scatter showed different rates of decline of σVV
surface roughness is accounted for in an extremely
and σHH with increasing incidence angle. Encour-
simple KA stationary-phase approximation. Co-
polar volume contributions are added incoher-
aged by observations of approximately spherical
ently to the direct backscatter calculated from the
grains in the snow surveyed, the authors con-
surface. With the addition of a hybrid first-order
structed inputoutput relations of the polarimet-
numerical solution in Ulaby et al. (1991) to ad-
ric quantities based on a modified Mueller matrix
dress the refrozen case, overall good agreement is
for orientation-independent scatterers, modified
shown between experimental observations and
by transmissivity factors. The latter assume
theoretical calculations. Having gained confidence
Fresnel-type interface effects and provide much
in the numerical model, Ulaby et al. (1995) run it
of the polarimetric behavior sought; the whole is
for a matrix of cases to generate broader informa-
tuned using the original measurements. While
tion on the dependencies of the backscattering
admittedly empirical, this model provides a struc-
cross section of snow at 35 and 94 GHz. From
ture consistent with basic physical mechanisms
these results a semi-empirical model is constructed
and common forms of their description, and it
in the form of a single equation. This equation
catches some basic polarimetric behavior. We note
may represent the simplest model of snow back-
that the inclusion of the surface effects is essen-
scatter from the point of utilization. It offers the
tial. Subsequently, Chang and his colleagues
great advantage that, for example, a large num-
(Chang et al. 1996) report and analyze snow
ber of scene pixels can be generated extremely
backscatter measurements at 35, 95, and 225 GHz.
rapidly for changing conditions. While the ulti-
Newly fallen snow in which grains still exhibit
mate equation rests on both data and theory, it
flattened, platelet-like geometry shows distinc-
requires faith that the numerical model extended
tive polarimetric effects, with decrease in magni-
the original data with sufficient fidelity.
tude and increase in phase in the correlation of
Narayanan and McIntosh (1990) study high-
horizontal and vertical copolar components. To-
frequency polarimetric backscatter from multi-
gether with information from the scattering mea-
layered snow. Their model treats multilayered
surements, this particle geometry is taken into
snow in terms of a cascade of scattering from a
account in a simple way in the construction of a
number of homogeneous layers with distinct
phase matrix. The resulting RT formulation
avoids both the rigor and complexity of the dense-
boundaries. The approach uses inputs from
medium treatments outlined below; calculations
ground truth measurements, which in their en-
tirety have included surface roughness, moisture
using it reflect the distinctive polarimetric obser-
content, density, hardness, particle size, and grain
vations.
The work by Chang et al. also shows instances
type. Total back-scattered power is the incoher-
in which the backscatter behavior is dominated
ent sum of surface reflection at the interfaces and
a very simply computed volume scatter. An ef-
by a thin refrozen crust on the snow. Together with
fort is made to include bistatic scattering effects
the evident effect of nonspherical particle geom-
and shadowing on the rough surface. Multiple
etry, the importance of the crust poses a consider-
able challenge for modelers. A layer only a few
scattering between layers and ice particles is ig-
nored. Transmission between layers is considered
wavelengths or grains thick (0.52.0 cm) may
to be simple Fresnel transmission of fields as
throw into question the applicability of an RT
volume-scattering analysis. In addition, one must
for incidence on a solid slab. Slab dielectric con-
stants are obtained from the Poldervan Santen
confront an essential scattering volume with rough
mixing formula for ice spheres and water, and
surface excursions that could be greater than the
volume scattering is computed as the simple sum-
thickness of the volume (layer) itself. In any case,
we note that reliance on the measured results in
mation of Mie scattering from individual grains
with a Rayleigh distribution of diameters. Weak
the construction of the recent U. Mass. models
surface scattering is computed using the station-
limits their predictive value and places them
ary-phase KA approximation. Reported co-polar
largely outside of the type of model sought here.
NRCS values computed from the model compare
Fung and Eom (1985) investigate the scatter-
ing and emission behavior of snow. The medium
favorably with measurements.
Another generation of empirically based mod-
is modeled as a densely packed matrix of ice
els has come from a group at the University of
spheres; distance-dependent terms are kept in the
Massachusetts, begining with Mead et al. (1993).
development of expressions for particle scatter-
Fully polarimetric measurements of snow back-
ing as input to the phase matrix. Limiting the
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