A propagation model for trees based on multiple scattering theory

Based on the multiple scattering theory, we derive a point scattering propagation model which allows an efficient computation of the diffuse component of the electromagnetic field scattered by a vegetation canopy. We show that our mode is in good agreement both with the original multiple scattering predictions and with measurements.

I. Introduction

In order to characterize the scattering effects due to trees with an acceptable complexity level, several electromagnetic models have been used (Multiple Scattering Theory [1], Radiative Transfert Theory [2], Volume Integral Equation [3]). Since its introduction by Twersky in 1967, the Multiple Scattering Theory has been widely applied and modernized in order to characterize various types of vegetation elements [4], [5], [6]. Branches, needles or leaves are modeled as homogeneous dielectric cylinders. Those single scatterers are located either uniformly [6], [7] or following specific schemes like fractal ones in the tree canopy [8]. The multiple scattering theory takes into account successive interactions between all scatterers, each scatterer being involved at most once in each scattering path. It results in a volumic characterization of the electromagnetic propagation properties in terms of amplitude scattering matrix, Radar Cross Section (RCS) and effective propagation constant. We derive a point scattering model that relies on those data and that is used to compute the scattering of a whole tree. Branches and leaves movements due to wind are taken into account.