294 
In the view of being close to a real context where measurements are contaminated by noise due to the 
instrument and to external conditions, a random noise component (gaussian distribution of zero mean and 
variance o=0.01) was added to the reflectance values and this operation was repeated 50 times. In total we 
analysed the results of 5 surfaces x 3 data sets x 50 noise x 4 optimization procedures: that is to say 3000 
inversions! The inversion of the FROSPECT+SAIL model consists in determining by iterations the set OF 
parameters P=(N, Cab, LAI, 01, Si) which minimizes A 2 defined as: 
3 n 
A 2 =YY[R a *s-Ruri(k,Q J ,P)] 2 (1) 
where Rmea is the measured and Rmod the modeled canopy reflectance. The summation is over the 3 CAESAR 
channels (Ai) and the n viewing angles (0j). The criterion used to stop the inversion is to assume convergence if 
the relative change occuring between two successive iterations is less than some prescribed quantity. The 
optimization methods have been compared in terms of accuracy and computation time: the accuracy, distance 
from the solution to the global minimum , is assessed by the Error defined as: 
Error = 
( 2 ) 
where p i and p ' are respectively the normalized values of the real and fitted parameters. The computation time 
(Cntr) can be defined as the mean number of calls to the function to be minimized. 
QN 
MQ 
SP 
GQ 
data set 
surface 
Error 
Cntr 
Error 
Cntr 
Error 
Cntr 
Error 
Cntr 
n=6 
A 
0.1899 
920 
0.3524 
132 
0.1166 
327 
0.6066 
2354 
B 
0.1770 
300 
0.1950 
104 
0.1235 
363 
0.1874 
1319 
C 
0.2464 
786 
0.2175 
239 
0.1326 
226 
0.0810 
2433 
D 
0.2571 
1131 
0.3476 
635 
0.1767 
275 
X 
X 
E 
0.0949 
321 
0.3965 
163 
0.2200 
378 
X 
X 
n=9 
A 
0.0804 
302 
0.0467 
82 
0.1302 
327 
0.2756 
1239 
B 
0.0135 
244 
0.2231 
65 
0.0276 
381 
0.0135 
1082 
C 
0.0049 
233 
0.0049 
61 
0.0049 
237 
0.0046 
968 
D 
0.1539 
550 
0.3281 
325 
0.1925 
356 
X 
X 
E 
0.0014 
188 
0.0324 
67 
0.0247 
477 
X 
X 
n=27 
A 
0.0215 
192 
0.0214 
62 
0.0218 
378 
0.0215 
977 
B 
0.0022 
193 
0.1458 
64 
0.0129 
351 
0.0022 
979 
C 
0.0015 
244 
0.0015 
54 
0.0015 
275 
0.0012 
917 
D 
0.0281 
244 
0.0281 
59 
0.0540 
420 
X 
X 
E 
0.0004 
173 
0.0004 
59 
0.0007 
407 
X 
X 
Table 2. Accuracy (Error) and computation time (Cntr) as determined for the different study cases (values are 
the average outputs of 50 noise-disturbed inversions). For each data set and each surface, the best performances 
in terms of Error and Cntr have been printed in bold. 
From a general point of view, it emeiges from Table 2 that, whatever the method, the more data values 
available the higher the accuracy. The computation time follows the opposite trend for QN, MQ, and GQ but it 
seems to be rather constant for SP. These two criteria are also dependent on the type of surface: for instance, 
inversions performed on surfaces A and D which correspond to dense and planophile canopies (high LAI and 
low 01 values) are the less efficient; this is not surprising because both visible and near infrared reflectances aim 
at saturation in such conditions. One can also notice great Error's for QG with surface A: a detailed analysis of 
the fitted parameters shows that N, 01, and Si are rather far from their actual values even if canopy reflectances 
are well reconstructed by the model. As already observed by Jacquemoud (1993) on reflectance spectra, it 
means that different sets of parameters can account for almost simil ar surfaces. Let us compare now the