United States
Environmental Protection
Agency
Radiation and Indoor Air (6602J)
Solid Waste and
Emergency Response (5101)
9355.0-59-FS
EPA 540-F-96/002
PB96-963301
January 1996
Fact Sheet: Documenting
Ground-Water Modeling at
Sites Contaminated with
Radioactive Substances
Quick Reference Fact Sheet
At many sites currently regulated by EPA or NRC
or managed by DOE, the principal concern is the
existence of—or potential for—contamination of
underlying aquifers. Compared to air, surface
water, and terrestrial pathways, ground-water
contamination is more difficult to sample and
monitor, which results in a greater reliance upon
mathematical models to predict the locations and
levels of environmental contamination. The types
of models used to simulate the behavior of radio-
nuclides in ground water are more complex than
models for surface water or atmospheric trans-
port, primarily due to the diversity of physical
settings possible at different sites. Also, the meth-
ods used to model ground water are not as stan-
dardized as those for other pathways, and there is
much less written on appropriate methods.
In 1991, a joint Interagency Environmental Path-
way Modeling Working Group was initiated
among EPA's Offices of Radiation and Indoor Air
and Solid Waste and Emergency Response, the
Department of Energy's Office of Environmental
Management, and the Nuclear Regulatory
Commission's Office of Nuclear Material Safety
and Safeguards. The purpose of the Working
Group is to promote the appropriate and consis-
tent use of mathematical models in the remediation
and restoration process at sites containing—or
contaminated with—radioactive materials or
mixed waste substances.
This fact sheet is one in a series that summarize
reports published by the Working Group. These
reports, which are identified in the References
section, are intended to assist those responsible
for identifying and implementing flow and trans-
port models in support of cleanup decisions at
hazardous and radioactive waste sites.
PURPOSE
The Working Group directed that a report be
written to describe a recommended method of
documenting ground-water modeling results
for hazardous-waste remediation sites. This
fact sheet summarizes the report, which is
entitled Documenting Ground-Water Modeling
at Sites with Radioactive Contamination. The
method described in the report is consistent
with the seven standards published by the
American Society for Testing and Materials
Subcommittee on Ground-Water and Vadose
Zone Investigations.
Adoption of the tenets in the report will en-
hance the understanding between modelers and
their managers of what may be expected in
model documentation; facilitate the peer-re-
view process by ensuring that modeling docu-
mentation is complete; ensure that institutional
memory is preserved; and institute greater con-
sistency among modeling reports.
INTRODUCTION
The report provides a guide to determining
whether proper modeling protocol has been fol-
lowed, and that common modeling pitfalls have
been avoided. As a guide to modelers, the report
demonstrates a thorough approach to document-
ing model applications in a consistent manner. A
review of 20 site-specific modeling studies at
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hazardous-waste remediation sites'described mis-
takes in all aspects of the modeling process, in-
cluding a misunderstanding of the model, misap-
plication of boundary or initial conditions, mis-
conceptualization, inappropriate data, improper
calibration or verification, insufficient uncertainty
analysis, and misinterpretation of simulation re-
sults. Any of these errors could lead to faulty
remediation decisions. A proper documentation
of modeling results answers the following
questions:
• Do the objectives of the simulation correspond
to the decision-making needs?
• Are there sufficient data to characterize the site?
• Is the modeler's conceptual approach consistent
with the site's physical and chemical processes?
• Can the model satisfy all the components in the
conceptual model, and will it provide the results
necessary to satisfy the study's objectives?
• Are the model's data, initial conditions, and
boundary conditions identified and consistent
with geology and hydrology?
• Are the conclusions consistent with the degree
of uncertainty or sensitivity ascribed to the
model study, and do these conclusions satisfy
the modeler's original objectives?
The recommended approach to evaluating mod-
els consists of three steps: (1) determining one's
objectives and data requirements for the project;
(2) properly developing a conceptual model for
the site, which describes the physical and chemi-
cal system that must be simulated; and (3) select-
ing and applying the model in a manner consis-
tent with the objectives and the site's known physi-
cal characteristics and input variables.
MODELING OBJECTIVES AND DATA
REQUIREMENTS
Ground-water modeling objectives usually de-
pend upon the stage of the remedial process.
