We now look at some unusual scattering behaviors that nevertheless occur often in remote sensing. Because of the longer wavelengths involved, some materials we image with radar act as hard targets in that they are capable of reflecting a very large proportion of the incoming wave front and thus can appear very bright. Examples of hard targets include metallic elements such as wire fences. Recall the forest example in the last lecture with the adjacent pasture fields. Other hard targets are facets directly aligned to the incoming radar beam such as roof facets and corner reflectors formed by paired horizontal surfaces and vertical structures. Examples include houses, tree trunks, and ships at sea. Because they are such strong reflectors, they tend to dominate the response of an individual radar resolution cell or pixel so that we revert to radar cross section to describe their scattering behavior rather than the scattering coefficient. We will now look at each of these in turn. First, consider simple metallic elements, such as wires appropriately aligned. A wire fence for example can act as a strong scatterer. While the analysis is complicated, we can note that, one, if the fence wire is aligned exactly at right angles to the incoming radar beam, which we call zero incidence angle in this context, and the electric field is in the plane of the wire, then it will reflect the beam strongly exhibiting a high radar cross section. Secondly, if the fence wire is of finite length, then it will also reflect strongly at angles just off zero incidence. Thirdly, if the electric field is not exactly aligned with the wire, there can still be some sizable reflection, particularly if the wire is thick. Finally, if the length of the wire or another elongated metallic element is a multiple of half a wavelength, the element is then called resonant and will give an extremely high response if it is correctly aligned to the incoming beam. Let's look at facet reflection. The roof of a building or another planar structure facing the incoming radar beam is called a facet scatterer. Its radar cross section is given by the formula shown on the slide. We call this it's bistatic radar cross section because the scattering or reflection occurs at an angle two Theta away from the incoming beam. Most of the time in radar remote sensing, we are interested in the case where Theta equal zero so that the radar cross section becomes four Pi times the square of the area of the facet with the dimensions expressed as a fraction of wavelength. Now we come to a very interesting mechanism and one which occurs surprisingly frequently in practice in a number of different forms. It is a manifestation of dihedral corner reflector behavior. The figure on the left shows a dihedral corner reflector. If it is large compared with the wavelength, then it's radar cross section within three decibels over 30-60 degrees is given by the left-hand equation. Now look at the right-hand figure, which is meant to represent the side of the building. The wall of the building has a radar image in the ground plane but the length of that image will depend on the incidence angle as indicated in the figure. It's radar cross section is therefore different from that of a simple dihedral corner reflector because the horizontal surface is not fixed. If we have a standing structure such as a building, then the formula on the right-hand side of this slide provides the appropriate model to use in order to understand its appearance in radar imagery. We can use that same dihedral corner reflector approach as the model for a tree trunk in radar imaging. As shown on the left-hand side here, the trunk has an image in the ground plane. Theoretically, we could use the expression for the radar cross section of a cylinder to help develop a model for the tree trunk ground combination. However, there is a simpler approach. If the trunk radius Y is large compared with the wavelength,it is simpler mathematically to represent the cylinder as an effective flat plate, as indicated in the right-hand diagram, with the equivalent widths as shown. The radar cross-section of the trunk standing on the surface is then given by the equation on the right-hand side. We need to make two modifications to the last expression to allow it to be used in real situations. First, for a tree, the vertical and horizontal materials are not ideal reflectors but are real substances such as wood and soil. We can account for that by introducing the power reflection coefficients for the trunk, that's row subscript T squared and the ground row subscript J squared into the expression for the red at cross-section. Secondly, we have to account for the attenuation of inner canopy that envelops the trunk. We can do that by adding a two-way absorption term, giving as the final radar cross-section of the tree the last formula on the slide. We now have a complete model for the trunk in a thorough situation and can use it to model the backscatter response of a forest in radar imaging. The backscatter curves shown here were produced from the expression for a tree trunk acting as a corner reflector as a function of canopy loss and with the parameters indicated here on the slide. Note that this is the first time we have seen backscattered drop away at small incidence angles. That is because the reflection of the vertical structure in the ground plane shrinks away as the angle becomes smaller. The falling backscatter at the high angles is the result of canopy attenuation, as can be appreciated when looking at the values of the extinction coefficient. Because of the pathway involving the ground in trunk scattering, the radar cross-section is a fairly strong function of the ground dielectric constant, as seen in the formula we derived for the radar cross-section of a tree. It will change, therefore, with changes in the ground material. Particularly if the ground changes from dry soil to water, as when a forest might be flooded. Remember the dielectric constant at microwave frequencies of dry soil is around five or so, whereas for water it is about 81. Therefore, a forest with a water understory will appear considerably brighter than one with a dry soil surface. As shown here, it will be about five decibels brighter. We see an example in the next slide. This slide shows an image of a forest in Australia is across a river and which receives annual floods with snow melts further upstream. The bright response corresponds to flood water from the river under the forest as a result of the corner reflector effect. In this study, the change in backscatter from dry to flooded understory was found from the image to be about 6.8 dB compared with 5 dB, we might expect from the change in dielectric constant of the understory from dry sort of water. However, in this region, the dry understory is unlikely to be sufficiently smooth as to be modeled fully by surface reflection coefficient. Instead, the surface may be more Lambertian, meaning less forward scatter in the dry double bounce model, and thus a larger difference when flooding occurs. So in summarizing this lecture, note that strong scatterers include metallic structures appropriately aligned to the incident radar beam, along with facets and corner reflectors. Next, In many cases strong scatterers will dominate the response of a radar resolution cell. Next, size of houses, trees, ships at sea, and ocean oil rigs will all give strong corner reflector responses. Next, trace without a dominant trunk will not behave as strong scatterers. Next, tree canopy attenuation has to be taken into account when modeling forests with strong scatterers, but not when considering buildings, ships, and oil rigs. Finally, changes in the ground surface can be assessed from radar imagery, even with a canopy, because of the change in power reflection coefficient. The second question draws your attention to the equivalent of canopy attenuation. The third question asked you to pay attention to cylindrical structures like tree trunks.