146
Chapter 16
distance between the measured bi-directional spectral reflectance factors and
the corresponding model simulations, in each available channel separately.
In a second step, the algorithm ranks the pre-selected biomes in
increasing order of the cost function separately in each channel, with a rank
of 0 for the best solution(s). This step thus ends with an ordered set of the
pre-defined solutions in each spectral channel individually.
In the last step, a quality index is evaluated to identify which entries in
the LUT lead to the smallest cost function in all spectral channels
simultaneously, and thus represent the most probable solutions. This quality
criterion is evaluated as follows:
where
is the number of biomes defined as possible solutions of the inverse
problem,
is the spectral weight associated with the corresponding spectral
band (set to 1 for all spectral bands in our application), and
specifies
the highest allowed rank beyond which the probability to find a given biome
is a priori considered very low. The radiative biome(s) for which
is
closest to 1 is (are) selected as the most probable solution(s). Since multiple
combinations of spectral ranks may give the same value for the function
there is no guarantee of finding a unique solution. The number of
solutions retrieved with an equal value of the quality criterion is controlled
by various factors, including the radiation transfer regime itself. Two or
more geophysical situations may lead to indistinguishable radiance fields
measured by the satellite. The noise inherent to the measuring instrument
will of course further blur the slight differences between the radiative
signatures of similar environments, and will lead to the identification of
multiple solutions.
3.
EXPERIMENTS AND RESULTS
The LUT contains the values of bi-directional reflectance factors
computed with the semi-discrete model for a large number of vegetation
types (made up of healthy green leaves only) and for an appropriate set of
illumination and observation angles. Table 1 lists the different “radiative
biomes”, which are defined in terms of the model parameters. The 35 biome
types considered here were selected to cover most typical radiance values (in
the red and near-infrared bands) actually observed with the AVHRR
instrument.
Chapter 16
distance between the measured bi-directional spectral reflectance factors and
the corresponding model simulations, in each available channel separately.
In a second step, the algorithm ranks the pre-selected biomes in
increasing order of the cost function separately in each channel, with a rank
of 0 for the best solution(s). This step thus ends with an ordered set of the
pre-defined solutions in each spectral channel individually.
In the last step, a quality index is evaluated to identify which entries in
the LUT lead to the smallest cost function in all spectral channels
simultaneously, and thus represent the most probable solutions. This quality
criterion is evaluated as follows:
where
is the number of biomes defined as possible solutions of the inverse
problem,
is the spectral weight associated with the corresponding spectral
band (set to 1 for all spectral bands in our application), and
specifies
the highest allowed rank beyond which the probability to find a given biome
is a priori considered very low. The radiative biome(s) for which
is
closest to 1 is (are) selected as the most probable solution(s). Since multiple
combinations of spectral ranks may give the same value for the function
there is no guarantee of finding a unique solution. The number of
solutions retrieved with an equal value of the quality criterion is controlled
by various factors, including the radiation transfer regime itself. Two or
more geophysical situations may lead to indistinguishable radiance fields
measured by the satellite. The noise inherent to the measuring instrument
will of course further blur the slight differences between the radiative
signatures of similar environments, and will lead to the identification of
multiple solutions.
3.
EXPERIMENTS AND RESULTS
The LUT contains the values of bi-directional reflectance factors
computed with the semi-discrete model for a large number of vegetation
types (made up of healthy green leaves only) and for an appropriate set of
illumination and observation angles. Table 1 lists the different “radiative
biomes”, which are defined in terms of the model parameters. The 35 biome
types considered here were selected to cover most typical radiance values (in
the red and near-infrared bands) actually observed with the AVHRR
instrument.