1. A Short Note on Selecting a Microwave Scattering or Emission Model A.K. Fung 1 and K. S. Chen 2 1 Professor Emeritus University of Texas at Arlington Arlington, TX 76019, USA 2 National Central University Chung-Li, Taiwan

2. Objective The surface scattering and emission or effective reflectivity model is one of the essential components in many applications of the microwave remote sensing of geophysical properties in the complex earth terrain. The objective of this talk is to summarize a number of points relevant to the selection of a scattering or an emission model for data interpretation from a statistically describable natural terrain.

3. General Comments on Model Parameters ● Model parameters are generally effective parameters representing the terrain physical or geometric properties, responsible for generating the data collected at a specific frequency or a range of frequencies. ● For an idealized single-scale statistical surface, model parameters must agree with the surface parameters. However, for unknown multi-scale surfaces, model parameters retrieved from a data set are effective parameters.

4. Exponential correlationMulti-scale Gaussian correlation

6. Using C gg Using C pp Despite the two functions appear very close to each other, there is a huge difference in backscattering because these two functions represent different surface curvatures. The curvature of the surface is an important consideration in scattering especially in the intermediate and high frequency region.

7. Points to Note in Scattering Model Selection-1 ● Scattering from a terrain is sensitive to the geometric properties (roughness and correlation) of the terrain surface. Dielectric property affects mainly the level of scattering and to a lesser extent the angular shape. ● Generally, a natural, unknown surface has many scales of roughness. If so, surface parameters selected based on a data set are effective parameters applicable only to a range of frequencies. ● Only scatterer sizes, smaller or comparable to the exploring wavelength, are responsible for scattering. Large roughness scales will act as tilted planes for smaller roughness scales. Hence, they should not appear as scatterers in the scattering model.

8. Points to Note in Scattering Model Selection-2 ● In the ideal case where there are no small scatterers riding on the large ones, we reach the geometric optics condition which is uncommon in a natural environment. ● In practice, scattering is more sensitive to surface correlation function than the surface height statistics. This may be the reason why many surface scattering models appear to work, even though their assumption of having Gaussian height statistics is incorrect. ● Whenever there are several sizes of scatterers present on a surface, the overall correlation function for the total surface looks like an exponential function. This is why in many cases the assumption of an exponential correlation function seems to work under low to medium frequency conditions.

9. Points to Note in Scattering Model Selection-3 ● When there is a surface cover, a volume scattering layer appears. In backscattering volume scattering tends to dominate mostly at large angles of incidence. This is because surface scattering is tapering off faster than volume scattering as the incident angle increases. Volume scattering is known to be more uniform in its angular distribution.

10. Points to Note in Emission Model Selection-1 ● Emission is very sensitive to boundary porosity characterized by its dielectric value. Boundary roughness can increase emission a little and roughness correlation has practically no effect on emission. ● A surface with a nonporous boundary will emit with a large separation between vertical and horizontal polarizations especially near the Brewster angle region (For example from a clean sea surface). As porosity increases, the separation between the polarizations will narrow (For example, a sea surface with a foam cover which serves as a porous layer to the sea surface).

11. Points to Note in Emission Model Selection-2 ● For surfaces with cover such as a vegetation cover, which has a small average dielectric constant, the emission from the vegetation layer is high and the separation between vertical and horizontal polarizations is small. Thus, emission from the surface below is masked by that from the vegetation layer. ● Snow and ice cover over water surface have a similar effect as stated above. Less obvious is the loose dirt cover over a bare soil surface. When the loose dirt layer is ignored in modeling, large error in emission will result.

12. Points to Note in Emission Model Selection-3 ● Whether there is a loose dirt cover over a bare soil surface can be detected by comparing the collected angular data. A surface without loose dirt will have a very large separation between vertical and horizontal polarizations near the Brewster angle region, where a peaking is seen in vertical polarization. ● Generally, a plowed field will lose more moisture at the air-soil interface than deeper down inside the soil. Hence, there is a gradual change in the dielectric constant as a function of depth creating a transition layer which must be included in the emission model for such surfaces.

13. Dry surface

14. Wet surface

15. Conclusions ● Data interpretation requires the selection of an applicable model. In most cases the failure in modeling is due to an inaccurate assumption about what should be modeled. ● This note summarizes some of the problems to assist users in model selection. ● Specific examples of the points stated in this paper can be found in “Microwave scattering and emission models for users” published by Artech House in 2010