantly affect total forest backscatter.
Apart from one laboratory study o f the bistatic scattering coefficient of litter sam­
ples (DeRoo et al., 1991), we find the literature lacking in studies o f forest floor scatter­
ing or its variability. There appear to be no direct, in-situ measurements o f floor scatter­
ing properties and their variability in different types of forest, probably because such
measurements are difficult to make. For want of a better alternative, forest backscatter
models generally utilize soil surface scattering models that were developed and tested
mainly on bare agricultural soils (e.g., Ulaby et al., 1982; Oh et al., 1992). On the basis
of these surface models it is evident that forest floor reflectivity and backscatter
coefficient fluctuate with changes in soil moisture content. Forest floor scattering proper­
ties may also vary from stand to stand within a forest type due to differences in soil sur­
face roughness and the litter layer.
Model studies indicate that these variations can significantly affect surface-related
backscatter and total forest backscatter, and may alter the backscatter-biomass relation­
ship. For example, backscatter simulations of boreal conifer forest at X- and C-band
( W polarization, 23° incidence angle) indicate that total forest backscatter increases with
increasing stem volume for dry soil, decreases with increasing stem volume for wet soil.
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72
and is almost constant across stem volumes for moist soil (Pulliainen et al., 1994). Wang
et al. (1994) observed similar trends in ERS-1 (C -W ) data from Iow-biomass (< 5
kg/m2) loblolly pine forest. In the same study, simulations indicated that forest back­
scatter increases with soil surface roughness. L-band backscatter increased with soil
moisture in walnut orchard (McDonald et al., 1990). In hemlock forest, modeled
surface-related backscatter at C-, L-, and P-band was negligible at 39° incidence, but
demonstrated strong angular dependence; at 30°, direct surface backscatter at P-HH was
comparable to canopy backscatter (Chauhan et al., 1991). hi Amazonian forest, canopy
scattering dominated total modeled forest backscatter at C- and L-band (Wang et al.,
1995a), so that variations in surface-related backscatter were insignificant, but at P-HH,
backscatter significantly increased with increases in soil moisture. From these and other
studies, we can say with confidence that the expression of surface-related scattering in
total forest backscatter depends on forest characteristics and radar wavelength, polariza­
tion and incidence angle, in addition to the forest floor properties.
In this paper, we study the sensitivity of loblolly forest backscatter to variations in
its forest floor properties. We are interested in how much variation in the backscatter
results from the range of the forest floor properties measured at the Duke Forest, North
Carolina. Specifically, how sensitive is total backscatter to the observed variation in soil
surface roughness, soil moisture content, litter depth, and litter moisture content? How
does sensitivity differ between C- and L-band, among HH, HV, and W
polarizations,
and over 20° to 60° incidence, for loblolly forest stands representing three biomass lev­
els? Under what circumstances can we ignore surface-related scattering, and when must
we take it into account? Our inquiry and results are limited to loblolly pine forest, but
the questions are of generic practical significance. Determining how much forest back­
scatter variation arises from forest floor scattering (and other sources) is prerequisite to
estimating the uncertainty in SAR backscatter-based estimates of forest biomass. Also, it
provides information about which bands and angles are insensitive to surface variation
and which, therefore, are reasonable to use in regressions. To answer these questions, we
conduct a sensitivity analysis using available ground data and the canopy backscatter
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73
model previously tested in loblolly forest (Wang et al., 1994; Wang et al., 1995b). We
also incorporate existing surface models, with the addition o f a litter layer model (DeRoo
et al., 1991).
2. Study area and methods
2.1. Ground data
2.1.1. Loblolly pine stand data
The forests utilized in this study are located in the Duke University Forest, North
Carolina. Loblolly pine (Pinus taeda L.) is the dominant species in the stands investi­
gated. The Duke Forest has been much studied as an example of old-field successional
chronosequence (Christensen and Peet, 1981). In general, the sequence begins with
colonization of an abandoned field by pines. During the establishment phase o f a stand,
pine density increases rapidly (in roughly 10 years) from 0 to the site-dependent max­
imum. Leaf area index (LAI) also increases to its maximum. Following establishment, at
stand age of about 15 years, the thinning phase begins and continues for about 50 years.
During this period, pine tree size increases and density declines, LAI holds constant, and
total biomass steadily increases to its maximum. Hardwoods gradually develop in the
understory. The transition phase to hardwood forest follows thinning. The pines die and
are replaced by hardwoods as the principal canopy trees. LAI and total biomass fall
below their peak pine forest levels. Some 150 years after initial establishment the stand
may achieve a steady state as a hardwood forest, containing few pines.
Because loblolly stand biomass levels corresponding to the various successional
stages are represented in Duke Forest in well mapped and easily accessible stands, Duke
Forest has proven to be a useful site for research on the relationship o f backscatter to
above-ground forest biomass (Dobson et al., 1992; Kasischke et al., 1994a; Wang et al.,
1994; Kasischke et al., 1995; W ang et al., 1995b, Harrell et al., 1997). During 1994-95,
Eric Kasischke and his colleagues at the Duke University resurveyed many loblolly
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74
stands in connection with the Shuttle Imaging Radar (SIR-Q campaign. The Duke team
provided the raw data for this study, including stand density and tree diameter at breast
height (dbh) (Harrell, personal communications, 1995-6). The detailed stand data,
together with allometric estimates o f loblolly canopy parameters based on them, allow us
to parameterize our canopy backscatter model.
For this study, we selected 3 loblolly stands, aged 15, 29 and 62 years, which we
designate as stands SI, S2 and S3 (Table 1). Crown dry biomass and total dry biomass
were estimated by regressions (Hepp and Bristler, 1982; Kasischke et al., 1994b). The
three stands represent the late establishment, early thinning, and late thinning (or early
transition) phases. The stands differ markedly in appearance and structure, and may also
be expected to differ in backscatter response to forest floor variations. The major
difference between SI and S2 is the greater tree size and canopy development of S2
(Table 1). Canopy biomass o f S2 is more than twice that of S I, and total biomass is
nearly 4 times as great. Some thinning has probably occurred in S2 since its establish­
ment, but its density is about the same as the younger SI; this may be attributable to site
differences. In contrast, stand S3 has thinned to less than half the density of S2. Canopy
biomass is the same in S2 and S3, but total biomass is larger in S3 because o f greater
bole volume. In short, SI is a dense stand of small trees with partially developed
canopy, S2 is an equally dense stand of somewhat larger trees with fully developed
canopy, and S3 is a fairly open stand o f large trees ranging up to 70 cm dbh.
2.1.2. Surface parameters
In April 1994, we measured soil moisture content, soil dielectric constant, and sur­
face roughness in the Duke Forest. Litter depth and moisture content were also sampled.
We studied 28 plots in 6 loblolly stands ranging from 8 to 90 years o f age.
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75
2.1.2.1. Soil moisture content, dielectric constant, and surface roughness
A total of 85 soil samples were collected to measure the soil moisture (Table 2).
The samples were taken from the top 10 cm o f soil beneath the litter layer. Individual
measurements of volumetric soil moisture ranged from 12—44%. Mean daily volumetric
soil moisture (for all stands measured on each day) varied from 24-31%.
Concurrent with the soil sampling we measured soil dielectric constant with a port­
able L-band dielectric probe. This was done to confirm the appropriateness of existing
models to estimate soil dielectric constant from volumetric soil moisture under Duke
forest soil conditions. Dielectric constant was measured at the surface (under litter) and
at 5 cm and 10 cm depths at each of three points clustered around each soil sample. The
3 depths and 3 samples were then averaged for each sample point. We determined that a
semi-empirical model (Ulaby et al., 1986) produced a satisfactory fit to our measured soil
moisture and dielectric data, and we used this model for all computations of soil dielec­
tric constant.
Two soil surface roughness parameters, RMS height and correlation length, are
needed for the surface backscattering models. For our field sampling, the soil "surface"
was defined as the interface between the layer of litter and loose duff and the more con­
solidated material below it. The surface may coincide with the A l soil horizon or may
lie above it in the 0 2 horizon. We sampled surface RMS height and correlation length in
28 randomly located plots in the 6 stands, hi each plot we measured 2 perpendicular
transects using a 4.6 m long pin frame (1.9 cm pin spacing). RMS height for individual
transects ranges from 0.8 to 5.7 cm, with a mean of 2.1 cm (Table 3). Correlation length
ranges from 6.7 and 58.6 cm, with a mean of 28.5 cm (Table 3).
2.1.2.2. Litter moisture content and depth on the forest floor
A rectangular wooden frame (approx. 0.34 m2) was positioned at a random location
within a 3 m radius of each plot center at the same time as dielectric and soil moisture
measurements were made. Litter within the frame was removed to the level of well
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76
consolidated compacted duff or mineral soil. Knives and pruning shears were used to cut
through the litter along the inside edge o f the frame. The litter was removed with the
fingers; our helpers were instructed to excavate carefully like archeologists, that is,
remove the loose litter only, but do not disturb the surface o f the soil or consolidated
organic layer where present. The samples were collected in paper bags which were then
placed in plastic bags and returned to the lab for drying and weighing. Measured
volumetric moisture content of the litter is 1.2-14.6% with a mean of 5.4% (Table 4).
Depth of litter (and loose duff) was estimated by measuring with a ruler at 10-15 points
with the sample frame. Since depth varied greatly from point to point, the estimates were
probably only accurate to about ±20%. The litter layer is about 1-9 cm thick with a
mean of 4 cm (Table 5).
2.2. Backscatter modeling of loblolly forest
To model the backscatter from the loblolly pine forest, we employ a microwave
canopy backscatter model (Wang et al., 1994; Wang et al., 1995b). For this study we
modified the surface models to account for effects of the litter layer. Because the cano­
pies of the loblolly pine stands are partially to fully closed, the canopy backscatter model
version designed for continuous tree canopies is used. The model is based on the radia­
tive transfer equation. Canopy, tree trunks, and ground surface are modeled as scattering
layers. The model consists of four major components, canopy scattering, trunk-ground
interactions, canopy-ground interaction, and direct-surface backscattering (Fig. I). The
canopy backscatter model has been tested and validated for several forests, including the
loblolly pine stands at the Duke Forest (Wang et al., 1994; Wang et al., 1995b). In those
papers, the authors also detailed the derivations of the model input parameters (such as
stand parameters and tree canopy parameters, etc.) from the field measurements of the
loblolly pine stands. The model gave reasonable predictions o f C- and L-band AIRSAR
backscatter from loblolly stands. This leads to some assurance that the model is well for­
mulated for the Duke loblolly forest and will give meaningful results in our sensitivity
study.
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77
Different surface backscatter models were utilized for C- and L-band, in accordance
with the validity regions of the models. Thus, the geometric optics model (Ulaby et al.,
1982) was used for C-band simulations, while a simple empirical model (Oh et al. 1992)
was used for L-band. Direct surface backscatter horn both models, and surface specular
scattering as well, was modified by the forest floor litter model.
2.3. Modeling the scattering from forest floor litter
Depending on thickness, composition, and moisture content, forest litter has the
potential to modify backscatter and specular scatter from the underlying soil surface. It is
not feasible to make direct measurements o f pine litter dielectric constant (with a field
dielectric probe) because the litter consists o f a loose mixture o f organic debris and air.
Pine litter roughness is also difficult to measure, and ill-defined as well. In a modeling
sense, the pine litter layer could be considered a loosely packed blanket o f randomly (and
horizontally) oriented needles on the ground. In their laboratory study o f bistatic scatter­
ing from forest litter samples, DeRoo et al., (1991) proposed a simple slab model for cal­
culating the specular reflectivity from a ground surface with litter present. We use
DeRoo’s method and model the litter layer as a lossy dielectric slab over a dielectric
half-space medium (soil). Based on this approach, the litter layer a) absorbs the incom­
ing microwave waves before and after the waves are specularly reflected by the underly­
ing soil surface, and b) changes the air-soil to a litter-soil interface, thereby changing the
relative dielectric constants at the soil surface (Fig. 2). Reflectivity from this model with
2-way attenuation from the litter layer is:
„
-2 o d /c o s e ,_
rslabpq= e
r 12pq
(1)
where d (m) is the depth of the litter slab, and 0 1 the incidence angle in the litter slab, a
(m_I) is the power attenuation coefficient of the litter layer, and
a = ko-p^r
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(2)
78
where kg (m-1) is radar wavenumber in the air. et and et" are the real and imaginary
parts of the dielectric constant o f the litter (£j). The et is computed from a regression
model for pine needle litter (DeRoo et al., 1991):
£i = £[ + M
(3)
E[ = I -t- 1.072p + 4.6mv_[ + 25.7mv_1/ f
(4)
£[" = 4.37mv_!
(5)
with
where p is bulk density o f the litter (g/cm3),
the litter volumetric moisture content,
and f (GHz) radar frequency. The T I2w (p, q = h, v) in Eq. (1) are the reflectivity ele­
ments of the pq polarizations at the Iitter-soil interface. The relative dielectric constant
(Ej.), i.e., soil £j divided by litter £| at the Iitter-soil interface, is
^ = £3 / 6!
(6 )
Because the soil surface at the Duke Forest is not smooth, we modify theTI2w with
a factor proposed by Barrick (1970) to account for decreasedspecularscatteringfrom a
non-smooth soil surface. The factor (F) is
F = e"2(kohcos0l)2
(7)
where h (m) is the roughness RMS height of the soil surface.
2.4. Model simulations and modeled sensitivity
The sensitivity of forest backscatter to soil surface and litter conditions was exam­
ined for each of the three loblolly stands (Table 1). Forest canopy parameters were fixed
for each stand, while the soil surface RMS height and correlation length, soil volumetric
moisture content (mv_s), litter volumetric moisture content (mv_[), and litter depth were
varied independently over a 5-D modeling region. The bounding values of the analysis
correspond to the ranges o f our Duke field data (Tables 2-5).
These values are
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79
11.6-43.8% for
0.8—5.7 cm for RMS height, 6.7-58.6 cm for coirelation length,
and 1.2-14.6% for m ^ .
For litter depth, 2.S-8.9 cm is used for S2 and S3, while
1.3—3.8 cm is used for S I, a thicker litter layer being physically unrealistic for the young
stand.
Simulations were carried out at C- and L-band, HH, HV, and VV polarizations, and
5 incidence angles (20°, 30°, 40°, 50°, and 60°) for the 3 stands. For each stand-anglepolarization-wavelength combination (with a total o f 90 combinations), backscatter simu­
lations were run for each node o f a 10x10x10x10x10 uniform grid in the 5-D modeling
region, i.e., at 10 equally spaced values on each parameter or axis. Thus, we have
100,000 modeled backscatter numbers after one simulation. We sort them to find the
minimum and maximum backscatter caused by the variations o f the surface parameters.
We then compute the ratio (expressed as a difference in dB) of the maximum total back­
scatter to the minimum total backscatter over the 5-D modeling region to show how large
a difference in total backscatter is expected over the full range of modeled surface param­
eters.
The ratios may be readily interpreted as a surface sensitivity index (SSI). It may
also be thought of as an indicator of the backscatter uncertainty introduced by surfacerelated backscatter variability. Since SSI is based on the range o f individual plot meas­
urements of surface and litter conditions (not on stand means) it is a conservative index.
It represents the modeled radar response to a "worst case" range of surface conditions
measured at the Duke site during our April 1994 field study.
Using SSI, we define the following sensitivity categories:
1)
insensitive case — SSI < 1 dB
2)
intermediate case — 1 dB < SSI < 3 dB
3)
sensitive case — SSI > 3 dB
We offer these categories as a reasonable (though somewhat arbitrary) guide for
interpreting the SSI in coniferous forest. The 1 dB and 3 dB thresholds come out of our
experience with ERS-1, AIRSAR and SIR-C data from Duke forest. Because we have
found that the G° measurements of two similar stands or two independent measurements
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80
of the same stand often differ by more than 1 dB, we would say agreement on the order
of 1 dB is quite good. Hence, if o° variation is less than 1 dB over the full range o f sur­
face variation, surface sensitivity may be considered low.
For comparison, the best
pass-to-pass and cross-swath calibration uncertainties achieved during the SIR-C missions
were estimated at 1.0 dB (Freeman et al, 1995). The 3 dB threshold for the sensitive
case is more solidly justified. Backscatter from loblolly stands over their full biomass
range (excluding very low biomass stands, i.e., <=1 kg/m2), imaged at the same
incidence angle within a single data-take, may span a o° range o f only about 3 dB (Har­
rell et al, 1997). Therefore, where changes in surface conditions bring about <y° varia­
tions exceeding 3 dB, the level of surface sensitivity is seriously problematic. Recogniz­
ing that the sensitivity categories are an interpretive overlay on our results, we present the
simulation data (Tables 6-9) as SSI numerical values, with sensitivity classes indicated by
the typeface.
3. Results
3.1. Modeled sensitivity of C- and L-band backscatter to soil surface and litter con­
ditions
Based on the above criteria, we can classify sensitivity o f modeled C-band forest
backscatter to surface parameters (Table 6). The sensitive cases are C-HH and C-VV at
0O = 20°-30° in stand SI and C-HH at 0O = 20° in S2. The insensitive cases are C -W
at 0O = 60° in S I, C-HH and C - W at 0O = 50°-60° in S2, C-HH and C - W at 0O =
30°-60° in S3, and C-HV for all incidence angles and stands.
At L-HH, with one exception, the backscatter is strongly sensitive to the surface
(Table 6). The exception is stand S3 at 0O = 60°, in which case greater canopy attenua­
tion of surface backscatter results in lower sensitivity. As is the case for C-HH and CW , surface sensitivity at L-HH decreases with increasing incidence. However, unlike
C-band, at 0O = 20°-40° sensitivity does not decrease monotonically with increasing
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81
biomass. L-HV is insensitive to the surface except for SI at 0O = 20°-40° and S2 at 0O
= 20°, where sensitivity is intermediate. L-HV sensitivity decreases with increasing
incidence and with increasing stand maturity. L - W is sensitive for all stands at steep
incidence angles and has intermediate sensitivity at shallow incidence (Table 6). hi con­
trast to the other bands, maximum L -W sensitivity is not found at the steepest incidence,
but at 0o=3Oo-4O°, and not for the youngest stand, but for the most mature.
3.2. Comparative sensitivity o f modeled backscatter to Individual soil surface and
litter param eters
So far, we have presented overall sensitivity o f backscatter to the soil surface and
litter parameters over the entire 5-D modeling region. In this section, we consider which
individual parameters have major influence on sensitivity for the various stand-anglepolarization-wavelength combinations. We are mainly interested in the combinations that
show intermediate to high sensitivity to the surface (Table 6). The insensitive cases need
not be analyzed further.
Modeled sensitivity of backscatter to each surface parameter varies within the 4-D
space formed by the other four parameters. To evaluate the sensitivity for each parame­
ter, we compute the range of o° (in dB) at each point in the 4-D space; the maximum
value thus obtained is reported (Tables 7-9). For example, C-HH backscatter for stand
SI at 0O = 20° has a maximum range of 5.3 dB over the whole 5-D modeling region
(Table 6). The range o f modeled backscatter obtained by varying mv_s over its range
reaches a maximum of 2 3 dB at some iocation(s) in the 4-D space formed by soil sur­
face RMS height, correlation length, n v u and litter depth (Table 7). Similarly, the max­
imum sensitivities obtained in this example by varying RMS height, correlation length,
mv_[, and litter depth over their ranges are 4.7, 4.7, 4.2, and 2.5 dB respectively. There­
fore, we find that for this example (i.e., C-HH, stand S I, 0O = 20°), modeled backscatter
is most sensitive to the surface roughness parameters and least sensitive to m ^ .
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82
For C-band we make the following observations (Table 7). For stand SI, C-HH
and C -W are sensitive to soil surface RMS height and correlation length, and mv_i at 0O
= 20°. Sensitivity decreases with increasing 0O, reaching borderline insensitive values at
0O = 50°-60°. Sensitivity to the individual surface parameters also decreases with stand
maturity, so that in S2 at 0o>4O°, C-band is insensitive (or nearly so) to all 5 parameters.
For S3, C-band has intermediate sensitivity to all the parameters at 0O= 20° and is insen­
sitive at larger incidence angles.
L-HH and L - W show intermediate to high sensitivity to the surface for all standangle combinations (Table 6). Therefore, there are more cases to consider at L-band
(Table 8) than at C-band (Table 7). L-HH and L -W have almost no sensitivity to sur­
face correlation length, but have at least intermediate sensitivity to the other four parame­
ters in most cases.
L-HH sensitivity to the four surface parameters of interest is highest for soil RMS
height, followed by litter moisture and depth, and then soil moisture (Table 8). Sensi­
tivity decreases with increasing 0O, except in the case of mv_j and litter depth for stand
SI, where the trend may be weakly the reverse. All four parameters have more effect on
S2 backscatter than backscatter from the other stands, though the stand-to-stand
differences in sensitivity are fairly small compared to incidence-related differences. The
lower sensitivity to litter moisture and depth in SI as compared to S2 and S3 is the
consequence of having modeled a thinner litter layer for SI than the other stands.
L -W is considerably less sensitive to the individual parameters than is L-HH
(Table 8). Sensitivity to RMS height is greatest and to litter depth is least. However,
there are only four sensitive cases, namely, RMS height in S2 and S3 at 0O = 30°-40°.
Otherwise, most cases fall into the intermediate sensitivity class, with the exceptions of
litter depth in SI (insensitive because of the shallow litter layer modeled) and a few cases
at the shallowest incidence angle. As was observed in relation to overall sensitivity of
L - W to the surface (Table 6), sensitivity to the individual parameters is highest at
moderate incidence angles rather than steep ones.
Also, L - W
sensitivity to the
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83
individual parameters (except for
and at shallow incidence angles) increases slightly
from the young to the mature stand.
L-HV shows intermediate sensitivity to mv_s for SI at 0O = 20°, and to RMS height
for SI at 0O = 20°—30° and S2 at 0O = 20°. L-HV is otherwise insensitive to the indivi­
dual surface parameters (Table 9).
4. Discussion
4.1. Patterns of sensitivity observed
Our simulation results (Tables 6-9) lead to the following generalizations:
1)
Modeled sensitivity to the surface at C-HV is almost nil.
L-HV sensitivity is low,
except for the Iow-biomass stand SI at 0O = 20°-40° and S2 at 0O = 20°; in these
cases sensitivity is intermediate. Therefore, surface conditions should not interfere
seriously with measurements o f forest canopy faackscatter at C-HV and L-HV, at
least at incidence angles greater than, say, 40°.
2)
At both C- and L-band, sensitivity o f co-polarized backscatter to the surface
decreases with increasing incidence angles, mainly because o f greater canopy
attenuation of surface backscatter at shallower incidence angles. At L -W at steep
incidence there is one exception to this rule. <J°i_w is smaller at 0O = 20° than at
30°. That is because at 0O = 20°, the ground-trunk reflection at the trunk surface
approaches the Brewster angle, resulting in reduced trank-ground backscatter.
3)
Co-polarized backscatter at L-band is much more sensitive to the surface than at Cband. This is attributable to greater canopy penetration at L - than C-band, and also
the greater contribution o f the trank-ground term at L-band. L-HH is very strongly
conditioned by the surface parameters at all incidence angles, while L -W is some­
what less affected, falling into the intermediate sensitivity range at 0O= 60°. Rather
unexpectedly, modeled L-band sensitivity does not decrease appreciably with
increasing stand maturity, except at L-HH at the shallowest incidence angles.
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84
4)
C-HH and C - W are found to be sensitive only for stand S I at 0O = 20°—30° and
S2 at 0O = 20°. At incidence angles o f 40° or greater, the influence of the surface
is intermediate to small.
5)
In cases where overall sensitivity to the surface is intermediate or greater, all five
surface parameters contribute to the sensitivity, with the exception of correlation
length, which has negligible effect at L-band. Surface RMS height is the most
influential parameter at L-band, owing to its control over trunk-ground backscatter.
The litter layer parameters are important sources o f sensitivity at C- and L-band. In
the case of stands S2 and S3 (in which modeled litter layer depth ranges up to 8.9
cm), litter depth and moisture content have a larger effect than soil moisture on
modeled L-HH backscatter.
4.2. Significance and limitations
Our modeling and analysis suggest that only at C-HV and L-HV (at shallow
incidence) can loblolly forest backscatter be assumed free of variation caused by five
forest floor parameters. The other bands studied are subject to varying degrees of surface
influence from these parameters, about which the analyst seldom has any information.
L-HH and L - W are especially sensitive to surface conditions, with L-HH changing by as
much as 7 to 9 dB over the range o f surface conditions modeled. The results seem to
argue against the use of L- or C-band co-polarized backscatter- (except perhaps C-band at
shallow incidence) for estimating forest biomass, unless some method can be developed
for correcting for surface-related backscatter.
Previously, we noted that the surface sensitivity index is conservative, in the sense
that the modeling region is bounded by the ranges of individual plot measurements of the
five surface parameters measured during our April, 1994 field work in Duke Forest As
one might expect the with in-stand variation in the surface parameters is greater than the
between-stand variation (Tables 2-5). In other words, much o f the variation occurs at
relatively fine spatial scales. We cannot, on the basis o f our sparse ground surface data,
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85
determine the actual spatial scales of surface parameter variation. Depending on SAR
pixel size and how the data is processed (filtering, segmentation, etc.), the c ° variations
caused by fine-scale surface variations may tend to average out, in which case actual sen­
sitivity could be substantially lower than SSI indicates.
On the other hand, we have understated the variability o f forest floor scattering pro­
perties by underestimating the ranges o f the five parameters modeled and also by exclud­
ing some potentially important surface parameters. Our field measurements were limited
to six stands in a fairly small geographic area over a period o f two weeks. If we had
made a more comprehensive study of the Duke Forest floor, we would probably have
measured wider ranges for RMS height, correlation length, and litter depth. Too, if we
had based SSI on the annual variation in moisture conditions, the soil and litter moisture
ranges would have been wider (lower minima). In order to keep the simulations manage­
able, we chose not to model several parameters, including local ground surface slope and
aspect, presence of snow cover, and freezing of the ground. Had we modeled wider
parameter ranges and included additional surface variables in the study, then SSI values
would no doubt have been greater than we reported.
Another issue that we need to acknowledge is the difficulty o f verifying the model­
ing results. Though the canopy model we used was previously demonstrated to be in
general agreement with SAR data from Duke Forest loblolly stands, and the surface
models are believed to be within their ranges of validity, this study exercises the compo­
site model outside the range o f conditions that have been empirically verified. Case in
point, the high SSI values modeled at L-HH and L - W are largely the result of large
trank-ground backscatter contributions over part o f the modeling range. We would like
to see stronger empirical support for the double-bounce reflection model over a wide
range of conditions. These potential weaknesses in the modeling are at present unavoid­
able, because it is exceedingly difficult to arrange empirical SAR studies that adequately
control for all the surface and forest variables.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
Limitations of the study notwithstanding, the high sensitivities modeled for L-HH,
L -W , and C-HH and C - W at 0O = 20°—30° (Table 6) should sound a note of caution.
If the true surface sensitivity even approaches our simulated SSI values, then it follows
that variation and fluctuation in the ground surface parameters cannot be ignored without
inviting large errors when estimating forest biophysical properties using L-HH and L -W .
On a more positive note, this study confirms the widespread understanding that C- and
L-band cross-polarized backscatter is very little affected by the surface, at least in con­
tinuous canopy forest.
4.3. Relation of backscatter-biomass correlation to surface moisture sensitivity
Harrell et al. (1997) report backscatter-biomass correlation coefficients (r) computed
for SIR-C backscatter acquired at 0O=32° at Duke Forest under moist forest floor condi­
tions (April 12, 1994) and dry conditions (October 3, 1994). Their data indicate that
correlations of backscatter to total biomass at L-HV, L - W and C-HV are greater on the
dry day than the wet day. At C-HH and C -W the correlations are weakly positive on
the dry day, becoming weakly negative on the wet day. At L-HH the positive correlation
is appreciably greater on the wet day than the dry day. The authors suggest that these
differences are "probably the result of the difference in moisture conditions." It would be
interesting to compare these correlation differences to our model predictions (as one
reviewer of our paper noted).
There are at least two ways in which increased soil moisture might affect
backscatter-biomass correlations. First, wet ground could increase or decrease the corre­
lations by changing the slope o f the backscatter-biomass relations. For radar bands at
which double-bounce backscatter is insignificant, an increase in soil moisture should lead
to an increase in direct surface backscatter from low-biomass vegetation that is greater
than the increase from mature forest. This increase would reduce the slope of the
backscatter-biomass relation (which is generally positive for dry surface conditions),
thereby weakening the backscatter-biomass correlations. In such a case, o° sensitivity to
surface moisture would be greater for a low-biomass stand than an high-biomass one.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87
On the other hand, in bands at which enhancement of double-bounce backscatter by wet
ground is stronger than enhancement o f direct soil backscatter, backscatter of the high
biomass stands could increase more than that of the low biomass ones for wet conditions,
leading to a steeper curve and increased correlation. In this case, we would expect highbiomass stand backscatter to be more sensitive to surface moisture than low-biomass
stand backscatter. Thus, we would predict 1) that, for radar bands that show greater
modeled moisture sensitivity for low than for high-biomass stands, correlation should be
lower for wet than for dry ground conditions, 2) that, where moisture sensitivity is
greater for high than low-biomass stands, correlation should be higher for wet than for
dry ground, and 3) that, where sensitivity to soil and litter moisture is low, there should
be little or no difference in backscatter-biomass correlation between wet and dry days.
A second way in which increased surface moisture might affect backscatter-biomass
correlations is by increasing the dispersion of backscatter data. Spatial variability of soil
moisture may be greater when the absolute level of soil moisture is higher, resulting in
greater scatter of the backscatter data and weaker correlations. It is unclear whether this
mechanism significandy affects the correlations.
Modeled C-HH and C - W backscatter at 0o=3O° (near the 32° incidence o f the
SIR-C data analyzed by Harrell et al.) has intermediate sensitivity to both soil and litter
moisture for stand S I, with sensitivity decreasing for higher biomass stands (Table 7).
Backscatter-biomass correlation coefficients for the dry/wet days are 0.120/-0J06 for CHH and 0.178/-0.042 for C -W (Harrell et al., 1997, Table 2). This is consistent with
our first expectation, i.e., greater surface moisture sensitivity in low than in high-biomass
stands is associated with lower correlation for wet than for dry ground. That the correla­
tion reverses sign on the wet day was previously observed in ERS-1 data (Wang et al.,
1994). Sensitivity at L-HV is low, but as with C-HH and C - W it decreases with
increasing stand biomass (Table 9). Here also, correlation is higher on the dry day than
on the wet day (dry/wet = 0.818/0.727). Soil moisture sensitivity of L-HH and L - W
varies little with biomass, but litter moisture sensitivity increases with biomass (Table 8).
The increase is most pronounced at L-HH which shows high sensitivity to litter moisture
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
in the intermediate and high-biomass stands S2 and S3. By our second expectation, both
L-HH and L -W should have a higher backscatter-biomass correlations on the wet day
than on the dry day. This is the case for L-HH (dry/wet = 0.162/0.425); however, con­
trary to our expectation, correlation at L - W is higher on the dry day (dry/wet =
0.604/0.462). Finally, although C-HV has very low modeled sensitivity to the surface
(Table 6), correlation is higher on the dry than on the wet day (dry/wet = 0341/0.168).
One possible cause for the discrepancies at C-HV and L - W is that the training data
set from which Harrell et al. compute their correlations includes three young loblolly
stands with very low total dry biomass, estimated at 0 3 6 kg/m2 and below, as compared
to the low-biomass stand SI o f our study, estimated at 6.55 kg/m2. Because of the very
low biomass of these three stands, backscatter from them is undoubtedly more sensitive
to surface moisture than is backscatter from stand S I. As a result, at C-HV and L-VV
the decrease in slope of the backscatter-biomass relations under wet surface conditions
should be greater for the data set o f Harrell et al. than in our simulations. This may help
explain the lower-than-expected correlations on the wet day at C-HV and L-VV.
Although we seem to be able to reconcile the backscatter-biomass correlations with
our modeled surface sensitivities, it is important to realize that the correlations from the
SIR-C data (at least for the Duke Forest data set) can be highly variable. For example,
in our own study o f the same SIR-C data takes (10/3/94 and 4/12/94), the backscatterbiomass correlation at L-HV for dry/wet = 0.693/0.586. This is consistent with Harrell et
al; our correlations are weaker than they report because we excluded the low biomass
stands. Our analyses are based on 21 stands (October) and 16 stands (April), utilizing
stand data provided by Harrell (personal communications 1995-96). Now consider the
L-HV correlations for a second pair of SIR-C data takes at 0O=26° from October 9, 1994
(dry) and April 17, 1994 (moist). Forest and ground conditions on these dates were very
similar to conditions on October 3 and April 12. In this case, however, the L-HV to
biomass correlations for dry/wet are 0300/0.687. That is, correlation is higher on the
wet day. This is one of many strange turnings in the Duke Forest SIR-C dataset that
needs to be understood before we can be confident of our interpretations.
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89
5. Concluding remarks
Our purpose was to study the effects o f variations in forest floor properties on radar
backscatter from loblolly forest. To this end, we examined the sensitivity of modeled Cand L-band backscatter to soil moisture content, soil surface roughness (RMS height and
correlation length), litter moisture content, and litter depth, in the forest. Stand parame­
ters, tree parameters, and the ranges of surface parameters used for the simulations were
based on field data from Duke Forest. The contribution o f surface-related backscatter to
total stand backscatter was evaluated for three loblolly stands representing different stages
of the development of the forest.
The modeling results indicated L-HH and L - W backscatter were highly sensitive to
the surface parameters. L-HH varied by as much as 7 to 9 dB as surface parameters
changed. C-HH and C - W backscatter was sensitive only for the low-biomass forest at
steep incidence angles and had moderate to low sensitivity otherwise. C-HV and L-HV
were insensitive to the surface, except that L-HV had slight sensitivity for the lowbiomass stand at steep incidence angles. In general, modeled sensitivity decreased with
increasing incidence angle and with increasing stand maturity.
If our results characterize the true sensitivity o f coniferous forest backscatter to
forest floor variation, the influence of surface-related backscatter at L-HH and L - W is
too great to be ignored. Surface effects may also be problematic at C-HH and C - W
except at shallow incidence angles. The evidence suggests that, unless surface-related
backscatter can be controlled for, forest classifications and regressions based on L-band
(and to a lesser degree C-band) co-polarized backscatter potentially contain large uncer­
tainties. How large depends on the variability o f forest floor properties across the study
region, on radar incidence angle, and on the data processing approach. On the other
hand, cross-polarized backscatter may be considered relatively free of surface-related
uncertainty except at steep incidence angles, at least in continuous canopy forest.
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6. References
Chauhan, N. S., R- H. Lang, and K. J. Ranson, 1991, Radar modeling o f a boreal forest,
IEEE Trans. Geosci. Remote Sens., vol. 29, no. 4, pp. 627-638.
Christensen, Jr., N. L. and Peet, R. K-, 1981, Secondary forest succession on the North
Carolina Piedmont, Forest Succession: Concepts and Applications (D. C. West, H.
H. Shugart, and D. B. Botkin, Ed), Springer-Verlag, New York, New York, pp.
230-245.
De Roo, R., Y. Kuga, M. C. Dobson, and F. T. Ulaby, 1991, Bistatic radar scattering
from organic debris of a forest floor, Proceedings o f IGARSS. vol. 1, pp. 15-18.
Dobson, M. C., F. T. Ulaby, T. Le Toan, A. Beaudoin, E. S. Kasischke, and N. Christen­
sen, 1992, Dependence of radar backscatter on coniferous forest biomass, IEEE
Trans, on Geosci. Remote Sens., vol. 30, no. 2, pp. 412-415.
Dobson, M. C., F. T. Ulaby, and L. E. Pierce, 1995, Land-cover classification and esti­
mation of terrain attributes using synthetic aperture radar, Remote Sens. Environ..
vol. 51, pp. 199-214.
Freeman, A., M. Alves, B. Chapman, J. Cruz, Y. Kim, S. Shaffer, j. Sun, E. Turner, and
K. Sarabandi, 1995, SIR-C data quality and calibration results, IEEE Trans, on
Geosci. Remote Sens., vol. 33, no. 4, pp. 848-857.
Harrell, P. A., E. S. Kasischke, L. L. Bourgeau-Chavez, and E. M. Haney, 1997, Evalua­
tion of approaches to estimating aboveground biomass in southern pine forest using
SIR-C data, Remote Sens. Environ., vol. 59, pp. 223-233.
Hepp, T. E. and G. H. Bristler, 1982, Estimating crown biomass in loblolly pine planta­
tions in the Carolina flatwoods, Forest Science, vol. 1, pp. 115-127.
Hussin, Y. A., R. M. Reich, and R. M. Hoffer, 1991, Estimating slash pine biomass
using radar backscatter, IEEE Trans, on Geosci. Remote Sens., vol. 29, no. 3, pp.
427-431.
