686 
The extinction coefficient of the radiation transport equation uses the G-function (geometry factor or area 
extinction coefficient), which was first introduced by Ross [1981]. Physically, G (Op) is the mean projection of 
a unit foliage area in the direction iip (per unit volume of canopy): 
where g^ (Gl) is the probability density of the distribution of leaf normals with respect to the upper 
hemisphere. In the following applications, we have used the theoretical distribution functions of leaf normal 
inclinations proposed by Bunnik [1978]. 
The area scattering phase function T (ÌT—Q) is given by: 
where f (£T—Q,£2 l) > s 0> e leaf scattering distribution function. 
For a leaf with outward normal Ql> H represents the fraction of the intercepted energy (from photons initially 
traveling in direction Q') that is re-radiated into a solid angle about the direction £2. Here, we will assume that 
the leaves follow a bi-Lambertian scattering model: 
Fig-3: Ratio of the albedos due to uncollided radiation (a), single scattering (b) and multiple scattering (c) to the 
total scattering by an erectophile canopy, illuminated from a solar zenith angle of 30°, with a soil albedo of 0.2. 
The respective contributions to the total scattering due to the various terms (uncollided radiation, single 
scattering and multiple scattering) are plotted on Fig-3 (in terms of albedo) as a function of the single scattering 
albedo (o>=rL+tL) and leaf area index (Lj); note that the above calculations are obtained using the 1-D DOM, 
and do not include the hot-spot representation. It can be seen that uncollided radiation plays a very important role 
(Fig-3a) in the reflectance, especially for small values of Lj (its effect is the most sensitive for erectophile 
canopies). The single scattering part (Fig-3b) represents more than 50% of the total albedo in most part of the 
plane, and the contribution of multiple scattering (Fig-3c) is less than 50% excepted for large to and Lj. So the 
approximation of isotropic scattering for calculating of the multiply scattered radiances is not expected to have a 
significant impact on the results, especially for flux estimates. 
2rt + 
2n + 
if (Q.Ql)(G' Gl) <0 ( r ^ = leaf reflection coefficient) 
(h = leaf transmission coefficient) 
if (G.G l )(G'.Q l ) > 0. 
2 - NUMERICAL RESULTS 
o.o6 
0.05 
o.o* 
0.03 
0.02 
0.01 
0.00 
Fig-4: Polar plot of the bidirectional reflectance factor for a 
planophile canopy with: 
solar zenith angle of 50° 
Lj=8. 
i 
£ 
Rs=0.075 
iL=0.0609 & t L =0.0429 
2rA=0.1