Electromagnetic wave scattering from vegetation with odd-pinnate compound leaves

Most existing EM scattering models for a vegetation medium assume that the leaves have an orientation distribution and each leaf scatters independently. For vegetations that possess compound leaves (for example leaves of a walnut tree) such an assumption is generally not valid. For this type of vegetation the leaves scatter in groups and it is each group, instead of each leaf, that scatters independently. An individual group of leaves scatters mostly coherently with a small degree of randomness in the spacing between leaves. The traditional radiative transfer approach can still be used but its phase function must be computed for a group of leaves patterned in accordance with the particular type of vegetation. To account for this group scattering effect for vegetation with odd-pinnate compound leaves we use a generalized antenna array theory. The scattered field of a group of leaves will be expressed as the product of the scattered field from a single leaf and an array factor. The corresponding power expression is averaged over the spacing between leaves which has a mean value and a random component. The vegetation medium is modeled as a half-space of randomly distributed and oriented odd-pinnate compound leaves. Theoretical analyses of the effects of the odd-pinnate compound leaves on the backscattering coefficient due to leaf size, spacing between leaves and the total number of leaves in a compound are carried out. It is found that the array factor or the coherence induced by the odd-pinnate compound leaves is important for vegetation media with a compound leave structure, especially when the size of leaves and the average spacing between adjacent leaves in the compound are comparable to the incident wavelength. Finally, the model predictions are compared with measurements from walnut trees where such a group scattering effect is expected.