Measurement and modelling of the vertical distribution of sunflecks, penumbra and umbra in willow coppice

A 3D model of Salix viminalis canopy describing the coppice as consisting of randomly located shoots is used to simulate the fractional areas of sunflecks, penumbra and umbra within the coppice canopy. The model is based on phytometrical measurements of willow coppice; results are compared with theoretical formulae, a simple model describing the canopy as consisting of randomly located plates, and measured canopy transmittance. The model predicts different sunfleck, penumbra, and umbra fractional areas compared with the simple plate model, differences in the distribution of direct solar irradiance in penumbra are less significant. The 3D model also indicates that the congregation of foliage into shoots induces the dependence of the clumping index on measurement height and solar zenith angle.