## Appendix B Bidirectional Reflectance Distribution Function (BRDF) [PERSON] _et al._[78] developed a three-parameters nonlinear semi-empirical model of Bidirectional Reflectance Distribution Function (BRDF), which is explained against the scattering phase function (\(P\)) as:  
\[BRDF(\theta_{s},\theta_{v},\varphi)=\frac{k_{0}\cdot[\cos^{k_{2}-1}(\theta_{v })\cdot\cos^{k_{2}-1}(\theta_{s})]}{[\cos(\theta_{s})+\cos(\theta_{v})]^{1-k_ {2}}}\cdot P(\gamma)\ \cdot[1+R(\gamma)] \tag{11}\]  
where  
\[\left\{\begin{aligned} & P(\gamma)=\frac{1  
The three coefficients \(k_{0}\), \(k_{I}\) and \(k_{2}\) were computed from observations performed for different sun-zenith (0\(\cdot\)), view-zenith (0\(\cdot\)) and relative-azimuth (\(\varphi\)) angles. The scattering angle (\(\gamma\)) is explained against them. This BRDF modeling is based on the product of three parts. The first one is a combination of the view- and sun-zenith angles derived from Minnaert [79]. The second one is the desired phase function \(P\) whereas the third one explicitly accounts for the hot spot [1 + \(R(\gamma)\)]. This model was tested on many data sets from airborne and spaceborne measurements performed with the Polarization and Directionality of the Earth Reflectance (POLDER) instrument [80, 81]. As demonstrated by [PERSON] [82] and [PERSON] _et al._[83], it is quite reliable on the bidirectional observations. The measurement-model difference is less than a few percent.  
In order to assess \(P\), the model was applied to the annual land-cover of the GLC2000 classification [84, 85]. In the following, we only consider the land-covers of \"_Mixed Forest_\" and \"_Evergreen Needle Leaf_\" (for both the January and July periods) which are the more representative of our sampled sites. Hence, \(\sim\)64 quasi-homogeneous samples of BRDF measured during the space mission PARASOL (Polarization & Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) were considered for each case.  
POLDER did not perform measurements at 355 nm (resp. 1064 nm), but the behavior of the 490 nm (resp. 865 nm) channel seems close to the one for the 355 nm (resp. 1064 nm) wavelength regarding the reflectance spectral dependency [50]. We thus consider the channels centered on 490 nm and 865 nm. Obviously, the pixel size of POLDER is much bigger than the spaceborne lidar footprint (e.g., 20 m in diameter) and the POLDER information is much more integrated. Nevertheless, this is the only spaceborne instrument making multidirectional measurements at the global scale.  
The sampling sites of the GLC2000 reference database are not located in France because the POLDER pixel size (\(\sim\)6 km) is not compatible with the homogeneity of French forests. They are not exactly the same from one month to another since certain scenes could be cloudy [85]. An example of the cumulative probability density functions (CPDF) derived from the assessments of \(P\) is given in Figure 11 for the \"_Mixed Forest_\" at 490 nm and 865 nm. The RMS at 865 nm is smaller than the one at 490 nm, because of the less absorption of trees.  
Figure 11: Cumulative probability density functions (CPDF) for the mixed forest at 490 or 865 nm, during July 2006. It was derived from the POLDER-3/PARASOL BRDFs databases. The gray areas highlight the standard deviation.