Download Crown closure estimation of oak savannah in a dry

. .  , 2003, . 24, . 9, 1811–1822
Crown closure estimation of oak savannah in a dry season with
Landsat TM imagery: comparison of various indices through
correlation analysis
BING XU, PENG GONG and RUILIANG PU
Center for Assessment and Monitoring of Forest and Environmental Resources
(CAMFER), 151 Hilgard Hall, University of California, Berkeley,
CA 94720-3110, USA; e-mail: [email protected]
(Received 6 February 2001; in final form 19 November 2001)
Abstract. In this paper, we assess the capability of Landsat Thematic Mapper
(TM) for oakwood crown closure estimation in Tulare County, California.
Measurements made from orthorectified aerial photographs for the same area
were used as a reference. The linear relationship between crown closure and
digital values of each band of the TM image was examined. TM Band 3 had the
highest correlation (r=−0.828; R2=0.687) with crown closure measurements.
The simple ratio (SR) and the normalized difference vegetation index (NDVI)
were generated for correlation analysis and only NDVI showed better correlation (r=0.836; R2=0.699) than use of single bands. An additional index
(NIRN−RN)/(NIRN+RN), called NDVIN, was experimented, NDVISQ (N=2)
and NDVICUB (N=3) showed some improvements over SR and NDVI (r=
0.855; R2=0.732 for N=3). Through multiple regression with all six bands, we
found that there was a considerable amount of improvement in variability explanation over any individual band or index tested (R2=0.803). NIR, red and blue
bands were able to adequately model crown closure as using all the six TM bands
(R2=0.802). Principal component analysis (PCA) and Kauth-Thomas (K-T)
transform were applied to reduce multi-collinearity among bands. The third
principal component and greenness in K-T transform showed similar effects to
those of NDVI. Transformation of digital numbers (DNs) to radiances kept the
results of single band and multiple band estimation the same, and did not improve
the index estimation very much. A simple radiometric correction of the TM image
improved results for the NDVI (r=0.840; R2=0.705) and NDVISQ estimation
(r=0.861; R2=0.741), but worsened estimation results of single band and
multiple bands.
1. Introduction
Crown closure is the percentage of forest canopy projected to a horizontal plane
over a unit ground area. It is an important parameter in ecological, hydrological
and climate models. Its measurement in the field is difficult and time-consuming
(Bonham 1989). This is particularly true over large areas. Although efficient sampling
strategies can be employed, such methods can be prone to error. Statistical correlation
analysis between the crown closure and spectral properties is dependent on the
accuracy of ground measured and remotely sensed data (Chen and Cihlar 1996).
Therefore, we used classification results from orthorectified aerial photographs at
International Journal of Remote Sensing
ISSN 0143-1161 print/ISSN 1366-5901 online © 2003 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/01431160210144598
1812
Bing Xu et al.
1 m ground resolution as ground data in this study. Landsat TM data were used as
regressors after geometric registration of the air photo and the satellite image.
The correlation between tree density and TM data was explored in an oak
savannah in southern Spain (Joffre and Lacaze 1993). It was found that the grey
level values of bands 2–5 were all negatively correlated with the tree density; the
NIR was the highest (r=−0.53). A recent study found a higher correlation between
savannah vegetation cover percentage and the red band of Landsat Multi-Spectral
Scanner (MSS) (R2=0.88) with a relatively small sample set (n=22) in eastern
Zambia (Yang and Prince 2000). Direct band transformation might provide a better
correlation. Normalized difference vegetation index (NDVI) was correlated with
canopy cover using Landsat TM (r=0.552) and MSS (r=0.698) and SPOT HRV
XS (r=0.718) data (Larsson 1993). Leaf area index (LAI), a parameter directly
related to crown closure, could be retrieved using NDVI derived from Landsat TM
data through linear or log linear models (Spanner et al. 1990, Gong et al. 1995,
Chen and Cihlar 1996). Estimation of canopy cover from multiple bands was investigated using airborne sensors, such as the Compact Airborne Spectrographic Imager
(CASI) for forest inventory (r varies from 0.76 to 0.94) (Baulies and Pons 1995) and
crown closure estimation of conifer forest (Gong et al. 1994). Multispectral data can
be transformed using principal component analysis (PCA) from a statistical point
of view and Kauth-Thomas (K-T) transform on a physical basis (Kauth and Thomas
1976). Some investigators found that redness was somehow more correlated with
canopy cover than greenness in boreal forest at high latitudes (Foster et al. 1994).
