1000 
observations and of the optimal illumination and viewing geometries for inverting BRDF models, and of the 
mini mal number of spectral bands necessary to retrieve the biochemical state variables remains a research 
issue. Work is currently under way in this area, but significant progress will probably still take time, (iv) 
Better results may be expected with improved figure of merit functions, and in particular with the use of 
weights to differentiate the contribution of each data item to the knowledge of the desired state variable. In 
the same vein, improvements in optimisation procedures and a better understanding of the impact of noise 
in the data or the independent variables should help extract more reliable products from remote sensing 
data, (v) Last but not least, the importance of establishing relations Y = g,( S) between the parameters 
of interest Y and the state variables S cannot be overstated, even though this effort is, strictly speaking, 
outside the scope of remote sensing. Ultimately, the existence and establishment of these relations justifies 
the use of remote sensing techniques. 
DIRECT (MOSTLY EMPIRICAL) METHODS 
The inversion of physical models against remote sensing data clearly constitutes a sound but scientifically 
involved approach. We can reasonably ask whether it would not be possible to assess the values of the 
variables of interest Y more directly by establishing relations of the type Y = g( Z). The answer appears to 
be yes, since a large number of algorithms are routinely used to retrieve information on terrestrial surfaces 
from direct manipulations of the measured signals. These methods are based on the analysis of images 
(pattern recognition, local variance, image structure), time variations (change detection), or the exploitation 
of spectral contrasts, as is done with all vegetation indices. Of course, the values of the variables of interest 
Y cannot be causally affected by the fact that the system is being observed, or by the numerical value 
of these measurements, so it is clear from the outset that such a relation is of a different nature than the 
physical models decribed in the previous section. The objective of setting up such relations is also clearly 
to estimate the values of the variables of interest Y, not to provide any new understanding of the physical 
processes that control the measurements. 
We now analyse the meaning and implications of this alternative approach to the estimation of Y. 
Three categories of variables of interest can be distinguished for this purpose: those that are state variables 
of the radiative transfer problem (i.e., the variables S of the previous sections), those that can be entirely 
determined as a function of these state variables, and those that depend on at least one other variable, not 
related to the radiative processes discussed above. Since there is an explicit physical or biochemical (causal) 
relation between the state variables S and the measurements Z, e.g ., through the models f\ and fo described 
above, we know a priori that these quantities are related, and we expect that relations of the type Y = g{ Z) 
can be established for any of these state variables. However, since (i) multiple state variables S are necessary 
to physically describe each of the measured values Z, and (ii) only an optimal (but not perfect) estimation of 
the state variables S can be retrieved through the numerical inversion of physical models against the data Z, 
we cannot expect that a relation linking multiple measurements to a single state variable provides a perfect 
deterministic estimation of the state variable of interest. Hence, this relation will be empirical, even if there 
is ample theoretical ground to justify its establishment. It is also worth noting that even if the variable of 
interest y happens to be a state variable, that does not guarantee that a relation Y = g( Z) is reliable or 
useful: the leaf area index is a state variable, but cannot be reliably estimated from vegetation indices when 
the canopy is deep enough. 
The establishment of a relation to estimate the chlorophyll concentration [cc] in the leaves from remote 
sensing measurements provides an example of this first category of variables: A relation can reasonably be 
established, since the presence of chlorophyll affects the spectral values of the reflectance and transmittance 
of these leaves, and these properties, in turn, affect the measurements. However, since the measurements tre 
also influenced by other factors, such as the presence of an atmosphere, or the structure of the canopy, we can 
hardly guarantee that a relation such as [cc] = g(Z) could be used to accurately determine the chlorophyll 
concentration anywhere and at all times. 
The case of the state variables of interest Y which can be computed explicitly and exclusively on the 
basis of the knowledge of the state variables S is very similar. However, if multiple state variables Sj are 
needed to estimate the variable of interest Y, the relation Y = g{Z) is equivalent to establishing multiple 
relations Sj = gj( Z), and then computing Y on the basis of the model g,, «morniing the latter exists. The 
accuracy of such a relation cannot be better than that of any of the implied relations p ; , even if the model