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the propagation of light in the canopy. The inversion problem reduces to minimizing A 2 . In most cases, the 
complexity of models prevents an analytical inversion so that numerical methods are required. There are a 
number of ways of achieving it. Search strategies refer to a variety of algorithms whose performances depend 
on many factors closely linked to the method of search but also to the model to be inverted. A typical 
recommendation should be to try several of them; this may result in excessive computation time and is bluntly 
unrealistic when thousands of inversions have to be performed, for example on pixels of a remote sensing 
image. According to the literature, it appears in practice that the choice of the optimization method is above all 
determined by the availability of an inversion routine in a mathematical library (IMSL, NAG, SAS,.„) and 
rarely guided by criteria of convergence, reliability, accuracy or computation time. These criteria have been 
used in Renders et al. (1992) to compare different optimization methods to invert a canopy bidirectional 
reflectance model with synthetic data. 
In this paper, we make an attempt to apply these methods to real conditions. We first analyze the 
performance of optimization methods with "noisy" synthetic data. Secondly, we use these methods with real 
data from the CAESAR (CCD Airborne Experimental Scanner for Applications in Remote Sensing) 
multispectral sensor for which radiometric data and some of the associated ground data were available. 
1 - DESCRIPTION OF THE MODEL AND THE MINIMIZATION METHODS 
1.1. The PROSPECT+SADL Model 
PROSPECT (Jacquemoud and Baret, 1990) is a radiative transfer model which simulates the leaf reflectance 
and transmittance from 400 to 2500 nm as a function of the leaf mesophyll structure parameter N, the 
chlorophyll a+b concentration Cab (pg cm -2 ), and the water depth Cw (cm). For given solar 6s and viewing 0o 
zenith angles, and a given relative azimuth <po angle, SAIL (Verhoef, 1984, 1985) calculates the canopy 
bidirectional reflectance using leaf optical properties, soil reflectance, and canopy architecture; the latter is 
represented by the leaf area index LAI, the mean leaf inclination angle 01, and the hot spot size-parameter Si 
defined as Si=L/H where L is the horizontal correlation length which depends on the mean size of the leaves 
and on the shape of the leaves, and H is the canopy height (Kuusk, 1991b). The association of the two models 
permits the simulation of canopy spectral reflectance for any configuration of measurement. By combining 
these spectra to the three CAESAR (Looyen and Dekker, 1991) gaussian filter functions centred on 550 nm (6A 
=30 nm), 670 nm (6A=30 nm), and 870 nm (6A=50 nm), we can reproduce the equivalent reflectance measured 
by this sensor (Figure 1). As these bands are outside the water absorption wavelengths, N, Cab, LAI, 01, and Si 
are the five independent variables of the PROSPECT+SAIL model that characterize the physical and biological 
properties of the plant canopy. The soil reflectance is assumed to be known: Figure 1 shows the spectral 
Figure 1. CAESAR spectral bands superposed 
on the reflectance spectra of the clayey soil used 
for the simulation study (—) and the bare soil 
selected in the Flevoland site for the application 
study (...). The typical reflectance spectrum of a 
plant canopy is also provided (—). 
400 600 800 1000 
Wavelength (nm) 
12. The Minimization Methods 
There are various kinds of optimization methods, often classified following their strategies of search: 
reflectance of the clayey soil we selected in this