Modeling ordered trunks at VHF with an effective description

Below VHF frequencies a forest may be accurately represented with an anisotropic effective permittivity that accounts for the average field within the foliage. At higher frequencies however, a quasi-static representation is no longer valid and coherent interaction of the scattered field must be accounted for. This paper provides an effective representation of a forest, which accounts for the zeroth harmonic interaction of the scattered field off the trunks. This is accomplished by assuming an ordered distribution of tree trunks, and when combined with a quasi-static description of the canopy (perturbed to provide a first order account of scattering) to create a propagation model of an orchard, valid up to UHF frequencies. To create an effective representation of tree trunks applicable beyond the quasi-static limit an effective representation based on a transfer matrix description is applied to an ordered array of cylinders. The ordered array of tree trunks, rather than a disordered forest is considered as this may be treated more easily and provides the most violently dispersive response. To account for the branches off the trunks a Lindenmayer algorithm may then be used to numerically simulate the branch density as a function of height, and from that an effective permittivity is determined based on the branch density and connectivity. Within this paper, specifically an ordered array of tree trunks is considered with size and spacing consistent with eastern white pines.