EPA/600/R-05/110
September 2005
Uncertainty and the Johnson-Ettinger Model
for Vapor Intrusion Calculations
by
James W. Weaver
Ecosystems Research Division
National Exposure Research Laboratory
Athens, Georgia 30605
Fred D. Tillman
National Research Council
National Exposure Research Laboratory
Athens, Georgia 30605
U.S. Environmental Protection Agency
Office of Research and Development
Washington, DC 20460
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Notice
The U.S. Environmental Protection Agency through its Office of Research and
Development funded and managed the research described here. It has been subject to the
Agency's peer and administrative review and has been approved for publication as an
EPA document. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
Vapor intrusion is a complex problem where EPA is continuing to develop policies and
guidance. This document presents the results of ORD-sponsored research and neither
states EPA policy nor requirements for assessment and clean up. The latest EPA policies
and requirements should be obtained from the EPA Office of Solid Waste and
Emergency Response.
11
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Abstract
The Johnson-Ettinger Model is widely used for assessing the impacts of
contaminated vapors on residential air quality. Typical use of this model relies on a suite
of estimated data, with few site-specific measurements. Software was developed to
provide the public with automated uncertainty analysis applied to the model. (See
http://www.epa.gov/athens/onsite.) An uncertainty analysis was performed on the model,
that accounted for synergistic effects among variable model parameters. This analysis
showed that a simple "one-at-a time" parameter uncertainty analysis provides a rough
guide for the uncertainty generated by individual parameters and allowed their ranking.
The one-at-a-time analysis, however, underestimated the uncertainty in the model results
when all or groups of parameters were assumed to be uncertain. An apparent increase in
simulated cancer risk caused by the uncertainty introduced from the input parameters was
as much as 1285%. The model response to the input parameters showed that for the
example studied, there was a positive skew in the model response to parameter variation.
in
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Foreword
The National Exposure Research Laboratory's Ecosystems Research Division (ERD) in
Athens, Georgia, conducts research on organic and inorganic chemicals, greenhouse gas
biogeochemical cycles, and land use perturbations that create direct and indirect,
chemical and non-chemical stresses, exposures, and potential risks to humans and
ecosystems. ERD develops, tests, applies and provides technical support for exposure
and ecosystem response models used for assessing and managing risks to humans and
ecosystems, within a watershed / regional context.
The Regulatory Support Branch (RSB) conducts problem-driven and applied research,
develops technology tools, and provides technical support to customer Program and
Regional Offices, States, Municipalities, and Tribes. Models are distributed and
supported via the EPA Center for Exposure Assessment Modeling (CEAM) and through
access to Internet tools (http://www.epa.gov/athens/onsite).
Intrusion of contaminated vapors into buildings ("vapor intrusion") can provide a
significant pathway for exposure to hazardous contaminants. Assessment of this
problem is difficult because of limitations of sampling methodologies, contamination in
external ambient air, internal sources and sinks of contaminants and, as discussed in this
report, uncertainty in model application. The work described in this report is intended to
set the stage for more widespread application of uncertainty analysis in site assessment,
and to provide readily-available tools to streamline the required calculation. To meet
this goal, three tools that are direct results of this work are available at
http://www.epa.gov/athens/onsite.
Eric J. Weber, Ph. D.
Director, Ecosystems Research Division
Athens, Georgia
IV
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Contents
Notice ii
Abstract iii
Foreword iv
Contents v
List of Figures vi
List of Tables vii
Acronyms and Abbreviations viii
1 Introduction 1
2 Background on the Johnson-Ettinger Model (JEM) 3
3 Models and Modeling 6
4 Uncertainty Calculations 8
5 Vapor Intrusion Uncertainty Calculation 12
6 Input Parameters 14
6.1 Building 14
6.2 Soil 16
6.2.1 Soil Properties (Hydraulic Conductivity, porosity, residual moisture
content, van Genuchten model "m") 17
6.2.2 Capillary Fringe 19
6.2.3 Calculated Soil Gas Flow Rate 20
6.3 Chemical 20
6.4 Output 22
7 Sample Simulations 23
8 Conclusions 31
References 32
9 Appendix 34
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List of Figures
Figure 1 Background screen giving a brief overview of the calculation 12
Figure2 The "about" screen that gives contact information for the model 12
Figure 3 The selection screen allows choices of models. Currently the only choices are
among input units 13
Figure 4 The input screen for entering fixed building parameters 16
Figure 5 The building input screen for entering building parameters that will be
considered variable 16
Figure 6 Variable soil inputs that consist of low and high values of each parameter and
two choices: to include capilary fringe or not; and to use a calculated gas flow rate or
values that are directly input on this screen 19
Figure 7 Option for use of capillary fringe. Here the capillary fringe calculation will not
be included since the problem is assumed to be a soil gas/indoor air problem 20
Figure 8 Options for calculating the soil gas flow rate. Here the soil gas flow rate will
not be calculated and the range of values will be 1 L/min to 10 L/min 20
Figure 9 The chemical input screen allows selection of the chemical and the temperature
range 21
Figure 10 Uncertainty Output after 4096 simulations 22
Figure 11 Example from the output screen that shows the results for the smallest alpha
value (1.59E-5). The corresponding values of A, B and C are given in the last three
columns 22
Figure 12 Results from uncertainty analysis using OSWER default as the baseline case
and +/- 25% parameter ranges 25
Figure 13 The numerator, denominator and calculated JEM alpha as function of the air
exchange rate 28
Figure 14 Response of the model to reduction in uncertainty in all inputs 29
Figure 15 Reduction in model uncertainty by fixing one parameter at a time 30
VI
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List of Tables
Table 1 Required number of simulations for four types of simulation 10
Table 2 Parameters used with ground water or soil gas sources and calculated or entered
soil gas flow rate 10
Table 3 Crack ratios, estimated crack thicknesses for the default problem of Section 7. 15
Table 4 Saturated and residual water contents from the Carsel and Parrish (1988) soil
parameter data set 17
Table 5 n and alpha parameters of the van Genuchten model from the Carsel and Parrish
(1988) soil parameter data set 18
Table 6 Hydraulic conductivity from the Carsel and Parrish (1988) soil parameter data
set 18
Table 7 Fixed parameters for the example simulation 23
Table 8 OSWER defaults, ranges and sources of variability for example simulation 23
Table 9 Risk parameters for the uncertainty calculation 25
Table 10 Single Parameters used for One-At-A-Time (OAT) uncertainty assessment of
the example problem 26
Table 11 Parameter groups for synergistic uncertainty analysis 26
Table 12 The impact of variation in air exchange rate on results 28
Table 13 Changes in apparent risk due to sequential fixing of uncertain parameters.... 30
Table 14 Relationships between basic input parameters and the maximum values of the
dimensionless groups A, B, and C. (The minimum values of these parameters occur with
the opposite choices of the basic input parameters.) 35
vn
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Acronyms and Abbreviations
EPA Environmental Protection Agency
CERCLA Comprehensive Environmental Response, Compensation, and Liability
Act
JEM Johnson-Ettinger Model
MDP Model Development Platform
OAT One at a time
OSWER Office of Solid Waste and Emergency Response
RCRA Resource Conservation and Recovery Act
Vlll
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1 Introduction
Vapors originating from subsurface contamination might migrate into residences
and cause an immediate threat, or if at lower, less detectable levels, a chronic health risk.
