formulation to far-field interparticle interaction
quencies of interest here are limited by, among
resulted in underestimation of computed back-
other things, the assumption of small permittiv-
scatter and overestimation of brightness temper-
ity variations.
atures. Computations with near-(intermediate-)
Investigators in collaboration with MIT re-
field effects between particles produce superior
searchers and others, at the University of Wash-
agreement to backscatter data shown for about 8
ington (UW), have developed a number of mod-
GHz. Tjuatja et al. (1992) build on this with their
els that may be applicable to snow and ice.
multilayer model that includes volume scatter-
Concentration has been on generic dense non-
ing, surface scattering, and volumesurface inter-
tenuous granular media and size distribution
action. With the volume component treated by
effects (Tsang and Ishimaru 1987; Ding and Tsang
RT, the surface scattering may be computed us-
1989, 1991; Wen et al. 1990; Tsang and Kong 1992).
ing Fung's integral equation method (e.g., Fung
A rigorous basis for dense-medium RT is pro-
and Pan 1987, Fung et al. 1992, Fung 1994) and
vided by Tsang et al. (1985) and Tsang (1992)
then added incoherently as a boundary condition
based on multiple-scattering-field theory. The pa-
on the volume. Although all volume scatterers
per by West et al. (1993) actively incorporates
are treated as spheres, the model is applied suc-
most of the developments leading up to it, and it
cessfully to sea ice. Snow-covered ice is only
is a good display of the revelations made possible
treated at 5 GHz, but frequencies as high as about
by the method. With variations and departures in
14 GHz are considered for ice alone. While this
each of the works cited, correlated scattering is
still remains somewhat below our desired fre-
incorporated via the QCA and QCACP for the
quency range, it does entail a treatment of scatter-
first moment of the field and the correlated lad-
ing elements that are large relative to the wave-
der approximation for the second moment, such
length, with dense media, in the sense that
that an intensity operator may be obtained that
non-far-field interaction of particles is included.
conserves energy. A size distribution is employed
Most recent investigations in the same frequency
for constituent particles with pair distribution
range with active sensing are reported by Fung et
functions calculated under the PercusYevick ap-
al. (1995). Passive sensing of snow-covered sea
proximations. Near-, intermediate-, and far-field
ice (Tjuatja et al. 1995) up to 90 GHz treats dense-
particle interactions are taken into account such
medium effects by calculating a P matrix includ-
that coherent effects are expressed in the near-
ing near-field and coherent interactions of ele-
and intermediate-field ranges. Many interesting
ments in a randomized 3-D grid. Simulated
features emerge from the numerical simulations,
behavior parallels that seen in measurements else-
such as less scattering from a dense correlated
where.
medium than from an equivalent independent
Substantial groundbreaking work on volume
scattering medium; much greater scattering from
scattering has come from researchers working at
a medium with distribution of particle sizes com-
MIT. Using an RT approach, Shin and Kong (1989)
pared with a monodispersed mixture of the same
calculate bistatic scattering coefficients for a two-
average radius; and the importance of multiple
layer random medium using all four Stokes pa-
scattering.
rameters (vector RT). In general, RT calculates
In treating the correlated scattering in dense
energy balances, and most phase effects are lost.
media, these DMRT approaches require the defi-
However, vector RT offers a partial compensa-
nition and computational treatment of a particle
tion in that general elliptically polarized inci-
pair distribution function (PDF). This function
dence and response states are included. The nu-
expresses the conditional probability of finding a
merical approach provides valid solutions for both
particle at a given distance from another, and it is
small and large albedos; azimuthal Fourier de-
directly related to the correlation function for the
composition is used, with Gaussian quadrature
medium. Its computational implementation is
and eigen analysis. Combined volume and rough
made tractable for spherical particles through
surface scattering effects are included by modifi-
employment of the PercusYevick approximation.
cation of the boundary conditions. KAGO sur-
Once PDF and other dense-medium consider-
face conditions are assumed. While measured data
ations are accounted for in determining the con-
are not treated, illustrative computer runs show
stituents of the basic energy balance equation, the
dominance of rough surface effects for incidence
form of that equation is essentially the same as
near nadir with volume scattering predominant
for CRT, hence the same numerical considerations
for large angles. Applications to media and fre-
apply to its solution. We note that multiple scat-
17
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