tion in our frequency range, in any case not with
In practice, surface and volume scattering ef-
meaningful tests against data. The ocean is attrac-
fects cannot be separated to the extent that the
tive for analysis because it is a rare example of
above discussion might suggest. Physical transi-
relatively pure surface scatter, despite sea spray
tions are frequently encountered in the media
and breaking waves. At the same time, there is
being sensed that contain elements of both or that
usually a lack of "ground" (water) truth on which
produce a kind of effect that cannot be accounted
to base analyses. One must simulate both the wa-
for by either or both in simple combination. For
ter conditions and the consequent electromagnetic
example, bare tilled or raked soil may be quite
response as functions of other variables, most no-
rough on the MM scale, with clumps and hetero-
tably wind speed. Rodriguez et al. (1992b) have
geneous protrusions containing vertical slopes,
performed Ku-band altimetry-oriented simula-
large void inclusions, and the like. From one point
tions of scattering from the ocean surface, based
of view, we confront a distinct (albeit complex)
on a simplified ocean spectral model driven by
scattering interface between air and sharply con-
wind speed. While there are some discrepancies
trasting soil media. From another view, we see a
in results relative to observations or other stud-
heterogeneous volume of scattering material over
ies, important agreements are achieved, particu-
a transition zone, beginning with a low density at
larly in connection with EM bias. This bias is
the highest point of soil protrusion and gradually
caused by two modulating mechanisms, one due
increasing in density, homogeneity, and continu-
to small-scale waves and the other a result of tilt
ity with depth. This surfacevolume scattering
due to large waves. The 1-D surface roughness
ambiguity is most likely to arise for very rough
bias calculations show proper trends with respect
surfaces, which are not entirely uncommon in
to both frequency and wind speed, based on in-
practice at MMW wavelengths. Certainly the tra-
dependent physical observations. Bias increases
ditional, mild roughness theories and their most
with wind speed, but ultimately saturates as wind
recent improvements will ultimately fail for suffi-
continues to rise. The computed sign of the EM
ciently rough transitions. It is also reported that
bias is correct relative to observations; the differ-
surface scattering approaches must be modified
ence in magnitude by a factor of two may be due
in the face of dielectric heterogeneity, even when
to use of the simple 1-D spectrum. UPM codes
the bounding upper surface is geometrically
containing 2-D roughness are nearing completion
smooth. Numerical simulations of an imaginably
and may offer more precise agreement. While the
soil-like medium with voids and inclusions near
wavelength in these simulations is approximately
the surface show behavior influenced significantly
half that at 35 GHz, it is close enough to encour-
by the subsurface character, even in cases where
age strong interest from the MMW point of view.
penetration by the radiation should be slight.
Despite the limitations of this combined ocean
Revelations provided by simulations may serve
electromagnetic study, it deserves to be singled
to indicate the best way (at present) to investigate
out as a source of simulations of some signifi-
medium configurations and effects such as these.
cance and validity.
Monte Carlo or other structured numerical ex-
While these newer approaches have pushed
periments may guide us toward the best ap-
the bounds of application of surface roughness
proaches at a more analytical or conceptual level.
treatments, it is still difficult or impossible to ad-
In any case, we do not yet have good methods for
dress a great many realistically rough surfaces
analyzing such cases with any real generality
with rms roughness heights greater than the inci-
and do not have good guidelines as to how to
dent wavelength and especially with large slopes.
proceed.
These constraints can be severe at MMW frequen-
cies for natural media such as soil, gravel, sand,
Statistical quantities and
moving water, or tree bark. In practice, most vol-
Monte Carlo calculations
ume-scattering models that attempt to combine
Let us pause for some general observations on
surface scattering adduce one of the "classical"
what we seek in any approach of the sort we are
formulations, such as KA with stationary phase.
considering, on what sort of quantities are to be
This can serve to provide an example of (interact-
employed, and on what the nature of the meth-
ing) surface and volume effects, but it rarely ap-
ods is that allows us to obtain them. Basically, for
proaches the full physical reality to which one
natural media, statistical quantities must be gen-
would like to apply these models, such as agri-
erated for the application medium. Most com-
cultural fields.
monly these consist of an rms variation of permit-
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