SPECIAL REPORT 96-25

The State of the Art of Modeling

Millimeter-Wave Remote Sensing

of the Environment

Kevin O’Neill October 1996
Abstract: A survey was undertaken of models for millimeter-wave (MMW) scattering and emission from environmental features, particularly in the vicinities of 35

and 94 GHz. The ultimate objective was to identify

models suitable for current or near-future application in

scene generation. The ideal model would be based on

first principles, would be readily available in facilitated

software, and would have reasonable requirements in

terms of computational resources and input parameters. At MMW frequencies, these requirements push

the frontiers of current science and technology. In most

applications, one must accept as a first approximation

the approaches currently under development in research settings. This report reviews the basic methods

and approaches underlying all available models in

terms of volume scattering, treatment of surfaces and

transitions, and the development of statistical quantities from rational physics. Very rough surfaces, locally

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steep surface slopes, and low-angle incidence can

rarely be treated entirely successfully, but recent developments offer the prospect of significant progress.

Volume and combined surface–volume scattering and

emission models are reviewed for application to land,

water, vegetation, snow, and ice environments. Most

are essentially works in progress, with theory and

validation currently building from earlier work at C and

X bands. Very sound capabilities are available for

treatment of common atmospheric features, with recent progress in modeling more complex meteorological events. Limiting consideration to truly available

codes, a list is provided for each of the above areas of

models and their sources. Because it is the most

comprehensive and is currently facilitated in terms of

software, the MIT EMSARS model is the foremost

condidate to serve as a platform for future addition and

development.
Special Report 96-25

The State of the Art of Modeling

Millimeter-Wave Remote Sensing

of the Environment

Kevin O’Neill October 1996

Prepared for

OFFICE OF THE CHIEF OF ENGINEERS

Approved for public release; distribution is unlimited.

US Army Corps


of Engineers

Cold Regions Research &


Engineering Laboratory
PREFACE

This report was prepared by Dr. Kevin O’Neill, Research Civil Engineer, of the

Civil and Geotechnical Engineering Research Division, Research and Engineering

Directorate, U.S. Army Cold Regions Research and Engineering Laboratory. This

project was funded by the Department of Defense as part of the Smart Weapons

Operability Enhancement (SWOE) Program.

This report was technically reviewed by Dr. Robert Davis and Dr. Harold

Boyne of CRREL.

The contents of this report are not to be used for advertising or promotional

purposes. Citation of brand names does not constitute an official endorsement or

approval of the use of such commercial products.

ii
CONTENTS

Page

Preface ....................................................................................................................... ii

Introduction............................................................................................................... 1

Methods and approaches ........................................................................................ 2

Volume scattering ............................................................................................. 2

Scattering from surfaces and transitions ....................................................... 4

Statistical quantities and Monte Carlo calculations .................................... 6

Applications .............................................................................................................. 8

Cultural features................................................................................................ 9

Atmosphere ........................................................................................................ 9

Vegetation .......................................................................................................... 11

Snow and ice ...................................................................................................... 15

Available computer codes....................................................................................... 19

MPM .................................................................................................................... 19

Enhanced RADTRAN....................................................................................... 20

Gasiewski radiative transfer model ............................................................... 20

Fung surface model .......................................................................................... 20

UPM surface model .......................................................................................... 20

GWU vegetation model.................................................................................... 21

Schwering and Johnson vegetation model ................................................... 21

UW snow model ................................................................................................ 21

EMSARS.............................................................................................................. 22

Literature cited.......................................................................................................... 22

Appendix A: List of workshop participants ........................................................ 27

Abstract ...................................................................................................................... 28

iii
INTRODUCTION

Recent improvements in technology and the

prospect of superior performance have greatly

increased interest in millimeter-wave (MMW) remote sensing. To assess the state of the art in the

accompanying modeling capabilities, a study was

undertaken with particular emphasis on implemented models, as opposed to disembodied

theory. This report summarizes the results of that

study. Its aim is to survey all available MMW

modeling of scattering, emission, and propagation–absorption in the natural environment, particularly in the spectral vicinity of 35 and 94 GHz.

The models are evaluated equally in terms of

validity and utility. In the context of this survey,

model means a theoretical formulation that is derived from first principles, such as Maxwell’s

equations or conservation of energy, and that is

incorporated in a tractable computational vehicle.

Thus, some work that constitutes a model in the

most general sense is recognized here for attention in the future, but it is not currently singled

out as available through accessible software. The

ultimate purpose for identifying, collecting, and

integrating an ensemble of such models is to generate energy field distributions, i.e., scenes, that

sensors might confront under the widest possible

variety of conditions. To achieve this generality,

models were sought based as much as possible

on first principles, with minimal reliance on empirical or arbitrarily tunable parameterization.

Truly useful models should be sufficiently simple and accessible that users other than the originators can run them. This requirement tests the

constraints of generality and first-principles validity. Due to the nature of the field, we may find

in many instances that the most rigorous models,

or perhaps the only rigorous models, are ensconced in sophisticated research structures. They

may require advanced, specialized knowledge,

extremely complex, difficult-to-obtain input data,

and intolerably large computational resources. At

least in extreme instances of this sort, such models cannot be pursued here for the purposes of

ultimate scene generation. At the same time, the

tension between generality and validity on the

one hand and simplicity and accessibility on the

other may force a degree of compromise in prioritizing models. The requirements may have to be

relaxed in some cases; in others, utility may be

achieved only by following an ongoing development or working with model originators over an

extended period. While the field is developing,

some applications may be best accomplished by

combining the capabilities of theoretical models

with organized, facilitated databases. In the latter

connection, documentation and programs exist

for extracting, manipulating, visualizing, and adding to the large amount of measured data that

has evolved over recent decades—e.g., FINRACS

(Borel et al. 1986) and material from Ulaby and

his co-workers at the University of Michigan

(Ulaby and Dobson 1989a, 1989b; Ulaby and Haddock 1990)

The specific information incorporated in this

survey is derived from a variety of sources: the

author’s personal knowledge and information direct from the open literature, discussion and communication with various recognized modelers, the

response of modelers to a questionnaire, and a

workshop (held on 13–15 May 1992) for a general

review and discussion of MMW modeling capabilities. (A list of workshop participants appears

in Appendix A.) Beyond the specific topics for

the workshop sessions, far-ranging discussions

took place to establish the boundaries and content of the current state of the art. In soliciting

The State of the Art of Modeling Millimeter-Wave

Remote Sensing of the Environment

KEVIN O’NEILL
information and taking note of models for this

report, emphasis was placed on the importance

of successful model verification as a selection criterion. In this context, verification means all testing and validation, including comparison of computations to common-knowledge expectations or

limits imposed by basic physics, comparison with

“exact” numerical solutions, or qualitative and

quantitative comparison with physical measurements.

The models of MMW propagation, scattering,

and emission may be sorted according to three

considerations:

1. Model type: physical process and basis, approach, methods and techniques used.

2. Applications: media considered and validation.

3. Computer codes: packages and their originators.

For the ultimate purpose of scene generation

we must deal with computer codes, so we sought

existing, facilitated, documented programs. Ideally these should be in integrated, modular packages, but single programs are also of interest if

they pose no insurmountable problems to integration into larger ensembles in standard languages. The codes must be directly accessible, in

the public domain or easily available for a modest cost, and should ideally have the prospect of

continuing support. Thus, our ultimate constraints

give a certain prominence to producers and active disseminators of finished software vehicles.

At the same time, it is recognized that the physical problems we are addressing are extremely

difficult. There is no well-established body of

valid, recognized, elaborated computer packages

as in some other areas, such as structural analysis

or heat transfer. Typically, the models we desire

are being generated at the frontiers of research as

pursued at the most advanced research institutions. For the most part, these institutions have

neither the resources nor the mandate to produce

polished software for dissemination. We recognize also that when energy has been devoted substantially to software polish and dissemination,

scientific rigor may have been left a bit behind.

Therefore, if our ultimate demand is for generality and fidelity to nature, we must also devote

attention to models that are in some intermediate

or even early stage of development as far as computer code is concerned. In the very least, doing

so provides valuable perspective on the more

available packages.

Before considering the specific codes, our most

basic sorting category for review is applications.

This is because we are asking what features we

are able to model for inclusion in a generated

scene: fallen and falling snow, fresh- and saltwater ice, bare soil, vegetated soil, vegetation

canopy, clouds and rain ...? While the availability of codes may determine our options in the

end, it is the need to model particular media and

configurations that drives both our quest for codes

as well as our drive to develop new methods. The

bulk of the Applications section is therefore organized according to applications.

The model types provide the broadest and most

far-reaching terms in which to consider the field.

Various general approaches are applied in models of substantially different media. The same general types of models also appear in many different computer codes. Therefore, we begin what

follows with a brief discussion of model types.

In summary: we converge on computer codes

by passing through model types and applications.

Some published models were eliminated at the

outset because they fail in some serious way to

meet one or more of these selection criteria. For

reasons explained above, the Applications section

and the next section of this report include items

that have distinct value but fail in one or another

way to meet our criteria ideally. Finally, in the

Available Computer Codes section, a subset of the

models considered first in terms of type and then

application is presented in terms of specific, available computer programs or packages.

METHODS AND APPROACHES

Volume scattering

In essentially all applications of interest here,

some type of randomness must be considered.

For volumes, the randomness has been included

by assuming that either

1. Dielectric properties vary continuously, with

a zero mean fluctuating term added to the

average permittivity, or

2. Dielectric properties have a discrete distribution, i.e., certain step changes in value

occur across boundaries of discrete embedded elements.

Idealized representative elements are often assumed, such as dielectric disks, spheroids, or

cylinders, possibly with statistical distributions

of size, shape, or orientation. The simple sum of

contributions from individual elements may suffice to compute the response when the medium is

2
diffuse, as in an aerosol, but the denser the media, the more interactions between the elements

must be included. In the limit of very dense media, with a great deal of contact between elements

or with continuous, tortuous intermixed phases,

it may no longer be a promising approach to regard the medium in terms of contributions from

discrete elements.

The distinction between continuous medium

and discrete scatterer theory is somewhat misleading, in that the former can generally deal with

discrete scattering elements as well. One merely

specifies a discrete permittivity distribution and

performs much the same computational motions

as for a continuous distribution, ending up with

essentially the same statistical descriptors for the

medium as under the discrete scatterer approach.

In either case, the statistical medium description

must be integrated into a set of equations covering the medium as a whole. The principal approaches have been via analytical wave theory

and radiative transport theory.

The perceived difficulty of applying wave

theory (WT) to an extremely complex mixture

has appalled some authors, to the extent that the

WT approach is sometimes dismissed out of hand.

Nevertheless, the brave beginnings of its recent

incarnations in the early ’80s have been followed

by the undaunted into formulations of ever greater

sophistication (e.g., Nghiem et al. 1990, Nghiem

1991). In principle, WT can include all multiple

scattering, diffraction, and interference effects. In

practice, it is limited by the difficulty of formulating the characteristics, behavior, and distribution

of constituent elements and then solving equations incorporating their interactions. Green’s

function-based integral equations are generally

used. Perhaps the simplest method for making

the integral equations tractable is the Born approximation, which has been used for increasingly complex configurations in recent years, e.g.,

an isotropic–anisotropic three-layer system with

rough surface (Borgeaud et al. 1986). The Rytov

and Foldy approximations are also applied to extend the range of validity or tractability. The distorted Born approximation extends the WT density and fluctuation strength range further,

particularly in conjunction with strong fluctuation theory. Recently, dense media formulations

have been advanced for media with particle-size

distributions, employing the quasi-crystalline approximation (QCA) and QCA with coherent potential (QCA–CP) and pair distribution functions

(Ding and Tsang 1991, Tsang and Kong 1992).

Whatever the current (evolving) limitations on

density (volume fraction) and particle size relative to wavelength, we note that important links

have been made between simulations based on

dense media theory and Monte Carlo calculations,

in effect verifying each. The latter have the advantage that true solutions of Maxwell’s equations may be obtained, including coherent interactions, and no adjustable parameters are introduced. Dense media theory calculations have

agreed well with Monte Carlo calculations of extinction rate for volume fractions up to 25% (Tsang

et al. 1992b); they have also agreed well with

laboratory data where input parameters were derived from measurement (Wen et al. 1990, Ishimaru and Kuga 1982 ).

In the radiative transport (RT) approach it is

assumed that interacting field components are

sufficiently uncorrelated so that addition of power,

as opposed to addition of fields, holds. Thus, an

energy balance equation is formulated in terms of

specific intensity, in scalar form for completely

unpolarized fields or in vector form in the sense

that the (modified) Stokes vector is the dependent variable when polarization is important.

Maxwellian underpinnings may reside in diffraction and interference effects expressed for the

behavior of constituent elements in the medium.

However, these are ultimately swallowed up

through the phase and extinction functions (matrices) in the intensity-based governing equation.

Comprehensive introductions to RT are provided

by a number of recognized sources (Chandrasekhar 1960, Ishimaru 1978, Tsang et al. 1985,

Ulaby et al. 1986). As in the WT approaches, researchers have built increasingly complex and diverse scattering elements into the medium formulations, treating increasingly complex shapes

and distributions of scattering elements and media. Although complex media descriptions may

be built into RT formulations more easily than for

WT, numerical solution can still be daunting. Iterative methods are sometimes used, though they

are suited primarily to sparse or weakly scattering media and are rarely carried beyond the second order. Kuga (1991) reports a system that provided third- and fourth-order iterations and

compared well with “exact” numerical solutions

obtained with the discrete ordinate method. While

the method requires low density and spherical

particles, it can deal with large particles. Rough

surfaces have been included in WT approaches

simply by incoherently adding the independently

calculated volume and surface scatter (e.g.,

3
Borgeaud et al. 1986), though this does not take

the volume–surface interactions fully into account.

In RT, rough surface effects can be included completely consistently, at least in principle, by modifying the boundary conditions; in general, RT

handles complicated configurations and media

profiles more easily than does WT.

The deficiencies of conventional or “classical”

RT are also to be noted. Its basis is less rigorous

than WT. Phase information is generally absent,

and coherent effects such as enhanced backscatter cannot be predicted. Other coherent effects

associated with layer bottom boundary reflections

are also not included. This may not be so important at MMW frequencies in instances when strong

attenuation occurs such that lower boundaries

may have little effect on measurements from

above. In addition, the underlying lack of correlation assumed in RT for the interaction of fields

associated with medium elements breaks down

for sufficiently dense media. These shortcomings

have given rise to recent formulations designed

to include some coherent effects. Tsang and

Ishimaru (1987) have introduced the radiative

wave equation approach to RT, and the modified

radiative transfer approach (MRT) has sought to

include some coherent effects since the late 1970s

(e.g., Tsang and Kong 1976, Zuniga and Kong

1980) with recent developments for more complicated media (Lee and Kong 1988, Lee and Mudaliar 1988, Mudaliar and Lee 1990). While the MRT

equations are ultimately of the same form as traditional RT equations so that similar solution

methods may be employed, the greater complexity of the MRT appears to limit its applicability at

present. While the emphasis in these references

has been on active remote sensing, this should

not obscure the prominence of RT for addressing

passive observations of the atmosphere. Numerous passive RT formulations applicable to terrain

features have appeared as well (e.g., Kong et al.

1979; Shin and Kong 1982, 1989; Tsang 1991).

Scattering from

surfaces and transitions

To date, our options in connection with surface scattering computation are relatively limited

in the sense that usually only mild to moderate

roughness of one kind or another can be treated.

The by-now “classical” approaches are based on

the assumption that physical optics or smallperturbation-method approximations are adequate. Lucid formulations of these methods are

presented in a variety of texts (Ishimaru 1978,

Tsang et al. 1985, Kong 1986) and, together with

their recent developments, are extensively reviewed (e.g., Ulaby et al. 1982, Fung et al. 1990).

Multiscale roughness formulations have been developed, combining disparate ranges over which

the approximate theories hold. Physical and numerical surfaces have been constructed and scattering behavior measured or obtained numerically to investigate the applicable ranges of

validity (e.g., Chen and Fung 1988, Fung et al.

1990, Lou et al. 1991). Ishimaru et al. (1991) performed numerical, analytical, and experimental

studies of very rough surfaces relative to the “classical” constraints. Their MMW experiments and

numerical analyses of surfaces with known statistics illuminate enhanced backscattering from

rough surfaces.

While significant questions remain as to the

detailed limitations of these theories, a consensus

emerges. This is reflected in the above references,

in those discussed below, and is summarized succinctly by figures published in various locations

by Ishimaru and his co-workers (e.g., Ishimaru

and Chen 1990). Generally speaking, it is difficult

to perform reliable calculations for rms surface

height fluctuations approaching or greater than

one wavelength or for rms slopes approaching

unity. Perturbation methods are preferable at

small correlation lengths, with physical-opticsbased methods more successful for larger rms

heights. The strength and appeal of these methods lie in their ability to provide information on

expected coherent and incoherent scattered field

properties based on the (statistical) spectral characteristics of the reflecting surfaces.

The Kirchhoff approximation (KA) constitutes

a physical optics (PO) approach in that it uses the

tangent plane approximation for surface fields to

express sources in the diffraction integrals. It assumes that scattering of the incident field may be

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

stated that PO assumes induced surface currents

equal locally to the corresponding geometrical

optics plane wave fields. The diffraction integrals

are very widely used in surface scattering formulation and computation in all the methods discussed here. As two-dimensional (surface coordinate) equivalents of their Green’s function-based

three-dimensional WT counterparts, they may be

viewed as expressions of Huygen’s principle or

4
simply as the results of various integrations and

manipulations of the underlying electromagnetic

wave equations. The integrands contain (usually)

unknown tangential field or equivalent current

values, which serve as sources of the general field

to be calculated. Use of the tangent-plane KA

approximations to obtain these surface sources

implies a large radius of curvature on the scattering surface relative to the incident wavelength.

This statement does not supply a very precise

criterion for range of validity, and investigations

have shown the importance of having a relatively

large correlation length, even for rms heights that

one might suppose corresponded to mild radii of

curvature (Thorsos 1988). Except in some deterministic cases, additional assumptions must typically be made (including small slopes and constant Fresnel reflection coefficients), otherwise

evaluation of the integrals cannot in general be

carried out. With the stationary phase approximation applied in the high frequency limit, one

obtains the geometrical optics approximation

(GO). This implies essentially that only parts of

the surface with local specular scatter toward the

observer contribute to the integral. The Fresnel

coefficients applied within conventional KA formulations have polarimetric content in the sense

that they are different for horizontal and vertical

polarizations. This inclusion of polarization effects is approximate at best, however, and one

should not expect complete and accurate polarimetry based on classical KA formulations.

Without the addition of special measures, such

formulations also do not conserve energy in

general, hence they do not provide reciprocal

information, i.e., the use of active to infer passive

behavior.

Over recent years the shortcomings of these

approximations in terms of shadowing and multiple reflection have been attacked, and higherorder versions have been constructed (Chen and

Ishimaru 1990, Ishimaru and Chen 1990). Successful application of these enhanced KA treatments is seen even at slopes on the order of unity,

with rms heights and correlation lengths somewhat greater than one wavelength. Thus, these

formulations may be capable of addressing the

roughest surfaces without handling the smallest

correlation length range. We note as an important

advance that energy is conserved in these calculations. At the same time, the introduction of the

shadowing and tapering functions is cumbersome

and requires further study. For the most part,

simulation of two-dimensionally rough surfaces

is still to come, awaiting the completion of more

tractable numerical treatments of fully vectorial

electromagnetic scattering.

In contrast to the PO-based approaches, the

small perturbation method (SPM) proceeds by

applying a correction factor to the field that would

be present on a flat surface located at the mean of

the actual surface. This factor is expanded in a

perturbation series. Small rms surface heights and

slopes are required. Relative at least to the more

basic KA formulations, SPM has the advantage of

being fully polarimetric in principle, although

cumbersome higher-order calculations may be required for reasonably accurate and complete polarimetry. Recently the phase perturbation method

(PPM) was introduced as an enhancement of SPM

(Winebrenner and Ishimaru 1985). Exploration of

the method by workers at the University of Washington and elsewhere has established a considerably wider range of application of PPM relative

to the more traditional SPM formulations (see

figure in Ishimaru and Chen 1990).

Fung et al. (1992) have extended earlier work

for perfectly conducting surfaces (Fung and Pan

1987) so that computations for dielectric surfaces

can be carried out in the same manner. The resulting integral equation method reduces to KA

and SPM terms at the appropriate limits for both

like and cross-polarized results. Good results are

shown with the new method for rms surface

heights on the order of the wavelength and slopes

(i.e., correlation length divided by rms height)

approaching 0.4.

The unified perturbation method (UPM) has

been introduced and tested by Rodriguez, Kim,

and their co-workers (Kim et al. 1992, Rodriguez

and Kim 1992, Rodriguez et al. 1992a). A perturbation expansion is used that converges over a

wider domain than SPM, and that converges in

the appropriate limits to the KA, SPM, and twoscale results. In the last case, this is accomplished

without the introduction of an artificial adjustable parameter for the spectral split. Recent 1-D

roughness tests show success in addressing surfaces with rms height approaching one wavelength with rms slopes less than or equal to about

0.8, for both horizontal and vertical polarizations.

In addition to the obvious merits of the UPM

system on the basis of this reported performance,

we pause to take note of a particular application

of the method to ocean backscatter simulation.

Little or no work has been done on ocean simula5
tion in our frequency range, in any case not with

meaningful tests against data. The ocean is attractive for analysis because it is a rare example of

relatively pure surface scatter, despite sea spray

and breaking waves. At the same time, there is

usually a lack of “ground” (water) truth on which

to base analyses. One must simulate both the water conditions and the consequent electromagnetic

response as functions of other variables, most notably wind speed. Rodriguez et al. (1992b) have

performed Ku-band altimetry-oriented simulations of scattering from the ocean surface, based

on a simplified ocean spectral model driven by

wind speed. While there are some discrepancies

in results relative to observations or other studies, important agreements are achieved, particularly in connection with EM bias. This bias is

caused by two modulating mechanisms, one due

to small-scale waves and the other a result of tilt

due to large waves. The 1-D surface roughness

bias calculations show proper trends with respect

to both frequency and wind speed, based on independent physical observations. Bias increases

with wind speed, but ultimately saturates as wind

continues to rise. The computed sign of the EM

bias is correct relative to observations; the difference in magnitude by a factor of two may be due

to use of the simple 1-D spectrum. UPM codes

containing 2-D roughness are nearing completion

and may offer more precise agreement. While the

wavelength in these simulations is approximately

half that at 35 GHz, it is close enough to encourage strong interest from the MMW point of view.

Despite the limitations of this combined ocean–

electromagnetic study, it deserves to be singled

out as a source of simulations of some significance and validity.

While these newer approaches have pushed

the bounds of application of surface roughness

treatments, it is still difficult or impossible to address a great many realistically rough surfaces

with rms roughness heights greater than the incident wavelength and especially with large slopes.

These constraints can be severe at MMW frequencies for natural media such as soil, gravel, sand,

moving water, or tree bark. In practice, most volume-scattering models that attempt to combine

surface scattering adduce one of the “classical”

formulations, such as KA with stationary phase.

This can serve to provide an example of (interacting) surface and volume effects, but it rarely approaches the full physical reality to which one

would like to apply these models, such as agricultural fields.

In practice, surface and volume scattering effects cannot be separated to the extent that the

above discussion might suggest. Physical transitions are frequently encountered in the media

being sensed that contain elements of both or that

produce a kind of effect that cannot be accounted

for by either or both in simple combination. For

example, bare tilled or raked soil may be quite

rough on the MM scale, with clumps and heterogeneous protrusions containing vertical slopes,

large void inclusions, and the like. From one point

of view, we confront a distinct (albeit complex)

scattering interface between air and sharply contrasting soil media. From another view, we see a

heterogeneous volume of scattering material over

a transition zone, beginning with a low density at

the highest point of soil protrusion and gradually

increasing in density, homogeneity, and continuity with depth. This surface–volume scattering

ambiguity is most likely to arise for very rough

surfaces, which are not entirely uncommon in

practice at MMW wavelengths. Certainly the traditional, mild roughness theories and their most

recent improvements will ultimately fail for sufficiently rough transitions. It is also reported that

surface scattering approaches must be modified

in the face of dielectric heterogeneity, even when

the bounding upper surface is geometrically

smooth. Numerical simulations of an imaginably

soil-like medium with voids and inclusions near

the surface show behavior influenced significantly

by the subsurface character, even in cases where

penetration by the radiation should be slight.

Revelations provided by simulations may serve

to indicate the best way (at present) to investigate

medium configurations and effects such as these.

Monte Carlo or other structured numerical experiments may guide us toward the best approaches at a more analytical or conceptual level.

In any case, we do not yet have good methods for

analyzing such cases with any real generality

and do not have good guidelines as to how to

proceed.

Statistical quantities and

Monte Carlo calculations

Let us pause for some general observations on

what we seek in any approach of the sort we are

considering, on what sort of quantities are to be

employed, and on what the nature of the methods is that allows us to obtain them. Basically, for

natural media, statistical quantities must be generated for the application medium. Most commonly these consist of an rms variation of permit6
tivity for volumes and of surface height for an

interface, or the equivalent, plus some measure of

the spatial scale and geometry of this variation,

most commonly through correlation length.

Loosely speaking, the correlation length indicates

the general size of a significant permittivity variation or of a discrete scatterer in a volume or the

lateral extent of a contour variation on a surface.

As such, correlation lengths may be anisotropic

in the sense that different lengths may apply in

different directions, as for elongated brine pockets in saline ice or narrow striations in a surface.

The fact that directional information can reside

in the correlation length underscores the significance of this quantity for polarimetric modeling.

We also note that the correlation length does not

entirely define the correlation function itself, given

that the former is typically only defined as the

distance over which the function decays by 1/e.

The entire function itself will depend on the case

considered; a Gaussian function is often used.

Note that the indication of a “Gaussian surface”

usually means that the correlation function or,

equivalently, the power spectrum of a surface has

the form of a negative exponential of distance

squared. This does not mean that the variation of

surface height is assumed to follow a Gaussian

probability distribution, though that is also often

the case.

The appearance of statistical quantities both in

remote sensing data and the modeling implies

some particular kind of averaging procedure. In

physical measurements this is performed, in effect, by the sensor. One footprint presumably

spans many patches or subregions, in each of

which a sufficient sample is present for statistical

quantities to apply meaningfully. Thus, integration is performed over each subregion patch, and

the ensemble of subregions is summed as well.

Quite significant questions remain as to the correspondence between the kind of averaging implied in the theoretical bases of our models and

that performed by any likely or conceivable sensor. Among other things, received data are likely

to contain effects due to the variability of medium properties at a number of different scales,

e.g., at both the subregion scale and at the scale of

the ensemble of subregions.

In model formulations, the averaging process

is typically carried out analytically, at a single

scale, in the process of constructing governing

relations. This means that the formulations are

ultimately stated in terms of the statistical quantities themselves, such as expected or coherent field

and the diffuse incoherent field or average power.

These theoretical average quantities presuppose

a certain kind of averaging, typically averaging

over an ensemble of surfaces, conceptually subjected to the same illumination regime and developed as realizations of the same statistical process. In this context, the correlation function, for

example, means the correlation value of quantities (e.g., surface heights at a given separation)

averaged over the ensemble of surfaces, not averaged

spatially over a single domain. The latter sense of

averaging, however, is often the one employed in

practice when a limited domain is characterized

experimentally to provide model input. While the

two averaging processes bear some relation, questions remain in any given application as to the

correspondences of the quantities obtained.

Lastly, we mention Monte Carlo techniques as

an approach to calculation of responses of random media. Such techniques have received a great

deal of attention as computing power has increased. The attraction of the non-Monte-Carlo

techniques resides in their ability to proceed directly in relating statistical and spectral features

of the modeled medium to the statistical properties of the received field or power. In such approaches, ensemble averaging is carried out analytically in the course of the formulation procedures; this is a result of the analytical simplicity

of the expressions used and the introduction of

limiting simplifications. By contrast, in Monte

Carlo simulation one calculates the response of

specific, geometrically defined (deterministic) medium samples, perhaps analogous to the “patches”

mentioned above. This is typically done numerically. Each of the samples is constructed to be an

individual realization of the hypothesized underlying statistical formation process. Once solutions

have been obtained for a sizable number of such

instances, they are added together to obtain effectively an ensemble average. Thus by “brute force”

one mimics the supposed process by which a sensor might accomplish its averaging integration

and also accomplishes a faithful rendering of the

kind of averaging assumed in the more approximate analytical models.

Monte Carlo techniques have the attraction that

many of the limiting assumptions needed to obtain results in the more analytical approaches can

be avoided. In addition, because the details of the

modeled media are known, there are no unknown

tunable parameters, the estimation of which can

render data-matching exercises suspect. In surface scattering, going beyond the constraints of

7
analytical approaches on scale of roughness or

severity of slopes means that one can work with

truly realistic surface profiles. This is accomplished, however, at impressive computational

cost: two-dimensionally rough surfaces are rarely

attempted, though we expect progress here in the

near future. True Monte Carlo treatment of volume scattering as is done for surfaces is currently

out of the question. The sheer detail required to

describe the internal geometry of a realistic volume of environmental material is insurmountable; the computational requirements will also be

invincible for the near future for solution of electromagnetic equations over a truly life-like variation of internal medium geometry.

Monte Carlo volume-scattering treatments in

a certain limited sense have been carried out in

the construction and analysis of collections of very

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

have used Monte Carlo procedures in achieving

arrangements of spheres to determine the statistical pair distribution functions needed for their

dense media volume-scattering calculations.

Tsang et al. (1992b) have solved Maxwell’s equations rigorously over similar dense media, for

cases with as many as 4000 spheres, presumably

with volume fraction limits imposed by the convergence of the iterative solution procedure. Good

solutions were obtained at densities of 25% by

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

have used Monte Carlo procedures to calculate a

cascade of idealized contributing scattering events

in vegetation. This statistical treatment of the contributing scattering events is fundamentally different from a rigorous deterministic analysis of

events on a precisely realistic geometry for later

ensemble averaging, i.e., for Monte Carlo treatment as meant here. In addition, because they

proceed on the basis of a photon transport equation and not Maxwell’s equation, coherent interactions as needed for dense media are absent; this

may suffice for some vegetation applications.

Tsang and his co-workers (1992b) are also evidently applying Monte Carlo WT analyses to obtain coherent and incoherent effects for vegetation that, though not dense, is clustered.

In summary, we should not look for volumescattering progress in the near future from the

ensemble averaging of numerical solutions of

Maxwell’s equations over truly realistic geometries in the same manner as is occurring for surfaces. Beyond this we note that pushing roughness limits using numerical solutions brings

dangers with its opportunities. Even in the more

analytical approaches, more information on the

distribution of the medium is generally required

than just rms variation and correlation length.

The specific character of the overall correlation

function is needed or assumed; in volume scattering density information is needed, and other

higher-order spectral or geometrical information

may be required for complete analysis. This is

particularly so when the limits of the approximate theories are exceeded.

It has been noted that a number of different

models may produce reasonable agreement with

observations even though they use contrasting

versions of the underlying physics, even when

the input data have been constrained by groundtruth measurements (Carsey 1992). Among other

things, this serves to re-emphasize the fact that

rms variation and correlation length do not

uniquely define the system. For more extreme yet

realistic media, we will have to recognize and

implement additional parameters that catch the

particular character of the variability, beyond what

is incorporated in the traditional quantities. This

makes sense and is even desirable: it says that we

need to focus on the identification of new, specific, distinguishing medium characteristics that

can be linked to some distinguishing statistical

character in the received data. Only by doing this

will we recognize realistically distinct media in

our sensed data. While overall this is likely to

mean that we must consider additional parameters, such as higher statistical moments, in some

instances it may mean that we discard altogether

one or more of the traditionally important medium quantities. One might even say that we require new physically based, probably case-dependent parameters and signal characterization

specifically to simplify our task to the point of

tractability.

APPLICATIONS

The following is suggested as a general scheme

of the media and physical features for which models are sought. In each case both active and passive polarimetric systems are ultimately desired.

Cultural features

– Buildings and transportation constructions,

urban/suburban environments, edges or

linear structures such as roads and wires.

Atmospheric applications

– Active propagation and emission horizon8
tally and up/down through profiles of clear

air, turbulence, dust, clouds, and precipitation.

Vegetation

– Low: Grass, fields, agricultural plantings,

shrubs, mostly single layer with diminished

importance of branches, greater importance

of leaves, blades, stalks.

– Tree canopy: Usually but not always twolayer, continuous/intermittent crown with

branches and seasonal or evergreen leaves/

needles, lower layer of trunks, horizontal

and nonhorizontal propagation; as for low

vegetation, possible significance of underlying ground/water surface.

Snow and ice

– Snow: Shallow/deep, uniform/layered,

wet/dry, smooth/rough.

– Ice: Fresh/saltwater, smooth/jumbled,

first-year/multiyear.

Exposed terrain and water bodies

– Rock: Rock-strewn terrains, or more monolithic formations that may be smooth except at MM scale, or may be steep, jagged

outcroppings.

– Soil: Wet/dry, rough/smoothly undulating, multiscale roughness.

– Water: Smooth/rough, moving/still, expansive/narrow.

– Subpixel patches: Mud puddles, ice patches, thaw/wet patches in snow ...

This list is something of a litany of objectives,

as context. What follows is a summary of what

has been done toward addressing this list.

Cultural features

Clearly one can attempt to analyze specific constructed elements such as wires, stairs, or windows. Here, however, we seek more generic capabilities applicable in relatively indiscriminate

remote sensing of a large-scale environment. Relatively little has been done to model lower-frequency microwave sensing of large-scale constructed or cultivated environments, and even less

is available in the public domain at MMW frequencies. A few measurements have been reported

(e.g., Violette et al. 1988), but without substantial

attempts at modeling. Beyond the obvious (such

as considering buildings or curbs as corner reflectors) we draw no inferences here for modeling

purposes. We note that the constructed or controlled nature of cultural features offers greater

regularity to the analyst on the one hand: swimming pools, walkways, and even lawns have relatively distinct edges. On the other hand, the sheer

variety of features and their distinctive forms is

so great as to prevent much generalization.

For well-defined structures and their environments it may sometimes be possible to use various programs in the suite available from the Georgia Tech Research Institute (Peifer et al. 1988, Faust

et al. 1989, Davis et al. 1992). This graphically

facilitated package offers capabilities for defining

structure geometry and then calculating returns

in terms of combined PO responses of an assemblage of simple shapes (scattering centers). In less

deterministic situations we may consider the possible presence of highly distinct structures at the

subpixel level, that is, a terrain category of

“patches,” each of which may be relatively easy

to model in itself but that must somehow be integrated statistically into an image effect. Rational,

or at least rationalized, schemes exist for constructing “fading” (speckle) in images from this

sort of process. Such schemes can be based on

reasonable or at least specific physical assumptions and procedures (e.g., Ulaby et al. 1982, 1986;

Yueh et al. 1991). While they come into play during the final steps of the scene generation sequence, we consider them to fall within the fringes

of the domain of modeling that we are pursuing

here. For this reason, no specific review of approaches and programs and no recommendations

in this area are included in this report.

Some expansive cultural features such as lawns,

bare tilled soil, or crop fields may be addressed

under other headings below.

Atmosphere

Many of the radiative transfer approaches listed

below can in principle be applied to atmospheric

dust and precipitation. Ishimaru and his co-workers have developed models that are in principle

applicable to rain or ice precipitation (Ishimaru

and Cheung 1980; Ishimaru et al. 1984a,b), and

others are directed at turbulence effects (Honig et

al. 1977, Ishimaru and Painter 1980). McMillan et

al. (1982) review applications of theory to measurement for MMW propagation. They conclude

that while in most cases agreement is “plausible,”

data have been inadequate to determine the extent to which this is fortuitous. Weinman (1989)

applies a Rayleigh–Gans model of MMW scattering from falling snow, with flakes considered to

be a polydispersion of equivalent randomly oriented circular disks. Disk dielectric constants are

obtained from the Bruggemann mixing rule with

estimated ice fractions in the equivalent flakes.

9
Theoretical comparisons with measurements are

good at 35 and 94 GHz, although Weinman emphasizes the need for access to more comprehensive data.

In general, efforts to model realistically complex meteorological events in a natural setting are

hampered by our inability to characterize the medium (lack of “air” truth, as it were). Despite

these difficulties we single out three sources of

simulation that have seen some notable application: the work by Gasiewski at the Georgia Institute of Technology, the RADTRAN program, and

the MPM program.

The most comprehensive and authoritative

data measurement and modeling basis for atmospheric attenuation/delay is provided by the

MPM model of Liebe and his colleagues (Liebe

1989, 1992; Liebe et al. 1989; Manabe et al. 1989).

The MPM model is the generally acknowledged

standard for predicting profiles of complex refractivity of the neutral atmosphere from 1 to

1000 GHz with contributions from dry air, water

vapor, suspended water droplets, and rain. For

clear air, the local line base (44 O2 plus 30 H2O

lines) is complemented by an empirical water–

vapor continuum. On the whole, the basis for the

relationships in the MPM program and its testing

lend it very high credibility. Possible shortcomings reside in missing trace gas spectra and the

empirical water–vapor continuum. The physical

origin of the latter is basically understood, but its

empirical construction could lead to errors in predictions for some atmospheric window ranges.

Even with these caveats, we note that the precision this model offers surpasses that of any other

model considered here. The most approximate

component may be the treatment of rain effects.

No attempt is made to engage in elaborate calculations for individual drops, which would require

drop shape and size distributions, variable permittivity of the water, and so on; similarly, no

complicated RT-type computations are employed

with an assumed or empirical phase matrix.

Rather, the refractivity of the rain is expressed

simply by a formula, with constituent terms and

factors developed from a least-squares fit to Mie

calculations based on a Marshall–Palmer dropsize distribution. Overall, this gratifyingly simple

code is easily implemented and can feed into the

more complex modeling vehicles discussed below.

Gasiewski has produced a program for calculating brightness temperature and associated statistics for planar stratified scattering atmospheres

over specularly reflecting surfaces for the 1–1000

GHz frequency range. Emphasis is more on the

handling of complex precipitation events. The atmospheric portion of the model is described by

Gasiewski and Staelin (1990); a wealth of details

on the formulation, sensitivity, and exploratory

runs and comparison with measurements is also

provided by Gasiewski (1993). In general, this RT

model assumes Rayleigh or Mie scattering from

spheres. Given the expected sparse distribution

of scatterers, models simpler than the Mie formulation are typically used to determine the form of

the phase matrix, which is less influential than

the other parameters. Both iterative and quadrature solutions are pursued, and both mono- and

polydispersed hydrometeor scattering and extinction are considered. Isotropic, Sobelev (two-term),

Rayleigh, Henyey–Greenstein, and two-stream

phase function formulations are offered. Ground

surface reflectivity is considered to be a minor

influence in the applications considered and is

typically assumed to be a convenient fixed value,

e.g., 5%. Downward-looking brightness temperatures were calculated for flight paths over a relatively complex summertime convective cell couplet, with concomitant data from weather radar

reflectivity used to determine hydrometeor size

distribution and phase profiles (Gasiewski 1993).

Agreement between observed and computed values is impressive. It appears that the model would

benefit from the inclusion of some polarimetric

effects under certain precipitation conditions. This

may be accomplished to some degree by including more asymmetric particle geometry and scattering; more general polarimetric ground surface

reflectivity is also planned.

The computational vehicle designated as

RADTRAN has been developed from work originally done at the Air Force Geophysical Laboratory to model atmospheric transmission and emission in the 30–300 GHz range (Falcone et al. 1979,

1982). The package is oriented toward passive

measurements and contains six each of clear atmosphere, cloud, and rain models as well as eight

humidity models in an attempt to cover a worldwide variety of conditions. The original RT formulation has been upgraded more recently by

Isaacs and his co-workers at Atmospheric and

Environmental Research, Inc. (Isaacs et al. 1988,

1989a,b,c). The enhancements allow RT simulation of polarized multiple scattering for cases that

involve various kinds of precipitation and surface emissivities. Jin and Isaacs (1987) show exploratory computations of hypothetical cases with

10
a polarimetric formulation in which the required

scattering functions are based on Mie scattering.

It appears that polarimetric effects enter essentially through the calculated terrestrial surface

emissivities. In any case, it is not clear that this

particular formulation has been built into the

RADTRAN package. The other papers referenced

above indicate that the package enhancements

avoid an on-line computation of precise Mie scattering for each specific particle size, phase, temperature, and frequency combination. Rather, interpolations are performed on parameterized

results of Mie scattering calculations for representative particle-size distribution functions under different conditions. The ultimate results appear to be accurate when compared with

calculations based on full-fledged Mie scattering

computations (Isaacs et al. 1988).

The enhanced RADTRAN is now designed to

handle emission from a variety of user-specified

types of surfaces. The surface or surface layer

models used are quite simplistic: calm ocean is

modeled as a dielectric slab; rough ocean, sea ice,

and wet and dry snow are modeled using discrete random scatterer inclusions and WT; and

vegetation and wet and dry soil are treated using

RT and a continuous random medium model.

These surface models enter significantly into calculations of polarized brightness temperatures

that compare reasonably with SSM/I data over

selected areas (Isaacs et al. 1989b), with further

comparisons needed over snow, sea ice, and soil.

It seems that essentially all of the specifically polarimetric content in the data comparisons enters

through these surface factors, rather than through

directional structure and scattering properties of

precipitation particles. We note that the extremely

approximate nature of these surface models makes

it unlikely that they would stand up to the kind of

testing applied elsewhere to more sophisticated

models with mixed results at best. Most features

of the original (1979) version of RADTRAN test

well against laboratory data; parts of the package

related to heavy precipitation and the most recent enhancements have seen only sketchy validation. Most recently (Pickle et al. 1993), the program was used to help quantify the uncertainty

in DMSP SSMT/T-2 water vapor sounder brightness temperature measurements. Under precipitation-free conditions with clear or partly cloudy

skies over land and sea, colocated radiosonde temperature and moisture profiles were used as input; outgoing radiance was calculated. In the context of both satellite and NASA ER-2 underflight

radiometer data, the model estimated sensitivities of the brightness temperature to variations of

moisture content.

Overall, the RADTRAN package has the substantial advantage that it is documented, facilitated, disseminated, and supported. It includes

many accepted, state-of-the-art formulation features for atmospheric modeling. Gasiewksi’s

model, which shows comparable care in formulation, currently eschews polarimetric effects and

treats the terrestrial surface extremely simply. It

shows good results against data for a complex

precipitation event, with simulations backed by

independent “air truth.”

Vegetation

Perhaps the simplest MMW canopy model is

the scalar RT formulation of Schwering et al.

(1988), which utilizes a parameter extraction and

solution system reported separately (Johnson and

Schwering 1985, Schwering and Johnson 1986).

Only horizontal propagation is considered, so that

no layer boundaries are encountered. Three elevations at different parts of a tree canopy are

treated, at seasons with and without leaves

present. This model has both the attraction and

the limitation that it was developed closely in

tandem with relevant data acquisition and processing. One can see immediately what the model

does in application to data from a two-layer

canopy of “real” vegetation (a “regularly planted,

well-groomed stand” of pecan trees), but it is not

clear how widely it might be generalized. The

formulation goes directly to the form of an assumed phase function, which is just the scalar

function

p (γ) = α(2/∆γ)

2 exp[– (γ/∆γ)2] + (1 – α)

where γ is the angle between the incident and

scattered directions of energy propagation, ∆γ is

the beam width of the forward lobe, and α is the

ratio of the forward-scattered power to the total

scattered power. Thus, a strong forward lobe and

an isotropic background are assumed. In addition to constituents of the scalar extinction coefficient, only the two parameters above are used,

and these must be estimated from experience or

with reference to some representative data. Still,

with reasonable values of the parameters there is

good qualitative agreement with the measured

data. Different behaviors are notable at different

levels in the canopy, with a strong coherent forward lobe at small optical depths. This compo11
nent broadens and decays rapidly with depth.

The very rapid decay at shallow depths is due

both to absorption and scattering, while beyond

shallow depths the attenuation is due almost entirely to absorption alone, as scattering only reproduces the incoherent component. There is a

fairly sharp transition to the much more slowly

decaying, isotropic intensity that ultimately predominates.

We dwell on this model in part because of its

attractive simplicity. It shows fidelity to the general character of the measured data without elaborate, costly, and perhaps unrealistic attempts to

define scattering and extinction matrices, without significant CPU time, and without consideration of coherent effects. While much more sophisticated models exist, one can question the

cost–benefit of pursuing them in light of inevitable uncertainties.

Test environments such as that used by Schwering et al. (1988) are desirable in that they are

relatively uniform and controlled, but one may

be wary of artificial effects due to their constructed

regularity. Tavakoli et al. (1991) perform an exercise similar to that of Schwering and his colleagues, measuring and modeling propagation

through a horizontal, planted vegetation canopy.

The plants constitute only a single layer (corn),

but as above their arrangement is quite orderly

relative to untrammeled nature. An attempt is

made to treat the medium as random within rows,

with some deterministic interaction between rows.

Thus it is a “semi-deterministic” field approach

featuring notable coherent phenomena, agreeing

impressively with the observed data. The point to

be made here, however, is that this latter study

was done at L band, so that individual leaves are

much smaller than a wavelength and stalks might

be considered smooth. In the azimuthal scanning

data presented by Schwering et al. (1988), there is

significant scintillation due to coherent effects not

accounted for in the model. The variations of signal strength are extremely rapid, however;

statistically the profiles are smooth or nearly flat,

and clearly the correlation length of millimeter

waves in a forest is extremely short. In addition,

the field rapidly becomes thoroughly depolarized. Effects of the sort pointed out by Tavakoli

and his colleagues were swallowed up in the

MMW regime by the strong scattering of the vegetation elements, rapidly producing a predominately incoherent field. Even structures viewed

grossly as linear and distinctly oriented (e.g., tree

trunks) may easily have bark that is so rough on

the MM scale that the linearity and orientation of

the trunks and branches is largely irrelevant.

Some of the models admirably constructed

from detailed analysis of idealized forest elements

may apply in UHF and microwave regions where

elements are often on the order of the incident

wavelength or smaller. In those models, Shwering

and his colleagues assert, only the forward-scattered incoherent component is likely to be important, together with the coherent component. They

emphasize their conviction that at MMW frequencies the incoherent, multiscattered component is

likely to be predominant and must be given corresponding importance in any modeling.

Ulaby et al. (1988) pursue the course set by

Schwering et al. (1988) by developing an RT model

at 35 GHz in conjunction with measurements.

Noting the geometrical diversity of the target trees

at MMW and expecting very weak polarization

dependence, they adopt the general form of the

scattering function in the equation above but with

the forward lobe represented as

2(1 + βs

–2) exp[– |γ|/βs],

in which βs is a measure of the effective beam

width of the forward lobe. The constituent parameters in this expression and extinction coefficients are derived from measurements on individual trees of a couple of types. While Schwering

and Johnson (1986) present a solution formulation that accounts for all orders of multiple scattering, and Schwering et al. (1988) emphasize the

advisibility of accounting for extensive multiple

scattering, Ulaby and his colleagues limit the formulation to first-order results. Calculated attenuation agrees well with observations.

Ulaby and his co-workers pursue this line of

investigation further by polarimetric measurement

and modeling of MMW scattering from a tree

canopy (Ulaby et al. 1990). The essential focus is

on the crown. Noting that “at millimeter wavelengths the penetration of foliage rarely exceeds 1

m,” they treat both the upper and lower canopy

boundaries as diffuse and nonreflecting. Despite

very substantial small-scale morphological differences between the tree types investigated (ficus vs. arbor vitae), the like-polarized (HH and

VV) scattering patterns were approximately the

same for each tree type, and those for the contrasting tree types also resembled one another.

The same held true for the cross-polarized pat12
terns. Ulaby and his co-workers have pursued

specific modeling and measurement of leaf-scattering patterns, with increasing morphological and

constitutional complexity for the leaves and with

increasing incident frequency (Senior et al. 1987,

Sarabandi et al. 1988, 1990). Nevertheless, Ulaby

et al. (1990) take the view that:

1. Truly realistic MMW phase functions for the

variety of vegetation elements cannot currently

be determined.

2. If they could be determined, realistically complex phase functions would be computationally

intractable.

3. The observations above for different tree

types warrant the use of a simple assumed scattering pattern and consequent phase function in

any case.

Phase functions similar to the two displayed

above are obtained from data for individual samples of the vegetation. Iterative first- and secondorder and “exact” numerical solutions of the vector RT equations are obtained. While it is unclear

why the second-order solutions should apply in

an evidently inappropriate albedo range, computed backscatter solutions compare favorably

with measured data.

While the result does not surpass these models

in rigor, Borel and McIntosh (1990) construct a

simple model for expressing backscatter from deciduous trees, including leaf orientation distributions. This can be seen as a step toward generality

and rational basis inasmuch as it includes a basis

for distinguishing the responses of different trees

in terms of the physical characteristics of their

constituents. Measurements at 35 and 94 GHz of

individual leaves were used to justify the use of

an average leaf radar cross section when computing the normalized radar cross section (NRCS). A

simple system is used to superpose the individual

leaf contributions, using orientation distribution

and incidence (viewing) angle. Orientation dependence in the results is used to justify similar

analysis of data from a variety of tree forms at 215

GHz. The modeling is quite approximate in that

fine-scale leaf roughness, polarization, and shadowing effects are neglected, among other things.

However, a noteworthy result of the combined

analysis and data is the observation that one is

able to distinguish returns from different

(planophil, erectophil) morphology classes, despite substantial differences between individual

members within each class, based on characteristic leaf orientation. This serves as a refinement of

the work by Ulaby and his colleagues, in that

McIntosh’s group shows differences in polarimetric returns distinctly as a function of tree type, or

at least class of tree type.

These observations are intended to highlight

the particular nature of MMW scattering from

environmental features, to serve as a warning

against the facile extension of lower-frequency

modeling approaches to MMW and to suggest

restraint on attempts to build sophisticated model

structures based on gross features. Having said

this, we proceed nevertheless, trusting that more

aggressive analysis will eventually provide useful tools beyond the otherwise extremely simplistic devices currently at our disposal.

Lang and his co-workers at George Washington University (GWU) have developed primarily

WT vegetation models for some time, attempting

to include more specific analytical characterization of the canopy scattering elements. In early

work, leaves are modeled as circular dielectric

disks (Lang 1981), with the addition of a flat lossy

ground surface and orientation statistics for lossy

leaves (Lang and Sidhu 1983). The Foldy approximation was used, implying sparse media, and

leaf sizes were assumed to be smaller than the

incident wavelength. Some attempt has been made

to include higher frequency effects in theory for

individual leaf-scattering behavior (Levine et al.

1983).

Some more recent RT work by Lang and his

colleagues approaches small wavelength limits

(Lang and Yazici 1989). The culmination of the

line of work by the GWU team in terms of an

available model is WT-based, allowing for different classes of scatterers in two layers, each with a

specific orientation distribution. Underlying surface roughness is treated by KA theory. Polarimetric backscatter coefficients are computed using the distorted Born approximation. The

formulation implies contributions from direct volume-scattering, a direct-reflected or double

bounce ground-vegetation term, a bottom reflection contribution, and a surface scatter term. Flat

or curved disks with circular or elliptical shapes

may be selected, as well as linear (cylindrical)

members. For the most part the programs are

oriented toward P, L, and C band; simulations

have used ground truth input and have been compared where possible with measured backscatter

for various canopy scales, including grass, soybeans, corn, and forest (e.g., Chauhan et al. 1991,

Saatchi et al. 1991). Formulations for thicker disks,

13
needle arrays, and resonant size cylinders are being included so the system can be used at MMW

wavelengths, with simulations performed at 10–

50 GHz. Experimental validation at these frequencies is reported to be underway.

Fung and his co-workers have also attempted

to build specific leaf and branch character into

vegetation models for frequencies higher than

those considered in previous models. Using the

Rayleigh–Gans approximation, a first-order RT

formulation is presented that should be valid for

leaf dimensions up to the size of the incident

wavelength (Karam and Fung 1989). Size variations are included through elliptic disk leaves

and needles for conifers. On the basis of simulations it is suggested that both like and cross polarizations may be needed to distinguish leaf type

effects on scattering behavior. As frequency increases, near-field effects enter increasingly in leafto-leaf field interactions. Fung et al. (1987) allow

leaves to be in the Fresnel zone of one another for

both disc and needle-shaped leaves. VV and VH

measurements are matched to calculated X-band

scatter for soybean plants. Liu and Fung (1988)

use an empirical parameterization of vegetation

material with a rough underlying ground surface

to perform polarimetric scattering computations

for k • a values approaching 4, where a is a characteristic leaf dimension. Comparisons of the computations with data are good. Karam and Fung

(1988) use a first-order RT formulation for randomly oriented dielectric cylinders to link surface scattering with that from a defoliated vegetative volume. While comparisons with data are

best for lower k • (a = cylinder radius) values,

favorable comparisons are seen as high as k • a =

2. While MMW frequencies strain these k • a limits, leaf sizes and branch radii up to some significant fraction of a centimeter could possibly be

accommodated at 35 GHz.

Tsang and his co-workers at UW, MIT, and GE

have developed vector RT models that may be

applicable to vegetation over rough-surfaced soil

(Tsang et al. 1990, Tsang 1991, Tsang and Ding

1991, Tsang et al. 1992a). First-order, second-order, and full-multiple scattering solutions are obtained. Extinction and phase matrices are calculated in such a way that energy is conserved and

reciprocity preserved. Application of the modules to measured data is awaited.

In an interesting new approach pursued separately by investigators at MIT and GWU, models

are designed to include the effects of vegetation

architecture. The needles on an evergreen, for example, are distributed with a randomness that is

structured by the basic tree morphology; they

cluster with predisposed alignment along twigs

and larger branch elements. Thus, the needles

may effectively form a random distribution of

arrays. Drawing on such observations of underlying architecture also allows incorporation of the

multiscale nature of vegetation systems. Yueh et

al. (1992) employ two scale branching models

with idealized independent scattering behavior

of individual elements. Calculated responses for

simple structures as a function of frequency and

incidence angle show an importance of coherent

or phase relations between constituent elements.

In application, including ground surface effects

and a hole-correction pair distribution function,

good agreement is obtained in comparisons with

polarimetric C-band data from soybean fields.

While greater small-scale coherence effects might

be anticipated at frequencies below C band, it

remains to be seen whether the approach produces significant revelations in the higher-frequency domain we are interested in.

Lang and Kavaklioglu (1991) pursue a related

modeling exercise in which they contrast the behavior of randomly oriented elementary needles

with that of randomly oriented arrays of such

needles. It is assumed that the radius of each

cylindrical needle is small compared with the

wavelength, which is a reasonable assumption at

35 GHz, if not at 94 GHz. While comparisons

with data are not indicated, the modeling evidently showed differences in response between

the random needles and random arrays of needles

when the wavelength was comparable to the array size. We cannot yet say that the concepts used

in these studies have been shown to be of great

relevance for MMW simulation. However, these

first results as well as the appealing rationale of

the basic concepts suggest strongly that this is an

area to watch.

We close this section with a brief mention of

Monte Carlo modeling. Chuah and Tan (1992a)

have proposed a model for backscatter from forest stands. Their approach is “Monte Carlo” in

that individual contributing scattering events

within the canopy are treated probabilistically and

then looked at in their intensity sum. As noted

above, this and any other such treatment based

on a cascade of statistical events differs fundamentally from the Monte Carlo treatments of surface scattering that have appeared recently. In the

surface scattering case, investigators calculate the

scattering deterministically from an entire, spe14
cifically described, generally realistic geometry.

This procedure is repeated many times for different example surfaces, and the ensemble of results

is summed coherently. In Chuah and Tan’s model,

the top layer consists of randomly oriented leaves

and branches, the next layer is a random distribution of trunks, and a randomly rough soil surface

forms the bottom boundary. The medium model

differs from that of Karam and Fung (1988) in

that Chuah and Tan assume a multilayer model

with a mixture of different classes of scatterers in

the top layer. Leaves are modeled as randomly

oriented dielectric circular disks or small needles;

branches and trunks scatter as infinite cylinders,

and the ground is treated using a GO-type limit

to the KA. The primary distinguishing feature of

the approach here is the use of a Monte Carlo

method to track photon transport through multiple scattering interactions in the media. Characterization of the interactions at each collision are

used to build up an overall transport picture in

terms of intensity, not field value as for a WT

approach. Using parameters considered to be justified by ground truth, the authors produce calculated backscatter from trees that compares well

with measurements at S and X bands.

A closely related approach is applied to the

computation of emission (Chuah and Tan 1992b,c).

Given its fundamental basis, we assume that

Chuah and Tan’s overall approach should produce results equivalent to an RT approach. For

this reason, together with the uncertain availability of code and support, we do not pursue it here.

However, it is an innovative approach that merits

continued attention, as it may eventually produce physical results or computational facilitation not obtainable otherwise.

Snow and ice

Hallikainen et al. (1987) use a simplified strong

fluctuation theory following Ishimaru (1978) to

model the extinction behavior of snow in the 18–

90 GHz range. Eighteen types of snow were considered, from newly fallen to refrozen. Agreement between computed and observed values is

good if the single free parameter of grain size is

tuned to a value somewhat less than the observed.

A very interesting observation emerges from the

study by Hallikainen et al. in connection with

surface scattering. Especially for the dry snow

considered, surface scattering is often considered

to be negligible at MMW frequencies. By implication, this is explained by the prominence of

particle-scale scattering, assumed to be as dominant near the edge of the medium as within its

interior. Hallikainen and his co-workers measured

extinction ranging from only a small number of

dB/m to about 500 dB/m. The latter occurred in

cases combining the highest frequencies and largest grain sizes. To be emphasized here are the

additional surface scattering losses that were inferred, ranging from a small effect to tens of dBs.

The larger surface effects were seen in cases including the highest frequencies, largest grain sizes,

and roughest surfaces in undisturbed samples.

We note particularly that the roughest surface

had rms height variations that were only on the

order of a couple of grain diameters. In other

words, the grains themselves appear to offer an

effectively roughened surface. At the highest frequencies, where this was most significant, penetration depth in the snow is effectively only some

tens of centimeters. This means that the surface

losses constituted an effect comparable in order

of magnitude to volume scattering over the depth

sensed. The significance of all this lies in the implication that one may have to model rough surface scattering to account accurately for all scattered energy, and the surface roughness treatment

may have to include particle scale effects as well

as more macroscopic surface considerations.

The version of strong fluctuation theory employed by Hallikainen et al. (1987) includes some

coherent effects associated with particle proximity. In a broader and more rigorous treatment

(see below), Tsang and Kong (1992) perform calculations for a dense medium with correlated scattering by particles near one another. The assumed

spherical particles are characterized by a size distribution, with sizes comparable to a wavelength.

Including these features in the model produces

quite good agreement with the same data. Full

calculation of the incoherent scattering is limited

by the use of the distorted Born approximation.

Others at the University of Michigan constructed and tested an RT model for scattering

from snow (Kuga et al. 1991, Ulaby et al. 1991).

MMW-scale scattering from assumed spherical

ice particles is treated by Mie scattering expressions to obtain the phase function; nonuniform

liquid–ice contact to be expected in small inclusions is modeled by assuming an equivalent “wet

air” background medium; the density of the medium is dealt with by the QCA in a manner less

complete than that of Wen et al. (1990); and the

equations are solved using the discrete ordinate

technique with Fourier decomposition of azimuthal components. The effect of upper snow

15
surface roughness is accounted for in an extremely

simple KA stationary-phase approximation. Copolar volume contributions are added incoherently to the direct backscatter calculated from the

surface. With the addition of a hybrid first-order

numerical solution in Ulaby et al. (1991) to address the refrozen case, overall good agreement is

shown between experimental observations and

theoretical calculations. Having gained confidence

in the numerical model, Ulaby et al. (1995) run it

for a matrix of cases to generate broader information on the dependencies of the backscattering

cross section of snow at 35 and 94 GHz. From

these results a semi-empirical model is constructed

in the form of a single equation. This equation

may represent the simplest model of snow backscatter from the point of utilization. It offers the

great advantage that, for example, a large number of scene pixels can be generated extremely

rapidly for changing conditions. While the ultimate equation rests on both data and theory, it

requires faith that the numerical model extended

the original data with sufficient fidelity.

Narayanan and McIntosh (1990) study highfrequency polarimetric backscatter from multilayered snow. Their model treats multilayered

snow in terms of a cascade of scattering from a

number of homogeneous layers with distinct

boundaries. The approach uses inputs from

ground truth measurements, which in their entirety have included surface roughness, moisture

content, density, hardness, particle size, and grain

type. Total back-scattered power is the incoherent sum of surface reflection at the interfaces and

a very simply computed volume scatter. An effort is made to include bistatic scattering effects

and shadowing on the rough surface. Multiple

scattering between layers and ice particles is ignored. Transmission between layers is considered

to be simple Fresnel transmission of fields as

for incidence on a solid slab. Slab dielectric constants are obtained from the Polder–van Santen

mixing formula for ice spheres and water, and

volume scattering is computed as the simple summation of Mie scattering from individual grains

with a Rayleigh distribution of diameters. Weak

surface scattering is computed using the stationary-phase KA approximation. Reported co-polar

NRCS values computed from the model compare

favorably with measurements.

Another generation of empirically based models has come from a group at the University of

Massachusetts, begining with Mead et al. (1993).

Fully polarimetric measurements of snow backscatter showed different rates of decline of σVV

and σHH with increasing incidence angle. Encouraged by observations of approximately spherical

grains in the snow surveyed, the authors constructed input–output relations of the polarimetric quantities based on a modified Mueller matrix

for orientation-independent scatterers, modified

by transmissivity factors. The latter assume

Fresnel-type interface effects and provide much

of the polarimetric behavior sought; the whole is

tuned using the original measurements. While

admittedly empirical, this model provides a structure consistent with basic physical mechanisms

and common forms of their description, and it

catches some basic polarimetric behavior. We note

that the inclusion of the surface effects is essential. Subsequently, Chang and his colleagues

(Chang et al. 1996) report and analyze snow

backscatter measurements at 35, 95, and 225 GHz.

Newly fallen snow in which grains still exhibit

flattened, platelet-like geometry shows distinctive polarimetric effects, with decrease in magnitude and increase in phase in the correlation of

horizontal and vertical copolar components. Together with information from the scattering measurements, this particle geometry is taken into

account in a simple way in the construction of a

phase matrix. The resulting RT formulation

avoids both the rigor and complexity of the densemedium treatments outlined below; calculations

using it reflect the distinctive polarimetric observations.

The work by Chang et al. also shows instances

in which the backscatter behavior is dominated

by a thin refrozen crust on the snow. Together with

the evident effect of nonspherical particle geometry, the importance of the crust poses a considerable challenge for modelers. A layer only a few

wavelengths or grains thick (0.5–2.0 cm) may

throw into question the applicability of an RT

volume-scattering analysis. In addition, one must

confront an essential scattering volume with rough

surface excursions that could be greater than the

thickness of the volume (layer) itself. In any case,

we note that reliance on the measured results in

the construction of the recent U. Mass. models

limits their predictive value and places them

largely outside of the type of model sought here.

Fung and Eom (1985) investigate the scattering and emission behavior of snow. The medium

is modeled as a densely packed matrix of ice

spheres; distance-dependent terms are kept in the

development of expressions for particle scattering as input to the phase matrix. Limiting the

16
formulation to far-field interparticle interaction

resulted in underestimation of computed backscatter and overestimation of brightness temperatures. Computations with near-(intermediate-)

field effects between particles produce superior

agreement to backscatter data shown for about 8

GHz. Tjuatja et al. (1992) build on this with their

multilayer model that includes volume scattering, surface scattering, and volume–surface interaction. With the volume component treated by

RT, the surface scattering may be computed using Fung’s integral equation method (e.g., Fung

and Pan 1987, Fung et al. 1992, Fung 1994) and

then added incoherently as a boundary condition

on the volume. Although all volume scatterers

are treated as spheres, the model is applied successfully to sea ice. Snow-covered ice is only

treated at 5 GHz, but frequencies as high as about

14 GHz are considered for ice alone. While this

still remains somewhat below our desired frequency range, it does entail a treatment of scattering elements that are large relative to the wavelength, with dense media, in the sense that

non-far-field interaction of particles is included.

Most recent investigations in the same frequency

range with active sensing are reported by Fung et

al. (1995). Passive sensing of snow-covered sea

ice (Tjuatja et al. 1995) up to 90 GHz treats densemedium effects by calculating a P matrix including near-field and coherent interactions of elements in a randomized 3-D grid. Simulated

behavior parallels that seen in measurements elsewhere.

Substantial groundbreaking work on volume

scattering has come from researchers working at

MIT. Using an RT approach, Shin and Kong (1989)

calculate bistatic scattering coefficients for a twolayer random medium using all four Stokes parameters (vector RT). In general, RT calculates

energy balances, and most phase effects are lost.

