Electromagnetic Scattering from Foliage and Vegetation:
Modelling and applications in Active Microwave Remote Sensing
3. Radiative Transfer Approach
Consider the problem of a plane wave in air incident onto an inhomogenous layer above a place ground half-space (see Figure 3). The equation of energy transfer describing the Stokes' intensity vector, I, within the layer can be written as:
where ke is the extinction coefficient matrix and S the source term arising from energy scattered from other directions into the direction of propagation by scatterers in the medium given by:
P is the phase matrix of the scatterer in the medium. This formulation is extended to study a vegetative consisting of mixture of different types of scatterers. A set of equations for iteration can be obtained by substituting the boundary conditions into Eq. (8). After the equation is solved the backscattered coefficient can be calculated using the backscattered specific in the air.
Fig3. Scattering Model for an inhomogeneous
Layer Above a semi-infinite planar
half-space
Figure 4 gives an example of comparison with measurement from a soyabean field where the canopy height is about 1.0 m. The field is modeled as a layer of circular disks, representing the leaves; and prolate ellipsoids representing the stems. Good agreement is obtained between measurement and theory for both co-and cross-polarizations except near nadir where the contribution from surface is significant. For simplicity, the soil surface has been modeled as a plane. To treat rough surface effect, a rough surface model can easily be included in the model.
Fig.4 Comparison of Radiative Theory and measurements from soyabean field at 1.1 GHz
