5 - ON THE INVERSION OF BIDIRECTIONAL REFLECTANCE MODELS 
Once a period of composition and a sampling period have been chosen, it is in principle possible to monitor in 
time all parameters k- appearing in Eq. (1). This possibility should be considered with caution, because the 
retrieval of a given parameter kj may be more or less sensitive to errors, either originating from the 
measurements themselves (inaccuracies of the atmospheric corrections for example), or from the fact that the 
considered bidirectional reflectance model may not be perfectly adequate. We briefly report below the error 
analysis of Leroy and Roujean (1994) as an illustration of this. Their approach consists first in an estimation of 
the relative errors A/?,•//?,-, associated with each measurement (n°i) of reflectance, and proceeding from 
expected inaccuracies of all input values entering the atmospheric correction process (water vapor, ozone, and 
aerosol contents, and aerosol type). The second step is to deduce the relative errors on each of the retrieved 
parameters Akj / kj,j = 0,1,2, resulting from input errors of observed reflectances. The results are shown in 
Table 2, which indicates for 3 test sites, the average amplification ratio of errors, that is, the ratio of the 
relative error on a parameter, divided by the relative error on input reflectances (both relative errors being 
averaged over the whole study period). Table 2 shows that the average amplification ratio of errors is generally 
smaller than 1, which may be considered as satisfactory. By contrast, this ratio is significantly larger than 1 for 
k] and k 2 , from 3.4 to 10.4. Thus whereas the time profile of the corrected reflectance ko is likely to represent 
a physical evolution of the surface related to vegetation changes, the parameters kj and k 2 are very sensitive to 
input noise-like fluctuations and much care should be exercised in any attempt of interpretaton of their 
temporal variations in terms of a physical evolution of the surface. Analysis of time profiles of ki and k 2 
shows in fact some appearance of erratic behaviour. Leroy and Roujean (1994) interpret the high sensitivity to 
noise of k! and k 2 as a consequence of the fact that AVHRR data occupy a too limited place in directional 
space, since 0^ and <f> vary very little during a period of composition . 
Several issu 
accuracy of the re 
experiments on sele 
application of a bidir 
with which atmosphf 
to improve in the ne: 
al., 1994), General C 
is our personal opin 
corrections are perfo 
of free parameters to 
compromises have bt 
better than the other; 
the corrected reflect 
examined in the cas 
(Diner et al., 1989), 
much larger than for 
be much better cover 
ACKNOWLEDGM 
The author thanks M 
copy of their manusc 
Visible 
Near Infrared 
i = o 
j=l 
J = 2 
j = o 
j=l 
j = 2 
arid Crau 
0.79 
6.38 
6.57 
0.68 
7.12 
3.89 
Valensole plateau 
0.72 
0.79 
3.54 
0.71 
3.62 
3.42 
Beauce plain 
1.23 
7.31 
5.48 
1.11 
10.4 
6.82 
Table 2 : Average amplification ratio of errors, for each parameter kj, j = 0,1, 2 (from Leroy and Roujean, 1994) 
Rahman et al. (1993) report that inversion of bidirectional models describing the coupled surface- 
atmosphere reflectance is indeed possible with AVHRR data, which apparently contradicts the above results. 
They develop a semi-empirical model of surface reflectance, which they couple with a simple atmospheric 
radiation transfer model, designed to fit a standard atmospheric code. The coupled model is then inverted 
against a whole year of AVHRR data over several stable desert sites in Northern Africa. As in Cabot and 
Dedieu (1994), the period of composition is taken to be the whole study period. The authors show that this 
procedure allows in the visible the retrieval of the time averaged aerosol optical thickness over the selected 
sites. However, the authors recall that this encouraging result should not obviate the fact it has been obtained 
over stable sites with a large study period, which can probably explain the apparent discrepancy between these 
results and those mentioned in the previous paragraph. Further work is clearly needed to clarify this issue. 
CONCLUSION 
This paper has described new methods of composition of satellite-derived reflectances, developed in the 
context of vegetation monitoring on regional or global scales. The cornerstone of these methods is the 
recognition of the fact that directional effects, and particularly those originating from the surface, are an 
important source of noise in time profiles of reflectances. Their principle is to apply a regression between an 
observed set of reflectances, corrected or not from atmospheric effects, and a model describing the 
bidirectional properties of the target. Several parameters are retrieved in this process, which permit to 
reconstruct a reflectance corrected from angular effects, with a correlative loss of temporal resolution. The 
major advantage of these methods, compared to previous methods such as the Maximum Value Composite 
method, is that the retrieved corrected reflectances can in principle be compared between different dates, 
between different places, and between different sensors provided they have similar spectral bands. 
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