Early (scoping) stages often need fast, efficient,
order-of-magnitude estimates of the extent of con-
tamination and the probable maximum radionu-
clide concentrations at specified locations.
Preliminary characterization data are often sparse,
1 "Evaluation of Subsurface Modeling Application at
CERCLA/RCRA Sites." U.S. EPA Center for Subsurface
Modeling Support, Ada, OK, 1995.
and subsurface flow and transport processes can
be limited to general considerations such as
whether flow is controlled by porous media or
fractures, or whether the wastes are undergoing
phase transformations. One of the most useful
analyses at this phase is to evaluate the interde-
pendencies of controlling parameters: How do
changes in one parameter affect the others and
the outcome of the modeling exercise? This un-
derstanding assists in properly focusing the site
characterization activities. At this early stage in
the process, it is important to use a modeling
approach where parameter values can be selected
systematically from the probable range to evalu-
ate what effects one or multiple parameters have
on rate of flow or concentration of contaminants.
Either a sensitivity analysis or—in the absence of
reasonable data—a conservative bounding ap-
proach (high and low probable estimates) can be
used, as long as the modeler properly documents
the uncertainty such assumptions create. For ex-
ample, distribution coefficients are often pub-
lished at neutral pH values. However, if acid
wastes are involved, even conservative values
could be too high. Because site-specific informa-
tion is often limited in the scoping phase, early
modeling objectives are usually designed to sup-
port the design of more ambitious site character-
ization studies. Such relatively simple objectives
can often be satisfied by one- or two-dimensional
models.
The site characterization phase typically provides
the first opportunity to gain a detailed under-
standing of the overall behavior of the system.
This leads in turn to a refinement of the concep-
tual model, and follows the iterative process of
data collection, analysis, and decision making.
The primary reasons for ground-water modeling
in the site characterization phase of the remedial
process are to refine the conceptual model; opti-
mize the site characterization program; support
the baseline risk assessment; and provide prelimi-
nary input into the remedy selection.
In many instances, several different approaches
to modeling will be taken to accomplish the ob-
jectives. For example, the output of analytical
modeling of the vadose zone, in the form of
radionuclide concentrations at the saturated/
unsaturated interface, may be used as input to
numerical models of the saturated zone. Similarly,
governing geochemical processes may have a
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significant impact on the transport of radionu-
clides, and can be simulated indirectly in the
analysis.
Table 1, on page 4, summarizes a checklist of key
questions a model documentation report should
answer in order to provide evaluators with a
reasonable opportunity to judge the model's suit-
ability for the application. For convenience, the
checklist is grouped into three categories: Objec-
tives and Data Requirements, which considers
whether the modeler has adequately considered
the purpose and scope of the model; Conceptual
Model Development, which ensures that the
modeler has documented the physical relation-
ships between the conceptual model and the
actual system; and Modeling Application, which
focuses on the model code selection, source term,
parameterization, uncertainties, and results. A
more detailed list of criteria is included in the full
report.
CONCEPTUAL MODEL
DEVELOPMENT
The conceptual model of a site is a diagrammatic
or narrative description of the condition of a site
and its setting. It describes the subsurface physi-
cal system, the variability of the aquifer, and the
types of contaminants found and their transport
mechanisms. As information about a site accu-
mulates, the conceptual model is revised and
refined into a set of hydrogeologic assumptions
and concepts that can be evaluated quantita-
tively. The conceptual model must be consistent
with the physical system and consistent inter-
nally. At a minimum, the conceptual model must
include the geologic and hydrologic framework,
hydraulic properties, sources and sinks, bound-
ary and initial conditions, transport processes,
and spatial and temporal dimensionality.
The formulation of a conceptual model is an
integral component of the modeling process. Since
the conceptual model is iteratively redesigned as
more data become available and as the remedia-
tion process progresses, some components of the
conceptual model may be simplified to meet lim-
ited objectives or data limitations. Such simplifi-
cation is valid because early modeling focuses on
the significance of specific parameters and their
effects on transport rather than on modeling
specific hydrogeologic transport processes. One-
dimensional models (point /receptor) or two-di-
mensional models (plume transport from source
to receptor horizontally and vertically) are com-
monly used in the scoping phase of a remedia-
tion. Since trends (rather than precision) are more
important during the early phase, ground-water
modelers make a number of simplifying assump-
tions early in the investigation: steady state con-
ditions; one- or two-dimensions; simplified
boundary and initial conditions; homogeneous
media; and simplified flow and transport
processes.
