629 
To address this 
> cover the same 
ie surfaces. The 
ce computed for 
tance over 
tgle. Solar 
tance over 
gle. Solar 
les. and a slight 
for the hot spot, 
lot spot can be 
tional data were 
fects outside the 
ging from - 15% 
w zenith angle). 
7c more than the 
a not appear for 
smaller solar zeni th angle s The off principal plane measurements show the same general features as over bare soil, with 
a directional behavior a bit more important (from -10% to 40%). 
3.3 Pecan orchard 
Variations of the reflectance fall in a range of -30% to 120% around nadir reflectance with an increase of this range with 
solar zenith angle. The different bands show different behaviors, the red band being seemingly the most influenced by 
viewing direction and the near infrared the least. A very smooth hot spot can be observed on aircraft measurements 
especially in visible bands whereas this feature appears sharply on AS AS data. Also, a peak appears in forward scattering 
direction, in visible bands, corresponding to specular reflection direction, possibly due to the presence of water below the 
pecan trees. The large solar angle data show very strong directional effects (from -50% to 200%). No perpendicular plane 
data were available for this target. 
4. Models and inversions 
4.1 Models 
In the wide variety of available bidirectional reflectance models, we selected only 7. The selection was based on basic 
principles of the model, its physical basis and the number of parameters it involves. Also some indications relative to the 
“Stability” of the model, when available, where found most useful and a good argument for the choice of the model. 
The 7 selected models are: 
4.1.1 Deering, Eck and Otterman (1990) 
This model is derived from geometrical considerations. It allows calculation of the bidirectional reflectances of a 
landscape composed of a lambertian background, covered with protrusions and facets. 
The parameters of the model are the reflectance of a facet, r, the transmittance of a facet, t, the lambertian fraction of 
scattered light, f, the reflectance applicable to the lambertian fraction, r 0 , the reflectance of a protrusion, supposed 
opaque, r p , and the projected surface of the obstacles, S. 
4.1.2 Hapke (1981) 
This model was specifically desrgned to study planetary surfaces, using satellite bidirectional measurements of their 
surface reflectance. Therefore, it can be considered applicable to homogeneous semi-infinite medium composed of 
uniformly distributed scatterers such as bare soil surfaces. The parameters involved in the formulation are the average 
single scattering albedo of the particles, to, the phase function asymmetry factor, 0 and two parameters to control 
respectively the width and the magnitude of the hot spot effect, h and S H . 
4.1.3 Rahman, Pinty and Verstraete (1992) 
This model, developed in order to simplify the use of bidirectional models, is essentially a parameterization of the 
Verstraete et al. (1990) model and includes the same function, G,, to describe the effect of leaf orientation. The 
parameters of this model are p 0 , which represents a mean level for the reflectances, and k and 0 which account for the 
anisotropy of the surface. 
4.1.4 Roujean, Leroy and Deschamps (1992) 
This semi empirical model is aimed at correcting satellite measurements for directional effects. It is based on two main 
considerations: a geometrical computation of reflection and shadowing on the surface, and scattering by a volume filled 
with facets. These two contributions are supposed to add linearly. The model includes three empirical parameters, ko, k, 
andk 2 . 
4.1.5 Shibayama and Wiegand (1985) 
This empirical model has been developed to compare various off-nadir measurements as if they were nadir reflectance 
values. Though initially designed for wheat canopies, it seems worthwhile to test it over unknown cover, even close to 
bare soil. The parameters of the model are the nadir reflectance, Rq, and a set of three empirical coefficients, Po, p,, and 
h 
4.1.6 Verstraete, Pinty and Dickinson (1990) 
This analytical expression for the bidirectional reflectance is based upon physical and geometrical considerations of the 
transfer of radiation through a porous medium. Though developed for horizontally homogeneous vegetative canopies, it 
is fairly applicable over a semi infinite medium composed of unif ormly distributed scatterers such as bare soil. 
The model parameters are the average single scattering albedo of the particles, co, the asymmetry factor, 0, a 
characterization of leave orientation, %„ and a parameter which could be related to the interception cross section of the