EPA concern over this problem resulted in the publication of a draft guidance for
assessing risks (US EPA, 2002) at Superfund1 and Resource Conservation and Recovery
Act (RCRA) corrective action sites2. The draft guidance, and that of some State
Agencies, uses the Johnson-Ettinger Model (JEM) (Johnson and Ettinger, 1991) as the
basis for screening decisions at sites. A companion document (Tillman and Weaver,
2005) describes these issues in more detail. Generally though, the JEM is used under
conditions of few measured or calibrated site-specific data. Where indoor air sampling is
not undertaken, there is consequently no opportunity for calibration of the model results
to site conditions nor corroboration by site-specific indoor air concentrations.
Consequently, there is a need for clear understanding of the uncertainties associated
with this model. Uncertainties exist in several arenas, including:
1. Model: Does the conceptual basis of the model adequately represent the field
site? Is there sufficient knowledge to make this determination?
2. Parameters: Do the choices of parameter values adequately represent the field
phenomena?
The work reported in this document addresses the second of these questions. Parameter
uncertainty is addressed because of the simplified nature and widespread acceptance of
the JEM. Given that the model is used frequently, its usage could be improved by, first,
understanding its uncertainties and, second, by providing the community with a readily-
available version that provided an automated uncertainty analysis. Uncertainty analysis
in general was recommended in the US EPA, User's Guide for Evaluating Subsurface
Vapor Intrusion into Buildings, where it is stated that:
"Because of the paucity of empirical data available for either bench-scale or field-
scale verification of the accuracy of these models, as well as for other vapor
intrusion models, the user is advised to consider the variation in input parameters
and to explore and quantify the impacts of assumptions on the uncertainty of
model results. At a minimum, a range of results should be generated based on
variation of the most sensitive model parameters" (US EPA, 2004).
This work does, in fact, address the ranges of sensitive parameters, but goes a necessary
step beyond to address the synergistic effects of simultaneous variation of multiple model
parameters on the JEM output.
1 Formally known as the Comprehensive Environmental Response, Compensation, and Liability Act
(CERCLA)
2 Leaking underground storage tank (LUST) sites were specifically excluded from coverage by the
guidance document.
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Johnson (2002) addressed the sensitivity and range of input studies in a detailed
study of JEM parameters and their variation (Johnson, 2002). Johnson's analysis focused
on variation of parameters taken one-at-a-time. His work also (Johnson, 2002, Appendix
A) was presented in terms of three dimensionless parameters that encapsulate all the
inputs to the original model. Although this provides a concise means to present results,
a fairly high degree of sophistication is needed for relating the results to the primary input
parameters. For these reasons, a software package was developed to perform an
automated uncertainty analysis using the primary inputs to the model. This software
provides options to perform the calculations on the original model formulation (Johnson
and Ettinger, 1991) and for some of the EPA additions (US EPA, 2004). Generally, this
work provides an alternate means of evaluating uncertainty in the model and is
complimentary to the prior work by Johnson (2002).
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2 Background on the Johnson-Ettinger Model (JEM)
JEM results are often given in terms of the "alpha" parameter (a) that is defined by
where CB is the concentration in the building and Cs is the concentration in the in the
source. For the following model results, the source can be treated as the soil gas below
the building or, as included in the EPA OSWER version of JEM, from the capillary
fringe. Both options are included in the software described below for consistency with
both approaches.
The JEM a is computed from
A exp(#)
a = -
where the dimensionless quantity A is given by:
-L^T **-&
A =
'T
where Dxe is the effective diffusion coefficient of the contaminant in soil [L /T], AB is
the subsurface foundation area [L2], QB is the volumetric flow rate of air in the building
[L3/T] and LT is the distance from contamination to the bottom of foundation [L]. The
air flow rate in the building, QB, is broken down into the building volume [L3], VB, and
the air exchange rate [T"1], EB.
The dimensionless quantity B is given by
D s C
~ DfN AB
where Qs is the soil gas flow rate into the building [L3/T], Lc is the thickness of the
foundation [L], Dce is the effective diffusion coefficient for the contaminant in the crack
[L2/T], and N is the crack ratio [dimensionless]. The crack ratio is defined by
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where Ac is the area of the crack [L2]. OSWER (US EPA, 2004) relates the crack ratio
to building properties by
Ar
N =
where We is the width of the crack [L]. Johnson and Ettinger (1991) use the assumption
that the floor/wall cracks and openings are filled with dust and dirt characterized by a
density, porosity and moisture content similar to that of the underlying soil to justify
equating DTeff and Dceff
The diffusion coefficient is estimated from the Millington-Quirk relationship
3! 3! 3I 3I
/i 3 n/33 a 3 n/33
eff - n A + ±IIL^_ neff - r> A w w
~
I A 'L TT 2 J A '1 TT
ij H 77 77 H 77
where DA is the air phase diffusion coefficient [L2/T], 9 A is the air-filled porosity [L3/L3],
r| is the porosity [L3/L3], DW is the water phase diffusion coefficient [L2/T], 9w is the
water content [L3/L3], and H is the Henry's Law Coefficient [unitless] (See US EPA,
2004). A depth-weighted average diffusion coefficient is used to average-out the effects
of layering in the vadose zone (Johnson and Ettinger, 1991).
The dimensionless quantity C is given by
C = ~Q~B
The indoor air concentration, CB itself is given by
C = oc C
for a soil gas source, and
CB = aaw CGW H
for a ground water source. The coefficients (XSG and (XGW are the attenuation factors
calculated for soil gas or ground water sources, respectively. The differences between
these two are described in Section 6.
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Taking this a step further for carcinogenic compounds at a specified cancer risk, the
allowable building concentration, CB-A, can be calculated from:
TRAT
URF EF ED
where TR is the target risk level [unitless], AT is the averaging time [T], URF is the
3-1-1
inhalation unit risk factor [M/L ]" , EF is the exposure frequency [T/T], and ED is the
exposure duration [T] (based on US EPA, 2001).
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3 Models and Modeling
Subsurface transport models are based on a mathematical statement of
conservation of mass. Ancillary relationships are needed to estimate fluxes that are used
in the mass conservation equation. Inputs to these models provide the means to quantify
the relationships for specific site conditions and are called the parameters of the model.
Other inputs represent the forcing functions that represent the boundary and initial
conditions. Generally the forcing function represents the input of contaminants into the
system, while the model parameters represent the transport properties of the media.
