needle arrays, and resonant size cylinders are be-
ample, are distributed with a randomness that is
ing included so the system can be used at MMW
structured by the basic tree morphology; they
wavelengths, with simulations performed at 10
cluster with predisposed alignment along twigs
50 GHz. Experimental validation at these frequen-
and larger branch elements. Thus, the needles
cies is reported to be underway.
may effectively form a random distribution of
Fung and his co-workers have also attempted
arrays. Drawing on such observations of under-
to build specific leaf and branch character into
lying architecture also allows incorporation of the
vegetation models for frequencies higher than
multiscale nature of vegetation systems. Yueh et
those considered in previous models. Using the
al. (1992) employ two scale branching models
RayleighGans approximation, a first-order RT
with idealized independent scattering behavior
formulation is presented that should be valid for
of individual elements. Calculated responses for
leaf dimensions up to the size of the incident
simple structures as a function of frequency and
wavelength (Karam and Fung 1989). Size varia-
incidence angle show an importance of coherent
tions are included through elliptic disk leaves
or phase relations between constituent elements.
and needles for conifers. On the basis of simula-
In application, including ground surface effects
tions it is suggested that both like and cross po-
and a hole-correction pair distribution function,
larizations may be needed to distinguish leaf type
good agreement is obtained in comparisons with
effects on scattering behavior. As frequency in-
polarimetric C-band data from soybean fields.
creases, near-field effects enter increasingly in leaf-
While greater small-scale coherence effects might
to-leaf field interactions. Fung et al. (1987) allow
be anticipated at frequencies below C band, it
leaves to be in the Fresnel zone of one another for
remains to be seen whether the approach pro-
both disc and needle-shaped leaves. VV and VH
duces significant revelations in the higher-fre-
measurements are matched to calculated X-band
quency domain we are interested in.
scatter for soybean plants. Liu and Fung (1988)
Lang and Kavaklioglu (1991) pursue a related
use an empirical parameterization of vegetation
modeling exercise in which they contrast the be-
material with a rough underlying ground surface
havior of randomly oriented elementary needles
to perform polarimetric scattering computations
with that of randomly oriented arrays of such
for k a values approaching 4, where a is a charac-
needles. It is assumed that the radius of each
teristic leaf dimension. Comparisons of the com-
cylindrical needle is small compared with the
putations with data are good. Karam and Fung
wavelength, which is a reasonable assumption at
(1988) use a first-order RT formulation for ran-
35 GHz, if not at 94 GHz. While comparisons
domly oriented dielectric cylinders to link sur-
with data are not indicated, the modeling evi-
face scattering with that from a defoliated vegeta-
dently showed differences in response between
tive volume. While comparisons with data are
the random needles and random arrays of needles
best for lower k (a = cylinder radius) values,
when the wavelength was comparable to the ar-
favorable comparisons are seen as high as k a =
ray size. We cannot yet say that the concepts used
2. While MMW frequencies strain these k a lim-
in these studies have been shown to be of great
its, leaf sizes and branch radii up to some signifi-
relevance for MMW simulation. However, these
cant fraction of a centimeter could possibly be
first results as well as the appealing rationale of
accommodated at 35 GHz.
the basic concepts suggest strongly that this is an
Tsang and his co-workers at UW, MIT, and GE
area to watch.
have developed vector RT models that may be
We close this section with a brief mention of
applicable to vegetation over rough-surfaced soil
Monte Carlo modeling. Chuah and Tan (1992a)
(Tsang et al. 1990, Tsang 1991, Tsang and Ding
have proposed a model for backscatter from for-
1991, Tsang et al. 1992a). First-order, second-or-
est stands. Their approach is "Monte Carlo" in
der, and full-multiple scattering solutions are ob-
that individual contributing scattering events
tained. Extinction and phase matrices are calcu-
within the canopy are treated probabilistically and
lated in such a way that energy is conserved and
then looked at in their intensity sum. As noted
reciprocity preserved. Application of the mod-
above, this and any other such treatment based
ules to measured data is awaited.
on a cascade of statistical events differs funda-
In an interesting new approach pursued sepa-
mentally from the Monte Carlo treatments of sur-
rately by investigators at MIT and GWU, models
face scattering that have appeared recently. In the
are designed to include the effects of vegetation
surface scattering case, investigators calculate the
architecture. The needles on an evergreen, for ex-
scattering deterministically from an entire, spe-
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