The conceptual model, which is based on the
modeler's experience and judgment, will become
more complex as more processes are identified
and interrelationships are incorporated. The trans-
formation of the conceptual model into a math-
ematical model will result in intrinsic simplifica-
tions of the system. For example, mathematical
models assume that input data may be scaled up
or down according to the needs of the simula-
tion — the same algorithms are applied whether
the simulation covers centimeters or kilometers.
Besides inherent simplifications, the modeler may
deliberately simplify the physical processes
through such typical assumptions as:
Scoping Phfty Simplifying Assumptions
• Flow through the unsaturated zone is vertical
and in one dimension
• Chemical reactions are instantaneous and
reversible
• Soil or rock is isotropic or homogeneous
• Flow is uniform and steady-state
Site Characterization ph.g-'y Assumptions
• Steady-state flow/transient transport
• Three-dimensional flow and transport
• Steady-state boundary and nonuniform initial
conditions
• Complex flow and transport processes
• System heterogeneity
As the site investigation proceeds into the reme-
dial phase, data are acquired that will be used to
evaluate feasible remedial alternatives. Optimiz-
ing a remedial design involves evaluating alter-
native screen depths, pumping rates, and well
locations to identify the most effective
configuration. Modeling objectives associated
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Table 1. Key Issues in Model Documentation
Objectives and Data Requirements
Are the purpose and scope outlined and consistent with decision making needs?
Are the data requirements outlined for the proposed modeling?
Are the sources of data and data uncertainties adequately discussed?
Conceptual Model Development
Are the physical and hydrological frameworks adequately described?
Is the nature of the contaminant source term described?
Is the conceptual model consistent with the field data?
Are the uncertainties and simplifying assumptions of the conceptual model justified?
Model Application
Code Selection
Is the rationale for code selection clearly presented for proposed code(s), and are the general fea-
tures, assumptions, and limitations, of the code(s) presented?
Is the code well documented and adequately tested?
Are the hardware requirements compatible with those available?
Model Construction
—Layering and Cridding
Do the nodes fall near pumping centers on wells and along the natural boundaries?
Is the grid oriented along the principal axes of hydraulic conductivity?
Is the grid at the appropriate scale for the problem?
Are strong vertical gradients within a single aquifer accommodated by multiple planes or layers
of nodal planes?
—Boundary and Initial Conditions
Are model boundaries consistent with natural hydrologic features?
Are the uncertainties associated with the boundaries and initial conditions addressed?
Are transient boundaries discussed?
—Model Parameterization
Are data input requirements fully described?
Are the model parameters within the range of reported or measured values?
Model Calibration
Are the calibration criteria presented and are the calibration procedures described in detail?
Does the calibration satisfactorily meet specified criteria?
Has the calibration been tested against actual field data and are discrepancies explained?
Is the calibrated model consistent with the conceptual model?
Sensitivity Analyses
Was a sensitivity analysis performed and is the approach to the sensitivity analysis detailed?
Was the relevance of the sensitivity analysis results to the overall project objectives discussed?
Are the results presented so that they are easy to interpret?
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with remedial alternative design generally are
more ambitious than those associated with the
site characterization phase. The remedial design
is the most challenging phase of the investiga-
tion. A number of processes that may not be
important to assessing baseline risk or to site
characterization may be essential to remedial
design:
• Three-dimensional flow and transport
• Matrix diffusion (pump-and-treat)
• Desaturation and resaturation of the aquifer
• Heat-energy transfer
• Sharp hydraulic conductivity gradients or
thresholds
• Multiple aquifers
• Movement from confined to unconfined
conditions
• Simulation of complex flow conditions.
MODEL APPLICATION
The proper application of a model is perhaps
more important than its selection. No matter how
well a model is suited to a particular application,
it will give misleading results if used improperly
or with incomplete or incorrect data. Conversely,
even a model with limited capabilities, or one
used at a site with limited data, can give useful
results if applied properly and with a full appre-
ciation of the model's limitations. A conceptual
model is a description of the present conditions
of a site. To predict future behavior, it is neces-
sary to develop a physical scale, analog, or math-
ematical model. Mathematical models are more
widely used simply because they are easier to
develop and manipulate.
