Estimating Conifer Forest Cover with
Thematic Mapper Data Using Reflectance
Model Inversion and Two Spectral Indices in
a Site with Variable Background Characteristics
Fraser Gemmell
T
his investigation tests the inversion of a geometric–
optical forest reflectance model and the utility of two
spectral indices (NDVI and SAVI) for estimating crown
cover in a conifer forest site, using Landsat Thematic
Mapper (TM) spectral data. Emphasis was placed on incorporating the effects of variations in the background
signatures into the inversion process. The inversion
methodology and the sources of error were tested using
simulated reflectance data. One-parameter inversions using constant background signatures could not retrieve
stand cover because a significant proportion of the total
variance in the spectral data resulted from background
variations. The spectral indices performed better than the
one-parameter inversions because the indices partially
reduced background effects, but could not provide estimates of cover. When the background signatures were
varied in three- and four-parameter inversions, inversion
performed better than the spectral indices, giving estimates of cover for the test stands. The biophysical basis
of the results are examined. The results indicate that
variations in the background signatures can be included
in the inversion in certain situations, and should be included when these effects are important. Inversion may
provide a more robust method for estimating forest characteristics from multispectral satellite data; however, further testing is needed. Elsevier Science Inc., 1999
Address correspondence to F. Gemmell, PO Box 5193, Leicester
LE2 2YW, United Kingdom. E-mail: fraser [email protected]
Received 27 July 1998; revised 15 December 1998.
REMOTE SENS. ENVIRON. 69:105–121 (1999)
Elsevier Science Inc., 1999
655 Avenue of the Americas, New York, NY 10010
INTRODUCTION
An investigation of existing methods for extracting forest
characteristics from optical satellite imagery suggests that
there are a limited range of methods (Hall et al., 1995a).
These methods can be empirically-based, including spectral vegetation indices (Rouse et al., 1973; Huete, 1988;
Pinty and Verstraete, 1992) or physically based, including
model inversion (Goel and Strebel, 1983; Strahler et al.,
1988; Woodcock et al., 1994; Privette et al., 1996).
Spectral vegetation indices have been very widely
applied with multispectral satellite data. Using spectral
indices is conceptually equivalent to solving an inverse
problem where all variables are fixed or assumed constant, except the one being evaluated (Verstraete and
Pinty, 1996); however, this can be a disadvantage if the
index is to be applied under conditions that are notably
different from those for which the index was developed.
McDonald et al. (1998) evaluated six well-known spectral
indices for providing information on conifer forest cover;
although the indices were sensitive to forest cover, the
indices were also significantly affected by variations in a
number of extraneous factors, including background reflectance, stand structure, and leaf area index. The utility
of spectral indices may thus be limited in the case of conifer forests. More robust methods are required for extracting forest characteristics from remotely-sensed data.
An alternative, objective method is a physically based
approach in which the inversion of a forest reflectance
model is used to estimate the biophysical characteristics
of the stand. An advantage of inversion techniques is that
they are applicable to all sites and sampling conditions
(Privette et al., 1996). Inversion involves adjusting model
0034-4257/99/$–see front matter
PII S0034-4257(99)00004-8
106
Gemmell
parameters until the model reflectance best matches the
measured reflectance (Goel, 1988; Privette, 1994). Inversion is rarely tested with satellite remote sensing data, although there are exceptions (Strahler et al., 1988; Franklin
et al., 1991; Woodcock et al., 1994; Wu and Strahler,
1994; Privette et al., 1996; Gemmell, 1998). Hall et al.
(1995a) note that more work needs to be done in this
area; in particular, this work should include testing using
real satellite data, where atmospheric effects are important, and include heterogeneous vegetation, where structural parameters are important.
Goel (1988) distinguished four types of canopy reflectance model: i) geometric–optical; ii) turbid medium;
iii) hybrids of i) and ii); iv) computer simulations. The
choice of canopy reflectance model depends on the nature of the surface under investigation and how the
model is to be used. Most canopy reflectance models are
not formulated to be invertible or difficult to invert
(Woodcock et al., 1997). To derive forest characteristics
from remotely sensed data, geometric–optical models are
recommended (Gauthier et al., 1991). In geometric–
optical models, the calculation of reflectance is simplified, thus facilitating the inversion process. Studies suggest that, in practice, geometric–optical forest models are
able to retrieve useful biophysical information (Hall et
al., 1995b; Peddle et al., 1996; Woodcock et al., 1997).
In this investigation, the Li and Strahler (1992a,b) geometric–optical model was used. Validation of the Li and
Strahler (1992a,b) model has shown reasonable agreement with measured bidirectional reflectances (Abuelgasim and Strahler, 1993; Schaaf and Strahler, 1994).
The primary objective of this investigation was to
test inversion of the Li and Strahler (1992a,b) model in
a conifer forest site, with the emphasis on incorporating
the effects of variations in the background signatures. A
secondary objective was to assess the utility of two spectral indices for reducing the effects of background variations in the TM data [the normalized difference vegetation index, NDVI (Rouse et al., 1973) and the soil
adjusted vegetation index, SAVI (Huete, 1988)] and to
compare the utility of model inversion with that of the
spectral indices. The first part of the paper summarizes
the Li and Strahler (1992a,b) model, and the spectral indices. The inversion problem and site characteristics are
described. The inversion methodology is then described.
Finally the results and discussion are presented.
FOREST REFLECTANCE MODEL
The forest reflectance model used here is the geometric–
optical bi-directional reflectance (BRDF) model of Li
and Strahler (1992a,b). The calculation of pixel reflectance is simplified and computed as a sum of the bulk
component signatures (sunlit and shadowed crown and
background components) weighted by their relative proportions, as viewed by the sensor. The Li and Strahler
(1992a,b) model calculates stand reflectance q in a given
spectral band as follows:
q5Rg·g1Rd·d1Rv·v1Rs·s,
(1)
where
Rg5signature of sunlit ground,
Rd5signature of shadowed ground,
Rv5signature of sunlit crown,
Rs5signature of shadowed crown,
g5proportion of sunlit and viewed background
in the pixel,
d5proportion of shadowed and viewed background,
v5proportion of sunlit and viewed crown surface,
as projected onto the background, and
s5proportion of shadowed and viewed crown
surface, as projected onto the background.
