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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