Accuracy of LAI calculations

When used to predict LAI from transmitted fraction, the functions used in the SunData software are accurate to within ±10% ±0.1 over the range of LAI less than 10 and Zenith Angle less than 60° when compared to the output of the full model.

The errors become larger for highly vertical leaves with a strong low sun, and users should avoid these conditions if possible.

In practice, the greatest errors are likely to follow from the differences between the real canopy and the idealised assumptions in the model.

Functions used to model canopy transmission

Diffuse light - cosine response sensor

The transmission of diffuse light through a canopy, as measured by a cosine corrected sensor, can be modelled by the following functions:

Given:

 

 

 

 

 

 

 

 

A ( x )

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.

 

 

 

1.38

 

 

0.007

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.15 x

 

 

 

 

 

 

 

 

 

 

 

 

B ( x )

 

 

4.32

 

 

 

2.60.exp( 2.75. x )

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C( x )

 

 

0.57

 

 

 

0.23.exp( 1.40. x )

 

 

 

 

 

 

 

 

 

 

 

τ

( x , L )

 

exp(

 

L )

 

 

 

A( x ). L3

.exp

 

B ( x ).LC( x)

 

diff

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

These curves give maximum errors of 0.009 in τ diff, with a maximum 6% error for

τdiff greater than 0.01 over the range L = 0 to 10 and x = 0 to 1000.

Diffuse light - hemispherical response sensor.

The previous analysis of diffuse light transmission is appropriate for a cosine- corrected sensor as it only considers the vertical component of the incident and transmitted light. This works as long as the leaf absorption in the PAR band is complete, and there is no scattering of the incoming light.

When we consider leaves with incomplete PAR absorption, some of the absorbed light is re-emitted in different directions to the original incoming light. Because of this we have to account for all of the incoming light, both horizontal and vertical components, and also be aware that the spatial intensity distribution of the light is modified by the canopy and varies through the canopy depending on the canopy leaf angle distribution.

The above analysis is now repeated to find the transmission of uniform diffuse light as measured by a sensor with a hemispherical response. The equivalent equation for the transmission fraction is:

 

 

 

 

 

 

 

π

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

.

2

. π .

 

 

 

.

 

 

 

 

 

.

 

τ

spher( x , L )

 

 

 

 

sin(

θ

)

exp(

 

K( x ,

θ

)

θ

 

 

 

 

 

 

 

 

2.π

2

 

 

 

 

 

L ) d

 

 

 

 

 

 

0

 

 

 

 

 

 

 

 

 

 

 

 

60 • LAI theory

Document code: SS1-UM-1.05

Page 59 Page 61
Page 60
Image 60
Delta Electronics SS1-UM-1.05 user manual Functions used to model canopy transmission, Accuracy of LAI calculations
Page 59 Page 61

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