data consisting of digital numbers or 
radiance values. However, generally, digital 
numbers or radiance values are linearly 
related to the corresponding reflectance 
factors of the object at the earth surface, 
but this calibration step is highly dependent 
on the irradiance and the atmospheric 
conditions during recording. Usually, the 
latter are not known accurately. As a result 
the step towards reflectance factors is 
expected to be difficult. However, in order 
to perform a multitemporal analysis, this 
step is essential. 
The Greenness and the PVI are vegetation 
indices that are often applied to satellite 
data. Since the previously derived WDVI (Eg. 
1) is related to these indices as seen 
before, it should be possible to derive a 
procedure for applying the WDVI to satellite 
data. 
ascertained for the red and near-infrared 
spectral band. Richardson & Wiegand (1977) 
also used clouds and cloud shadows. It may 
also be investigated whether objects like 
cities (constant reflectance factor in time) 
can be used for this purpose. The 
near-infrared/red ratio of the digital 
numbers of soil objects after offset 
correction offers the value for the constant 
C in Eq. (2) : 
[DN(nir)-a 2 ]/[DN(red)-a 1 ] = b 2 /b 1 .R(nir)/R(red) 
= b 2 /b^.C 
(3) Calculation of the WDVI. 
In Eq. (1) the WDVI was defined as: 
WDVI = R(nir) - C.R(red) 
In terms of DN this WDVI can be written as: 
3.2 Concept 
The relationship between digital number (DN), 
measured at the sensor in terms of a 
radiance, and the reflectance factor (R) of 
an object can be described in the general 
form (cf. Clevers, 1986): 
DN = a + b . R (4) 
in which DN, a, b and R all are wavelength 
dependent. 
For a red and near-infrared spectral band, 
respectively, we may write: 
DN(red) = a i + b i ■ 
. R(red) 
(4a) 
DN(nir) = a 2 + b 2 
. R(nir) 
(4b) 
WDVI = (DN(nir)-a 2 )/b 2 - C.(DN(red)-a 1 )/b 1 
= l/b 2 .[(DN(nir)-a 2 ) - K.(DN(red)-a 1 )] (6) 
with K = b 2 /b^.C. 
The term [(DN(nir)-a 2 ) - K.(DN(red)-a^)] 
is called the WDVI for satellite data 
(WDVI sat ). It can now be calculated. Problem 
is the factor l/b 2 which is unknown. This 
means that Eq. (6) does not offer an accurate 
atmospheric correction procedure in a 
multitemporal analysis. The WDVI may be used 
in a multitemporal analysis of satellite data 
if the factor l/b 2 does not vary much between 
recording dates. The same conclusion was 
drawn for the Greenness and the PVI (Jackson 
et al., 1983a, 1983b). Suggestions for a more 
general solution are given in the next 
section. 
Since the WDVI is based on a straight soil 
line through the origin of a near-infrared - 
red feature space plot, a possible procedure 
could consist of the following three steps: 
(1) Offset correction. 
Perform an offset correction for the red and 
near-infrared spectral band, respectively 
(cf. darkest pixel method; e.g. Sabins, 1978; 
Jensen, 1986). The offset correction for each 
band is performed by ascertaining the DN of a 
dark object (e.g. water or clouds) or the 
minimum value of the histogram of a complete 
image in the relevant band, and subsequently 
subtracting this value from all pixel values 
in that spectral band. In terms of Eq. (4) 
this implies: 2 
A problem might arise if the offset 
correction cannot be performed due to the 
absence of water bodies in the image. Still 
the WDVI can be calculated as before, based 
upon the digital numbers of the soil features 
used for ascertaining the slope of the soil 
line (see before). This soil line can be 
written as: 
DN(nir) = A + B . DN(red) (7) 
It is easy to deduce that: 
A = a 2 - K . a 1 , and 
B = K. 
As a result Eq. (6) can be written as: 
WDVI = l/b 2 .[ DN(nir) - B.DN(red) - A ] (8) 
[DN(red) - a 1 ] = ^ . 
. R(red) 
(5a) 
[DN(nir) - a 2 ] = b 2 
. R(nir) 
(5b) 
(2) Slope soil line estimation. 
It is assumed that one soil line (which runs 
through the origin after the offset 
correction) is valid for a complete image. 
The digital pixel values of dark and bright 
soil objects (if present) in the image are 
Eq. (8) is similar to Eq. (6) except that no 
offset correction is needed. For a multi 
temporal analysis, the factor l/b 2 is still 
a problem. 
If only one recording date has to be 
analysed (monotemporal analysis), atmospheric 
correction does not play an essential role 
for many applications (often only relative 
differences are required). Then, the factor 
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