All models are based on simplification and approximation. Models designed for
the same problem can be based on vastly different assumptions. These assumptions can
and do introduce limitations. Understanding of general types of models and their
common assumptions and the way that a specific model of interest was developed is
critical for choosing, applying and evaluating model usage. Without this knowledge
model selection, usage and interpretation are at best uninformed and there is a very weak
basis for critical evaluation of model results.
An important division between types of models is that between analytical and
numerical models. Analytical solutions are based on mathematical functions that are or
have the potential to be exact solutions of the transport equation. Analytical solutions of
the transport equation
cannot simulate heterogeneous formations,
require the assumption of one-dimensional flow,
only represent uniform flow,
includes transport by advection in the direction of flow only, and
do not allow representation of irregular boundaries.
Numerical models are based on approximations that that are formulated over necessarily
small parts of the simulation domain. The two most common numerical methods are
finite difference and finite element, both of which require a grid to be placed over the
domain. This provides a way to identify these modelsif there is a gridded domain then
the model is most likely to be a numerical model; otherwise the model is analytical.
Requirements for application of models are described in detail by Anderson and
Woessner (1992) and Zheng and Bennett (1995) and are echoed by the US EPA,
Committee on Regulatory Environmental Modeling (Pascual et al., 2003). These and
similar guidelines have been proposed and described in many other publications. The
material that follows matches the common threads of these proposals: Use of models
requires development of a conceptual model of site conditions followed by selection of a
model that matches those conditions. The location and types of boundary conditions
must be chosen and parameterized. Parameter values must be assigned based on site
conditions. These are either taken from site-specific measurement, literature values or
other estimates. Site data, which for contamination problems, includes concentrations,
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are used to test the model predictions. Input parameters and forcing function values can
be adjusted to match site data. That this is a legitimate activity follows from:
imprecision in measurement of input parameters, spatial variability in media properties
that do not allow measurement of properties at all points, inability to measure all
parameters because of technical, programmatic or cost limitations. A calibrated model
has essentially been forced to match a set of field data. By taking this process one set
further, the calibrated model is tested against a data set that was not used in calibration.
The model has then been demonstrated to match existing data and in the best case, match
a data set which was not used in calibration. Iteration may be required for further
adjustment of parameters. At the end of this process, uncertainty in model results has
been reduced to the minimum level possible (See Pascual et al., 2003, page 11).
Model applications which are not subjected to the process described above have
an inherently higher level of uncertainly in their results. Without site specific
measurement of model outputs (i.e., concentrations), it is not possible to assure that a
model represents subsurface conditions. In cases where few parameters are measured
and outputs are not measured, the uncertainty in results shall be high. In these cases, a
single set of parameters can not provide a certain result. Although average parameter
values may be used in a simulation, the model results which also appear as a single set of
values, do not convey any information on the degree of certainty in the results. It may be
possible in some cases to define generic best or worst case parameter sets that could be
run singly and represent the best or worst case results. These are not necessarily
identifiable in advance, but must be established by evaluating the model behavior.
As a summary, the U.S EPA, Committee on Regulatory Environmental Models
recommended a set of best practices that included:
peer review of models,
assessment of data quality,
corroboration of model results with data,
sensitivity analysis, and
uncertainty analyses.
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4 Uncertainty Calculations
Johnson and Ettinger state in their original paper (Johnson and Ettinger, 1991):
"Here we [...] formulate a heuristic model for predicting the
intrusion rate of contaminant vapors into buildings through
foundations... This model can be used as a risk assessment
screening-level tool; it can be used to identify sites, or contaminant
levels, for which contaminant exposures through a vapor inhalation
pathway may cause adverse health effects. It can also be used as a
tool to help identify sites where more detailed numerical
simulations or field sampling are appropriate."
To achieve these goals the model must be appropriate for the site and building conditions
and be properly parameterized. This work focused on the impacts of parameterization,
specifically considering how the model behaves when inputs are uncertain. Inputs are
surely uncertain when
1. model inputs are not measured on a site-specific basis,
2. spatial variability is not considered, and
3. model results are not corroborated against measurements.
Oreskes (2003) presented a framework for understanding the scientific usage of models,
and stated that:
"Models can never fully specify the systems that they descried, and therefore are
always subject to uncertainties that we cannot fully specify".
To begin to specify uncertainty, the JEM was re-implemented in a Java package called
the Model Development Platform (MDP) (Weaver, 2004). This software allows the JEM
to be run directly from the Internet and is available at the web address:
http://www.epa.gov/athens/onsite.
The approach taken to assessing uncertainty was to assume that some simple
parameters of the model should be known to a sufficient degree of accuracy to be input as
constants. The presumed constant parameters of the JEM are the building length and
width, foundation thickness, depth of the bottom of the foundation below grade, and
chemical of interest. Several parameters are use to estimate the temperature-dependent
Henry's constant of the chemical of interest. These parameters are also all treated as
constants and are embedded within the software.
All other parameters of the model are assumed to be uncertain with a known
range of possible values. For this analysis, the range of values were presumed to be
known, but not statistical distributions of the parameters. The desire was to apply a
screening approach that could account for multiple parameter uncertainty, without
introducing more uncertain quantities such as statistical distributions of parameters. Thus
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the range of each parameter was estimated by determining a low and high value. The
model was run for every possible combination of the high and low values. From the
results, the highest and lowest values of a, A, B, and C are determined. This procedure
contains two implicit assumptions. First, that each parameter is uniformly distributed and
as a result, equally probable. Second, that the extreme values of the model result occurs
from parameters set to the limits of their ranges. In all cases tested, the extremes were
found to occur at these endpoints. Correlation between parameters is neglected on the
presumption that the parameter values vary only over a small range where each
combination is possible regardless of correlations among them. The results, then, should
be interpreted as giving implausible range of output, given the ranges of the inputs.
Each result is assumed to be equally probable and the intent is to define the best and
worst case outputs. Further details on the background for this approach are given in the
Appendix.
For nominally more precise and more powerful uncertainty analyses (like Monte
Carlo simulation), statistical distributions and correlations are required. It is instructive
to note that the Monte Carlo method was developed for the inherently random simulation
associated with radioactive decay (Metropolis and Ulam, 1949). In examples cited by
Metropolis and Ulam, the probabilities are easily assigned (i.e., the direction a an emitted
neutron takes after nuclear fission). For other problems, such as the JEM for subsurface
vapor transport, the probabilities are difficult to assign on a problem-specific basis, and
particularly where site assessment protocols call for limited data collection. Thus the
desire in this work was to provide a screening analysis that accounted for the
uncertainties and synergies among parameters.
The uncertain parameters of the JEM were assumed to include the temperature,
some building parameters and all soil parameters. Specifically the latter two were the:
enclosed space mixing height,
floor-wall crack width,
indoor air to subsurface pressure differential,
air exchange rate,
hydraulic conductivity,
vadose zone thickness,
porosity,
residual water content,
effective water saturation,
parameter "m" of the van Genuchten model,
mean particle diameter, and
soil gas flow rate.
