We now want to look at the intriguing possibility of imaging below the surface with radar, along with the mechanism we call volume scattering. Not all of the energy incident on a surface is scattered. As seen in the last lecture, some is transmitted across the boundary and into the surface medium. There it is absorbed by losses, usually very close to the surface. Sometimes though, the losses are small enough to allow significant propagation into the medium, so that the energy is then scattered by buried features, allowing those features to be imaged. The loss of power density with propagation into the surface medium can be described by a simple exponential equation in which the exponent is called the absorption coefficient. It is given by the second formula on the slide, in which we see it is a function of wavelength, the dielectric constant of the medium, and its conductivity via the so-called imaginary part of the dielectric constant. Based on those equations, we can make a number of important observations. If kappa, the absorption coefficient, is large then power density drops quickly with distance into the medium. Kappa is smaller for longer wavelengths, indicating that there is better transmission into the surface material at longer wavelengths. We now define the penetration depth delta as that value of r at which the power density has dropped to 1/e of its value just under the surface. The diagram in this slide shows the penetration depth at L band as a function of moisture content. Note that for very dry media, we can get penetrations of several meters. It is important to note that the signal doesn't stop after the penetration depth. Depth is just a convenient measure of how quickly it falls away. Objects several penetration depths below the surface can still return measurable signals to the surface, noting that absorption happens, of course, on both the forward, or incident, and backward, or reflected, paths. This is a wonderful example of the ability of spaceborne SIR to image below the surface of very dry sands. The top image is an optical color infrared photo, and the bottom is a shuttle imaging radar C composite radar images, with the color assignments shown. The radar energy has penetrated below the sand sheet to reveal an old paleo channel of the Nile River, as shown. Adjacent buried drainage patterns are also visible in the bed rock under the sand sheet. We now turn to the scattering of radar energy from volume media, such as tree canopies, shrubs, and sea ice. Those types of media contain many individual scattering sites that are harder to identify but which collectively contribute to a backscattered signal, as in the diagram shown on the slide. A simple model of this type of behavior has been devised by assuming that the medium consists of a cloud of water droplets. They are the scatterers. Known as the water cloud model, it gives the scattering coefficient of the volume medium as shown by the equation on the slide. Note that it is a function of the thickness of the canopy and the volume metric properties of scattering coefficient and extinction coefficient. Note also that the loss of energy from the signal is a result of scattering by the fine particles of water. We can use that model to simulate volume scattering behavior. The diagram here compares volume scattering with very rough surface scattering in which we see that volume scattering is even less dependent on incidence angle than the roughest of surfaces. Although many surfaces might show a small specular component near the origin for surface scattering, except for this very rough case, there is never any specular component with volume scattering. Here we make two important observations about volume scattering, one to do with polarization dependence, and the other concerned with the frequency or wavelength dependence of the volume extension coefficient. The simple water cloud model of volume scattering is based on a set of small spherical scatterers. It therefore generates no cross-polarized returns. In general, however, volume scattering is highly depolarizing, which means it causes a cross as well as a co-polarized signal. That is because the scatter is are not spherical but have geometric shapes, such as found with twigs and leaves. As with like or co-polarized behavior, that is HH or VV, the cross-polarized, HV or VH, backscatter signal is very insensitive to incidence angle, but is usually much lower in magnitude than the level of the co-polarized response. The extinction coefficient for volume scattering is strongly dependent on wavelength, meaning that energy loss through the canopy is also wavelength-dependent. If the canopy has low loss, then imaging can be performed of the underlying medium, such as the soil surface and trunks underneath the tree canopy, and the water surface in the case of sea ice. In general, tree canopy attenuation is almost negligible at P band, it's very low for L band, it can be moderate at C band, and is generally high for X band. Although not a very good image, this JERS-1 image of a forested region in Australia shows how much higher the volume response of the forest is compared with the surrounding grassland. Both are vegetated, but the grassland at L band is behaving more like a surface scatterer. So in summary for this lecture, radar energy can penetrate very dry surfaces at long wavelengths. The absorption coefficient and the depth of penetration are strong functions of moisture content. Volume scattering is a weak function of incidence angle. In general, there are both cross and co-polarized components of volume scattering. Volume scattering is in general stronger than surface scattering at longer wavelengths. The canopy extinction coefficient for volume scattering is a strong function of wavelength. And finally, canopies appear almost transparent at P band but look like strong opaque scatters at X band. The second question here concentrates on the relevance of penetration depth. Bowler first asks you to think about a scattering mechanism that we will meet in the next lecture.