The fractions in Eq. (1) are calculated from geometrical
considerations and take into account the overlap between
illumination and viewing shadows. Calculation of the
fraction v5f·(12g) includes the probabilities of mutual
shadowing between tree crowns as follows (Schaaf et al.,
1994):
(12Gv·Pv·Mv /Gc)
1(12b)·F,
(12M)
f5b·F·
(2)
where Gc is the area of sunlit crown projected in the view
direction; Gv is the area of view shadow of a single ellipsoid on the background; F5Gc /G where G is the area of
background shaded in either view or illumination directions by a single ellipsoid; Pv is the conditional probability that a crown surface element will face the Sun given
that it is mutually shaded from view; Mv is the mutual
shadow proportion in the view direction; M is the mutual
shadow proportion; Eq. (2) holds while the view zenith
angle hv is greater than the illumination zenith angle hi.
Otherwise the Pv·Mv is replaced by Pi·Mi if it is a larger
value; Pi is the conditional probability that a crown surface element will face the viewer given that it is mutually
shaded from illumination; Mi is the mutual shadow proportion in the illumination direction. The quantity b is a
weighting factor varying between 0 and 1 that determines whether the stand is composed primarily of trees
of random heights (little mutual shadowing) or trees of a
uniform height (and, therefore, a great amount of mutual
shadowing exists between tree crowns). Li and Strahler
(1992a) gave a simple equation for determining b based
on the upper and lower bounds of the height distribution
of crown centers:
b5(12(h22h1)/4·b)2 .
(3)
where h1 and h2 are the lower and upper bound of the
height distribution of crown centers, and b is the vertical
half-axis of the ellipsoid (crown).
A more rigorous estimate of b was presented in Li
and Strahler (1992b), but it was also stated that the more
Inversion of Geometric–Optical Reflectance Model
complex estimate gave results that were not significantly
different to those obtained using the simpler estimate of
b. Thus Eq. (3) is used to estimate b here. For further
details the reader is referred to Li and Strahler (1992a,b)
and Schaaf et al. (1994).
The component signatures (which are estimated empirically) represent a combined signature including the
effects of direct and diffuse radiance and include all orders of scattering (Woodcock et al., 1997). A primary
concern in the inversion of a geometric–optical model
over many stands is the extent to which the component
signatures remain constant from one stand to another.
The crown signatures are a complex function of speciesdependent factors including crown structure, crown
depth, and foliage spectral properties, as well as Sun–
sensor geometry and atmospheric conditions. However,
for a given conifer species (within a single scene), it may
be reasonable to treat the crown signatures as constants,
since variations in stand reflectance resulting from variations in the crown signatures between different stands
may be small, relative to variations arising from other
stand characteristics (such as cover). This simplifying assumption, of constant crown signatures, is necessary for
the inversion of a geometric–optical model. Variations in
the background signatures can be significant, and in
these situations the background signatures cannot be
treated as constants. However, if variation in the background signatures can be taken into account in the inversion process, then the difficulties of background variations may be at least partially overcome.
Terrain alters stand reflectance in three ways. First,
sloping terrain changes the areas of the shadows cast on
the background. Second, mutual shadowing relations between tree crowns are altered. The net result is to alter
the relative proportions of the illuminated and shadowed
components observed by the sensor. These effects were
taken into account by transforming the geometric relationships among the Sun–sensor geometry and the crown
shape into the coordinate system of the slope, so that the
problem reduces to that of a flat surface (Schaaf et al.,
1994). Third, the component signatures are modulated
relative to flat terrain. Following Woodcock et al. (1997),
the magnitude of Rg was corrected by the cosine of the
angle between the solar illumination vector and the normal to the surface. Rd was assumed independent of terrain since it is relatively small in magnitude. The signatures of the crown surfaces Rv and Rs were not corrected
for terrain since trees are always vertically oriented.
SPECTRAL VEGETATION INDICES
The NDVI is shown in Eq. (4) as follows (Rouse et al.,
1973):
(q 2q )
NDVI5 NIR R ,
(qNIR1qR)
(4)
107
where qNIR is the near-infrared reflectance and qR is the
red reflectance.
The SAVI was derived specifically to reduce soil
brightness effects using red and near-infrared bands, and
assumes a linear (but not specific) relationship between
red and near-infrared soil reflectances. Graphically, the
SAVI involves shifting the origin of the reflectance spectra plotted in red and near-infrared spectral space to account for first order soil–vegetation interactions, and differential red and near-infrared flux extinction through
vegetated canopies (Huete, 1988). The SAVI is shown in
Eq. (5) as follows (Huete, 1988):
SAVI5(11L)·
(qNIR2qR)
(qNIR1qR1L)
(5)
where L is an adjustment factor. It is possible to determine different values of L according to vegetation
density; however, a single adjustment factor of L50.5
(used here) was shown to reduce soil brightness effects
throughout a range of densities tested (Huete, 1988).
PROBLEM DEFINITION
Overall, the test site was complex, and a number of different sources of variance were contained within the TM
data. The main factors contributing to variance in the
TM data for the test site are shown in Figure 1. While
image–plot registration errors and errors in the forest
cover data are not features of the TM data, these are
included in Figure 1 because they affect both the calibration of the component signatures and evaluation of
the accuracy of the parameters derived from remote
sensing. Image–plot registration errors were reduced to
a minimum by accurate spatial registration of the data
set, described below.
The inversion problem was to estimate some useful
forest characteristic from the TM data, the DTM, and
some general knowledge of the forest characteristics,
without any specific knowledge of the individual stand
characteristics. One limitation of a single TM image is
that, due to correlations between spectral bands, TM
data is two- or, at most, three-dimensional in nature for
conifer forests (Horler and Ahern, 1986). For a unique
determination of p canopy parameters from q measurements, p must be less than or equal to q, and should be
quite a bit less for a non linear relationship (Goel, 1988).
Thus it was only possible to estimate a limited number
of variables by inversion using TM data. Cover was chosen as the single variable to be estimated by inversion
since cover can be correlated with timber volume in
some sites. Figure 2, for example, shows cover and timber volume for the test stands used in this investigation.
However, inversion to obtain cover was only possible if
the remaining factors, shown in Figure 1, could be taken
into account in the inversion process.
The problem was simplified as follows. First, eleva-
108
Gemmell
Figure 1. Factors affecting the Landsat Thematic Mapper (TM) spectral
data in the test site. While image-plot
registration errors, and errors in the
forest cover data are not features of
the TM data, these are included in
Figure 1 because they affect both the
calibration of the component signatures, and evaluation of the accuracy
of the parameters derived from remote sensing.
tion, slope, and aspect were obtained from the DTM. Elevation was used in atmospheric correction; slope and aspect were used in the reflectance model to calculate
stand reflectance. Second, the data set was stratified according to species composition. In practice, stratification
based on species composition may be carried out on the
basis of existing forest inventory maps. This enabled the
“species-dependent” group of the forest factors identified
in Figure 1 to be treated as constants in the inversion
process; these were the crown shape and the crown component signatures. Third, a random spatial distribution
Figure 2. Cover and timber volume for the test stands.
was assumed for all stands, in keeping with the underlying assumption in the reflectance model. Fourth, sensitivity analysis of the reflectance model was used to establish that reflectance was relatively insensitive to structural variations at low covers. This enabled a single estimate of stand structure to be used in the inversion for
all the test stands, the majority of which had a crown
cover of less than 0.5. Finally, sensitivity analysis was
used to establish that it was necessary to take account of
variations in the background signatures in the inversion;
both cover and the background signatures were subsequently included in the inversion process.
