terns. Ulaby and his co-workers have pursued
the work by Ulaby and his colleagues, in that
specific modeling and measurement of leaf-scat-
McIntosh's group shows differences in polarimet-
tering patterns, with increasing morphological and
ric returns distinctly as a function of tree type, or
constitutional complexity for the leaves and with
at least class of tree type.
increasing incident frequency (Senior et al. 1987,
These observations are intended to highlight
Sarabandi et al. 1988, 1990). Nevertheless, Ulaby
the particular nature of MMW scattering from
et al. (1990) take the view that:
environmental features, to serve as a warning
1. Truly realistic MMW phase functions for the
against the facile extension of lower-frequency
variety of vegetation elements cannot currently
modeling approaches to MMW and to suggest
be determined.
restraint on attempts to build sophisticated model
2. If they could be determined, realistically com-
structures based on gross features. Having said
plex phase functions would be computationally
this, we proceed nevertheless, trusting that more
intractable.
aggressive analysis will eventually provide use-
3. The observations above for different tree
ful tools beyond the otherwise extremely simplis-
types warrant the use of a simple assumed scat-
tic devices currently at our disposal.
tering pattern and consequent phase function in
Lang and his co-workers at George Washing-
any case.
ton University (GWU) have developed primarily
Phase functions similar to the two displayed
WT vegetation models for some time, attempting
above are obtained from data for individual sam-
to include more specific analytical characteriza-
ples of the vegetation. Iterative first- and second-
tion of the canopy scattering elements. In early
order and "exact" numerical solutions of the vec-
work, leaves are modeled as circular dielectric
tor RT equations are obtained. While it is unclear
disks (Lang 1981), with the addition of a flat lossy
why the second-order solutions should apply in
ground surface and orientation statistics for lossy
an evidently inappropriate albedo range, com-
leaves (Lang and Sidhu 1983). The Foldy approxi-
puted backscatter solutions compare favorably
mation was used, implying sparse media, and
with measured data.
leaf sizes were assumed to be smaller than the
While the result does not surpass these models
incident wavelength. Some attempt has been made
in rigor, Borel and McIntosh (1990) construct a
to include higher frequency effects in theory for
simple model for expressing backscatter from de-
individual leaf-scattering behavior (Levine et al.
ciduous trees, including leaf orientation distribu-
1983).
tions. This can be seen as a step toward generality
Some more recent RT work by Lang and his
and rational basis inasmuch as it includes a basis
colleagues approaches small wavelength limits
for distinguishing the responses of different trees
(Lang and Yazici 1989). The culmination of the
in terms of the physical characteristics of their
line of work by the GWU team in terms of an
constituents. Measurements at 35 and 94 GHz of
available model is WT-based, allowing for differ-
individual leaves were used to justify the use of
ent classes of scatterers in two layers, each with a
an average leaf radar cross section when comput-
specific orientation distribution. Underlying sur-
ing the normalized radar cross section (NRCS). A
face roughness is treated by KA theory. Polari-
simple system is used to superpose the individual
metric backscatter coefficients are computed us-
leaf contributions, using orientation distribution
ing the distorted Born approximation. The
and incidence (viewing) angle. Orientation de-
formulation implies contributions from direct vol-
pendence in the results is used to justify similar
ume-scattering, a direct-reflected or double
analysis of data from a variety of tree forms at 215
bounce ground-vegetation term, a bottom reflec-
GHz. The modeling is quite approximate in that
tion contribution, and a surface scatter term. Flat
fine-scale leaf roughness, polarization, and shad-
or curved disks with circular or elliptical shapes
owing effects are neglected, among other things.
may be selected, as well as linear (cylindrical)
However, a noteworthy result of the combined
members. For the most part the programs are
analysis and data is the observation that one is
oriented toward P, L, and C band; simulations
able to distinguish returns from different
have used ground truth input and have been com-
(planophil, erectophil) morphology classes, de-
pared where possible with measured backscatter
spite substantial differences between individual
for various canopy scales, including grass, soy-
members within each class, based on characteris-
beans, corn, and forest (e.g., Chauhan et al. 1991,
tic leaf orientation. This serves as a refinement of
Saatchi et al. 1991). Formulations for thicker disks,
13
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