217 
absorption for 
nproved and 
srical solution 
Lthin nine 
rete layer, 
fas described 
5d on a theory 
the transfer 
Lffusing media, 
fard fluxes 
Allen et al. 
îclude 
the Duntley 
Lytical model 
rvation 
id is an 
i and his 
tes plant 
fication) and 
is are carried 
plifications 
Lk, 1981). 
aits model 
action 
factions of 
not introduce 
netry to 
anents as 
set of 
3 model is 
Ltrarily 
a three- 
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dividing the 
s usually 
iaracteristies 
nd optical 
ractical 
tances for 
oasis is 
of relation- 
.ni-empirical 
atroduced 
1 background. 
correction 
verified by 
1. 
ETATION 
eflectance 
AI; 
between 
physically 
nd in order 
to be done; 
(preferably 
in a visible 
istance, the 
soil in the 
reason soil 
sor geometry 
n canopy, soil 
1 projection 
erequisite for 
new definition 
ith the 
soil should be 
la). Further, 
r to be able 
fraction of 
. soil that is 
sun 
sensor 
— 0 - 
Figure 2: Schematic presentation of a simplified 
reflectance model for vegetation and soil combined. 
Figure 1: Schematic presentation to illustrate aspects 
of the new definition of soil cover. 
C = covered soil; N = soil not covered or illuminated, 
a: Soil illuminated by the sun. 
b: Soil visible to a sensor, 
c: Illuminated soil visible to this sensor. 
illuminated by the sun as well as directly detectable 
by the sensor) will be classified as the fraction of 
soil that is not covered (figure lc). The complemen 
tary fraction will now be defined as soil cover 
("apparent soil cover"). In the special situation of 
the sensor looking vertically downwards, this 
definition of soil cover is equivalent to the relative 
vertical projection of green vegetation, the relative 
area of the shadows included. 
In order to ascertain whether there is a useful 
relationship between infrared reflectance and LAI for 
green vegetation, the former should be corrected for 
soil background, because it may influence infrared 
reflectance independently of the LAI. The infrared 
reflectance is then calculated for the situation of 
the visible background being completely black and 
not reflecting any radiation. This corrected infrared 
reflectance value is then used to estimate LAI. 
Let us consider the simple situation of a surface, 
partly covered with green vegetation and partly bare 
(figure 2). The fraction of the surface covered with 
vegetation is called soil cover, B. If the reflectance 
of the soil is called r and the reflectance of the 
s 
vegetation r , then the total measured reflectance, 
r, will equaY: 
r = r v . B + r s . (1-B) (1) 
A green band will be denoted by the subscript g 
and equation (1) is then written as: 
r = 
g 
v,g 
s, g 
(1-B) 
( 2) 
The reflectance of vegetation in a green band (r ) 
may be regarded as being independent of the numbed 
of leaf layers, because leaf transmittance in the 
green is assumed to be negligible. Hence equation (2) 
describes the linear relationship between the 
reflectance in a green band and soil sover, if the 
soil reflectance can be considered to be constant 
(constant soil moisture content). 
Analogously, by attaching the subscript r to a red 
band reflectance, we have: 
r 
r 
r 
v,r 
B + r 
s,r 
(1-B) 
( 3) 
Because r can also be regarded as being independent 
of the number of leaf layers, this equation describes 
the linear relationship between red reflectance and 
soil cover. 
For an infrared band the subscript ir will be used 
and equation (1) is then written as: 
r. 
xr 
r . . B + r 
v,ir s,ir 
(1-B) 
( 4) 
In this equation r . is not independent of tne number 
of leaf layers, so V ife r may not be regarded as a con 
stant. This means that the reflectance measured in 
an infrared band (r. ) is not a linear function of 
• i lr 
soil cover. 
For estimation of LAI the corrected reflectance r' 
could be used. It is (according to equation 1) defined 
as: 
r' = r - r . (1-B) = r . B (5) 
s v 
The corrected reflectance is the reflectance one would 
have obtained with a black background. 
In order to obtain the corrected infrared reflectance 
equation (5) first has to be applied to the infrared 
band: 
r ! 
ir 
r. 
xr 
r 
s, ir 
(1-B) 
( 6) 
B can be ascertained by means of equation (2) or (3) . 
However, the reflectance of bare soil and of vegeta 
tion in a green or red band should be known. Although 
it is quite often possible to ascertain a good estimate 
for the reflectance of vegetation (complete cover), 
estimating the reflectance of bare soil poses greater 
difficulties. The reflectance of a soil may change 
very rapidly, according to soil moisture content. 
Also, very large local differences in soil moisture 
content may occur. At low soil cover this may cause 
large inaccuracy if neither the soil moisture content 
nor the actual reflectance of the soil are known. To 
obtain an accurate estimate of LAI one either has to 
know or to measure the reflectance of the bare soil, 
or one has to derive a relation that is less dependent 
on differences in soil moisture content. 
For many soil types, reflectance in the different 
spectral bands does not differ very much (e.g. Condit, 
1970); often there is a slight increase in reflectance 
with increasing wavelength. However, often the ratio 
of the reflectance in two spectral bands is independent 
of the soil moisture content: