Delta Electronics SS1-UM-1.05 user manual Modelling incomplete PAR absorption and scattering

This was again calculated numerically and curves fitted to the data with similar accuracy as above. The curves fitted are:

	Given:			P ( x )	1		0.4.exp( 0.1. x ).( atan( 0.9.x )				0.95 )
				Q( x )		0.255. atan( x )			0.6
				R( x )		exp(		x )
				P ( x ). LQ( x)			R( x ). ln( 1			L )
τ	spher	( x , L )	exp

Diffuse light transmission (hemispherical response sensor)

	Transmission	1
	fraction
Leaf Angle
Distribution					Vertical
		0.1
	τ spher ( 0 , L )
Vertical
Spherical	τ spher ( 1 , L )
Horizontal	τ spher ( 1000 , L )	0.01			Spherical
					Horizontal
	0.001		2	4	6	8	10
		0

L Leaf Area Index

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 the light 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.

SunScan User Manual v 1.05 LAI theory • 61