Two statistical models for radar terrain return

A statistical approach to radar backscattering from terrain is taken in this paper. The normalized radar cross section,
\sigma_{0}
, has been computed for two different terrain models. The value of
\sigma_{0}
, is obtained for both models as a function of grazing angle,
\theta
, and radiation wavelength,
\lambda
. The first model is a distribution of isolated independent scatterers such as corner reflectors. For such surfaces a wavelength dependence for
\sigma_{0}
is obtained, and, depending upon the density of scatterers and their average size, the theoretical results indicate that the local dependence of
\sigma_{0}
on
\lambda
can be as
\lambda^{-6}, \lambda^{-4}
or
\lambda^{-2}
. For such surfaces,
\sigma_{0}
is independent of
\theta
. Where reflection occurs from specularly reflecting facets on the surface and where the distribution of surface slopes is Gaussian, the
\theta
dependence turns out to be of the form
e^{-k cot^{2}\theta/2s_{0}^{2}}
where
s_{0}
is the standard deviation of the surface-slope distribution. The precise form of
\sigma_{0}
depends upon the space spectrum of the slopes. Two cases are worked out, one where such a spectrum is flat out to some cutoff, and the other where the space spectrum has a single peak at a particular wave number. In either case, for small enough
\lambda,\sigma_{0}
varies as
\lambda^{-2}
. As the wavelength becomes large compared to the facet size, the facet no longer behaves as a specular reflector and instead becomes more like an isotropic scatterer. For any particular wavelength one may expect that the radar return be the result of the addition of two types of backscattering. The large facets will behave as specular-type reflectors, while the smaller facets will act as the isotropic scatterers discussed in the first model.