630
canopy, 2rA. It also uses the scattering phase function of Henyey-Greenstein (1941) and a function, k,, which depends on
leaf orientation.
4.1.7 Verhoef (1984)
The Scattering by Arbitrarily Inclined Leaves (SAIL) model computes extinction and scattering coefficients inside a
canopy overlaying a lambertian soil. The distribution of the inclination of the leaves is discretely represented and, in this
implementation, no hot spot is accounted for. Considering the type of canopies to be studied, uniform distribution was
chosen.
The free parameters are p„ bare soil reflectance, p, and T lt leaf reflectance and transmittance and L, Leaf Area Index.
4.2 Method
The selected algorithm for the parameter retrieval is the minimization of the distance between predicted, p^, and
measured, p^, reflectances, using a least square computation. This minimization is achieved by the simplex algorithm
implemented in the Matlab library (The Mathworks, Inc.). The outputs of the procedure are the retrieved parameters p,
simulated reflectances, in the same geometrical configurations as the N available measurements and hemispherical
reflectances, i.e. direct albedos, as a function of solar zenith angle.
4.3 Inversion
The results of the fits are evaluated in terms of root mean square error (rjn.s.e„ Table 1) and correlation coefficient, C
(Table 2) . Most of the models predict closely the measured reflectances in all the spectral bands, even if a spectral
dependency can be observed on the statistics of the fit (Figure 3) realized using ASAS measurements. The main feature
of these plots is that the best fitting models are most of the time of empirical or semi empirical type.
Table 1 Root Mean Square Errors (,10 2 reflectance) of the fits of the different models, over the different sites,
for the Aircraft data spectral bands
Model
TM1
Cotton
XS1
XS2
XS3
TM1
Pecan
XS1
XS2
XS3
TM1
Soil
XS1
XS2
XS3
Deering
0.19
0.26
0.19
6.40
0.41
1.37
0.96
1.60
0.62
0.81
0.92
1.45
Hapke
0.13
0.12
0.13
8.43
0.68
0.92
1.50
5.18
0.88
1.70
2.60
3.52
Rahman
0.13
0.12
0.13
0.69
0.72
0.85
1.47
0.85
0.36
0.35
0.47
0.63
Roujean
0.14
0.15
0.13
1.16
0.68
0.85
1.22
1.30
0.63
0.63
0.78
0.80
Shibayama
0.17
0.19
0.18
1.12
0.62
0.74
1.12
1.12
0.63
0.71
0.99
1.17
Verstraete
0.12
0.11
0.13
1.11
0.30
0.45
0.81
1.44
0.59
0.69
0.92
1.00
Verhoef
0.16
0.28
0.20
5.08
1.06
1.33
1.84
2.93
0.88
0.99
1.47
1.75
Table2 Correlation coefficients of the fits of the different models, over the different sites,
for the Aircraft data spectral bands
Model
Cotton
Pecan
Soil
TM1
XS1
XS2
XS3
TM1
XS1
XS2
XS3
TM1
XS1
XS2
XS3
Deering
0.90
0.97
0.94
0.92
0.96
0.69
0.96
0.97
0.95
0.95
0.97
0.96
Hapke
0.95
0.99
0.97
0.68
0.89
0.88
0.82
0.81
0.91
0.76
0.78
0.77
Rahman
0.96
0.99
0.97
1.00
0.95
0.96
0.94
0.99
0.98
0.99
0.99
0.99
Roujean
0.95
0.99
0.97
0.99
0.89
0.89
0.88
0.98
0.95
0.97
0.98
0.99
Shibayama 0.91
0.99
0.95
0.99
0.91
0.92
0.90
0.99
0.95
0.96
0.97
0.97
Verstraete
0.96
1.00
0.97
0.99
0.98
0.97
0.95
0.98
0.96
0.97
0.98
0.98
Verhoef
0.94
0.97
0.95
0.99
0.74
0.75
0.86
0.91
0.90
0.92
0.94
0.94
4.4 Parameter retrieval
Among all the models, the SAIL model is the only one that involves explicitly optical properties of the leaves as
parameters. Still, some others, such as Verstraete or Hapke, include parameters that allow to retrieve these optical
characteristics. As it has been described in Pinty et al. (1990), it is possible, once the single scattering albedo and the
phase function parameter are known, to compute leaf hemispherical reflectance and tr ansmi ttance. Another model,
Deering, involves facet reflectance and transmittance and one can assume that these facets could be representative of the
leaves.
The results of the retrievals is showed on figure 4. As it could be expected, Hapke and Verstraete models give very similar
results for visible bands, for ASAS data as well as for aircraft data. The only significant discrepancy can be observed