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The options of running the original JEM or a modified version influence the number of
parameters (Table 1) treated as being uncertain. If the capillary fringe is excluded
(original JEM) then the mean particle diameter is not used. If the soil gas flow rate is
used (original JEM), then the hydraulic conductivity and pressure differential are not
used. If definitive values can be assigned for the potentially uncertain parameters, the
software allows a single value to be used. This, in turn, reduces the number of
simulations by a factor of two for each parameter set to a fixed value.
An alternative to this approach would be to vary each parameter individually,
requiring at most 26 runs of the model (two runs per parameter listed above). As will be
shown, this simple "one at a time" (OAT) analysis underestimates the uncertainty in the
output. OAT underestimates uncertainty when there are synergistic effects or
interactions among parameters (see Campolongo et al., 2000). The form of the JEM
indicates that there are interactions among parameters because they occur as multipliers
or divisors of each other. Most notably are the three dimensionless parameters (A, B, and
C) formed from combinations of basic inputs.
Table 1 Required number of simulations for four types of simulation.
Simulation
Type
Soil Gas to
Indoor Air
Capillary
Fringe to
Indoor Air
Calculated
Soil Gas
Flow Rate
y
n
y
n
Parameters
Always Fixed
4
4
4
4
Potentially
Variable
11
9
12
11
Maximum
Number of
Simulations
2048
512
4096
2048
Table 2 Parameters used with ground water or soil gas sources and calculated or entered soil gas
flow rate.
Parameter
Hydraulic conductivity
Thickness
Porosity
Residual Water Content
Calculated Soil Gas
Flow Rate
Ground
Water
Source
y
y
y
y
Soil Gas
Source
y
y
y
y
Estimated Soil Gas
Flow Rate
Ground
Water
Source
n
y
y
y
Soil Gas
Source
n
y
y
y
10
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Water Content
van Genuchten "m"
Particle Diameter
Soil Gas Flow Rate
Mixing Height
Floor-wall Crack Width
Pressure Differential
Temperature
Total
y
y
y
n
y
y
y
y
12
y
y
n
n
y
y
y
y
n
y
y
y
y
y
y
n
y
n
y
n
n
y
y
y
n
y
9
11
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5 Vapor Intrusion Uncertainty Calculation
The uncertainty calculation is packaged into a Java Applet that runs from the US
EPA web site at http://www.epa.gov/athens. The applet is known to run with either the
Microsoft Internet Explorer, Netscape Navigator or Firefox web browsers. A Java run
time environment must be installed and enabled. When visiting the web site, the
background (Figure 1) and about screens (Figure 2) give a brief overview of the
calculation and contact information for the model.
Vapor Intrusion
Background
Select a Model
Uncertainty Range Calculation for the Johnson Ettrnger Model:
What ranges of attenuation factors can be expected from specified ranges of model inputs?
This question is answered by running the model is run 2" times
(where n is the number of variable parameters,
that can be changed for each simulation)
A set of best and worst case results is accumulated from these runs
Run
Pause
Resume
Stop
Select a model before pushing 'run'
Figure 1 Background screen giving a brief overview of the calculation.
Vapor Intrusion
Background
Select a Model
Fixed Building Inputs
Variable Building Inputs
Variable Soil Inputs
Chemical Inputs
Uncertainty Output
About
Vapor Intrusion Uncertainty Model
Jim Weaver
Ecosystems Research Division
National Exposure Research Laboratory
Office of Research and Development
United States Environmental Protection Agency
Athens, Georgia
January 8,2005
Run
rtodel has completed.
Figure 2 The "about" screen that gives contact information for the model.
12
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The "Select a Model" screen (Figure 3) gives choices for input models. The Java
code used to build this model allows for the inclusion of various choices of models. In
this case, the main choices only relate to input unit sets. Future development may include
alternate model formulations. Once the selection of a model has been made, as shown in
Figure 3, the interface is populated with input and output screens appropriate to the
choice of model.
Vapor Intrusion
Background
Select a Model
Fixed Building Inputs
Variable Building Inputs
Variable Soil Inputs
Chemical Inputs
Uncertainty Output
About
Uncertainty Range Calculation:
Select the desired model from the list
Select Model/Test Problem
J&E Model Uncertainty Calculation (English Units) *
Run
Pause
Resume
Stop
Select a model before pushing 'run'
Figure 3 The selection screen allows choices of models. Currently the only choices are among input
units.
13
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6 Input Parameters
For the current JEM model there are four input screens for the model. These are
shown in Figure 4 through Figure 9.
6.1 Building
The simplest parameters defining the building are assumed not to vary (Figure 4).
These include the length [ft] and width [ft] of the building and the foundation thickness
[ft]. The foundation may be below grade, as in the case of a basement. Thus this depth
[ft] may also be specified.
Building parameters that are harder to specify are treated as potentially uncertain
(Figure 5). These are, in order of entry:
Enclosed space mixing height [ft]
Floor-wall crack width [mm]
Indoor air to subsurface pressure differential [g/cm-s2]
Air exchange rate [hr"*]
For each uncertain parameter a low and high value are entered. These should be chosen
to cover the entire likely range of values for the parameter. Where little information
exists on parameter values, running the model for a several orders-of-magnitude variation
provides a conservative approach for assessing the potential impacts on indoor air
quality.
Enclosed space mixing height: The mixing height represents a concept that the
contaminated vapors emerge from cracks in the floor/slab of a residence and are then
mixed with the ambient air in the building. In order to avoid directly simulating this
mixing process, a height is selected to form a zone over which the contaminant vapors are
assumed to be distributed uniformly. OSWER selected a mixing height of 2.44 m (8 ft)
for one-story slab-on-grade homes and 3.66 m (12 ft) for basement homes. The latter
number reflects an assumption that there is some mixing from the basement into an upper
story, but limited to less that the full height of the upper story (or the mixing height might
be 7.32m (16 ft)).
Crack ratios were estimated and reported in various publications (Table 3). While all the
others presented ranges of one order of magnitude or greater, ASTM 1739-95 presented a
only single crack ratio value. Using the parameters for the OSWER-derived example
problem presented in Section 7, crack width ranges were calculated. These ranges
reflect a variety of assumptions concerning this parameter.
14
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Table 3 Crack ratios, estimated crack thicknesses for the default problem of Section 7.
Publication
Nazaroff(1992),
Revzan et al.
(1991)
Nazaroff et al.