SITE CHARACTERISTICS AND FOREST DATA
Site Characteristics
The Canal Flats test site, located in southeast British Columbia, is 30 km310 km (300 km2) with an elevation
range of 1700 m. The site has very mountainous terrain
and some flat valley areas. The area is mainly forested
with Douglas-fir, larch, spruce, balsam, and lodgepole
pine as the dominant tree species. The site is dominated
by low to medium crown closures and poor to medium
site quality. Stand timber volumes were generally less
than 300 m3 ha21, although the volumes of some stands
could reach 500 m3 ha21. Age varied between 100 years
and 250 years, excluding regenerating areas. The site is
moisture limited with steeper west-facing slopes containing the forest stands with the greatest volumes.
Forest Data
The forest attribute data consisted of 220 measurement
plots. In one area of the site, old-growth Douglas-fir
comprised over 80% of the species composition of the
forest and the data from the 44 plots for this area were
Inversion of Geometric–Optical Reflectance Model
109
Table 1. Details of the Test Scene
Geometric
Forest
Solar zenith 378
Observation zenith 08
Slopes 2–278, mean 148
Sun–slope azimuth difference range 4–1738, mean 788
Elevation range 1040–1480 m, mean 1330 m
Species Douglas-fir
Stand age 100–250 years
Covers 0.02–0.65
Crown shape5spheroid
Mean tree height h 20 m
Crown vertical half-axis b50.2 h
Crown radius r50.1 h
Mean height of crown center above ground50.8 h
Mutual shadowing parameter50.25
selected for this investigation. Table 1 summarizes details
of these stands. Covers ranged from as little as 0.02 up
to a maximum of 0.65. Stand background characteristics
were quite variable, particularly in the very low density
stands of poor site quality where ground vegetation and
rocks existed.
For model inversion, it was necessary to estimate
constant values for both tree crown geometry and the
height variability of tree crowns. In addition, the mutual
shadowing calculation (Li and Strahler, 1992a) required
knowledge of the density of the stand. Since cover was
to be estimated, and thus was the variable to be adjusted
in the inversion, an estimate of density N was made from
cover512exp(2N·p·r2). This was done by assuming a
constant crown radius r for all stands, estimated as 0.1
h, where h was an estimate of mean tree height. The
effects of these approximations on the results of inversion were tested by using the actual tree heights (from
which crown radius could be estimated) in the inversion
process. It was found that the errors in the retrieved values of cover, introduced by these approximations, were
small for the test stands. This was because mutual shadowing was small in the test stands, for two reasons: First,
covers (densities) were fairly low, and thus mutual shadowing was also relatively small; second, stand structure
was complex, and this also contributed to low mutual
shadowing in the test stands.
For Douglas-fir aged greater than 100 years (all 44
stands), the ratio of the crown vertical half-axis b to
crown radius r was estimated as 2 and mean crown
height h was estimated at 20 m. A spheroidal crown
shape was assumed in accordance with the reflectance
model. Stand structure was generally complex in these
old-growth stands, and in the field it was apparent that
stands had uneven tree heights. It is well known that
older Douglas-fir stands may have multiple canopy layers
with numerous gaps (Cohen and Spies, 1992). Gaps resulted from natural causes, and it was also known that
selective logging of trees had occurred in the site. Stand
structure was therefore observed to be closer to the ran-
dom case of Li and Strahler (1992a,b); that is, illumination and viewing shadows were nearly independently
scattered on other crowns. A range of heights of twice
the vertical half-axis of the crown was estimated for the
fir stands, and b was calculated as 0.25.
Further evidence of stand structure can be found by
inspecting a red/near-infrared plot of the stands. Figure
3 shows two cover trajectories as simulated by the Li and
Strahler (1992a) model using the geometrical data in Table 1 and the mean component signatures (estimated below) and assuming flat terrain. The position of the zero
cover point in Figure 3 does not correspond to the mean
Figure 3. Cover trajectories for a low (b50.0, solid line) and
a high (b50.8, broken line) mutual shadowing case for the
test scene. The values plotted on the figure at either end of
the solid cover trajectory are covers. Also plotted are the
TM3 and TM4 reflectances for the test stands. The test
stands appear to follow a linear “trajectory” closer to that of
the low mutual shadowing case.
110
Gemmell
background signatures described below because of the
cosine correction for slope–aspect effects in the magnitude of the background signature. The upper trajectory
corresponds to trees of quite a uniform height (a high
degree of mutual shadowing among tree crowns, b50.8)
while the lower trajectory corresponds to trees of a very
variable height (the random case, b50.0). In Figure 3,
the calibrated and atmospherically corrected TM reflectance data in Bands 3 and 4 are plotted for the 44 Douglas-fir stands. The effects of both variable background
signatures and terrain strongly affected the distribution
of the stands in Figure 3, and thus the stands did not
fall on the same cover trajectory. However, the overall
pattern of the stands appears to follow a more or less
linear path similar to that of the random case cover trajectory in Figure 3. Since all 44 stands consisted of oldgrowth forest with species composition greater than 80%
fir, the effects of age and species composition on the
variance in the data may have been relatively less than
the effects of background variability and terrain.
GEOMETRIC AND
RADIOMETRIC PREPROCESSING
The data set consisted of TM imagery, a digital terrain
model (DTM, absolute positional accuracy 12 m; spatial
resolution, 75 m), and forest attribute data obtained by
field work on the ground. The subsequent analysis of the
data set was dependent on accurate spatial integration of
these data, and considerable work was done in order to
ensure accurate spatial integration. Geocoded TM imagery from August 1990 was acquired from the Canada
Center for Remote Sensing (CCRS) production facilities
and then geometrically corrected for terrain effects using
data from the DTM. Forest cover data were precisely
located and digitized in a Geographic Information System (GIS), and converted to raster format to be used
in the image processing routines. Further details on data
acquisition and geometric correction of the data set can
be found in Gemmell (1995). The complete data set was
geometrically registered to an root mean square error
(rmse) of 25 m, or less than one TM pixel (30 m). Each
of the forest plots was assumed to represent at least a
50 m350 m area of forest, and the TM image was sampled within a pixel window located over each coregistered plot.
