The understanding of the information contained within the active (and passive)
polarimetric radar signals from polar surfaces is an extremely complex problem. Shi et al. (1992a) state the urgent requirement for a polarimetric model to assist with the analysis and understanding of the scattering from polar surfaces.
Deficiencies of existing models as discussed above (section 2.2) show that the interaction of electromagnetic waves at oblique incidence on dielectric material may be explained by the inclusion of effective dielectrics. The polarization state of the incident, reflected and transmitted signals should be considered and the phase of these signals should also be preserved to account for the effect of multiple reflections within layered medium (such as snowpack). The complex dielectric constant of the geophysical material should also be considered and the depths of the surface and subsurface layers should be included in the analysis.
The polarization ratio calculated by existing rough surface models - for example, the Small Perturbation Model, using the relationship as derived by Barrick and Peake (1968) - has been found to be too high for rough surfaces (Durden, 1986). This relationship does not account for the low polarization ratio of the measured AIRSAR data over snow
surfaces. These snow surfaces appear smooth for P band AIRSAR, so quasi-specular scattering may be assumed.
All these factors are included in the new model.
2.3.1 Basis of new model.
A theoretical polarimetric model based on conservation of energy is developed to assist with the understanding of polarimetric radar signals. The reflected, transmitted and absorbed energies are calculated by considering the interaction of the radar with the imaged terrain. This is simulated by considering the interaction of the incident electromagnetic radar wave with the complex dielectric of natural materials (which is dependent largely on the water content). The amplitude and phase components of the electromagnetic wave are considered so phase coherency is maintained. This is achieved using complex matrix analysis.
The new model includes the use of effective dielectrics to explain the interaction of polarimetric electromagnetic waves at obhque incidence.
2.3.1.1 Active signal.
The forward reflected polarimetric signal may be calculated for any incident polarization state, for any input frequency and for the full range of incidence angles for any system of layers of different complex dielectric material and depths. This calculated theoretical polarimetric signal is plotted on a normalized 3D plot (normalized output power versus change in ellipticity from -45 to +45 degrees, and orientation 0 to 180 degrees
corresponding to the format of the measured AIRSAR data).
2.3.1.2 Passive signal.
The absorbed component may be equated to the passive emitted energy for the system of simulated layers as the ability to emit is directly proportional to the absorbivity of the material. The VV and HH absorbed components are therefore directly related to the vertical and horizontal polarization brightness temperatures Tgy and Tgj^ as measured by passive microwave radar systems (section 3.4.1).
2.3.1.3 Matrix analysis.
This theoretical complex matrix based program determines the polarimetric reflected signal from a system of n layers of complex dielectric material of independent depths. The passive emitted signal is also calculated by consideration of the absorbed energy.
A plane wave model is adopted to trace the path of the incident radar wave through the system of layers at any incident angle and for any operating frequency. The Fresnel reflection at dielectric interfaces is considered and the absorption within the layers of material is calculated due to the attenuation of the radar signal in the lossy dielectric. The complex dielectric content of the material is considered so information of both the amplitude and phase of the wave is retained.
A full range of polarimetric incident waves is modelled ( the ellipticity and orientation of the input wave vary from -45 to 45 degrees and 0 to 180 degrees corresponding to the
2.3.2 Assumptions and deficiencies of new model.
A plane wave model is adopted to trace the path of the incident radar wave. Actual systems may produce edge effects due to the physical size of the beam. This may be removed using calibration data for specific systems and details of the individual antenna characteristics.
Quasi-specular scattering is assumed, so the model is only valid for near normal incidence for the active response. Measured data of the backscatter of snow over the full range of incidence angles away from nadir are given in figure 2.10 (Ulaby and Dobson, 1989). To extend the model further (for greater incidence angles for the active response) the new model should be combined with a model of the backscatter of snow, possibly by adapting the Small Perturbation Model and including the empirical results (section 2.1.4.3).
The model is valid for a complete range of incidence angles for passive systems for smooth surfaces only. The effect of rough surfaces may possibly be included by combining the quasi-specular response (as calculated using the new model) with the response for rough surfaces using an existing rough surface model (for example, the Small Perturbation Model).
The effect of rough surfaces is not included for the work in this thesis as the snow surface appears smooth for P band AIRSAR (section 2.2.1).
The effect of scattering from inhomogenieties may also be included in the model (section 2.2.2). At present the model assumes homogeneous layers of dielectric material. The effect of a gradual change in dielectric constant within a layer may be simulated by introducing a series of matrices to describe the response. The effect of scattering from smaU particles within a layer may be considered using Mie scattering (Bom and Wolf,
1980).
At AIRSAR frequencies the snowpack appears homogeneous and the individual grain size of the snow particles is much smaller than the operating wavelength so Mie scattering is not included for the work in this thesis (section 2.2.2.2).
In addition, the polarization ratio gives indiscernible difference for Mie scattering from spherical particles. As the polarization ratio of the linear polarization states are used in the analysis of the polarimetric data this is assumed to be unaffected by Mie scattering from individual particles (section 2.2.2.2).
The polarization response from larger cylindrical ice lenses is investigated in this thesis using existing models of the scattering characteristics of cylindrical objects (Ulaby and Elachi, 1990). This information may be added to the model. The shape of the 3D polarimetric response depends on the orientation of the cylinders - it is similar to the response for direct scattering for horizontal cylinders, whereas the vertical cylinders give an unsymmetrical polarization response plot (section 2.2.2.3).