IAPRS & SIS, Vol.34, Part 7, “Resource and Environmental Monitoring", Hyderabad, India,2002
leaves calculated with the PROSPECT model are used as input
parameters for the SAIL model.
3.2.3 The SOLSPEC model
A simple solar spectral model is used to transform the
directional reflectance on top of canopy to spectral band
radiances L^ at the sensor. The SOLSPEC solar spectral model
(BIRD 1984) calculates direct normal E^. and diffuse
direct
irradiances E^ Ls at tilted surfaces as well as the diffuse
percentage SKYL^ of the incoming radiation, which is an input
parameter of the SAIL model. Input to SOLSPEC includes date,
time and position, the surface orientation, the temperature, the
amount of precipitable water vapour, ozone, and the surface air
pressure.
(EÀ EA S SKYE )- SOLSPEC(date,time,...) (3)
No further atmospheric corrections are applied. Given the total
incoming radiation E^ 4 Eine and the directional
direct
reflectance of the vegetation canopy vo, the spectral band
radiances L# at the sensor can be calculated.
I = (E d um * E d n jo à (4)
mc
3.2.4 The sensor model
A sensor model is applied to transform the continuous spectral
band radiances L* at the sensor into band specific grey values
gt . First the spectral sensitivities of the sensor bands are
phys-mod
taken into account to calculate representative spectral radiances
for each band. Then with given calibration constants of the
sensor and the representative spectral band radiances grey
A ~ e
values Cm can be calculated.
3.2.5 The empirical model
As mentioned above the grey values EUR , have to be fitted
to the grey values gi. actually occurring at the investigated
test site using simple parameters such as offset a^ and scale p^
for each sensor band. These parameters are assumed to be
constant for each dataset. This linear fitting is necessary due to
simplifications made in the physical models and uncertainty of
constant model parameters.
The model-predicted sensor grey values g^ de are calculated
by linear transformation of the grey values a „a using
À À Ag, 4
& model = +b & phys-mod ©)
Figure 1. illustrates the calculation of the model-predicted
sensor grey values gi from input parameters using the
described physical and empirical models.
3.3 Inversion process
During the inversion process, an optimal set of variable input
parameters is estimated from the given grey values by non-
linear and linear optimisation methods for each pixel (v. Figure
1.). In our approach the inversion of the applied models was
conducted by the global optimisation method simulated
annealing (HELLWICH 1999) followed by a conventional /east-
squares adjustment using a Gauss-Markov model (MIKHAIL
1976) with weighted observations. There is a redundancy of five
for each pixel with the measured grey values sa in nine
spectral bands as observations and four unknown vegetation
parameters, LAI, chlçp, Cm, and €, In addition the offset a^ and
scale b^ are introduced as unknown parameters as well as
observations. The introduction of pseudo observations a*=0 and
b*=1 with low weights supports the inversion process. The
pseudo observations decrease the influence of weak ground
control points and reduce ambiguities.
The empirical parameters a^ and 5^ should be estimated once
for each dataset, which leads to 2x9 additional unknown
parameters for a single dataset. The ground truth parameters
measured on the selected ground control points are also
introduced as observations being uncertain to a degree
corresponding to the acquisition method. All other input
parameters are assumed to be known and constant in the
inversion process. Now the unknown empirical parameters and
the vegetation parameters for each pixel can be estimated in a
simultaneous least-squares adjustment. For this approximate
values for the unknown vegetation parameters are necessary.
First approximate values for the offset and scale parameters can
be estimated through linear regression with the grey values
A A
DER and measured grey values g” of at least two ground
control: points. Then approximate values for the unknown
vegetation parameters are estimated using simulated annealing.
As an alternative, standard values of the unknowns may be used
as approximate values.
The poor robustness of the inversion process is the main
problem. The inversion fails, if vegetation parameters leave the
definition range or the maximum number of iterations is
reached. To improve the accuracy and robustness some
enhancements have been implemented.
e Pixels not representing the main crop, e.g. tracks of
agricultural machines and weed, are eliminated from
the estimation process. For the extraction of these
disturbances, some classification methods have been
suggested (KURZ et al. 2000).
e Robustness and accuracy are improved by averaging
grey values of neighbouring pixels belonging to
homogenous areas.
e To restrain the vegetation parameters inside the
definition range a penalty technique was applied
during simulated annealing. If vegetation parameters
leave the definition range during the least squares
adjustment the parameters are set back to values at the
edge of the definition range. If this procedure is not
successful, the corresponding point will finally be
eliminated.
4. RESULTS
4.1 Database
The investigations were conducted under the umbrella of the
Forschungsverbund Agrarôkosysteme München (FAM,
Research Network Agricultural Ecological Systems Munich),
which is presently using the Daedalus multispectral scanner as
standard remote sensing instrument. For the /.5km^ FAM test
sites in north of Munich, Daedalus multispectral scanner data
and colour-infrared aerial photography were acquired. Flight
dates were 28 June 2000 and 27 June 2001, when winter wheat
changes to maturity. The Daedalus multispectral scanner
operates in 1 spectral bands of the VIS, NIR, SWIR and TIR
spectra. Nine of these channels are used in the inversion
process. The ground pixel size amounted to 1.33 m. The
Daedalus image data were geocoded by matching with ortho
imagery with a ground pixel size of 0.06 m. The influences of
the wide scan angle (RICHTER 1992) on the radiometry of the
Daedalus scanner were corrected by DLR.
At several fields with winter wheat randomly distributed
measurement sites were selected each year. At these sites as
C. Qu dut «i» w-
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