In this next set of four lectures, we will look at how radar energy scatters from the earth's surface. This treatment is important in understanding radar images and in many ways, is similar to the importance of spectral reflectance curves in optical remote sensing. We will look at surface scattering, volume scattering, strong or corner reflector scattering and scattering from the surface of the ocean. Along the way, we will discover some interesting and unusual facts about how microwave energy interacts with the surface. Consider a beam of microwave energy incident vertically on a surface as shown in the diagram. To analyze what happens, we have to work in terms of electric fields and we describe the properties of the surface in terms of electrical quantities, the dielectric constant and sometimes it's conductivity. Conductivity does not appear often, but dielectric constant is a material property that is central to radar imaging. The dielectric constant of air is one. Whereas most natural media have dielectric constants in the range of about one to 80 or so. The diagram shows three components of electric field, that incident on a surface, that component reflected from the surface and that component transmitted into the surface medium. Note the definition of reflection coefficient on the right-hand side of this slide for vertical incidents. It is determined exactly by the dielectric constant of the medium. We can also define a power reflection coefficient as shown and a transmission coefficient. We don't use transmission coefficient very often in remote sensing. If we consider dry soil at microwave frequencies, the dielectric constant is about four, said that the power reflection coefficient is about 0.11. That tells us that only about 11 percent of the incident power is reflected. The remainder is transmitted into the surface. The surface therefore, would look quite stark in an image. By comparison, for water at microwave frequencies, the dielectric constant is much larger, about 81, so that the power reflection coefficient is about 0.64, telling us that about 64 percent of the incident power is reflected. The surface therefore would have a light tone in a radar image at vertical incidence. Water is a strong determinant of radar scattering, because it has a major impact on the dielectric constant of a substance. The diagram on this slide shows its effect on the dielectric constant or soil. The imaginary part is related to the conductivity of the soil, which tells us how effectively it will conduct electricity. Now, consider oblique rather than vertical incidence, but still with a smooth surface. If a beam of microwave energy is obliquely incident to a surface, as shown in the diagram, the reflection coefficient becomes polarization dependent. The two formulas given here show that fact. One is the reflection coefficient for horizontal polarization and the other, the reflection coefficient for vertical polarization. Reflection from a smooth surface is called specular, since it is mirror-like, because the reflected field is away from the incident radiation, that is from the radar itself, the surface appears black in imagery. Examples of this include, calm water bodies such as lakes and smooth soil surfaces. Now, consider rough surfaces. Most real surfaces exhibit some form of roughness when being imaged by radar as indicated in the figures here. We now wish to understand the backscattering properties of rough surfaces. However, how do we know beforehand whether we should consider a surface as rough? Well, we use the Rayleigh criterion for that purpose. Note that the decision is related to wavelength, incidence angle and the variation in height of the surface. In the previous slides, we looked at scattering from smooth to approximately rough surfaces. Now, what about the other extreme? A surface that is very rough? Such a surface is called Lambertian for which the backscattering coefficient is as shown in the equation here. Notice that it is independent polarization. It is possible to derive scattering models for surfaces with roughness ranges between pure specular and Lambertian. But those derivations are beyond the scope of this course. We do, however, show results on the next slide. This slide shows three surface scattering models which indicate how the scattering coefficient varies as a function of incidence angle and surface roughness. It is important to have a feel for these types of behavior, particularly for how smooth and very rough surfaces behave. Surface scattering is sensitive to polarization. This graph illustrates the HH and VV lack responses of a moderately rough surface, and it's HV cross polarized response. Remember, this spins at the incident radiation was vertically polarized as it was in the VV case. But there were some horizontally polarized scattering, as well as the vertical component. When cross polarized responses occur, we sometimes say deep polarization has taken place. In this slide, we summarize in two diagrams, surface scattering behavior as a function of the common wavelengths found in radar remote sensing, as a function of surface roughness and as a function of surface dielectric constant. All wavelengths show strong dependence on the dielectric constant of the surface material. Given that dielectric constant is a direct indicator of moisture content. This shows the importance of surface moisture in effecting the tone of a radar image. Note that higher moisture contents give a bigger radar response. Variations in surface roughness show more strongly at the longer radar wavelengths. At X band, it might be hard to discern such changes. So the image will have a more uniform tone overall, irrespective of whether the roughness of the surface might vary across the same. But note that in general, a rougher surface will give a bigger radar response. This slide shows a classic radar image recorded by the short-lived Seasat satellite in 1978. The enhanced backscatter, that is, the lighter regions, resulted from increased soil moisture owing to the effect of a storm to the West and the subsequent storm cells that traveled to the North East both late on the day prior to image acquisition. In summary, the reflected field in radar for smooth surfaces is determined by the reflection coefficient of the air surface interface. Secondly, the reflection coefficient is a function of the surface material dielectric constant, which in turn is a strong function of moisture content. Thirdly, when viewed a obliquely as in a radar looking to the side, a smooth surface will appear black in imagery since there is little or no backscatter. Next, as surface roughness increases, the level of backscatter and thus the radar image tone increases. Backscatter from smooth surfaces is a strong function of incidence angle. Whereas backscatter from rough surfaces is a weak function of incidence angle. Apart from specular scattering, backscattering from rough surfaces will have a cross polarized, that is an HP or VH component, which is also a weak function of incidence angle. Finally, longer radar wavelengths are more affected by surface roughness than shorter wavelengths. The second question here, start thinking about the choice of Bragg law parameters for particular applications.
