Borgeaud et al. 1986), though this does not take
presented in a variety of texts (Ishimaru 1978,
the volumesurface interactions fully into account.
Tsang et al. 1985, Kong 1986) and, together with
In RT, rough surface effects can be included com-
their recent developments, are extensively re-
pletely consistently, at least in principle, by modi-
viewed (e.g., Ulaby et al. 1982, Fung et al. 1990).
fying the boundary conditions; in general, RT
Multiscale roughness formulations have been de-
handles complicated configurations and media
veloped, combining disparate ranges over which
profiles more easily than does WT.
the approximate theories hold. Physical and nu-
The deficiencies of conventional or "classical"
merical surfaces have been constructed and scat-
RT are also to be noted. Its basis is less rigorous
tering behavior measured or obtained numeri-
than WT. Phase information is generally absent,
cally to investigate the applicable ranges of
and coherent effects such as enhanced backscat-
validity (e.g., Chen and Fung 1988, Fung et al.
ter cannot be predicted. Other coherent effects
1990, Lou et al. 1991). Ishimaru et al. (1991) per-
associated with layer bottom boundary reflections
formed numerical, analytical, and experimental
are also not included. This may not be so impor-
studies of very rough surfaces relative to the "clas-
tant at MMW frequencies in instances when strong
sical" constraints. Their MMW experiments and
attenuation occurs such that lower boundaries
numerical analyses of surfaces with known statis-
may have little effect on measurements from
tics illuminate enhanced backscattering from
above. In addition, the underlying lack of correla-
rough surfaces.
tion assumed in RT for the interaction of fields
While significant questions remain as to the
associated with medium elements breaks down
detailed limitations of these theories, a consensus
for sufficiently dense media. These shortcomings
emerges. This is reflected in the above references,
have given rise to recent formulations designed
in those discussed below, and is summarized suc-
to include some coherent effects. Tsang and
cinctly by figures published in various locations
Ishimaru (1987) have introduced the radiative
by Ishimaru and his co-workers (e.g., Ishimaru
wave equation approach to RT, and the modified
and Chen 1990). Generally speaking, it is difficult
radiative transfer approach (MRT) has sought to
to perform reliable calculations for rms surface
include some coherent effects since the late 1970s
height fluctuations approaching or greater than
(e.g., Tsang and Kong 1976, Zuniga and Kong
one wavelength or for rms slopes approaching
1980) with recent developments for more compli-
unity. Perturbation methods are preferable at
cated media (Lee and Kong 1988, Lee and Muda-
small correlation lengths, with physical-optics-
liar 1988, Mudaliar and Lee 1990). While the MRT
based methods more successful for larger rms
equations are ultimately of the same form as tra-
heights. The strength and appeal of these meth-
ditional RT equations so that similar solution
ods lie in their ability to provide information on
methods may be employed, the greater complex-
expected coherent and incoherent scattered field
ity of the MRT appears to limit its applicability at
properties based on the (statistical) spectral char-
present. While the emphasis in these references
acteristics of the reflecting surfaces.
has been on active remote sensing, this should
The Kirchhoff approximation (KA) constitutes
not obscure the prominence of RT for addressing
a physical optics (PO) approach in that it uses the
passive observations of the atmosphere. Numer-
tangent plane approximation for surface fields to
ous passive RT formulations applicable to terrain
express sources in the diffraction integrals. It as-
features have appeared as well (e.g., Kong et al.
sumes that scattering of the incident field may be
1979; Shin and Kong 1982, 1989; Tsang 1991).
approximated locally as if reflection were from a
flat surface with slope equal to the tangent to the
actual curved surface. Alternatively, it may be
Scattering from
stated that PO assumes induced surface currents
surfaces and transitions
To date, our options in connection with sur-
equal locally to the corresponding geometrical
face scattering computation are relatively limited
optics plane wave fields. The diffraction integrals
in the sense that usually only mild to moderate
are very widely used in surface scattering formu-
roughness of one kind or another can be treated.
lation and computation in all the methods dis-
The by-now "classical" approaches are based on
cussed here. As two-dimensional (surface coordi-
the assumption that physical optics or small-
nate) equivalents of their Green's function-based
perturbation-method approximations are ade-
three-dimensional WT counterparts, they may be
quate. Lucid formulations of these methods are
viewed as expressions of Huygen's principle or
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