K-T greenness/redness ratio (GR ratio) was found to provide a higher correlation
(r=0.81) with brush canopy cover in rangeland using Landsat MSS data (Boyd
1986). Among the studies, none compared a number of approaches at the same
study site.
In this paper we report the exploration of single band, vegetation indices, multiband regressions, multi-spectral transformation for crown closure estimation using
Landsat TM imagery. Conversion of digital numbers (DNs) to radiance was tested.
A simple radiometric correction of the image that attempted to reduce Rayleigh
scattering of the atmospheric effect was also applied and evaluated in this study.
2. Data acquisition and preparation
Our study area is a hardwood rangeland in Tulare County, California, USA. It
is covered by oakwood, bare soil, grass and shrubs. The Landsat TM image was
taken in August 1995. The false colour composite of the TM image is shown in
figure 1. Crown closure in this area is generally less than 20%. Due to the
Mediterranean climate in California, the sky in the summer months is usually crystal
clear. Grasses are dead and dry during the dry summer months. The reflectance of
soil and dry grasses is higher than that of oak tree leaves in the visible bands of the
TM image. The red colour in figure 1 shows crown coverage. Sample pixel values
from Issabelly Lake in the same TM scene were taken as dark target to do radiometric
correction. It was assumed that radiance was inversely proportional to the 4th power
of the spectral wavelength due to Rayleigh scattering (Lillesand and Kiefer 1994).
The path radiance over water bodies in each band was calculated and subtracted
from the spectral signals of each band (Gong and Zhang 1999).
The airphoto mosaics, shown in figure 2, were taken in the dry season 2 months
later than the satellite imagery. The airphotos (scale 1:40 000) were scanned at 1 m
ground resolution. The scanned photographs were orthorectified using a digital
Crown closure estimation with L andsat T M imagery
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Figure 1. Study site in Tulare County of California in a standard false colour display of the
Landsat TM imagery.
Figure 2. Aerial photograph corresponding to figure 1.
photogrammetric software package. GCPs (ground control points) measured with
GPS (global positioning system) equipment were used to derive the photographic
stations and they were subsequently used in stereo model development and orthorectification. The TM image was georeferenced with respect to the corresponding
orthorectified aerial photograph. Therefore, each pixel in the TM image corresponded
to 30 pixels by 30 pixels in the aerial photograph. In each ‘transparent’ mask
(corresponding to one pixel) of the TM image over the 30 pixels by 30 pixels of the
aerial photograph, we were able to calculate the crown closure. Image processing
such as image thresholding and classification was applied to derive land-cover types
from the aerial photographs. The surface cover classification results were used to
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Bing Xu et al.
calculate the percentage of crown closure, grass and soil for each corresponding
pixel on the TM image. The classification results from the aerial photograph are
shown in figure 3. We randomly chose 130 samples from the sunlit sites for this
study. Pixels on shaded sides of the scene require topographic correction, which will
be dealt with elsewhere.
3. Crown closure estimation by single band or indices
For each of the 130 sample pixels, we extracted the DNs from the six bands of
the TM image covering the blue, green, red, near-infrared and two middle infrared
spectral ranges. Linear relationships can be observed from the scatterplots (figure 4).