(1985)
Figley and
Snodgrass
(1992)
ASTME1739-95
VOLASOIL
Johnson and
Ettinger(1991)
Crack ratio
Minimum
0.0001
0.01
0.000001
0.001
Maximum
0.001
0.01
0.0001
0.01
Crack width (mm) for
conditions of Section 7
Minimum
0.25
Hairline
25
0.0025
2.5
Maximum
2.5
5
25
0.25
25
Comment
Back-calculated from
measured soil gas flow
rates into buildings
Most measured cracks
< 1 mm
Default
"Good" and "bad"
foundations,
respectively
Illustrative values
OSWER selected a default building air exchange rate of 0.25 hr" , based on a data set that
included 2844 homes divided by season and geographic region (U.S. EPA, 2004). A
value near the lower end (lesser air exchange) for the composite data was selected (0.25
hr"1 versus 0.21 hr"1), given the range of 0.21 hr"1 to 1.48 hr"1. Other work referenced by
OSWER suggests bounds of 0.1 hr"1 to 2 hr"1.
If the value of a potentially variable parameter can be fixed to a single value, then
the software accommodates this possibility. Entering the same value as both the low and
high values fixes the value and eliminates it as an uncertain parameter. The number of
simulations is reduced by a factor of 2 for each such fixed parameter.
15
-------
# Vapor Intrusion
Background
Select a Model
Chemical Inputs
Uncertainty Output
About
Run
Select a model before pushin
|
Building Width [ft] 328084
i
Building Length [ft] 328084
I
Foundation Thickness hi] 05
1 i
Depth below grade to bottom of foundation [ft] 65617 |
I Pause I Resume | Stop
3 'run1
Figure 4 The input screen for entering fixed building parameters.
I Vapor Intrusion [-JfnJpRJ
Background
Select a Model
Low value High value
Enclosed space mixing height [ft] 110 140 I
Fixed Building Inputs Floor-wall crack width [mm] 05 1.5
Variable Building Inputs
Variable Soil Inputs
Chemical Inputs
Uncertainty Output
About
Run
Indoor to subsurface pressure differential [g/cm-s2] 3 0 . 0 50.0
Air exchange rate [ 1 .'hr] 021 ^48
Pause Resume Stop
Select a model before pushing 'run'
Figure 5 The building input screen for entering building parameters that will be considered
variable.
6.2 Soil
Because of limited measurement at field sites, imprecision in measurement
techniques and spatial variability, all soil parameters are presumed to be uncertain
(Figure 6). The soil parameters include the:
hydraulic conductivity [cm/s],
thickness (depth to water table) [ft],
porosity [dimensionless],
residual moisture content [dimensionless],
effective saturation [dimensionless],
van Genuchten model parameter "m", and
mean particle diameter in the capillary fringe[cm].
16
-------
Two questions are given the user concerning the capillary fringe and the soil gas flow
rate. These are discussed separately below.
6.2.1 Soil Properties (Hydraulic Conductivity, porosity, residual
moisture content, van Genuchten model "m")
The van Genuchten (1980) model represents the soil capillary pressure curve by a
function given by
e-e.
6-9
1
l+(ah)n
where 0W is the water content, 0wr is the residual water content, 0m is the saturated water
content, and a [1/L], n, and m are fitting parameters. Further, the saturated moisture
content, 0m, is usually taken as the porosity and m is set equal to the quantity 1 - 1/n for
mathematical convenience. Data are fit to the van Genuchten model for determining
appropriate values of a, 0wr, 0m, and m.
Tabulations of soil properties have been made from agricultural soils (e.g., Carsel
and Parrish, 1988) that show that there is a great deal of variability associated with each
Soil Conservation Service (SCS) soil type. Even though a sandy soil, for example, may
underly a building, there are many types of sand that differ in their hydraulic behavior.
Additionally, because soils are typically heterogeneous, the capillary properties of soils
can vary greatly at one site. Therefore, because capillary pressure curves are typically
not measured at vapor intrusion sites, the selection of capillary properties by SCS soil
class names does not assure that representative values are used in simulation. A range of
possible values for each SCS soil type are given in Table 4, Table 5, and Table 6.
Table 4 Saturated and residual water contents from the Carsel and Parrish (1988) soil parameter
data set.
Soil Type
Clay
Clay Loam
Loam
Loamy Sand
Silt
Silt Loam
Silty Clay
Silty Clay
Loam
Sand
Sandy Clay
Sandy Clay
Loam
Sandy Loam
Saturated Water Content (6m)
Sample
size
400
364
735
315
82
1093
374
641
246
46
214
1183
mean
0.38
0.41
0.43
0.41
0.46
0.45
0.36
0.43
0.43
0.38
0.39
0.41
Standard
deviation
0.09
0.09
0.10
0.09
0.11
0.08
0.07
0.06
0.06
0.05
0.07
0.09
Residual Water Content (Ow)
Sample
size
353
363
735
315
82
1093
371
641
246
46
214
1183
mean
0.068
0.095
0.078
0.057
0.034
0.067
0.070
0.089
0.045
0.100
0.100
0.065
Standard
deviation
0.034
0.010
0.013
0.015
0.010
0.015
0.023
0.009
0.010
0.013
0.006
0.017
17
-------
Table 5 n and alpha parameters of the van Genuchten model from the Carsel and Parrish (1988)
soil parameter data set.
Soil Type
Clay
Clay Loam
Loam
Loamy Sand
Silt
Silt Loam
Silty Clay
Silty Clay
Loam
Sand
Sandy Clay
Sandy Clay
Loam
Sandy Loam
van Genuchten n
Sample
size
400
364
735
315
82
1093
374
641
246
46
214
1183
mean
1.09
1.31
1.56
2.28
1.37
1.41
1.09
1.23
2.68
1.23
1.48
1.89
Standard
deviation
0.09
0.09
0.11
0.27
0.05
0.12
0.06
0.06
0.29
0.10
0.13
0.17
van Genuchten a (m"1)
Sample
size
400
363
735
315
82
1093
126
641
246
46
214
1183
mean
0.80
1.9
3.6
12.4
1.6
2.0
0.5
1.0
14.5
2.7
5.9
7.5
Standard
deviation
1.2
1.5
2.1
4.3
0.7
1.2
0.50
0.60
2.9
1.7
3.8
3.7
Table 6 Hydraulic conductivity from the Carsel and Parrish (1988) soil parameter data set.
Soil Type
Clay
Clay Loam
Loam
Loamy Sand
Silt
Silt Loam
Silty Clay
Silty Clay
Loam
Sand
Sandy Clay
Sandy Clay
Loam
Sandy Loam
Hydraulic Conductivity (m/d)
Sample
size
114
345
735
315
88
1093
126
592
246
46
214
1183
mean
0.048
0.062
0.25
3.5
0.060
0.11
0.0048
0.017
7.1
0.029
0.31
1.1
Standard
deviation
0.10
0.17
0.44
2.7
0.079
0.30
0.026
0.046
3.7
0.067
0.66
1.4
18
-------
Vapor Intrusion
Background
Select a Model
Fixed Building Inputs
Variable Building Inputs
Variable Soil Inputs
Chemical Inputs
Uncertainly Output
About
High and Low values per Layer (L)
Hydraulic Conductivity [cm/s]
Thickness [ft]
Soil Porosity
Soil Residual Moisture Content
Water Saturation (% of pore space)
van Genuchten m
Mean Particle Diameter [cm]
Use capillary fringe?
