A hybrid model for electromagnetic scattering from forest canopies

The radiative transfer (RT) theory is the most widely used method for characterizing electromagnetic scattering behavior of a forest stand. Although this method is computationally rather efficient, it suffers from a number of shortcomings when applied to the forest problem. A fundamental problem in application of RT to a forest problem stems from the fact that the trunk layer extends through a large portion of the random medium. In this case derivation of the extinction and phase function based on the single scattering properties of an isolated trunk renders erroneous results. In this paper a hybrid method for forest-like media having a lower layer consisting of long vertical cylinders above a dielectric ground plane and an upper layer consisting of smaller weakly scattering particles is developed. The lower layer is treated using an analytical solution and the upper layer is treated using RT theory. The two concepts are combined through the use of an analytically derived extinction through the cylinder layer. Issues related to multiple scattering, coherence and integration of the RT source functions are also discussed in the context of the hybrid model. Finally, application of the model to a simple two-component random medium consisting of dielectric cylinders and small metallic spheres is presented and the results are compared with results derived from RT theory and a second order Monte Carlo simulations