l/b 2 is only a scaling factor, which is 
constant for a whole image on a clear day. As 
a result, the WDVI sat is a suitable index 
since it corrects for soil background 
yielding relative differences. 
3.3 Atmospheric correction for the WDVI 
As seen in the previous section, the WDVI 
applied on satellite data still offers 
problems if a multitemporal analysis is 
requested (cf. Eq. 6). Originally, this index 
was derived for reflectance factors, not for 
digital numbers. The WDVI can be applied to 
satellite data correctly if an estimation of 
b 2 in Eq. (4b) can be obtained. In fact this 
corresponds to finding a procedure for 
converting the digital numbers to reflectance 
factors first, and subsequently applying the 
original WDVI concept. A first approach may 
be application of an atmospheric model for 
deriving reflectance factors for each 
spectral band (e.g. Verhoef, 1985). A second 
approach may be an empirical approach using 
only surface information. The first approach 
is beyond the scope of this paper; the second 
approach will be elucidated further. 
In order to extract reflectance factors 
from satellite data based only on surface 
information, it is necessary to estimate the 
coefficients a.^ a 2 and b lf b 2 in Eq. (4a) 
and (4b). The coefficients a 1 and a 2 are 
already estimated through the offset 
correction in section 3.2. In order to 
estimate the coefficients b^ and b 2 , it is 
necessary to have a second feature with known 
reflectance characteristics. This may be a 
point on the soil line (bright soil or parts 
of a city). It was found before that built up 
areas (concrete) have a constant reflectance 
factor of 20-35% in red and near-infrared 
(Colwell, 1983). If available, such areas 
seem to be suitable as a second calibration 
point (in addition to water surfaces). This 
approach is comparable to the approach 
applied before with multispectral aerial 
photography by applying reference targets in 
the field (Clevers, 1988b). 
4. EXAMPLE OF TM 
The above theory was tested for a Thematic 
Mapper scene of an agricultural area in the 
Netherlands. The study area was one of the 
new polders (Oost-Flevoland). The acquisition 
date of the images was 22 August 1984. A 
scene of 480 lines and 500 pixels per line 
was analysed. 
(1) Correlation matrix. 
The correlation matrix of the six reflective 
TM bands is given in Table 1. 
Bands 1, 2 and 3 were highly correlated, so 
were bands 5 and 7. Moreover, the former 
three appeared to be correlated clearly with 
the latter two for this scene. Band 4 shows 
hardly any correlation with the other bands. 
This confirmes the assumption that most 
Table 1: Correlation matrix for the TM scene 
analysed. 
1 
2 
TM 
3 
Band 
4 
5 
1 
1.00 
2 
0.96 
1.00 
3 
0.95 
0.96 
1.00 
4 
-0.34 
-0.15 
-0.29 
1.00 
5 
0.69 
0.80 
0.76 
0.25 
1.00 
7 
0.93 
0.94 
0.92 
-0.17 
0.86 
information can be caught with a red (TM band 
3) and a near-infrared (TM band 4) spectral 
band. This does not mean that the other bands 
cannot yield valuable additional information 
(in particular TM band 5), but for many 
applications the combination of a red and a 
near-infrared band may be sufficient. The 
original TM bands 3 and 4 are given in Figs. 
1 and 2, respectively. 
(2) Training set. 
First of all, a training set of 50 pixels 
was chosen consisting of the following 
features: water, urban area, bright soil, 
dark soil, small vegetation and dense 
vegetation. The water pixels offer the values 
for the offset correction (Table 2). 
Table 2. Offset values for the TM scene 
analysed. 
TM Band 
Offset value 
1 
77 
2 
28 
3 
20 
4 
13 
5 
3 
7 
1 
Fig. 3 illustrates the feature space plot of 
TM band 4 against band 3. The position of the 
soil line can be seen in this figure. 
(3) Offset correction. 
Subsequently, the offset correction can 
simply be performed by subtracting the offset 
values given in Table 2 from all pixel 
values. 
(4) Slope soil line. 
In order to calculate the WDVI sat of Eq. (6) 
the slope of the soil line must be 
ascertained from Fig. 3. This resulted into 
an estimated value of 1.23 (K in Eq. 6). 
WDVI sa t is now calculated as: 
WDVTgat = (TM4-13) - 1.23*(TM3-20). 
After normalization: 
WDVIsat = 0.631*(TM4-13) - 0.776*(TM3-20). 
440