Imhoff, M. L., 1995, A theoretical analysis of the effect o f forest structure on synthetic
aperture radar backscatter and the remote sensing o f biomass, IEEE Trans. Geosci.
Remote Sens., vol. 33, no. 2, pp. 341-352.
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Kasischke, E. S., L. L. Bourgeau-Chavez, N. L. Christensen, Jr., and E. Haney, 1994a,
Observations on the sensitivity of ERS-1 SAR image intensity to changes in
aboveground biomass in young loblolly pine forests. Int. J. Remote Sens., vol. 15,
pp. 3-16.
Kasischke, E. S., N. L. Christensen, Jr., and E. Haney, 1994b, Modeling of geometric
properties of loblolly pine tree and stand characteristics for use in radar backscatter
models, IEEE Trans. on GeoscL Remote Sens., vol. 32, no. 4 pp. 800-822.
Kasischke, E. S., N. L. Christensen, Jr., and L. L. Bourgeau-Chavez, 1995, Correlating
radar backscatter with components o f biomass in loblolly pine forests, IEEE Trans,
on Geosci. Remote Sens., vol. 33, no. 3, pp. 643-659.
Kasischke, E. S., J. M. Melack, and M. C. Dobson, 1997, The use of imaging radar for
ecological applicarions-a review, Remote Sens. Environ., vol. 59, pp. 141-156.
McDonald, K. C., M. C. Dobson, and F. T. Ulaby, 1990, Using MIMICS to model Lband multiangle and multitemporal backscatter from a walnut orchard, IEEE Trans,
on Geosci. and Remote Sens. vol. 28, no. 4, pp. 477-491.
Oh, Y, K. Sarabandi, and F. T. Ulaby, 1992, An empirical model and an inversion tech­
nique for radar scattering from bare soil surfaces, IEEE Trans, on Geosci. Remote
Sens., vol. 30, no. 2, pp. 370-381.
Pulliainen, J. T., K. Heiska, J. Hyyppa, and M. T. Hallikainen, 1994, Backscattering pro­
perties of boreal forests at the C- and X-bands, IEEE Trans. Geosci. Remote Sens.,
vol. 32, no. 5, pp. 1041-1050.
Ranson, K. J. and G. Sun, 1997, An evaluation of AIRSAR and SIR-C/X-SAR images
for mapping northern forest attributes in Maine, USA, Remote Sens. Environ., vol59, pp. 203-222.
Ulaby, F. T., Moore, R. K., and Fung, A. K., 1982, Microwave Remote Sensing: Active
and Passive, vol. II, Addison-Wesley Publishing Company, Reading, Mass.
Ulaby, F. T., Moore, R. K., and Fung, A. K., 1986, Microwave Remote Sensing: Active
and Passive, voL III, from theory to applications, Artech House, Inc., Dedham,
MA.
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Wang, Y., E. S. Kasischke, J. M. Melack, F. W. Davis, and N. L. Christensen, Jr., 1994,
The effects of changes in loblolly pine biomass and soil moisture variations on
ERS-1 SAR backscatter. Remote Sens. Environ., vol. 49, pp. 25-31.
Wang, Y., L. L. Hess, S. Filoso, and J. M. Melack, 1995a, Understanding the radar backscattering from flooded and non-flooded Amazonian forests: results from canopy
backscatter modeling, Remote Sens. Environ., vol. 54, pp. 324-332.
Wang, Y., F. W. Davis, J- M. Melack, E. S. Kasischke, and N. L. Christensen, Jr.,
1995b, The effects of changes in forest biomass on radar backscatter from tree
canopies, Int. J. Remote Sens., vol. 16, no. 3, pp. 503-513.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table L Characteristics o f 3 loblolly pine stands, Duke Forest, NC
SI
S2
S3
15
29
62
# of trees/ha
2061
2108
950
min./max. dbh (cm)
5/22
5/40
5/70
mean dbh (cm)
11.0
15.1
19.8
one standard deviation o f dbh (cm)
43
7.7
15.4
22.46
47.43
46.84
mean tree height (m)
9.6
12.7
16.1
mean canopy depth (m)
4.6
5.6
6.6
canopy dry-biomass (kg/m2)
1.22
238
. 2.57
total dry-biomass (kg/m2)
6.55
25.08
Stand
stand age (yrs)
basal area (m2/ha)
35.61
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94
Table 2 Measured soil volumetric moisture content (%) for 6 loblolly pine stands.
n
mean
s.d.
range
8
21
23.9
8.0
14.9 - 42.2
23
11
27.0
8.6
19.5—43.8
=25
21
25.8
7.3
15.4 - 40.6
62
19
24.5
7.9
11.6 - 38.7
= 65
10
30.9
7.8
2 1 .9 -4 3 .0
= 90
3
26.8
2.6
24.0 - 29.2
all
85
25.8
7.8
1 1 .6 -4 3 .8
stand age (yrs)
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95
Table 3 Measured soil surface roughness parameters for 6 loblolly pine stands.
RMS height (cm)
correlation length (cm)
n
mean
s.d.
range
mean
s.d.
range
8
12
2.1
0.6
0.9 - 3 2
33.2
10.6
12.8 - 47.5
23
8
1.8
0.9
1 .0 -3 .6
21.3
123
6 .7 -4 6 .1
=25
12
2.4
1.3
0.9 - 5.7
32.7
10.6
16.6 - 48.8
62
10
2.5
1.2
1.1 - 4 2
27.7
9.1
14.9 - 40.0
=65
8
2.0
0.8
1.0 - 3 2
23.9
13.6
8.4 - 52.4
=90
6
2.0
0.9
0.8 - 3 2
27.9
17.0
13.4 - 58.6
all
56
2.1
1.0
0.8 - 5.7
28.5
12.0
6.7 - 58.6
stand age (yrs)
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Table 4 Measured volumetric moisture content (%) of litter layer
for 6 loblolly pine stands.
n
mean
s.d.
range
8
9
5.9
1.7
3.5 - 9.1
23
7
8.7
3.7
3.8 - 14.6
=25
18
3.7
1.7
1.2 - 5.9
62
13
5.1
2.0
2.0 - 8.5
=65
11
6.5
32
3.2 - 14.5
= 90
3
3.8
13
2.9 - 5.5
61
5.4
2.8
1.2 - 14,6
stand age (yrs)
all
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Table 5 Measured litter layer depths (cm) for 6 loblolly pine stands.
mean
s.(L
range
8
18
2.1
0.9
13 - 3.8
23
11
4.8
1.0
3.8 - 6.4
=25
18
3.9
1.2
•0
62
15
3.7
12
2 5 - 6.4
=65
15
65
1.6
3.8 - 8.9
= 90
3
32
0.6
2.5 - 3.8
all
80
4.0
1.9
13 - 8.9
VO
1
n
stand age (yrs)
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98
Table 6 Simulated maximum range o f C- and L-band total backscatter (dB) over
the modeled 5-D surface parameter space. The parameter ranges are: volumetric
soil moisture (11.6-43.8%), soil surface RMS height (0.8—5.7 cm), soil surface
correlation length (9.6—58.6 cm), litter moisture content (1-2—14.6%), and litter
layer depth (1.3—3.8 cm for SI, 25-8.9 cm for S2 & S3). Roman font is used for
L-HV
L -W
7.3 •
2.3
33
u>
o0
33
33
7.3
1.5
3.6
0
o
2.9
0.2
2.8
6.7
1.2
3.7
50°
1.8
0.2
1.4
5.8
0.9
35
60°
1.4
0.1
0.9
45
0.5
2.1
20°
3.1
0.1
2.7
9.6
1.3
3.0
30°
1.8
0.1
1.4
8.8
0.8
4.0
0 0
O in
O
1.5
0.1
1.3
7.4
05
3.8
0.8
0.0
0.5
55
0.3
2.9
60°
0.4
0.0
05
3.1
0.1
1.4
to
o0
2.1
0.0
2.3
85
1.0
3.6
0 0
O O
1.0
0.0
0.9
7.0
0.7
45
0.6
0.0
05
53
0.4
43
Oi
o0
the insensitive case, italic for the intermediate case, and bold fo r the sensitive case.
0.2
0.0
0.1
3.6
0.2
2.9
60°
0.0
0.0
0.0
1.4
0.0
1.2
Stand
00
C-HH
C-HV
C -W
SI
20°
55
0.1
5.4
0.2
S2
S3
L-HH
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Simulated maximum range o f C-HH and C-VV total backscatter (dB)
for each soil surface and litter parameter over the modeled region
Soil Surface
Litter Volumetric
Litter
Moisture Content
RMS Height
Correlation Length
Moisture Content
Depth
*0
C-HH
C-VV
C-HH
C-VV
C-HH
C-VV
C-HH
C-VV
C-HH
C _w
SI
20°
2.3
2,3
4.7
5.3
4.7
5.3
4.2
4.3
2,5
2,6
30°
1.6
1.6
2.6
3.1
2.6
3,0
2.6
2,5
1,5
1,5
O
1.4
1.5
1.8
2,4
1.8
2,4
2.3
2.3
1.4
1,3
50°
0.8
0,8
0,8
1,1
0.8
1.1
1,4
1.2
0,9
0.7
60°
0.6
0,6
0,4
0,6
0,4
0,6
1,2
0,8
0,7
0,5
20°
1.5
1.4
2.5
2.6
2.5
2,6
2.7
2,3
1.8
1.6
30°
0.9
0.7
1.1
1.2
' 1.1
1,2
1,6
1.2
1.0
0,8
0,7
0,7
0.6
0.9
0,6
0.9
1,3
1.2
0,9
0,8
O
1.1
1.2
1.6
2,2
1,6
2.2
1,8
2,0
1.2
1,3
S2
S3
o
Stand
o
Soil Surface
O
Soil Volumetric
O
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 7
for each soil surface and litter parameter over the modeled region
Moisture Content
RMS Height
Correlation Length
Moisture Content
Depth
L-HH
L-VV
L-HH
L-VV
L-HH
L-VV
L-HH
L_ w
2,9
2.6
2,2
1.8
1.3
1,9
2,1
2.3
2.3
1.8
5.0
0.3
0.2
0.1
0,1
0.0
0,1
0,0
0,1
1,2
1,3
1,4
1,4
1,1
0,9
0.1
1.9
2,0
2,1
2,3
2.4
1,5
1,3
1,5
1,6
2,4
1.1
2,3
2,8
2.3
1.2
0.1
oo
Litter
©s
Litter Volumetric
L-VV
1,7
0,7
20°
3.1
7.1
1.5
0.0
0.1
4.3
1,8
3.6
30°
2,7
2,3
1.6
7.1
3.2
0.0
0,1
4.3
3.6
5.7
3.1
0.0
0.0
4.2
3.6
2,1
0.0
0,0
3.5
2,4
2,4
1,9
1.5
1,9
0.9
1,7
2.1
2,2
2,0
1,2
1,7
0.8
0.0
0.0
2.2
0,9
2,8
1,6
20°
1,9
2,3
2,4
2,0
6.8
1,5
0.0
0,2
4.0
2,2
3.3
6.0
3.3
0.0
0,1
3.7
4.3
3.3
0.0
0.1
3.2
2,6
2,1
0,0
0.0
2,4
2,6
2,6
1,9
3.1
O
2,9
2.5
1,9
1,3
2,6
1,9
1.7
2,1
2,0
1,5
60°
0.5
1.1
0.8
0.7
0.0
0,0
1,0
0,9
0,7
0.6
20°
40°
O
o
O
o
o
30°
oo
S3
Soil Surface
L-HH
30°
S2
Soil Surface
©
sO
SI
Soil Volumetric
On
%
Stand
O
tn
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 8 Simulated maximum range of L-HH and L-VV total backscatter (dB)
5.8
5.3
4.1
'
3.4
0,9
0,9
0,9
1,9
1,4
0,7
o
I— *
8
for each soil surface and litter parameter over the modeled region
Soil Surface
Litter Volumetric
Litter
M oisture Content
RMS Height
Correlation Length
M oisture Content
Depth
L -H V
L -H V
L -H V
L -H V
L -H V
*0
SI
20°
1.3
1.8
0.0
0.8
0,6
0,9
1.3
0.0
0,6
0.4
0,7
1.0
0.0
0,5
0.4
0.7
1.1
0.0
0,8
0,6
©
S2
CM
Stand
oo
Soil Surface
©o
Soil Volumetric
o
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Table 9 Simulated maximum range of L-HV total backscatter (dB)
incidence
s
V\
d
p m
l® ft» ,
^ i w X ^ v '^ w X v . 'J v S l 'j v S 1
M ' X<
canopy
j f l
;& vA'i'S
W
P
.&ix®
trunk
surface
c — canopy scattering
d —trank-ground interactions
m —canopy-ground interactions
s -- direct surface backscatter
s_r —surface-related scattering (s_r = d + m + s)
total backscatter ( t) = C + d + m + s = C + s_r
Fig. 1
Santa B arbara m icrowave canopy backscatter model
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103
air
“
Fig. 2
soil £, = (£,./£,)
A close-up view o f m odeled surface scattering
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104
Chapter 5:
Microwave backscatter from Duke Forest loblolly pines:
An analysis o f the SIR-C data and its use in forest biomass estimation
Abstract
This study examines C- and L-band backscatter acquired over 21 loblolly pine
stands in Duke Forest, North Carolina, during 10 passes of the Shuttle Imaging Radar
(SIR-C) in April and October, 1994. Biomass o f the stands ranges from 3.5-44.5 kg/m2.
Within any radar band-polarization combination and data take, the maximum o° range
among the stands was 3.6 dB; in most cases it was 2-3 dB. A cosine law model fit the
relation of o° to radar incidence angle, with residual RMS deviations o f 0.4-0.7 dB, com­
parable to the standard deviation o f c°. A a° increase o f =1 dB in 2 data takes
corresponded to wet forest canopy. L-HV and L - W backscatter was higher for October
than April, despite drier soil in October. Biomass-<r° correlations were strongest at L-HV
(up to r=0.68) and at C-HH for 0O= 54° (r=0.74). Correlations were higher for northlooking than south-looking data takes, but appeared unrelated to incidence angle or soil
moisture. Multiple linear regressions of biomass versus o°, adjusted to equalize mean
forest a 0 among data takes, yielded adjusted R2 up to 0.57. The best regression model
for each data take required a different combination of SIR-C bands. RMS errors of
biomass estimation for the best 10% of cases were 7.4-8.25 kg/m 2 when estimated from
the regression data, and 8.58-10.32 kg/m 2 when estimated from a different data take.
RMS error decreased with the number of bands included in the model for estimates based
on the regression data, but increased with the number of bands for estimates from
different data. Analysis of the propagation of o° variance through the linear regression
models confirms that prediction error increases with the number o f bands and o° variabil­
ity. The c° variation of individual stands in successive data takes was larger than can be
accounted for by signal fading, and may stem from forest asymmetry or topographic
effects. Tests of three non-linear models indicate they may be less sensitive than linear
models to a° variation over some biomass ranges.
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105
1. Introduction
In this chapter I describe and analyze the SAR data acquired over loblolly pine
stands in Duke Forest, North Carolina, during the Shuttle Imaging Radar (SIR-C) mis­
sions in April and October, 1994. The shuttle SAR successfully recorded 10 multiple
polarization C- and L-band images, which were subsequently processed and calibrated at
NASA’s Jet Propulsion Laboratory. (For background, see Stofan et al., 1995; Freeman et
al., 1995). The Duke SIR-C data set is o f particular interest for the study of microwave
backscatter response to variation in forest characteristics for two reasons: First, SIR-C
provides the only space-bome, multi-band, multi-polarization SAR imagery o f forest
presently available to researchers. Secondly, the Duke Forest is a well-surveyed experi­
mental forest comprising stands of many ages and stages o f development, making possi­
ble a comparison of SAR response to forests over a wide range of biomass levels.
Many studies demonstrate a dependence of microwave backscatter on forest biophy­
sical properties including biomass. The possibility o f exploiting this dependence in order
to estimate forest biomass and monitor forest change regionally and globally continues to
motivate SAR forest research (cf. Kasischke et al., 1997). hi some studies R2 values of
0.90 or greater have been reported for regressions of backscatter versus total aboveground
biomass or stem volume. The strongest correlations are generally at L- and P-bands, HV
polarization (eg., Dobson et al., 1992; Beaudoin et al., 1994). In other studies the corre­
lations are weaker (eg., Baker et al., 1994; Moghaddam et al.,-1994; Rauste et al., 1994;
Harrell et al., 1997). The scatter in forest o° data varies from site to site and temporally
(see Chapter 1). It appears that correlations are strongest for monospecific plantations
with homogeneous, even-aged stands and under dry forest conditions; however, this pos­
sibility has not been systematically researched.
In addition to the scatter in SAR data which can lead to large uncertainties in back­
scatter estimation, a widely observed limitation in backscatter-biomass regressions is
"saturation," i.e., the backscatter-biomass curve levels out at a fairly low biomass level.
Saturation potentially limits SAR-derived biomass estimation to the small fraction of
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106
Earth’s forests that have total aboveground biomass o f less than about 10 kg m-2 (Imhoff,
1995a). Several approaches have been proposed to overcome saturation and improve
regression-based biomass estimates. Ranson and Sun (1994) found that the ratios PHV/'C-HV and L-HV/C-HV could discriminate higher biomass levels than P-HV o r L-HV
alone. Kasischke et. al. (1995), observing a strong correlation between branch biomass
and backscatter, developed a two-step approach in which branch biomass is first
estimated from multi-band backscatter by linear regression, and then total biomass is
estimated from branch biomass using allometric relations. Dobson et al. (1995) pointed
out that, although microwave extinction in the canopy may place an upper limit on
biomass that may be estimated, much of the observed data scatter and "apparent satura­
tion" is the result of combining different forest structural types in a regression and o f fail­
ing to take into account that biomass increases as the square o f tree trunk diameter
whereas backscatter increases as the square of tree height. Based on these insights, Dob­
son et al. (1995) proposed a three step procedure in which 1) multi-band SAR images are
segmented into structurally homogeneous stand classes, 2 ) within each class, tree height,
basal area, and crown biomass are estimated from backscatter by regression, and 3) total
biomass is estimated allometrically. This indirect method produced biomass estimates
from a single SIR-C data take that were accurate up to a biomass level of 25 kg m-2.
Both the Kasischke and Dobson methods require detailed allometric knowledge o f the
forest, which limits their practical application.
Harrell et al. (1997) compared the above three methods to simple direct multiple
regression of o° versus total biomass, utilizing SIR-C data from Duke Forest loblolly
stands on two dates. RMS error of biomass estimation was largest for the L-HV/C-HV
ratio method, indicating this method is probably contraindicated for this site and SAR
data. When all stands were included in the analysis, simple regression yielded the most
reliable biomass estimates of any of the 4 methods. When the high-biomass stands
(> 2 0 kg m-2 or > 10 kg m-2) were excluded, simple regression had equal or greater accu­
racy than the other methods for one data take, but was less accurate than the Kasischke
or Dobson-based methods for the other. Harrell et al. (1997) suggest that high RMS
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107
errors of the two indirect methods on the first date may be attributable to moist site con­
ditions. It should be noted that the Dobson-based method used in the comparison study
estimated height, basal area and crown biomass by means o f simple, linear multiple
regressions on backscatter, whereas Dobson et al. (1995) included band ratios and
exponentials in their regression models. The greater complexity of the models o f Dobson
et al., (1995) may account in part for the lower RMS errors of their biomass estimates;
however, other factors such as differences in stand homogeneity o f the Michigan and
Duke forests may also have come into play. At present, it is an open question whether
any of these four approaches will lead to a practical and broadly applicable biomass esti­
mation methodology, or whether, as Imhoff (1995a) argues, the biomass estimation capa­
bility of SAR is limited to low-biomass applications such as monitoring forest regenera­
tion.
Whatever regression approach is adopted, for SAR-based biomass estimation to
become a practical tool (i.e., one that provides accurate biomass estimates for Forest B at
Time 2 based on the regression model developed for Forest A at Time 1), effects o f
backscatter variability on estimation accuracy need to be addressed. Variations in soil
and leaf surface moisture, tree dielectric constant, forest phenology, imaging parameters,
calibration, and other variables may lead to biomass prediction error, the magnitude of
which depends on the regression model. Because the SAR analyst is unlikely to have
much knowledge of at least some o f the sources o f variation in practical applications, the
radar bands and incidence angles used in the regression model should ideally be insensi­
tive to scene variations. Also, it may be helpful to time the SAR acquisitions to avoid
rapidly changing forest conditions (Kellndorfer et al., 1998). It seems clear that to select
a good regression model and to estimate uncertainty in regression-based biomass esti­
mates, one has to consider how accurately the models predict biomass under realistic con­
ditions of backscatter variability.
Backscatter modeling has been valuable for understanding general patterns and
trends in backscatter response to varying forest parameters (Richards et al., 1987; Ulaby
et al., 1990; Sun et al., 1991; Karam et al., 1992; McDonald and Ulaby, 1993; Beaudoin
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108
et al., 1994) and for identifying potential limitations o f the SAR data (e.g., Wang et. al.,
1998; Imhoff, 1995b). Knowledge gained through backscatter modeling studies can sup­
ply the foundations for building regression models (e.g., Dobson et al., 1995). Neverthe­
less, there are at least two reasons to suspect backscatter modeling may not provide use­
ful estimates of backscatter variability. First, backscatter models lack full realism. To
give one example out of many, even in discontinuous canopy models o f microwave
scattering (Sun et al., 1991; Wang et al., 1993; MacDonald and Ulaby, 1993; Sun and
Ranson, 1995) the spatial arrangement o f canopy elements is idealized. The idealization
is desirable for modeling the general backscatter trends, but it does not allow investiga­
tion of backscatter variability associated with spatial differences in canopy architecture or
ground surface characteristics. Second, forest variations are not known at the level of
detail that would be needed to formulate and parameterize a completely realistic model.
However realistic are the models, and however detailed are the forest data, in the end one
must return to the empirical data to evaluate how reliably biomass (and other forest
parameters) can be estimated under real conditions.
The present study is for the most part an empirical case study, the purpose o f which
is to document and understand variation in backscatter from loblolly forest observed in
the SIR-C data. My data set includes backscatter from 10 data takes for 21 loblolly
stands, whose estimated total dry biomass ranges from 3.5 to 44.5 kg m-2 (7 to 84 years
of age). Because 4 of the data takes were acquired in April and the other 6 in October,
forest phenology and moisture conditions vary markedly. Incidence angle also varies
(19.1-53.6°). Thus, the data set spans a wide range o f imaging conditions that lead to
variations in backscatter, backscatter variance, correlations of backscatter to biomass and
other forest parameters, and the form o f linear regression model that best fits the biomass
estimates. In this paper I investigate the specific contributions of incidence angle, surface
moisture, phenology and total biomass to backscatter variation. I also consider how well
biomass-o0 regression models developed for one data take perform when applied to
different data takes, how variation in <J° propagates into uncertainty in biomass estima­
tion, and what model formulations are most robust to o° variation.
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109
This study differs in several important respects from other SIR-C backscatterbiomass studies. First, I compare 10 data takes, whereas most studies examine one or
two, or at most three. Analyzing multiple cases allows me to observe backscatter changes
in relation to site conditions and incidence angle. Second, I undertake a comparison of
biomass versus ct° regression models o f all 10 SIR-C data takes in order to determine
how well a model based on one data take can predict biomass from another. This sort of
comparison does not appear elsewhere. Third, I exclude from the study low biomass
forests (<3.5 kg/m2) that correspond to the steeply sloping region o f the backscatterbiomass graph, concentrating instead on the flatter, more linear region o f the curve
(biomass >3.5 kg/m2). Other studies have focussed on low biomass forest, or have
included the full biomass range (down to bare soil), or have applied an upper biomass
limit (e.g., 10, 15 or 20 kg/m2). As a result, the picture is incomplete as to what forest
conditions, band combinations, and incidence angles favor estimating biomass at levels
that are typical of most forests; it is my aim here to help complete this picture. My
approach could be criticized on the grounds that invoking the 3.5 kg/m 2 biomass cut-off
virtually guarantees failure in biomass estimation from the outset, due to effects of satura­
tion. I will address this issue in the discussion section (§4.2).
2. Study area and methods
2.1. Loblolly forest stand data
The study sites are located in the Duke University Forest, North Carolina. Loblolly
pine (Pinus taeda L.) is the dominant species in all stands investigated. The Duke forest
loblolly stands have been much studied as an example of "old-field" successional chronosequence (Christensen and Peet, 1981; Kasischke and Christensen, 1990). They have
also been the focus of research on the sensitivity of radar backscatter to above-ground
forest biomass (Dobson, et al., 1992; Kasischke, et al., 1994a; Kasischke, et al., 1995;
Wang, et al., 1995, Harrell et al., 1997). The interested reader is referred to these papers
for background on the loblolly stands, allometric relations, and biomass computation (see
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110
also Chapters 2-4 of this dissertation).
For this study I selected 21 loblolly stands, a subset o f those studied by Eric
Kasischke and his colleagues at the Duke University. The stands are located in the Dur­
ham, Blackwood, and Eno divisions o f Duke Forest. The youngest stands are densely
stocked and are almost pure loblolly pine, whereas the more mature ones have partially
closed canopies and a hardwood understory. Hardwoods constitute no more than 10% of
stand biomass for any o f the stands (Harrell et al, 1997). The stands range in area from
3 to 28 ha, in age from 7-84 years, and in total dry biomass from 3.5 to 44.5 kg/m 2
(Table 1). Harrell et al. (1997) also present data for four stands within the study area
with low biomass (0.14-3.15 kg/m2). I did not include them for the following reasons:
First, it has already been demonstrated in many studies that the biomass o f low biomass
forests (less than 5-10 kg/m2) can be estimated by SAR, at least in level-ground, monospecific forests. Second, inclusion of such stands anchors the regression curve with
high-leverage points and in doing so may inflate the regression R2. Third, the low values
tend to force the regression curve to a shape that may not be best for the biomass range
of interest. Fourth, the low values reduce the RMS errors o f biomass estimation, which
may be misleading.
The stand data (Table 1) derives from resurveys in 1994-5 o f stem density, tree
height, and tree diameter at breast height (dbh), as published in Harrell et al. (1997).
Dense, young stands were surveyed with the point-quarter method, with >20 sample
points on 2-4 transects. The more mature stands were sampled with 10 to 30 plots, each
100-200 m2, located randomly along 2-4 transects. Biomass o f aboveground component
tree parts and total aboveground dry biomass were computed from the dbh and stem den­
sity data using allometric relations developed and validated in Duke Forest by Kasischke
et al. (1994b). Analysis o f field biomass sampling error was not provided, but by my
computation uncertainty in measured biomass may be as large as ±4 kg/m 2 (Chapter 2,
§2). My own biomass estimates using raw data supplied by Harrell (pers. comm, 19956 ), and using the same allometric method, differed appreciably from those published by
Harrell, with mean absolute difference of 4.1 kg/m 2 for the 21 stands (Chapter 2).
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Ill
However, biomass-o0 correlations (using my SIR-C o ° data) were similar for the two
biomass data sets. Therefore, to facilitate future comparisons, I adopted the published
data from Harrell et al. (1997).
Stand locations and ID’s were known from forest stand maps provided by Harrell
(pers. comm., 1994-1997). Digital maps were provided as Arc/Info coverages by Laura
Bourgeau-Chavez of ERIM (pers. comm., 1995). I prepared an accurate digital base map
for this study by registering the digital stand map to U.S.G.S. Digital Orthophotos o f the
region. Following'overall registration, individual stand polygons were adjusted to con­
form to the stand boundaries, as interpreted from the orthophotos in conjunction with the
digital and paper stand maps. Having the orthophotos co-registered with the stand out­
lines aided registration o f the SAR data to the stand map (Fig. 1).
For parts of the analysis, it was helpful to group the stands into age/biomass
groups, so as to filter out the random backscatter variations o f the individual stands. I
chose the break-points o f 9.0 and 26.0 kg/m2 to divide the stands into three roughly
equal-sized groups. The groupings are necessarily arbitrary, as is the choice of 3 groups,
because biomass varies continuously. They are also arbitrary in that the groupings could
be made on the basis of crown biomass, mean dbh, or other factors. These other group­
ings may be more directly linked to backscatter than is biomass. In comparing several
criteria for grouping, I found that while a few stands shift up or down from "medium" to
"high" or "medium" to "low" from one grouping to the next, a dramatic redistribution of
stands between groups does not occur. The relative stability o f the groupings is related to
the high correlation of the variables and the allometric origins of the biomass estimates
(see Chapter 2).
2.2. SIR-C Data and Processing
SIR-C/X-SAR acquired 10 data takes of Duke Forest at C- and L-band. Four were
from the April, 1994, flight (SRL-1) and 6 from the October, 1994, flight (SRL-2) (Table
2). X-band data were also acquired but were not used in this study. All data are fully
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112
polarimetric (mode 16) except for the October 1 data take which is at HH and HV polari­
zations (mode LI). Incidence angles are 19°-32° for April and 23°-54° for October.
Nominal resolution varies from 6 .2-8.2 m in azimuth and 11.4-24.4 m in range. The
shuttle heading was roughly 40° East o f North (ascending orbit) for all data takes. The
antenna was north-looking (left) for 4 takes and south-looking (right) for the remaining
ones. All data were acquired near dawn or in the pre-dawn hours (about 4 to 7 AM local
time).
2.2.1. Processing
I received calibrated, single-look, slant-range data for all passes from the Jet Propul­
sion Laboratory (JPL). The processing sequence was as follows:
1)
Prepare accurate stand masks by registering the Duke University forest cover maps
to U.S.G.S. digital orthophotoquads (using the Arc/Info Grid program).
2)
Extract the study area subregion from the 10-byte compressed format SAR data
supplied by JPL.
3)
Uncompress the data for each subregion (extracted in Step 2) to generate single­
byte a 0 images, with pixel values rescaled from decibels to 0-255. Save the scale
factors for rescaling the single-byte images back to true calibrated o° values. The
output images are HH, HV, VV and total power for each o f the 2 frequency bands
(Table 3). (The programs for this step were implemented in IPW image processing
system at U.C.S.B. by Yong Wang, based on JPL’s uncompression software.
Total power is computed as [ o°HH + <T°w + 2 <J°hv] ! 4.)
4)
Process the data for each subregion (extracted in Step 2) to create single-byte
decomposition images. This process allocates co-polarized backscatter into "even"
and "odd" bounce components so as to separate backscatter generated via different
scattering pathways. There are 9 output images for each band (Table 3). (The
software is by Yong Wang. See: Wang and Davis, 1997; Cloude, 1992; van Zyl,
1994)
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113
5)
Import the 4 a° and 9 decomposition images for each data take into the Arc/Info
Grid program as 13-layer images ("grid stacks").
6)
Warp the stand masks for the 3 forest divisions (Durham, Blackwood, and. Eno)
separately to register them with each data take, using a 2nd or 3rd order polyno­
mial fit. Make local adjustments to the position of the stands in the warped stand
masks as needed to fit the SAR images.
7)
Overlay the stand masks on the SAR images and extract the pixel values for each
of the 21 stands and 13 bands. Create a histograms of the pixel values for each
stand and band. Export the histograms to text files.
8)
Apply the saved scaling factors to the histograms to reconvert the 0-255 values to
calibrated o°, and compute the stand statistics Curing the S-Plus statistical package).
Statistics for each stand include mean, median and lower quartile o f o° (dB),
coefficient of variation o f o° (linear), and stand means for the 9 decomposition
bands. (Stand mean o° was computed from linear data and then converted to dB.)
Post processing of SAR data typically includes rectification and resampling o f the
SAR data (e.g., Harrell et al., 1997) or filtering to reduce speckle (e.g., Dobson e t al.,
1995). By comparison, the processing sequence in this study was unusually direct. No
filtering, rectification, resampling or other manipulations were applied to the SAR data.
Instead, the stand mask was warped to register to each data take and then used as a
"cookie cutter” on the original (uncompressed) data. Because I do not plan to overlay the
various data takes or perform any other mapping tasks, there was no need to warp or
resample the SAR data. As a result the data extracted for each stand retains the original,
unaltered single-look statistics.
One possible criticism of this procedure is that the 1-byte data representation may
not provide high enough radiometric resolution. I reason as follows: The single-look
Duke SIR-C data span a maximum range of 75 dB (-40 to 35 dB) (using an arbitrary -40
dB noise threshold). An individual pixel valued 0 to 255 can have a quantization error of
no more than ± Vi of 75/256, or ±0.15 dB. The maximum quantization error o f 0.15 dB
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114
for a single pixel is much smaller than fading variation (i.e., reinforcement and cancella­
tion o f the microwaves), due to which individual pixels vary greatly (>±30 dB) (see
§2.2.2). Furthermore, quantization error o f the pixels is random and will tend to cancel
in computing the mean; therefore, the aggregate error o f the stand means due to quantiza­
tion will be trivially small.
A second concern could be that o° was not adjusted for local surface slope. My
rationale is that the forest is mainly a volume scatterer. Because a large and variable pro­
portion of the total backscatter originates in the canopy (independent o f the ground sur­
face), a surface slope adjustment is probably inappropriate, at least for gently sloping ter­
rain like Duke Forest (Chapter 2). The surface and double-bounce scattering fraction of
the total backscatter could possibly be adjusted to compensate for the surface slope using
a scattering model-based algorithm, but to do so might introduce errors greater than those
corrected.
Achieving accurate registration o f the stand mask to Duke forest SAR images was
essential, because most of loblolly stands are adjacent to other vegetation types or to
roads, electric power corridors, etc. (Figure 1). To minimize the contamination o f stand
backscatter by these various scattering sources (as can result from the slant imaging
geometry and misregistration), I created a 25 m buffer inside the stand boundaries. A
larger border was not possible due to the small size o f some of the stands (=3.0 ha
before and =1.5 ha after buffering). Initial tests showed that a 2nd or 3rd order polyno­
mial fit provided marginally acceptable registration of the ground control points, but local
errors were >50 m in some areas near stands. The errors are probably attributable to
local topography; though topography is gentle, elevation does vary by roughly 200 m
within the study area. To overcome topographic distortion, I attempted to use an algo­
rithm that reprojects the location of each pixel based on shuttle ephemeris data and USGS
30 meter Digital Elevation Models (J.C. Shi, pers. comm., 1998; Albright et al., 1998).
In principal, this sort of approach to terrain correction is practicable and it may be
indispensable for survey of large areas. A similar algorithm produced ±25 m accuracy
for ERS-1 and JERS-1 data (Kellndorfer et al., 1998). However, the registration errors
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115
that I obtained were unacceptably large (hundreds of meters), possibly due to inaccuracies
in the DEM or ephemeris data, or errors in my implementation. The required accuracy
was eventually achieved by 1) dividing the scene into three sub-scenes, corresponding to
the Blackwood, Eno, and Durham forest divisions (these divisions are separated by about
10 km), 2 ) registering the stand map to each sub-scene separately using a polynomial fit,
and 3) making local shifts to stand locations in the resulting warped stand maps. These
local adjustments were determined on the basis of the observed misregister of roads and
other visible references near each stand.
Color composites o f two o f the Durham division sub-images are included (Figures
2-3) to give the reader a sense o f the range of Duke Forest SIR-C image quality and
some appreciation for the registration problem. Fig. 2 shows DT#113a, which has the
steepest incidence angle, largest ground-range pixel area, and wettest conditions o f all the
data takes (Table 2). Fig. 3 shows DT#49o, which was acquired at 0O=32.8° under dry
conditions, and is one of the clearer images. The warped outlines of the (buffered)
stands are shown in yellow. One cannot be confident o f the exact stand locations in
these images, especially in the poorer resolution image (DT#11330). Figures 2-3 may be
compared to the undistorted Durham orthophoto showing the stand outlines (lug. 1).
2.2.2. Backscatter uncertainty
I made no attempt to improve on JPLTs calibration o f the SIR-C data (Freeman et
al., 1995). Reported absolute calibration uncertainties (L-band/C-band) are ± 2 3 dB/±2.2
dB (SRL-1) and ±2.0 dB/±3.2 dB for (SRL-2). The pass-to-pass uncertainties are 1.0 dB
smaller than the absolute, x.e., ±1.3 dB/±1.2 dB (SRL-1) and ±1.0 dB/±2.2 dB for (SRL2). Cross-swath uncertainty is 1.0 dB for both bands and missions.
A second major source of uncertainty is fading. For single-look backscatter from a
distributed target such as dense forest, C° is expected to have a Rayleigh distribution
(Ulaby and Dobson, 1989). In this case, standard deviation o f O0 for a uniform forest
stand will be equal to the stand mean, and coefficient of variation (cv) will be unity. For
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116
the Duke SIR-C data, I computed cv for each stand, SAR band, and data take, cv ranges
from 0.80 to 1.86, with a median o f 1.04; 96% of the values are between 0.90 and 1.20.
