Agriculture Reference
In-Depth Information
Table 9.4
Evaluating the effect of interfering factors by coefficients and by their geometric means
Factors and coefficients
Zenith
Clouds
Soil
Geom. mean
CzCcCs
Standard spectral indices
Cz
Cc
Cs
3
Reflectance at 550 nm (green)
4.5
0.2
6.6
1.9
Reflectance at 670 nm (red)
7.2
0.8
8.4
3.6
Reflectance at 800 nm (near-infrared)
5.1
5.7
1.2
3.2
Ratio of near-infrared to red reflectance
7.4
4.9
7.9
6.6
Ratio of near-infrared to green reflect.
12.9
4.2
19.0
10.8
Normal. differ. veget. index (NDVI)
11.9
2.7
12.6
7.4
Soil adjusted vegetation index (SAVI)
11.5
7.4
32.4
14.4
Red edge infl. point, num. differentiat.
45.9
10.7
21.8
22.0
Red edge inflect. point, appr. formula
61.9
12.7
10.1
19.8
Large coefficients mean low interferences (From Heege and Reusch
1996
)
to the change of the interfering factor such as the solar zenith-angle, the cloud-cover
or the colour of the soil. Hence the coefficients represent the respective signal to
noise ratio. Its suffixes z, c, and s stand for the zenith angle, the cloud cover or the
soil colour respectively.
In Table
9.4
, the coefficients of the interfering factors are listed. The larger the
coefficients are, the lower the interference by the respective noise factor is and
hence the more reliable the reflectance index is.
Since
natural illumination
provided the reflectance and consequently all three
interference factors are important, it seems reasonable to use the mean of the coef-
ficients as criterion. Instead of arithmetic means,
geometric means
are listed in the
right column of Table
9.4
. This is because generally geometric means are superior
to arithmetic means when normalized results or ratios are averaged. And this is the
case with the coefficients.
Regarding the geometric means, the best results -
i.e.
the lowest average noise
- can be obtained with the
red edge inflection point
indices. These indices on the
one hand depend very clearly on the nitrogen supply of the plants (Table
9.3
) and on
the other hand are not much influenced by the interfering factors. The widely used
normalized difference vegetation index (NDVI) is on the average much more
affected by these interfering factors. The soil adjusted vegetation index (SAVI) as
well as the ratio of the near-infrared to green reflectance can be regarded as candi-
dates in intermediate positions. However, when looking at the individual interfer-
ence factors or its coefficients, it can be seen that the average “noise” ranking of the
soil adjusted vegetation index results from the very low influence that in this case is
exerted by the factor soil (red soil column in Table
9.4
). On the other hand, the out-
standing rankings of the red edge inflection point indices originate from the low
influence (large coefficients) that the radiation factors zenith angle and clouds have.
If solely
artificial illumination
provides the reflectance, noise from changing
solar zenith angles or from varying cloud covers practically is excluded. Hence
from the coefficients listed, only the factor soil remains (Table
9.4
). However, this
