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Mesures physiques et signatures en télédétection

J. Iaquinta & B. Pinty
Université Blaise-Pascal, Laboratoire de Météorologie Physique, URA 267/CNRS,
F-63177 Aubière Cedex, France.
This model presents an improvement of the original model by Verstraete et al. [1990] in order to account for the
effects due to an underlying soil below the vegetation canopy. The singly scattered component is solved exactly
using an analytical hot-spot description. The multiply scattered component is approximated on the basis of a
Discrete Ordinates Method reduced to a one-angle problem. This model is then compared to others existing
reference models and it is also used in an inversion procedure to examine its performances for real remote sensing
KEYWORDS: Bidirectional Reflectance Factor, Hot-spot, Inversion.
The global monitoring of the state and evolution of the terrestrial surfaces requires a quantitative interpretation of
satellite measurements at a very high spatial and temporal resolution. This interpretation of remotely sensed data
should rely on the inversion of physically based models representing the radiance field emerging from the
medium under study. The highly anisotropic behavior of the bidirectional reflectance over a vegetation canopy, in
the optical domain, requires a careful and accurate modeling of radiation transfer. This implies that we are able to
link the biological and physical properties characterizing the surface to parametric radiative quantities including
the phase function (which describes the angular distribution of the energy scattered by a particle), the single
scattering albedo (ratio of the scattered energy to the total energy either scattered or absorbed) and the leaf area
index (area of one-side leaf surface projected onto a horizontal plane). In general, it is not possible to find an
analytical solution for the total radiance field, except for the single scattering contribution, and consequently
numerical schemes have to be used for solving exactly the integro-differential equation with appropriate boundary
conditions. In this paper we present a new model where the single scattering component, including the hot-spot
and the underlying soil effects, is given explicitly through an analytical solution and where the multiply scattered
radiance, which is more difficult to handle, is approximated using a Discrete Ordinates Method (DOM), reduced
to a one-angle problem. This modeling approach is clearly based on a compromise (and hence some
approximations) between purely analytical (fast) and numerical (accurate, but very time consuming) methods.
Therefore, the model we propose appears as a good candidate for inversion purposes to the extent that any
inversion technique will require computationally cheap formulations.
In the first section of this paper, we present the model and describe the modelling strategy. Test examples are
shown in the second section, together with a comparison between the results obtained from our model and those
given by (1) Nilson & Kuusk’s model [1989], in which the multiple scattering is calculated according to the
Schwarzschild approximation, and (2) the more accurate results given by the resolution of the transport equation
using a complete 3-D DOM [Myneni R. B. and Asrar G., 1993]. In the third section, we apply an inversion
technique against synthetic data generated by our model and the 3-D DOM code. The results are discussed in light
of the ability of retrieving accurately and simultaneously the leaf area index and the optical properties of the
Fig-1: Schematic decomposition of the radiation field. Fig-2: Geometry of illumination and observation.