The correlation coefficient (r), R-squared (R2), and residual standard errors (rse) are
reported in table 1. The DN in the red band is negatively correlated with the crown
closure (r=−0.828), and explains 68.7% of data variability. The superior performance of the DN in the red band of the TM image agrees with that of the MSS image
(Yang and Prince 2000). However, the DN of the NIR band (band 4) has a low
correlation with crown closure (r=0.222). For band 4 in figure 4, the fitted line
traverses through the empty space of data clusters, compromising the cluster with
no crown closures. Samples with 0% crown closure and high DNs in the red band
are mainly covered by grass, soil or both. In general, 0% crown closure should be
included in an analysis. We also carried out analysis without sample points of 0%
crown closure as pixels with 0% crown closure can be determined by image classification. It is interesting to note that removing those samples with 0% closure did not
affect much of the results except for the NIR band with which some improvement
in correlation (r=0.456) was obtained. It caused a slight decrease in correlation for
bands 2 and 3 (table 1).
Our results in the NIR band are different from those of Joffre and Lacaze (1993),
although the environments are similar. The TM data in Joffre and Lacaze (1993)
were collected in late spring and the homogeneous herbaceous background had
stronger reflectance than the trees. A reduction in crown closure would increase the
Figure 3. Pseudo colour display of classification results of the aerial photograph (red: crown
closure; green: grass; white: soil).
80
1.0
30
40
40
90
50
60
70
80
1.0
Crown Closure
0.8
1.0
0.6
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Crown Closure
0.2
80
30
TM 3
0.0
70
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20
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1.0
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Crown Closure
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TM 2
0.0
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Crown Closure
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TM 1
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Crown closure estimation with L andsat T M imagery
60
80
100
TM 4
120
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160
20
TM 5
40
60
80
TM 7
Figure 4. Scatter plots of crown closure (%) against DN of each TM band.
Table 1. Statistical analysis between single bands with crown closure*.
Crown closure
TM1
TM2
TM3
−0.791 −0.795 −0.828
(−0.802) (−0.794) (−0.811)
R-squared (R2)
0.626
0.632
0.687
(0.643)
(0.630)
(0.657)
Residual standard error (rse)
0.191
0.189
0.175
(0.201)
(0.205)
(0.197)
Correlation coefficient (r)
TM4
0.222
(0.456)
0.050
(0.208)
0.304
(0.299)
TM5
TM7
−0.733 −0.734
(−0.767) (−0.779)
0.538
0.540
(0.588)
(0.607)
0.212
0.212
(0.216)
(0.211)
*Values in brackets are after removing 0% crown closure
Bold number indicates the highest correlation, while italicized number indicates the lowest
correlation among different bands (columns). This notation is applicable to all the tables in
this paper.
reflectance in the NIR band. Our data were acquired in late summer when grassland
was dead. Thus only the increase of crown closure would increase the reflectance in
the NIR. The negative correlations with other bands in our study were caused by
the dry background with greater reflectivity than the crowns. Transforming DNs to
radiance with a linear model (Markham and Barker 1986) kept the correlation
coefficient with individual band the same. This is well explained by the least squares
theory (equation (1)) that the DNs multiplied by a constant c in each band will not
change the final result but the slope of the estimated line, since the absolute values
of the regressors (brightness values in each band) are changed. The subtraction term
was so small that it could be neglected. In the equation, y is observation (crown
Bing Xu et al.
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closure from aerial photograph), ŷ is estimator (crown closure to be estimated), and
X is regressor (radiance or DN from the TM image).
ŷ=cX((cX)∞(cX))−1(cX)∞y=X(X∞X)−1X∞y
(1)
Simple radiometric correction by subtracting a constant obtained by only approximating the Rayleigh scattering of the atmospheric condition for each band did not
improve the correlation. The slope of the estimated line was kept the same, and the
intercept term was changed instead (equation (2)). The estimate result is not the
same as that without radiometric correction.
ŷ=(X−c)((X−c)∞(X−c))−1(X−c)∞y≠X(X∞X)−1X∞y
(2)
Correlation analysis with vegetation indices was made (table 2). SR, the DN ratio
between the NIR and the red band, did not improve the correlation when compared
with the result from the analysis of the red band. Apparently the poor correlation
between NIR and crown closure was the reason for the poor performance of SR.