Calculate soil gas flow rate?
(Optional) Soil gas flow rate [L/min]
Low
High
1.0E-4
l.6E-4
15.0
0.35
o.4
0.1
os
30.0
40.0
0.15
0.2
0.02
l!03
Do not
Do not
1.0
10.0
Run
Pause
Resume
Stop
Select a model before pushing 'run1
Figure 6 Variable soil inputs that consist of low and high values of each parameter and two choices:
to include capilary fringe or not; and to use a calculated gas flow rate or values that are directly
input on this screen.
6.2.2 Capillary Fringe
The original JEM model assumed that the source of indoor air contamination was
the soil gas. OSWER extended the original model to include a calculation of partitioning
across a simplified representation of the capillary fringe. The capillary fringe is
simplified as a zone of uniform water content, extending a certain distance above the
water table. The capillary fringe water content is determined from
'cz-R
where 0CZ is the water content of the capillary zone, 0CZ.R is the residual water content of
the capillary zone r|cz is the porosity of the capillary zone and m is the van Genuchten
model parameter "m" of the capillary zone. The capillary zone height [cm], hcz, is
determined from the mean particle diameter using the empirical function:
19
-------
015
where 9 is the mean particle diameter of the capillary zone [cm] (US EPA, 2004).
Using the capillary fringe in the computation assumes that contaminated ground
water is the source of indoor air contamination. The choice between these two options is
shown in Figure 7, that shows an example where the capillary fringe calculation is not
used.
Use capillary fringe?
Do not
Figure 7 Option for use of capillary fringe. Here the capillary fringe calculation will not be included
since the problem is assumed to be a soil gas/indoor air problem.
6.2.3 Calculated Soil Gas Flow Rate
The soil gas flow rate can be entered directly in liters per minute on the last line
of input. When this input is intended to be used, the soil gas flow rate is not calculated
(i.e., the selection "Do Not" is made). This option is shown in Figure 8 where the soil
gas flow rate, is not to be calculated and that the range of simulated values will be 1
L/min to 10 L/min.
Calculate soil gas flow rate?
Do not
(Optional) Soil gas flow rate [L/min] 10 10.0 j
Figure 8 Options for calculating the soil gas flow rate. Here the soil gas flow rate will not be
calculated and the range of values will be 1 L/min to 10 L/min.
The OSWER default value of 5 L/min was based upon the assumption that coarse
grained soils/backfill underlying a house control the entry of vapors. Flows may be
much lower under other circumstances as the OSWER range of 1 L/min to 10 L/min was
determined for coarse-grained soils only.
6.3 Chemical
Chemical properties are assigned in the model by picking the chemical name.
From this, the model selects the air and water phase diffusion coefficients and the
temperature-adjusted Henry's law coefficient. The temperature can be treated as a
variable parameter (Figure 9).
20
-------
r - UM- l-» T" ' -1
§ Vapor Intrusion
Background
Select a Model
Fixed Building Inputs
Variable Building Inputs
Variable Soil Inputs
Chemical Inputs
Uncertainly Output
About
1
Temperature [C]
Chemical Name
Run Pause
-ow value High value
12.5
79016.0 (TCE) H
Resume
17.5
Stop
Select a model before pushing 'run1
Figure 9 The chemical input screen allows selection of the chemical and the temperature range.
21
-------
6.4 Output
The model output is given as the minimum and maximum values of several
outputs of the model (Figure 10). Each row of output gives an extreme value of an output
along with the corresponding values of the other outputs (here, A, B, and C). For
example reading across the first row of results (Figure 11), the smallest value of alpha
(1.59E-5) corresponds to A of 1.909E-5, B of 2047.0, and C of 9.501E-5.
Vapor Intrusion
Background
Select a Model
Fixed Building Inputs
Variable Building Inputs
Variable Soil Inputs
Chemical Inputs
Uncertainty Output
About
Simulations Completed
Smallest Alpha
Largest Alpha
Smallest A
Largest A
Smallest B
Largest B
Smallest C
Largest C
Alpha
Run
Model has completed.
Figure 10 Uncertainty Output after 4096 simulations.
Alpha ABC
Smallest Alpha :
Figure 11 Example from the output screen that shows the results for the smallest alpha value (1.59E-
5). The corresponding values of A, B and C are given in the last three columns.
22
-------
7 Sample Simulations
A set of simulations were performed to study variation in the JEM model results
given reasonable ranges of input values (Table 7 and Table 8). The values in Table 8
were drawn from the OSWER document (US EPA, 2004) and use the ranges of values
either explicitly reported or set to an amount of variation equal to +/- 25% of the OSWER
default value. For this example, the contaminant was trichloroethene in a sandy loam
soil, and its source was the soil gas. The soil gas flow rate was not calculated from the
soil parameters, but rather input directly.
Table 7 Fixed parameters for the example simulation.
Fixed Parameter
Building Width
Building Length
Foundation Thickness
Depth to Contamination
Chemical
Value
32ft
32ft
0.32 ft
6.15ft
trichloroethene
Table 8 OSWER defaults, ranges and sources of variability for example simulation.
Parameter
Mixing height [ft]
Floor-wall crack width [mm]
Air exchange rate [hr"1]
Depth below grade [ft]
Porosity
Residual moisture content
Moisture content
Soil gas flow rate [L/min]
Temperature [C]
Variability
Source
OSWER range
OSWER range
OSWER range
+/- 25%
+/- 25%
+/- 25%
OSWER range
OSWER range
+/- 25%
Values
Low
8
0.5
0.1
22.1
0.29
0.029
0.039
1
11.25
OSWER
default
12
1
0.25
29.5
0.387
0.039
0.103
5
15.0
High
16
5
1.5
36.9
0.484
0.049
0.17
10
18.75
A baseline simulation using the fixed parameter values and the OSWER defaults (Table 7
and Table 8) generated an a value of 6.48 x 10"4. To compare results from various
23
-------
simulations, this baseline attenuation coefficient was used to calculate indoor air and soil
gas concentrations assuming 1 x 10"6 excess cancer risk level. The corresponding soil
gas concentration was 34.16 ug/m3 and the associated indoor air concentration was
0.0221 ug/m3. All subsequent results from the model were presented in terms of
increased (or decreased) cancer risk relative to this base case.
