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2 - THE INVERSION PROCEDURE 
2.1. The data set. 
Two field experiments have been used: Broom's Bam (England, 52.16° N-0.34° E) in 1989 and Grignon 
(France, 1° N-1.58° E) in 1990. They are described in details by Malthus (1990, 1991). In both experiments, 
sugar beet (Beta vulgaris L) plots were grown to provide a wide range of canopy leaf area index by varying the 
sowing date, plant density. Chlorophyll concentration was also manipulated by inducing chlorosis either by 
transmitting the yellow virus or spreading various quantities of herbicides. For each plot, the chlorophyll 
concentration C ab , water equivalent thickness and leaf area index LAI were measured. We evaluated the 
mean leaf inclination angle 0, by two methods: The first one involved direct clinometer measurements on three 
plots during the Broom's Bam experiment and found an average value of 43.4°. This was done on four plots 
during the Grignon experiment that provides an average value of 35.3°. Because of the difficulty to get an 
accurate value of 0, through direct clinometer measurement, a second method was developped. It was based on 
the analysis of the directional variation of gap fractions measured with hemispherical photographs (Baret et al., 
1993). It demonstrated that an ellipsoidal distribution with and average leaf inclination value of 28.6° allowed a 
good description of gap frequencies. The disagreement between actual leaf inclination measurements and the 
average leaf inclination estimated through hemispherical photographs was attributed to the regularity of the 
canopy. The size and shape of the leaves as well as canopy height were also measured. Soil backgrounds were 
manipulated on most of the plots. This was performed by placing artificial backgrounds (trays of peat or sand, 
white or black fabrics) under the canopy. This resulted in 96 plots expressing a large range of variation of leaf 
area index (0<LAI<5), chlorophyll concentration (10<C aft ,<50 pg.cnr 2 ), equivalent water thickness 
(0.025<C H ,<0.050 cm 1 ) and soil backgrounds (0.05<p s <0.80). 
Canopy reflectance spectra were acquired at nadir using the GER MK IV IRIS 
spectroradiometer. It has two fields of view of 3° x 6.5° and was fixed at 5m above the canopy. One field of 
view was looking at the target, while the other was looking at a white panel (Barium sulfate) to correct for the 
irradiance conditions. Radiometric measurements were acquired in 975 contiguous bands from 350 nm to 2500 
nm with a spectral resolution of 2 nm, 4 nm, and 5 nm respectively for the 400-1000 nm, 1000-1800 nm. and 
1800-2500 nm domains. A minimum of 3 replications were performed on each plot allowing a good spatial 
representativity and some smoothing of the radiometric signal. The fraction of diffuse radiation was recorded 
over the duration of the experiment. During radiometric measurements, the sun zenith angle was in the 25-35° 
range. Absolute bidirectional reflectance were derived from laboratory measurements of the spectral and 
bidirectional behavior of the reference panel. We applied gaussian filters of selected widths and positions to 
simulate the 224 AVIRIS (Green, 1992) wavebands. Due to atmospheric water absorption, the 1352-1451 nm 
and 1757-1949 nm spectral regions were not used so that 188 wavebands were available in practice. Using the 
spectral response of the six Thematic Mapper (TM) filter functions, we also simulated the equivalent signal 
measured by this sensor (Markham and Barker, 1985). 
2.2. The models 
SAIL model (Verhoef, 1984, 1985) assumes the canopy to be horizontally homogeneous and infinitely 
extended, made of lambertian scatterers randomly distributed. The azimuth of the scatterers is assumed to be 
randomly distributed while the zenith angle (leaf inclination) follows an ellipsoidal distribution characterized 
by the average inclination angle. Although using a very simple description of canopy structure and rough 
approximation of the radiative transfer equation, SAIL model has already been tested with success on soybean 
(Goel and Thompson, 1984a, b) and maize (Major et al., 1992). The initial version of SAIL model was 
modified to take into account the hot-spot effect as suggested by Kuusk (1991). It is described by a hot-spot 
parameter (s) defined as s=LIH where L is the horizontal correlation length that depends on the size and shape 
of the leaves, and H is the canopy height. Leaf reflectance and transmittance are derived from the PROSPECT 
model (Jacquemoud and Baret, 1990). This model caricatures the leaf as a stack of N identical elementary 
layers defined by their refractive index and an absorption coefficient. The absorption coefficient is assumed to 
be a linear combination of the specific absorption coeffcients of each absorbing material, weighed by their 
concentration. For simplicity, only chlorophyll and water were explicitely taken into account and assumed to bp 
homogeneously distributed in the leaf. The radiative transfer computation considered only upward and 
downward hemispherical fluxes inside the leaf. 
The measurement configuration is defined by zenith 0 O and azimuth <p c viewing angles, solar 
zenith angle 0 S and fraction of diffuse radiation skyl(k). The fraction of diffuse radiation was described by the