Delta SS1-UM-1.05 User Manual download pdf (Page 57)

SunScan User Manual v 1.05 LAI theory •

••

• 57

The next section derives the transmission of light from a uniform overcast sky

through a uniform infinite canopy of black leaves of constant LAI with an ellipsoidal

leaf angle distribution.

Let the sky have uniform brightness of 1 per steradian over the hemisphere.

The radiance of a strip around the sky at angle θ is given by:

...

sin( )

and the irradiance on a horizontal surface due to that strip is given by

....

sin( )

cos( )

The total irradiance due to the hemisphere is obtained by integrating over the

complete sky area:

...

sin( )

cos( )

For each strip of sky, the transmitted radiation is given by

exp( )

where K is the extinction coefficient from Campbell,

so the total transmitted radiation is

I d

....

sin( )

cos( )

exp( )

K( ),x

and the transmission fraction τ is given by I/I

diff

(),xL

....

sin( )

cos( )

exp( )

K( ),x

This integral was evaluated numerically over the range x = 0 to 1000 and L = 0 to

10, and is graphed below for three different values of

1 2 ... 52 53 54 55 56 57 58 59 60 61 62 ... 85 86

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Delta SS1-UM-1.05 User Manual Page 57