The effect of clumping on canopy scattering and its directional properties: a model simulation using spectral invariants

Abstract

The spectral invariants theory predicts that the bidirectional reflectance factor (BRF) of a vegetation canopy can be expressed in terms of the canopy interceptance (i0), the recollision probability (p), and the directional escape probability (ρ). These spectral invariant parameters together form a novel canopy structural parameter – the directional area scattering factor (DASF). The DASF can be retrieved from remotely sensed hyperspectral imagery and has been found to be useful, e.g. for the separation of tree species. The spectral invariants theory, however, does not provide an interpretation of which specific canopy structural properties are captured by the DASF. In this study, we examined the possible link between the DASF and the canopy clumping index (β). A simple model was designed to simulate the effect of β on canopy first order scattering, which was assumed to govern the directional behaviour of the DASF. The model is based on a modified spectral invariants approach, where the assumption of constant p is relaxed so that the first order recollision probability (p1) and single scattering are calculated separately, and canopy BRF is expressed as the sum of the first and multiple order components. Simulations were performed on model canopies, where radiation penetration is described using a traditional statistical approach but allowing non-random foliage distributions caused by clumping. The results indicated a strong dependency between the modelled DASF and the canopy clumping index.