Digital Signal Processing Reference
In-Depth Information
Table 8.3
Validity ranges of the Kirchhoff approximation and its different
regimes (From
Zhurbenko 2011
)
Method
Equations
Validity limit
kl > 6 and l
2
>2:7
and R
0
KA
8.25
XY=
(far-field)
KGO
8.30
-
8.33
(lin.pol.)
k > 2 and
8.40
and
8.41
(circ.pol.)
R
0
XY=
KPO
8.42
and
k < 1 and
Ulaby et al.
(
1982
, Appendix 12C)
slopes
< 0:25 and
R
0
XY=
the Doppler effects. The Doppler effects due to the surface scattering geometry
(projections of the different velocities along the propagation path) were described
in Sect.
8.4
and Eq.
8.6
.
8.6.2
Summary of Other Methods
As listed in
Elfouhaily and Guérin
(
2004
), more than 30 different approaches
and methods have been reported to deal with electromagnetic scattering off rough
surfaces. That reference performs an exhaustive review of several aspects of them
all. This section will compile brief summaries of the most popular ones.
Small Perturbation Method (SPM):
This method tries to find a solution to the
partial differential boundary equation by expanding the field in a perturbation
series of the slopes of the surface (
Rice 1951
,
1963
). The SMP is a good model
for small slopes statistics (both standard deviation of the sea surface height
and correlation length below the electromagnetic wavelength), it is the most
appropriate for Bragg scattering issues, and to assess polarimetric performances.
Two-Scale Composite Model (2SCM):
This approach sums the contribution of
the large scale roughness and the small scale effect to the scattered field. While
the large scale contribution is modeled through the KGO, the small roughness
contribution is the SPM solution averaged over the statistics of the tilt of
the large scale sea surface characterization (
Bass and Fuks 1979
;
Valenzuela
1978
). Besides the non-coherent received power scattered from smooth and large
slopes oriented in the appropriate direction (KGO), it is also possible to receive
additional power from other non-specular mechanisms, such as diffraction and
Bragg resonance. These mechanisms are produced in the sea surface roughness
small scale and when the radius of curvature is smaller than the electromagnetic
wavelength. Given that most of the Earth reflecting surfaces present a continuous
roughness spectra, the main problem of the 2SCM is to define the limit between
large and small scales in which to apply KGO and SPM respectively.
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