TM spectral data were converted to calibrated radiances and then to top-of-the-atmosphere Lambertian reflectances using calibration data and equations contained
in Markham and Barker (1986). Atmospheric–elevation
correction was then applied to the spectral data using the
6S radiative transfer code (Vermote et al., 1997), and the
elevation data sampled from the DTM. A “dark target”
approach (Teillet and Fedosejevs, 1995) was used in
which the 6S code was used to determine the aerosol
optical depth input that gave the observed (image-based)
Table 2. Component Signatures Estimated by Inversion
from the TM, DTM, and Forest Data
TM3
TM4
TM5
Rv
Rs
Rg
Rd
0.019
0.302
0.136
0.004
0.030
0.000
0.029
0.213
0.110
0.004
0.030
0.000
dark target reflectance at the output. A “continental”
aerosol model was assumed for the site, and the appropriate standard model atmosphere for the latitude and
time of year was used. Teillet and Fedosejevs (1995) estimated the uncertainty (which results primarily from the
assumed value of the dark target reflectance) in surface
reflectance retrieval with the dark target method to be
0.01 absolute reflectance units in TM Band 3 for typical
conditions. This uncertainty is of a similar magnitude to
the actual reflectance values in TM Band 3 for dark
stands of coniferous forest where a significant fraction of
the stand consists of shadow. However, errors in the absolute reflectance values arising from atmospheric correction should not affect the variance in the reflectance
data since atmospheric correction is applied to the whole
scene and thus results in a more or less uniform shift of
the data points in spectral space. In this investigation,
where component signatures were estimated from the
imagery, atmospheric correction helps in signature estimation since it aids in the assessment of the realism of
the component signatures retrieved from the imagery.
Atmospheric correction assumed a Lambertian surface
and a constant solar zenith angle (that of a flat surface).
Thus the spectral data were corrected for atmospheric–
elevation effects but relative to a flat surface. The spectral data were uncorrected for slope–aspect effects which
were subsequently taken into account in the reflectance
model inversion process.
Direct measurements of the component signatures
were not available for the test stands. However, it was
possible to estimate the component signatures using inverse modeling with the TM data, the DTM, and the
known forest characteristics for a number of selected
“calibration” stands. The crown signatures Rv and Rs
were obtained using two stands of high shadow cover,
where the effects of the background on stand reflectance
were small. The background signatures Rg and Rd were
then obtained using the 10 stands of lowest cover, together with the estimated values of Rv and Rs. As many
as 10 stands were used since the background signatures
were more variable. Full details of method used for signature estimation in this investigation can be found in
Gemmell (1998). The signatures are given in Table 2. In
the analysis of the inversion results below, the 10 lowest
cover stands used to determine the background signatures were not included so as not to bias the results. This
left 34 test stands for analysis. The two higher cover
Inversion of Geometric–Optical Reflectance Model
Table 3. Parameter Ranges Used in Sensitivity Analysisa
COVER
SLOPE (deg)
BETA
Rg (red)b
Rg (NIR)b
a
b
Lower
Upper
Increment a
0
0
0
0.05
0.10
1
60
1
0.12
0.30
0.1
9
0.1
0.1
0.1
Table 4. Inputs Used in Simulations
Geometric
Forest
Solar zenith5308
Observation zenith508
Crown shape5spheroid
Crown radius r52.5 m
Crown vertical half-axis b57.5 m
Mean height of crown center above ground
h515 m
Increment510% of theoretical range.
Value for flat terrain.
stands used to determine the crown signatures were included since any bias introduced by their inclusion
should have been small.
SENSITIVITY ANALYSIS
Sensitivity analysis of the reflectance model was used to
estimate the impact of variations in the background signatures on stand reflectance, relative to variations due to
cover, structure (b), and slope effects. The four parameters (background signature, cover, structure, and slope)
can be varied independently of one another in the reflectance model. The method employed to analyze model
sensitivity was as follows (Privette et al., 1994): 500 synthetic stands were simulated by use of a random number
generator to produce parameter values within reasonable
and physically plausible limits (Table 3). Stand aspect
was assigned randomly as either a slope facing the Sun
or a slope facing away from the Sun since these aspects
cause maximum terrain effect. For a given synthetic
stand, each parameter was in turn perturbed by 10% of
its theoretical range, and a new stand reflectance was
computed. The absolute difference in reflectance between the original stand and the reflectance produced by
a parameter’s perturbation was recorded. There were
two possibilities to handle the data generated in this way.
One method was to apply principal component analysis
to the data. Since the first principal component was in
the direction of maximum variance, the contribution of
a given parameter to this axis could be taken as a measure of the models sensitivity to that parameter (Privette
et al., 1994). An alternative method, used here, was to
group the data according to the cover of the synthetic
stand (into cover bins of 0.1 cover increments) and interpret the mean differences produced for each parameter.
Sensitivity analysis was applied using the geometrical
data and the constant crown and shadow signatures of
Table 4.
Essentially, Figure 4 shows the relative impact of the
four variables on stand reflectance. For the red band
(Fig. 4a) reflectance can be seen to be most sensitive to
the background signature, except at high covers. Figure
4a indicates that the success of model inversion may be
highly dependent on the nature of the spatial variability
111
Component Reflectances,
Value for Flat Terrain
Rv
Rd
Rs
Red
NIR
SWIR
0.03
0.01
0.01
0.4
0.1
0.1
0.04
0.00
0.00
of Rg in a given site. It can be seen that sensitivity to b
was small while sensitivity to both cover and slope was
greater at low covers.
For the near-infrared band (Fig. 4b) reflectance was
also very sensitive to the magnitude of the illuminated
background signature at low covers. However, reflectance was more sensitive to the three parameters slope,
cover, and b, relative to the background signature, than
in the red band. This can be explained as follows. A
given perturbation in slope, cover, or b resulted in a
change in the relative proportions of the illuminated and
shadowed components; however, for the near-infrared
band, a greater sensitivity resulted because the absolute
values of the differences between the component signatures in the near-infrared band were greater than those
in the red band. On the other hand, a constant perturbation in the background signature resulted in the same
change in stand reflectance at both red and near-infrared
bands. Sensitivity to cover and b increased with cover
and was greatest at higher covers where mutual shadowing had a significant influence.