By the central limit theorem (Bhattacharyya and Johnson, 1977), standard deviation o f
stand mean c° (i.e., fading error) may be estimated as sd /^N
where sd is the standard
deviation of the single look data and N is the number of pixels in a stand. For the Duke
data, N varies from 134 to 4478 depending on stand size and ground range pixel area and
sd ranges from 0.018 to 0.55 (linear m2 /m 2). Using the above expression, I calculated
fading error for all stands for each data take and SAR band. The range o f fading error is
0.066 to 0.440 dB, with a median o f 0.166 dB. Fading error is >lA dB for 16% of cases.
Fading error is smallest for data takes 49a, 145a, 33 and 49, and largest for 113a and
113o, the two data takes with steepest incidence.
2.2.3. Forest conditions during data takes
During the April, 1994 mission, moisture conditions and forest phenology varied.
During the first data take (April 12), the soil was moist and the new season’s leaves had
barely begun to appear in the understoty. Due to rain on 4/13 and early 4/16, the ground
was wet to saturated during the 4/16 overflight. The needles were damp or wet. As
there was no further rainfall during the first mission (apart from a trace noted at the Dur­
ham station on 4/17), soil moisture declined through the final two data takes. Soil mois­
ture was measured daily throughout the mission by Kasischke and his associates at Duke
University and by a team from U.C.S.B. Average volumetric moisture content o f the
sampled stands ranged from about 25% on 4/12 to 34% on 4/16 (Fig. 5). (These aver­
ages were compiled from data provided by Harrell, personal communication, 1994-5, and
Day, unpublished report, 1994). Meanwhile, between 4/12 and 4/18 the understory
transformed from brown to green, as broad-leaf trees and shrubs came into leaf. It is
likely that the loblolly needles were moist during the early morning data acquisitions; the
needles were wet during the 4/16 data take.
Conditions during the October mission were dry and stable with the exception of
the final (Oct. 10) data take, during which a light rain fell. September had been dry; only
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117
2.5 cm of rain fell at the Durham station from Sept. 5-25. No precipitation was recorded
between Sept. 25 and Oct. 9. Average volumetric soil moisture during the first (Oct. 1)
data take was 10% (as computed from Harrell’s data). Because there was no rain, and
volumetric moisture was already low, I assume (but cannot verify) that it did not change
significantly between Oct. 1 and Oct. 9. During the final (Oct. 10) data take, soil surface
moisture must have been slightly higher than 10% due to the rain early that morning.
There was probably little moisture on the foliage during the first 5 October data takes,
but on the final day the trees were wet. Forest phenology in October differed from the
April mission in several respects. The understory broad-leaf trees and shrubs were fully
leafed out. The loblolly needle density was roughly twice that o f April, as the seasonal
needle flushes had occurred (Harrell et al., 1997; Kinerson et al., 1974). The distribution
of water (and dielectric constant) within the trees may have been different for the two
missions due to the difference in soil moisture and also to seasonal physiological fluctua­
tions, which to my knowledge are not well documented (Gates, 1991). Recent work indi­
cates new needles may have a dielectric constant on the order of 1 lA times higher than
old needles (Franchois et al., 1998). Unfortunately, the only actual data available are
limited measurements o f trunk dielectric constant in April, with no October measurements
for comparison.
2.3. Methods of Analysis
2.3.1. Correlation of SAR data to measured forest characteristics
As a preliminary exploration of the relation between SAR returns and loblolly stand
characteristics, I computed the correlation of the stand means, medians, and lower quartiles of the SAR <y° bands, and the stand means of the decomposition bands (Table 3), to
various forest stand parameters. These were: total aboveground dry biomass (B), log(B),
stand age, basal area, mean tree diameter at breast height (dbh), mean tree height, and
stem density. The correlations were used in two ways, first, to determine which bands
show a promisingly strong relation to which parameters (in order to steer the analysis
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118
productively), and second, to discern whether the strength of SAR-fotest relations is
affected in some apparent way by either radar incidence angle or forest moisture condi­
tions or seasonal changes.
2.3.2. Differences In o° due to incidence angle
a 0 is a measure of surface backscatter defined with respect to a unit area on the
horizontal ground plane, whereas y is defined with respect to the incident area orthogonal
to the radar ray. The two coefficients are related by o° = y cos(0o), where 0O is radar
incidence angle (Ulaby et al., 1982). The forest microwave backscatter coefficient
expressed as y is less sensitive to incidence angle change than is o°, but may still show
some angular dependence owing to the complex angular response o f canopy and surfacerelated scattering mechanisms (Ulaby et al., 1986). A cosine law is sometimes used to
reduce incidence angle effects from SAR data that is presented as a 0. The expression
o° = lOnlog 10[c o s (e 0)] + k
[ 1]
where n=l and k is a constant has been applied to fit forest SAR data (Beauchemin et al.,
1 9 9 5 ).
To examine the incidence angle dependence of o° for the Duke SIR-C data, I com­
pared three methods for fitting the data: 1) general cosine law (both n and k free) using
minimum root mean square deviation as the goodness of fit criterion, 2 ) same as ( 1), but
setting n=l (the equivalent of presenting the data as y), and 3) linear least squares regres­
sion. Because the first five October SIR-C data takes were similar apart from incidence
angle and calibration error, I fit the October data using the three methods. I then used
the fit curves as a basis for examining the deviations o f the other 5 data takes acquired
under different conditions.
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119
2.3.3. Differences in
cP due to moisture and phenologic changes
To provide evidence o f whether the observed differences between measured a 0 in
April and October are reliable estimates o f differences in actual o° (i.e., a property o f the
forest) caused by changes in moisture and phenology, or whether they are more likely a
consequence of calibration error o r other factors, I compared SIR-C data to backscatter
model predictions.
In this analysis, I first examined the April to October difference in measured SIR-C
o° for two pairs o f data takes, each pair consisting o f an April and an October take at
nearly the same incidence angle. The data pairs are 49a and 49o (0O=32.1°, 32.8°) and
129 and 145o (0O=26.6°, 26.4°). (0O within each pair is closely enough matched that
incidence effects can safely be ignored.) Next, I compared these observed differences to
the differences predicted by the Santa Barbara Microwave Backscatter Model for continu­
ous forests (Wang et al., 1994; Wang et al., 1995). The same three loblolly stands are
modeled here as in Chapter 4 o f this dissertation, and the modeling is identical except
that the litter-layer is omitted (Wang, unpublished data). The stands represent low,
medium and high biomass forest (see §2.1 above and Chapter 4, Table 1). Volumetric
soil moisture estimates used for this modeling are 24% and 9% for 49a and 49o, and
32% and 9% for 129 and 145o (differing slightly from those given in Table 2). The two­
fold increase in needle load assumed to have taken place during the summer (Kinerson, et
al., 1974) is accounted for by modeling 2000 needles/m3 in April and 4000 needles/m 3 in
October. Other seasonal factors that could affect backscatter, including leaf growth in
understory trees and shrubs, changes in stem and needle dielectric constant, and leaf sur­
face moisture, are not modeled due to lack o f reliable data.
2.3.4. Multiple regression to predict forest biomass from o°
Multiple regressions o f total dry biomass versus <J° were carried out for all data
takes for following reasons: 1) to determine which SAR band combinations afforded the
best fit, 2 ) to compare optimal band combinations and model coefficients among the data
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120
takes, 3) to assess whether some of the data takes (i.e., incidence angles +■ forest states)
produce stronger regressions than others, 4) to evaluate how well regression models
based on one data take can predict biomass using backscatter from a second data take.
The "leaps" program (in S-Plus statistical package) was used to identify the 10
combinations of 1-6 radar bands for each data take that produced the highest adjusted R2
(R~), defined as:
R^= l - ( — ) ( 1 - R 2)
n-p
[2]
where n is the number of observations and p is the number of explanatory variables in
the regression (Montgomery and Peck, 1982). Note that R2 can take on negative values.
R2 is a reasonable criterion for determining the optimal subset of bands, because (unlike
simple R2) it does not increase with the addition o f regressor variables unless they have
explanatory power (Montgomery and Peck, 1982). The regression approach and rationale
is as follows:
1)
I use direct regression to predict biomass. The work of Harrell et al. (1997) indi­
cates that the indirect and LHV/CHV approaches offer little if any improvement
over ordinary least squares multiple regression (see § 1.).
2)
The regressions are formulated as field-estimated biomass versus o° (dB). I used
linear biomass rather than logarithm of biomass. Examination of scatterplots of
and regression diagnostic plots (including residuals vs. predicted biomass, residuals
vs. a 0, and normal quandle plots of residuals) did not indicate that log transforma­
tions or more complex models were necessary or appropriate.
In previous SAR
studies of Duke loblolly forests, the logarithm of biomass has been used in the
regressions (Harrell et. al., 1997; Kasischke et al., 1995). However, in those stu­
dies the minimum stand biomass was very low (0.14 and 0.6 kg m-2) compared to
3.52 kg m~2 in this study. Exclusion o f Iow-biomass stands may be the reason the
log transform is unnecessary here.
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121
3)
On the basis o f the single-band correlations o f various SAR measures to biomass
and other biophysical parameters (§3.2), I limited the regression analyses to
biomass versus stand mean o° (L- and C-bands, 3 polarizations). The other bands
(such as
g°
lower quartile and decomposition bands) and other parameters (such as
mean dbh and basal area) do not have higher SAR-forest correlations than those of
biomass to o°, though in some cases the correlations are comparable
4)
To permit comparison among the regression models obtained for different data
takes, all data takes were adjusted so that mean G° o f the 21 stands matches that of
the corresponding band of data take #49o. These G° shifts balance the data set by
removing the overall effects of incidence, forest state, and calibration error, without
altering the relationship between stands within a data take.
5)
The regressions were weighted to take into account differences in CT° variance and
number of pixels in a stand. This was judged important because the number of
pixels per stand, and hence o° variance, varies greatly among the stands; the lowvariance stands should be given greater weight in the regressions. Regression
weights should be proportional to the l/var(y) (Montgomery and Peck, 1982), that
is, the inverse of the variance of the stand biomass observations.
Variance o f the observations is unknown, but it can be estimated from the variance
o f the biomass predictions of the regression as follows:
var( yj) = var ( y£) / h;
[3]
where y{ is the biomass observations, y£ is predicted biomass, and hi is the diagonal
elements o f the hat matrix (X (X 'X )-1 XO (Montgomery and Peck, 1982, p. 115).
Because v ar(y£) would be cumbersome to compute for the large number of models
tested, I substituted into [3] the more readily computed quantity cv^/N, where cv
is the coefficient of variation of o° and N is the number o f pixels in a stand. I
hypothesized that this quantity would be approximately proportional to v ar(y £) for
the following reasons: First, assuming the Rayleigh fading model, for repeated
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122
observations o f the same stand, variance o f c° is proportional to the square of its
mean and inversely proportional to the number of pixels in the stand (Ulaby and
Dobson, 1989; see also §2-2.2). For single-look data (i.e., n=l), if variance of a 0
deviates from the square o f its mean, as is the case for the Duke SIR-C data
(Appendix I), it does so in proportion to cv2. Therefore, although the data does
not stricdy adhere to the Rayleigh model, it is reasonable to hypothesize that
v a r(o °) will be approximately proportional to cvVN. Second, if v ar(o °) is
assumed equal and independent for all bands in a linear regression model to predict
biomass (yt) for a stand, then var(y;) is proportional to v a r(o ° ) (see §2.3.6 and
§3.6).
I confirmed that c \r /N
v ar(y £), by means of Monte Carlo simulations, in which
stand biomass was predicted using coefficients from unweighted regressions. The
predictions were repeated using subsets o f N pixels randomly drawn from those o f
large forest stand, until a stable estimate of var( y,-) was obtained. These simula­
tions were repeated for a number o f different SAR images, regression models,
stands, and values of N. In all tests cv^/N was highly correlated to the Monte
Carlo estimates o f var(y£), with r>0.99. Hence, it follows from [3] that, to a good
approximation,
var(y j) <*= (cvV N ^/hj
[4]
Therefore, I used the following regression weights for all biomass-<r° regressions:
weights = 1 / (var(yt))
o c h ^ N /c v 2
[5]
2.3.5. Accuracy of biomass estimation by the regression models
As discussed atlength in Chapter 1, if one acquiresSAR data
on differentoccasions,measurements of
from a forest stand
o° will vary due to errors in measuring a ° (e.g.,
calibration error, fading, misregistration, etc.) and to actual variation in <J° from forest
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123
scene changes (e.g., phenology, soil moisture, tree dielectric constant, etc.)- Conse­
quently, although R2 and R~ signify goodness of fit for a particular regression data set,
they may have little value in appraising the usefulness o f a regression model for making
biomass predictions from other SAR data sets.
To evaluate the predictive capabilities o f the regression models, the models were
tested with the SAR data from all 10 riara takes, and the SAR predictions were compared
to the field biomass measurements. Accuracy is reported as root mean squared error,
defined as RMSE = ( £ ( field—SAR) 2 / N ) I/2. I distinguish two cases. In the first (Case
A), the o° data used to build the regression model are also used to estimate biomass,
while in the second (Case B), the regression model from one data take is applied to o°
data from a second data take. (Harrell et al., 1997, focused on the third case, predicting
biomass from different stands, using the same data take upon which the regression is
based.) Case A should generally (but not necessarily) yield a higher R~ and lower RMSE
than Case B. As an empirical way of investigating how the regression models impact
biomass estimation error, I compared how errors of the two types vary as a function of
model size (number of bands) for the data set as a whole and for subsets o f the data
takes.
2.3.6. Robustness of biomass estimates to o° variation
Observed biomass estimation error, as discussed above, has several sources in addi­
tion to variability of measured o°. These include errors in field sampling and allometric
formulas and inadequacies of the regression model. The part of the error attributable to
field-based biomass measurement may be as large as 4 kg/m2 (§2.2). The part attribut­
able to variability in measured (J° has direct bearing on the extrapolation of a regression
relation to other SAR data sets. Error propagation analysis provides a means to separate
out and examine how variance in <3° may affect RSME.
Variations in measured <3° propagate through the regression model into biomass
estimation errors, the magnitudes of which depend on the model. Errors in one of the
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124
SAR bands may be unrelated to errors in the other bands. Examples o f such independent
errors include fading and SAR channel imbalance (assuming it varies randomly among
data takes). On average, independent errors tend to partially cancel. They may be com­
bined by taking the square root of the sums of their squares. So, using generic notation,
if V = f(x, y ,...), its standard deviation is calculated as:
[6]
(Taylor, 1982) where s* and Sy are the standard deviations of o° in two SAR bands com­
puted for a number of data takes. For other types of error (eg., variations in absolute
system calibration), deviations may be non-independent among bands; such errors com­
bine algebraically, and so may either tend to reinforce or cancel depending on the regres­
sion model. Finally, for some error types, deviations may be partially correlated among
the bands (eg., c° fluctuations due to changes in forest state); these errors combine as do
independent errors, but with additional terms that account for the correlations.
It is beyond the scope of this study to carry out a full analysis o f the propagation of
error from o° through regression models and into biomass estimates. (The hard part of
such an analysis is to adequately characterize and quantify the sources of error and to
model their effects on o°, after which the error propagation problem can be handled
straightforwardly with Monte-Carlo simulations.) Instead, I examine the propagation
problem by reframing it in a simplified form. The simplification is that the o° errors are
equal and independent among the SAR bands. This is not completely realistic, since
many sources of error of the correlated and non-independent types are ignored. How­
ever, if a realistic estimate of independent error is made, the simplified approach leads to
an estimate of a lower bound on estimated biomass error. Note that this lower bound
error estimate depends only on the regression model and the error of the a 0 data used for
the predictions; errors in field sampling, allometric biomass estimation, in the SAR "train­
ing data" upon which the regression is based, and inadequacies of the model may further
increase biomass prediction error.
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125
23.6.1. Error propagation in biomass-o0 linear regression models
Given the assumption that c° variance is independent and equal for all SAR bands,
equation [6 ] may be rewritten as
pi
where sdB is the standard deviation o f estimated biomass, s d ^ is the standard deviation
o f c°, and —— are the partial derivatives o f the biomass regression model with respect
obnd
to the SAR bands. This expression is evaluated as follows: For a first-order multiple
linear regression model of the form B = a + b c °bndl + cc°blld2 , where B is predicted
biomass and bnd refers to a frequency-polarization combination (e.g., L-HH), the partial
derivatives
are
=b
and
* jo
—c ,
so the propagated error is
simply
sdB = sdsarvb2+ c r . Because all terms are first order, the partial derivatives evaluate to
simple scalars. Therefore, sdB is directly proportional to sd,^ and to the square root of
the sum of the squares o f the regression coefficients; sdB does not vary with biomass.
Using uncertainties representative o f the SIR-C data, I apply [7] to compute lower
bounds for uncertainty in estimated biomass for a subset of my regression models. o°
uncertainties in the range of ±0.25 to ±1.0 dB are used in the calculations. I believe this
is an appropriate range of values based on calculated fading uncertainty (0.066-0.44 dB,
§2.2.2) and the reported SIR-C H H -W amplitude imbalance (0.6-0.7 dB, Freeman et al.,
1995) (though o° changes due to fluctuations in forest state may be >1 dB). After pro­
pagating these errors through the regression models, I compare the observed RMS error
from the regressions to the propagated biomass error from the same models.
2 5 .6 2 . Error propagation in three non-linear models
Finally, I compute the lower biomass error bounds for three non-linear SARbiomass regression models. The error propagation behavior of first-order multiple regres­
sion models may be inherently problematic for biomass-o 0 regression. Indirect or ratio-
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126
based
models might be more robust, that is, insensitive to variations in measured c°. To
explore this possibility, I evaluated error propagation for three indirect regression models.
The models and the o° data are from published analyses o f SIR-C data from northern
Michigan coniferous forest (Dobson et al., 1995). The models do not apply directly to
loblolly forest, but similar non-linear models might apply. The point o f this inquiry is to
gain insight into how propagated error in biomass estimates varies among alternative
forms of model as compared to linear regression models.
The models are the Lowland Conifer (LCM), Jack Pine (JPM) and Red Pine (RPM)
models (Dobson et al., 1995, Table V). The models for total biomass are constructed
hierarchically from lower level models that predict height, basal area and crown biomass
that were obtained by exhaustive regression methods (Craig Dobson, pers. cotnm., 1995).
As the models are quite complex, I include here the computations for LCM only. By
combining expressions and simplifying, LCM may be rewritten as follows:
B = 1 6 .2 1 5 + 0 .9 7 1 l h v
+ 0 .1 3 5 ( ( 1 3 6 .8 2 6 -t-1 4 .5 1 9 l h v — 1 4 3 I 9
l w
) ( 1 2 . 0 1 2 + 1 .1 6 2 l
w
- 1 . 1 6 2 c h v ) ) 0 -7115
[8 ]
where B is biomass, and LHV, LW and CHV are o° in dB. Assuming the o° errors (i.e.,
standard deviations) in the three SAR bands are 0.5 dB and independent, then equation
[7] becomes
sd»=0-5V<irav>2+ <aESv>2+ Cl§v>2
PI
Partial derivatives for the LCM model were found using the Mathematica program. They
are:
3B _ Q9 7 u ___________ 139459
(12.012+1.162(LW-CHV))_
((136.826-14319 (LW-LHV)) (12.012+1.162 (LVV-CHV)))0-2*85
3LHV
9B
3L.W
_ (0.0960525 (1.162 (136.826-14.519 (LVV-LHV)) -14.519 (12.012+1.162 (LW-CHV))))
((136.826-14319 (LW-LHV)) (12.012+1.162 (LW-CHV)))02*85
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127
3B
3CHV
________ -0.111613 Cl36.826 -14.519 (LW-LHV))_________
((136.826-14.519 (LW-LHV)) (12.012-t-1.162(LW-CHH)))12**5
Unlike the case of simple, first-order regression, the partial derivatives o f the LCM (and
the other two non-linear models discussed here) are functions o f o°, and thus vary with
biomass. To evaluate the partial derivatives in order to calculate sdB by Eq.[9], it is
necessary to substitute <r° values into the above expressions. Lacking exact a 0 values for
LHV. LW and CHV, I inferred their approximate ranges from the figures in Dobson et al.,
(1995). This made it possible, by plotting all combinations o f small increments of the
three variables, to graph the possible ranges for sdB versus predicted biomass, and
thereby observe the general pattern of variation o f propagated estimation error accom­
panying changes in estimated biomass.
3. Results
3.1. Overview of backscatter characteristics
There are several features o f the data worth noting at the outset. First, o° varies
strongly as a function of 0O at C-band, and less strongly at L-band (Figs. 4a-b, 8a-b).
Second, the maximum range o f <5° among the 21 stands is 3.61 dB (Table 4) which is
roughly on the same order as the variations in median c° among the 10 data takes (Table
5). Third, contrary to my expectations, measured o° is not higher on moist-soil days than
on dry-soil days. For example, comparing data takes 129 and 145o (both at 0O=26°, but
with different soil moistures, 31% and 10% respectively), L-HV and L-VV backscatter
are significantly higher (1.7-1.8 dB) for the drier day (Table 5). Finally, by coincidence,
0O and soil moisture for the April data takes are inversely correlated (r= -0.93), so that
their effects on o° may be difficult to separate. The SIR-C data (including mean, median,
lower quartile, coefficient of variation o f o°, and decomposition o f scattering power) are
summarized in Appendices I-HI.
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128
3.2. Correlation of SAR data to estimated forest characteristics
Examination of the correlations of o° mean, median, lower quartile and decomposed
scattering power to each o f the forest parameters (Appendix IV), shows none of the alter­
native SAR measures has consistently higher correlation to forest parameters than does
mean a 0. Nor do any of the forest parameters have consistently higher correlation to the
radar bands than does biomass. Correlations of logarithm of biomass, mean dbh, tree
height, and stand age to o° are generally similar to (though not as strong as) correlations
of biomass to c°. This is not surprising since all the forest parameters are intercorrelated
(Kasischke et al., 1995) and all except age are estimated from the same field data. Corre­
lations of stem density to o° are generally opposite in sign to those of age and dbh
because the stands thin as they mature. (The correlations of o° to biomass are strongly
correlated to the correlations of <J° to the other forest variables, with r values of 0.90-0.95
for density and basal area and 0.97-0.99 for the other variables). In short, while there
may be value in treating dbh, height, density as separate variables (as in the indirect
regression approach), and while there may be some complementary information in the
lower quartile, decomposition bands, etc., I defer analysis o f those variables to a future
study, and concentrate here on the relation o f linear biomass to o°.
The biomass-o0 correlations are highly variable among the data takes (Table 6 ).
Three of the data takes differ from the others in obvious ways are DT# 113a (very wet
ground, steep 0O = 19.1°), DT# 17 (shallow 0O= 53.6°), and DT# 161 (rain during
acquisition). Putting these aside, the other 7 data takes have large variations in biomass
correlation. L-HV has the most consistent r values (0.22-0.68); in the other bands, r rev­
erses sign from one day to the next without apparent cause. As evidenced by a correla­
tion versus incidence plot on which October and April data takes are identified (Fig. 5),
the variability in correlation cannot be attributed to seasonal factors (including moisture).
However, it appears that whether the antenna was pointed toward the north-east (leftlooking) or south-west (right-looking) may influence the strength o f the biomass-o0 corre­
lations (Fig. 6 ). With few exceptions, the north-looking data takes have higher r values
than the South-looking ones. Since the north-looking takes tend to be at larger incidence
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129
angles than the south-looking ones, 60 may be the operative variable, but there are other
reasonable explanations, including: 1) Topography: Slope within stands is small, but
could affect the mixture of scattering mechanisms. 2) Forest asymmetry: The dielectric
properties or branch architecture may differ when the stands are viewed from the NorthEast and South-West- 3) A SIR-C idiosyncrasy: The radar system may have performed
differently in the left and right orientations. The observed variability suggests that the
biomass-o0 relation may be sensitive to extraneous influences. This suggestion is a
echoed and amplified in the comparison o f the correlations obtained in this study (Table
6) with those reported by Harrell et al. (1997). Though the underlying biomass and
SIR-C data are identical in the two studies, differences in the reported correlations are
substantial, possibly as a consequence o f using different subsets of stands and different
SAR data processing procedures. Thus, the biomass-o0 relation may lack robustness not
only to differences in conditions o f acquisition, but to details of processing as well.
As anticipated, data takes 113a and 161 have low biomass-o0 correlations at L-HV
(Table 6). Of the 3 data takes identified as different above, it is DT# 17 (dry soil,
0O= 53.6°) that contains the surprise. O f all the data takes #17 has highest correlation at
L-HH (r=0.55) and C-HH (r=0.74).
For visual reference, scatterplots of o° versus
biomass for DT #17 C-HH and DT #49o L-HV (one o f the highest L-HV correlations)
are included (Fig. 7). The C-HH correlation is interesting, and I will return to it in the
discussion section (§ 4.2).
3.3. Differences in o° due to incidence angle
The cosine law (§23.2) fits the October o° data well, and it appears to be a suitable
model of the relation o f o° and 0O (Figs. 8a-b). The figures show the o° mean o f all
stands for the 5 October data takes. C-HH (with n=2.179) is the band most sensitive to
0O; C -W , H-HH, and L-HV (n < 1.0) are the least sensitive. RMS errors of fit o f the
data to the cosine model range from 0.24 to 0.39 dB. Comparing RMS errors for the
cosine law and linear least squares fit (Table 7), the cosine law with n as a free variable
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130
fits the data better than the linear model for four o f the SAR bands, while at C-HH and
C - W the linear fit is slightly better. The cosine law with n= l has higher error than with
n free for three of the bands.
How well do the April data fit the cosine law relation developed for October data?
In Figures 9a-b, I superimpose the c° means for the April data on the curves from Fig­
ures 8a-b.
At C-band (Fig. 8a) DT# 161 (the rainy October day) and DT#113a
(0O= 19.1°, wet ground) are on the order o f 1 dB o r more above the curve, but otherwise
the April data fits the October curve closely. At L-band, DT# 161 is also >1 dB high,
but DT# 113a is near the curve. The other April data takes are close to the curve at LHH, and 0.7-1.3 dB below it at L-HV and L -W . It is likely that the elevated o° of data
takes #113a and #161 is a consequence of the wet trees and soil on the days o f those
overflights. Also, it is possible that the lower o° for L-HV and L - W in April reflects a
real change in forest scattering properties between April and October. However, It
should be bome in mind that the absolute calibration uncertainty is over 2 dB (§2.2.2),
and all the observed deviations from the cosine law curve fall within the range of possi­
ble calibration error. The RMS errors of fit of mean o° to the cosine law curve are com­
parable to the standard deviations of c° for the 21 stands in each data take, averaged over
the 10 the data takes (Table 8). When mean o° o f the three age/biomass groups (§2.1)
was plotted versus 60 (not shown), the three group means were tightly clustered for each
data take, differing by no more than =1 dB. Cosine law curves fit separately to the
means of each group differed only slightly from each other.
3.4. Differences in o° due to moisture and phenologic changes
The modeled differences between April and October o° (Table 9) appear to have lit­
tle resemblance to those o f the SIR-C data (Table 10). In Table 10, April-October
differences in median o° for the three age/biomass stand groupings (§2.1) are given
instead of the individual G° differences for stands #64, #41 and #7. This was done
because the individual stands are small (300-500 pixels) and their measured o° is vari­
able, due to fading.
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131
Modeled a 0 for all 3 stand classes is higher in April than October by 0.2 to 1.0 dB
because o f greater scattering and reflection from the wetter April soil. The largest
differences are at HH and W polarizations, which have appreciable surface-related back­
scatter, and at the steeper incidence angle, due to greater canopy penetration. For SIR-C,
measured a 0 from the same stands is in most cases greater in October than April, except
at C-HV and C -W .
At L-HH and L - W , the model predicts a decrease in cr° of 0.4 to 1.0 dB from
April (wet soil) to October (dry soil); SIR-C shows a increase o f 0.0-2.0 dB. At L-HV,
the model predicts a slight (0.2-0.3 dB) decrease; SIR-C shows an increase (1.0-2.0 dB).
At C-HH, the model predicts 0.9-1.0 dB decrease; SIR-C shows an increase o f 0.1-0.9
dB. At C-HV and C -W , the model predicts a decrease and agrees closely with the SIRC (except for the low-biomass group at the steeper incidence angle).
The discrepancies between the model and data for the 27° pair of data takes range
up to 2.7 dB, while for the 32° pair, the largest discrepancy is 1.4 dB. Because the
discrepancies differ by nearly 2 dB in some cases, I reason that at least part o f the
discrepancy, possibly half of it, may be caused by calibration error. This is plausible,
because the pass-to-pass calibration error is estimated to be ±1.2 and ±1.3 dB for C- and
L-bands within the April mission, and ±2.2 and ±1.0 dB within the October mission, and
absolute calibration error is estimated to be 1.0 dB greater (Freeman et al., 1995). Furth­
ermore, that all polarizations at L-band decrease together suggests a calibration shift. It
is also plausible that incorrect modeling is partly responsible, particularly since the C-HH
discrepancies differ from the C -W ones by more than the estimated 0.6 dB channel
imbalance. Also, the discrepancies are appreciably larger for the low-biomass group than
the other groups (except at L-HH and L -W ), which implicates the modeling. The lower
a 0 values for L-HV and L - W for April, as compared to October, might possibly be
explained by seasonal redistribution of water in the trees and the accompanying changes
in dielectric constant. The modeling is open to question, because, apart from the seasonal
change in pine needle load (which was modeled), changes in forest phenology and tree
dielectric constant were not known and could not be modeled.
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132
Regardless o f whether the observed differences in o° arise from forest phenologic
changes, calibration, or other cause, SIR-C data contain o° fluctuations o f up to = 2 dB,
even after mitigating fading effects (by comparing groups o f stands rather than individual
stands) and controlling for incidence (by using incidence-matched data take pairs).
3.5. Biomass - <y° regression results
No one regression model is best for all the data takes, as indicated by adjusted R2
(R2 ). The best band combination is different for each data take (Table 11). The best 10
band combinations for each o f the 10 data takes condense to 49 unique combinations
(Table 12). To highlight the better models, those with R2> 0.40 are printed in bold face.
The highest R2 (0-57) is produced by a model composed o f 4 co-polarized bands (C-HH,
C -W , L-HH, L -W ) for DT# 113a and a 2-band (C-HH, C -W ) model for DT# 17.
That these are the strongest regressions is a surprise, because the wet ground and steep
incidence angle (0O=19.1°) of DT# 113a should lead to strong surface-related scattering,
and the shallow incidence (0O=53.6°) of DT# 17 should permit little canopy penetration
at C-band. The regressions of data takes 145a and 161 are extremely weak; in the case
of DT# 161 this is probably related to moisture on the leaves from rain during the
overflight, but for DT# I45a there is no apparent explanation. R values for DT# 145o
are somewhat higher than for DT# 145a (but the only DT# I45o models with I ? >0.25
are large, i.e., at least 4 bands). Some of the strongest regressions are for DT 49a and
113o, despite moist ground for the former and relatively steep incidence (22.6°) for the
latter. In general, the larger models (4-6 bands) have high R2 for a larger number of data
takes than do the smaller models.
Because some of the 49 band combinations show low R2 for most or all of the data
takes, I excluded the lowest-scoring models from further analysis, retaining only the 36
band combinations for which R~>0.40 for at least 2 data takes. For each of the 36 band
combinations, I computed mean R~ of the 10 data takes and of the following four sub­
sets of the data takes: N-looking only, S-looking only, April only, and October only.
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133
The median of the mean. R r for all data takes is 0.29, and for the subsets it is 0.39, 0.28,
0.29 and 0.34, respectively. Thus, overall, the north-looking and October data takes have
somewhat stronger biomass-cr0 regressions than the south-looking and April data takes.
If the best models explain just over half o f the data variance, how accurately do
they estimate biomass? Not well. For the best 10% o f all estimates, RMS error is 7.409.95 kg/m2. This is consistent with the results o f Harrell et al. (1997). In that paper, for
direct regressions that include the full range o f biomass, reported RMS errors are 8.10
and 9.25 kg/m2.
In examining the biomass estimation errors, I consider two cases: "A" (estimation
from the same data used to generate the regression) and "B" (estimation from different
data) (§2.3.5). The best 10% o f all Case A estimates had RMS errors o f 7.40-8.25
kg/m2, while the best 10% o f Case B estimates had RMS errors of 8.58-10.32 kg/m2.
Figure 10a is an example showing one of the better biomass estimates (RMSE = 9.33
kg/m2) plotted against field-measured biomass. (The circles represent the 21 stands; the
area of the circles is proportional to the regression weights.) In this figure, DT# 49a is
used for both the regression and prediction (Case A). In Figures lOb-d, the same regres­
sion model is applied to other data takes. From the figures, it can be appreciated that an
RMS error o f 9-10 kg/m2 implies some predictive value, but the predictions with RMS
error of 12.63 kg/m2 (Figure 10c) are of doubtful value.
In Figure 11, I compare Case A and B biomass estimation errors for the the entire
data set and all 36 band combinations. For each band combination, biomass regressions
were run for all data takes to generate the model coefficients. Each model was then
applied to predict biomass from the same data (Case A) and the other 9 data takes (Case
B). For each model size, the mean RMSE o f all "A" predictions and mean RMSE o f all
the "B" predictions were plotted (the bottom and top curves, respectively). The pattern is
clean When estimating biomass from the regression data, error decreases as the number
of bands increases. When estimating it from other data takes, error increases with
number of bands. Because the SAR data takes have been adjusted to equalize their
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134
means (§2.3.4), it should be reasonable to expect a model based on one data take to make
good estimates from another, but this is not the case. One cause o f increasing RMSE
with increasing model size for Case B estimates may be that the biomass-o0 relation
varies differently in the different bands from data take to data take. If that is the case, a
similar increase in estimation error with model size should be observed for the propaga­
tion of o° variance through the regression models (see §2.3.6), which is the topic of the
next section. The decrease in RMSE with increasing model size for Case A estimates
indicates that adding additional bands explains additional variance, but there is no
assurance that the additional variance explained is biomass-related, as opposed to unre­
lated noise. A plausible interpretation of Figure 11 is that as SAR bands are added to the
regression, the model becomes more and more specific to the underlying data (and its
noise content), while becoming less and less o f a good fit to a second data set that differs
(even if the difference is in the noise).
Have these results been obtained simply because the 10 data takes are highly vari­
able? For the Duke SIR-C data, even if I restrict the analysis to less diverse subsets of
the data takes (excluding DT# 17 and 161 entirely), the pattern is similar to that shown in
Fig. 11. Comparing N-looking to S-looking and April to October subsets (Fig. 12), there
are no examples in which adding bands improves the biomass estimate from data takes
other than the one used to develop the regression model. It is possible that if forest con­
ditions, incidence, and flight path were closely matched, the same model could cross over
from one data take to the next, but this data set does not allow me to explore that possi­
bility.
Figure 12 offers further evidence that the N-looking data are superior to the Slooking (Fig. I2a-b). Not only do the regression models based on N-looking data takes
make better biomass estimates from the same data than do the other groups (Fig. 12b-d),
but the estimates from other N-looking data takes (Fig. 12a, middle curve) are consider­
ably better than the corresponding estimates in the other examples. That the estimates
from N-looking models applied to S-looking data (top curve) are the poorest in the
analysis underscores how dissimilar the N- and S-looking groups are.
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Differences
135
between the April and October data take subsets are less dramatic (Kg. I2c-d).
3.6. Error propagation In the regression models
In order to investigate how o° error (sd^) propagates into biomass estimation error
(sdB), I selected a subset of 15 o f the better SAR band combinations (from Table 12),
each containing from 1 to 6 bands (i.e., all possible model sizes). For each band combi­
nation, I computed sdB from the coefficients of the biomass-C0 regression o f each data
take (for that band combination), using values of s d ^ that ranged from 0.25-1.0 dB (see
§2.3.6.1, Eq. [7]). This procedure was repeated for each of the 15 SAR band combina­
tions. Mean sdB was then computed from the sdB values of all data takes and band com­
binations of the same size (same number of bands), yielding a single average sdB for
each model size and s d ^ value. These data (Fig. 13) show that, for the linear biomass-c0
regression models that are applicable to the loblolly forest SAR data, propagated estima­
tion error increases with model size and standard deviation of c°. Furthermore, as the
SAR data becomes more variable, the increase in sdB with model size becomes more pro­
nounced, as indicated by the increase in slope of the curves with increasing s d ^
The increase in propagated error with model size (Fig. 13) parallels the observed
increase in Case B RMS error (Figs. 11-12). Evidently, c° variability o f 0.5-1.0 dB
could account for a large fraction of the RMS error of biomass estimation. This is the
range of dispersion of mean c ° in the 10 data takes following cosine law correction for
90 (Table 8). Propagated o° error may be responsible for the steep increase in RMS
error as the number of bands increases from 1 to 3 (Kg. 11). The leveling out of the
upper curve above model size 3 in Fig. 11 is not predicted by the error propagation
results, and suggests other causes.
