cifically described, generally realistic geometry.
nant near the edge of the medium as within its
This procedure is repeated many times for differ-
interior. Hallikainen and his co-workers measured
ent example surfaces, and the ensemble of results
extinction ranging from only a small number of
is summed coherently. In Chuah and Tan's model,
dB/m to about 500 dB/m. The latter occurred in
the top layer consists of randomly oriented leaves
cases combining the highest frequencies and larg-
and branches, the next layer is a random distribu-
est grain sizes. To be emphasized here are the
tion of trunks, and a randomly rough soil surface
additional surface scattering losses that were in-
forms the bottom boundary. The medium model
ferred, ranging from a small effect to tens of dBs.
differs from that of Karam and Fung (1988) in
The larger surface effects were seen in cases in-
that Chuah and Tan assume a multilayer model
cluding the highest frequencies, largest grain sizes,
with a mixture of different classes of scatterers in
and roughest surfaces in undisturbed samples.
the top layer. Leaves are modeled as randomly
We note particularly that the roughest surface
oriented dielectric circular disks or small needles;
had rms height variations that were only on the
branches and trunks scatter as infinite cylinders,
order of a couple of grain diameters. In other
and the ground is treated using a GO-type limit
words, the grains themselves appear to offer an
to the KA. The primary distinguishing feature of
effectively roughened surface. At the highest fre-
the approach here is the use of a Monte Carlo
quencies, where this was most significant, pen-
method to track photon transport through mul-
etration depth in the snow is effectively only some
tiple scattering interactions in the media. Charac-
tens of centimeters. This means that the surface
terization of the interactions at each collision are
losses constituted an effect comparable in order
used to build up an overall transport picture in
of magnitude to volume scattering over the depth
terms of intensity, not field value as for a WT
sensed. The significance of all this lies in the im-
approach. Using parameters considered to be jus-
plication that one may have to model rough sur-
tified by ground truth, the authors produce cal-
face scattering to account accurately for all scat-
culated backscatter from trees that compares well
tered energy, and the surface roughness treatment
with measurements at S and X bands.
may have to include particle scale effects as well
A closely related approach is applied to the
as more macroscopic surface considerations.
computation of emission (Chuah and Tan 1992b,c).
The version of strong fluctuation theory em-
Given its fundamental basis, we assume that
ployed by Hallikainen et al. (1987) includes some
Chuah and Tan's overall approach should pro-
coherent effects associated with particle proxim-
duce results equivalent to an RT approach. For
ity. In a broader and more rigorous treatment
this reason, together with the uncertain availabil-
(see below), Tsang and Kong (1992) perform cal-
ity of code and support, we do not pursue it here.
culations for a dense medium with correlated scat-
However, it is an innovative approach that merits
tering by particles near one another. The assumed
continued attention, as it may eventually pro-
spherical particles are characterized by a size dis-
duce physical results or computational facilita-
tribution, with sizes comparable to a wavelength.
tion not obtainable otherwise.
Including these features in the model produces
quite good agreement with the same data. Full
calculation of the incoherent scattering is limited
Snow and ice
Hallikainen et al. (1987) use a simplified strong
by the use of the distorted Born approximation.
fluctuation theory following Ishimaru (1978) to
Others at the University of Michigan con-
model the extinction behavior of snow in the 18
structed and tested an RT model for scattering
90 GHz range. Eighteen types of snow were con-
from snow (Kuga et al. 1991, Ulaby et al. 1991).
sidered, from newly fallen to refrozen. Agree-
MMW-scale scattering from assumed spherical
ment between computed and observed values is
ice particles is treated by Mie scattering expres-
good if the single free parameter of grain size is
sions to obtain the phase function; nonuniform
tuned to a value somewhat less than the observed.
liquidice contact to be expected in small inclu-
A very interesting observation emerges from the
sions is modeled by assuming an equivalent "wet
study by Hallikainen et al. in connection with
air" background medium; the density of the me-
surface scattering. Especially for the dry snow
dium is dealt with by the QCA in a manner less
considered, surface scattering is often considered
complete than that of Wen et al. (1990); and the
to be negligible at MMW frequencies. By impli-
equations are solved using the discrete ordinate
cation, this is explained by the prominence of
technique with Fourier decomposition of azi-
particle-scale scattering, assumed to be as domi-
muthal components. The effect of upper snow
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