In summary, the results of sensitivity analysis indicated that 1) variations in the background signatures
would preclude the retrieval of forest cover unless these
variations could be taken into account in model inversion
and 2) because sensitivity to b was small at low covers,
the assumption of a constant value of b in the inversion
should be reasonable.
MODEL INVERSION
In this section inversion of the Li and Strahler (1992a,b)
model was tested. The overall inversion method followed
was that recommended by Goel (1988). Initially, inversion was tested by using simulated reflectance data for a
wide range of stand characteristics. Subsequently, the effects of errors in the simulated reflectance data were examined. Finally, inversions were tested using reflectance
data simulated with the same conditions as those that existed in the test scene.
112
Gemmell
Table 5. Variables Tested with Inversion
Covers
Solar Zenith
Rg (red)
Rg (NIR)
Rg (SWIR)
BETA
Slope (deg)
Sun–slope azimuth (deg)
Figure 4. Results of sensitivity analysis of the Li and Strahler
(1992a) reflectance model: a) red band; b) near-infrared
band. The figures show the relative sensitivity of stand reflectance to the factors.
The general inversion problem is as follows (Privette
et al., 1994). Given a set of empirical reflectance measurements, determine the set of independent model parameters such that the computed reflectances best fit the
measured reflectances. The fit of the empirical data is
determined by the merit function e2 defined as [Eq. (6)]
n
e25 o [qj2qjm]2 ,
j51
(6)
where qj is the reflectance for a given spectral band and
Sun–sensor geometry, qjm is the analogous model esti-
21 Covers (0.0–1.0)
15
35
0.02
0.05
0.3
0.25
0.05
0.1
0
0.4
0
20
0
180
55
0.08
0.15
0.15
0.8
40
mate, and n is the number of reflectance samples. A
penalty function was used to constrain the parameter values to within physically plausible limits. Once the best
fit was achieved (e2 was minimized), the parameters producing that fit were considered the best estimates of the
true surface values. Minimization was carried out using
a conjugate direction set method [subroutine POWELL
(Press et al., 1992)].
In this investigation, the emphasis was on the use of
TM data to invert the model because TM 30 m imagery
is suitable for spatial discrimination of stand level information (e.g., 100 m*100 m). Red (TM3), near-infrared
(TM4), and short-wave infrared (TM5) bands were included. TM1 and TM2 were not included because these
were very highly correlated with TM3, while TM7 was
not included because it was very highly correlated with
TM5. TM Bands 3, 4, and 5 have been found to contain
the great majority of information in TM spectral data for
conifer forest (Horler and Ahern, 1986).
Inversion was tested initially by simulating stand reflectance for a number of synthetic stands and subsequently inverting the model with these reflectance data.
The covers retrieved by inversion were then compared
to their true values. For practical reasons, a number of
model parameters were kept constant in all simulations
and these were selected to be representative of conifer
stands based on published data (Table 4); these parameters were selected either because stand reflectance was
found to be relatively insensitive to the given parameter
(in the case of height for TM viewing geometries; Rs and
Rd), or because the variation of a parameter was of less
concern than others, and its value could be estimated for
a given species of conifer (in the case of the crown
depth/width ratio, and Rv). Table 5 gives the values of
the parameters varied in this experiment. Twenty-one
covers in the range 0.0–1.0 (increment 0.05), three solar
zenith angles, three sets of background reflectances,
three b values, three slopes, and two aspects were tested,
giving a total of 3402 stands. The solar zenith angles in
Table 5 were selected in order to represent the majority
of solar zenith angles encountered by the TM sensor.
Background reflectances were based on values from the
literature and were selected in order to represent a range
of background types, ranging from a vegetated background to a bare soil background.
Inversion of Geometric–Optical Reflectance Model
113
Figure 5. Results of inversion of the Li and Strahler (1992a) model for the 3402 synthetic test stands, where random
gaussian noise of 5% variance was added to the reflectance data: a) red and near-infrared bands used in the inversion; b)
red, near-infrared, and short-wave infrared bands used in the inversion. The error bars indicate two standard deviations
of the retrieved cover values.
Initially, cover was the only parameter varied in the
inversion with all other parameters known, and only red
and near-infrared bands were used. Cover was accurately
retrieved in all 3402 cases. Inversions were then repeated with various levels of noise added to the reflectance data (Privette et al., 1994). This procedure helps
to determine how robust the inversion process is for a
given model (Goel, 1988). Reflectance data obtained
from a satellite may contain significant noise, which can
arise from quantization effects, for example, and could
potentially limit the scope of application of a particular
model. In this experiment, reflectances were simulated
as above, but random gaussian noise of 5% variance was
added to the simulated reflectances; the mean value of
the noise was zero. The result of inversions using these
reflectance data is shown in Figure 5a, and it can be
seen that a fair amount of scatter in the retrieved covers
was present.
The possibility that a third band would reduce the
effects of noise in the reflectance data was examined.
Red, near-infrared, and short-wave infrared bands were
included. In this experiment, reflectances were simulated
as above with random gaussian noise of 5% variance
added to the simulated reflectances. Figure 5b shows the
results when all three bands were included; it can be
seen the ranges of the cover estimates were significantly
reduced compared to those seen in Figure 5a. Overall,
the inclusion of a third band helped to reduce the effects
of noise in the reflectance data.
In these inversions with simulated data, cover was
the only variable, and all other parameters were known.
However, variations in the background signatures can be
important in conifer forests, and presented a difficulty in
the test site. Sensitivity analysis of the reflectance model
indicated that very strong interactions between cover and
background variations occur at low and medium covers.
It was hypothesized that cover could not be estimated by
inversion unless the background signatures were known.
However, the background signatures were not known on
an individual stand basis, and so an attempt was made
to estimate the background signatures, together with
cover in the inversion process. Initially, this appeared not
to be possible since there were now more variables
(cover, and the three background signatures) than there
were measurements (TM3, TM4, and TM5). However, a
number of further experiments using simulated data indicated that estimates of both cover and the relevant
background signatures could be made on the basis of two
bands (TM3 and TM4, or TM4 and TM5), or three
bands (TM 3, 4, and 5), under similar conditions to those
found in the test scene. These experiments and the key
results are summarized.
Experiments based on red and near-infrared bands
included: i) one-parameter inversions for cover with the
background signatures assumed known in the inversion
(as above); ii) two-parameter inversions, including cover
and the background signature in one band, where the
background signature in the remaining band was assumed to be known; iii) three parameter inversions, including cover and the background signatures in both
114
Gemmell
Figure 6. Cover trajectories for the test scene assuming a) low mutual shadowing (b50.0) and b) intermediate mutual shadowing (b50.4). The full curves indicate the true cover trajectories, using the mean background signatures for the test stands, while
the broken curve in b) indicates an artificial cover trajectory corresponding to another background signature point. The rectangle shows the ranges used to constrain the background signatures in the inversion. The values plotted on the figure are covers.
bands, where the background signatures in both bands
were assumed unknown. In addition, four-parameter inversions using red, near-infrared, and short-wave infrared
bands, with background reflectances assumed unknown
in all three bands, were tested.
Two sources of error were found in the inversions,
both resulting from local minima. The first type of error
occurred in the three- and four-parameter inversions,
where the number of unknowns was greater than the
number of spectral bands, but did not occur in two- and
three-parameter inversions where the number of unknowns was equal to the number of spectral bands. This
type of error resulted from the wrong background signature point being found in the inversion, and its magnitude depended on the initial starting values for the signatures being varied in the inversion, relative to the
original background signatures of the synthetic stands.
This first type of error was not found to be a serious
problem when the background signatures were appropriately constrained, and reasonable estimates of the original stand characteristics were obtained in most cases. An
example of this type of error is given. Figure 6a shows
a cover trajectory for the test scene based on random
shadowing (b50.0). In this case, the trajectory is linear,
and the point of maximum cover is the darkest point in
both red and near-infrared bands. The rectangle shows
the ranges used to constrain the background signature
values for the test stands in the inversion. Figure 7a
shows the results of inversion using the simulated red
and near-infrared reflectances for the situation shown in
Figure 6a. It can be seen that the inversion quite successfully retrieved cover at all covers; the small errors in
estimated cover were inevitably related to errors in the
estimated values of the background signatures—these
were the first type of error.
The second type of error resulted from the nonlinearity of the cover trajectories in multispectral space; and
occurred where mutual shadowing was significant, at
high covers, in two-, three-, and four-parameter inversions. In general, the severity of these errors was dependent on the shape of the cover trajectory, which in turn
was a function of the positions of the component signatures and the degree of mutual shadowing. These errors
occurred because of the close proximity at high covers,
of different segments of different trajectories originating
from different background points; in these cases, there
was no approximate determination of the correct set of
stand characteristics in the inversion. However, for low
to intermediate mutual shadowing (b,0.4), this second
type of error did not occur at lower covers (,0.7), and
thus was not considered a source of error for the test
stands. An example of this type of error is given. Figure
6b shows a case where b was set to 0.4, that is, intermediate mutual shadowing, but with all other conditions the
same as in the case shown in Figure 6a. Two cover trajectories are shown; the lower trajectory is the true one,
and both cover trajectories can be seen to converge at
higher covers. The result of inversions for the true case
are shown in Figure 7b. It can be seen that significant
errors occurred in the estimated covers at higher covers.
Inversion of Geometric–Optical Reflectance Model
115
Figure 7. The results of model inversion for the corresponding cases shown in Figure 6.
For example, in the case of the 0.8 cover stand, the value
of cover estimated by inversion was 0.43 and the background signatures retrieved in this case were those of the
top, left point of the rectangle used to constrain the signatures. The wrong cover trajectory (the upper one) was
found in this case.
In order to explore the wider applicability of inver-
sion, for handling variations in background signatures, inversions were extended to simulated reflectance data sampled at off-nadir and dual-view angles. One example is
described: Figure 8a shows an intermediate mutual shadowing case for the test scene- the same case as Figure 6b.
The two cover trajectories shown are the nadir one, and
also the trajectory obtained with a 408 view angle (the
Figure 8. a) Two cover trajectories (corresponding to a nadir view and a 408 view, respectively) for the test stands assuming intermediate mutual shadowing (b50.4). The rectangle shows the ranges used to constrain the background signatures in the inversion. b) The results of inversion using red, near-infrared, and short-wave infrared bands obtained at two view angles (nadir and
408) for the case shown in a).
116
Gemmell
Table 6. Results of Inversion Experiments Using TM3 and
TM4, and the Spectral Indicesa
Experiment
Correlation
1-parameter
2-parameter (red)
2-parameter (NIR)
3-parameter
NDVI
SAVI
20.01
20.08
0.51
0.61
0.50
20.40
a
The correlation between covers estimated by inversion and those
measured on the ground is given. Red and near-infrared (NIR) indicate
which background signatures were varied, along with cover, in the inversion.
Sun–sensor azimuth difference was zero). The results of
inversion using six reflectance measurements (sampled at
both views, in the red, near-infrared, and short-wave infrared bands, respectively), are shown in Figure 8b. In
this case cover was retrieved accurately in all cases, and
the two types of error described above did not occur.
Thus inversions using real multispectral data, sampled at
two view angles, may help to improve cover estimates.
However, further work is needed to test this result.
RESULTS FOR THE TEST STANDS
The results are given as the correlation between cover
retrieved by inversion and measured cover, or between
a given spectral index and measured cover. The utility
of single band TM data was briefly examined. However,
correlations between single TM bands and cover were
found to be low (20.32, 20.38, and 20.34 for TM
Bands 3, 4, and 5, respectively) and the use of single
band TM data was not explored further.
Initially, inversion was tested using only red and
near-infrared bands (TM3 and TM4) in order to provide
an even comparison with the spectral indices, since these
are based only on these two bands. Inversion was tested
first using constant background signatures. For each of
the test stands, model inversion was applied using all the
peripheral information available for the stand including
Sun–sensor–slope geometry (variable, obtained from the
DTM), the geometrical crown constants, the mutual shadowing parameter b (constant), and the four component
signatures from each band (constant). The cover that minimized the differences between modeled and observed
TM reflectances was taken to be the best estimate.
Table 6 gives the results of inversion using TM3 and
TM4, and the results for the spectral indices. In the case
of the one-parameter inversion for cover, using the mean
background signatures, there was no correlation between
the estimated and measured cover. Inversions were then
tested allowing for variable background signatures. This
included two-parameter inversions (cover and the background signature in one band) where the background
signature in the other band was held constant at its mean
value; and three-parameter inversions (cover and the back-
ground signatures in both bands). In these experiments
the background signatures were constrained to lie within
ranges estimated from the low cover stands. When both
cover and the red background reflectance were varied in
a two-parameter inversion, this had very little effect on
the correlation. This may be explained by the fact that
the red background reflectance was very low for most of
the test stands, and thus variations in the red signature
were relatively less important. However, when both cover
and the near-infrared background signature were varied in
a two-parameter inversion, the correlation was increased
markedly to 0.51. This indicated that variations in the
near-infrared background signature were important for
the test stands. The three-parameter inversion (cover,
and both the red and near-infrared background signatures) gave a higher correlation since variations in both
signatures were taken into account (Fig. 9a).
