Scattering model for a pine tree employing VIE with a broadband MLFMA and comparison to ICA

In this paper, we present accurate calculations of electromagnetic wave scattering from a high-detail pine tree model, which includes also the needles. We have deployed a volume integral equation (VIE) model, which takes into account high-order reflections between all scatterers, even between single needles. The pine tree is modeled as a realistic collection of dielectric cylinders. With the help of our calculations, we assess the importance of multiple scattering inside the pine canopy and the contribution of the needles to the scattering. We compare our calculations with a much simpler model output to determine the validity conditions for simplified approaches. As the simpler model, we use an infinite cylinder approximation (ICA) model which uses a truncated cylinder approximation and takes into account only the first-order reflections from single cylinders. Both models are bistatic, fully coherent, and fully polarimetric models suitable in calculating the scattering from a large and general collection of dielectric cylinders. Our results show that, for the C-band calculations, the VIE model output differs significantly from the simple ICA model output, indicating the importance of the higher order scattering between the needles and branches. However, for the L-band, the accurate VIE model gives similar results as the ICA model, indicating that, in this case, the higher order scattering between the needles can be neglected.