Delta-T Devices SunScan SS1 User Manual page 52

Note: in the following equations derived in MathCAD, different conventions
are used for some symbols. Equality is represented by =, and tan
expressed tan(θ)
The extinction coefficient, K, is calculated as follows:
, x 
K(
Where:
x is the ELADP
θ is the zenith angle of the direct beam.
The transmitted fraction of incident direct light is given by:
 dir
where L is the canopy LAI.
Transmission of Diffuse Light
Campbell's analysis applies only to a beam of light from a specific
direction, which is the Direct solar beam in our case. Even under strong
sunlight, the Direct fraction rarely exceeds 80% of the Total incident
radiation, so penetration of the Diffuse component of incident radiation is
also important.
There is a misconception that the extinction coefficient for Diffuse light is
independent of canopy Leaf Angle Distribution, but this is not the case as
the following analysis shows. As the following graph also shows,
transmission of Diffuse light does not obey a simple Beer's law curve, so
cannot be represented by a single extinction coefficient, except in the
case of a horizontal LAD.
52  LAI theory
2
.
2
x
)
.
x 1.702 (
3

K( , 0 )
2

K( , 1 )
 1
K( 100 , )
0
.
, x  L
exp( K( )
2
tan( ) 
0.708
x 1.12 )

)
2
(θ) is
SS1 User Manual v3.3