Delta-T Devices SunScan SS1 User Manual page 59

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 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.
The results were then analysed in terms of La, the LAI of a canopy of
black leaves that would give the same transmission as a canopy of LAI L
assuming incomplete absorption, all other factors being equal.
. L (
L a 1 g( 1 a ) )
L is the "true" LAI,
L is the LAI that when used in the black leaf model, gives the same
a
transmission as L used in the complete model.
a is the leaf absorptivity in the PAR band.
The function g varied with all the other parameters in a complex way, but
most strongly with x, the leaf angle distribution parameter, and with solar
zenith angle for the direct beam. The following equations represent quite a
crude approximation to the full model, but give satisfactory results for most
situations. If any given transmission fraction is inverted using the
approximation, the LAI calculated is within ±10% ±0.1 of the "true" LAI
indicated by the full model, except for x near 0 (extreme vertical leaves)
and zenith angle > 60 (strong low sun).
g diff 0.5
For diffuse light:
For direct
2 5
. . . .
g dir exp( 1.5 x ) 0.2 0.7 zen 0.2 zen 0.3
beam:
where: x
is the ellipsoidal leaf angle distribution parameter
zen is the solar zenith angle in radians.
LAI theory  59
SS1 User Manual v3.3