The curves in Fig. 13 represent average lower bounds for sdB (§2.3.6.1) averaged
over several models and 10 data takes. Propagated error for a given model size varies
depending on the band combination and to an even greater degree on the SAR data,
which determines the regression coefficients (Fig. 14). Each bar o f this boxplot figure
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136
represents the sdB values calculated for the 10 data takes for one o f the 15 band combina­
tions. (The boxplots show the median, middle 50% and extremes o f the data.) Thus a 4-6
band combination, with sbB = 5 kg/m2 for one data take, may have sbB = 15—20 kg/m2 for
another. The 1- and 2-band models have the lowest minimum, maximum and mean
biomass estimation error o f all the combinations tested.
The error propagation properties o f the non-linear models employed in Dobson et
al. (1995) are different from those o f the linear models discussed above. Patterns of pro­
pagated error for the LCM, JPM and RPM models (§23.6.2) are shown in Figs. 15-17.
In these figures, sbB is computed as was illustrated for the LCM in §23.6.2. The range
of c ° values spanned by each SAR band (estimated based on graphs in Dobson et al.,
1995) is shown in the upper right of the figures. The "wide” range (plotted with ".”) is a
conservative estimate of the data limits, outside o f which the forest o° values almost cer­
tainly do not fall, while the "narrow" range (plotted with "X") is the probable data range.
The regression models (e.g., Eq. [8] in §2.3.63) were run with all possible combinations
of integer values for o° of the 3 SAR bands within the narrow and wide ranges to gen­
erate estimated biomass values. (For instance, the number o f points plotted for the wide
range on Fig. 15 is 504, i.e., 9 L-HV values X 8 L - W values X 7 C-HV values.) The
same c ° values were then used to compute the partial derivatives so that the correspond­
ing sdB could be calculated by Eq. [9]. In all cases, s d ^ = 0 3 dB. The maximum forest
biomass levels for which the models were trained and applied by Dobson et al. are indi­
cated on the figures.
For each model, sdB varies with o° and therefore, with predicted biomass. Although
the figures do not provide exact sdB estimates, they do show the probable sdB range and
reveal the general patterns of the sdB versus biomass relations. For LCM, sdB decreases
with biomass, and the greatest error is for the Iow-biomass stands (Fig. 15); for the other
models, error increases with biomass (Figs. 16-17). For LCM, <J° variability of 0.5 dB
could result in propagation error of 4-6 dB. For JPM and RPM, error should be smaller
(sdB < 3 kg/m2), at least for low-biomass stands. Since sdB is proportional to sdsar (Eq.
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137
[9]), if fluctuations in forest conditions and SAR calibration lead to greater o° variability,
say, sdsju- = 1.0 dB, then the estimation errors would double. In summary, when the LCM
is applied to data takes other than the one used to build the regression model, the estima­
tion errors may be quite large for low-biomass stands, perhaps comparable to or greater
than those of the 1-band L-HV regression model (Fig. 14). The JPM and RPM models
appear (at least within their ranges o f applicability) to be more robust to a 0 variability
than the first-order regression models.
4. Discussion
4.1. Variability of o°
Within any of the 10 data takes and 6 bands, the maximum range of o° for the 21
stands (with biomass range of 3.5-44.5 kg/m2) is 3.6 dB (Table 4). At L-HV, often
regarded as the most effective biomass sensing band, the range is only 2-3 dB; it is even
lower for the two shallow-incidence data takes (DT#’s 17 and 33) and the two lowperformance ones (145a and 161). With only 2-3 dB dynamic range available, to
discriminate even 3 biomass groups requires that variation in overall forest o° from all
causes be controlled to <0.5 dB (or maybe even less). The SIR-C data from Duke lob­
lolly stands exceeds this level, even after controlling for incidence angle effects (Table 8,
Figs. 9a-b). The >1 dB elevation of o° for DT #161 and fo r DT #113a at C-band (Figs.
9a-b) are readily explained by presence of water on the trees. The causes of low o°
values at L-HV and L - W for 3 of the April data takes (Fig. 9b) are unknown, but could
reflect forest change or calibration error. Apart from these deviations, all but a few data
points lie within 0.5 dB o f the cosine model curve (Figs. 9a-b). This is cause for cau­
tious optimism. By using a fixed incidence angle, improving calibration, comparing data
from the same season and in some way eliminating rainy day data, it might be possible to
reduce the variability of average measured o° of the loblolly forest to under 0.5 dB.
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138
4.2. Biomass estimation error
The optimism does not extend to the prospects for SAR-based biomass estimation.
The single-band G°-biomass correlations vary erratically among the data takes for all
bands, being least variable at L-HV (Table 6). Even for pairs o f data takes that have
similar radar incidence angles and forest conditions, (such as DT #129 and 145a, or DT
#49o and 145o) the correlations are dissimilar. Also, the a 0 ranges within these data
pairs differ by up to =1 dB (Table 4). Thus, while it may be possible to stabilize the
overall average G° o f the forest, the c° variability of individual stands in successive data
takes may be excessive. Part of this variability is caused by fading. However, recalling
that median fading error is only 0.17 dB and that fading error is below 0.25 dB in 84%
of all instances (§2.2.2), it appears that most of the variability must be caused by other
factors (Chapter 1). Radar look direction is one such factor that stands out as potentially
important (§3.2, §3.5), and though the mechanism is uncertain, it may have to do with
surface topography, asymmetry of forest architecture or variation o f tree dielectric con­
stant (Chapter 1).
The c° variability that underlies the erratic a°-biomass correlations propagates into
error of Case B biomass estimation (§3.5-3.6) through linear regression models and also
non-linear, indirect models. For linear regression models, estimation error increases
rapidly with the number o f SAR bands in the model (up to 3 bands), while for the non­
linear models tested, estimation error depends on predicted biomass in complex ways. In
either type of model, the variability of G°-biomass response demonstrated in the correla­
tions should lead to large errors in biomass estimation.
The variability o f the c°-biomass relation is also evidenced by the diversity of band
combinations and models that yielded the highest R? for the different data takes (Tables
11-12). Every one of the 10 data takes calls for a different band combination in its best
regression model.
Among the best 36 models, the RMS errors for the best 10% o f Case A predictions
were 7.40-8.25 kg/m2, and for the best 10% of Case B predictions were 8.58-10.32
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139
kg/m2. These errors appear large relative to the total biomass range (3.5-44.5 kg/m2), but
perhaps not so large when one considers that the best models have RMS errors o f 7.4
and 8.25 kg/m2 for the two cases, and that the mean biomass o f the stands is 19.7 kg/m2.
That is, under the most favorable conditions, biomass estimates in mature forest may be
accurate enough to be useful. The absolute levels of error obtained in this study are
probably less important than the issue of variability of measured o° discussed above.
That is because there are several features o f this study that make high estimation errors
expected, if not inevitable.
The first of these features, is the exclusion of low biomass stands (<3.5 kg/m2) from
the study. It is well known that saturation leads to large biomass prediction errors for
forests in the upper o f the biomass range of this study. Yet, it is useful to document the
magnitude of estimation errors for these forests, as they have importance in many appli­
cations. Forests at the low end of the biomass spectrum (<15 kg/m2) have been more
thoroughly studied in previous work. It is also useful to examine how the model type
and size impact estimation error, so as to determine what sort of model performs best for
the higher biomass forest and which models are most robust across varying data takes.
The regression and error propagation analyses (§3.5-3.6) show that the linear models are
unstable to o° variability among data takes. Unfortunately, this finding does not automat­
ically extrapolate to low-biomass forest, though backscatter o f low-biomass forest should
be more variable, due to a greater influence of the ground surface. In a follow-up study,
I plan to examine biomass estimation error for a subset o f the Duke data with biomass
<18 kg/m2.
A second likely cause of high biomass estimation error in this study is uncertainty
in field measured biomass. As indicated in Chapter 2, biomass uncertainty may be as
large as 4 kg/m2, due to stand inhomogeneity and inadequate sampling, made worse in
this study by the small regression sample size (21 stands). If field biomass error is in
fact that large, it could account for a large fraction of the biomass estimation errors and
may bias the estimates. It could also account for the similarly high errors reported by
Harrell et al., (1997), and might help explain why the indirect modeling strategies
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140
performed poorly in that study. Errors in "ground truth" are often, as in this study, not
well quantified, and have been known to exceed those o f the remotely sensed data (Cur­
ran and Williamson, 1985).
Third, direct, linear models may be ill-posed for biomass-c0 regression, because c°
is not linearly related to biomass (Dobson et al., 1995). With linear models, "apparent
saturation” occurs at a biomass level below that caused by true, extinction-driven satura­
tion. It has been shown that non-linear, indirect regression can produce lower estimation
errors, presumably by representing the biomass relation more accurately than is possible
with a linear model. Hence, part o f the estimation error o f this study may be attributable
to "apparent saturation." However, as acknowledged by Dobson et al. (1995), indirect
models may not necessarily perform well for Case B estimation. It cannot be assumed
they will yield smaller estimation errors than linear regression models for Case B.
Nevertheless, the analysis o f error propagation does suggest the possibility that estimation
errors might in some cases be lessened by using non-linear models (§3.6, Figs. 15-17),
making this an interesting subject for further study. Beyond the essentially unexplored
question of whether or not indirect regression can reduce Case B estimation errors, there
is a crucial practical issue. Models that require detailed allometry and fine-level forest
classification so as to correctly model the biomass-c0 relation are necessarily impractical
for large scale remote sensing, and have little application outside o f test studies. For that
reason, linear regression may remain the best approach, notwithstanding saturationinduced biomass estimation error.
4.3. Which biomass-c0 regression model?
The regression and error propagation analyses (§3.5-3.6) indicate that Case B
biomass estimation error increases rapidly as the linear regression model expands from 1
to three bands. Therefore, small models of 1 or 2 bands are clearly preferred over larger
ones, at least for this forest and SAR data. Based on results of backscatter modeling
(Chapter 4), L-HH and L-VV are expected to be the most sensitive of the bands tested to
ground surface roughness and soil moisture, and these bands should be avoided. This
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141
was not confirmed by the SIR-C results (Table 10); however, calibration error may have
masked the effects of soil moisture on a°.
L-HV at moderate incidence (22°-44°) has the consistendy highest correlations to
biomass in the data set, up to r=0.68, but for two data takes r<0.30 (Table 6). C-HH at
shallow incidence (54°) in DT #17 is of interest. The o°-biomass correlation is 0.74, and
regressions that include this band have high R2 (0.48-0.57). In principle, at such a shal­
low incidence angle, backscatter at at C-band should originate in the upper canopy, with
little canopy penetration. Is the high correlation caused by biomass-related variation in
upper canopy architecture, or some other factor?
One possibility is that C-HH is
responding to canopy gaps and spaces between trees, which become larger and more
numerous as the forest matures. It has been reported that at C-HH the contrast between
clear-cuts and surrounding forest increases with 60 (Banner and Ahem, 1995). The same
effect was hypothesized for ponderosa pine forest in northern California (Day, 1993).
Further study of C-band backscatter at shallow incidence is warranted. A combination o f
L-HV at moderate incidence and C-HH at shallow incidence might be prove effective for
biomass sensing, though awkward to implement
5. Conclusions
This study examines the backscatter from 21 loblolly forest stands in Duke Forest
for the 10 SIR-C data takes acquired during April and October, 1994, over a variety o f
radar incidence angles and forest conditions. The 21 stands range from 3.5-44.5 kg/m2
dry biomass and 7-84 years of age. The maximum o° range among these stands within
any SIR-C band and data take is 3.6 dB; in most cases it is 2-3 dB. After correcting for
incidence angle effects with a cosine law model, the residual scatter of mean o° of the
data takes is comparable to the variation associated with biomass. Biomass correlates to
c° as well as or better than do any other available forest parameters (logarithm o f
biomass, mean dbh or tree height, density, etc.). Biomass-o0 correlations do not appear
to depend strongly on incidence angle or soil moisture, but the north-looking data takes
have higher correlations than the south-looking ones. L-HV (0O=22°-44°) and C-HH (0q
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142
=54°) have the highest o° biomass correlations (r=0.68 and 0.74).
Observed o° differences associated with forest moisture and phenologic changes
between the April and October SIR-C flights do not agree with modeling results.
Modeled o° is higher in April than October for all bands, but SIR-C a 0 at C-HH, L-HH,
L-HV, and L - W is higher in October than April- The discrepancies, as large as 2 dB,
may be attributable to calibration error or failure to correctly model the seasonal changes
in forest phenology.
Following adjustments to equalize mean forest o° among the data takes (so as to
make regression models comparable), linear multiple regressions of biomass versus c°
were run to determine the best 10 models for each data take. Regressions o f biomass
versus o° explained just over half the biomass variance for the best regression models.
The models were highly variable; for every data take, a different SAR band combination
was called for in the best regression model.
RMS errors of biomass estimation were 7.4-8.25 kg/m2 for the best 10% o f cases,
in which the estimate was made from the same data as used for the regression model.
Errors were 8.58-1032 kg/m2 for the best 10% o f cases in which the model was applied
to a different data take. RMS error decreased with the number of bands in the regression
model for estimates based on the same data that generated the model, and increased with
model size when the model is applied to other data. The interpretation is that variability
of backscatter from the individual forest stands in successive data takes, propagates into
errors in predicted biomass, and that (for the linear models used) this propagated error
increases as the number of bands increases. This is the case even when moisture condi­
tions and incidence are similar and calibration error has been compensated. The o° varia­
bility is larger than can be accounted for by fading, and may stem from forest asym­
metry, topographic effects, variation in tree dielectric constant or other factors. Analysis
of error propagation through the linear models supports this interpretation. An analysis
of error propagation through three non-linear, indirect models suggests the possibility that
some non-linear models may have error propagation properties that could be useful in
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143
SAR-based biomass estimation applications.
For the purpose of extrapolating linear regression models to predict biomass from
data takes other than the one that underlies the model, small models with 1 to 2 bands
are preferable to larger models, because small models are less sensitive to o° fluctuations
among data takes. Based on the results o f this study, C-HH at shallow incidence (50°60°) and L-HV at moderate incidence (=30°) may be an effective combination for
biomass estimation in higher biomass forests, and should be given further study.
6. References
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Banner, A. V., and F. J. Ahem, 1995, Incidence angle effects on the interpietability o f
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Beauchemin, M., K. P. B. Thomson, and G. Edwards, 1995, Modelling forest stands with
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Beaudoin, A., T. Le Toan, S. Goze, E. Nezry, A. Lopes, E. Mougin, C. C. Hsu, H. C.
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Table 1
Measured loblolly stand biophysical characteristics
(from Harrell et al., 1997, Table 1)
stand
#
age
(yrs)
dbh
(cm)
density
(stems/ha)
basal area
(m2/ha)
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
62
23
23
29
53
40
29
60
15
8
10
11
13
11
13
7
55
81
40
84
46
43.8
23.0
26.3
28.4
42.1
37.2
233
38.1
103
6.5
13.1
12.9
103
113
14.6
9.9
40.9
46.8
26.0
44.2
39.6
244
813
810
790
235
350
792
310
1608
3303
1705
1414
2808
1099
1919
2360
171
195
418
242
206
3631
35.72
45.25
51.79
32.02
49.60
34.52
4630
13.56
1230
20.00
11.16
32.47
10.39
32.70
20.71
22.98
32.93
22.43
35.82
25.76
dry
height total
biomass
(kg/nr)
(m)
32.7
18.3
17.0
23.8
32.1
33.2
25.1
31.0
11.7
6.7
7.7
8.9 113
9.4
123
5.8
38.4
29.1
18.5
33.0
27.4
35.61
17.43
21.17
44.46
28.39
27.76
25.08
31.84
635
3.62
6.47
4.93
6.78
3.52
9.24
5.26
26.39
31.85
15.80
39.92
21.50
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T able 2
S um m ary o f S IR -C d ata ac q u isitio n s fo r D u k e F orest, N o rth C aro lin a
date acquired (1994, mo/day)
4/12
4/16
NASA data take #
my code #
49,31
49a
o*
look direction (N=north, S=south)
mode
4/18
10/1
10/2
10/3
113,30
4/17
129,20
145,20
17,21
33.21
113a
129
145a
33
32,1
19,1
26,6
32,0
17
53,6
N
16
S
S
16
16
S
16
N
11
6; 17
6,7/4,5
4:57
6,7/5,2
15,0/6,2
49,31
49o
10/7
113,30
H3o
10/9
145,10
!45o
44.3
32,8
22,6
25,2
N
16
N
16
S
16
26,4
S
16
16
6:28
5:09
6,7/5,2
4:24
6.7/5,2
6.7/5,2
4:36
4:15
7:05
6:46
6.7/5,2
13.3/5.0
6,7/5,2
14.9/8,2
66
8/9
19,9/7.4
83
3/28
11,4/8.2
50
6,7/4.9
14.8/6,9
61
JPL processing run #
57
3/28
11805
24.4/8,2
106
5/10
12170
6.7/5,2
17.8/8,2
78
3/28
11808
12835
moisture conditions
volumetric soil moisture (%)
moist
25
v.wct
34
wet
31
v,moist
28
41184
dry
10
4/27
41341
dry
<10
4/27
41339
dry
<10
phenology
rapid change,
leafing out
-.............>
leaf-on,
new needles on
local time (EDT)
pixel spacing (slant rng/az, m)
nominal resolution ( " )
pixel area (ground rng., m2)
date processed (1995, mo/day)
stable,
20,8/8,2
91
5/11
41422
dry
<10
—
18,0/8,2
78
5/17
41434
dry
<10
10/10
161.10
161
S
4:01
17,9/8,2
82
8/5
42120
It. rain
>10
Table 3
Processed SIR-C data output bands
(Yong Wang, pers. comm. 1997, see §2.2.1)
band #
0
1
2
3
4
5
6
7
8
9
10
11
12
description
hh cross-product
hv cross-product
vv cross-product
total power ( [hh+2hv+w]/4 )
total scattering power from odd # o f reflections (SP-O)
total scattering power from even# o f reflections (SP-E)
SP-O from HHxHH*
SP-O from W xV V *
SP-E from HHxHH*
SP-E from W xV V *
% of SP-O in total power
% of SP-E in total power
% of SP-C (cross-polarized) in total power
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
152
T able 4
DT#
49a
113a
129
145a
17
33
49o
113o
145o
161
Table 5
DT#
49a
113a
129
145a
17
33
49o
113o
I45o
161
a 0 range (dB) for 21 D uke F orest loblolly stands
C-HH
C-HV
C-VV
L-HH
L-HV
L-VV
2.04
2.77
3.11
2.41
2.96
2.27
2.23
3.46
2.98
3.61
1.97
3.22
2.06
1.58
2.07
1.22
1.52
226
1.88
2.12
2.09
2.47
3.15
2.29
NA
2.24
2.13
2.56
3.29
3.34
2.13
3.26
1.82
2.03
2.70
1.90
2.19
2.27
2.28
2.75
3.03
2.21
2.25
1.63
1.15
1.78
2.96
2.30
2.80
1.16
1.62
235
1.32
232
NA
137
2.63
2.00
2.41
2.48
M edian o° (dB) for 21 Duke Forest loblolly stands
C-HH
C-HV
C-VV
L-HH
L-HV
L -W
-9.05
-5.89
-7.94
-8.73
-11.61
-9.70
-8.70
-7.26
-7.62
-6.57
-14.10
-11.70
-13.84
-14.42
-1635
-1436
-14.44
-13.59
-14.14
-12.63
-8.97
-722
-8.67
-8.66
NA
-939
-9.62
-8.48
-9.08
-8.14
-6.78
-5.64
-6.21
-637
-7.99
-7.07
-6.88
-6.34
-5.83
-5.05
-12.92
-11.40
-13.00
-12.74
-13.58
-12.62
-11.78
-11.99
-11.29
-10.62
-8.24
-633
-8.59
-8.08
NA
-8.60
-7.84
-7.15
-6.79
-5.76
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T able 6
C orrelations (r) o f m ean o° vs. biom ass
DT#
0O(deg.)
C-HH
C-HV
C -W
L-HH
L-HV
L -W
49a
113a
129
145a
32.1
19.1
26.6
32.0
0.46
-0.24
0.13
-0.03
0.46
-0.50
0.21
-0.18
038
-0.57
0.43
0.16
0.49
-0.52
-032
-0.34
0.68
031
0.60
0.22
038
0.09
0.26
-0.46
17
33
49o
113o
145o
161
53.6
44.3
32.8
22.6
26.4
25.2
0.74
0.43
0.48
0.11
-0.19
-033
037
0.11
0.55
-0.20
-0.34
-0.40
na
035
0.47
-0.53
-0.17
-0.31
035
0.49
0.43
-0.10
-038
-0.46
031
0.57
0.65
0.66
0.26
-0.14
na
0.51
0.67
036
-0.15
-0.29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
154
T able 7
M odels o f o° to incidence relation
cos law , n free
C-HH
C-HV
C -W
L-HH
L-HV
L -W
k
n
2.179 -6.623
1.291 -13.282
0.931 -8.417
0.997 -5.729
0.975 -11.287
1.505 -6.516
cos law, n=l
RMSE
k
0.294
-7.872
0372 -13.59
0391
-8364
0.249
-5.726
0.239 -1136
0359
-6.899
linear regression
int.
RMSE
0.892
-4.050
0.426 -11.862
0.392
-7.448
0.249
-4.590
0339 -10.211
0.337
-5.203
slope
-0.136
-0.078
-0.053
-0.061
-0.059
-0.078
Table 8 RMS deviation from cosine law (10 DTs),
compared to standard deviation of o° for the 21
stands in each DT, averaged over the 10 the DTs
RMSE of fit to cos law (dB)
s.d. of data (dB)
C-HH
C-HV
C -W
L-HH
L-HV
0.70
0.72
0.70
0.57
0.61
0.72
0.41
0.63
0.71
0.56
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RMSE
0363
0.439
0346
0376
0394
036 5
155
T able 9
M odeled o° difference (A pril-O ctober) for three representative stands
stand #
age
biomass
e0
C-HH
C-HV
C -W
L-HH
L-HV
L -W
64
15
6.55
27°
32°
1.0
0.9
0.6
0.3
1.0
0.4
0.8
1.0
03
03
0.6
0.8
41
29
25.08
27°
32°
1.0
0.9
0.4
03
0.6
0.6
1.0
03
03
03
0.9
0.4
7
62
35.61
27°
32°
0.9
0.9
0.3
0.3
0.4
0.5
1.0
03
03
03
0.8
0.5
11
7
= 27
= 32
26
58
6
8
C-HH
-0.4
C-HV
C -W
L-HH
L-HV
L -W
-0 3
0.5
-0.3
0.5
i
©
vo
0o(deg.)
0.0
-2.0
-1.2
-2.0
-0.1
0.7
0.8
-0.4
-0.1
-1.4
-1.2
-1.8
-0.4
0.7
0.4
-0.6
-1.5
-1.0
-1.6
-0.3
= 27
= 32
-0.1
0.7
0.3
= 27
=32
-0.4
-0 3
0.6
0.2
i
31.8
N
01
19.3
age
(yrs)
o
5.3
mean
VO
mean
biomass
(kg/m2)
SIR-C o° difference (April-October) for three age/biomass groups
i
o
Table 10
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156
Table 11 Best weighted least squares regressions of biomass vs. o° for
the 10 Duke SIR-C data takes, based on maximum adjusted R2
linear regression coefficients
C-HH C-HV C -W L-HH L-HV
DT#
R2
R2
49a
0.611
0.482
21533 -5.846
113a
0.657
0.571
-68.84
7.073
-15362
129
0.575
0.469
246.26 -7.430
9.871
14366
3.390
145a
0.318
0.198
10732
5.787
8.973
-9.212
17
0.613
0.570
33
0.637
0.547
151.72
49o
0.526
0.474
179.05
113o
0.570
0.522
175.69
145o
0.581
0.441
-23.90
161
0.279
0.199
-10632
const
56.65 15.477
-4.761
L -W
5.820 16.859
11.905
5.887
-7.070
-6.826
-16.926
14.829 13.681 12.001
12.054
6.966
-9.119 18.160
-22.096
14.451
-3.966 18.108
-5.476 -11.033
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-6.637
157
Table 12 Adjusted Rr for weighted regressions of biomass vs. o° for
band combinations that are among 10 best combinations for at least I data take
[1] LHV
[2] CHHXHV
[3] CW J-HV
[4] CHV.CWXHV
[5] CHH.CHV
[6] CHH.CHVXHV
[7] CHH
[8] CHH.CHV.CWi.HV
[9] CHV
[10] CHV.CVVXHVi.W
[11] CHH.CHV.CW XHVXW
[12] CHV.CVVXHHXHV X W
[13] CHV.CVVi.HHi.HV
[14] CW XHHXHV
[15] C W X H V X W
[16] CHH.CHV.CVVXHH.LHVXVV
[17] CHH.CVVXHHXW
[18] CHH.CHV.CWXHH.LW
[19] CHH.CWXHHXHV.LW
[20] CVVXHHXW
[21] CHV.CVVX H H X W
[22] C W X H H X H V X W
[23] CHH.CVVXHHXHV
[24] CHH.CWXHH
[25] CHVXHHXHV
[26] CHVXHH XHVXVV
[27] LHHXHVXW
[28] LHHXHV
[291 CHH.CHVXHHXHV
[30] CHHXHHXHVXW
[31] CHH.CHVXHHXHV.LW
[32] CHV.CVVXHH
[33] CHH.CVVXHV X VV
[34] CHH.CHV.CW XW
[35] CHH.CHV.CWXHH
[36] CHV.CVV.LVV
[37] CHH.CVVXW
[38] CHH.CHVXHH
[39] CHHXHH
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[41] LHH
[42] CHVXHH
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[44] CHH.CHVXHVX W
[45] C V V X W
[46] CH H XW
[47] CHVXHHXW
[48] CVVXHH
[49] C H V X W
33 49o Il3o 145o 161
49a 113a 129 145a 17
0.43 0.00 033 0.00 -0.01 039 0.40 0.41 0.02 -0.03
0.42 -0.02 036 -0.07 0.48 0.32 0.41 0 37 -0.05 0.02
0 .4 ? 037 034 0.01 na 0.29 0.41 0 3 0 -0.06 0.00
0.42 039 030 0.11 na 0.30 0 3 9 0.48 031 0.00
0.16 0.18 -0.06 -0.11 037 0.15 0.23 0.01 0.02 0.07
0 38 0 35 031 -0.10 034 039 0 3 9 0.42 0.24 0.01
0.17 0.01 -0.04 -0.05 032 0.14 0.19 -0.04 -0.01 0.06
0 3 4 038 0.45 0.03 na 0 36 0 3 5 0.49 039 -0.06
0.17 031 -0.01 -0.02 0.03 -0.04 0 2 7 -0.01 0.07 0.12
0.47 036 036 0.14 na 0 3 2 0.42 0.46 0.41 -0.02
0.48 0 3 4 0.44 0.06 na 0 3 4 0 3 8 0.45 0.40 -0.10
0.45 031 038 0.07 na 0 3 2 0.41 0.41 0.44 -0.01
0.43 0.46 039 0.13 na 0 3 5 0 3 6 0.43 0.42 0.04
0.46 0.49 0.41 0.08 na 0.42 0 3 6 0.47 0.15 0.12
0.48 0 3 4 030 020 na 038 0.46 0.48 0.03 0.04
0.47 0 3 2 0.45 0.00 na 0.49 0 3 6 0.41 0.41 -0.05
0 38 037 037 -0.01 na 030 0.42 0 3 8 -0.07 0.09
0.40 0 3 6 032 0.00 na 0.46 0 3 8 033 -0.06 0.03
0.45 0 3 4 0.47 0.04 na 0 3 2 0.40 0.45 0.06 0.01
0 3 5 0 3 6 035 0.05 na 0.36 0.45 0 38 -0.02 0.14
0 3 4 034 030 0.07 na 0 3 1 0.42 0.34 -0.03 0.07
0.45 03 4 0.42 0.13 na 0.39 0.44 0.45 0.11 0.07
0.42 03 2 0.46 -0.05 na 03 7 0 3 1 0.47 0.12 0.07
0.18 03 2 0.15 -0.06 na 0 3 2 0.16 031 0.02 0.15
0.41 0.40 0.43 0.00 0.19 036 0 3 9 0.49 0 2 2 0.10
038 0.43 0.43 0.09 na 031 0.42 0.48 0.18 0.04
0.41 0.29 0.43 0.14 na 036 0.40 0 3 1 0.17 0.06
0.45 0.26 0.42 0.05 033 0.40 0 3 5 0 3 2 0.20 0.11
0 3 5 036 0.44 -0.01 030 0.46 0 3 6 0.47 030 0.07
0 38 0.30 037 0.05 na 0 3 5 0.45 0.46 0.11 0.06
033 038 0.43 -0.03 na 0.42 0.41 0.45 0.30 0.00
0 3 2 0.42 0.10 0.13 na 0.41 0.22 0.26 0.04 0.11
0.48 033 0.47 0.12 na 0 2 4 0.42 0.49 -0.04 -0.03
0.41 037 033 0.06 na 0 3 2 0.41 039 -0.09 -0.02
0.14 0.49 0.09 0.05 na 0.37 0.16 0.25 0.00 0.07
036 037 0.15 0.12 na 0 3 2 0.44 0.42 -0.06 0.04
0.43 038 037 0.06 na 0.23 0.44 0.44 -0.14 0.04
0.17 03 4 0.00 0.02 034 026 021 -0.06 0.03 0.12
0.17 0.19 0.02 0.03 0.48 033 0.20 -0.07 0.06 0.18
0.40 03 5 0.37 0.02 0.44 039 0 3 6 0.47 0.15 0.12
0 3 0 033 0.05 0.07 027 0.20 0.14 -0.04 0.10 0.17
033 038 0.08 0.01 021 0.15 0.25 -0.07 0.08 0.14
0 37 030 0.46 0.05 na 0 3 2 0 3 0 0.44 039 -0.01
0 37 0 3 2 026 0.08 na 0.36 0.42 0 3 7 031 -0.02
0 39 038 0.16 0.11 na 0.29 0.47 0.44 -0.09 0.10
0 39 -0.01 -0.03 0.13 na 0.28 0.47 0.23 -0.06 0.08
0 36 0.43 0.16 0.07 na 0.23 0.41 0 3 7 0.04 0.10
0 3 4 0.44 0.16 0.03 na 030 0.22 0 2 7 0.05 0.20
031 0 34 -0.01 0.13 na 0.17 0.43 0.32 0.02 0.08
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure I
D igital orthophoto o f D uke Forest D urham Division
show ing stand outlines
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2
C o lo r com posite SIR-C im age (D T # 113a) o f D uke Forest
D urham D ivision (R,G,B = L-H H , L-H V , L-VV)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
L60
Figure 3
Color composite SIR-C image (DT# 49o) of Duke Forest
Durham Division (R,G3 = L-HH, L-HY, L -W )
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
radar incidence
N_
N= north-looking
S= south-looking
N_
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Day of April, 1994
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2
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3
9
Day of October, 1994
10
Fig. 4a C-band Sigma-0, mean (+/- 1 sd) of 21 Duke Stands
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
162
radar incidence
N.
N= north-looking
S==south-looia'ng
N.
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9
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Day of October, 1994
Fig. 4b L-band Sigma-0, m ean (+/-1 sd) of 21 Duke Stands
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
163
c
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0 = Octobei
Q-VV
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20
30
40
th e ta (deg)
50
20
30
40
th e ta (deg)
50
Fig. 5 Sigma-0 - biom ass correlations versus incidence angle
with April and October data takes identified
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
164
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S = south
c-vv
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20
40
30
th e ta (deg)
50
20
30
40
th e ta (deg)
50
Fig. 6 Sigma-0 - biomass correlations versus incidence angle
with north and south-looking data takes identified
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165
C-HH vs. biomass, DT #17 (October, incidence=53.6 deg.)
(dB)
mean sigma-0
IX)
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t
in
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10
20
30
biom ass (kg/m2)
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mean sigma-0
(dB)
L-HV vs. biom ass, DT #49o (October, incidence=32.8 deg.)
in
i
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10
20
30
biom ass (kg/m2 )
40
Fig. 7 Examples of Sigma-0 vs. Biomass, with least squares lines
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166
S 2
Y= 10n*log10[cos(theta)] +K
22.6
n= 2.179
2 6.4
k= -6.623
RMSE = 0.294^
44.3
53.6
radar incidence angle (deg.)
C-HV. .
CD
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22.6
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n= 1.291 k= -13.282
32.8
RMSE = 0.372
44.3
53.6
radar incidence angle (deg.)
CO
C-VV
1\
CO
CM
Y= 10n*log10[cos(theta)] +K
22.6
26.4
n= 0.931
k = -8.417
RMSE = 0.391
32.8
radar incidence angle (deg.)
Fig. 8 a
O c to b e r M ean S ig m a-0 with c o s in e law fitted c u rv e s, C -b a n d
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
167
L-HH
CO
Y=_10n*Iog10[cos(theta)] +K
22.6
26.4
n= 0.997
k= -5.729
32.8
radar incfdence angle (deg.)
L-HV-
E
05 2*
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Y= 10n*Iog10[cos(theta)]+K
22.6
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- RMSE = 0.239
32.8
53.6
radar incidence angle (deg.)
L -W
<D
Y= 10n*log10[cos(theta)] +K
22.6
26.4
n= 1.505 k= -6.516
RMSE = 0.259
32.8
radar incidence angle (deg.)
Fig. 8b October Mean Sigma-0 with cosine law fitted curves, L-band
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
168
C-HH-
(curve is fit to the October data only)
22.6
26.4
53.6
radar incidence angle( deg.)
.C-HV.
CM
CO
(curve is fit to the October data only)
22.6
26.4
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radar incidence angle( deg.)
C -W
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October data
April data
■ DT #16t
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(curve is fit to the October data only)
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44.3
radar incidence ang(e( deg.)
Figure 9 a
C -b an d S ig m a-0 fo r 10 d a ta ta k e s , with O ct. c o s law c u rv e s
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
169
L-HH
(curve is fit to the October data only)
22.6
26.4
53.6
32.8
radar incidence angle( deg.)
L-HV
O
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(curve is fit to the October data only)
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radar incidence angle( deg.)
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April data
DT #161
W - 1 s .i
(curve is fit to the October data only)
22.6
26.4
32.8
radar incidence angle( deg.)
Figure 9b
L -band S ig m a-0 for 10 d a ta t a k e s , with O ct. c o s law c u rv e s
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
170
40-
weighted regression L-HV v s. biomass
Regression c o e fs from DT *49 (April)
Data from DT * 49 (April)
b) DT #49a predicting #49o
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Regression c o e fs from OT *49 (April)
Data from DT #145 (April)
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10
predicted biomass (kg/m2)
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weighted regression L-HV vs. biomass
Regression co efs from D T #49 (April)
Oata from D T #49 (OcL)
0
predicted biomass (kg/m2)
a) DT #49a predicting #49a
20
30
40
d) DT #49a predicting #113o
40-
30-
30-
20-
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10-
10-
weighted regression L-HV vs. biomass
R egression c o e fs from DT *49 (April)
D atafrom D T #li3(O cL )
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RM S error = 12.63 kg/m‘
20
30
40
10
field-measured biomass (kg/m2)
Fig. 10
RMS error= 9 .5 9 kg/m
0
10
20
40
30
field-measured biomass (kg/m2)
R egression-estim ated vs. field-m easured biom ass
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171
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# of SIR-C bands in th e regression
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Effect of model size on biom ass estimation error
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172
b) Coefs. from S-looking DTs
a) Coefs. from N-looking DTs
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Fig. 13 Mean error in predicted biomass propagated
from s.d. of sigma-0 through linear regressions
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
s.d. of predicted biomass (kg/m2)
174
1
2
3
4
m odel s iz e (n bands)
5
6
Fig. 14 Distribution of propagated biomass error among 10 d f s
10 coef. sets) for 15 SAR band com bos, with s.d. of sigma-0 = 0.5dB
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
175
estimated s.d. of predicted biomass (kg/m2 )
7
sigma-0 ranges (dB)
wide {•) narrow frc)
L-HV -14:-23 -16:-19
6
5
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C-HV -14:-20 -15:-18
4
3
2
1
0
10
20
30
SAR-predicted biomass (kgfin2)
Fig. 15 Propagated error for Lowland Conifer Model
(from Dobson et al., 1995), with s.d.= 0.5 dB
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
176
estimated s.d. of predicted biomass (Kg/m2)
sigma-0 ran g es (dB)
6
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20
30
SAR-predicted biomass (kg/m2)
Fig. 16 Propagated error for Jack Pine Model
(from Dobson et al., 1995), with s.d.= 0.5 dB
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T "
40
177
sigma-0 ranges (dB)
estimated s.d. of predicted biomass (kg/m 2)
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SAR-predicted biomass (kg/m2)
Fig. 17 Propagated error for Red Pine Model
(from Dobson et al., 1995), with s.d.= 0.5 dB
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40
178
Chapter 6:
C oncluding remarks
As o f the beginning of 1999, the developm ent of methods for SAR-based estimation
o f forest structural properties and biomass is still a work in progress, the outcome o f
which is difficult to prophesy. Kasischke e t al. (1997) note that
"... there are two camps in this debate: those who take the view the glass
is half empty, for example, the saturation level for biomass in radar
imagery is fairly low (Waring et al., 1995; Imhoff, 1995a); and the view
expressed in this review that the glass is half full, for example, the
single-frequency/polarization saturation levels can be overcome using
multi-channel data or multistep approaches.”
