SunScan User Manual v 1.05
LAI theory
••••
61
This was again calculated numerically and curves fitted to the data with similar
accuracy as above. The curves fitted are:
Given:
Diffuse light transmission (hemispherical response sensor)
Modelling incomplete PAR absorption and scattering
Radiation models have been used for many years to calculate the effects of scattering
in the canopy e.g. Norman & Jarvis (1975). Wood's model incorporates Campbell’s
ellipsoidal leaf angle distribution and the effects this has on transmission of both
Direct and Diffuse light.
The model splits the canopy into layers of LAI 0.1, extending to a sufficient depth to
absorb all of the incident light. Incident light above the top layer was a known
fraction of Direct (at a given zenith angle) and Diffuse light. The amount of light
absorbed by a layer, assuming completely black leaves, was calculated. The fraction
of this absorbed light re-emitted by the leaves was then assumed to be re-emitted in
all directions uniformly (see Monteith & Unsworth, 1990, p85 onwards) .
The light level at any point in the canopy is then the light calculated assuming
complete absorption, plus the sum of the light re-emitted by each canopy layer,
attenuated by the intervening layers.
These calculations had to take full account of both horizontal and vertical light
components. This involved an iterative solution and a lot of computer time. Finally,
the light intensity as measured by a cosine corrected sensor was calculated.
P ( )
x
1
.
.
0.4 exp(
)
.
0.1 x
(
)
atan(
)
.
0.9 x
0.95
Q( )
x
.
0.255 atan( )
x
0.6
R( )
x
exp(
)
x
τ
spher(
)
,
x L
exp
.
P ( )
x
L
Q( )
x
.
R( )
x
ln(
)
1
L
0
2
4
6
8
10
0.001
0.01
0.1
1
τ
spher (
)
,
0 L
τ
spher (
)
,
1 L
τ
spher (
)
,
1000 L
L
Transmission
fraction
Vertical
Spherical
Horizontal
Leaf Angle
Distribution
Horizontal
Spherical
Vertical
Leaf Area Index