Figure 10 shows the spectral indices plotted against
cover for the test stands. It should be noted that the
scales of the vertical axis are different in Figure 10,
which is a result of the different range of values present
for each index. The NDVI had greater absolute correlation with cover than the SAVI in this case. The NDVI
performed as well as the two-parameter inversion in
which the near-infrared signature was varied, and both
indices performed considerably better than the one-parameter inversion in which the background signatures were
treated as constant. Although the NDVI does not specifically account for soil line effects, this index performed
best of the two indices.
Table 7 gives the results of the inversions using TM4
and TM5. Again, the one-parameter inversion had no
utility for estimating cover. The two-parameter inversions
gave only marginal improvements in the correlation in
this case. In contrast to the two-parameter inversion using red and near-infrared bands, varying the near-infrared signature while holding the signature in TM5 constant gave a poor result. This may be because TM5 had
a greater dynamic range than TM3 in this case, and thus
using the mean value (that is, the wrong value for most
of the stands) of the background signature in TM5 resulted in relatively large errors in the inversion, despite
the fact that variations in the near-infrared signature
were included. The three-parameter inversion (cover,
and both near-infrared and short-wave infrared background signatures) gave a higher correlation again, since
variations in both signatures were taken into account.
Table 8 gives the results of the inversions using
TM3, TM4, and TM5. Again, the one-parameter inversion had no utility for estimating cover. Inversions allowing variations in single background signatures, while
holding the remaining signatures constant, did not significantly improve the correlations for the inversions based
on the three TM bands; however, again varying the nearinfrared signature had the greatest impact of the three
signatures. Three-parameter inversions, which allowed
for variations in background signatures in planes (that is,
Inversion of Geometric–Optical Reflectance Model
117
Figure 9. Results of model inversion for the test stands: a) inversion using only red and near-infrared bands; b) inversion
using red, near-infrared, and short-wave infrared bands.
in the red/near-infrared, the red/short-wave infrared, or
the near-infrared/short-wave infrared, respectively) gave
some improvement only in the case of near-infrared/
short-wave infrared signatures. Again, it appeared that
varying the background signature in one or two bands,
while using a mean signature for the remaining band(s)
had an adverse effects on the inversion result. Finally,
the four-parameter inversion (cover, and the three background signatures), which performed best overall, show-
ed a marked improvement in the correlation to 0.76. The
relationship between measured and estimated cover for
this case is shown in Figure 9b.
DISCUSSION
It was apparent that model inversions with constant
background signatures could not provide information on
stand cover. The underlying reason for this was that a
Figure 10. Cover and a) NDVI and b) SAVI for the test stands.
118
Gemmell
Table 7. Results of Inversion Experiments Using TM4
and TM5a
Experiment
Correlation
1-parameter
2-parameter (SWIR)
2-parameter (NIR)
3-parameter
0.01
0.07
0.16
0.65
a
The correlation between covers estimated by inversion and those
measured on the ground is given. Short-wave infrared (SWIR) and nearinfrared (NIR) indicate which background signatures were varied, along
with cover, in the inversion.
significant proportion of the total variance in the spectral
data was due to background variations. This was supported by observations on the ground, and by inspection
of high spatial resolution (3-m) spectral imagery, where
the background signatures were observed to be variable
in the site. In addition, sensitivity analysis of the reflectance model indicated that stand reflectance was relatively most sensitive to variations in the illuminated background signatures. Difficulties in model inversion caused
by variations in background signatures have been noted
by other investigators (Woodcock et al., 1997).
Both spectral indices performed considerably better
than the one-parameter inversion in which the background signatures were treated as constant. This might
be expected to some extent, since the indices enabled
some of the variation due to the background signatures
to be taken into account. It is helpful here to examine
the spectral indices in red/near-infrared spectral space.
Figure 11a shows a single cover trajectory for the test
stands starting from the mean background point. Also
shown in Figure 11a are the NDVI isolines. It should be
noted that the scale of the red axis is exaggerated relative
to the near-infrared axis in Figure 11. At least three factors must be considered in the interpretation of the performance of a given index in this site: first, the sensitivity
of the index to cover; second, the sensitivity to background variations; and third, the sensitivity to slope–
aspect effects. In Figure 11a it can be seen that, at low
Table 8. Results of Inversion Experiments Using TM3, TM4,
and TM5a
Experiment
1-parameter
2-parameter
2-parameter
2-parameter
3-parameter
3-parameter
3-parameter
4-parameter
(red)
(NIR)
(SWIR)
(red,NIR)
(red,SWIR)
(NIR,SWIR)
Correlation
20.03
20.05
0.22
0.06
0.22
0.01
0.54
0.76
a
The correlation between covers estimated by inversion and those
measured on the ground is given. Red, near-infrared (NIR), and shortwave infrared (SWIR) indicate which background signatures were varied,
along with cover, in the inversion.
covers, the NDVI isolines were almost parallel to the
cover trajectory, indicating that sensitivity of the NDVI
to cover was small for the test stands. However, the
NDVI isolines were also fairly parallel to the near-infrared axis (relative to the red axis) in the region of the
cover trajectory. Thus, the NDVI was relatively insensitive to variations in the near-infrared background signature. Figure 11 also shows a “terrain trajectory” for the
test stands based on the mean signatures and a cover of
0.4. In this case, slope was varied in the principal plane
of the Sun, in 58 increments, ranging between 408 for
slopes facing towards the sun, to 408 for slopes facing away
from the Sun. The principal plane contains the maximum
variation in stand reflectance due to slope–aspect effects.
It can be seen that the terrain trajectory was parallel to
the NDVI isolines in this case. Despite its insensitivity to
cover, the NDVI performed best of the two indices examined, because of its relative insensitivity to near-infrared
background variations and its insensitivity to slope–aspect
effects. In both these respects, the NDVI performed
similarly to the two-parameter inversion in which the
near-infrared background signature was varied.
In the case of the SAVI (Fig. 11b), the isolines can
be seen to have a greater component perpendicular to
the cover trajectory at lower covers, relative to the case
of the NDVI. This indicates that the SAVI was more sensitive to cover than the NDVI in this region. However,
the SAVI isolines are orientated with a greater perpendicular component to the near-infrared axis than in the
case of the NDVI, and thus SAVI was more sensitive to
variations in the near-infrared background signature. In
addition, the SAVI isolines had a greater perpendicular
component to the terrain trajectory, and thus a greater
sensitivity to slope–aspect effects than the NDVI. In this
case, the sensitivity of the SAVI to variations in the nearinfrared background signature, and to slope–aspect effects, appeared to outweigh its increased sensitivity to
cover, since the correlation between the SAVI and cover
was lower than in the case of the NDVI (Table 6).
