empirical coefficients. For this purpose, different simulation
studies with synthetic sensor data have been conducted based on
varying ground control and mass points constellations. The
theoretical accuracies are estimated for different combinations
of ground control and mass points. Using the accuracies at all
synthetic points, the RMS (root mean square error) for each
vegetation parameter expressed in percent of the mean value has
been calculated. The results show that the RMS's of the
vegetation parameters remain constant by using at least two
ground control points (v. Figure 5. left), whereas the RMS's
increase by using less than two ground control points, i.e.
inversion with real data would fail, because most vegetation
parameters leave the definition range. Furthermore the
accuracies become higher by using more mass points (v. Figure
5. right), ie. each point contributes information to the
estimation of the empirical coefficients.
Note, that the accuracies and robustness of the inversion depend
also on the quality of the measurements at ground control points
and the spectral distribution of these points. For practical
applications the ground control points have to be selected before
or during the data acquisition and should ideally cover the
whole range of grey values in each band. Unfortunately, the
selection can be based only on the visual appearance of the
fields unless there are multispectral data available before or
during the data acquisition. Thus, the selection of ground
control points is based only on the visual bands independent of
the grey values of these points in all other bands.
IAPRS & SIS, Vol.34, Part 7, "Resource and Environmental Monitoring". Hyderabad, India,2002
Generally spoken, the robustness of the inversion process can be
increased by using more than one ground control point. In this
case the ground control points should be spectrally well
distributed in their visual appearance. Using one or less ground
control points, accuracies and robustness may be poor. By using
only one ground control point, the grey values in the visible
bands of this point should lie near the centers of the grey value
range for acceptable accuracies.
4.4 Influence of constant model parameters
During the inversion process the constant model parameters
have to be set to realistic values, which are partly difficult to
determine. Uncertainties of constant model parameters
influence the inversion process, but can be attenuated through
the empirical fitting of the physical models. Our goal is to
investigate which constant parameters can be set to any values
within the definition range and which should be adjusted to the
actual situation. Thus, the accuracies of the vegetation
parameters are computed as a function of constant parameters,
which vary within their definition range. Results of different
simulation studies show that only the soil reflectance influences
the accuracies of the vegetation parameters. All other constant
parameters can be set to any values, because a variation of these
parameters only slightly influences the accuracies.
Figure 6. shows a simulation study with synthetic data to
demonstrate the influence of wrong soil reflectances on the
accuracies.
rR oH HX
foe 999-9
—e- Empirical coefficient a
-o- Empirical coefficient b
—— Leaf area index
—x- Chlorophyll content
—x-- Specific dry matter
x. Water content
80; 60!
T 60 L m
Lu 3s
N N
M 20|
20r[ & CZ 7
car E Ô-
TO mm =m mm
ge ) ; Su 0
0 1 2 3 4 20
Number of ground control points
Figure 5. Simulation studies with synthetic sensor data: Relation between the number of ground control points and the RMS errors
of the estimated parameters (left) and relation between the number of mass points and the RMS errors of the estimated
parameters (right).
40 60 80
Number of mass points
—6— Empirical coefficient a
-o- Empirical coefficient b
—3»*— Leaf area index
—*- Chlorophyll content
—x.- Specific dry matter
x. Water content
200 T 7 T 150
150; j 3 "a
=z j' JE pe 1007
T / X AN =
o 1090] A 7f 0
= y =
a & 50;
50r
7 SN A
0 à mem i 0 à
A* E D C B A
Soil type
Figure 6. Simulation studies with synthetic sensor data to demonstrate the efficiency of the empirical model: Theoretical RMS
errors of the estimated parameters, which are calculated by model inversions with varying soil types [according (STONER
and BAUMGARDNER,1981): A4 organic-dominated, B minimally altered, C iron-affected, D organic-affected, E iron-
dominated] and three ground control points. The synthetic sensor data are created using the reflectance of the marked (*)
soil type and finally inverted with "wrong" soil reflectances of five soil types. Left: inversion of synthetic data generated
D CC B
Soil type
with soil type 4 (dark soil). Right: inversion of synthetic data generated with soil type C (bright soil).
m mA A M... 040... 80. M —M M Uu MM UL RR AS
m p 65 0p peed PS eed)
beo ppl
b CS — ML
