id model takes soil and 
strongest driver of the 
ids and occurrences of 
nations' have therefore 
reflectances are shown 
decrease in the visible 
:getation result in high 
t except Zj , £2 and cl 
ad of 3200 °Q roughly 
eriod. These errors are 
allocation coefficient a 
t is displayed on figure 
ref) and the first guess 
Fig. 3 Seasonal profile of reflectances. Open circles are the synthetic weekly 'observations' computed with the 
LAI time profile from the reference simulation. The visible reflectance ranges from 0.18 (bare soil) to 0.044 at 
maximum canopy development. The near infrared ranges from 024 (bare soil) to 0J7. The solid line 
represents daily reflectances obtained with the first guess parameters. 
3J.2. Assimilation of ’clean’ data. The cost function J(u), which is minimized to find the best agreement 
between model and observations, was computed as follows: 
7(11,£2,a) = X [(pr"-PS“) 1 +(p^T’-PS") 1 ] (2) 
i-1.52 L 
where p““ 1 is the visible reflectance of week i computed from the vegetation model with current Zj Z2 
is the corresponding near infra-red reflectance; and p£* are the 'observed' reflectances obtained for 
week i with the reference simulation. This cost function exhibits discontinuities and local plateaux in response 
to Zj or Z2 variations. For this reason, we chose the downhill simplex method (Matlab, from The Math Works, 
Inc.) to minimize it. This algorithm allows a very good retrieval of the parameters (table 1) when clean 
observations are assimilated in die model. 
GPP 
NPP 
1010 
625 
740 
392 
1011 
625 
Z1 (°Q 
Z2(°Q 
a 
ref 
600 
3200 
0.480 
1st guess 
1000 
3700 
0.45 
retrieval 
602.9 
3201.9 
0.479 
’ and NPP values drop 
¡0 respectively, mainly 
Tadiance are depleted. 
>00 Od too w 
ce simulation. Positive 
the dominant process, 
?n. bottom) Difference 
y develops earlier and 
wading to high positive 
photosynthetic rate is 
Table 1 : reference parameters (ref) and retrieved parameters after assimilation of 'clean observations'. GPP 
and NPP values are in g C m-2 year-1 
These parameters result in the same LAI profile as the reference one. Bearing in mind the strong assumption of 
a 'perfect model', one can notice that reflectances for the periods when LAI is lower than 3 allow the restitution 
of the complete profile of LAI, when model knowledge is taken into account. In this perspective, it is 
particularly interesting to study the stability of the assimilation scheme. 
3.3.3. Assimilation of noisy 'observations'. As a step towards real data, we investigate the behavior of the 
assimilation scheme when a gaussian noise is added to each synthetic observations. The objective is to asses 
the quality of the retrieved parameters and the consequences on the carbon fluxes. The assumption of a perfect 
model still holds, but this simulates perturbations of the satellite measurements. The noise has a zero mean and 
a standard deviation of 0.02. This value corresponds to 16% of the mean visible reflectance and 5% of the 
mean near infrared reflectance. The results of 50 minimizations are displayed in table 2.