will persist for a 
time series, the 
ations of NDV1 
turbances in the 
the cause of the 
, which is valid, 
;). Paltridge and 
-ERR data on an 
92) propose to 
rents taken in a 
d expert system 
tioned methods 
abtained by the 
itial use. 
)EL ON AN 
inal reflectance 
te recent work 
on on the other 
the respective 
at instrumental 
s accurately as 
., 1990) or the 
n that of input 
es, and aerosol 
acquired, in a 
measurement 
Sun and view 
llues (Rmodf' 
vhich reads 
( 1 ) 
( 2 ) 
The 
:rvations. The 
be called the 
ce time series 
the sampling 
on, since the 
gh frequency 
icy when the 
In turn, time series of the kj parameters permit to reconstruct time series of modelled reflectances 
according to Eqs. (1) and (2). The accuracy of the procedure may be considered as good if the regression 
residue S, given by 
1 N 2 
6 2 =-2[ ( ^- ( ^mod ) *] (3) 
i=1 
is sufficiently small (N in Eq. (3) is the total number of data in an annual vegetation cycle). Finally, the kj 
parameters are used to derive, at the sampling frequency, a reflectance corrected from bidirectional effects, 
R C orr=8(k o.*i. k m) ■ ( 4 ) 
The corrected reflectance R corr may be the bidirectional reflectance evaluated for determined and fixed sensor 
and sun directions (in this case g = f and the Sun and view angles are assigned to prescribed values), or a 
direct albedo (reflectance averaged over the viewing directions) with a given Sun elevation, or the so-called 
diffuse albedo (direct albedo averaged over possible solar directions), or any other combination of the kj. 
3 2 - Vegetation monitoring 
This technique has been applied on a series of 8 months of NOAA-11 AVHRR data, from March to October 
1989, on 7 test sites in France representative of semi-arid, cultures, and forests sites (Roujean and Leroy, 1991; 
Leroy and Roujean, 1994). In these works, the period of composition and sampling period have been chosen 
equal to 30 days and 10 days respectively. The used calibration coefficients have been those recommended by 
Holben et al. (1990), and cloud screening has been made using basically the approach of Derrien et al. (1992) 
(comparison of radiances or combinations of radiances in the visible and in the thermal infrared to 
predetermined values). Atmospheric corrections are applied using the 5S code (Tanr6 et al., 1990). The aerosol 
optical depth is derived from visibility measurements performed daily at metorological stations neighboring 
the test sites, and the aerosol phase function is taken from a climatology. The water vapor amount is obtained 
from a meteorological short-range weather forecast model coupled with radiosounding measurements, which 
provides on a 30 km grid an estimate of water vapor amount. Ozone content is derived from a climatology. 
The chosen surface bidirectional reflectance model is the 3-parameter semi-empirical linear model of 
Roujean et al. (1992b), which may be written as 
R(0 i ,0 v ,(t)) = k o +k 1 / 1 (0 i ,e v ,(t)) + k 2 / 2 ( 0 J ,e v , 4 .) (5) 
where fj and f 2 are given simple analytical functions which depend only on the geometrical angles. The model 
has been designed so that fj and f 2 vanish for a nadir viewing sensor and a sun at zenith. Thus Icq represents the 
surface reflectance with this geometric configuration and has been chosen to represent the corrected 
reflectance mentioned above in Eq. (4), while the two other parameters, kj and k 2 , are indicators of non- 
Lambertian characteristics of the reflectance. The model of Eq. (1) has been built using simple physical 
representations of the surface, taking into account shadowing effects and volume scattering properties of 
canopies and bare soils. These physical representations have been used as a guide to obtain the functional 
dependence of the surface reflectance upon the Sun and view angles. A series of assumptions has then been 
made to reduce the number of surface parameters to 3, and to linearize the model as a function of its surface 
parameters (ko, kj, k 2 ) so that it is easily applicable to satellite data (see Roujean et al., 1992b). 
The results are illustrated in Figure 4, which represents, for the Valensole plateau, and Beauce test 
sites in the visible and near infrared bands, the superimposed time series of (i) observed surface reflectances, 
(ii) modelled surface reflectances, and (iii) corrected reflectances ko- It is qualitatively apparent that the 
modelled reflectances fit remarkably well (Figure 4, Valensole site) or rather well (Figure 4, Beauce site) 
the observed surface reflectances. This is direct evidence that the large short-term fluctuations are indeed 
due to directional effects, and that the applied surface bidirectional reflectance model (Eq. (5)) is somehow 
appropriate to describe these effects. The retrieved time series of corrected reflectances ko have a smooth 
aspect and filter out the short-term fluctuations. A striking feature of Figure 4 and analogous figures for the 
other sites is that ko is generally somewhat larger than the monthly averaged observed reflectance, 
especially when the solar zenith angle 0 S becomes large in early spring and late fall. This is not surprising 
since ko (a surface reflectance observed at nadir with a Sun at zenith) should be higher than the reflectance 
25