NDVI, which took advantage of both the high variability of the NIR band among
different land-cover types and the relatively stable prediction of the red band, showed
a slight improvement over the red band. Since NDVI showed a minor improvement
over the red band and SR, we are led to speculate that the wider spectral variability
between the NIR and the red band after normalization may help improve the
correlation. This may be caused by reduction of illumination differences on the sunlit
sides of the hills. It seemed to us that the spectral difference between the NIR and
red bands is the primary contributor in the correlation analysis, thus we attempted
to enlarge this difference by taking the difference of powered DNs. NDVISQ,
NDVICUB, NDVIN are defined in the following equations (equation (3)). The
NDVIN can be expressed by SR.
SR=
NDV IN7
NIR
R
(3)
NIRN−RN SRN−1
=
for N=1, 2, ...
NIRN+RN SRN+1
when N=2 we have NDVISQ, when N=3 we have NDVICUB.
In this exploration, we tested a number of indices. We found that NDVISQ,
NDVICUB produced better regression results than SR, NDVI and other higher
ordered NDVIN (N4). We can see from the quadratic curve that the correlation
Table 2. Correlation analysis between vegetation indices derived from raw digital values and
crown closure*.
Crown closure
SR
NDVI
Correlation
coefficient (r)
R-squared
(R2)
Residual
standard
error (rse)
0.782
(0.748)
0.611
(0.560)
0.194
(0.223)
0.836
(0.804)
0.699
(0.646)
0.171
(0.200)
NDVISQ NDVICUB Redness
0.851
(0.824)
0.725
(0.679)
0.164
(0.191)
0.855
(0.838)
0.732
(0.702)
0.162
(0.183)
−0.730
(−0.765)
0.533
(0.585)
0.213
(0.217)
*Values in brackets are after removing 0% crown closure
Greenness
(G−R)/(G+R)
0.837
(0.811)
0.700
(0.657)
0.171
(0.197)
−0.822
(−0.804)
0.676
(0.646)
0.177
(0.200)
Crown closure estimation with L andsat T M imagery
1817
coefficient (r) increases as order N increases reaching its maxima when N=3, then
decreases abruptly as N further increases (figure 5 lower right). There is no significant
difference between the correlation coefficients when N is at 2 or 3, so the optimal N
is 2 and 3 (figure 5).
Transforming DN to radiance did not improve the correlation with vegetation
indices. We could first look at the transformation formula and the coefficients we
applied below (Markham and Barker 1986).
Radiance(i)=L MIN(i)+
L MAX(i)−L MIN(i)
DN(i) i=1, 2, ..., 6
DNMAX
L MIN=(−0.15, −0.28, −0.12, −0.15, −0.037, −0.015)
(4)
L MAX=(15.21, 29.68, 20.43, 20.62, 2.719, 1.438)
DNMAX=256
1.0
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0.0
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Crown Closure
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0.0
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Crown Closure
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1.0
The corresponding coefficients of L MIN and L MAX are −0.15 and 20.62 for the
NIR band, and −0.12 and 20.43 for the red band. There is a 1‰ larger scaling
(slope) effect for the NIR than the red reflectance, however, a bigger cut (3%) of the
intercept term for the NIR than that for the red band. The combined up-scaling and
downshifting effects of the radiance transformation would not be able to considerably
enlarge the spectral differences between the NIR and the red bands. Therefore, the
NDVI and NDVIN using radiance did not improve the correlation over the DNs
by much (table 2 and table 3).
The radiometric correction based on Rayleigh scattering applied a simple subtraction from the transformed radiance. A larger constant was subtracted from the red
0.0
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correlation coef
0.0
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NDVISQ
1.0
NDVI
0.0
0.2
0.4
NDVICUB
0.6
0.8
1.0
2
4
6
8
10
N
Figure 5. Regression between crown closure (%) and NDVIN (N=1, 2, 3); plot of correlation
coefficient vs. N varying from 1 to 10.
