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LAI theory
Document code: SS1-UM-1.05
LAI theory
In this section we shall explain as fully as we can how the SunScan computes its
readings of leaf area index, and what the main limitations and provisos are in
interpreting these for real canopies.
Ingredients of the LAI computation method
There are three broad areas contributing to the final result.
Geometric analysis
The first is the analysis of what happens to a ray of light passing through the canopy.
In order to do this, we have to make some general assumptions about the canopy, i.e.
uniformity, randomness and total absorption by canopy elements. This was done by
Campbell (1986) for a beam of light from a single direction (the Direct solar beam)
passing through a canopy with a generalised ellipsoidal leaf angle distribution
function. This function allows a wide range of different canopy types to be described
by the value of a single parameter ELADP.
Wood then integrated Campbell’s result over the whole sky to give a description of
the transmission of Diffuse light through the same canopy. This is important because
the transmission of Diffuse light is different, and in reality there is usually a
combination of both Direct and Diffuse illumination. In particular, the analysis
shows that Diffuse transmission is strongly dependent on the leaf angle distribution,
a point which has not generally been recognised.
These functions are integrals which do not have direct analytical solutions, so have
to be solved numerically, and computable functions fitted to the results. This has
been done to a high degree of accuracy, improving on Campbell’s original
approximation.
Incomplete absorption - more elaborate analysis
The above analysis based on black leaves is relatively straightforward. However,
real leaves also reflect or scatter some of the light that falls on them. Typically, only
about 85% of the incident light is absorbed. This means that in reality, every leaf
element in the canopy is re-emitting light, as well as absorbing it, which makes the
situation much more complicated.
Because the direction of any particular light ray can be changed by reflection or
scattering, it means the spatial distribution of the light changes through the canopy.
Therefore it is no longer adequate to consider just the vertical component of the light
(as measured by a cosine corrected sensor), the horizontal component must also be
included. This is why Wood’s analysis also considers a hemispherical response
sensor (which measures both horizontal and vertical components).
The relentless advance of computing power has made it possible to model the
situation in ways that were not feasible in the past. By integrating the "black leaf"
analysis into a computer model Wood has calculated the light levels in the canopy
across the whole range of canopy and incident light parameters.