My reading o f the literature, echoed in the analyses in this dissertation, suggests that,
more to the point, our comprehension o f the biomass estimation problem is only "half
full." It is well established that backscatter contains information on forest structure and
biomass.
Several studies have identified and begun to address the structural sub­
problems, that is, a) SAR response varies with forest structural type, and b) forest back­
scatter is related to biomass only indirectly, through forest structural parameters (Imhoff,
1995b; Dobson et al., 1995). However, less attention has been paid to extraneous factors
whose influence on backscatter is comparable to o r greater than that of forest structure.
To be sure, many model sensitivity studies have been carried, out, but it is difficult to
bridge the gap between most model studies and design o f practical methods for SAR
remote sensing of forest. Furthermore, the role o f biomass regression models in estima­
tion error has been largely ignored in the literature. Estimation o f forest biomass at
regional to global scales will be realizable only if methods can be developed that are able
to overcome (or are insensitive to) both structural diversity and extraneous sources of
backscatter variability.
This dissertation is centered around two studies o f loblolly pine stands in Duke
Forest. The first is a backscatter modeling study that asks the question, "How much
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179
variation in backscatter is expected to result from the actual range o f variation in forest
floor scattering properties, measured in the forest?” Model results indicate that
and
a 0LyY are sensitive to variations in soil surface roughness and litter layer thickness, and
to fluctuations in soil and litter moisture content. Modeled o°CHH and G °cvv are sensi­
tive to surface conditions only for Iow-biomass forest and steep incidence angles. (Max­
imum variations o f these bands for 0o>4O° and low-biomass forest are about 2 dB.)
o°Lhv *s slightly sensitive to roughness and moisture for moderate to steep incidence
angles in low-biomass forest. (For 0o^3O°, maximum variation in a°LHv *s 0-9 dB over
the range o f soil moisture.) o°CHv is insensitive to forest floor variations.
The second study is an analysis o f SAR data acquired in ten SIR-C overflights o f
the Duke loblolly pine forest- The 21 forest stands studied range from 7-84 years o f age
and from 3.5-44.5 kg/m2 total dry biomass. The maximum range of o° among stands (in
any given SAR band and data take) is approximately 2-3 dB. This is comparable to the
scatter in a 0 caused by SIR-C calibration error and fluctuation in forest conditions. Mul­
tiple linear regressions of biomass versus CT° explain, at most, slightly more than half the
biomass variance. RMS errors o f regression-based biomass estimation are 7.4-10.0 kg/m2
in the best 10% o f cases. This relatively poor accuracy (in comparison with the mean
stand biomass o f 20 kg/m2) is attributable to a combination o f factors, including stand
structural diversity, inaccuracies in field-based biomass estimates and fluctuations in
forest variables. Accuracy of linear regression-based biomass estimates increases with
the number o f radar band/polarization combinations included in the regression model for
estimates based on the data used to generate the model, but accuracy decreases with
model size for estimates based on a different data take than used in the regression. Thus,
small models of 1-2 radar channels appear more robust to variations among data takes
than do larger models. An analysis of error propagation of the regression models gen­
erated in the study also shows that the sm aller models should have lower error. Models
other than multi-channel linear combinations might be preferable from the standpoint of
error propagation.
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180
These studies do not offer much support to the "glass is half full " camp. The
modeling results indicate that L-HH and L -W are sensitive to fluctuations in soil and
litter moisture and to site-specific variations in soil surface roughness and litter charac­
teristics. Other work shows that L-HV and C-band vary by up to 3 dB with fluctuations
in canopy water content and water on leaves or needles. Thus, all the SAR channels
available on SIR-C are sensitive to some kind o f extraneous variation. It is inconceivable
to collect sufficiently detailed ground truth to correct for such variations in regional or
larger scale studies. Considering that the level of variability may exceed the "biomass
signal," the possibility of SAR-based biomass estimation methods that are accurate
enough to be useful is uncertain, or even doubtful.
On the other hand, there have been few (if any) SAR biomass retrieval studies
designed to outsmart sources o f variation. It is not inconceivable, for instance, to esti­
mate some of the ground parameters from remotely sensed data (including SAR). It may
be possible to develop a multi-temporal strategy to identify data takes that have good
biomass-separation characteristics, and then estimate within-scene relative biomass using
regression models designed to minimize selected sources o f variability. Regressions of
biomass versus the L-HV/C-HV band ratio have not been considered in this study, due to
the high RMS errors of biomass prediction reported by Harrell et al. (1997). Yet, the
ratio regression is potentially less sensitive to <7° variation than is direct regression; that
has been its appeal. The ratio approach is not a proven dead end, and it may be possible
to improve results by applying different data processing methods (e.g., filtering). Another
option is to reduce the complicated and demanding problem o f biomass estimation to the
much simpler problem of within-scene, coarse-level biomass classification.
This dissertation does not examine o° variability o f the lowest biomass forest (<3.5
kg/m2). Because surface-related scattering in low-biomass forest is comparable to or
greater than that o f higher biomass forest (Chapter 4), <y° variation should be no sm aller
in the low-biomass case. However, because the <J° versus biomass curve is steepest at
the low-biomass extreme, the same level of o° variation should result in sm aller biomass
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
181
estimation errors in the low-biomass case. For that reason, the effects o f o° variability
on biomass estimation in low-biomass forest need further investigation.
The results of this study are largely negative, in that the possibility o f SAR-based
biomass estimation is not affirmed. However, insofar as the dissertation sheds light on
the problem of o° variability and its effects on biomass estimation error, it leads toward a
more complete understanding o f the biomass estimation problem, and may help define
directions for future research.
References
Dobson, M. C., F. T. Ulaby, L- E. Pierce, T. L. Sharik, K. M. Bergen, J. Kellndorfer, J.
R. Kendra, E. Li, Y. C. Lin, A. Nashashibi, K. Sarabandi, and P. Siqueira, 1995,
Estimation o f forest biophysical characteristics in northern M ichigan with SIR-C/XSAR, IEEE Trans, on Geosci. and Remote Sens. vol. 33, no. 4, pp. 877-895.
Harrell, P. A., E. S. Kasischke, L. L. Bourgean-Chavez, and E. M. Haney, 1997, Evalua­
tion of approaches to estim ating aboveground biomass in southern pine forest using
SIR-C data, Remote Sens. Environ., vol. 59, pp. 223-233.
Imhoff, M. L., 1995a, Radar backscatter and biomass saturation: Ramifications for global
biomass inventory, IEEE Trans, on Geosci. and Remote Sens. vol. 33, no. 2, pp.
511-518.
Imhoff, M. L., 1995b, A theoretical analysis o f the effect o f forest structure on synthetic
aperture radar backscatter and the remote sensing o f biomass, IEEE Trans. Geosci.
Remote Sens., vol. 33, no. 2, pp. 341-352.
Kasischke, E. S., J. M . M elack, and M. C. Dobson, 1997, The use o f imaging radar for
ecological applications—a review. Remote Sens. Environ., vol. 59, pp. 141-156.
Waring, R. H., J. B. Way, E. R- Hunt, Jr., L. Morrissey, K. J. Ranson, J. F. Weishampel,
R. Oren, and S. E. Franklin, 1995, Imaging radar for ecosystem studies, Bioscience,
vol. 45, no. 10, pp. 715-723.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
182
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#113.30
(4/16/94
e0=19.1°
S-looking)
CV (linear)
m ean o° (dB)
stand
ID
N
pixels
hh
hv
vv
Lp.
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
304
343
134
286
241
419
238
137
568
264
328
1467
989
1415
1204
656
896
2270
660
1277
680
-5.12
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-8.09
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-8.40
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-8.27
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-8.67
hh
hv
vv
Lp.
1.10 0.97 1.02 0.75
1.00 0.94 1.03 0.69
0.86 0.95 0.95 036
1.10 1.04 1.11 0.73
1.07 1.00 1.05 0.71
1.02 1.14 1.09 0.71
1.08 1.20 1.02 0.69
1.10 1.00 0.97 0.66
0.99 1.09 1.14 0.65
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1.45 .0.94 1.06 0.92
1.09 1.01 1.05 0.69
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1.03 1.15 1.02 0.70
1.13 1.06 1.02 0.68
0.99 1.11 1.17 0.69
1.01 1.04 1.03 0.68
1.13 1.04 1.13 0.83
0.97 1.05 1.04 0.63
1.12 1.05 1.15 0.76
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183
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#113.30
(10/7/94
0O=22.6°
m ean o° (dB)
S-looking)
C V (linear)
ID
pixels
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vv
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12
14
25
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41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
347
424
166
307
323
471
263
164
690
332
375
1200
842
1180
907
823
1001
2613
834
1484
861
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1.01
1.07
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0.99
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1.07
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1.12
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0.91
1.15
1.16
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0.98
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1.20
1.05
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0.98
0.98
0.72
0.72
0.67
0.73
0.74
0.76
0.59
0.66
0.83
0.86
0.79
0.70
0.60
0.71
0.64
0.82
0.72
0.74
0.76
0.66
0.67
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184
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#129.20
(4/17/94
e0=26.6°
m ean o° (dB)
stand
ID
N
pixels
hh
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
404
486
195
350
346
534
312
183
795
387
439
1419
1003
1405
1080
978
1187
3024
930
1714
959
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-13.92
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-8.77
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S-looking)
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-11.07
-9.68
-1031
-10.14
-939
-9.91
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-10.41
-933
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-10.85
-10.93
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-10.28
-11.60
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-1022
-9.77
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hh
hv
vv
0.97 1.03 0.91
1.04 0.95 1.01
0.97 0.93 0.98
122 1.14 122
123 0.95 1.10
1.12 1.11 1.14
1.11 1.07 0.99
0.89 1.08 0.99
1.01 1.01 1.01
126 136 124
1.08 .1.08 1.01
1.04 0.97 1.09
1.04 1.03 1.01
1.02 1.02 1.04
1.00 1.05 1.01
1.08 1.02 0.99
1.02 1.00 1.03
1.09 1.03 1.00
1.17 1.05 1.10
1.07 1.01 1.04
120 1.06 1.20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
t.p.
0.63
0.64
0.64
0.86
0.81
0.81
0.69
0.64
0.66
0.92
0.67
0.68
0.67
0.65
0.61
0.70
0.66
0.67
0.77
0.70
0.88
185
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#145.20
(4/18/94
e0=32.0°
S-Iooking)
CV (linear)
m ean o° (dB)
stand
ID
N
pixels
hh
hv
w
Lp.
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
510
638
254
380
392
613
394
247
1045
518
528
1692
1194
1660
1292
1149
1473
3690
1136
2161
1140
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hh
hv
0.99 0.99
1.04 1.04
.0.99 1.12
1.09 1.08
L07 1.00
1.08 0.96
0.90 1.01
1.05 0.98
1.06 1.09
1.08 1.05
1.12 .0.89
0.99 1.04
0.93 1.07
1.08 0.97
0.99 1.05
1.05 1.05
1.19 1.08
1.02 1.05
1.08 1.00
1.06 1.01
1.07 1.09
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
vv
t.p.
1.10
0.93
0.98
0.97
1.09
1.18
0.95
1.15
1.06
1.02
1.11
1.06
1.05
1.03
1.04
1.07
1.03
1.11
1.06
1.07
1.04
0.67
0.65
0.65
0.70
0.69
0.76
0.58
0.80
0.68
0.69
0.70
0.64
0.63
0.68
0.63
0.70
0.71
0.70
0.73
0.70
0.69
186
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#145.10
(10/9/94
0O=26.4°
m ean a 0 (dB)
stand
ID
N
pixels
hh
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
401
474
188
347
336
527
307
179
779
375
427
1375
959
1356
1050
950
1174
2975
907
1696
931
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-1539
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-938
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-13.99
-934
-13.73
-8.60
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-837
-14.67
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-14.76
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S-looking)
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hh
hv
vv
t.p.
-10.46
-9.77
-11.12
-11.07
-9.68
-9.97
-10.07
-11.06
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-10.94
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-10.41
-11.40
-9.63
-10.62
-1037
-10.31
-9.82
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-10.82
-1037
0.97
1.05
1.03
139
1.10
1.13
0.98
1.01
1.13
0.96
1.18
1.02
1.00
0.99
1.08
1.00
1.09
1.04
1.04
1.00
1.08
0.99
1.04
1.01
0.97
1.07
1.00
1.05
1.04
1.08
1.11
1.02
1.01
0.98
1.09
0.93
1.03
1.03
1.02
1.05
1.05
1.09
0.98
1.12
1.03
1.12
LOO
1.16
0.97
0.99
1.01
1.07
1.17
1.04
1.06
1.05
1.07
1.05
1.02
1.06
1.09
1.04
1.14
0.68
0.76
0.64
0.83
0.70
0.79
0.67
0.65
0.71
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0.88
0.66
0.66
0.68
0.66
0.66
0.72
0.73
0.72
0.68
0.81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
187
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#161.10
(10/10/94
e0=25.2°
mean o°(dB )
S-looking)
CV (linear)
stand
ID
N
pixels
hh
hv
w
t.p.
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
412
471
190
350
330
529
315
187
783
376
448
1381
984
1356
1048
968
1201
3003
918
1704
934
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hh
hv
0.92 1.05
1.05 1.02
1.00 1.00
1.04 1.04
1.13 1.06
1.24 0.96
1.04 1.10
1.03 0.97
1.00 1.04
0.97 1.06
1.28 1.02
1.11 1.00
1.15 1.16
1.08 1.08
1.06 1.07
1.09 1.07
0.98 1.04
1.07 1.09
1.17 1.06
1.09 1.09
1.19 1.04
w
t.p.
1.07
1.19
1.04
1.05
1.09
1.08
0.93
0.82
1.15
1.06
1.05
1.17
1.16
1.01
1.05
1.09
1.04
1.05
1.09
1.04
1.08
0.60
0.78
0 37
0.72
0.76
0.80
0.64
0.61
0.69
0.69
0.80
0.74
0.77
0.69
0.67
0.74
0.66
0.73
0.76
0.72
0.83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
188
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#17.21
(10/1/94
0O=53.6°
m ean o° (dB)
N -looking)
CV (linear)
stand
ID
N
pixels
hh
hv
hh
hv
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
361
462
182
299
341
467
269
180
740
361
426
1372
974
1357
1051
948
1059
2648
892
1538
896
-10.55
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1.05
1.04
0.94
138
1.04
0.99
1.01
0.96
0.97
1.00
031
1.01
1.00
1.09
1.16
1.02
1.10
1.14
1.07
1.67
1.10
1.12
0.98
1.14
1.14
1.03
1.04
1.07
0.88
1.11
0.93
1.19
1.05
1.07
1.01
1.10
1.05
1.02
1.06
1.08
1.17
1.01
Note: This data take was acquired in M ode 11 (HH and HV only).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
189
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#33.21
(10/2/94
0O=44.3°
N -Iooking)
CV (linear)
m ean o °(d B )
stand
ID
N
pixels
hh
hv
w
t.p.
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
608
759
304
488
554
785
466
300
1255
609
712
2323
1635
2297
1761
1591
1791
4478
1476
2603
1484
-9.25
-9.47
-10.07
-9.78
-9.99
-9.70
-9.86
-9.92
-9.49
-10.79
-9.27
-10.48
-9.91
-936
-9.98
-10.01
-9.11
-8.99
-9.45
-832
-8.89
-1437
-14.91
-15.07
-14.75
-14.83
-14.77
-15.14
-13.92
-14.10
-15.08
-14.09
-14.84
-14.58
-14.08
-14.68
-1436
-14.39
-14.20
-14.47
-14.01
-1431
-936
-10.03
-10.08
-9.15
-9.94
-9.66
-9.85
-93 5
-10.15
-10.68
-8.44
-9.76
-10.07
-8.98
-939
-10.14
-9 30
-9.00
-93 7
-8.89
-93 6
-11.12
-11.60
-11.89
-1135
-11.74
-1152
-11.73
-11.26
-11.45
-1238
-10.71
-11.85
-11.70
-10.96
-11.49
-11.76
-11.07
-10.86
-11.20
-1059
-10.92
hh
hv
1.05 1.01
1.05 0.97
1.12 1.06
136 138
1.18 130
1.06 0.99
0.99 1.02
1.08 1.01
1.09 1.10
1.01 0.97
1.04 .1.06
0.99 1.05
0.98 0.98
1.03 1.00
1.21 1.07
1.07 1.05
1.04 1.06
1.10 1.07
1.04 1.07
1.07 1.13
1.34 1.12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w
t.p.
1.04
0.98
0.98
1.07
l.ll
1.01
1.01
1.05
1.02
1.02
134
1.09
1.03
1.02
1.15
1.03
1.08
1.09
1.07
1.07
1.12
0.65
0.66
0.66
0.82
0.74
0.65
0.67
0.69
0.65
0.62
0.74
0.70
0.63
0.65
0.79
0.64
0.69
0.74
0.71
0.73
0.83
190
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#49.31
(4/12/94
0O=32.1°
N -looking)
CV (linear)
m ean a 0 (dB)
stand
ID
N
pixels
hh
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
531
670
271
416
488
670
402
267
1103
547
639
2127
1486
2109
1608
1456
1558
3864
1290
2264
1276
-8.36
-8.42
-10.09
-9.05
-9.64
-8.79
-9.71
-8.96
-9.21
-8.93
-9.49
-9.74
-9.41
-8.70
-9.81
-9.78
-8.42
-8.45
-9.37
-8.05
-8.52
hv
w
t.p.
-8.16 -10.03
-13.07
-8.71 -1033
-14.20
-9.58 -1130
-14.22
-13.97
-8.68 -10.70
-14.44
-9.60 -11.39
-13.76
-9.38 -10.82
-8.97 -11.14
-14.27
-14.25 -10.15 -1138
-9.08 -10.81
-13.53
-9 35 -10.90
-14.10
-8.88 -10.93
-13.89
-9.68 -1133
-14.72
-931 -11.06
-13.90
-8.48 -10.51
-14.01
-14.96 -10.09 -11.77
-9.87 -11.68
-14.99
-838 -10.42
-13.96
-830 -1037
-13.72
-1434
-8.82 -10.96
-9.86
-8.06
-13.02
-837 -10.48
-14.46
hh
1.09
1.02
1.00
1.05
0.94
134
1.09
1.00
1.08
1.07
1.00
1.09
1.00
1.07
1.12
1.02
1.05
1.15
1.06
1.17
1.04
hv
w
Lp.
1.00 1.11 0.74
1.08 0.95 0.67
0.98 1.16 0.66
1.05 1.07 0.71
1.04 1.07 0.64
1.08 1.04 0.75
0.96 1.10 0.69
1.04 0.94 0.66
1.09 1.06 0.69
1.02 1.01 0.66
0.99 1.12 0.65
1.01 1.00 0.65
1.00 1.07 0.62
1.07 1.06 0.69
0.96 1.03 0.67
0.96 1.01 0.63
1.07 1.12 0.69
1.06 1.08 0.72
1.02 1.04 0.65
1.07 1.07 0.75
0.99 1.06 0.71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
191
Duke SIR-C Mean Backscatter and Coefficient o f Variation
C-Band
DT#4931
(10/3/94
e0=32.8°
N -Iooking)
C V (linear)
m ean o° (dB)
stand
ID
N
pixels
hh
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
493
627
252
402
456
638
375
242
1019
500
595
1907
1342
1889
1438
1350
1441
3634
1212
2116
1204
-833
-9.17
-10.04
-8.81
-8.70
-8.70
-9.46
-8.49
-8.79
-9.57
-8.60
-9.80
-8.78
-8.59
-9.70
-9.26
-7.81
-8.09
-8.29
-7.82
-8.61
hv
w
t.p.
-13.89
-8.88 -10.49
-9.87 -11.42
-14.89
-9.90 -11.80
-14.99
-13.98
-959 -10.95
-15.06
-9.63 -11.16
-13.75
-9.62 -10.86
-14.77 -1031 -11.65
-9.94 -11.05
-14.45
-958 -10.98
-14.18
-15.27 -1033 -11.83
-14.36
-8.96 -10.73
-15.09 -10.52 -11.95
-14.44
-9.83 -11.12
-1455
-952 -10.96
-15.09 -10.68 -11.96
-14.46 -10.04 -11.41
-9.04 -1036
-14.08
-13.87
-8.62 -1028
-14.42
-8.95 -10.61
-13.75
-8.55 -10.12
-14.03
-9.43 -10.82
hh
1.04
1.13
0.96
1.04
1.06
0.98
0.95
0.90
1.07
1.01
1.03
0.98
1.06
1.00
1.06
1.05
1.06
1.11
1.03
1.16
1.15
hv
w
1.00 1.15
1.06 1.07
0.97 1.15
0.98 0.97
1.03 1.12
0.98 1.01
1.05 0.93
0.98 0.96
0.99 1.05
1.12 1.08
.1.03 1.03
1.05 1.04
1.02 1.02
1.01 0.98
1.08 1.05
1.02 1.08
1.00 1.06
1.06 1.11
1.01 1.08
1.07 1.09
1.03 1.03
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
t.p.
0.70
0.70
058
0.63
0.74
0.62
0.59
0.61
0.66
0.66
0.65
0.64
0.69
0.64
0.67
0.67
0.70
0.73
0.71
0.78
0.73
192
Duke SIR-C Mean Backscatter and Coefficient o f Variation
L-Band
stand
ID
N
pixels
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
304
343
134
286
241
419
238
137
568
264
328
1467
989
1415
1204
656
896
2270
660
1277
680
DT#113.30
(4/16/94
e0=I9.I°
C V (linear)
m ean o° (dB)
hh
hv
-5.59 -10.89
-4.53 -11.71
-5.20 -12.07
-6.92 -1135
-6 3 7 -11.29
-531 -1035
-6.96 -10.63
-5.92 -1139
-5.28 -11.19
-4.07 -11.98
-5.73 -1230
-5.10 -11.40
-6.96 -12.07
-4.72 -1033
-4.02 -10.94
-4.71 -12.07
-5.64 -10.79
-6.10 -11.15
-7.28 -12.11
-6.60 -1132
-6.18 -1234
S-looking)
w
Lp.
hh
hv
w
t.p.
-534
-6.78
-633
-6.53
-7.06
-5.26
-6.88
-6.53
-6.65
-6.49
-7.30
-6.42
-7.61
-535
-6.54
-5.88
-6.07
-6.37
-6.94
-6.95
-737
-738
-739
-7.91
-831
-8.42
-731
-838
-8.05
-7.79
-7.30
-8.44
-7.68
-9.03
-6.92
-7.11
-7.45
-7.66
-8.03
-8.92
-8.52
-8.70
1.14
1.04
0.95
1.04
1.00
1.16
1.01
0.99
1.14
1.40
1.03
1.08
1.12
1.05
1.15
1.19
138
1.12
0.99
1.06
1.06
1.02
0.95
0.97
1.18
0.87
1.00
0.97
0.94
0.92
0.93
0,95
1.14
1.03
1.19
1.11
1.09
1.08
1.00
1.01
1.08
1.09
1.05
1.08
0.92
0.97
1.00
1.09
0.84
1.02
0.96
1.05
1.11
1.02
1.03
1.08
1.02
1.27
0.96
1.01
1.08
1.02
0.97
0.74
0.66
034
0.62
0.61
0.78
0.61
0 37
0.66
0.90
0.73
0.69
0.69
0.74
0.75
0.89
0.75
0.67
0.64
0.69
0.68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
193
Duke SIR-C Mean Backscatter and Coefficient o f Variation
L-Band
stand
ID
N
pixels
86
1200
87
842
1180
907
823
12
14
25
33
38
41
44
64
68
88
93
95
105
106
107
108
112
1001
2613
834
1484
861
(10/7/94
e 0 = 2 2 .6 °
m ean cr1a (dB)
S-looking)
C V (linear)
hh
hv
vv
t.p.
hh
hv
-5.91
-5.89
-63 4
-6.47
-5.19
-6.06
-6.98
-6.95
-6.41
-6.36
-6.26
-6.14
-7.46
-6.28
-6.06
-539
-6.50
-6.25
-6.75
-6.95
-6.69
-1139
-11.99
-1230
-11.83
-10.79
- 11.00
-1132
-11.69
-11.99
-12.61
-12.95
-12.58
-12.77
-13.09
-11.67
-11.98
-12.17
-1137
-12.49
-11.75
- 12.11
-6.42
-6.99
-7.85
-6.85
-6.43
-6.43
-6.69
-6.85
-7.57
-7.15
-8.42
-731
-838
-7.61
-6.94
-7.14
-7.23
-6.70
-7.73
-733
-7.84
-8.03
-836
- 8.88
1.02
0.96
1.17
0.71
0.98
1.09
1.04
1.08
1.08
1.15
1.01
1.02
0.66
1.16 0.99
1.03 0.93
1.10 0.97
1.11 1.09
1.04 0.95
1.17 1.08
1.11 0.99
1.11 1.03
1.03 0.96
1.07 1.00
0.96 1.03
0.98 1.01
0.99 1.01
1.15 1.14
1.14 1.08
1.05 1.05
1.06 1.05
0.71
0.61
0.68
1.10
1.10
0.63
0.67
*0
00i
78
347
424
166
307
323
471
263
164
690
332
375
7
DT#113.30
-7.60
- 8.00
-8.57
- 8.68
-8.77
-8.75
-9.20
-8.77
-9.68
-8.97
-8.34
-8.17
-8.74
-8.31
-9.10
-8.85
-9.02
1.00
1.03
1.12
1.06
1.00
1.03
1.08
1.01
1.03
1.00
1.02
1.06
1.06
1.02
w
1.00
1.12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Lp.
0.68
0.66
0.65
0.64
0.68
0.71
0.67
0.64
0.64
0.70
0.61
0.72
0.67
0.64
194
Duke SIR-C Mean Backscatter and Coefficient o f Variation
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#129.20
(4/17/94
90=26.6°
CV (linear)
m ean o °(d B )
N
pixels
hh
hv
404
486
195
350
346
534
312
183
795
387
439
1419
1003
1405
1080
978
1187
3024
930
1714
959
-6.45
-5.53
-5.90
-7.03
-5.86
-6.69
-6.39
-5.74
-5.97
-5.81
-6.48
-6.11
-7.35
-6.15
-6.20
-5.61
-6.21
-6.66
-731
-7.17
-6.81
-13.05
-12.82
-11.94
-12.64
-12.35
-13.00
-12.65
-13.12
-12.95
-13.60
-14.19
-1337
-1338
-13.83
-13.00
-13.34
-1236
-12.71
-12.92
-12.73
-13.54
vv
S-Iooking)
tp .
-9.17
-7.99
-8.71
-8.12
-8.78
-8.40
-930
-8.48
-8.91
-8.59
-9.26
-7.96
-9.06
-8.04
-9.07
-8.86
-9.16
-8.83
-9.02
-8.19
-9.73
-9.02
-937
-9.03
-8.93 - 10.00
-9.26
-838
-9.24
-8.64
-8.99
-8.63
-8.98
-8.05
-9.31
-835
-9.84
-8.96
-9.69
-8.83
-9.84
-9.28
hh
hv
vv
1.09 0.99 1.00
0.95 1.02 0.92
1.41 1.23 1.12
1.04 0.99 1.07
0.94 1.07 1.04
1.07 1.01 1.11
1.05 1.00 0.97
1.00 0.92 1.08
1.01 1.03 0.97
0.99 1.48 1.02
1.02 0.97 1.08
1.00 0.98 0.99
1.04 0.97 1.02
0.99 0.96 1.04
1.14 0.99 1.03
1.09 1.04 1.08
1.06 1.06 0.95
1.07 1.03 1.03
1.07 0.99 0.98
1.00 1.09 0.97
1.13 1.06 1.03
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
t-P0.65
0.59
0.87
0.65
0.60
0.71
0.65
0.65
0.65
0.69
0.70
0.65
0.66
0.67
0.73
0.73
0.65
0.68
0.65
0.61
0.72
195
Duke SER-C M ean Backscatter and Coefficient o f Variation
86
87
88
93
95
105
106
107
108
112
510
638
254
380
392
613
394
247
1045
518
528
1692
1194
1660
1292
1149
1473
3690
1136
2161
1140
-6.72
-5.80
-6.23
-6.80
-5.96
-6.09
-6.63
-6.77
-6.41
-6.19
-6.10
-6.17
-7.64
-5.90
-6 3 7
-5.61
-6.13
-6.60
-7.26
-7.31
-6.87
-12.47
-13.20
-13.42
-12.65
-12.48
-11.87
-12.52
-13.20
-12.58
-13 3 5
-13.50
-12.57
-12.48
-13.41
-12.12
-12.79
-12.34
-12.74
-12.79
-12.94
-1335
w
-8.05
-8.00
-8.52
-7.82
-8.00
-7.67
-9.61
-831
-739
-8.08
-8.52
-7.84
-7.41
-7.84
-8.25
-8.35
-9.29
-8.90
-8.77
Lp.
hh
hv
w
Lp.
1.08
1.00
1.00
1.01
1.00
1.01
0.94
0.64
0.67
0.75
0.64
-8.89
-9.14
-9.41
-8.77
-8.74
-9.04
-9.83
-9.12
-8.87
-9.11
&
78
hv
S-looking)
C V (linear)
1
00
68
hh
0
12
14
25
33
38
41
44
64
e0=32.0°
m ean c° (dB)
N
pixels
001
7
(4/18/94
n
stand
ID
DT#145.20
1
00
L-Band
-9.74
-8.92
-8.74
-8.66
-8.94
-9.29
-9.89
-9.83
-9.66
1.01
1.03
1.10
1.07
1.08
1.02
0.92
1.08
1.03
1.11
1.02
1.01
1.04
1.02
1.07
1.06
1.08
1.07
1.03
1.01
1.04
1.05
0.93
0.96
0.97
1.08
1.07
0.99
0.98
0.92
1.11
0.99
1.12
1.03
1.04
1.03
1.12
1.16
0.98
1.04 0.68
1.13 0.69
1.13 0.69
1.02 0.60
1.05 0.65
1.06 0.66
1.06 0.69
1.08 0.65
1.05 0.59
1.02
1.02
1.03
1.04
1.04
1.06
1.07
1.00
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.66
0.63
0.70
0.66
0.68
0.67
0.65
0.65
196
Duke SIR-C M ean Backscatter and Coefficient o f Variation
L-Band
stand
ID
7
12
88
93
95
105
106
107
108
112
S-looking)
CV (linear)
hh
hv
w
t.p.
hh
401
474
188
347
336
527
307
179
779
375
427
1375
959
1356
1050
950
1174
2975
907
1696
931
-5.85
-4.98
-6.41
-6.92
-4.89
-5.67
-6.04
-5 33
-5.90
-5.86
-5.68
-4.93
-6 3 9
-5.04
-5.11
-4.72
-5.83
-5.63
-7.00
-6.48
-6.34
-11.68
-11.27
-10.88
-11_55
-1030
-1152
-11.40
-10.92
-11.07
-13.10
-12.55
-11.34
-1139
-11.70
-1033
-1135
-11.16
-11.02
-1155
-11.24
-12.13
-6.48
-6.43
-7.02
-7.96
-555
-6.73
-7.09
-7.78
-8.10
-759
-831
-9.02
-7.03
-8.07
-833
-8.08
1.16
001
86
87
m ean <y° (dB)
N
pixels
00
00
1
68
78
0O=26.4°
(10/9/94
VO
14
25
33
38
41
44
64
DT#145.10
-7.66
-7.03
-6.70
-6.49
-6.79
-6.28
-6.40
-637
-658
-7.06
-6.93
-7.27
-8.79
-839
-7.68
-8.22
-7.84
-7.39
-7.46
-7.89
-7.88
-8.73
-8.40
-8.67
1.00
0.99
1.02
1.08
0.98
0.91
1.00
0.95
1.05
0.98
1.01
1.02
1.01
1.03
0.98
0.94
1.04
1.03
0.97
1.04
hv
vv
Lp.
1.10 0.93
0.99 1.00
0.92 1.33
1.06 1.00
0.89 1.11
1.04 1.08
0.94 0.91
0.98 1.01
1.01
1.08
0.92
1.03
0.99
0.99
1.02
1.09
1.04
1.02
1.10
1.00
1.09
0.65
0.65
0.73
0.61
0.64
0.62
055
057
1.10 0.62
0.99 0.64
1.07 0.65
1.05 0.68
1.03 0.61
1.01
0.66
0.96 0.63
1.06 0.65
1.00 0.60
1.04 0.64
1.06 0.65
1.03 0.62
0.99 0.69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
197
Duke SIR-C Mean Backscatter and Coefficient of Variation
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
N
pixels
412
471
190
350
330
529
315
187
783
376
448
1381
984
1356
1048
968
1201
3003
918
1704
934
DT#161.10
(10/10/94
0O= 25.2°
S-looking)
CV (linear)
m ean c° (dB)
hh
hv
w
Lp.
hh
-5.02
-3.90
-4.44
-6.65
-4.93
-4.82
-4.96
- 6.00
-5.39
-5.05
-5.37
-4.66
-4.90
-4.65
-5.24
-4.56
-5.47
-538
-5.27
-5.17
-5.56
-10.46
-10.19
- 10.86
-11.08
-10.08
-1034
-10.82
- 11.01
-10.41
- 11.12
-11.16
-1031
-10.63
-10.67
- 10.00
-10.05
-1034
-10.62
-1031
-10.65
-10.81
-5.66
-531
-5.22
-7.67
-5.48
-5.25
-5.65
-5.19
-5.82
-6.15
-5.90
-5.61
-534
-5.80
-5.54
-5.76
-6.30
-5.81
-6.08
-6.16
-6.82
-7.17
-638
-6.85
-8.67
-638
-6.90
-7.23
-7.49
-737
-7.50
-7.57
-7.02
-7.12
-7.11
-7.11
-6.93
-7.60
-7.41
-739
-7.46
-7.88
1.16
0.97
0.84
1.08
hv
w
1.03 0.96
Lp.
0.69
1.01 1.02 0.63
1.11 0.97 038
1.10 0.91 0.62
1.02 1.02 1.02 0.62
134 1.07 1.03 0.71
1.09 0.97 0.93 0.66
0.93 1.01 1.17 0.66
0.93 1.03 1.00 0.61
1.00 1.04 0.96 0.64
1.04 1.04 1.00 0.63
1.02 0.99 1.00 0.63
0.96 1.04 0.98 0.63
1.02 1.06 1.00 0.64
1.00 1.11 1.04 0.64
1.03 1.04 1.06 0.68
1.00 1.02 0.98 0.61
1.07 1.03 1.04 0.66
1.07 1.03 1.00 0.62
1.01 1.05 1.00 0.61
1.00 1.08 1.13 0.66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
198
Duke SIR-C Mean Backscatter and Coefficient of Variation
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#17.21
(10/1/94
e0=53.6°
mean c° (dB)
N-looking)
CV (linear)
N
pixels
hh
hv
hh
hv
361
462
182
299
341
467
269
180
740
361
426
1372
974
1357
1051
948
1059
2648
892
1538
896
-7.88
-7.95
-7.74
-7.10
-7.99
-7.89
-9.08
-8.12
-8.27
-151
-8.52
-8.41
-8.13
-8.28
-8.91
- 8.21
-7.70
-7.86
-8.36
-6.38
-7.34
-13.10
-13.93
-13.78
-13.58
-13.23
-13.88
-14.09
-13.20
-13.08
-13.64
-13.59
-13.45
-13.19
-14.07
-13.18
-13.95
-13.71
-13.64
-13.56
-12.94
-13.41
0.96
1.18
0.98
1.23
1.14
1.05
0.99
0.90
1.02
1.01
0.98
1.15
0.97
1.01
1.03
1.05
1.11
1.03
0.98
1.02
1.02
1.18
1.05
1.03
0.97
1.08
l .l l
0.98
1.00
1.02
1.10
1.06
1.86
1.01
1.05
0.98
1.00
1.10
0.99
0.99
1.30
0.97
Note: This data take was acquired in M ode 11 (HH and HV only).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
199
Duke SIR-C Mean Backscatter and Coefficient o f Variation
L-Band
stand.
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#33.21
(10/2/94
e0=44.3°
CV (linear)
mean o °(d B )
N
pixels
hh
hv
608
759
304
488
554
785
466
300
1255
609
712
2323
1635
2297
1761
1591
1791
4478
1476
2603
1484
-6.54
-6.40
-7.04
-7.21
-6.85
-6.55
-8.30
-6.56
-6.91
-7.13
-7.40
-7.75
-7.56
-7.71
-7.95
-7.40
-6.60
-7.07
-7.85
-6.60
-6.99
-11.83
-13.07
-12.62
-1239
-13.45
-12.14
-12.46
-12.15
-1233
-13.61
-12.81
-12.84
-12.56
-13 3 5
-12.69
-13.00
-1234
-1237
- 12.86
-1238
-1331
w
N -Iooking)
Lp.
