689 
exiting at the top of the canopy directly attributable to the soil (As), partly due to uncollided radiation and to 
multiple scattering: 
As(i2 0 ) = T- ip°(i2 0 ^')fi'di2' + P M (Q 0 )-P M Rs=0. W 
fKl 
2rt + 
L T 
As (%) 
(red) (near-infrared) 
1. 
76.16 
39.39 
3. 
17.89 
11.02 
5. 
2.03 
4.12 
7. 
0.21 
1.72 
Table-3: Percentage of the albedo due to brightness 
of the soil. 
This table shows that the retrieval of the leaf area index (Lj) / soil albedo (Rs) is questionable for leaf area 
indices greater than 3. since the signal is poorly conditioned (this means that the inversion process is in trouble 
for large L-p). 
3.2 - Data-set from Myneni & Asrar’s model 
The same inversion procedure was applied against bidirectional reflectance data generated using the complete 
DOM (Myneni & Asrar) with the same model parameters as in section 3.1. The results summarized in Table-4 
indicate that the values of the parameters are well retrieved in the red. In the near-infrared, big discrepancies can 
be observed between the true and retrieved values despite the apriori negligible differences we documented 
between our model and the DOM. If it is confirmed by further studies, this result emphasizes the need for a very 
accurate representation of multiple scattering contribution. 
L T 
HL 
tL 
Rs 
RMS 
1. 
0.0607 
0.0429 
0.2000 
0.9901 
0.0608 
0.0430 
0.1972 
0.29E-04 
2. 
0.0607 
0.0429 
0.2000 
1.9763 
0.0599 
0.0417 
0.1974 
0.41E-04 
3. 
0.0607 
0.0429 
0.2000 
3.0024 
0.0604 
0.0424 
0.2024 
0.34E-04 
1. 
0.4357 
0.5089 
0.2500 
1.7287 
0.4294 
0.5706 
0.0000 
0.53E-02 
2. 
0.4357 
0.5089 
0.2500 
2.2406 
0.4319 
0.5681 
0.0001 
0.30E-02 
3. 
0.4357 
0.5089 
0.2500 
2.6295 
0.4522 
0.5474 
0.0000 
0.10E-01 
Table-4: Retrieved values for the model parameters. 
red 
band 
near-infrared 
band 
CONCLUSION 
In its original formulation, the model proposed by Verstraete et al. [1990] doesn't include a representation of the 
soil effects. This limitation has been overcome in the present study. The model we developed is based on 
physical formulation derived from the radiation transport equation coupled to the hot-spot function given by 
Verstraete et al. In a direct mode, this model compares favorably well with previously proposed approaches and 
its accuracy and fastness (between 50 and 100 times faster than the DOM in inversion) make it a good candidate 
for further remote sensing applications. The inversion scheme shows that the properties of the leaves (reflection 
and transmission coefficients) are always well assessed. However, it was also shown that slight departures of 
only 2 to 5% in the bidirectional reflectance factor can lead to significantly different values for the retrieved 
optical thickness and soil albedo. This point must be investigated in the near future. 
APPENDIX 
Uncollided radiation I® (L,(i) is characterized by the following set of equations and boundary conditions: