analytical approaches on scale of roughness or

analytical approaches, more information on the

severity of slopes means that one can work with

distribution of the medium is generally required

truly realistic surface profiles. This is accom-

than just rms variation and correlation length.

plished, however, at impressive computational

The specific character of the overall correlation

cost: two-dimensionally rough surfaces are rarely

function is needed or assumed; in volume scatter-

attempted, though we expect progress here in the

ing density information is needed, and other

near future. True Monte Carlo treatment of vol-

higher-order spectral or geometrical information

ume scattering as is done for surfaces is currently

may be required for complete analysis. This is

out of the question. The sheer detail required to

particularly so when the limits of the approxi-

mate theories are exceeded.

ume of environmental material is insurmount-

It has been noted that a number of different

able; the computational requirements will also be

models may produce reasonable agreement with

invincible for the near future for solution of elec-

observations even though they use contrasting

tromagnetic equations over a truly life-like varia-

versions of the underlying physics, even when

tion of internal medium geometry.

the input data have been constrained by ground-

Monte Carlo volume-scattering treatments in

truth measurements (Carsey 1992). Among other

a certain limited sense have been carried out in

things, this serves to re-emphasize the fact that

the construction and analysis of collections of very

rms variation and correlation length do not

simple shapes. For example, Ding et al. (1992)

uniquely define the system. For more extreme yet

have used Monte Carlo procedures in achieving

realistic media, we will have to recognize and

arrangements of spheres to determine the statisti-

implement additional parameters that catch the

cal pair distribution functions needed for their

particular character of the variability, beyond what

dense media volume-scattering calculations.

is incorporated in the traditional quantities. This

Tsang et al. (1992b) have solved Maxwell's equa-

makes sense and is even desirable: it says that we

tions rigorously over similar dense media, for

need to focus on the identification of new, spe-

cases with as many as 4000 spheres, presumably

cific, distinguishing medium characteristics that

with volume fraction limits imposed by the con-

can be linked to some distinguishing statistical

vergence of the iterative solution procedure. Good

character in the received data. Only by doing this

solutions were obtained at densities of 25% by

will we recognize realistically distinct media in

volume. Alternatively, Chuah and Tan (1992a,b,c)

our sensed data. While overall this is likely to

have used Monte Carlo procedures to calculate a

mean that we must consider additional param-

cascade of idealized contributing scattering events

eters, such as higher statistical moments, in some

in vegetation. This statistical treatment of the con-

instances it may mean that we discard altogether

tributing scattering events is fundamentally dif-

one or more of the traditionally important me-

ferent from a rigorous deterministic analysis of

dium quantities. One might even say that we re-

events on a precisely realistic geometry for later

quire new physically based, probably case-depen-

ensemble averaging, i.e., for Monte Carlo treat-

dent parameters and signal characterization

ment as meant here. In addition, because they

specifically to simplify our task to the point of

proceed on the basis of a photon transport equa-

tractability.

tion and not Maxwell's equation, coherent inter-

actions as needed for dense media are absent; this

may suffice for some vegetation applications.

Tsang and his co-workers (1992b) are also evi-

dently applying Monte Carlo WT analyses to ob-

The following is suggested as a general scheme

tain coherent and incoherent effects for vegeta-

of the media and physical features for which mod-

tion that, though not dense, is clustered.

els are sought. In each case both active and pas-

In summary, we should not look for volume-

sive polarimetric systems are ultimately desired.

scattering progress in the near future from the

ensemble averaging of numerical solutions of

Maxwell's equations over truly realistic geom-

etries in the same manner as is occurring for sur-

urban/suburban environments, edges or

faces. Beyond this we note that pushing rough-

linear structures such as roads and wires.

ness limits using numerical solutions brings

dangers with its opportunities. Even in the more

Active propagation and emission horizon-

8