However, vector RT offers a partial compensation in that general elliptically polarized incidence and response states are included. The numerical approach provides valid solutions for both

small and large albedos; azimuthal Fourier decomposition is used, with Gaussian quadrature

and eigen analysis. Combined volume and rough

surface scattering effects are included by modification of the boundary conditions. KA–GO surface conditions are assumed. While measured data

are not treated, illustrative computer runs show

dominance of rough surface effects for incidence

near nadir with volume scattering predominant

for large angles. Applications to media and frequencies of interest here are limited by, among

other things, the assumption of small permittivity variations.

Investigators in collaboration with MIT researchers and others, at the University of Washington (UW), have developed a number of models that may be applicable to snow and ice.

Concentration has been on generic dense nontenuous granular media and size distribution

effects (Tsang and Ishimaru 1987; Ding and Tsang

1989, 1991; Wen et al. 1990; Tsang and Kong 1992).

A rigorous basis for dense-medium RT is provided by Tsang et al. (1985) and Tsang (1992)

based on multiple-scattering-field theory. The paper by West et al. (1993) actively incorporates

most of the developments leading up to it, and it

is a good display of the revelations made possible

by the method. With variations and departures in

each of the works cited, correlated scattering is

incorporated via the QCA and QCA–CP for the

first moment of the field and the correlated ladder approximation for the second moment, such

that an intensity operator may be obtained that

conserves energy. A size distribution is employed

for constituent particles with pair distribution

functions calculated under the Percus–Yevick approximations. Near-, intermediate-, and far-field

particle interactions are taken into account such

that coherent effects are expressed in the nearand intermediate-field ranges. Many interesting

features emerge from the numerical simulations,

such as less scattering from a dense correlated

medium than from an equivalent independent

scattering medium; much greater scattering from

a medium with distribution of particle sizes compared with a monodispersed mixture of the same

average radius; and the importance of multiple

scattering.

In treating the correlated scattering in dense

media, these DMRT approaches require the definition and computational treatment of a particle

pair distribution function (PDF). This function

expresses the conditional probability of finding a

particle at a given distance from another, and it is

directly related to the correlation function for the

medium. Its computational implementation is

made tractable for spherical particles through

employment of the Percus–Yevick approximation.

Once PDF and other dense-medium considerations are accounted for in determining the constituents of the basic energy balance equation, the

form of that equation is essentially the same as

for CRT, hence the same numerical considerations

apply to its solution. We note that multiple scat17
tering should normally be significant in dense

media. Thus, computational maneuvers that rely

on weak or insignificant multiple scattering are

unlikely to apply. Using the DMRT approach,

Wen et al. (1990) show the convex relation between extinction and particle density that has been

observed in measurements (e.g., Ishimaru and

Kuga 1982, Gibbs and Fung 1990).

DMRT simulations show a relation between

interparticle correlation and size distribution effects. While Wen et al. (1990) show reasonable

agreement with snow backscatter measurements,

they assume a uniform grain size. More reasonable physical parameters produce good agreement

when a grain size distribution is employed (West

et al. 1993). Most simulations up through the work

of West et al. assume Rayleigh scattering, i.e., ka <

1, which limit applicability to the bottom of the

MMW frequency range. (This limitation is not

inherent in the basis of DMRT.) In this regime, for

independent scattering, the scattering cross section increases as the sixth power of particle radius a. Thus, it should not be surprising that

DMRT calculations based on a Rayleigh distribution of sizes produces backscatter on the order of

15 dB greater than that from a uniform distribution, with size equal to the mode radius in the

distribution. A relatively small number of larger

particles can produce a disproportionately great

effect. At the same time, the increase in scattering

by the larger particles in a nonuniform distribution is not nearly as great as one would expect

from the sixth-power law. The point is that the

close proximity of the smaller particles to the

larger particles reduces the overall correlation

length of the medium, which is expressed through

the PDF.

These results suggest that both dense-medium

and particle-size-distribution effects must be

treated, and must be treated together, for highfidelity simulations. For a particular application,

i.e., to snow, one might hope that it could be

possible to develop an “equivalent” uniform particle size. That is, if snow tends to come in various

particular micromorphologies with particular attendant particle distributions, it might be possible to develop systematically a corresponding

fictional uniform particle size that would give the

correct results in simulations. This particle size

would in general be different from the average

particle size. It is questionable that such a quantity could be implemented so as to portray accurately all effects of interest, e.g., polarization effects. Hopes are even more dim for development

of an “equivalent” CRT formulation that lacks

detailed realism in the mechanisms incorporated

but that also somehow reliably produces correct

behavior.

In principle, there is no problem in including

different species as well as different sizes of particles in DMRT formulations. This suggests that

water inclusions might be modeled as small ringshaped or otherwise nonspherical inclusions at

points of particle contact. However nonspherical

particles interfere with the established strategies

for the necessary PDF-related computations. Because the liquid water inclusions are small, their

shape may not be so important and they might be

modeled as many very small spheres concentrated

somehow in the smaller crevices of the medium.

Ding et al. (1993) have produced “sticky” particle

formulations, by which specified degrees of particle clustering can be achieved in the numerical

construction of the medium. Beyond its possible

relevance for the inclusion of liquid water, this

sort of formulation has shown promise in producing more realistic morphology and scattering

behavior (Shih et al. 1995). Extreme degrees of

anisotropic “stickiness” might successfully treat

some of the anisotropic particle effects mentioned

above. In any case, ongoing work at MIT seeks

ways to generate dense distributions of spheroidal particles, together with their correlation/PDF

functions. As in nature, some degree of average

particle orientation is forced by the density of the

medium.

The particle basis for DMRT formulations heretofore imposes considerable computational burden as the particles become large relative to the

wavelength. Restricting particles to a spherical

shape facilitates both PDF and scattering determination as dimensions increase, inasmuch as

Mie scattering schemes may be employed. However, to date most formulations and computations have been performed assuming particles that

are small enough to warrant the assumption of

simpler Rayleigh scattering. When nonspherical

grains are treated, however, the Mie scattering

formulations are inapplicable. When particles are

relatively large, the details of their shape have

more effect on overall scattering behavior and

one has less liberty to just assume a somehow

equivalent sphere. In response to this, work at

MIT has also been directed into correlation functions for “bicontinuous” nongranular geometries.

In the end, this may be both simpler and more

18
successful than the particle-based approaches,

which in any case are somewhat artificial for most

applications to snow.

While ice and snow are logically considered

together, one must distinguish the particular

problems associated with each. Until recently,

few MMW sea-ice studies could be found with

comparisons of simulations to data, exceptions

being the work of Lee and Mudaliar (1988) and

Mudaliar and Lee (1990). At present, one does

well to begin with the wealth of detail on seaice phenomenology and sensing, measurement

and modeling, and theory and evaluation as

presented in the volume edited by Carsey (1992).

A chapter by Winebrenner and others on theoretical modeling of sea-ice microwave/MMW

behavior recounts the testing of various contrasting models on three reasonably well-characterized saline ice samples over a frequency

range that includes some of our span of interest. Any applicable model must somehow include the effects of elongated, oriented brine

pockets or bubbles in the ice. Alternatively, it

can concentrate on the complementary shape of

the individual crystals defining the boundaries

of those pockets. Models tested (and their originators) were designated to include independent

Rayleigh scattering layers (Drinkwater); dense

media RT (Tsang and West); dense-medium

theory with integral equation method for rough

surface (DMT–IEM, by Fung and his co-workers); many-layer strong fluctuation theory (SFT

by Stogryn/Grenfell); polarimetric SFT (Nghiem and the MIT team); and MRT (Lee and

Mudaliar). The reader is referred to the above

reference for the details of these studies. Particularly in certain aspects and certain frequency

domains, successes are shown, although many

questions remain. Among other things, models

based on rather different physical mechanisms

sometimes still manage to provide more or less

the same (correct) answers. This raises the question of how much seemingly good results derive from modeling technique and manipulation, as opposed to incorporation of mechanisms

that truly correspond to the dominant physical

processes. Most of the work reported in Carsey’s

(1992) volume was part of a large ongoing effort, with some additional results reported elsewhere. The reader is referred to IGARSS’94

(1994), with somewhat fewer sea-ice papers in

IGARSS’95 (1995) showing MMW content.

AVAILABLE COMPUTER CODES

In this section we provide information on specific models and their sources. The entries are

listed by source and are grouped more or less by

area of application. For each model or package,

information is given on applications, model features and approach, and source contact. Comments on each include information such as location of reference discussion in the body of the

report, limitations and advantages, and status of

code testing and facilitation. In some instances

considerations of code documentation, availability, ease of use, and support are subsumed in the

category “code usability.”

Many notable models discussed in this report

are not mentioned below because they failed in

some way to meet our general criteria for inclusion (e.g., insufficient information from originators, complexity or resource requirements beyond

the feasibility limits, unavailability of code, reliance on empirical quantities, lack of application/

testing against geophysical media, unlikely future support for the code, etc.). This should not be

interpreted as a negative judgment on the scientific validity or research value of such models.

MPM

Features

Computes complex refractivity profiles together with power attenuation and propagation

delay rates as functions of frequency, humidity,

or pressure for air, with possible inclusion of water vapor, haze, fog/cloud, and rain.

Comments

Refer to the discussion under Atmosphere, in

the Applications section.

Input factors may be frequency, barometric

pressure, RH, temperature, haze type, suspended water-droplet concentration, and rain

rate. In different versions of the model, the user

inputs a range for one of the first three variables

and fixed values for some or all of the remaining

ones. Rain treatment is very simple. The code is

easy to use, with plentiful comments and references embedded.

Source/contact

Dr. Hans J. Liebe

NTIA/ITS.S1

19
325 Broadway

Boulder, CO 80303

Phone: (303) 497-3310

Enhanced RADTRAN

Features

Computes atmospheric attenuation and brightness temperature for typical atmospheric paths,

including effects of clear air, fog, cloud, and rain,

with polarized surface emissivities.

Comments

Refer to the discussion under Atmosphere, in

the Applications section.

Improvements by Atmospheric and Environmental Research, Inc., of the 1979 Air Force Geophysics Laboratory program; core treatment of

gas and aerosol effects is solid; newer RT algorithm treats multiple scattering from precipitation; the formulations of terrestrial surface effects

are very approximate; limited validation of recent enhancements; code documented, disseminated, and supported; more extensive validation

is underway.

Contact/source

Dr. Vincent J. Falcone

Geophysics Laboratory

Air Force Systems Command

United States Air Force

Hanscom AFB, MA 01731-5000

Phone: (617) 377-4029

Dr. Ronald G. Isaacs

Atmospheric & Environmental

Research, Inc.

840 Memorial Drive

Cambridge, MA 02139

Phone: (617) 547-6207

Gasiewski radiative

transfer model

Features

Computes brightness temperature and associated statistics for planar stratified scattering atmospheres over specularly reflecting surfaces.

Comments

Refer to the discussion under Atmosphere, in

the Applications section.

