is is typically the case 
t the measured signal 
be useful in practical 
sets of the atmosphere 
estimated from them, 
nations, and probably 
t. Initially, vegetation 
t part, one in the red 
ntion was given to the 
id Tanre, 1992; Pinty 
by Holben, 1986) were 
minimising dVI/dSj. 
ears. 
ablished, one for each 
i indices and variables 
precipitations to large 
lumber of independent 
ided by this practice: 
index, or if more than 
Zk, these variables are 
unless these relations 
d treatment than will 
ising instrument, even 
: spectral responses of 
ons y = g( Z) already 
nsors currently under 
of s imil ar sensors, for 
he number of channels 
lonstrated by pointing 
From two wide-band 
i vegetation index, the 
« this albedo from the 
i, namely those that 
than being able to 
parameters can be 
mally, these models 
Z(r,f,A,n) 
[t. s<yi) 
Y(f,t) H 
Figure 6: Graphical representation of the goal of remote sensing, showing the special 
status of empirical BRDF models. 
Empirical BRDF models have been developed since early this century, in particular to characterise the 
directional reflectance of the surface of the Moon as observed from the Earth ( e.g ., Minnaert, 1941). The 
models of Roujean et al. (1992), and of Rahman el al. (1993), intended for use with remote sensing data 
from space, provide but two recent examples of this approach. The main drawbacks of this approach are as 
follows: 
Theorem 10. Empirical BRDF models of the type Z = h(X, P) cannot provide any understanding of the 
processes controlling Z, nor do they characterize the system in terms of the variables of interest Y. 
Why do we develop these models, since they do not fulfill either of the two objectives (provide an 
understanding of the processes controlling the measurements and characterise the observed system) stated 
&t the start of this paper? Because these simple models can be used effectively in the following three 
specific applications: (i) to provide the shape of the BRDF as a lower boundary condition for atmospheric 
or vegetation models, (ii) to generate the reflectances that would have been observed under a controlled 
geometry of illumination and observation, and (iii) to estimate the directional hemispherical reflectance 
(albedo) of the surface by integrating the sampled BRDF over all viewing angles. 
The use of an empirical BRDF model in any one of these three applications presupposes that this model 
can reliably and accurately represent the bidirectional reflectance of the medium under arbitrary geometries 
of illumination and observation. Since these models cannot be validated in the strict sense advocated by 
Pinty and Verstraete (1992), extra care must be given to the verification of their performance for a wide 
variety of angular conditions and surface types. 
CONCLUSIONS 
Various sectors of economic activity and scientific inquiry require repetitive, high spatial resolution data 
on the state and evolution of the environment. Sensors on board satellite platforms appear to provide the 
only economically feasible solution available today to collect relevant information at these scales and reso 
lutions. The dichotomy between the natures of the measured signals and the variables of interest prompted 
a discussion of the feasibility of retrieving useful information on the variables of interest from the space 
measurements. It was also argued that the physical understanding of the physics of the signal was necessary 
to develop and support practical applications, and to gain knowledge on the fundamental processes that 
govern the evolution of these environments. 
A variety of approaches exist to exploit remote sensing data. Detailed physical models can incorporate 
much explicit knowledge of the structure and properties of complex media, but do not easily lend themselves 
to operational applications. Simpler but still physical models may be inverted against remote sensing data, 
but this process results in the retrieval of the state variables controlling the transfer of radiation in the 
medium. All of these models embody our knowledge of the radiative transfer processes that control the 
measured signals. The inversion of such models also provides an objective way to estimate the state variables 
of the radiative transfer problem. The values of other variables of interest may be deduced, provided they 
depend on one or more of these state variables. This same restriction also applies to direct empirical methods, 
including vegetation indices. These methods currently support many practical applications, but suffer from 
various intrinsic limitations. Finally, empirical BRDF models have been found useful only in very specific 
applications. 
I