shown that a similar approach can be applied 
to yellowing cereals, resulting into the same 
vegetation index. When satellite data are the 
information source, atmospheric correction is 
very important (Clevers, 1986, 1988b). 
Attention will be paid also to this aspect of 
a multitemporal analysis. 
2. SIMPLIFIED REFLECTANCE MODEL FOR 
ESTIMATING LAI (CLAIR) 
2.1 Introduction 
Recently, Clevers (1988a, 1989) has described 
a simplified, semi-empirical, reflectance 
model for estimating LAI of a green canopy 
(vegetative stage). In this model it is 
assumed that in the multitemporal analysis 
the soil type is given and soil moisture 
content is the only varying property of the 
soil. For estimating LAI a "corrected" 
(adjusted) infrared reflectance factor was 
calculated by subtracting the contribution of 
the soil in line of sight from the measured 
reflectance of the composite canopy-soil 
scene. This corrected infrared reflectance 
factor was ascertained as a weighted 
difference between the measured infrared and 
red reflectance factors (called WDVI = 
weighted difference vegetation index), 
assuming that the ratio between infrared and 
red reflectances of bare soil is constant, 
independent of soil moisture content (which 
assumption is valid for many soil types). 
Subsequently this WDVI was used for 
estimating LAI according to the inverse of a 
special case of the Mitscherlich function. 
This function contains two parameters that 
have to be estimated empirically from a 
training set. 
2.2 CLAIR model 
The simplified reflectance model derived by 
Clevers (1988a, 1989) consists out of two 
steps. Firstly, the WDVI is calculated as: 
WDVI = r ir - C.r r (1) 
with r^ r = total measured near-infrared 
reflectance factor 
r r = total measured red reflectance 
factor 
and C = 
(2) 
r 
s, ir 
r 
s,r 
= near-infrared reflectance factor 
of the soil 
= red reflectance factor of the 
soil. 
empirically from a training set, but they 
have a physical interpretation (Clevers, 
1988a). Equation (3) is the inverse of a 
special case of the Mitscherlich function 
(Mitscherlich, 1923). The combination of Eqs. 
(1) and (3) is the simplified, semi- 
empirical, reflectance model: CLAIR model 
("Clevers Leaf Area Index by Reflectance" 
model). 
The main assumption was that C is a 
constant, meaning that the ratio of the 
infrared and red reflectance of the soil is 
independent of the soil moisture content. The 
validity of this assumption for many soil 
types is confirmed by results obtained by 
e.g. Condit (1970) and Stoner et al. (1980). 
For many soil types, there is only a slight 
monotonie increase in reflectance with 
increasing wavelength (e.g. Condit, 1970). 
For application of Eq. (1) in estimating 
LAI, a weighted difference between the 
infrared and red reflectance must be 
ascertained and then Eq. (3) must be used. 
In this regard r^ in Eq. (3) will be the 
asymptotically limiting value of the weighted 
difference between infrared and red 
reflectance at very high LAI. 
The vegetation index derived in Eq. (1) is 
similar to the Greenness of Kauth and Thomas 
(1976) for the two-dimensional case (see 
below), on the restriction that they used 
digital numbers (not reflectance factors). 
The assumption given in Eq. (2) describes a 
soil line, which can be defined by the vector 
(1,C) in a scatter plot of near-infrared 
against red data. A two-dimensional 
"greenness index" (in terms of the Greenness 
of Kauth and Thomas) could be defined 
orthogonal to this soil line: 
greenness index = r^ r - C.r r . 
This equals the WDVI in Eq. (1). 
Moreover, the vegetation index derived in Eq. 
(1) is also similar to the perpendicular 
vegetation index of Richardson and Wiegand 
(1977). By introducing the assumption 
r s r = C in Eq. (2) , this means that 
thé slope of the soil background line of 
Richardson and Wiegand equals 1/C (red 
against near-infrared plot). If it is assumed 
that the intercept does not differ 
statistically from zero, it can be shown 
that PVI = (1/(C 2 +1)) 1//2 . (r ir -C.r r ), 
with C being soil-specific. By working with 
reflectance factors the ratio in Eq. (2) 
appears to be constant, and so the intercept 
is indeed zero. This PVI also equals the 
above two-dimensional greenness index after 
normalization, assuming there is just one C 
valid. 
Secondly, the relation between WDVI and LAI 
is given by: 
LAI = -1/a . ln(l - WDVI/r^ ^) (3) 
The combination of Eqs. (1) and (3) is called 
the semi-empirical reflectance model. 
Parameters a and have to be estimated 
3. APPLICATION OF CLAIR MODEL TO 
SATELLITE DATA 
3.1 Background 
The described CLAIR model in section 2 is 
based on reflectance factors. Thus, this 
model is not directly applicable to satellite 
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