The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
Far-red line: D= miA+C] (3)
N1R line'. D= m 2 .X,+c 2 (4)
where m and c represent the slope and intercept of the straight
lines, respectively. At the intersection, the two lines have equal
wavelengths and D values. Therefore, the REIP, which is the
wavelength at the intersection, is given by:
R1EP
LEM
- (c, - c 2 )
Oi - m 2 )
(5)
Partial least squares regression (PLSR) is a technique that
reduces the large number of measured collinear spectral
variables to a few non-correlated latent variables or factors
while maximizing co-variability to the variable(s) of interest
(Atzberger et al., 2003; Cho et al., 2007; Geladi and Kowalski,
1986; Hansen and Schjoerring, 2003). The latent variables
represent the relevant information present in the measured
reflectance spectra and are used to predict the dependent
variables (here, biophysical and biochemical grass
characteristics). As with other linear calibration methods, the
aim is to build a linear model:
content. The best performing indices and the band positions are
tabulated in Table 2.
It can be observed from Table 2 that narrow band SAVI2 had
somewhat higher correlations than narrow band NDVI with the
studied variables. However, the coefficients of determination
between the grass characteristics and the indices were relatively
low. Studying regions where R 2 >0.6 for LAI and canopy
chlorophyll content (CCC) revealed that LAI had a strong
influence on the selection of suitable bands for estimating
canopy chlorophyll content. The similarity in the observed
patterns is obviously due to the high correlation between the
two variables (not shown).
600 800 1000 1200 1400 1600 1800 2000 2200 2400
Wavelength nm
Figure 1. 2-D correlation plots illustrating the coefficient of
determination (R 2 ) between narrow band SAVI2 and LAI.
Y=X|3+e (6)
where Y is the mean-centred vector of the response variable
(grass characteristics), X is the mean-centred matrix of the
predictor (spectral reflectance), P is the matrix of coefficients,
and e is the matrix of residuals.
The optimum number of factors was estimated by leave-one-out
cross-validation. A common way of using cross-validation for
this estimation is to select the number of factors that minimizes
the RMSE (Geladi and Kowalski, 1986). To prevent collinearity
and to preserve model parsimony, the condition for adding an
extra factor to the model was that it had to reduce the root mean
square error of cross-validation (RMSE C v) by >2% (Cho et al.,
2007; Kooistra et al., 2004). In addition, coefficients of
determination (R 2 ) between measured and predicted values in
the cross-validation were used to evaluate the relationships
found. The PLSR analysis was performed using the TOMCAT
toolbox 1.01 within MATLAB (Daszykowski et al., 2007).
3. RESULTS
Variables
Narrow
band VI
X,[nm]
R 2
LAI
NDVI
1105/1229
0.61
SAVI2
1998/1402
0.64
CCC
NDVI
1141/1150
0.68
SAVI2
1211/1086
0.69
Table 2. Band positions and R 2 values between the best narrow
band NDVI and SAVI2 (derived from 2-D correlation plots of
different data sets) and grass variables.
For the best performing narrow band index, cross-validated R 2
and relative RMSE (RRMSE = RMSE/mean) were computed
from linear regression models (Table 3). As can be observed
from this table, compared with narrow band NDVI, narrow
band SAVI2 gave slightly higher R 2 and lower RMSE values
for LAI and canopy chlorophyll content. The better
performance of SAVI2 compared with NDVI is probably due to
the fact that SAVI2 is less sensitive to external factors such as
soil background effects.
3.1 Hyperspectral vegetation indices
NDVI and SAVI2 narrow band vegetation indices were
calculated from the measured canopy reflectance spectra, using
all possible two-band combinations. The coefficients of
determination (R 2 ) between these narrow band vegetation
indices and the grass canopy characteristics were computed. An
illustration of these results is shown for LAI in the 2-D
correlation plot in Figure 1. The meeting point of each pair of
wavelengths in a 2-D plot corresponds to the R 2 value of LAI
and the vegetation index calculated from the reflectance values
in those two wavelengths. Based on the R 2 values in the 2-D
correlation plots, band combinations that formed the best
indices were determined for LAI and canopy chlorophyll
Variables
Narrow
band VI
R 2 cv
RRMSE CV
LAI
NDVI
0.60
0.34
SAVI2
0.63
0.33
CCC
NDVI
0.67
0.36
SAVI2
0.68
0.35
Table 3. Performance of narrow band vegetation indices for
predicting grass variables in Majella National Park, Italy.