Bing Xu et al.
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Table 3. Correlation analysis between vegetation indices derived from radiance and crown
closure*.
Crown closure
NDVI
Correlation
coefficient (r)
R-squared (R2)
0.836
(0.803)
0.699
(0.646)
0.171
(0.200)
Residual standard
error (rse)
NDVISQ NDVICUB Redness
0.852
(0.825)
0.726
(0.680)
0.163
(0.190)
0.855
(0.839)
0.731
(0.704)
0.162
(0.183)
−0.693
(−0.732)
0.481
(0.536)
0.224
(0.229)
Greenness (G−R)/(G+R)
0.839
(0.811)
0.704
(0.657)
0.17
(0.197)
−0.832
(−0.817)
0.693
(0.668)
0.173
(0.194)
*Values in brackets are after removing 0% crown closure
band, and a smaller constant was subtracted from the NIR band. It can be expected
from the former rationale that the transformation might be able to produce some
improvements, because we had enlarged the radiance difference between NIR and
red bands. This turned out to be true (table 4).
4. Crown closure estimation by multiple bands and combination of components
The above analysis only took one band or a transformation between two bands
into consideration. Would additional bands further improve the correlation? We
made use of the three visible, the NIR and the two MIR bands to do multiple
regression. We had achieved a considerable amount of improvement based on the
result of a high R-squared value of 80.25% (the p-value is 0). The six-band regression
explained the most variability among all the above-mentioned approaches, which
was reasonable. The residual standard error, 0.170, did not drop and remained at a
similar level to that of NDVI. We knew that the degree of freedom of the multiple
regression model was no longer n-2 or 130-2, but n-6 or 130-6. The residual standard
error, denoted by rse, was calculated by the following formula.
rse2=( y−Xb̂)T (y−Xb̂)/(n−p)
(5)
where n is sample size, p is number of regressors and b̂ is a p×1 vector, the estimated
coefficient for each regressor.
There is a trade-off here between the sum of squared errors and the degree of
freedom. Although the sum of squared errors may become smaller by using six bands
instead of two bands, the degree of freedom also becomes smaller. The resulting rse
may therefore be kept at a similar level.
Based on the fact that the model estimation using bands 1, 3 and 4 only was
Table 4. Correlation analysis between crown closure and vegetation indices derived from
raw digital values after doing radiometric correction*.
Crown closure
NDVI
NDVISQ
NDVICUB
Correlation coefficient (r)
0.840
(0.841)
0.705
(0.707)
0.169
(0.169)
0.861
(0.864)
0.741
(0.746)
0.159
(0.157)
0.856
(0.855)
0.733
(0.732)
0.161
(0.162)
R-squared (R2)
Residual standard error (rse)
*Values in brackets are derived from radiance
Crown closure estimation with L andsat T M imagery
1819
15
20
25
1.0
-40
-20
-40
-75
-70
PC 4
-65
-60
0
20
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Crown Closure
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1.0
0.6
0.0
0.2
0.4
Crown Closure
0.2
0.0
-80
-20
PC 3
0.8
1.0
0.8
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0.4
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Crown Closure
-30
PC 2
0.0
-85
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Crown Closure
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Crown Closure
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Crown Closure
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1.0
statistically significant (i.e. the p-value is small enough when a is at 0.05 significance
level in the F-test), we only chose these three bands for the regression. The multiple
R2 accounted for 80.18% of the data variability, remaining at the same level as that
using all six bands. The residual standard error was kept as low as 0.168 with 127
degrees of freedom. The analysis of variance gave a p-value of 0.93 while doing a Ftest for the model with all the bands and with bands 1, 3 and 4, showing no significant
difference between the two models. We conclude that the red, NIR and the blue
band modelled the crown closure estimation as adequately as using all six bands.
