nent broadens and decays rapidly with depth.
trunks) may easily have bark that is so rough on
The very rapid decay at shallow depths is due
the MM scale that the linearity and orientation of
both to absorption and scattering, while beyond
the trunks and branches is largely irrelevant.
shallow depths the attenuation is due almost en-
Some of the models admirably constructed
tirely to absorption alone, as scattering only re-
from detailed analysis of idealized forest elements
produces the incoherent component. There is a
may apply in UHF and microwave regions where
fairly sharp transition to the much more slowly
elements are often on the order of the incident
decaying, isotropic intensity that ultimately pre-
wavelength or smaller. In those models, Shwering
dominates.
and his colleagues assert, only the forward-scat-
We dwell on this model in part because of its
tered incoherent component is likely to be impor-
attractive simplicity. It shows fidelity to the gen-
tant, together with the coherent component. They
eral character of the measured data without elabo-
emphasize their conviction that at MMW frequen-
rate, costly, and perhaps unrealistic attempts to
cies the incoherent, multiscattered component is
define scattering and extinction matrices, with-
likely to be predominant and must be given cor-
out significant CPU time, and without consider-
responding importance in any modeling.
ation of coherent effects. While much more so-
Ulaby et al. (1988) pursue the course set by
phisticated models exist, one can question the
Schwering et al. (1988) by developing an RT model
costbenefit of pursuing them in light of inevi-
at 35 GHz in conjunction with measurements.
table uncertainties.
Noting the geometrical diversity of the target trees
Test environments such as that used by Schwer-
at MMW and expecting very weak polarization
ing et al. (1988) are desirable in that they are
dependence, they adopt the general form of the
relatively uniform and controlled, but one may
scattering function in the equation above but with
be wary of artificial effects due to their constructed
the forward lobe represented as
regularity. Tavakoli et al. (1991) perform an exer-
2(1 + βs2) exp[ |γ|/βs],
cise similar to that of Schwering and his col-
leagues, measuring and modeling propagation
in which βs is a measure of the effective beam
through a horizontal, planted vegetation canopy.
The plants constitute only a single layer (corn),
width of the forward lobe. The constituent pa-
but as above their arrangement is quite orderly
rameters in this expression and extinction coeffi-
relative to untrammeled nature. An attempt is
cients are derived from measurements on indi-
made to treat the medium as random within rows,
vidual trees of a couple of types. While Schwering
with some deterministic interaction between rows.
and Johnson (1986) present a solution formula-
tion that accounts for all orders of multiple scat-
Thus it is a "semi-deterministic" field approach
tering, and Schwering et al. (1988) emphasize the
featuring notable coherent phenomena, agreeing
advisibility of accounting for extensive multiple
impressively with the observed data. The point to
scattering, Ulaby and his colleagues limit the for-
be made here, however, is that this latter study
mulation to first-order results. Calculated attenu-
was done at L band, so that individual leaves are
ation agrees well with observations.
much smaller than a wavelength and stalks might
Ulaby and his co-workers pursue this line of
be considered smooth. In the azimuthal scanning
investigation further by polarimetric measurement
data presented by Schwering et al. (1988), there is
and modeling of MMW scattering from a tree
significant scintillation due to coherent effects not
canopy (Ulaby et al. 1990). The essential focus is
accounted for in the model. The variations of sig-
on the crown. Noting that "at millimeter wave-
nal strength are extremely rapid, however;
lengths the penetration of foliage rarely exceeds 1
statistically the profiles are smooth or nearly flat,
m," they treat both the upper and lower canopy
and clearly the correlation length of millimeter
boundaries as diffuse and nonreflecting. Despite
waves in a forest is extremely short. In addition,
very substantial small-scale morphological dif-
the field rapidly becomes thoroughly depolar-
ferences between the tree types investigated (fi-
ized. Effects of the sort pointed out by Tavakoli
cus vs. arbor vitae), the like-polarized (HH and
and his colleagues were swallowed up in the
VV) scattering patterns were approximately the
MMW regime by the strong scattering of the veg-
same for each tree type, and those for the con-
etation elements, rapidly producing a predomi-
trasting tree types also resembled one another.
nately incoherent field. Even structures viewed
The same held true for the cross-polarized pat-
grossly as linear and distinctly oriented (e.g., tree
12
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