Microwave scattering model for grassland and short vegetation canopies

The prediction of microwave scattering from grasslands is complicated by two physical characteristics of these canopies. The first is the relatively small vertical extent of the vegetation which at low frequencies mandates the use of a coherent scattering formulation. In this case, the total scattering power is not just the summation of the scattered power of each constituent element; the inner product terms are significant as well. To account for these coherent terms, the relative physical locations of the canopy constituents, as well as their individual scattering, must be known. The other difficulty with predicting the scattering from grassland is the preponderance of long constituent elements extending from the top of the canopy down to the soil surface. These elements, therefore, cannot be modeled as point targets illuminated by a uniform plane wave. However, if the diameters of the constituents are electrically small, an approximation can be employed which leads to an easy scattering solution for long, thin dielectric cylinders illuminated by a non-uniform plane wave. Using Foldy´s theorem, the coherent wave in the vegetation canopy can be estimated, and the scattered fields for each long thin constituent element immersed in this non-uniform wave can then be determined. The scattered field from each element is then coherently added to the scattered field of the other elements of the plant, and again to the scattered fields from the other plants of the canopy