An RT solution for absorbing atmosphere and

Mie scattering from precipitation; very simple surface emissivity factors, with general user-specified (constant) bistatic scattering coefficient inclusion under development; as with RADTRAN,

polarimetric effects from precipitation are generally lacking; aspherical hydrometeor formulation

is under development; code usability: “Undergraduate students at Georgia Tech have been able

to obtain useful results from the model within a

few hours.”

Source/contact

Professor Al Gasiewski

Department of Electrical Engineering

Georgia Institute of Technology

Atlanta, GA 30332-0250

Phone: (404) 894-2934

Fung surface model

Features

Integrated and facilitated surface scattering

model based on SPM, KA, or the integral equation approach.

Comments

Refer to the discussion under Scattering from

Surfaces and Transitions, in Methods and Approaches

section.

PC-oriented, user-friendly software and documentation under development; user inputs choices

of rms height, correlation length, and possibly

correlation function, program displays results

compared with user input data; subject to parameter field limits of each technique; integral equation approach most permissive, requiring primarily rms slope less than about 0.4.

Source/contact

Professor Adrian Fung

University of Texas at Arlington

Arlington, TX 76019

Phone: (817) 273-3422

UPM surface model

Features

Unified perturbation method producing complete bistatic cross sections for E and H polarization; Gaussian and power law surface spectra are

included so far, others are possible.

20
Comments

Refer to the discussion under Scattering from

Surfaces and Transitions, in the Methods and Approaches section.

The formulation reduces where appropriate to

KA, SPM, and two-scale theories, with greater

overall range of convergence but similar input

requirements; 1-D roughness code is available, 2-

D reported nearing completion; possible inclusion of 1-D roughness finite element and method

of moments codes for Monte Carlo simulation;

bistatic results allow inference of reciprocal passive behavior; upcoming 2-D roughness treatment

would allow fully polarimetric treatments and

possible integration with specific ocean modeling

capability.

Source/contact

Dr. Ernesto Rodriguez and Dr. Yunjin Kim

Jet Propulsion Laboratory

California Institute of Technology

4800 Oak Grove Drive

Pasadena, CA 91109

Phone: (818) 354-9500

GWU vegetation model

Features

WT-based approach to sparse layer over half

space with classes of scatterers having orientation distributions.

Comments

Refer to the discussion under Vegetation, in the

Applications section.

Some ground-vegetation multibounce paths are

included, but overall the model treats two-layer

single scattering theory with attenuation; KA treatment of rough ground surface; polarimetric backscatter coefficients are calculated. Previous formulation and especially validation at frequencies

no higher than C band, with recent developments

oriented toward at least X-band and higher; documentation status is unknown.

Source/contact

Professor Roger Lang

Department of Electrical Engineering

and Computer Science

George Washington University

Washington, DC 20052

Phone: (202) 994-6083

Schwering and Johnson

vegetation model

Features

Scalar RT treatment of vegetation field with

surface but no deep boundary; computes propagation from which backscatter can be obtained.

Comments

Refer to the discussion under Vegetation, in the

Applications section.

Very simple model that relies on measured or

estimated two-parameter phase function; satisfactory simulation of data on which phase function was based; limited generality; program could

be made available and documentation developed

at small to moderate cost.

Source/contact

Dr. Robert Johnson

Textron Defense Systems, MS 3106

201 Lowell St

Wilmington, MA 01887

Phone: (508) 657-1721

UW snow model

Features

Computes polarimetric surface and volume

scatter and emission from snowpacks under different moisture conditions.

Comments

Refer to the discussion under Snow and Ice, in

the Applications section.

Assumed spherical particles allow calculation

of pair distribution function and consequent dense

medium approach; formulation includes particlesize distribution with the presence of moisture;

developments are anticipated in connection with

MIT personnel and Shi from UCSB. The validation is encouraging, and the code usability has

potential. Documentation status is unknown. Continuing developments are currently underway.

Source/contact

Professor Leung Tsang

Electromagnetics of Remote Sensing Laboratory

Department of Electrical Engineering

University of Washington

Seattle, WA 98195

Phone: (206) 685-7537

21
EMSARS

Features

EMSARS, or Electromagnetic Model for Scattering Applied to Remote Sensing, is a general

active and passive polarimetric computational

package for generic anisotropic volume and surface scattering with layered media.

Comments

Surface scattering modules can treat perturbed

quasi-periodic surface, reducing to classical twoscale random rough surface, or “classical” KA,

GO, SPM. Rough surface effect added incoherently to WT and RT volume scattering; treatment

of vegetation layers and individul trees; integrated

code and documentation exist with ongoing debugging; prospective union with UW dense medium/snow model; importantly, integrated capability has been developed from GIS/map data

through simulation to scene generation.

Source/contact

Professor Jin Au Kong and Dr. Eric Yang

Center for Electromagnetic Theory

and Application

Research Laboratory of Electronics

Massachusetts Institute of Technology

Cambridge, MA 02139

Phone: (617) 253-8535

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C.T. Swift (1986) File of normalized radar cross

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Borgeaud, M., J.A. Kong and F.C. Lin (1986) Microwave remote sensing of snow-covered sea ice.

Proceedings of IGARSS ’86, Zurich, p. 133–138.

Carsey, F. (Ed.) (1992) Microwave Remote Sensing

of Sea Ice. American Geophysical Union Monograph 68, Washington, D.C.

Chandrasekhar, S. (1960) Radiative Transfer. New

York: Dover.

Chang, P.S. J.B. Mead, E.J. Knapp, G.A. Sadowy,

R.E. Davis and R.E. McIntosh (1996) Polarimetric backscatter from fresh and metamorphic snow–

cover at millimeter wavelengths. IEEE Transactions on Antennas and Propagation, 44: 58–73.

Chauhan, N.S., R.H. Lang and K.J. Ranson (1991)

Radar modeling of a boreal forest. IEEE Transactions on Geoscience and Remote Sensing, 29(4): 627–

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Chen, M.F. and A.K. Fung (1988) A numerical

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Chuah, H.T. and H.S. Tan (1992a) A radar backscatter model for forest stands. Waves in Random

Media, 2: 7–28.

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emission model for vegetative medium using

Monte Carlo method: Part I. Journal of Electromagnetic Waves and Applications, 6(7): 799–834.

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emission model for vegetative medium using

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Davis, J.L. et al. (1992) TRACK 4.2: Radar cross

section and tracking simulation users guide. Georgia Technical Research Institute. Atlanta: Georgia

Institute of Technology.

Ding, K.H. and L. Tsang (1989) Effective propagation constants in media with densely distributed dielectric particles of multiple sizes and

permittivities. Chap. 3 in Progress in Electromagnetics Research (PIER1) (J.A. Kong, Ed.). New York:

Elsevier.

Ding, K.H. and L. Tsang (1991) Effective propagation constants and attenuation rates in media

of densely distributed coated dielectric particles

with size distributions. Journal of Electromagnetic

Waves and Applications, 5(2): 117–142.

Ding, K.H., C.E. Mandt, L. Tsang and J.A. Kong

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26
Dr. Kevin O’Neill (Moderator)

USACRREL

72 Lyme Rd

Hanover, NH 03755

Dr. James (Pat) Welsh

SWOE Program Manager

SWOE Program Office

USACRREL

72 Lyme Rd

Hanover, NH 03755

Prof. Adrian Fung

University of Texas at Arlington

Arlington, TX 76019

Prof. Al Gasiewski

Department of Electrical Engineering

Georgia Institute of Technology

Atlanta, GA 30332-0250

Dr. Ronald Isaacs

Atmospheric & Environmental Research Inc.

840 Memorial Drive

Cambridge, MA 02139

Prof. Akira Ishimaru

Electromagnetics of Remote Sensing Laboratory

Department of Electrical Engineering

University of Washington

Seattle, WA 98195

Dr. Junjin Kim

Jet Propulsion Laboratory

4800 Oak Grove Drive

Pasadena, CA 91109

Prof. Jin Au Kong

Center for Electromagnetic Theory and Applications

Research Laboratory of Electronics

Room 26-305

Massachusetts Institute of Technology

Cambridge, MA 02139

Prof. Roger Lang

Department of Electrical Engineering

and Computer Science

George Washington University

Washington, DC 20052

Dr. Hans Liebe

NTIA/ITS.S1

325 Broadway

Boulder, CO 80303

Mr. Steve Lohmeier

Microwave Remote Sensing Laboratory

University of Massachusetts

Amherst, MA 01003

Prof. Robert McIntosh

Microwave Remote Sensing Laboratory.

University of Massachusetts

Amherst, MA 01003

Prof. Leung Tsang

Electromagnetics of Remote Sensing Laboratory

Department of Electrical Engineering

University of Washington

Seattle, WA 98195

Dr. Eric Yang

Center for Electromagnetic Theory

and Applications

Research Laboratory of Electronics

Massachusetts Institute of Technology

Cambridge, MA 02139

APPENDIX A : LIST OF WORKSHOP PARTICIPANTS

MMW MODELING WORKSHOP, 13–15 MAY 1992

27
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16. PRICE CODE

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maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,

including suggestion for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington,

VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

October 1996

The State of the Art of Modeling Millimeter-Wave Remote Sensing

of the Environment

Kevin O’Neill

U.S. Army Cold Regions Research and Engineering Laboratory

72 Lyme Road Special Report 96-25

Hanover, New Hampshire 03755-1290

Office of the Chief of Engineers

Washington, D.C. 20314-1000

Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161

Algorithms Modeling Surface scattering 33

Emission Remote sensing Volume scattering

Millimeter-wave (MMW) Software

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

A survey was undertaken of models for millimeter-wave (MMW) scattering and emission from environmental

features, particularly in the vicinities of 35 and 94 GHz. The ultimate objective was to identify models suitable

for current or near-future application in scene generation. The ideal model would be based on first principles,

would be readily available in facilitated software, and would have reasonable requirements in terms of computational resources and input parameters. At MMW frequencies, these requirements push the frontiers of current

science and technology. In most applications, one must accept as a first approximation the approaches currently

under development in research settings. This report reviews the basic methods and approaches underlying all

available models in terms of volume scattering, treatment of surfaces and transitions, and the development of

statistical quantities from rational physics. Very rough surfaces, locally steep surface slopes, and low-angle

incidence can rarely be treated entirely successfully, but recent developments offer the prospect of significant

progress. Volume and combined surface–volume scattering and emission models are reviewed for application

to land, water, vegetation, snow, and ice environments. Most are essentially works in progress, with theory and

validation currently building from earlier work at C and X bands. Very sound capabilities are available for

treatment of common atmospheric features, with recent progress in modeling more complex meteorological

events. Limiting consideration to truly available codes, a list is provided for each of the above areas of models

and their sources. Because it is the most comprehensive and is currently facilitated in terms of software, the MIT

EMSARS model is the foremost condidate to serve as a platform for future addition and development.

For conversion of SI units to non-SI units of measurement consult ASTM Standard E380-93, Standard Practice for Use of the

International System of Units, published by the American Society for Testing and Materials, 1916 Race St., Philadelphia, Pa.

19103.