Delta SS1-UM-1.05 User Manual download pdf (Page 60)

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• LAI theory Document code: SS1-UM-1.05

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:

These curves give maximum errors of 0.009 in τ

ττ

diff

, with a maximum 6% error for

ττ

diff

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:

spher

(),xL

...

sin( )

exp( )

K( ),x

A( )x

0.15 x

1.38

0.007

B( )x 4.32

2.60 exp( )

2.75 x

C( )x 0.57

0.23 exp( )

1.40 x

diff

(),xL

exp( )L

A( )xL

exp

B( )xL

C( )x

1 2 ... 55 56 57 58 59 60 61 62 63 64 65 ... 85 86

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Delta SS1-UM-1.05 User Manual Page 60

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