To get rid of the high correlation among different bands, we orthogonalized the
columns of the regression bases formed by the spectral values of the samples and
established a new set of orthogonal coordinates system. The approaches we applied
here were PCA and K-T transform. Distribution variability of land-cover types was
needed to enlarge the contrast between group signatures. The linear regression using
each component is shown in figure 6. The 3rd principal component shows the best
fitting result, which is almost the same as that of the red band among all six
components (r=−0.825; R2=0.681). When we used all six components together,
we found that the only significant term in the regression was the 3rd principal
component. When we combined the 3rd principal component with the 2nd principal
component to model the crown closure, we got a similar result to that using the red
and the NIR band directly. The R2 and the rse were 78.92% and 0.173. PCA, picking
the principal components by putting the data variance in order, did not lead to a
better estimation for crown closure than that of the original six bands. The components explaining greater sample variability (such as the 1st and 2nd components) are
not better at predicting variables for crown closure estimation.
-160
-140
-120
PC 5
-100
-80
60
80
100
120
PC 6
Figure 6. Regression between crown closure (%) and principal components.
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Bing Xu et al.
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The K-T transform is orthogonal and endows physical meaning to each axis. We
picked up redness and greenness. Greenness, supposed to be an indicator of
vegetation vigour, showed a rather good prediction of crown closure. The estimation
result of greenness is similar to that of NDVI as shown in table 2, table 3 and
figure 7. (G-R)/(G+R) estimation, where G indicates greenness and R indicates
redness, did not improve the result of the single component estimation. This indicates
that the idea of NDVI could not be simply borrowed here.
5. Summary and conclusions
Data preparation and ground data generation is critical to crown closure estimation. Careful classification of the aerial photographs and sample selection was done
to reduce possible errors. Based on the experiments of this study, we have the
following conclusions for the savannah type of oakwood lands during the dry season:
120
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Redness
200
220
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1. The red band in the TM image is the best for crown closure estimation
among the six individual bands.
2. The NIR band itself is the last band one should use to predict crown closure
due to the high variability among different land-cover types. Removing
samples with crown closure of 0% only increases the predicting power of
this band, and slightly improves the correlation with the two middle infrared
bands. However, it degenerates the differentiating power of other bands and
of the combined use with other bands.
3. NDVI, the combined use of the NIR and red bands, may improve the
estimation results over the red band by a small amount.
4. Our newly proposed index, NDVISQ and NDVICUB (NDVIN, when N=
2 and N=3) produced better results than NDVI (a special case of NDVIN,
when N=1). Enlarging the variability of NIR and the red to some extent
and stretching the difference between the two bands were helpful in crown
closure estimation.
5. The six bands of the TM image give us the best estimation in terms of
encompassing variability. However, the contribution of three of the bands
was insignificant, indicating multi-collinearity among the six bands.
6. The NIR, red and blue band adequately modelled the crown closure and
slightly reduced residual standard error in comparison with the use of all
six bands.
-20
-10
0
10
Greenness
20
30
0.6
0.8
1.0
1.2
(G-R)/(G+R)
Figure 7. Regression between crown closure (%) and redness, greenness and (G−R)/(G+R)
derived from K-T transform.
Crown closure estimation with L andsat T M imagery
1821
7. The third principal component in the PCA works similarly to the red band.
The combined use of the third and the second principle component gives
a similar result to that of NDVI in terms of variability explanation and
standard error.
8. The greenness in a K-T transform achieves similar estimation results to that
of NDVI.
9. Transformation of the DNs to radiance will not significantly improve the
estimation due to the inadequate increase in differentiating power of the NIR
and the red band by applying the coefficients provided.
10. Simple radiometric correction slightly improves NDVI and NDVISQ
estimation. However, it degrades single band and multiple band regression.
Further research on radiometric correction needs to be done to provide a more
accurate estimation and to explain how atmospheric condition influences the solar
radiance in each band of the TM image. More research on transformation of original
bands is needed to further improve the estimation results. The shadow problem
caused by topography needs to be solved before we can make use of the shaded side
of the imagery for crown closure estimation.
Acknowledgments
This research was partially supported by NASA (NCC5-492) and the Integrated
Hardwood Rangeland Management Program of California.
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