A Short Note on Selecting a Microwave
Scattering or Emission Model
A.K. Fung1 and K. S. Chen2
1Professor
Emeritus
University of Texas at Arlington
Arlington, TX 76019, USA
2National
Central University
Chung-Li, Taiwan
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.
General Comments on Model
Parameters
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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.
Exponential correlation
Multi-scale Gaussian correlation
Using Cgg
Using Cpp
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.
Points to Note in Scattering Model
Selection-1
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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.
Points to Note in Scattering Model
Selection-2
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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.
Points to Note in Scattering Model
Selection-3
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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.
Points to Note in Emission Model
Selection-1
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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).
Points to Note in Emission Model
Selection-2
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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.
Points to Note in Emission Model
Selection-3
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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.
Dry surface
Wet surface
Conclusions
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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