From the calculated soil gas concentration of 34.16 ug/m3, the increase/decrease
in risk was calculated for various scenarios corresponding to differing levels of parameter
uncertainty. The first experiment evaluated the risk associated with one-at-a-time
uncertainty due to individual parameters of the model. These results are presented as
items A through I in Figure 12 and Table 10, and show how the calculated risk changes
by considering uncertainty in various input parameters. The risk can decrease below the
default-parameter case (column 3 of Table 10) when a "best case" parameter set is
encountered. Alternately, the risk may increase when a "worst case" is encountered
(column 4 of Table 10). These results indicate that there can be an apparent risk that is
due to an increase in parameter uncertainty. Reducing parameter uncertainty reduces this
apparent risk. Generally, the results also showed skewed results toward increased risk,
even though most parameter ranges were balanced about the defaults (Table 8). Figure
12 shows that there is an insignificant to modest increase in risk due to increasing the
single parameters over their default values. Some parameters caused no increase in risk
at all (floor-wall crack width and temperature). Of the single parameter simulations, only
the air-exchange rate caused an increase in risk above 100%.
When taken in groups, however, synergies among related sets of parameters
become evident (Figure 12 and Table 11). Subsurface and building properties were taken
as two independent groups for evaluation. The subsurface was further divided into two
sets for simulation. First were the soil properties: porosity, residual water content and
water content. Their variation as a group produced an increased cancer risk of 117.9%
(row J of Table 11), more than that produced by any single member of this group. The
second of the subsurface parameter sets included these same soil parameters, but added
depth to the contamination and soil gas flow rate. The risk increased by 262.3% over the
baseline scenario (row K of Table 11). From the single parameter results, it is seen that
changing each of these parameters produced modest increases in risk. Taken together,
however, the increase in risk was higher. The next group contained the building
parameters: mixing height, floor-wall crack width, and air exchange rate. Individually
these parameters increased risk by 50.1%, 0.0% and 150.0%, respectively. Varying these
parameters together the increase over the default risk was 274.9% (row L of Table 11).
Omitting the floor-wall crack width resulted in the same 274.9% increase in risk, so the
impact of this parameter was not amplified by its inclusion in the group.
Parameters that were judged as being the least-known were also grouped together.
Most of these (excepting the floor-wall crack width) produced increases in risk on their
own. Together the uncertainty in these parameters increased the risk by 941.6% (row M
of Table 11). When all uncertain parameters were included in the calculation the
increased risk was 1258.4% (row N of Table 11).
24
-------
Table 9 Risk parameters for the uncertainty calculation.
Risk Parameter
Averaging Time, AT
Inhalation Unit Risk Factor, URF
Exposure Frequency, EF
Exposure Duration, ED
Source Concentration
Value
70 yr
0.0001 ICug/m3)-1
350 d/yr
30 yr
34.16ug/m3
1400% -,
1200% -
^ 1000% -
sS
g 800% -
o
i 600% -
u
S) 40°% "
c
U 200% -
0% -
-200% -
all
parameters
most-likely
unknox^ns
building
properties
subsurface
properties
-o o 0 , J ^ ) {
ABCDEFGHI
soil
properties
'
i
i
J E L M N
Uncertain Variable(s)*
Figure 12 Results from uncertainty analysis using OSWER default as the baseline case and +/- 25%
parameter ranges.
25
-------
Table 10 Single Parameters used for One-At-A-Time (OAT) uncertainty assessment of the example
problem.
Code
A
B
C
D
E
F
G
H
I
Parameter
Groups
Single
Single
Single
Single
Single
Single
Single
Single
Single
Parameters
Floor- Wall Crack Width
Temperature
Soil Residual Water Content
Soil Gas Flow Rate
Porosity
Sample Depth
Mixing Height
Water Content
Air Exchange Rate
Change in Risk Given Uncertainty
in Results
Decreased Risk
0.0%
0.0%
-7.6%
-44.1%
-34.9%
-20.5%
-25.0%
-53.8%
-83.3%
Increased Risk
0.0%
0.0%
7.8%
11.0%
33.1%
34.7%
50.1%
65.2%
150.0%
Table 11 Parameter groups for synergistic uncertainty analysis.
Code
J
K
L
M
N
Parameter
Groups
Soil Properties
Subsurface
Properties
Building
Properties
Least-known
Parameters
All Parameters
Parameters
Porosity
Residual Water Content
Water Content
Sample Depth
Porosity
Residual Water Content
Water Content
Soil Gas Flow Rate
Mixing Height
Floor- Wall Crack Width
Air Exchange Rate
Mixing Height
Floor- Wall Crack Width
Air Exchange Rate
Porosity
Residual Water Content
Water Content
Soil Gas Flow Rate
Building Mixing Height
Floor- Wall Crack Width
Air Exchange Rate
Sample Depth
Porosity
Residual Water Content
Water Content
Soil Gas Flow Rate
Temperature
Change in Risk Given Uncertainty
in Results
Decreased Risk
-74.7%
-83.2%
-87.5%
-97.4%
-97.9%
Increased Risk
117.9%
262.3%
274.9
941.6%
1258.4%
26
-------
Most of the ranges presented in Figure 12 are skewed toward increased risk.
Examination of the parameter ranges (Table 8), however, shows that most of the
parameter ranges were symmetric about the default value. Thus, the input ranges do not
suffice to explain the skew of the results. Figure 13 shows the numerator, denominator
and value of the JEM a as a function of the air exchange rate. The highest a, and
therefore highest apparent risk, occurred for the lowest value of the air exchange rate (0.1
hr"1). This value is proportionately higher than the lower apparent risk at the high end of
the air exchange rate range (1.5 hr"1). Thus, the results are skewed toward higher
apparent risk. When the JEM a is deconstructed into its numerator and denominator, it
is clear that the denominator is insensitive to air exchange rate and that the pattern in the
a values is due to the numerator.
The numerator of the JEM a contains the term:
A exp(#)
where
A l
A oc - =
^B ' B
and B does not depend on the air exchange rate. Since the A term is inversely
proportional to the air exchange rate, EB, the steep drop in the JEM a and its numerator
result from hyperbolic function behavior evident in both the formula and the Figure 13
results.
27
-------
8
LLJ
-------
The response of the JEM to reduced uncertainty ranges was evaluated by running
sets of simulations where all parameters were assumed uncertain, but where the ranges
were reduced from one simulation to the next. The response of the model was expressed
as a function of normalized inputs. Input variability was expressed by
x =
V-
where Ax is the range of input values and
results were represented by
is the default or median value. Similarly, the
where Ay is the range of outputs (here JEM a) and yd is value produced by the simulation
using the default or median values.3 Figure 14 shows the response of the model to
variation in the uncertainty in each of the model inputs. The sample problem presented in
this section is plotted to the far right hand side of the figure (x' of 16). Beginning with
the sample problem, the variability in each parameter was reduced by a fixed percentage
until the there is no variability left. At this point, all parameters are certain as there is no
range in either input or output. The plot shows that as the uncertainty in the model inputs
increases, there is a proportionately greater increase in the uncertainty in the output (a).
S Ax/xd
Figure 14 Response of the model to reduction in uncertainty in all inputs.
y' could, of course, be generalized to include more than one output by including a
summation.