There are two reasons why the three-parameter inversion performed better than the spectral indices. First,
variations in slope and aspect were taken into account in
model inversion, while these could not be explicitly taken
into account by the indices. Second, variations in the
background signatures in all directions (in red and nearinfrared spectral space) were taken into account in the
three-parameter inversion. Thus model inversions outperformed the spectral indices on the basis of TM3
and TM4.
The spectral indices should have some utility for
providing broad estimates of conifer forest cover using
TM data, and could be applied in sites where the peripheral data required for model inversion are not available.
Indeed, in situations where the forest background is particularly variable, and these effects cannot be included
in the inversion process, spectral indices should have
Inversion of Geometric–Optical Reflectance Model
119
Figure 11. Spectral index isolines for a) NDVI and b) SAVI. The thick, solid line shows a cover trajectory for the test stands
using the mean background signature. The broken line shows a terrain trajectory for a test stand (cover 0.4), where variations are shown between a 408 slope facing towards the Sun (upper end of the trajectory) to a 408 slope facing away from
the sun (lower end).
greater utility than inversion. However, indices should be
selected according to the characteristics of the site under
investigation since an index that is optimal under one
particular set of conditions may not be optimal under another set. Further, it is clear from Figure 11 that the
SAVI does not have a unique value for a given cover
over much of the cover range, and that it would not be
possible to distinguish between lower and higher covers
on the basis of SAVI.
Four-parameter inversions (cover, and the background signatures in TM Bands 3, 4, and 5) performed
best overall, and Figure 9b indicated that at least rough
estimates of cover could be made for the test stands.
When variation in the background signatures were taken
into account, the addition of TM5 improved the correlation (from 0.61 to 0.76). The short-wave infrared band
has been noted by a number of authors to have utility in
discriminating conifer forest characteristics (Horler and
Ahern, 1986; Gemmell, 1995). There are two likely reasons for the utility of TM5. First, TM5 has a greater dynamic range than TM3, and thus quantization effects
should have less of an adverse effect in TM5. Experiments with simulated reflectance data (above) indicated
that inversions using three bands gave more accurate results than inversions using only two bands, because the
effects of noise in the spectral data were reduced by using three bands. The contrast between shadowed and illuminated components is greater in this band relative to
shorter wavelength bands, since the diffuse sky irradiance impinging on the stand is relatively small. This
should be an advantage in the inversion of a geometric–
optical model which relies on good separation of the
component signatures in spectral space. Second, there
may be fewer sources of variation in the crown component signatures in the short-wave infrared band, which
should help in the inversion. For example, variations due
to foliage condition/chlorophyll content are not present
in the short-wave infrared band, while these could potentially be important in the red band. The fact that
TM5 gave a slightly better result than TM3, in the threeparameter inversions using two bands, also suggests that
TM5 had greater utility than TM3.
The overall approach taken in this investigation was
to identify the key factors contributing to variance in the
TM data, and, where possible, to take these factors into
account in the inversion process. In the case of terrain,
these factors were included on a stand-by-stand basis,
since the terrain data could be obtained from the DTM.
In the case of cover and background variations, these
were included directly into the inversion. However, other
sources of variation could not be accounted for, and it
was apparent that significant scatter in the results still
remained (Fig. 9b). Some of this scatter very likely occurred because the precise values of the background signatures were not found in the inversion. Experiments
with simulated data above indicated that, although the
approximate values of the background signatures could
be found in most cases when the number of unknowns
exceeded the number of spectral bands, the approximate
values of the background signatures could not always be
120
Gemmell
found. Another cause of this scatter was very likely due
to other unknown stand characteristics. These included
natural variations in the spatial distribution of trees,
structure, crown geometry, and the crown signatures.
Variations in the spatial distribution of trees are regarded
as important (Chen and Leblanc, 1997; Woodcock et al.,
1997). In addition, it was known that selective logging
had occurred in the site which would also cause departures from the random spatial distribution assumed in
the reflectance model. However, it was not possible to
take variation in these factors into account, as well as
variations in cover and background signatures, using only
TM spectral data, since this would have increased the
difficulties caused by local minima in the inversion.
In this work, prior stratification of the test stands,
on the basis of existing inventory data, into fir-dominated
stands helped reduce the variability in the data due to
species composition. Thus, the question arises as to what
other information might be obtained from existing inventory data. For example, some basic information on bulk
stand structure might be obtained from stand age, which
is known to affect the structural complexity of the stand,
and this may then help in the inversion process. Thus
work is needed to define optimum methodologies for
model inversion, taking into account the information
available, correlations between inventory data layers and
the measured properties from remote sensing, and the
accuracy of forest cover data.
Another area that requires work is how to incorporate additional information from remote sensing into the
inversion process. It was found above using simulated data
that the use of spectral data sampled at two view angles
helped to increase the accuracy of the inversion result in
that particular situation. The use of spectral data samples
at two or more view angles might provide the extra information necessary to enable an additional parameter to be
included in the inversion process, and thus help to increase the accuracy of the inversion results.
CONCLUSIONS
A number of conclusions can be drawn from this investigation:
• One-parameter inversions using constant background signatures could not retrieve stand cover
because a significant proportion of the total variance in the spectral data resulted from background variations. The assumption of constant
background spectral signatures in model inversion is unlikely to be adequate in situations
where background variations are significant.
• The spectral indices (NDVI and SAVI) performed better than the one-parameter inversions
because the indices partially reduced background
effects, but could not provide accurate informa-
tion on cover. The spectral indices tested should
have some utility for providing broad estimates
of conifer forest cover using TM data in sites
dominated by low covers, and could be applied
in sites where the peripheral data required for
model inversion are not available.
• When the background signatures were included
in the inversion, inversion performed better than
the spectral indices. The greatest correlation between measured covers and those estimated
from inversion was found using TM Bands 3, 4,
and 5; although inversions using two bands (either TM3 and TM4, or TM4 and TM5) had
some utility also. The results indicate that variations in the background signatures can be included in the inversion in certain situations, and
should be included when these effects are important. Further testing is thus required.
• Further work is needed to investigate methods
for incorporating additional information into the
inversion process, both from existing inventory information and from remote sensing, taking into
account the information available and correlations between inventory data layers and the measured properties from remote sensing.
The author would like to thank the Natural Science and Engineering Research Council (NSERC) Canada for funding in this
work. The author is grateful to the anonymous reviewers for
their constructive comments on the manuscript.
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