58
••••
LAI theory
Document code: SS1-UM-1.05
Diffuse light transmission (cosine corrected sensor)
Modelling the canopy transmission
Accounting for incomplete absorption of PAR by the canopy elements, and
scattering of light within the canopy is complicated. It is no longer sufficient to
consider only the vertical component of PAR (i.e. as measured by a cosine-corrected
sensor) because scattering effectively transfers power between the horizontal and
vertical components, so the canopy changes the spatial distribution of power in the
PAR flux as it is transmitted down through the canopy and reflected back up.
A multi-stream computer model was set up to calculate these effects as follows.
Assumptions
•
The canopy is an infinite, uniform, horizontal slab, with leaf elements randomly
distributed in proportion to the surface area of an ellipsoid, as described by
Campbell.
•
The incident light consists of a component from a point source at a given zenith
angle (the Direct Beam); and a Diffuse component of equal intensity from every
point in the sky (Uniform Overcast Sky).
•
The canopy either has sufficiently high LAI that light reflected back from the
ground below is negligible, or the reflectance of the ground is similar to that of
the canopy.
•
Of the light intercepted by the leaf element, a fraction
a
(absorption) is totally
absorbed. The remainder is re-emitted uniformly in all directions.
0
2
4
6
8
10
0.001
0.01
0.1
1
τ
diff(
)
,
0 L
τ
diff(
)
,
1 L
τ
diff(
)
,
1000 L
L
Transmission
fraction
Leaf Angle Distribution
horizontal
spherical
vertical
vertical
Leaf Area Index
horizontal
spherical
vertical
