Equation fitting and inversion

The results of the computer modelling, while accurate, are not suitable for use in a field instrument. It takes many minutes of processing on a fast PC to calculate light transmission for any given conditions using the model, and the Psion Workabout is not a fast computer!. The model calculates values of light transmission for a given LAI, whereas the SunScan measures light transmission. This means that the functions have to be inverted to work back to LAI, which is more difficult.

To give you immediate results in the field, computable functions have been fitted to the model data, and it is these that are solved to give LAI to reasonable accuracy from the parameters measured by the SunScan system.

Note! Wood’s SunScan equations are copyright, and you should not copy them without written permission unless for purposes of scientific debate or publication, in which case they should be fully acknowledged.

Theory versus reality

We believe that Wood’s SunScan equations accurately reflect the assumptions that the modelling is based on.

By far the largest uncertainties are bound to be caused by

•the mismatch between the real canopy architecture and the simplifying assumptions built into the fundamental analysis

•to a lesser extent the uncertainty in the numerical values of ELADP estimated for your canopy.

With these caveats, the values of LAI for your canopy, even if of uncertain accuracy, will provide valid trends for a given canopy (e.g. canopy growth in a season), and valid comparisons between different canopies of similar architecture (e.g. trial plots of different cultivars of the same species). If you are able to compare SunScan estimates with actual harvested samples from time to time, this will enable you to calibrate out any systematic errors due to your canopy not matching the SunScan assumptions.

If you wish, you can force the SunScan calculations to be equivalent to older, less sophisticated inversions by setting some of the parameters to appropriate values. For example, setting ELADP to 1024 (horizontal leaves) and Absorption to 1.0 will give you the simple Beer’s law inversion.

Derivation of Wood’s SunScan canopy analysis equations

The major assumptions

•The canopy is an infinite, uniform, horizontal slab, with leaf elements randomly distributed in proportion to the surface area of an ellipsoid, as described by Campbell.

•The incident light consists of a component from a point source at a given zenith angle (the Direct beam); and a Diffuse component of equal intensity from every point in the sky (Uniform Overcast Sky).

•The canopy either has sufficiently high LAI that light reflected back from the ground below is negligible, or the reflectance of the ground is similar to that of the canopy.

•Of the light intercepted by the leaf element, a fraction a (absorption) is totally absorbed. The remainder is re-emitted uniformly in all directions.

SunScan User Manual v 1.05

LAI theory • 55

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Delta Electronics SS1-UM-1.05 user manual Derivation of Wood’s SunScan canopy analysis equations, Major assumptions
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