Symposium on Remote Sensing for Resources Development and Environmental Management / Enschede / August 1986 
215 
The derivation of a simplified reflectance model 
for the estimation of LAI 
J.G.P.W.Clevers 
Dept, of Landsurveying and Remote Sensing, Wageningen Agricultural University, Netherlands 
ABSTRACT: Information about crop reflectance obtained from the literature suggests that reflectance factors in 
the near-infrared are most suitable for estimating leaf area index (LAI). A problem arises if a multitemporal 
analysis is required. Soil moisture content is not constant during the season and differences in soil moisture 
content greatly influence soil reflectance. A correction for soil background has to be made when ascertaining 
the relationship between reflectance and crop(characteristics. 
Since in the literature no satisfactory solution for correcting for soil background was found, an appropriate 
simplified reflectance model for estimating LAI is presented. First of all, an apparent soil cover is defined. 
Then, a corrected infrared reflectance is calculated by subtracting the contribution of the soil from the mea 
sured reflectance. The assumption that there is a constant ratio between the reflectances of bare soil in 
different spectral bands, independent 6f soil moisture content, enables the corrected infrared reflectance to 
be calculated without knowing soil reflectances. Subsequently, this corrected infrared reflectance is used for 
estimating LAI according to the inverse of a special case of the Mitscherlich function. Simulations with the 
SAIL model confirmed the potential of this simplified (semi-empirical) reflectance model for estimating LAI. 
1 INTRODUCTION 
Remote sensing techniques enable information about 
agricultural crops to be obtained quantitatively, 
instantaneously and, above all, non-destructively. 
During the past decades knowledge about remote 
sensing techniques and their application to fields 
such as agriculture has improved considerably. 
Bunnik (1978) demonstrated the possibilities of 
applying remote sensing in agriculture, particularly 
with regard to its relation with crop characteristics 
such as soil cover, leaf area index (LAI) and dry 
matter weight. LAI is regarded as a very important 
plant characteristic because photosynthesis takes 
place in the green plant parts. 
One of the main results of the work done by 
Bunnik (1978) was the identification of five wave 
lengths based on optimum information about variation 
in relevant crop characteristics. These wavelengths 
were: one in the green at 550 nm, one in the red at 
670 nm, one in the near-infrared at 870 nm and (to 
a less extent) two in the middle-infrared - one at 
1650 nm and the other at 2200 nm. In the literature 
there is a certain consensus that bands in the green, 
red and near-infrared regions are optimal if infor 
mation about vegetation is to be obtained (e.g. 
Kondratyev & Pokrovsky, 1979). 
From the literature it is evident that, in the 
visible region, vegetation absorbs much radiation 
(for photosynthesis) and shows a relatively low 
reflectance. This is especially true in the red 
region, because of the large absorption of this 
radiation by the chlorophyll in the leaves. In the 
near-infrared region the opposite occurs. The spec 
tral reflectance in this region is high. In the 
visible and near-infrared region the reflectance and 
transmittance of a green leaf are approximately equal 
(e.g. Goudriaan, 1977; Youkhana, 1983). 
The low transmittance of a green leaf in the 
visible region implies that in this region only the 
reflectance of the upper layer of leaves determines 
the measured reflectance of that canopy. In the near- 
infrared region the transmittance of a green leaf is 
in the order of 50%, and there is hardly any infrared 
absorptance by a green leaf. In this situation leaves 
or canopy layers underneath the upper layer contri 
bute significantly to the total measured reflectance. 
This contribution decreases with increasing depth in 
the canopy (and is negligible from 6-8 layers onwards). 
This multiple reflectance indicates that the infrared 
reflectance may be a suitable estimator of LAI. 
Soil reflectance has an important influence on the 
relationship between reflectance and LAI. At low soil 
cover, soil reflectance contributes strongly to the 
measured reflectance in the different spectral bands. 
For a given soil type, soil moisture will be the main 
factor determining soil reflectance. An increasing 
moisture content of the soil causes the reflectance to 
decrease, but the relative effect of soil moisture on 
the reflectance at distinct wavelengths is similar 
(Bowers & Hanks, 1965). Janse & Bunnik (1974) noticed 
that reflectance decreases with increasing soil 
moisture content, but this decrease is almost indepen 
dent of wavelengths between 400 nm and 1000 nm for a 
sandy soil. This means that the ratio of the reflec 
tance in two spectral bands in this interval is nearly 
independent of soil moisture content. Results obtained 
by Condit (1970) and Stoner et al. (1980) confirm that 
the ratio of the reflectance in two spectral bands is 
independent of the soil moisture content. 
The starting point of the study of this paper were 
calibrated reflectance factors in the green, red and 
near-infrared. These may be obtained, for instance, by 
means of multispectral aerial photography. The 
radiometric calibration and atmospheric correction of 
such measurements are described by Clevers (1986a, 
1986b). The main aim was to investigate some index or 
model, derived from reflectance factors, for estima 
ting LAI in a multitemporal analysis. In order to 
enable such a multitemporal analysis a correction for 
soil background should be made. The ideal model for 
practical applications is one that is simple and 
requires the least number of input variables. For 
instance, if the agronomist has to ascertain a leaf 
angle distribution (necessary for some existing 
models), he will probably prefer to collect the 
conventional field data as he has always done.