Model application is the process of choosing and
applying the appropriate algorithms capable of
simulating the hydrogeologic system as defined
by the conceptual model. Mathematical ground-
water models are classified as either deterministic
or stochastic. Deterministic methods assume that
a process leads to a uniquely definable outcome,
while stochastic models presume that all out-
comes are inherently uncertain and must be char-
acterized in terms of probabilities. Put another
way, deterministic models result in a specific
value for specified points, stochastic models pro-
vide the probability of a specific value occurring
at any point. Stochastic models are relatively
recent, and are still used primarily for research.
Deterministic models—both numerical and ana-
lytical—are more widely used.
Analytical deterministic models are based on the
solution of applicable differential equations that
describe an idealized system. The solution of
these equations give quantitative estimates of the
extent of contaminant transport. These models
are relatively easy to use, can be solved with a
calculator, and generally require only limited
site-specific data. Most available analytical mod-
els assume a uniform and steady flow, which
requires the system to be homogeneous and iso-
tropic with respect to hydraulic conductivity.
Unfortunately, these models do not lend them-
selves to solutions when boundary conditions
are complex. Therefore, if a realistic expression for
hydraulic head or concentration over the site can-
not be written from the governing equations and
boundary or initial conditions, more sophisticated
numerical methods must be used. Numerical meth-
ods can account for complex geometry and
heterogenous media, as well as for dispersion,
diffusion, and chemical processes (sorption, pre-
cipitation, radioactive decay, ion exchange, deg-
radation). Numerical methods require a digital
computer, greater quantities of data than analyti-
cal methods, and an experienced modeler.
Scoping Calculations
In practice, it is usually not necessary to develop
mathematical expressions for all elements of the
conceptual model, particularly in early phases of
the project. There are four primary sources by
which radioactivity can contaminate ground-
water: leaching from surface impoundments;
wastes injected below the water table; leaching
from contaminated surface soils; and recharge
from contaminated surface waters such as rivers
or lakes. Detailed methods to calculate release
rates and analyze fates are presented in Appen-
dix B of the report, and may be used either to
develop initial conditions or verify the methods
used by modelers for their scoping phase.
When analyzing a radionuclide release to ground
water, potential release mechanisms should be
evaluated first, including the source mechanism
or mechanisms, their physical and chemical prop-
erties, and their age. Estimation of release in-
volves quantifying radionuclide concentrations
present in the waste or leachate and the volume
of the leachate or direct release rate. There are
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usually two processes that control the fate of
radionuclides during transport from the source
area: geochemical transport processes (such as
sorption, ion exchange, and precipitation) and
radioactive decay. The former processes can ei-
ther facilitate or retard contaminant flow, but
decay always results in a loss of activity of the
original radionuclide. However, the modeler must
consider the potential ingrowth of toxic daughter
products, depending upon the time scale of the
model.
Mathematical screening methods do not explic-
itly simulate processes that influence the trans-
port of radionuclides; these processes are gener-
ally combined into a single term designated the
distribution coefficient (Kd). Distribution coeffi-
cients are discussed qualitatively in Appendix A
of the report, along with a number of limitations
inherent to the assumptions surrounding the use
of Kd. Analytical models are generally able to
simulate steady-state flow conditions. However,
because the data available during the scoping
phase rarely support transient simulations, com-
mon analytical methods may be more effective
than numerical methods that depend on more
sophisticated (but inadequate) data. It is much
easier to conduct sensitivity analyses with ana-
lytical rather than numerical models.
Uncertainty in the analyses should be empha-
sized in the scoping phase model. Data collection
itself can introduce uncertainty, and, when com-
bined with the system's natural randomness, may
lead to wide variations in results. In practice,
much of the effort in early modeling studies
should focus on the significance of uncertainty
associated with specific parameters rather than
on modeling specific hydrogeologic properties.
Since uncertainty is expressed as a probability
distribution around each of the parameters, it is
important to select a model where individual
values can be selected systematically from the
range of results and substituted into the govern-
ing flow equations. If this is done properly, the
effects of a single parameter may be evaluated.