-7.90
-8.89
-9.48
-9.09
-8.44
-9.48
-8.40
-9.49
-9.75
-9.00
-9.05
-8 .10
-9.01 -10.14
-9.21
-8.63
-9 3 4
-8.24
-9.96
-9.09
-9.94
-9.27
-9.87
-8 3 2
-9.66
-8.35
-10.19
-9.17
-9.93
-8 3 9
-9.97
-9.18
-9.31
-8.60
-9.40
-8.41
10.10
-9.08
-9.14
-8.15
-9.68
-8.60
hh
hv
w
1.07 1.05 1.03
0.96 1.08 0.94
0.91 1.02 0.90
0.97 1.07 1.01
137 0.97 1.01
1.02 1.05 0.94
1.00 1.11 0.95
1.18 0.97 1.00
0.95 0.99 1.03
0.97 1.03 1.07
0.95 1.00 0.99
1.02 1.00 1.05
1.09 1.09 1.02
1.05 1.06 1.01
1.01 1.03 0.96
1.02 0.99 1.12
0.98 1.01 0.99
1.06 1.02 1.05
1.10 0.98 1.00
130 1.10 1.09
1.12 1.04 1.04
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Lp.
0.68
0.61
036
0.61
0.79
0.63
0.60
0.66
0.60
0.60
0.62
0.62
0.63
0.63
0.62
0.64
0.61
0.66
0.63
0.86
0.68
200
Duke SIR-C Mean Backscatter and Coefficient o f Variation
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#49.31
(4/12/94
e0=32.1°
CV (linear)
m ean o° (dB)
N
pixels
hh
hv
531
670
271
416
488
670
402
267
1103
547
639
2127
1486
2109
1608
1456
1558
3864
1290
2264
1276
-6.62
-6.70
-7.52
-6.25
-6.75
-5.76
-7.00
-6.26
-7.02
-5.99
-7.44
-7.61
-7.17
-7.23
-7.62
-6.78
-6.53
-7.02
-7.89
-6.24
-6.29
-12.63
-14.56
-13.57
-12.55
-12.83
-12.30
-13.38
-12.53
-13.01
-13.51
-13.35
-13.59
-12.90
-14.12
-12.92
-14.16
-12.74
-12.60
-13.51
-11.53
-12.78
w
N-Iooking)
tp .
-8.04
-9.17
- 8.20
-9.64
-9.90
-8.42
-8.24
-9.05
-8.17
-932
-735
-8.47
-832
-9.60
-7.34
-8.76
-8.28
-931
-7.90
-8.99
-8.76
-9.92
-8.95 -10.13
-8.24
-934
-8.63
-9.96
-8.51
-9.83
-8.60
-9.73
-7.98
-9.14
- 8.20
-9.40
-8.96 -1033
-7.52
-838
- 8.22
-9.11
hh
hv
w
t.p.
1.04 0.60
0.93 0.69
1.11 0.91 0.64
1.10 1.00 1.05 0.65
1.08 1.01 1.08 0.69
132 0.99 1.06 0.74
0.93 1.05 1.12 0.63
1.01 1.03 0.93 0.63
0.98 0.97 1.06 0.62
0.98 0.97 0.95 0.61
1.10 0.99 1.03 0.70
1.02 0.99 1.01 0.63
1.00 1.01 1.00 0.60
1.06 1.10 0.97 0.66
0.97 1.02 1.01 0.60
1.02 1.03 1.00 0.66
1.00 1.10 1.07 0.64
1.09 0.99 1.04 0.67
1.04 1.03 1.05 0.64
1.10 138 1.04 0.72
1.05 1.02 1.00 0.67
0.98
1.09
1.13
0.92
0.99
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
201
Duke SIR-C Mean Backscatter and Coefficient o f Variation
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
N
pixels
493
627
252
402
456
638
375
242
1019
500
595
1907
1342
1889
1438
1350
1441
3634
1212
2116
1204
DT#4931
(10/3/94
0O= 3 2.8°
m ean o° (dB)
N -looking)
C V (linear)
hh
hv
w
Lp.
hh
hv
w
-6.01
-6.88
-7.16
-7.05
-733
-5.60
-736
-5.93
-6.98
-631
-7.41
-7.04
-6.60
-7.41
-6.88
-6.45
-6.06
-6.11
-7.41
-537
-6.52
-11.04
-1239
-11.68
-11.77
-11.79
-1130
-12.72
-11.44
-11.64
-12.86
-12.85
-1238
-1139
-13.45
-11.78
-12.91
-1132
-11.69
-1234
-10.49
-11.93
-7.64
-8.12
-7.66
-733
-8.47
-7.08
-7.74
-7.68
-7.84
-8.27
-9.12
-8.08
-7.50
-8.60
-8.29
-8.54
-7.70
-7.37
-8.28
-6.49
-7.92
-839
-931
-9.03
-8.97
-9.40
-8.10
-9.49
-8.48
-9.02
-9.15
-9.92
-939
- 8.68
-9.90
-9.15
-931
-8.47
-8.51
-9.49
-7.61
-8.93
1.03
0.98
1.06
0.98
1.02
0.93
0.97
1.02
1.11
1.10
1.00
0.94
0.96
0.94
1.05
1.08
0.99
1.09
1.05
1.05
1.04
0.95
1.19
1.04
1.19
0,98
0.99
1.04
1.02
1.09
1.04
1.06
1.04
0.96
1.73
1.03
1.09
0.99
1.05
0.98
132
1.00
1.01
Lp.
0.63
1.02 0.62
0.91 034
1.06 0.65
1.05 0.65
1.03 039
1.00 0.62
1.04 0.62
1.02 0.65
1.05 0.66
1.04 0.63
1.02 0.65
1.01 0.61
0.96 0.63
1.01 0.60
0.98 0.67
1.03 0.59
1.03 0.65
1.03 0.63
1.24 0.96
0.98 0.61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
202
Duke SIR-C Median Backscatter and Lower Quartile
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#113.30
(4/16/94
e0=19.1°
S-looking)
low er quartile (dB)
m edian o° (dB)
hh
hv
vv
t-P-
hh
hv
-7.49
-5.61
-7.78
-8.79
-7.35
-735
-831
-8 3 i
-7.49
-7.78
-735
-7.92
-8.50
-6.48
-7.63
-7.63
-735
-7.06
-735
-8.21
-7.92
-13.92
-12.78
-15.28
-15.28
-11.88
-13.01
-14.71
-14.60
-13.01
-12.78
-13.01
-12.56
-13.92
-12.78
-13.46
-13.24
-13.69
-13.92
-13.46
-14.37
-14.60
-9.79
-8.64
-930
-1036
-7.77
-8.93
-8.93
-9.79
-9.50
-9.50
-8.06
-835
-9.21
-7.49
-8.93
-7.77
-8.93
-8.93
-8.06
-9.79
-9.21
-9.16
-8.10
-9.95
-9.95
-8.37
-8.90
-9.42
-11.97
-937
-12.26
-12.84
-10.81
- 11.68
- 11.68
-11.97
- 11.10
-11.97
-1032
-11.97
-1236
-10.23
-1139
-11.97
- 11.68
-10.81
-1139
- 11.68
-1236
-1732
-15.96
-1833
-19.81
-15.96
-1732
-17.55
-19.13
-17.32
-16.41
-16.64.
-16.64
-1833
-17.09
-17.77
-17.09
-1735
-18.00
-17.32
-18.45
-18.91
- 10.22
-8.90
-9.16
-8.63
-8.90
-9.95
-7.84
-9.16
-8.63
-9.16
-8.90
-8.90
-9.95
-9.69
vv
t.p.
-12.95 -11.81
-1238 -1032
-14.10 -12.33
-14.68 -13.13
-1132 -10.48
-12.95 -11.54
-1238 -11.54
-13.53 -12.07
-13.82 - 11.01
-12.95 -11.28
-11.52 -10.75
-11.80 - 11.01
-12.95 -11.81
-9.95
-11.52
-12.95 -11.28
-12.09 -10.75
-13.53 -11.28
-12.95 - 11.01
-12.38 - 11.01
-14.10 -11.81
-12.95 -11.81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
203
Duke SIR-C Median Backscatter and Lower Quartile
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#113.30
(10/7/94
e0= 22.6°
S-Iooking)
low er quartile (dB)
m edian o° (dB)
hh
hv
w
t.p.
-10.03
- 7.44
-9.46
-8.59
-8.02
-8.02
-8.59
-9.02
-8.59
-83 0
-8 39
-9.75
-10.90
-9.17
-9.17
-9.46
-8.30
-8.02
-8.59
-839
-9.46
-14.94
-14.94
-16.15
-15.82
-14.28
-14.72
-15.16
-14.72
-15.16
-15.82
-14.28
-1538
-15.82
-15.16
-15.38
-15.16
-1538
-15.16
-14.28
-16.26
-15.82
-10.84
-936
-10.69
-11.40
-8.86
-1035
-9.99
-9.99
-9.71
-1035
-8.01
-10.27
- 11.12
-837
-1037
-8.86
-1035
-9.71
-8.86
-10.84
-9.99
-10.81
-93 4
-11.33
-10.81
-934
-10.05
-1036
-11.07
-10.30
-10.17
-9.79
-10.81
-1138
-10.05
-10.81
-10.05
-1036
-10.30
-9.79
-11.07
-11.07
hh
hv
-13.20 -1934
-11.76 -18.46
-13.49 - 20.22
-12.91 -19.12
-12.05 -1834
-11.76 -1834
-12.91 - 20.00
-12.63 -17.80
-12.05 -19.12
-11.76 -19.78
-12.63 - 18.24
-13.49 -19.12
-14.64 -19.78
-13.20 -19.12
-13.20 -18.68
-13.20 -18.90
-12.63 -19.12
-1234 -18.90
-12.91 -18.46
-12.63 - 20.22
-12.91 -19.78
vv
t.p.
-14.80
-13.95
-15.37
-15.37
-1234
-1432
-13.95
-13.95
-13.39
-14.80
-11.97
-14.52
-14.80
-1234
-13.95
-12.82
-14.24
-13.95
-1234
-14.52
-13.95
- 12.86
-11.84
-13.12
-1337
-11.84
-1235
-12.35
- 12.86
-12.35
-12.60
-1138
-13.12
-13.63
-12.09
-12.60
-12.60
-12.60
-1 2 35
-11.84
-13.12
- 12.86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
204
Duke SIR-C Median Backscatter and Lower Quartile
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#129.20
(4/17/94
e0=26.6°
S-looking)
low er quartile (dB )
median o° (dB)
hh
hv
w
c.p.
hh
hv
vv
t.p.
-10.60
-8.90
-9.16
-10.73
-9.16
-955
-9.69
-9.95
-8.90
-10.21
-10.47
-10.47
-11.78
-9.42
-10.99
-9.69
-9.42
-9.42
-8.90
-10.21
-9.42
-16.14
-14.69
-15.66
-15.90
-15.17
-15.90
-15.41
-15.17
-14.93
-16.38
-15.17
-15.90
-16.86
-15.66
-16.86
-1638
-15.41
-14.93
-14.93
-15.90
-15.66
-10.80
- 10.01
-11.06
- 10.01
-9.75
-10.54
- 10.01
-9.75
-9.75
-11.84
-1158
-11.06
-11.84
-10.54
-11.58
-10.80
-1054
-9.49
-8.97
-10.54
- 10.01
-11.81
-10.36
-1133
-1133
-1 0 3 6
-11.08
-10.84
-11.08
-1 0 3 6
-1 1 5 7
-11.57
-1 1 5 7
-12.78
-11.08
-1 2 3 9
-1 13 3
-10.84
-10.60
- 10.12
-1133
-10.84
-14.91
-12.82
-1256
-14.65
-1256
-13.61
-13.08
-14.39
-12.04
-13.87
-14.13
-14.39
-15.43
-13.08
-15.17
-13.34
-13.34
-13.34
-13.08
-13.87
-13.61
-20.48
-1831
-19.27
-19.03
-1937
-1951
-1937
-1937
-19.03
-2033
-18.7?
-19.75
-20.96
-1951
-20.72
-19.75
-1951
-19.03
-19.03
-1951
-19.99
-14.45
-13.93
-1533
-14.19
- 12.88
-13.93
-13.40
-14.71
-13.93
-15.75
-15.49
-1533
-15.75
-14.45
-15.49
-14.97
-14.45
-13.66
- 12.88
-13.93
-14.19
-13.98
-1239
-13.26
-1336
-12.78
-13.26
-12.53
-13.26
-12.29
-13.98
-13.74
-13.74
-14.71
-13.02
-14.22
-13.50
-12.78
-12.53
-12.29
-13.50
-13.26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
205
Duke SIR-C Median Backscatter and Lower Quartile
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#145.20
(4/18/94
0o=32.Oo
S-looking)
low er qu artile (dB )
m edian o° (dB)
hh
hv
vv
Lp.
hh
hv
vv
tp .
-11.26
-9.63
-10.99
-10.18
-9.90
-10.72
-10.45
-9.63
-10.18
-10.18
-10.72
-10.72
-11.39
-10.04
-10.72
-10.45
-10.18
-10.45
-9.90
-11.26
-10.99
-15.99
-1532
-16.21
-16.44
-14.88
-16.44
-15.99
-16.21
-15.99
-15.10
-1532
-16.44
-16.88
-15.55
-1631
-16.88
-16.21
-15.99
-15.10
-16.44
-16.66
-11.59
-9.20
- 10.00
-10.80
-9.73
-11.33
-9.73
-9.73
-10.53
-10.53
-10.80
-1133
- 11.86
-10.27
-11.06
-11.06
-9.73
-10.53
-9.73
-10.53
-10.27
-12.09
-1033
-11.31
-11.57
-10.79
-11.83
-11.31
-11.05
-11.31
-11.05
-11.57
-11.83
-12.35
-11.05
-11.83
-11.83
-11.05
-11.57
-10.79
-11.83
-11.57
-1431
-13.16
-1434
-13.70
-13.97
-14.78
-1434
-13.16
-14.24
-13.70
-1434
-1431
-15.06
-13.97
-1431
-13.97
-13.97
-14.24
-13.97
-15.06
-14.78
-20.22
-19.33
-19.77
-20.44
-18.66
-19.99
-19.77
-20.22
-19.77
-18.44
-19.10
-19.99
-20.88
-1933
-19.99
-20.44
-19.99
-19.99
-19.10
-19.99
-20.44
-1538
-12.92
-13.45
-13.98
-13.72
-1531
-13.72
-13.45
-14.25
-1431
-15.04
-15.04
-1538
-14.25
-15.04
-15.04
-13.19
-14.78
-13.72
-1431
-1431
14.17
12.87
13.65
13.65
13.13
14.43
13.13
1339
13.65
13.13
13.65
13.91
14.43
13.13
13.65
13.91
13.13
13.65
12.87
13.91
13.65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
206
Duke SIR-C Median Backscatter and Lower Quartile
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#145.10
(10/9/94
0O=26.4°
m edian o° (dB)
1
S-looking)
quartile (dB)
hh
hv
w
Lp.
hh
hv
vv
Lp.
-9.05
-9.05
-9.93
-11.40
-8.75
-9.34
-8.46
- 10.22
-9.34
-9.93
-8.75
-9.64
- 10.22
-8.46
-9.93
-9.64
-9.05
-9.05
-8.75
-9.64
-9.05
-1634
-1539
-16.43
-1634
-15.39
-15.85
-15.62
-16.08
-1539
-17.00
-15.16
-15.85
-16.08
-15.16
-15.62
-15.62
-15.85
-15.62
-15.62
-16.54
-1634
-10.62
-10.62
-11.78
-11.78
-9.89
-10.62
-10.62
-11.49
-10.62
-11.49
-9.16
-10.91
-12.36
-1033
-11.05
-10.33
-10.91
-10.33
-10.04
- 11.20
- 11.20
-10.89
-10.61
-11.73
-12.28
-1033
-11.17
-11.17
-11.73
-10.89
-11.73
-10.06
-11.17
- 12.00
-10.33
-11.45
-11.17
-11.17
-10.61
-10.61
-11.45
-11.17
-13.17
-13.17
-13.76
-1533
- 12.88
-13.47
- 12.88
-1435
- 12.88
-13.47
- 12.88
-13.47
-14.06
-12.29
-13.76
-13.76
-13.47
- 12.88
-1238
-13.47
-13.17
-20.45
-1930
-2 03 2
-20.45
-19.07
-19.76
-19.99
-21.60
-19.76
- 20.68
-19.07
-1933
-19.99
-19.07
-1 9 30
-19.76
-1933
-1930
-19.53
- 20.22
- 20.68
-14.69
-14.40
-1536
-16.44
-13.82
-14.40
-14.69
-15.85
-15.27
-15.56
-13.82
-14.69
-16.14
-14.11
-14.69
-14.40
-14.69
-14.40
-14.11
-14.98
-15.27
-13.40
-13.12
-13.95
-14.79
-12.84
-13.40
-12.84
-13.95
-12.84
-13.95
-13.12
-13.12
-14.23
-12.56
-13.12
-13.12
-13.40
-12.84
-12.56
-13.67
-13.67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
207
Duke SIR-C Median Backscatter and Lower Quartile
C-Band
stand
ED
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#161.10
(10/10/94
0o=25-2°
S-Iooking)
1
quartile (dB)
m edian o° (dB)
hh
hv
-8.54
-7.66
-9.70
-9.26
-122
-8.25
-8.25
-8.54
-834
-7.96
-7.08
-8.25
-9.12
-131
-9.12
-7.66
-834
-8.25
-7.96
-9.12
-8.25
-15.12
-13.26
-14.07
-15.59
-13.73
-13.73
-14.42
-14.19
-14.19
-14.89
-13.49
-13.96
-15.12
-13.73
-14.89
-14.19
-14.19
-14.66
-14.19
-15.35
-15.12
w
Lp.
-11.03 -10.62
-9.42
-9.31
-11.32 - 11.02
-9.88 -10.75
- 8.88
-8.45
-9.88
-9.95
-9.95
-9.59
-9.31 - 10.22
-10.17
-9.95
-10.46 -10.49
-8.61
-8.45
-9.95
-9.88
-10.17 -10.49
- 8.88
-8.73
-11.03 -10.75
-9.68
-9.59
-10.17 - 10.22
-9.59
-9.95
-9.42
-931
-10.46 -10.75
-9.95
-9.59
hh
hv
w
t.p.
-12.03
-10.87
-13.49
-12.91
-11.74
-12.33
-12.03
-12.03
-1233
-12.03
-12.03
-12.33
-12.91
-11.45
-12.91
-11.74
-12.91
-11.74
-12.03
-13.20
-12.33
-1934
-17.91
-18.84
-19.07
-16.75
-17.45
-19.54
-18.61
-18.61
-18.38
-17.68.
-18.14
-18.61
-17.68
-18.84
-1838
-17.91
-1838
-18.61
-1934
-18.84
-14.47
-13.04
-15.62
-14.18
-12.46
-1332
-13.32
-14.18
-14.18
-14.47
-12.46
-13.90
-13.90
-12.75
-15.33
-13.61
-14.47
-13.61
-13.32
-14.18
-13.61
-1236
-1139
-12.63
-12.63
- 11.02
-12.09
-11.56
-1236
-12.09
-12.36
-11.29
-12.09
-12.63
- 11.02
-12.90
-12.09
-1236
-12.09
-11.82
-12.90
-12.36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Duke S IR -C Median Backscatter and Lower Quartile
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#17.21
(10/1/94
median o° (dB)
0O= 53.6°
N-Iooking)
low er quartile (dB)
hh
hv
hh
-12.09
-13.15
-13.15
-13.15
-13.15
-13.15
-13.42
-13.28
-13.42
-13.95
- 12.88
-14.21
-13.42
-13.42
-14.74
-13.68
-12.62
- 12.88
-13.15
-12.09
-12.35
-17.86
-18.08
-17.40
-18.31
-18.99
-1854
-19.44
-16.73
-17.86
-1854
-17.86
-19.21
-18.76
-18.08
-19.21
-18.08
-17.86
-18.08
-18.08
-17.18
-17.86
-16.07
-17.14
-16.87
-17.14
-17.14
-17.67
-16.87
-16.61
-17.67
-17.14
-17.40
-18.20
-17.40
-17.14
-18.73
-17.94
-16.61
-16.61
-17.14
-15.81
-1654
hv
-21.70
-21.25
-22.15
-21.92
-23.05
-22.60
-23.51
-2057
-21.92
-22.60
. -21.92
-22.83
-22.15
-21.92
-22.83
-21.92
-21.47
-21.92
-21.92
-20.80
-21.92
Note: This data take was acquired in M ode 11 (HH and HV only).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
209
Duke SIR-C Median Backscatter and Lower Quartile
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#33.21
(10/2/94
0O=44.3°
N-looking)
lower quartile (dB )
median o° (dB)
hh
hv
w
Lp.
hh
hv
vv
Lp.
-10.97
-11.50
-11.77
-12.04
-11.77
-11.50
-11.64
-1130
-1130
-1230
-10.97
-12.04
-11.50
-10.97
-11.77
-11.77
-10.71
-10.71
-1134
-10.44
-11.24
-16.06
-16.31
-17.07
-17.32
-17.07
-1631
-17.07
-15.81
-16.06
-1636
-15.56
-16.31
-16.06
-15.81
-16.31
-16.31
-16.06
-16.06
-1631
-15.81
-16.06
- 11.10
-11.63
-11.76
-10.84
-11.89
-1136
-11.36
-10.97
-11.89
- 12.68
-1031
-11.63
-11.63
-1037
-1136
-11.89
- 11.10
-10.84
- 11.10
-10.57
- 11.10
-11.71
-1237
-1233
-1237
-12.69
-12.04
-12.69
-12.04
-12.04
-13.02
-1138
-12.69
-12.37
-11.71
-12.69
-1237
-11.71
-11.71
-12.04
-11.38
-12.04
-14.97
-1530
-1530
-1533
-15.77
-14.97
-15.23
-1530
-15.23
-16.83
-1530
-16.03
-15.23
-14.70
-16.03
-15.77
-14.70
-14.70
-14.70
-13.90
-14.70
-2034
-20.60
-20.09
-2135
-20.85
-20.09
-20.60
-1939
-2034
-20.34
-19.08
-2034
-19.84
-19.59
-20.60
-20.09
-20.09
-19.84
-20.34
-19.59
-20.09
-15.83
-1537
-16.09
-14.52
-15.57
-14.78
-15.30
-1530
-16.09
-16.09
-13.99
-15.57
-15.57
-14.78
-1530
-16.09
-14.78
-14.78
-14.78
-14.52
-15.04
-13.68
-14.34
-1 4 3 4
-14.34
-15.00
-14.01
-14.67
-14.01
-14.34
-15.00
-14.01
-14.67
-14.34
-13.68
-14.67
-1 4 3 4
-14.01
-14.01
-14.01
-13.68
-14.01
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
210
Duke SLR-C M edian Backscatter and Lower Quartile
C-Band
DT#49.31
(4/12/94
e0=32.1°
I
m edian o° (dB)
stand
ID
hh
hv
vv
t.p.
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
-10.20
-9.94
-11.26
-10.73
-10.99
-10.73
-11.52
-10.73
-10.99
-10.73
-11J26
-11.52
-10.73
-10.47
-1132
-11.52
-10.20
-10.47
-11.26
-9.68
-10.20
-14.94
-15.83
-16.05
-15.83
-16.05
-15.49
-15.83
-16.05
-15.60
-15.83
-1538
-1627
-15.60
-15.83
-16.71
-1627
-15.83
-15.60
-16.27
-14.72
-16.05
- 10.10
- 10.10
-11.92
-1036
- 11.66
-11.14
- 10.88
-11.40
- 10.88
-11.14
- 10.88
-11.40
-11.14
- 10.10
- 11.66
- 11.66
-10.36
- 10.10
-10.62
-9.84
- 10.10
-10.72
-1 1 2 2
- 12.21
-11.71
-11.96
-11.46
-11.96
-11.96
-11.46
-11.71
-11.71
- 12.21
-11.71
-1 1 2 2
-12.46
- 12.21
- 11.22
- 11.22
-11.71
-10.72
-11.46
hh
N -looking)
quartile (dB)
hv
-14.16 -18.93
-13.89 -20.04
-14.42 -19.37
-14.95 -19.82
-14.69 -2026
-14.69 -19.82
-16.00 -19.82
-14.16 -19.60
-15.21 -19.15
-14.95 -19.37
-14.69 -19.15
-15.74 -20.26
-14.95 -19.37
-14.42 -19.60
-15.48 -20.26
-15.21 -2026
-13.89 -19.82
-14.42 -1937
-14.95 -20.04
-13.37 -18.49
-14.16 -19.82
vv
Lp.
-13.74
-13.74
-1634
-1426
-15.82
-15.04
-15.04
-15.04
-14.78
-1530
-14.52
-15.04
-15.30
-14.00
-15.82
-15.30
-1432
-14.00
-14.26
-13.48
-14.00
-1320
-1320
-14.44
-13.70
-14.20
-13.70
-13.95
-14.20
-13.70
-13.95
-13.45
-14.20
-13.70
-1320
-14.44
-14.44
-13.45
-13.20
-13.70
-12.71
-13.45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
211
Duke SLR-C Median Backscatter and Lower Quartile
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#49.31
(10/3/94
60=32.8°
N -looking)
low er qu artile (dB)
m edian cr° (dB )
hh
hv
vv
t.p.
hh
hv
-1037
-10.65
-11.20
-10.51
-10.65
-10.10
-10.93
-9.82
-10.37
-11.48
-10.65
-1130
-1031
-1037
-11.48
-10.93
-9.54
-9.82
-10.10
-9.82
-10.65
-15.47
-16.64
-16.64
-15.47
-16.87
-15.24
-16.41
-16.64
-15.71
-17.34
-16.17
-16.64
-15.94
-16.17
-16.64
-16.17
-15.71
-15.71
-16.17
-15.47
-15.71
-11.04
-11.87
- 12.00
-11.04
-11.73
-1132
-11.87
-1139
-1132
-11.87
-10.49
-12.42
-1139
-11.04
-12.42
-11.87
-10.77
-10.49
-11.04
-10.49
-1132
-1139
- 12.20
- 12.20
-1139
-1230
- 11.66
- 12.20
-11.93
- 11.66
-12.47
-11.39
-12.74
-11.93
- 11.66
-12.74
-1230
- 11.12
- 11.12
-11.39
-10.85
- 11.66
-14.25
-1433
-15.91
-14.25
-13.97
-13.97
-14.80
-13.14
-14.53
-14.80
-1433
-15.08
-13.97
-14.25
-15.36
-1433
-13.42
-13.97
-13.97
-13.70
-14.53
-19.68
-2038
-20.14
-1931
-20.61
-19.68
-20.38
-20.61
-19.44
-21.31
-19.91
-20.38
-19.91
-19.91
-20.61
-20.14
-19.68
-19.68
-19.91
-19.21
-19.91
vv
t.p.
-14.90 -1335
-16.01 -1435
-16.01 -14.35
-15.18 -13.82
-15.45 -14.08
-14.90 -1335
-15.73 -14.08
-15.18 -14.08
-14.90 -13.82
-15.73 -14.62
-1435 -13.55
-16.01 -14.62
-15.45 -13.82
-14.90 -13.55
-1638 -14.62
-15.73 -14.08
-1435 -13.28
-14.35 -13.28
-14.90 -13.55
-1435 -13.28
-14.90 -13.82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
212
Duke SIR-C Median Backscatter and Lower Quartile
L-Band
DT#113.30
(4/16/94
0O= I9 .I°
m edian cr° (dB)
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
S-looking)
low er quartile (dB)
hh
hv
w
t.p.
hh
hv
-7.30
-5.91
-6.54
-8.70
-7.94
-7.18
-8.45
-7.18
-7.43
-6.29
-7.18
-6.92
-8.96
-6.67
-6.16
-6.92
-8.20
- 8.20
-8.96
- 8.20
-7.94
-12.29
-13.15
-14.00
-12.93
-12.93
-12.51
-12.29
-12.51
-12.51
-13.15
-13.79
-13.36
-14.00
-12.08
-12.72
-14.21
-12.72
-12.72
-13.79
-1336
-14.43
-7.02
-8.31
-7 3 4
-8.05
-8.57
-7.28
-7.79
-8.05
-7.79
-8.18
-8.83
-8.05
-9.34
-7.28
-8.18
-8.57
-7.54
-8.05
-8.83
-8.57
-8.83
-8.31
-831
-8.31
-9.00
-9.23
-8.08
-8.77
-8.54
-8.54
-8.42
-9.00
-8.31
-9.92
-7.85
-8.08
-8.77
-8.54
-8.77
-9.69
-9.23
-9.46
-10.74
-10.23
-9.72
-12.27
-1130
-1130
-12.78
-1135
-10.99
-1033
-1135
-10.74
-1232
-10.74
-10.23
-1135
- 12.01
- 12.01
-12.78
-1237
-11.76
-1636
-1636
-1836
-16.13
-1636
-15.92
-16.13
-16.98
-15.92
-16.77
-17.41
-17.41
-17.84
-15.92
-16.77
-18.05
-16.56
-1636
-17.84
-17.41
-17.84
vv
-10.89
-12.43
-11.40
- 11.66
-11.92
-11.40
- 11.66
-12.95
-11.92
- 11.66
. -12.95
- 11.66
-13.21
- 11.66
-11.92
-12.69
-11.40
-11.92
-12.95
-12.17
-12.43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
t.p.
-1038
-10.15
-10.15
-11.07
-10.84
-10.15
-10.84
-10.38
-10.38
-10.61
-1130
-10.61
-11.99
-9.92
-10.15
-11.53
-10.61
-10.84
-11.53
-1130
-11.76
213
Duke SIR-C Median Backscatter and Lower Quartile
L-Band
DT#11330
(10/7/94
e0=22-6°
S-looking)
low er quartile (dB)
m edian a 0 (dB)
stand
ID
hh
hv
w
t.p.
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
-7.69
-7.41
-8.25
-8.25
-6.85
-7.69
-8.80
-8.80
-8.25
-8.11
-7.69
-7.69
-9.08
-8.25
-7.69
-6.85
-7.97
-7.97
-8.80
-8.80
-8.25
-13.00
-13.31
-15.08
-13.63
-12.80
-13.21
-13.21
-14.04
-13.63
-14.46
-14.46
-14.46
-14.25
-14.66
-13.21
-14.04
-14.25
-13-21
-14.04
-13.63
-14.04
-8.43
-8.71
-9.26
-8.15
-7.88
-8.15
-7.88
-8.71
-9.26
-8.71
-9.81
-9.26
-10.37
-9.54
-8.71
-9.26
-8.71
-8.43
-9.54
-8.98
-9.54
-8.71
-8.98
-9.52
-8.98
-8.44
-8.71
-9.25
-9.25
-9.52
-9.25
-10.06
-9.52
-10.32
-9.79
-8.98
-8.98
-9.52
-8.98
-9.79
-952
-9.79
hh
hv
-11.03 -16.53
-1159 -17.78
-12.43 .-19.03
-12.70 -17.16
-10.20 -16.12
-12.43 -16.95
-12.70 -1756
-13.26 -17.36
-12.15 -1756
-12.70 -19.23
-1159 -18.82.
-1159 -18.19
-1354 -17.99
-11.87 -18.61
-1151 -17.36
-11.03 -17.78
-12.15 -17.99
-11.87 -16.95
-12.70 -18.19
-12.43 -17.78
-12.43 -17.99
w
t.p.
-1258
-12.03
-13.69
-1251
-12.03
-12.03
-1258
-12.58
-13.14
-12.58
-14.24
-12.86
-13.97
-13.69
-12.58
-13.14
-12.86
-12.31
-13.14
-13.14
-13.41
-11.13
-11.13
-11.67
-10.86
-1052
-10.86
-11.13
-11.67
-11.40
-11.94
-11.67
-11.40
-12.47
-11.94
-10.86
-11.13
-11.67
-11.13
-12.21
-11.40
-11.94
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
214
Duke S IR -C Median Backscatter and Lower Quartile
L-Band
DT#129.20
(4/17/94
e0=26.6°
m edian o° (dB)
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
S-looking)
low er quartile (dB)
hh
hv
w
Lp.
hh
hv
vv
Lp.
- 8.22
-723
- 8.22
-8.47
-723
-8.47
-7.97
-7.47
-7.72
-6.98
-8.47
-7.72
-8.96
-7.72
- 8.22
-7.23
-7.97
- 8.22
-8.72
-8.47
-8.72
-14.74
-14.74
-1431
-1431
-13.88
-1433
-14.53
-14.09
-14.74
-1635
-15.61
-14.74
-15.17
-1539
-14.74
-14.96
-1431
-1433
-1433
-1433
-15.39
-935
-9.31
-10.25
-10.25
-1037
- 10.02
-9.55
-10.48
-1025
-9.78
-11.42
-10.72
-10.48
- 10.02
-10.48
-10.72
-9.55
- 10.02
-10.48
-10.25
-10.95
-9.78
-9.32
-9.78
-12.19
-10.70
-11.45
-12.69
-1820
-17.98
-17.76
-17.76
-1735
-18.41
-1820
-17.98
-18.41
-19.92
-19.71.
-18.63
-18.84
-1928
-18.20
-19.06
-17.98
-18.41
-18.20
-18.41
-19.06
-13.30
-13.76
-14.47
-14.00
-14.23
-14.00
-1239
-14.70
-14.47
-1333
-14.94
-1423
-14.23
-13.76
-1423
-14.23
-1333
-14.00
-14.00
-14.23
-14.94
-11.87
-11.17
-11.87
- 12.10
-11.64
-12.33
-11.87
-11.87
-11.87
-11.87
-12.56
- 12.10
-12.80
- 12.10
-11.87
- 12.10
-11.87
- 12.10
-12.56
- 12.10
-12.80
- 10.01
-932
- 10.01
-9.66
-9.78
-9.78
-9.78
-10.48
- 10.01
-10.71
- 10.01
- 10.01
-9.78
-9.55
- 10.01
-10.71
-10.24
-10.71
-1 1 2 0
-12.94
-12.19
- 11.20
-11.45
-11.45
-11.94
-11.70
-12.69
-11.45
-12.19
-10.95
-12.19
-12.19
-13.19
-12.44
-12.44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
215
Duke S IR -C Median Backscatter and Lower Quartile
L-Band
DT#145.20
(4/18/94
S-Iooking)
e0=32.0°
I
m edian o° (dB)
quartile (dB )
stand
ID
hh
hv
W
Lp.
hh
hv
vv
Lp.
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
-8.55
-7.72
-8.00
-8.83
-7.72
-8.00
-8.27
-8.00
-8.27
-7.72
-8.00
-7.86
-9.38
-7.72
-8.00
-7.45
-8.00
-8.27
-9.10
-8.83
-8.55
-13.98
-14.84
-15.27
-14.20
-13.98
-1355
-14.20
-14.63
-14.20
-14.63
-15.49
-14.41
-13.98
-15.06
-13.55
-14.41
-13.98
-14.63
-14.41
-14.63
-15.06
-9.89
-9.63
-10.15
-9.89
-9.37
-9.89
-9.37
-11.73
-10.15
-9.37
-9.89
-10.15
-10.42
-9.37
-8.97
-9.37
-9.89
-10.15
-10.94
-10.94
-10.42
-10.00
-9.72
-10.00
-10.00
-9.72
-9.44
-9.86
-1055
-9.72
-9.72
-10.00
-9.72
-10.27
-9.72
-9.44
-9.44
-9.72
-10.00
-10.55
-10.55
-10.27
-12.41
-1158
-10.76
-12.96
-11.86
-12.14
-12.14
-11.86
-11.86
-11.58
-12.14
-11.86
-12.96
-11.31
-12.41
-11.58
-11.86
-12.41
-13.24
-12.96
-12.41
-1850
-1850
-18.93
-18.07
-17.42
-17.21
-18.07
-1828
-18.07
-18.28
-19.57
-18.50
-17.85
-18.71
-16.99
-18.28
-17.85
-18.50
-18.07
-18.50
-18.71
-13.82
-1356
-14.34
-1330
-13.82
-14.08
-13.82
-1539
-13.56
-1330
-13.82
-13.56
-14.08
-13.03
-12.77
-13.56
-13.56
-13.82
-15.13
-14.34
-14.61
-11.93
-11.66
-1221
-11.93
-11.66
-11.66
-11.93
-12.21
-11.93
-11.66
-11.93
-11.66
-1221
-11.66
-11.38
-11.66
-11.66
-11.93
-12.76
-12.49
-12.49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
216
Duke SIR-C Median Backscaiter and Lower Quartile
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#145.10
(10/9/94
0O=26.4°
S-looking)
low er quartile (dB)
m edian cr° (dB)
hh
hv
vv
Lp.
hh
hv
w
t.p.
