a polarimetric formulation in which the required
radiometer data, the model estimated sensitivi-
scattering functions are based on Mie scattering.
ties of the brightness temperature to variations of
It appears that polarimetric effects enter essen-
moisture content.
tially through the calculated terrestrial surface
Overall, the RADTRAN package has the sub-
emissivities. In any case, it is not clear that this
stantial advantage that it is documented, facili-
particular formulation has been built into the
tated, disseminated, and supported. It includes
RADTRAN package. The other papers referenced
many accepted, state-of-the-art formulation fea-
above indicate that the package enhancements
tures for atmospheric modeling. Gasiewksi's
avoid an on-line computation of precise Mie scat-
model, which shows comparable care in formula-
tering for each specific particle size, phase, tem-
tion, currently eschews polarimetric effects and
perature, and frequency combination. Rather, in-
treats the terrestrial surface extremely simply. It
terpolations are performed on parameterized
shows good results against data for a complex
results of Mie scattering calculations for repre-
precipitation event, with simulations backed by
sentative particle-size distribution functions un-
independent "air truth."
der different conditions. The ultimate results ap-
pear to be accurate when compared with
Vegetation
calculations based on full-fledged Mie scattering
Perhaps the simplest MMW canopy model is
computations (Isaacs et al. 1988).
the scalar RT formulation of Schwering et al.
The enhanced RADTRAN is now designed to
(1988), which utilizes a parameter extraction and
handle emission from a variety of user-specified
solution system reported separately (Johnson and
types of surfaces. The surface or surface layer
Schwering 1985, Schwering and Johnson 1986).
models used are quite simplistic: calm ocean is
Only horizontal propagation is considered, so that
modeled as a dielectric slab; rough ocean, sea ice,
no layer boundaries are encountered. Three el-
and wet and dry snow are modeled using dis-
evations at different parts of a tree canopy are
crete random scatterer inclusions and WT; and
treated, at seasons with and without leaves
vegetation and wet and dry soil are treated using
present. This model has both the attraction and
RT and a continuous random medium model.
the limitation that it was developed closely in
These surface models enter significantly into cal-
tandem with relevant data acquisition and pro-
culations of polarized brightness temperatures
cessing. One can see immediately what the model
that compare reasonably with SSM/I data over
does in application to data from a two-layer
selected areas (Isaacs et al. 1989b), with further
canopy of "real" vegetation (a "regularly planted,
comparisons needed over snow, sea ice, and soil.
well-groomed stand" of pecan trees), but it is not
It seems that essentially all of the specifically po-
clear how widely it might be generalized. The
larimetric content in the data comparisons enters
formulation goes directly to the form of an as-
through these surface factors, rather than through
sumed phase function, which is just the scalar
directional structure and scattering properties of
function
precipitation particles. We note that the extremely
p (γ) = α(2/∆γ)2 exp[ (γ/∆γ)2] + (1 α)
approximate nature of these surface models makes
it unlikely that they would stand up to the kind of
where γ is the angle between the incident and
testing applied elsewhere to more sophisticated
scattered directions of energy propagation, ∆γ is
models with mixed results at best. Most features
the beam width of the forward lobe, and α is the
of the original (1979) version of RADTRAN test
ratio of the forward-scattered power to the total
well against laboratory data; parts of the package
scattered power. Thus, a strong forward lobe and
related to heavy precipitation and the most re-
an isotropic background are assumed. In addi-
cent enhancements have seen only sketchy vali-
tion to constituents of the scalar extinction coeffi-
dation. Most recently (Pickle et al. 1993), the pro-
cient, only the two parameters above are used,
gram was used to help quantify the uncertainty
and these must be estimated from experience or
in DMSP SSMT/T-2 water vapor sounder bright-
with reference to some representative data. Still,
ness temperature measurements. Under precipi-
with reasonable values of the parameters there is
tation-free conditions with clear or partly cloudy
good qualitative agreement with the measured
skies over land and sea, colocated radiosonde tem-
data. Different behaviors are notable at different
perature and moisture profiles were used as in-
levels in the canopy, with a strong coherent for-
put; outgoing radiance was calculated. In the con-
ward lobe at small optical depths. This compo-
text of both satellite and NASA ER-2 underflight
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