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IAPRS & SIS, Vol.34, Part 7, "Resource and Environmental Monitoring", Hyderabad, India,2002
Output .- | Empirical model | E Input parameters
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Figure 1. Overview of the applied physical and empirical models
3. METHODOLOGY
3.1 Overview
Modelling of radiative transfer is usually established in the
forward direction, i.e. the model follows the way of the photons
from the sun to the observer to calculate sensor grey values
given some information about the surface and atmosphere. The
reverse direction is also referred to as model inversion with
given sensor grey values to derive information about the surface
and atmosphere. Figure 1. shows the combination of several
physical and a linear empirical model in the forward and reverse
mode. The model input is divided into constant and variable
parameters. The variable parameters, leaf area index,
chlorophyll content, specific dry matter and specific water
content, are part of the input parameters as well as the target
parameters of the model inversion. These parameters are chosen
because they show the highest variability within single fields,
whereas the other input parameters, e.g. the soil reflectance or
the leaf angle distribution, are assumed to be known and
constant. Output parameters of the physical models are sensor
grey values Chiro , that have to be fitted to grey values gl.
actually occurring at the test site. We use a linear empirical
model to attain fitted model-predicted grey values g^ der *
During the model inversion variable parameters are calculated
given the measured grey values. The model inversion is
conducted by a least-squares adjustment in combination with
simulated annealing.
In the following chapter a more detailed description of the
applied physical and empirical models with all input parameters
is given.
3.2 Physical and Empirical Models
3.2.1 The SAIL model
The SAIL model (VERHOEF 1984) calculates the directional
reflectance on top of the canopy as a function of structural and
spectral properties of the vegetation/soil medium. A functional
relation between vegetation- and soil parameters and directional
reflectance ,* can be sketched by
p^ - SAIl(LAL LAD, pj c, p? SKYE a, 2,2,,,) (1)
The vegetation canopy is considered as a homogeneous layer
characterised by leaf area index LAI, leaf angle distribution
LAD, as well as reflectance Pi and transmittance 7 / of the
leaves. Other input parameters of the SAJL model are soil
reflectance E diffuse percentage SKYL^ of the incoming
radiation, azimuth angle «a of the observer with respect to the
azimuth angle of the sun, zenith angle z of the observer, and
zenith angle z,,, of the sun.
3.2.2 The PROSPECT model
The PROSPECT model (JACQUEMOUD and BARET 1990)
provides hemispherical reflectance P and hemispherical
A A .
transmittance 7, of fresh leaves over the whole solar domain
given only four parameters
(p, 7?) - PROSPECT (chl,,,c,,.c,. N) (2)
The variables are the content of chlorophyll a and b chl,, the
specific dry matter c,, the specific water content c,, and a
structure parameter .N. The reflectance and transmittance of
