Delta SS1-UM-1.05 User Manual download pdf (Page 58)

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• 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

diff

(),0L

diff

(),1L

diff

(),1000 L

Transmission

fraction

Leaf Angle Distribution

horizontal

spherical

verticalvertical

Leaf Area Index

horizontal

spherical

vertical

1 2 ... 53 54 55 56 57 58 59 60 61 62 63 ... 85 86

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Delta SS1-UM-1.05 User Manual Page 58

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