Where the possible range is impracticably large,
the analyst may have no other recourse than to
evaluate the high and low values and await the
collection of better data. Sensitivity analyses are
therefore very useful in guiding the design of
monitoring or site characterization studies. It is
relatively easy to develop conservative estimates
of the extent of contamination or the down-field
concentration of contamination based on high-
or low-end values of probable data values.
Site Characterization Modeling
One of the primary objectives in site character-
ization modeling is to obtain sufficient data for a
defensible (and more realistic) site-specific ap-
proach. Reliance on conservatively high values
may lead to problems during site characteriza-
tion or baseline risk assessment phases. For ex-
ample, reliance on conservatively high hydrau-
lic conductivities could interfere with calibra-
tion to known values, or predictions of higher
ground-water flow and concomitantly lower
down-field contaminant concentrations. For these
reasons, application of the model during the site
characterization phase is more sophisticated and
should be managed by experienced personnel.
The four steps in model application are (1) code
selection; (2) model construction; (3) model cali-
bration; and (4) sensitivity/uncertainty analysis.
The greatest difficulty in selecting appropriate
computer code is not in determining capabilities
but rather in determining which capabilities are
necessary to support remedial decision making
at a particular site. However, the model's "pedi-
gree" is also important to consider, and must be
described. Availability of source code, history of
use, documentation, testing, and necessary hard-
ware each should be considered when deciding
whether the model will produce acceptable—
and accepted—results.
Model construction is the process of transform-
ing the conceptual model into mathematical terms
that comply with physical boundaries and ac-
cepted laws. For example, the continuum of pos-
sible values inherent in natural systems is re-
placed by a series of discrete blocks or elements,
and three-dimensional space is divided into grids.
The issue is to divide up the domain in as realistic
a manner as possible. The finer the size of each
"block" in the grid, the more accurate the nu-
merical solution. However the more blocks there
are, the more difficult and time-consuming it
will be to run the model. Similarly, any model
that simulates transient concentrations requires
the use of time steps. There is a direct relation-
ship between numerical accuracy, grid density,
and time-step size. Fortunately, there is a satis-
factory numerical criterion for selecting the time
step for a model. Boundary conditions must be
described in terms of where water is flowing into
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and out of the system. Since physical boundaries
can be permeable, impermeable, or semiperme-
able, the model boundaries can be treated either
as a constant or variable specified flux, or as a
constant head, depending upon which best de-
scribes the physical conditions.
Model calibration refers to the trial-and-error ad-
justment of parameters of the ground-water system
by comparing the model's output and measured
values. A model is calibrated by determining a set of
parameters, boundary conditions, and hydraulic
stresses that generate simulated potentiometric sur-
faces and fluxes that match field-measured values
within an acceptable range of error. Ground-water
flow models may be calibrated automatically against
preset criteria. A contaminant transport model is
usually calibrated more subjectively, since data on
concentrations are usually inadequate to permit
accurate calibration. Also, contaminant transport
equations contain more parameters than flow trans-
port equations, so it is more difficult to develop an
automated method. No established protocol cur-
rently exists for determining whether a model has
been satisfactorily calibrated. However, there are
several common ways of reporting calibration re-
sults, the most common of which is to list the mea-
sured and simulated heads together with their dif-
ferences and some average of the differences.
After the model has been calibrated, sensitivity analy-
ses should be conducted and reported to determine
the sensitivity of the model's output to variations (or
uncertainties) in the input parameters. The most
common practice for carrying out sensitivity analy-
ses is to repeat simulations using a series of simu-
lated values, and to compare results with those
obtained using the calibrated values. Sensitivity
analyses will identify the main contributors to the
observed variation in results, and are performed
iteratively. However, sensitivity analyses alone will
not identify a flawed conceptual model. Uncertain-
ties arising from the numerical solution of a math-
ematical model are resolved when verifying the
computer programs. Uncertainty resulting from the
scenarios selected for modeling is best addressed by
a systematic examination of a scenario's possible
components and by assigning probability through
such techniques as a Monte Carlo analysis.
