Spectral Invariant Behaviour of a Complex 3d Forest Canopy

We present an attempt to apply the spectral invariant approach to canopy scattering of a complex forest canopy. Spectral invariant theory describes a method of expressing photon scattering as a function of purely structural properties of the canopy, the so-called photon recollision probability, p – the probability of a scattered photon undergoing further collision rather than escaping the canopy can be used to describe the main impacts of structure on total canopy scattering. We apply a new spectral invariant formulation for canopy scattering (Lewis et al., 2007) to a detailed 3D structural model of Scots pine. This description assumes energy conservation (by definition in derivation of spectral invariant terms), and that p approaches a constant value when the scattered radiation is wellmixed (when the escape probabilities in the upward and downward direction, ri and ti respectively, approach each other after some finite number i of scattering interactions). We explore the behaviour of the resulting scattering from the complex models and apply the spectral invariant model description to the resulting scattering. We show that the behaviour of the spectral invariant terms (p, r, t) are superficially similar to cases for simple canopies consisting of reflecting and transmitting disks, particularly for lower LAI/density cases. However, the dominance of trunks in the higher density/LAI cases violates the spectral invariant model assumptions. We suggest it may be possible to consider the scattering behaviour of the trunks and vegetation separately, considering the recollision probabilities pneedle and ptrunk independently. * Corresponding author.