-7.92
-6.54
-7.92
-8.47
-6.81
-7.09
-7.64
-6.26
-7.37
-7.64
-737
-6.54
-7.92
-6.81
-6.81
-6.26
-7.09
-737
-8.75
-830
-830
-13.78
-12.85
-12.61
-13.08
- 11.68
-13.32
-13.32
-12.85
-13.08
-14.72
-14.02
-13.08
-13.08
-13.32
-12.15
-13.08
-13.08
-12.61
-13.32
-13.08
-13.78
-7.78
-7.78
-9.88
-9.74
-7.50
-8.62
-8 3 4
-9.46
-8.62
-9.18
-8.62
-8.34
-8.34
-8.34
-7.78
-8.06
-7.78
-8 3 4
-8.90
-8.62
-8.90
-8.74
-8.16
-9.03
-9.61
-7.59
-8.74
-8.74
-8.74
-8.74
-9.61
-9.03
-8.45
-8.74
-8.45
-8.16
-8.16
-8.45
-8.45
-932
-9.03
-9.32
-11.51
-10.41
-11.79
-12.07
-10.41
-10.96
-10.96
- 10.68
-1131
-1234
-10.96
-10.13
-12.34
- 10.68
-10.41
-10.41
-10.96
-10.96
-12.62
-11.79
-12.34
-1733
-1730
-1636
-17.76
-15.19
-1733
-1636
-17.06
-1639
-18.93
-1733
-16.83
-1639
-1730
-15.89
-17.30
-16.59
-16.59
-1733
-16.59
-18.00
-11.98
-1236
-1534
-13.10
-1236
-12.26
-12.26
-12.82
-12.82
-13.10
, -13.66
-11.70
-12.26
-1236
-11.42
-12.26
-11.70
-12.26
-12.82
-1236
-11.98
-10.77
-10.48
-11.64
-11.64
-9.61
-10.77
-11.06
-10.48
-10.77
-11.35
-11.06
-10.48
-10.77
-10.77
-10.19
-10.19
-10.19
-10.48
-1135
-11.06
-11.35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
217
Duke SIR-C Median Backscatter and Lower Quartile
L-Band
DT#161.10
(10/10/94
e0=25.2°
m edian c° (dB)
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
S-looking)
low er quartile (dB)
hh
hv
w
Lp.
hh
-7.12
-5.42
-5.70
-8.82
-6.55
-7.12
-7.12
-7.12
-6.84
-6.27
-7.12
-6.27
-6.27
-62.7
-6.84
-627
-6.84
-7.12
-7.12
-6.84
-7.12
-12.42
-11.95
-13.00
- 12.88
-11.71
-12.18
-12.18
-12.65
-11.95
-13.12
-13.35
-11.95
-12.42
-12.42
-12.18
-11.95
-12.65
-12.18
-11.95
-12.42
- 12.88
-7.21
-7.50
-721
-8.92
-7.50
-6.64
-6.93
-7.21
-7.50
-7.50
-7.78
-6.93
-6.93
-7.50
-7.21
-7.50
-7.78
-7.50
-7.50
-7.78
-8.92
-8.13
-732
-7.05
-9.20
-7.72
-7.59
-8.13
-8.13
-7.86
-8.13
-8.13
-7.59
-7.86
-7.86
-7.86
-7.59
-8.13
-8.13
-7.86
-8.13
- 8.66
-10.52
-9.11
-9.11
- 12.22
-10.24
-10.81
-11.09
-11.09
-10.81
-10-52
-1137
-1034
-1034
-1034
-10.52
-1034
-10.81
-10.81
-11.37
-10.52
-11.09
hv
w
-16.16 -10.92
-15.45 - 11.20
-16.16 -10.63
-17.79 -12.63
-15.92 -10.92
-15.69 -10.92
-1639 -10.92
-1732 -11.49
-16.16 -11.49
-17.09 -1130
-17.09 . -11.49
-15.45 -10.92
-16.16 -10.92
-16.62 -10.92
-16.16 - 11.20
-16.16 -11.49
-16.16 - 11.20
-16.16 -11.49
-16.16 -11.77
-16.16 -11.77
-16.62 -12.63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
t.p.
- 10.01
-9.20
- 10.01
-11.08
-9.47
- 10.01
- 10.01
-10.28
-9.74
- 10.01
-10.54
-9.74
-9.74
-9.74
-9.74
-10.28
-10.28
-1038
- 10.01
-10.28
-10.81
218
Duke SER-C Median Backscatter and Lower Quartile
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#17.21
(10/1/94
m edian o° (dB)
0O= 53.6°
N -looking)
low er quartile (dB)
hh
hv
hh
hv
-9.14
-9.90
-9.52
-9.14
-10.15
-9.65
-10.41
-9.14
-10.15
-8.89
-10.28
-10.41
-9.90
-9.90
- 10.66
-10.15
-9.39
-9.65
-10.15
-8.89
-9.14
-14.60
-15.61
-1539
-14.83
-14.83
-15.27
-15.95
-15.05
-15.05
-15.05
-15.61
-15.05
-15.05
-15.95
-14.83
-15.50
-1530
-15.05
-15.27
-15.05
-14.83
-13.44
-1430
-1430
-13.44
-14.45
-13.44
-14.45
-13.69
-13.95
-12.94
-13.95
-1430
-13.44
-13.44
-14.71
-13.95
-13.19
-13.95
-1430
- 12.68
- 12.68
-18.65
-19.32
-19.55
-18.87
-18.42
-20.00
-1932
-18.42
-18.42
-18.20
-20.22
-18.42
-19.10
-19.77
-18.87
-19.32
-1932
-18.87
-18.87
-18.65
-18.87
Note: This data take was acquired in Mode 11 (HH and HV only).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
219
Duke SIR-C Median Backscatter and Lower Quartile
(10/2/94
0O=44.3°
m edian c° (dB)
ED
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
hh
-8.39
-7.64
-8.64
-8.90
-9.65
-839
-9.90
-9.02
-8.39
-8.64
-8.90
-9.40
-9.40
-9.40
-9.65
-9.15
-8.14
-8.90
-9.65
-839
-8.90
hv
vv
-9.74
-1339
-14.95 -10.48
-9.74
-14.73
-9.99
-1437
-14.95 -10.48
-9.25
-13.82
-10.48
-1437
-13.36 -10.24
-9.99
-14.27
-15.41 -10.97
-14.38 -10.97
-14.50 -10.24
-9.99
-1437
-15.18 -10.73
-9.99
-14.27
-14.50 -10.97
-14.04 -10.24
-14.04 -10.24
-14.38 -10.73
-9.74
-14.04
-14.95 -10.24
N-looking)
low er quartile (dB)
Lp.
hh
hv
-934
- 10.12
- 10.12
- 10.12
-10.69
-9.83
-10.69
- 10.12
-9.83
-10.41
-10.41
-10.41
-10.41
-10.98
-10.41
-10.41
-9.83
- 10.12
-10.69
-9.83
-10.41
-12.16
-11.40
- 12.66
-12.41
-13.66
-11.91
-13.91
-12.16
-11.91
-12.41
-12.41
-13.16
-12.91
-13.16
-13.41
-12.91
-12.16
- 12.66
-13.91
-12.16
-12.91
-17.69
-18.60
-18.60
-18.37
-19.51
-17.69
-18.14
-18.37
-17.91
-19.05
w
t.p.
-13.19 -11.56
-14.42 -12.13
-12.94 -11.56
-13.93 -12.13
-14.91 -12.71
-13.68 -11.85
-14.17 -12.71
-14.17 -12.13
-13.68 -11.85
-14.91 -12.71
-14.17 -12.71
-18.14 -14.17 -12.42
-18.14 -13.68 -12.13
-18.83 -14.42 -12.71
-18.37 -13.68 -12.71
-18.37 -14.91 -12.71
-17.91 -14.17 -11.85
-17.69 -14.17 -12.13
-18.14 -14.66 -12.71
-17.91 -13.68 -11.85
-18.60 -13.93 -12.71
>
DT#33.21
1
00
L-Band
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
220
Duke SIR-C Median Backscatter and Lower Quartile
L-Band
stancj
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#4931
(4/12/94
e0=32.1°
m edian o° (dB)
hh
-8.19
-8.95
-9.20
-7.94
-8.70
-7.94
-8.44
-8.19
-8.44
-7.69
-9.20
-9.20
-8.70
-8.95
-9.20
-8.44
-8.19
-8.95
-9.45
-8.07
-7.94
hv
vv
-9.97
-13.95
-16.12
-9.22
-15.47
-9.97
-14.39 - 10.22
-14.39 - 10.22
-8.97
-13.95
-15.26 -10.09
-8.97
-14.39
-14.60 - 10.22
-15.04
-9.47
-14.60 - 10.22
-15.26 -10.72
-9.97
-14.49
10.22
-15.91
-14.60 - 10.22
-15.69 - 10.22
-14.60
-9.72
-14.17
-9.97
-15.04 -10.72
-8.97
-13.30
-9.72
-14.39
N -looking)
low er quartile (dB)
Lp.
hh
hv
w
Lp.
-9.87
-10.38
-10.89
-9.74
- 10.12
-935
- 10.12
-9.61
- 10.12
-9.61
-10.64
-10.64
- 10.12
-10.64
-10.38
-10.38
-9.87
- 10.12
-10.89
-9.35
-9.87
-11.70
-12.70
-12.95
-11.45
-12.70
-11.95
-11.95
-11.95
-12.45
-11.45
-12.95
-12.95
-12.70
-12.95
-12.70
-1230
-11.95
-12.70
-13.70
- 12.20
-11.70
-18.08
-19.81
-19.16
-18.73
-18.73
-17.86
-18.95
-17.86
-18.51
-19.16
-18.73.
-18.95
-18.29
-19.81
-18.29
-19.38
-1831
-18.08
-18.51
-17.43
-18.08
-13.22
-13.72
-12.97
-14.22
-14.22
-12.97
-14.22
-12.72
-13.97
-12.97
-14.22
-14.72
-13.97
-13.72
-14.22
-13.97
-13.72
-13.72
-14.72
-12.97
-13.47
- 11.66
-12.43
-12.43
- 11.66
-12.18
-11.41
-12.43
-11.41
-12.18
- 11.66
-12.69
-12.69
-11.92
-12.69
-12.43
-12.43
- 11.66
-12.18
-12.95
-11.41
-11.92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
221
Duke SIR-C Median Backscatter and Lower Quartile
L-Band
DT#49.31
(1 0 /3 /9 4
e0=32.8°
median o° (dB)
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
N -looking)
low er quartile (dB)
hh
hv
w
t-p.
hh
hv
w
t.p.
-7.94
-8.19
-9.20
-8.44
-9.45
-6.93
-9.20
-7.18
-8.70
-8.06
-8.95
-8.95
-7.94
-9.20
-8.44
-8.44
-7.69
-7.69
-8.70
-7.18
-8.19
-13.24
-1434
-13.02
-13.46
-13.68
-13.02
-14.34
-13.46
-13.24
-14.56
-13.90
-13.90
-13.24
-15.22
-13.46
-14.78
-13.02
-1334
-13.68
-12.59
-13.68
-9.16
-9.65
-8.42
-9.40
-10.14
-9.16
-9.40
-9.40
-9.40
-10.14
-10.63
-9.65
-9.16
-10.14
-9.89
-10.14
-9.40
-8.91
-9.89
-8.67
-9.40
-9.04
-9.82
-9.43
-9.56
-9.95
-8 3 2
-10.35
-9.04
-9.82
-9.82
-10.61
-10.08
-9 3 0
-10.61
-9.82
-10.08
-9.04
-9 3 0
-10.08
-8.52
-9.56
-11.73
-12.23
-11.98
-12.23
-13.24
- 11.22
-12.99
- 11.22
-12.99
-12.23
-12.99
-12.99
-1233
-12.74
-12.48
-1233
-11.73
-11.73
-12.48
- 11.22
-11.73
-16.75
-18.07
-16.75
-17.41
-18.07
-16.97
-18.07
-16.53
-17.63
-1839
-1831.
-17.63
-16.75
-18.95
-17.85
-18.73
-17.19
-16.97
-17.19
-16.53
-17.19
-12.83
-13.56
-13.07
-13.56
-14.05
-13.32
-12.83
-13.81
-13.56
-14.30
-15.03
-13.81
-13.32
-13.81
-14.05
-13.81
-13.32
-12.83
-14.30
-1238
-13.07
-11.13
-11.91
-11.65
-1139
-12.17
-10.61
-11.91
-11.13
-11.65
-11.91
-12.70
-11.91
-11.13
-12.44
-11.65
-12.17
-10.87
-11.13
-12.17
-10.61
-11.65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
222
Decomposition o f Duke SIR-C Data
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#113.30
(4/16/94
0O=19.1°
S-Iooking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd w
-4.43
-3.80
-6.97
-5.51
-428
-4.32
-5.47
-5.26
-5.51
-5.59
-3.90
-4.68
-6.06
-3.24
-4.93
-4.15
-4.48
-4.24
-3.58
-5.60
-4.57
-9.67
-7.77
-8.04
-9.63
-8.57
-9.91
-8.28
-11.43
-7.76
-7.83
-8.14
-8.99
-9.15
-7.89
-9.19
-938
-10.14
- 10.11
-8.86
-10.61
-10.27
-631
-5.67
-9.24
-7.32
-6.89
-6.61
-7.70
-7.50
-8.00
-8.04
-5.94
-7.35
-8.63
-5.48
-7.26
-6.76
-6.99
-6.45
-6.20
-7.86
-6.99
-8.97
-8.40
-10.84
-10.16
-7.69
-8.17
-9.39
-93 3
-9.11
-9.27
-8.19
-8.05
-9 3 5
-7.20
-8.74
-7.62
-8.05
- 8.2 2
-7.02
-9.50
-8.28
even hh ieven w
-1133
-9.64
-10.85
-12.35
-1137
- 12.02
-10.62
-13.45
-9.60
-10.19
-1137
-11.75
-11.61
-10.17
-11.72
-11.95
-12.39
-1233
-11.41
-13.02
-12.85
-14.70
-1230
-1136
-12.97
-11.95
-14.01
- 12.00
-15.73
-12.36
-11.64
-10.92
-12.26
-12.79
-11.76
-12.73
-12.85
-14.07
-14.07
-12.40
-1433
-13.76
odd
even cross
03 6
0.50
0.44
0.50
0.47
031
0.48
038
0.44
0.41
031
0.48
0.46
0.51
0.49
0.52
034
0.55
0.55
0.53
0.55
0.19
0.25
03 3
0.27
0 35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.21
038
0.18
0.30
030
0.25
0.25
0.29
0.25
0.25
0.22
0.21
0.22
0.21
0.21
022
025
034
022
0.23
028
028
024
024
037
039
0.24
0.28
0.25
0.24
0.26
0.26
0.25
0.24
0.24
0.26
0.23
223
Decomposition o f Duke SIR-C Data
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#11330
(10/7/94
e0=22.6°
S-Iooking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd w
even hh even w
odd
even
cross
-5.73
-4.59
-5.98
-5.58
-4.56
-4.92
-6.06
-5.94
-4.98
-4.52
-4.46
-6.17
-7.71
-4.96
-6.37
-5.08
-5.54
-4.98
-4.68
-6.07
-5.89
-14.10
-11.22
-12.64
-13.64
-11.86
-11.87
-11.87
-12.87
-11.70
-12.06
-10.78
-11.75
-12.22
-12.06
-11.31
-11.79
-11.45
-11.99
-12.09
-11.97
-12.74
-8.26
-6.93
-8.54
-7.68
-7 3 4
-6.73
-838
-8 32
-738
-6.83
-7.14
-8.87
-10.67
-7.99
-9.03
-839
-7.65
-7.06
-735
-839
-837
-9 37
-8.42
-9.54
-9.74
-7.79
-939
-10.05
-9.68
-8.69
-832
-7.79
-9.50
-10.76
-7.94
-9.74
-7.81
-9.66
-9.18
-8.05
-10.05
-9.25
-1737
-13.47
-15.34
-1531
-1439
-13.49
-14.01
-15.72
-14.25
-14.38
-13.51
-1431
-1532
-15.41
-14.08
-14.86
-13.39
-14.25
-15.07
-14.06
-15.41
0.58
037
0.61
0.62
038
0 38
0.56
0.56
0.56
0.63
0.56
034
0.50
0.59
0.51
0.57
035
0 38
0 39
037
0.58
0.15
030
0.16
0.14
0.18
0.18
0.19
0.17
031
0.16
0.19
031
033
0.18
0.23
0.19
0.17
0.27
0.23
0.23
0.24
035
034
0.24
0.27
0.23
031
0.25
034
037
0.23
036
0 32
0 34
0.23
0 34
0.21
0.22
0.19
033
-16.92
-15.18
-15.99
-18.12
-15.46
-16.84
-16.02
-16.09
-15.22
-15.85
-14.05
-1536
-1533
-14.75
-14.55
-14.74
-15.90
-15.90
-15.13
-16.16
-16.11
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.20
0.21
224
Decomposition of Duke SIR-C Data
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#129.20
(4/17/94
0O=26.6°
S-looking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd vv even hh even vv
-7.14
-6.12
-6.89
-6.08
-5.12
-5.74
-5.99
-6.51
-5.75
-7.19
-7J7
-7.16
-8.34
-6.42
-8.07
-6.40
-6.58
-5.91
-4.83
-6.39
-5.56
-13.31
-10.62
-11 JO
- 12.11
-11.66
-12.55
-11.63
-13J5
-10.58
-11.81
-12 J2
-12.42
-13.29
-11.84
-12.46
-1223
-11.27
-1 U I
-11.76
-12.72
-12.08
-9.73
-8.75
-8.82
-9.25
-7.90
-821
-8.93
-9.62
-8.19
-9.46
-9.76
-9.79
-11.15
-9.03
-10.90
-8.75
-9 JO
-8.75
-7.64
-9.17
-8.27
-10.63
-9.54
-11J 3
-8.90
-8 J5
-9.34
-9.09
-9.40
-9.41
-11.09
- 11.10
-10.60
-11.55
-9.87
-1125
-10.17
-9.90
-9.10
-8.04
-9.64
-8.90
-16.07
-12.67
-13.63
-14.88
-14.41
-15.63
-13.87
-16.26
-12.72
-14.18
-15.42
-15.34
-16.33
-14.45
-15.11
-14J2
-13.84
-13.96
-15.16
-15J4
-14.47
-16.57
-14.79
-15.11
-15 J 6
-14.98
-15.55
-15.54
-16.48
-14.67
-15.58
-1529
-15.52
-16.25
-15.30
-15.85
-16.37
-14.76
-14.71
-14.43
-16.20
-15.83
odd
even
cross
0.55
0.51
0.48
0 54
0.57
0.55
0.55
056
0 52
051
0.53
0.52
0.52
0.53
05 2
0.55
0.50
0.53
058
055
056
0.20
0.25
0.26
0.25
0.25
0.23
0.25
0.24
0.26
0.23
0.25
0.27
0.26
0.27
0.25
0.25
0.24
0.25
0.25
0.23
0.25
0.23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.23
027
021
0.20
0.20
0.21
0.18
0.25
024
0.19
0.22
0.21
0.22
0.23
0.22
0.24
02 1
0.19
0.20
0.21
225
Decomposition o f Duke SIR-C Data
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#145.20
(4/18/94
e0=32.0°
S-Iooking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd vv
even hh ieven w
odd
even
cross
-7.68
-5.74
-7.14
-6.78
-6.04
-7.29
-7.26
-5.71
-7.09
-6.52
-6.89
-7.31
-8.42
-639
-7.58
-7.12
-6.32
-6.82
-5.96
-7.07
-7.06
-1234
-1138
-11.64
-12.98
-11.51
-12.14
-11.17
-11.61
- 11.02
-11.67
-12.51
-12.78
-12.49
-12.43
- 12.00
-11.89
-11.41
-12.29
-12.07
-13.38
-1231
-10.79
-8 3 5
-11.04
-9 3 0
-9.24
-1033
-10.69
-8.72
-9.96
-9.28
-9.84
-10.07
-1 13 2
-9.00
-1031
-9.74
-9.46
-9.78
-9.11
-10.46
-10.42
-10.58
-8.96
-9.43
-1034
-8.87
-1035
-9.89
-8.67
-1033
-9.78
-9.93
-10.58
-11.34
-9.61
-10.67
-1035
-9.20
-9.88
-8.83
-9.73
-9.73
-14.99
-1438
-14.58
-15.88
-1439
-14.83
-14.62
-1437
-14.26
-14.95
-15.60
-15.47
-1538
-15.57
-1530
-14.69
-1437
-15.42
-15.11
-16.62
-1530
-15.78
-1439
-14.71
-16.11
-14.45
-15.48
-13.75
-14.71
-13.83
-14.42
-15.44
-16.15
-15.74
-15.29
-14.83
-15.11
-14.28
-15.18
-15.06
-16.17
-15.12
032
037
031
03 5
033
0.50
0.52
038
031
0.52
. 0.54
033
0.49
03 5
031
033
03 5
0.54
0.54
0.55
0.53
032
030
034
031
0.27
0.23
0.24
0.24
035
035
0 33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.22
0.24
035
030
035
0.21
0.19
031
0.25
0.20
0.23
0.24
032
0.21
0.20
030
03 3
0.22
034
0.27
0.27
036
036
0.25
0.26
0.24
0.22
0.25
0.26
0.25
0.24
226
Decomposition of Duke SIR-C Data
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#145.10
(10/9/94
0O= 26.4°
S-looking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd w
even hh
even vv
-6.46
-5.71
-7.41
-6.91
-5.29
-5.78
-5.65
-7.09
-6.17
-6.69
-3.92
-6.68
-7.57
-5.52
-6.92
-6.38
-6.35
-5.69
-5.35
-6.79
-6.08
-11-55
-11.55
-11.90
-1350
-12.79
-11.94
-13.48
-13.07
-11.51
-13.06
-13.01
-11.34
-13.23
-11.92
-11.94
-11.93
-12.15
-12.04
-1235
-12.71
-12.70
-8.75
-7.97
-9.42
-9.55
-7.80
-8.05
-7.80
-9.21
-8.37
-9.16
-6.15
-9.19
-9.73
-7.81
-9.43
-9.02
-8.62
- 8.02
-7.73
-9.22
-8.15
-1033
-9.62
-11.71
-10.32
-8.93
-9.67
-9.73
- 11.20
-10.15
-10.33
-7.88
-1034
-11.64
-9.39
-10.49
-9.79
-1034
-9.52
-9.09
-10.47
-1030
-14.09
-13.82
-13.80
-15.78
-14.52
-14.10
-15.66
-15.62
-13.65
-14.72
-15.78
-13.57
-15.42
-14.19
-14.54
-14.75
-14.43
-14.43
-14.83
-15.06
-14.90
-15.10
-15.43
-16.46
-17.40
-17.65
-15.98
-1732
-16.62
-15.62
-18.01
-1632
-1538
-17.25
-15.84
-15.41
-15.14
-16.03
-15.80
-15.92
-16.51
-16.68
odd
0.55
0.56
0.52
031
0.59
0.57
0.60
0.54
0.52
0 38
. 0.61
0.52
0 33
0 37
0.51
034
0.54
036
0 39
0 36
0.58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
even cross
0.24
033
031
0.23
033
036
0 34
033
033
0.25
0.25
0.20
0.22
0.17
0.24
0 32
034
0.26
0.24
0.26
0.25
0.25
0.24
0.23
0.24
0.21
034
033
0.17
0.20
0.17
0.21
0.21
0.20
0.23
0.21
0.21
030
0.18
0.21
0.20
0.22
227
Decomposition of Duke SIR-C Data
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#161.10
(10/10/94
e0= 25.2°
S-Iooking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd w
even hh
even w
<
odd
even
cross
-6.41
-4.39
-8.58
-5.64
-3.96
-4.66
-5.48
-6.11
-5.60
-5.28
-3.50
-5.46
-5.95
-4.15
-6.43
-5.04
-5.88
-5.01
-4.63
-6.06
-4.66
-1139
-1035
-9.74
-1237
-9.90
-10.09
-10.45
-10.42
-10.76
-1137
-9.89
-1034
-10.19
-9.81
- 10.68
-9.70
-11.47
-11.13
-10.64
-11.48
-11.29
-839
-6.65
-1137
-830
-6.21
-6.70
-731
-8.34
-8.04
-7.28
-5.82
-7.79
-8.48
-6.43
-837
-732
-8.34
-73 4
-7.12
-8.42
-6.91
-10.43
-833
-11.82
-9.00
-7.90
-8.90
-9.75
-10.04
-936
-9.62
-737
-9.25
-9.52
-8.02
-10.54
-8.92
-9.50
-8.84
-8.26
-9.82
-8.60
-13.45
-1235
-11.73
-14.78
-12.04
-11.92
-13.70
-12.71
-12.95
-13.41
-12.27
- 12.68
-12.51
-12.40
-12.89
-11.96
-13.98
-13.42
-13.16
-13.64
-13.50
-15.60
-14.40
-14.08
-1637
-14.06
-14.73
-1334
-14.32
-14.79
-15.62
-1339
-14.14
-14.02
-1337
-14.69
-13.60
-15.03
-15.01
-1433
-1533
-15.27
034
032
0.37
0.56
0.57
0.52
0.55
0.52
0.52
0.57
0.56
0.52
0.49
034
0.49
0.51
0.53
0.56
03 5
033
0.57
0.21
0.25
0.24
0.31
0.24
0.25
0.25
0.24
0.27
0.26
033
0.24
0.26
0.25
0.24
0.27
0.24
0.28
0.24
0.25
0.25
0.23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
033
0.33
0.20
0.18
0.23
0.21
0.21
0.22
030
030
032
035
0.21
0.24
0.25
030
030
0.20
0.22
0.20
228
Decomposition o f Duke SIR-C Data
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#33.21
(IQ /2/94
0O=44.3°
N -looking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd w
even hh
<
even w
odd
even
cross
-7.71
-7.85
-8.42
-7.43
-8.19
- 8.10
- 8.10
- 8.21
-8.16
-9.21
-6.88
-8.38
-8.36
-7.38
-7.81
-8.55
-7.41
-7.09
-7.54
-6.72
-7.21
-11.84
-13.13
-12.76
-13.42
-12.99
- 12.22
-12.85
-11.70
-12.48
-13.07
-12.48
-12.99
-12.62
-12.24
-13.03
-12.41
-12.31
-12.47
-12.56
-12.44
-12.38
-10.48
-1058
-1136
-10.79
-1125
-11.19
- 11.11
-1123
-10.81
-1229
-1036
-11.79
-11.32
-1053
-11.04
-11.44
-10.35
-10.09
- 10.68
-952
- 10.00
-10.98
-11.17
-11.51
- 10.12
-11.15
- 11.02
- 11.10
-11.26
-11.57
-12.15
-9.46
- 11.02
-11.42
-10.25
-10.61
-11.70
-10.50
- 10.11
-10.43
-9.96
-10.45
-1534
-15.89
-16.00
-16.67
-16.00
-15.05
-15.87
-15.81
-15.32
-16.08
-15.77
-1628
-15.49
-15.58
-16.65
-15.53
-15.17
-15.49
-1557
-15.42
-15.34
-14.44
-16.40
-1556
-1621
-16.00
-15.40
-15.85
-13.83
-15.69
-16.08
-1522
-15.72
-15.78
-14.92
-15.50
-1534
-15.47
-15.45
-1558
-15.49
-15.45
0.49
051
0.49
0.54
0.52
0.49
051
0.48
0.48
0.46
_ 0.52
0.50
0.49
0.51
0.51
0.48
0.51
0.53
0.51
0.53
0.51
0.24
027
026
027
025
026
026
025
028
0.28
0.29
0.27
0.27
028
027
027
0.28
026
026
026
026
0.26
022
024
022
022
0.25
0.24
0.24
0.24
0.25
0.21
0.23
0.23
0.22
0.22
0.24
0.23
0.21
0.23
0.21
0.23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
229
Decomposition o f Duke SIR-C Data
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#49.31
(4/12/94
0O= 32.1°
N -looking)
decom posed scattering pow er (dB )
odd
even
-6.21
-6.79
-8.38
-6.95
-8.18
-7.40
-7.63
-8.73
-7.60
-7.23
-7.46
- 8.01
-7.97
-6.87
-8.34
-8.27
-6.68
-6.49
-7.46
-6.32
-6.46
-12.31
-11.57
- 12.00
-1234
-11.81
- 11.86
-12.16
-10.50
-11.55
-12.37
-12.06
-12.52
-11.40
-11.48
-1230
-12.25
-11.69
-11.74
-11.72
-10.98
- 12.21
odd hh odd vv even hh
-934
-9.69
-1137
-10.03
-11.23
-10.18
- 11.02
-11.19
-10.80
-10.08
-10.78
-11.04
-11.03
-9.95
-11.16
-11.19
-9.68
-9.61
-10.64
-934
-935
-9.11
-9.92
-1 1 2 1
-9.88
- 11.12
-10.63
-10.28
-1235
-10.43
-10.43
-10.19
- 11.02
-10.93
-9.82
-1136
-11.37
-9.69
-9.41
-10.30
-933
-9.40
-1538
-1437
-15.48
-15.98
-14.78
-14.41
-15.54
-12.93
-1435
-1526
-15.39
-15.65
-14.47
-14.73
-1535
-15.34
-14.40
-14.74
-1534
-13.96
-15.27
fraction
even vv
odd
-1523
-14.80
-14.63
-14.81
-14.88
-15.40
-14.79
-14.16
-14.80
-1530
-14.77
-15.44
-14.35
-14.24
-15.49
-15.20
-15.00
-14.76
-14.19
-14.02
-15.13
0.52
032
0.47
032
0.49
0.47
0.49
0.44
0.47
0.52
0.49
0.49
0.46
030
0.48
0.49
0.53
032
0 30
030
0.55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
even
cross
020
0.28
024
030
0.26
0.26
0.28
0.27
0.27
0.28
0.27
0.28
0.27
0.28
0.25
027
0.27
0.25
026
0.26
0.27
0.24
024
0 23
022
0.25
0.25
0.24
0.29
025
0.20
0.22
0.24
0.26
0.25
0.25
0.24
0.22
0.22
0.24
0.23
0.22
230
Decomposition o f Duke SIR-C Data
C-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#4931
(10/3/94
e0=32.8°
N -looking)
fraction
decom posed scattering pow er (dB)
odd
even
-6.90
-7.58
-9.23
-7.18
-735
-7.43
- 8.12
-7.19
-7.38
-7.91
-6.78
-8.50
-7.49
-6.95
-8.43
-7.96
-6.43
-6.40
-6.66
-6.16
-6.96
-11.41
-13.03
-10.85
-12.95
-12.54
-11.96
-12.77
- 12.86
-12.23
-13.80
-1251
-12.80
-1232
-13.14
-13.07
-12.39
- 12.01
-11.97
-1236
- 12.02
-12.95
odd hh odd vv
-952
-1030
-1252
-9.90
-9.89
-10.05
-10.62
-953
- 10.01
-10.64
-9.66
-11.24
-10.03
-9.49
-10.97
-10.60
-8.81
-9.18
-938
-8.83
-9.62
-1033
-10.92
- 12.00
-1054
-10.67
- 10.88
-11.71
- 11.00
-10.81
-1133
-9.94
-11.81
-11.06
-10.49
-11.98
-1137
-10.17
-9.66
-9.98
-955
-1035
even hh
ieven w
odd
even
cross
-1454
-15.59
-13.66
-1536
-14.89
-14.42
-15.68
-15.26
-14.91
-16.16
-15.26
-15.28
-14.85
-15.82
-15.66
-15.02
-14.64
-14.65
-14.83
-14.68
-15.44
-1432
-1656
-14.03
-16.60
-1634
-15.63
-15.89
-16.61
-15.65
-1759
-15.95
-16.42
-15.87
-16.49
-1653
-15.78
-15.42
-15.34
-15.77
-15.41
-16.58
0.49
0 54
0.39
054
0.53
0.49
0.51
0.52
0.50
0.54
054
0.49
0.50
05 5
0.50
0.49
054
0.54
053
0.53
0.53
0.25
030
0.34
0.19
033
0.23
033
0.23
033
031
0.26
0 36
0.27
038
0.24
0.28
0.26
0.25
0.27
035
0.24
0.27
0.26
0.25
03 7
0.27
0.25
0.25
0.24
0 35
0.27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.21
0.24
0.24
030
033
034
0.21
031
033
0.21
0.20
231
Decomposition o f Duke SIR-C Data
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#113.30
(4/16/94
e0=19.1°
S-iooking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd w
even hh
even w
odd
even
cross
-4.00
-4.23
-5.24
-5.40
-4.76
-3.48
-5.69
-4.07
-3.97
-2.76
-4.44
-3.65
-5.51
-3.30
-3.60
-2.87
-4.22
-4.67
-5.60
-5.45
-5.15
-7.66
-732
-6.46
-8.62
-10.34
-8.23
-8.61
-10.57
-9.49
-10.73
-10.23
-9.75
-10.25
-7.94
-7.41
-11.03
-8.49
-8.73
-9.43
- 8.68
-9.10
-7.08
-6.16
-7.75
-8.57
-7.41
-6.50
-8.91
-6.90
-6.22
-4.72
-6.74
-6.06
-822
-6.05
-5.61
-5.43
-6.94
-7.43
-8.76
-823
-7.59
-6.98
-8.69
-8.86
-828
-8.15
-6.49
-8.49
-7.31
-7.90
-7.12
-820
-725
- 8.86
-629
-7.92
-6.38
-7.55
-7.93
-8.46
-8.60
-8.81
-10.95
-9.57
-8.76
-11.97
-13.14
- 11.11
-11.32
-12.90
-1226
-12.71
-1224
- 12.11
-12.98
-10.51
-9.15
-12.92
-10.42
-11.27
-10.35
0.48
0.45
0.46
0.48
0.27
0.32
0.32
0.25
025
023
021
0.21
0.50
0.44
0.53
0.51
0.62
0.54
0.56
0.49
0.51
0.50
0.60
0.48
0.48
0.49
0.46
0.51
0.24
0.26
0.19
-1 1 2 2
-11.92
-12.63
-11.41
-11.73
-1 1 2 0
-1327
-1126
-11.94
-1423
- 12.66
-15.11
-14.15
-1321
-13.57
-11.42
- 12.21
-15.51
-11.48
-1127
-1227
-11.97
-12.51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 .2 2
0.2 2
0.27
0 28
025
0.30
0.27
0.27
0.17
0.22
0.22
0.20
025
0.24
0.27
026
0.24
0.23
0.23
026
0.17
0.26
0.25
0.24
0.27
0.26
0.22
0.26
027
027
0.27
0.23
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Decomposition of Duke SIR-C Data
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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233
Decomposition o f Duke SIR-C Data
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#129.20
(4/17/94
e0=26.6°
S-looking)
fraction
decom posed scattering pow er (dB )
odd
even
odd hh
odd vv
even hh
<even w
odd
even
-5.85
-6.08
-7.92
-6.80
-6.28
-5.75
-6.54
-6.58
-5.99
-4.92
-5.87
-6.02
-6.66
-5.44
-5.96
-5.15
-6.00
-630
-6.81
-6.75
-6.57
-9.00
-7.28
-6 3 0
-8.82
-7.89
-9.65
-7.80
-7.50
-8.77
-1036
-10.35
-9.21
-10.19
-9.77
-9.09
-9.70
-8.38
-8.93
-9.78
-9.53
-9.74
-830
-7.98
-933
-1035
-12.04
-10.75
-10.65
-937
-10.07
-11.47
-10.72
-9.43
-10.15
-10.59
-10.70
-9.61
-10.43
-9.98
-10.08
- 10.20
- 10.86
-10.72
-10.91
-11.07
-9.18
-8.03
-11.35
-9.60
-12.30
-9.70
-9 3 6
-10.63
-12.63
-11.96
-10.85
-12.78
-11.78
- 11.12
-1133
-10.62
- 11.12
-1 23 2
-11.87
-1139
-1334
-11.79
-10.83
-1235
-12.78
-13.02
-1231
-12.35
-13 3 6
-1433
-15.41
-14.22
-13.67
-14.08
-13.36
-1436
-12.34
-12.96
-13.45
-1333
-14.36
0 30
0.43
035
0.41
0.42
030
0.45
0.41
0.46
0.57
033
0.48
0.49
0.53
0.47
0.51
0.45
0.45
0.47
0.46
0.47
0.26
0.35
0.37
0.32
0.32
0.25
0.31
0.35
0.30
0.23
0.26
0.28
0.26
0.26
0.28
0.27
030
0.30
037
037
0.29
- 10.02
-9.03
-8.26
-8.08
-9.11
-8.30
-7.78
-6.82
-7.93
-7.88
-8.83
-7.54
-7.87
-6.89
-8.16
-8.57
-9.00
-8.97
-8.56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
cross
03 3
0.22
0.27
037
0.26
0.25
0.25
034
0.24
0.20
0.2 2
0.23
035
031
035
032
035
035
0.27
0.27
0.24
234
Decomposition o f Duke SIR-C Data
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#145-20
(4/18/94
80=32.0°
S-looking)
decom posed scattering pow er (dB)
odd
even
odd hh
odd vv even hh
even w
-7.01
-6.70
-6.51
-7.23
-5.53
-6.35
-6.88
-7.25
-6.33
-5.84
-6.00
-5.92
-7.08
-5.56
-6.06
-5.73
-6.29
-6.49
-7.67
-7.08
-6.96
-8.08
-6.84
-7.61
-7.93
-8-59
-7.62
-7.37
-8.81
-8.32
-7.77
-8.23
-8.39
-9.34
-8.43
-7.83
-7.65
-7.99
-8.52
-8.72
-9.23
-8.64
-9.15
-8.78
- 8.68
-936
-7.75
- 8.68
-9.66
-9.10
-8.62
-8.48
-7.97
-8.04
-9.89
-7.70
-8.65
-7.84
-8.40
-8.73
-9.76
-9 JO
-9.21
- 11.12
-10.90
-10.58
-113 6
-9.50
-10.17
- 10.12
-11.84
-10.23
-9.25
-10.39
-10.08
-10.32
-9.66
-9.55
-9.87
-10.45
-10.44
-11.82
-11.08
-10.90
-11.93
-11.23
-11.47
-11.70
-12.77.
