A Monte Carlo coherent scattering model for forest canopies using fractal-generated trees

A coherent scattering model for tree canopies based on a Monte Carlo simulation of scattering from fractal-generated trees is developed and verified. In contrast to incoherent models, the present model calculates the coherent backscatter from forest canopies composed of realistic tree structures, where the relative phase information from individual scatterers is preserved. Computer generation of tree architectures faithful to the real stand is achieved by employing fractal concepts and Lindenmayer systems as well as incorporating the in situ measured data. The electromagnetic scattering problem is treated by considering the tree structure as a cluster of scatterers composed of cylinders (trunks and branches) and disks (leaves) above an arbitrary tilted plane (ground). Using the single scattering approximation, the total scattered field is obtained from the coherent addition of the individual scattering from each scatterer illuminated by a mean field. Foldy´s approximation is invoked to calculate the mean field within the forest canopy that is modeled as a multilayer inhomogeneous medium. Backscatter statistics are acquired via a Monte Carlo simulation over a large number of realizations. The accuracy of the model is verified using the measured data acquired by a multifrequency and multipolarization synthetic aperture radar (SAR) [Spaceshuttle Imaging Radar-C (SIR-C)] from a maple stand at many incidence angles. A sensitivity analysis shows that the ground tilt angle and the tree structure may significantly affect the polarimetric radar response, especially at lower frequencies