Baseline Risk Assessment
A baseline risk assessment typically addresses
three objectives: (1) assessing the magnitude and
sources of current and potential health risks; (2)
refining site characterization studies; and (3) iden-
tifying contaminants of potential concern and
exposure assumptions. In most cases, estimating
flow and transport through the unsaturated zone
is an integral component of the risk assessment,
particularly if the compliance point is near the
source. The release rates, concentrations, and re-
tention times within the unsaturated zone will
influence receptor concentrations far more than
flow and transport in the aquifer. Risk-based model
subcomponents consist of infiltration, source re-
lease rates, source and leaching strength, fate and
transport in the unsaturated zone, and fate and
transport in the saturated zone. Risk-based codes
typically are not calibrated, however, because the
required data from the unsaturated zone are rarely
available. Evaluation of the parameters during
sensitivity analysis is therefore especially
important.
Predictive Simulations
The final stage of model application is to perform
predictive simulations with the optimal param-
eters obtained from model calibration. These
simulations test specific issues of the contamina-
tion problem and provide guidance for risk-man-
agement decisions. Typical objectives of predic-
tive simulation studies include: (1) the future
behavior of ground water and contaminant
plumes; (2) comparing alternative remediation
schemes such as barriers or pumping wells; and
(3) the responses of the ground-water system to
various design configurations, such as different
pumping or recharge operations.
CONCLUSIONS
Modeling reports must be evaluated in the con-
text of the model's purpose. The most common
mistakes are in using a model that is more sophis-
ticated than appropriate for the available data, or
in using a model that does not accurately account
for the flow and transport processes that domi-
nate the physical system. The reviewer should
determine whether the modeler's analysis is con-
sistent with the requirements for the decision at
the specified stage of the regulatory or remedia-
tion project. The data required should be relevant
to the flow, fate, and transport processes being
simulated, and the sources for each data element
should be described. A common problem with
modeling studies lies with their discussion (or
lack of one) of uncertainties, including uncertain-
ties in data, assumptions, and sensitivities. The
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conceptual model should be consistent with the
field data, and should be well within recom-
mended boundary and initial conditions. The
calibration process should be described in detail.
While calibration may not be required in all cases,
the report should explain why calibration was
not done. Source terms, release rates, leachate
concentrations, and decay and daughter-ingrowth
(of radioactive decay products) must be docu-
mented carefully.
Evaluations of models often receive more atten-
tion from decision makers than the simulations
themselves. For this reason, it is the reviewer's
responsibility to judge whether he or she has the
necessary expertise to interpret the data and as-
sess the model's concept, as well as to evaluate
the results.
CONTACTS
If you have any questions on any off the reports
sponsored by the Interagency Working Group,
please contact:
Beverly Irla
Radiation Protection Division
Office of Radiation and Indoor Air (6602J)
U.S. Environmental Protection Agency
Washington, DC 20460
(202) 233-9396
Paul Beam
U.S. Department of Energy
Office of Environmental Restoration
EM-451/CLOV BLDG.
19901 Germantown Road
Germantown, MD 20874-1290
(301) 903-8133
Sam Nalluswami
U.S. Nuclear Regulatory Commission
Office of Nuclear Material Safety and Safeguards
(T-7F27)
Washington, DC 20555
(301)415-6694
Superfund Hotline
U.S. Environmental Protection Agency
Office of Solid Waste and Emergency Response
401 M Street SW (5203G)
Washington, DC 20460
(800) 424-9346
REPORTS IN THIS SERIES
• Documenting Ground-Water Modeling Results At
Sites Contaminated with Radioactive Substances,
EPA 540-R-96-003, March 19%.
• Three Multimedia Models Used at Hazardous and
Radioactive Waste Sites, EPA 540-R-96-004, March
19%.
• Technical Guide to Ground-Water Model Selection at
Sites Contaminated with Radioactive Substances,
EPA 402-R-94-012, September 1994.
• Environmental Pathway Models—Ground-Water
Modeling in Support of Remedial Decision-Making
at Sites Contaminated with Radioactive Material,
EPA402-R-93-009, March 1993.
• Environmental Characteristics of EPA, NRC, and
DOE Sites Contaminated with Radioactive
Substances, EPA402-R-93-011, March 1993.
• Computer Models Used to Support Cleanup
Decision-Making at Hazardous and Radioactive
Waste Sites, EPA 402-R-93-005, March 1993.
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