-12.04
-1131
-1339
-12.49
-11.65
-11.94
-1232
-1334
-12.49
-1131
- 12.12
-1237
-1231
-12.84-12.92
-12.89
-10.38
-8.81
-9.91
-10.29
-10.69
-951
-9.60
-10.56
-10.42
-10.06
-10.62
-10.72
-1159
-10.61
-10.25
-9.55
- 10.02
-10.72
- 10.86
-11.65
- 10.66
fraction
odd
even
cross
0.41 0.32
039 039
03 9 0.38
0.40 0 3 4
0.48 0.28
0.41 031
0.36 039
0.43 03 2
0.43 0.31
0.45 0.33
0.46 0.32
0.45 0.30
0.42 0.29
0.49 0.30
0.44 030
0.45 0.33
0.42 0.33
0.44 0.31
039 0.33
0.43 0.30
0.43 0.33
037
032
032
036
034
038
035
035
035
032
032
034
039
032
036
032
036
0.25
038
0.27
034
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
235
Decomposition o f Duke SIR-C Data
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#145.10
(10/9/94
e0=26.4°
S-looking)
decom posed scattering pow er (dB)
odd
even
odd hh
-4.73
-4.46
-5.09
-6.51
-4.03
-4.60
-5.03
-6.16
-4.88
-5.55
-4.49
-4.38
-5.21
-4.31
-4.75
-4.23
-4.97
-4.62
-5.82
-5.29
-5.18
-8.27
-7.29
-9.31
-8.56
-6.81
-8.67
-8.88
-6.61
-8.63
-8.16
-9.49
-7.68
-8.15
-8.18
-6.80
-7.25
-7.46
-8.28
-8.72
-8.77
-9.34
-7.41
-6.99
-7.99
-8.92
-7.13
-7.11
-7.67
- 8.12
-7.48
-7.60
-7.04
-6.53
-8.33
-6.59
-7.25
-6.46
-7.83
-7.12
-8.74
-8.05
-7.76
odd vv even hh
- 8.11
- 8.00
- 8.21
- 10.20
-6.95
-8.17
-8.44
-10.58
-8.37
-9.80
- 8.01
-8.47
- 8.12
-8.19
-8.34
-8.17
-8.15
- 8.21
-8.91
-8.58
- 8.68
- 11.10
-9.30
-1152
-1123
-8.83
-11.15
-11.13
-8.57
- 11.12
-10.67
-11.40
-10.05
-10.81
-10.28
-9.22
-9.50
-10.16
-10.97
-11.81
-11.61
-11.89
fraction
even vv
odd
-11.51
-11.63
-1322
-11.92
- 11.10
-1227
-12.84
-10.98
0.48
0.48
0.45
0.41
0.45
030
031
0 35
0.48
0.44
033
0.47
0.45
030
0.42
0.50
0.45
0.48
0.46
0.47
0.50
-1 2 2 1
-11.77
-14.03
-11.44
-11.55
-1237
-1031
-11.16
-10.81
-11.64
-11.63
-11.94
-12.83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
even cross
0.28
028
024
03 0
028
025
0.24
0.36
0.25
0.34
0.24
0.28
0.27
026
031
0.27
030
0 25
0.27
0.25
0.24
024
024
031
029
027
025
025
029
0.28
022
0.22
024
027
024
027
0.23
026
026
028
028
0.25
236
Decomposition o f Duke SIR-C Data
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#161.10
(10/10/94
0O=25.2°
S-looking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd w
even hh
<even vv
odd
-3.78
-2.68
-2.96
-5.36
-3.67
-3.72
-3.58
-4.55
-4.16
-4.35
-3.75
-3.70
-3.57
-3.59
-4.00
-3.86
-4.44
-4.03
-4.36
-4.14
-4.75
-7.74
-8.25
-8.09
-10.18
-7.58
-6.92
-8.11
-6.92
-7.78
-7.24
-9.01
-7.24
-7.87
-7.73
-7.44
-6.90
- 8.01
-8.05
-152
-7.95
-8.19
-6.31
-4.79
-5.60
-7.88
-6.32
-6.37
-6.28
-8.09
-6.82
-6.82
-6.51
-6.35
-6 .2 2
-6.07
-6.82
-6.39
-7.01
-6.78
-7.11
-6.68
-7.18
-7.34
-6.81
-6.35
-8.93
-7.04
-7.12
-6.93
-7.11
-155
-7.99
-7.02
-7.10
-6.96
-7.21
-7.21
-7.42
-7.93
-1 3 2
-7.65
-7.68
-8.43
-10.87
-11.19
-10.77
-12.73
-10.45
-10.05
-10.73
-10.17
-10.94
-9.76
-11.78
-9.60
-10.72
-10.17
-10.36
-9.21
-10.72
-10.98
-9.87
-10.53
-10.62
-10.62
-113 4
-11.49
-13.66
- 10.68
-9.83
-11.55
-9.69
-10.64
-10.82
-12.27
-10.98
-11.06
-11.40
-10.52
-10.73
-11.34
-11.14
-11.30
-11.44
- 11.88
0.48
0.53
0.55
0.49
0.48
0.48
0.50
0.45
0.47
0.46
0.55
0.48
0.51
0.50
0.47
0.47
0.47
0.49
0.47
0.48
0.48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
even
cross
0.26
0.22
0.26
0.25
0.23
0.21
0.22
0.29
0.26
0.26
0.26
0.25
0.27
0.24
0.25
0.25
0.24
0.25
0.27
0.26
0.27
0.26
0.27
0.26
0.28
0.26
0.26
0.24
0.30
0.26
0.30
0.21
0.27
0.25
0.25
0.26
0.27
0.26
0.25
0.26
0.26
0.25
237
Decomposition o f Duke SIR-C Data
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#33.21
(10/2/94
e0=44.3°
N -looking)
fraction
decomposed scattering power (dB)
odd
even
-5.91
-8.93
-6.49
-8.93
-8.60
-6.92
-6.73
-9.12
-8.68
-7.03
-8.87
-6.08
-7.48 -10.19
-6.24 ' -9.21
-6.50
-8.86
-9.05
-7.16
-7.02
-9.91
-9.47
-7.08
-6.67
-9.73
-9.57
-7.44
-9.88
-7.08
-9.44
-7.23
-6.45
-8.82
-6.44
-9.44
-7.15 -10.23
-8.82
-6.18
-8.68
-6.93
odd hh
odd vv
-8.47
-8.45
-928
-9.19
-9.14
-831
-10.14
-830
- 8.88
-939
-927
-9.78
-932
-9.76
-9.82
-9.56
-8.60
-8.80
-9.51
-8.44
-9.37
-9.42
- 10.88
- 10.68
-1038
-1 1 2 0
-10.04
-10.91
-10.16
-1025
-11.13
-10.96
-10.44
-10.09
-1127
-10.38
-11.06
-1035
- 10.21
-10.92
-10.09
-10.61
even hh ieven vv
odd
even cross
-10.97
-10.63
- 11.00
-11.62
- 10.68
-1132
-12.93
- 11.02
-1128
-11.06
-11.96
-12.03
-12.35
-11.94
-12.48
-11.46
-10.91
- 11.88
-12.83
- 11.20
-10.75
0.44
0.47
0.44
0.43
0.42
0.45
0.43
0.44
0.44
0.43
0.46
0.44
0.45
0.43
0.44
0.43
0.45
0.45
0.44
0.45
0.43
029
0.29
0.31
0.29
033
028
0.28
0.28
0.30
0.32
0.27
0.29
0.28
031
0.28
0.30
0.30
0.27
0 27
0.29
0.32
-13.18
-13.81
-1235
-12.72
-13.01
-1234
-13.50
-13.90
-12.57
-1336
-14.16
-12.98
-13.16
-13.34
-1332
-13.72
-13.02
-13.11
-13.69
-1238
-12.92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
027
0.24
0.25
028
0 25
027
0.29
0.27
0.26
0.25
0.27
027
027
0.26
028
0.27
0.26
0.28
0.29
0.26
0.25
238
Decomposition o f Duke SIR-C Data
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#49.31
(4/12/94
e0=32.1°
N -looking)
fraction
decom posed scattering pow er (dB)
odd
even
odd hh
odd vv
even hh
even vv
-6.52
-7.02
-7.67
-5.92
-6.61
-5.68
-6.88
-6.40
-7.20
-6.15
-7.36
-7.19
-6.46
-7.05
-6.96
-6.42
-6.63
-6.46
-7.40
-5.98
-5.89
-8.18
-7.79
-8.23
-8.84
-8.37
-7.44
-8.50
-7.18
-8.05
-7.67
-8.85
-9.59
-9.36
-8.90
-9.50
-9.20
-7.85
-9.06
-9.67
-7.91
-8.90
-8.91
-9.53
-10.40
-8.09
-8.95
-8.02
-9.52
-8.88
-9.60
-8.31
-9.59
-9.65
-9.03
-9.40
-9.62
-8.63
-9.07
-9.00
-9.93
-8.43
-8.03
-10.25
-10.61
-10.96
-9.94
-1039
-9.49
-1030
-10.05
-10.94
- 10.21
-11.34
-10.84
-9.97
-10.84
-10.34
-10.40
-10.30
- 10.00
-10.95
-9.63
- 10.00
-10.49
-9.91
-10.63
-10.84
-10.75
-9.66
-10.61
-9.73
-1031
-9.82
-11.51
-11.89
-11.75
-1139
-11.94
-1136
-10.07
-11.39
-12.15
-10.29
-11.08
- 12.02
-11.91
-11.97
-13.16
-12.13
-11.42
- 12.66
-10.67
- 11.68
-11.74
-12.25
-13.46
-13.07
-12.62
-13.16
-13.27
-11.84
-12.89
-1338
-11.65
-12.95
odd
even cross
0.45 03 0
0.44 03 6
0.41 03 5
0.48 0.26
0.42 0.32
0.45 0.31
0.44 033
0.39 0 37
03 9 0 3 6
0.45 0.35
, 0.42 0.33
0.45 0.30
0.46 0.28
0.43 0.35
0.44 0.30
0.48 0.31
0.42 0.34
0.44 0.29
0.43 0.31
0.43 0.29
0.48 0.28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
035
030
034
035
035
034
033
0.23
035
031
035
035
036
032
037
031
0.24
0.27
0.26
0.27
0.25
239
Decomposition of Duke SIR-C Data
L-Band
stand
ID
7
12
14
25
33
38
41
44
64
68
78
86
87
88
93
95
105
106
107
108
112
DT#49.31
(10/3/94
0O=32.8°
N-looking)
fraction
decom posed scattering pow er (dB )
odd
even
odd hh
odd w
even hh
even w
odd
even
cross
-5.78
-6.21
-6.68
-6.50
-7.78
-5.25
-6.99
-5.45
-6.26
-5.60
-7.26
-6.48
-6.19
-6.76
-6.41
-6.28
-6.01
-5.41
-6.49
-4.53
-6.23
-7.97
-9.19
-8.30
-8.23
-7.95
-7.64
-8.44
-8.55
-8.89
-9.66
-9.35
-8.92
-8.06
-9.66
-9.03
-8.80
-7.77
-8.54
-9.76
-7.87
-8.36
-7.73
-8.73
-931
-9.56
-10.36
-7.91
-9.93
-7.71
-8.85
-7.71
-9.44
-8.99
-8.74
-9.13
-8.76
-833
-836
-7.82
-9.16
-7.01
-8.67
-10.27
-9.77
-10.07
-9.47
-1135
-8.63
-10.06
-9.38
-9.77
-9.77
-1131
-10.05
-9.72
-10.52
- 10.20
-10.56
-9.93
-9.11
-9.85
-8.16
-9.89
-10.90
-11.46
-1134
-10.62
-1034
-9.46
-11.33
-10.71
-11.54
-11.90
-11.71
-11.46
-10.71
-1230
-11.41
-10.98
-10.06
-10.99
-1230
-1039
-10.63
-11.08
-13.11
-1135
-11.96
-11.69
-1238
-1138
-12.60
-12.32
-13.60
-13.13
-12.45
-11.48
-13.08
-12.78
-12.84
- 11.66
-12.19
-13.42
-11.46
-1238
0.42
0.46
0.39
0.40
0.36
0.46
0.43
0.46
0.43
0.51
0.44
0.44
0.42
0.47
0.43
0.48
0.43
0.46
0.46
0.46
0.43
039
038
031
031
0.34
0.29
0.32
0.27
0.28
0.25
0.29
0.29
03 0
0.29
0.28
038
0.29
0.28
0.25
0.26
0.30
03 9
036
030
0 38
030
03 5
035
037
039
0.24
0 37
0.27
0 38
034
0 38
0.24
0 38
0.26
0.29
0.27
037
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
240
Correlation (R) between SAR bands and biomass (21 stands)
I. Sigma-0 bands
c49a
c l 13a
cl29
c!45a
cI7
c33
c49o
c l!3 o
c!45o
cl61
I49a
1113a
1129
1145a
117
133
149o
HI3o
I145o
1161
LOWER QUARTILE
MEDIAN
MEAN
hh
hv
w
tP
hh
hv
w
tP
0.46
-0 3 4
0.13
-0.03
0.74
0.43
0.48
0.11
-0.19
-0.33
0.49
-0.52
-0.32
-0.34
0.55
0.49
0.43
-0.10
-038
-0.46
0.46
-0 30
031
-0.18
0.27
0.11
035
-0.20
-0 3 4
-0.40
0.68
0.21
0.60
0.22
0.21
037
0.65
0.66
0.26
-0.14
038
-0 3 7
0.43
0.16
NA
035
0.47
-033
-0.17
-031
038
0.09
036
-0.46
NA
031
0.67
036
-0.15
-039
0.47
-0.46
038
0.03
NA
037
032
-031
-033
-036
0.63
-038
0.03
-037
NA
0.65
0.63
039
-031
-0.40
0.47
-037
0.05
-0.04
0.63
031
034
036
-030
-037
0.42
-0.43
-0.25
-033
036
03 4
0.42
-0.14
-033
-037
0.42
-035
031
-0.14
031
-036
0.47
-0.09
-038
-039
0.61
037
0.64
0.19
034
033
0.57
030
0.24
-0.06
038
-0 35
0.47
0.18
NA
039
0.42
-0.45
-0.16
-0.12
0.40
034
031
-0 3 4
NA
033
037
0.62
-0.16
-039
0.41
-0.45
032
-0.02
NA
03 9
034
-0 3 2
-033
-0 3 6
036
-0.14
0.17
-0 38
NA
030
0.64
0.46
-0.14
-0.44
hh
hv
0.47 034
-037 -033
-0.07 0 3 2
0.01 -037
0.65 031
030 -0.24
0.44 0.44
030 -0.02
-036 -037
-033 -031
0.43 034
-039
0.23
-033
0.64
-036
0.12
03 4
0.15
0 3 2 035
035
0.61
-0.09 0.59
-0.13 0.13
-03 2 -0.18
vv
tP
033
-0 34
030
034
NA
033
037
-0.40
-0.21
-0.12
034
030
0.16
-033
NA
031
0.57
0.49
0.00
-0.31
032
-0 3 8
032
-0.08
NA
032
0.43
-0 3 4
-0 3 5
-0 3 7
0.60
0.01
0.16
-0 3 9
NA
0.49
0.63
0.43
-0.10
-0.41
n. Decomposition bands (see Chapter 5, Table 3)
odd even
c49a
c ll3 a
cl29
cI45a
cI7
c33
c49o
cI13o
cl45o
cI61
149a
1113a
1129
1145a
117
133
I49o
11130
1145o
1161
037
-0.16
0.36
0.14
NA
0.41
0.40
-0.08
-0.14
-033
0.49
-0.48
-0.47
-033
NA
039
034
-0.04
-0.40
-033
0.24
-0.61
-0.16
-0.22
NA
0.14
036
-0 35
-036
-0 35
0.39
039
0 38
-0.08
NA
038
0.68
0.61
-0.06
-0.35
odd_hh odd_w
0.41
-0.02
0.21
0.01
NA
0.45
038
0.17
-0.13
-033
0.40
-039
-036
-0.41
NA
035
030
-039
-0.47
-033
032
-033
0.48
035
NA
032
0.40
-0.40
-0.14
-030
039
-0.18
-0.19
-036
NA
0.48
0.47
0.34
-031
-0.29
even_hh even_w
0.19
-0.53
-0.17
-031
NA
0.06
0.38
-0.21
-0.25
-0.49
0.42
0.07
036
-0.07
NA
030
0.63
0.44
-0.14
-0.45
032
-0.62
-0.10
-031
NA
0.14
032
-0.80
-0 30
-0 35
030
030
035
-0.10
NA
034
039
0.70
0.10
-0.19
odd% even% cross%
030
0.48
033
0 32
NA
0.49
0.07
039
-0.02
0.14
0.02
-037
-0 34
-039
NA
-0.01
-035
-038
-039
-0.12
-0.14
-0.41
-0 35
-0.13
NA
-0.16
-0.08
-0.43
0.05
-0.19
-03 2
0.40
037
0.12
NA
-0.11
032
032
0.04
-0.12
-0.09
-0.28
-0.11
-034
NA
-0.63
0.04
0.17
-0.02
0.08
030
0.41
0.61
0.41
NA
0.13
0.29
031
0.46
033
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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“ o p o o Z o o d d dodddZ doddp
243
Correlation (R) between SAR bands and mean tree height (21 stands)
I. Sigma-0 bands
MEDIAN
MEAN
hh
c49a
cII3a
c!29
cl45a
c!7
c33
c49o
c ll3 o
cI45o
cl61
I49a
1113a
1129
1145a
117
03
I49o
I113o
lI45o
1161
030
-0.16
0.23
-0.01
0.70
031
0.55
0.13
-0.02
-033
0.41
-030
-0.29
-033
038
0.50
0.41
-0.15
-030
-031
hv
w
0.40 0 3 6
-032 -0.41
032 032
-0.09 033
031
NA
0.14 031
031
0.46
-0.07 -031
-0.19 -0.14
-030 -033
0.65 0 3 9
0 3 2 0.07
0.61 0 3 7
0 3 4 -0.47
0.21 NA
030 0 3 0
0.69 0.64
0.68 0 3 2
036 0.07
0.04 -0.08
tP
hh
0.47
-031
038
0.13
NA
0 39
034
-0.17
-0.10
-0.24
038
-0.25
0.05
-0 3 4
NA
0.64
0.62
035
-0.05
-0.19
031
-0.08
033
0.01
0.63
0.43
0.63
0 39
0.09
-038
033
-0.44
-038
-031
0.42
033
0.43
-0.18
-035
-039
hv
032
-039
033
-0.07
034
-0.13
0.45
0.05
-030
-030
037
033
0.68
0.29
037
030
0.62
033
031
0.10
LOWER QUARTILE
w
tP
hh
038
-0.40
035
032
NA
034
036
-036
-0.09
-0.07
0.43
037
0 39
-036
NA
037
037
036
0.04
-0.13
0.44
-033
036
0.11
NA
031
030
-0.17
-0.05
-033
03 0
-0.12
0.17
-0 3 4
NA
0.45
0.65
037
0.04
-036
030
-0.11
0.07
-0.07
0.63
039
030
034
-0.08
-0.16
039
-0.40
-0.36
-0.31
0.19
0.15
033
-0.09
-0.07
-0.20
vv
hv
0.13 030
-038 -0.40
0.18 0.62
-031
0.32
0.24 NA
-0.17 031
0.36 0.40
0.05 -0.29
-0.24 -0.04
-0.15 -0.05
039
032
0 3 7 039
0.69 0.18
0 3 7 -0.42
0.11
NA
0.26 031
0.66 0.60
0.61 0.48
0.27 0.18
0.07 -0.15
EL Decomposition bands (see Chapter 5, Table 3)
c49a
cl 13a
cI29
cl 45a
cl7
c33
c49o
cII3o
cI45o
cI61
I49a
1113a
1129
1145a
117
133
149o
H13o
1145o
1161
036
-0.04
0.44
0.19
NA
0.40
0.44
-0.10
-0.04
-0.15
038
-0.49
-0.46
-0.50
NA
0.60
0.29
-0.12
-034
-0.20
034
-039
-0.05
0.02
NA
0.27
039
-03 7
-0.12
-0.40
0.42
036
0.43
-0.12
NA
039
0.70
0.64
0.00
-0.14
odd_hh odd_w
0.40
0.04
039
-0.02
NA
030
0.44
0.15
0.01
-0.14
0.27
-0.57
-0.56
-0.41
NA
037
0.16
-0 34
-0.40
-033
031
-0.13
035
038
NA
037
039
-0.42
-0.11
-0.15
035
-0.22
-0.18
-030
NA
0.46
0.43
035
0.00
-0.14
even_hh even_w
035
-0.46
-0.09
0.02
NA
0.29
0.41
-0.08
-0.07
-0.37
0.43
0.13
031
-0.05
NA
0.30
0.66
0.44
-0.09
-038
030
-0.65
0.05
0.02
NA
0.17
033
-0.64
-0.13
-039
037
038
037
-031
NA
034
039
0.74
0.15
0.04
odd%
0.18
031
033
033
NA
0.41
0.09
0.08
0.09
0.13
-0.15
-0.67
-034
-039
NA
0.07
-038
-0.69
-0.22
-0.18
14)
odd even
0.01
-0.48
-031
-0.02
NA
-0.08
-0.06
-0.22
-0.07
-034
-0.17
0.48
038
0.07
NA
-0.07
0.25
0.63
-0.03
-0.04
cross%
-0.21
-033
-0.22
-0.42
NA
-0.65
-0.05
036
-0.08
0.17
033
0.47
0.61
0 30
NA
0.04
0 36
0.61
0.45
032
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tp
034
-038
035
0.02
NA
033
0.47
-0.08
-0.12
-0.14
034
0.09
0.14
-039
NA
0.47
0.65
0 32
0.07
-0.18
244
Correlation (R) between SAR bands and stem density (21 stands)
I. Sigma-0 bands
c49a
cl 13a
c!29
cl45a
cI7
c33
c49o
c!13o
cl45o
c!6 i
149a
1113a
1129
1145a
117
03
l49o
lI13o
U45o
1161
hh
hv
-0.57
-0.01
-036
-0.10
-0.76
-0.63
-0.67
-0.21
-0.17
0.05
-033
0.43
0.23
0.20
-0.42
-032
-0.41
0.00
0.18
0.26
-035
0.19
-0.40
0.00
-032
-033
-035
0.00
0.04
0.03
-035
-033
-0.47
-0.16
-0.16
-034
-036
-035
-036
-0.07
w
LOWER QUARTILE
MEDIAN
MEAN
tP
-0.46 -033
0.14 0.10
-0 3 8 -0.49
-0.41 -0 3 4
NA
NA
-0.44 -035
-0.63 -0.67
0 3 4 -0.01
-0.08 -0.11
0.05 0.05
-0.44 -0.46
-0.14 0 3 0
-0.14 -0.01
0 3 2 033
NA
NA
-0 3 5 -035
-0.46 -0 3 2
-0.42 -0 34
-0.13 -0.01
0.10 0.17
hh
hv
w
tp
hh
hv
-0 3 4
-0.09
-039
-0.05
-0.72
-038
-0.70
-031
-0 39
0.04
-033
038
032
0.17
-0.42
-033
-03 7
0.04
0.18
031
-039
035
-0.45
-0.02
-037
-0.07
-0.44
-0.16
0.12
0.07
-031
-031
-038
-0.07
-032
-0.40
-0.49
-039
-0 34
-0.09
-0.46
0.16
-0.62
-036
NA
-0.44
-0.49
0.10
-0.15
-0.09
-033
-033
-033
0.40
NA
-037
-0.43
-0.42
-0.09
033
-031
0.14
-0.49
-0.18
NA
-0.48
-0 3 9
0.02
-0 3 0
0.01
-0 3 6
0.12
-0.09
037
NA
-0 3 6
-0 3 4
-031
-0.08
032
-0.61
-0.01
-0.19
0.04
-0.69
-0.65
-034
-038
-0.14
0.01
-0.16
035
037
032
-035
-0.10
-031
-0.08
0.02
0.18
-0.12
0.26
-035
0.10
-033
-0.02
-037
-0.12
0.13
0.01
-033
-0.14
-032
-0.05
-0.09
-0.22
-035
-0.50
-0.18
-0.11
w
-0.42 -0.42
0.20 0.16
-0.65 -0.43
-039 -0.10
NA
NA
-037 -0.47
-035 -0 3 7
0.05 -0.08
-0.19 -0.08
-0.09 0.00
-038 -0 3 9
-033 -0.03
-0.04 -0.05
0.47 0 3 4
NA
NA
-0.14 -0 3 5
-0.49 -0.49
-036 -0 3 3
-0.19 -0.12
0.21 0 3 3
II. Decomposition bands (see Chapter 5, Table 3)
odd even
c49a
c l 13a
c!29
cl45a
cI7
c33
c49o
c ll3 o
cl45o
cI6I
149a
1113a
1129
1145a
117
133
149o
llI3 o
H45o
1161
-0.46
-0.21
-036
-0.33
NA
-032
-038
-0.10
-0.15
-0.02
-0.31
036
0.34
0.36
NA
-0 32
-037
-0.02
0.08
0.22
-0 3 2
0.61
0.00
0.05
NA
-0.42
-0.40
0.31
-0.03
032
-0 3 2
-0 3 6
-0 3 0
032
NA
-0.41
-0.55
-0.47
0.02
0.04
odd_hh odd_w
-0.49
-0 3 4
-0.45
-0.12
NA
-0.60
-0.55
-036
-0.19
-0.01
-0.25
0.46
0.42
0.18
NA
-0 3 5
-032
0.14
031
0.23
-0.40
-0.15
-0.61
-030
NA
-039
-0 37
0.15
-0.08
-0.03
-039
0.10
0.13
0.49
NA
-03 2
-031
-0 3 5
-0.08
0.17
even_hh even_w
-033
031
0.07
0.05
NA
-0.42
-0.42
0.11
-0.04
039
-031
-0.04
-03 4
0.12
NA
-037
-034
-033
0.11
0.13
-031
0.64
-0.12
0.04
NA
-0 3 0
-0 3 5
0.47
-0.04
031
-0 3 0
-0.48
-0 3 6
033
NA
-0 3 5
-0.43
-0 5 4
-0.12
-0.05
odd% even% cross%
-033
-0.68
-0.40
-0 37
NA
-0.43
-0.17
-0.18
-03 2
-033
0.15
0.49
0.41
0.16
NA
-0.04
0.25
050
0.07
031
0.09
0.64
036
031
NA
0.18
0.11
0.24
0.14
033
0.14
-036
-0.28
0.03
NA
-0.02
-0.14
-0.46
0.11
-0.02
tP
034
03 3
031
035
NA
0 59
032
-0.11
032
-0.10
-0.31
-0.33
-0.46
-0.33
NA
0.03
-03 9
-0.40
-0.29
-0 3 2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
245
Correlation (R) between SAR bands and basal area (21 stands)
I. Sigma-0 bands
MEAN
hh
c49a
c l 13a
cl2 9
cl45a
c!7
c33
c49o
cI13o
cl45o
c l6 I
149a
1113a
1129
1145a
117
133
l49o
U13o
U45o
1161
0.09
-0 3 4
-0.07
-0 3 0
039
0.19
0.13
-0.09
-0.27
-0 3 4
031
-03 9
-0.25
-031
0.25
035
031
-O .ll
-0 3 0
-0 3 2
hv
0.17
-0.56
0.01
-038
0.16
-0.13
032
-0.15
-0.35
-038
0.47
-0.01
037
037
0.12
038
038
0.64
0.40
0.02
w
-0.02
-0.61
0.13
0.04
NA
0.13
0.15
-036
-031
-037
031
-0.08
0 32
-033
NA
0.42
034
0.40
-0.05
0.05
LOWER QUART1LE
MEDIAN
tp
0.07
-033
0.02
-0.12
NA
0.11
0.18
-032
-032
-036
0.46
-039
0.06
-0.28
NA
034
031
031
-0.08
-0.08
hh
hv
w
0.19 0.17 -0.02
-035 -03 9 -0.49
-0.11 0.00 031
-0.15 -03 7 0.07
0 3 4 0.18 NA
0.07 -0 3 2 031
0.08
035 039
0.10 -0.05 -0.44
-0.33 -0 36 -0 30
-0.48 -0 3 5 -0 3 2
0.19 0.42 0.44
-0.25 0.03 0.03
-035 0.60 0.17
0 3 5 -0 3 4
-031
NA
0 37 0 3 5
0.15 0 3 2 0 3 8
035
0.40 0 3 6
-0.11 0.46 0.44
-0.21 0 3 9 -0.17
-0.32 -0.05 -0.02
tp
0.04
-0 32
-0.05
-0.15
NA
0.04
0 30
-030
-037
-0.41
036
-0.16
0.09
-036
NA
0.40
039
0.40
-0.02
-0.11
hh
039
-035
-0.21
-0.03
031
0.26
0.18
0.00
-030
-039
035
-033
-0.28
-0.28
-0.06
0.18
0.53
-0.18
-0.08
-0.07
hv
0.06
-030
0.08
-039
0.18
-031
032
0.08
-032
-037
0.45
-0.01
0.65
036
-0.12
0.20
0.60
030
0.24
-0.07
vv
tP
-0.05
-0.48
033
0.14
NA
0.16
-0.01
-0.42
-038
-0.21
033
0.01
0.01
-0.37
NA
0.44
0.44
037
-0.15
-0.11
-0.01
-0.60
0.00
-0 3 4
NA
0.14
0.14
-0.25
-0.45
-03 3
0.45
-0.02
0.10
-0 3 2
NA
0.44
035
038
-0.08
-0 3 2
II. Decomposition bands (see Chapter 5, Table 3)
odd even
c49a
c l 13a
c l 29
cI45a
c !7
c33
c49o
cl 13o
cl45o
cI6I
I49a
II I3a
1129
1145a
117
133
I49o
1113o
11450
1161
-0.03
-031
0.09
-0.08
NA
0.16
0.02
-038
-035
-035
034
-0.49
-038
-035
NA
030
031
-0.05
-033
-0.01
030
-0.48
-035
-0.06
NA
0.04
0.40
-038
-0.29
-0.17
0.29
036
0.47
0.11
NA
030
0.64
0.42
0.02
-034
odd_hh odd_w
0.02
-0.17
-0.02
-032
NA
031
0.01
-0.08
-0.21
-035
0.21
-033
-0.62
-031
NA
0.44
0.07
-0.24
-0.46
-0.09
-0.07
-0.47
0.18
0.08
NA
0.10
0.02
-030
-039
-034
034
-033
-036
-0.48
NA
0.45
037
035
-0.10
0.09
even_hh even_vv
0.17
-0.44
-033
0.02
NA
-0.05
0.44
-0.13
-031
-0.08
031
0.26
034
0.13
NA
0.15
0.62
038
-0.01
-0.41
0.16
-0.45
-0 3 2
-0.12
NA
0.08
035
-0 37
-0.18
-0.27
0.24
0.41
0.64
0.05
NA
0.18
032
030
0.06
-0.03
odd% even% cross%
-0.16
030
0.18
0.04
NA
0.29
-0.25
0.01
-0.13
-0.25
0.06
-039
-0.62
-0.56
NA
0.19
-0.41
-0.43
-033
0.15
0.14
-031
-036
0.15
NA
-0.03
031
-0.23
0.05
033
-037
030
0.48
037
NA
-039
030
038
0.01
-0.27
0.16
-038
0.10
-031
NA
-0.46
033
039
0.10
034
0.23
0.21
0.63
0.41
NA
0.16
031
037
0 32
0.06
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
246
Correlation (R) between SAR bands and stand age (21 stands)
I. Sigma-0 bands
c49a
c l!3 a
c!29
cL45a
cI7
c33
c49o
c!13o
cI45o
cl61
149a
1113a
1129
1145a
117
133
149o
1113o
I145o
1161
LOWER QUARTILE
MEDIAN
MEAN
hh
hv
w
tP
hh
hv
w
tp
hh
hv
vv
tp
035
-0.14
0.25
0.00
0.78
039
0.65
0.14
0.01
-020
035
-0.54
-0 34
-0.40
0.45
031
0.46
-0.16
-0 32
-033
0.46
-03 4
036
-0.04
034
0.29
03 6
-0.08
-0.17
-0.19
0.67
0.22
035
0.22
039
0.49
0.69
0.61
032
0.02
0.44
-036
034
036
NA
039
0.61
-0.41
-0.08
-0.19
034
0.02
0.14
-039
NA
0.47
0.63
0.45
0.04
-0.09
0 34
-0.29
0.42
0.16
NA
030
0.66
-0.12
-0.06
-031
034
-032
-0.04
-0.47
NA
0.63
0.64
039
-0.08
-031
035
-0.06
03 6
-0.01
0.70
034
0.70
038
0.13
-033
036
-0.48
-039
-035
0.47
032
0.46
-0.21
-039
-037
.0 3 8
-0 3 7
0.40
-0.01
037
0.00
0.44
0.07
-0 3 2
-033
0.62
034
0.63
0.16
032
031
0.62
0.48
037
0.10
0.44
-036
0.61
032
NA
0.40
0.48
-026
-0.01
-0.03
0.40
0.17
02 9
-0.49
NA
0.48
037
0.46
0.01
-0.16
031
-032
0.40
0.11
NA
0.42
0.60
-0.14
0.03
-0.19
0.46
-0 32
0.07
-0.49
NA
0.44
0.65
031
-0.01
-027
038
-0.07
0.09
-0.08
0.72
0.65
036
034
0.01
-0.11
0.19
-0.43
-035
-037
033
0.13
036
-0.07
-0.13
-0.21
0.24
-038
021
-0.16
035
-0.04
038
0.05
-035
-0.18
0.65
0.15
0.60
0.13
020
029
0.70
0.56
0.23
0.06
0.40
-0 3 7
0.64
027
NA
033
031
-0 2 0
0.01
-0.02
032
0.18
0.09
-033
NA
035
038
0.41
0.14
-0 3 2
0.42
-0 32
037
0.03
NA
0.42
035
-0.05
-0.05
-0.15
0.49
-0.01
0.07
-0.43
NA
0.44
0.62
033
0.05
-032
n . Decomposition bands (see Chapter 5, Table 3)
odd even
c49a
c l 13a
cI29
cl45a
cI7
c33
c49o
clI3 o
cl45o
cl61
149a
1113a
1129
1145a
117
133
149o
I113o
1145o
1161
0.41
0.02
0.48
0.24
NA
0.48
036
-0.04
0.00
-0.12
0.35
-030
-0.46
-0.54
NA
0.61
03 8
-0.12
-035
-0.24
0.41
-0.64
-0.07
-0.07
NA
0.36
0.42
-038
-0.09
-0.41
036
0.26
034
-0.27
NA
035
0.60
036
-0.03
-0.09
oddjih odd_w
0.45
0.07
034
0.02
NA
038
034
0.18
0.05
-0.12
0 35
-038
-034
-0.41
NA
0.60
0.27
-0.32
-0.39
-027
036
-0.06
038
0.43
NA
034
034
-0.32
-0.06
-0.11
03 0
-033
-021
-037
NA
0.46
0.46
020
-0.02
-0.15
even_hh even_w
039
-0 3 2
-0.13
-0.09
NA
035
0.45
-0.14
-0.08
-037
034
0.02
034
-0 20
NA
039
036
0 36
-0.14
-03 2
031
-0.69
0.06
-0.05
NA
035
037
-036
-0.07
-0.40
034
030
0.47
-035
NA
038
032
0.67
0.15
0.06
odd% even% cross%
021
0.61
0.40
0.31
NA
0.42
0.14
0.13
0.15
0.18
-0.19
-0.60
-0.49
-030
NA
0.09
-0.27
-0.65
-020
-0.21
-0.04
-036
-039
-0.16
NA
-0.18
-0.07
-033
-0.10
-0.28
-0.20
0.41
032
-0.01
NA
-0.12
0.09
037
-0.05
0.03
-0.21
-0.24
-0.24
-032
NA
-037
-0.21
0.19
-0.13
0.12
0.41
0.46
0 39
0.48
NA
0.07
0 36
038
0.44
0.29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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