995 
to acquire a fundamental 
:e, to assess the feasibility, 
;h objectives will lead to s 
or predicting its evolution, 
two objectives can be at- 
nother approach. We hope 
cation in future model and 
: observation of terrestrial 
st of the arguments could 
1 infrared or microwaves). 
>nal radiative information, 
lered as additional dimen- 
rious modeling approaches 
cm under observation and 
have attempted to express 
led to support a dogmatic 
the use and development 
issions, result in a greater 
;e ever better research and 
SNALS 
m of high level integrated 
carbon between terrestrial 
ed Y. On the other hand, 
only record gravitational 
■ radiation (or reflectance) 
denoted Z (bold symbols 
les therefore hinges on the 
l space can be interpreted 
this quantitative relation, 
vill hopefully become clear 
!• 
e variables of interest Y on 
opment of physically-baaed 
they aim at explaining the 
laracterise the state of the 
i general, measurements 1 
at the surface, but, rather, 
by the radiative properties S of the various media in which the radiation propagates, and their associated 
physical processes. These variables S are the state variables of the radiative transfer problem, «.e., the set of 
independent physical quantities that need to be specified in the equations of radiation transfer to describe 
the observed radiances or reflectances. Formally, these physical models can be written 
Z = f(8) (1) 
The development of models to understand the physics of the measurements, a necessary step to fulfill 
the second stated objective, results in a new situation, depicted in Figure 2. 
Z 
/J 
s 1 ? 
\? 
Y 
Figure 2: Graphical representation of the goal of remote sensing when the existence of 
the radiative state variables has been recognised. 
The requirements for a variable to be a state variable of the radiative transfer problem is that it must be 
a fundamental measurable quantity necessary for the description of the physical interactions between the 
incoming radiation and the medium under study. Two categories of state variables S control the measure 
ments made in space: those that describe the properties of the media (atmosphere, vegetation, soil) with 
which the radiation interacts (e.g., position, sise, shape, orientation, or density of the objects constituting 
these media), and those that control the properties of the scatterers (e.g., aerosol phase function, leaf re 
flectance and transmittance, pigment concentration). Clearly, some of these state variables may turn out 
to be variables of interest, depending on the intended application of remote sensing techniques (the LAI of 
vegetation canopies is a case in point), but we will continue to refer to Y as high level integrated variables 
of interest such as those evoked earlier. It will be seen that if a particular variable of interest Yj is not a 
state variable and does not ultimately depend on them, then remote sensing measurements cannot a priori 
provide any information on that variable. 
Physicists have accumulated extensive experience on the problem of radiation transfer, and recent 
reviews of the models available in the optical domain have been published (e.g., Goel, 1988; Asrar, 1989; 
Myneni and Ross, 1991; Hapke, 1993). Two types of radiation transfer models can be distinguished at this 
stage, depending on whether they can be practically inverted on an operational basis or not. An accurate 
description of the transfer of radiation in complex media requires detailed models capable of describing the 
three-dimensional structure of these media, as well as the specifics of the physical interactions between the 
electromagnetic waves and the absorbing and scattering elements. The main constraint on the development 
of these models is to represent as faithfully as possible the physics involved; the conceptual or computational 
complexity of these models is of secondary importance, because they are used almost exclusively in direct 
node, i.e., to estimate the exitance or reflectance of a system which is otherwise fully characterised. The 
importance of these models results from the deeper understanding they provide and the opportunity they 
offer to define and test simplifications and assumptions, or to design reliable parameterisations for use in 
more operational models. 
On the other hand, there is also a need for physically-based models capable of describing the radiation 
transfer in terms of a small number of state variables, whose values can be retrieved by inverting these 
models against the observations. These simpler models are usually based on specific hypotheses, such as 
the plane-parallel assumption, or two-stream approximations, but their development is further constrained 
hy the need to keep the number of model parameters (state variables) as limited as possible, because of the 
computational requirements imposed by model inversion in operational applications. Figure 3 shows these 
two approaches, where / designates the complex and possibly computationally expensive models, S,» stands