29
-------
Conversely, the uncertainty in the model output could be reduced one parameter
at a time by reducing input parameter uncertainty. The one-at-a-time uncertainty analysis
results presented in Table 10, indicate that individually, the air exchange rate, water
content, mixing height, source depth, and porosity have the greatest impact on the model
output uncertainty. Of these increasing the air exchange rate increased risk by the most,
150%, when treated as the only uncertain parameter. Eliminating its uncertainty while
still acknowledging uncertainty in all other parameters, reduced the apparent increased
cancer risk from 1258.4% to 443.4% (Figure 15 and Table 13). Fixing the value of each
parameters in turn reduced the apparent increased cancer risk due to uncertainty in model
inputs to 20.6%.
£
w
E
o
(3
O
c
(V
O)
c
rs
O
ItUU/O
1200% -
1000% -
800% -
600% -
400% -
200% -
0% -
-200% -
- 1
1
| | ' { 1
1 1 1
1 ! 1
~D > -> (U g.-
"CD 5' "§:
Additional Fixed Parameters
Figure 15 Reduction in model uncertainty by fixing one parameter at a time.
Table 13 Changes in apparent risk due to sequential fixing of uncertain parameters.
Additional Fixed
Parameter
None
Air Exchange Rate
Water Content
Mixing Height
Source Depth
Porosity
Cancer Risk
Low
2.1xlO"8
1.3 x 10"7
2.5 x 10"7
3.3 x 10"7
4.0 x 10"7
5.3 x 10"7
OSWER
Default
Case
l.OxlO"6
l.OxlO"6
l.OxlO"6
l.OxlO"6
l.OxlO"6
l.OxlO"6
High
1.6 xlO"5
5.4 x 10"6
3.4 xlO"6
2.2 x 10"6
1.6 xlO"6
1.2 xlO"6
Change in Risk Given
Uncertainty in Results
Decrease
-97.9%
-87.4%
-75.1%
-66.8%
-60.3%
-46.6%
Increase
1258.4%
443.4%
235.1%
123.4%
63.2%
20.6%
30
-------
8 Conclusions
Many of the input parameters of the Johnson and Ettinger model have significant
associated degrees of uncertainty, particularly when the model is used in a generic sense
where parameters are not measured on a site-specific basis nor calibrated to measured
indoor air concentrations.
OAT Results: One-at-a-time (OAT) uncertainty analysis, as would be typically
performed due to the difficulties of evaluating all possibilities, gives a rough guide to the
model output uncertainty associated with any single parameter. A ranking can be made
from OAT results of the uncertainties associated with each parameter. The response of
the model to variation in parameters is, however, nonlinear and varies over its range of
values (illustrated by Figure 13). The example problem showed that the model was
insensitive to the floor-wall crack width and the temperature. Conversely the air
exchange rate was the single most sensitive input parameter of the model.
Synergistic Effects: When many or all parameters of the model are considered
uncertain, synergistic effects create greater uncertainty in the model results than when
only one parameter is varied. The example given showed an increase in cancer risk of
almost 1300% over the default case. Uncertainty in the input parameters generates
apparent cancer risk that is due only to the parameter uncertainty. That is, the additional
risk is not due to any "real" factor operating in the field. Varying some of these estimates
by fairly modest amounts caused the estimated risk to increase (or decrease) by a
dramatic amount.
The JEM equation is nonlinear and its response to parameter variation is
decidedly nonlinear also. Accounting for input parameter uncertainties resulted in
apparent cancer risks that were usually skewed toward increased risks. In the case of the
air exchange, rate this behavior was shown to be due to the model equation structure
itself: the denominator is insensitive, while the numerator was inversely proportional to
this parameter. This alone generated the increased apparent cancer risk in the model
results.
Use of the JEM in screening of sites for vapor intrusion should account for input
parameter uncertainty. Simulation using default parameters, generally picked at the
midpoint of their possible ranges, does not correctly represent the possible model outputs.
Standard approaches for application of models as presented in Section 3, indicate that a
necessary step in model application is calibration of results to field data. In situations
where the model is not calibrated to measured indoor air data, and subsequently
demonstrated to have predictive capability, the input parameters cannot be assured to
represent the properties of the flow system. By performing an uncertainty analysis, as
presented here, a range of potential outputs is revealed to the decision maker. An
informed choice can then be made concerning the risks simulated by the model.
-------
References
Anderson, M.P. and W. Woesner, 1992, Applied Groundwater Modeling, Academic
Press, San Diego, 381pp.
Carsel, R. F. and R. S. Parrish, 1988, Developing joint probability distributions of soil
water retention characteristics, Water Resources Research, 24(5), 755-768.
Campolongo, F., J. Kleijnen, and T. Andres, 2000, Screening methods, Chapter 4 of
Sensitivity Analysis, A. Saltelli, K. Chan, and E. M. Scott eds., Wiley, pp. 65-80.
Johnson, P.C., 2002, Identification of Critical Parameters for the Johnson and Ettinger
(1991) Vapor Intrusion Model, American Petroleum Institute No. 17.
Johnson, P. C. and R. A. Ettinger, 1991, Heuristic model for predicting the intrusion rate
of contaminant vapors into buildings, Environmental Science and Technology, 25,
1445-1452.
Metropolis, N. and S. Ulam, 1949, The Monte Carlo Method, Journal of the American
Statistical Association, 44(247) 335-341.
Nazaroff, W.W., 1988, Predicting the rate of 222Rn entry from soil into the basement of a
dwelling due to pressure-driven air flow, Radiation Protection Dosimetry, 24(1),
199-202.
Oreskes, N., 2003, The role of quantitative models in science, in The Role of Models in
Ecosystem Science, Charles D. Canham, Jonathan J. Cole and William K.
Laurenroth, Princeton University Press, pp 13-31.
Pascual, P., N. Steiber, and E. Sunderland, 2003, Draft Guidance on the Development,
Evaluation, and Application of Regulatory Environmental Models, US EPA, The
Council for Regulatory Environmental Modeling., www.epa.gov/crem/library.
Tillman, F.D. and J.W. Weaver, 2005, Review of Recent Research on Vapor Intrusion,
US EPA, in Review.
United States Environmental Protection Agency, 2001, Supplemental Guidance for
Developing Soil Screening Levels for Superfund Sites, Peer Review Draft,
OSWER 9355.4-24.
U.S. Environmental Protection Agency, 2002, Draft Guidance for Evaluating the Vapor
Intrusion to Indoor Air Pathway from Groundwater and Soils, USEPA Office of
Solid Waste and Emergency Response.
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-------
U.S. Environmental Protection Agency, 2004, User's Guide for Evaluating Subsurface
Vapor Intrusion into Buildings, Office of Emergency and Remedial Response,
Washington, DC,
van Genuchten, M. T., 1980, A closed-form equation for predicting the hydraulic
conductivity of unsaturated soils, Soil Science Society of Americal Journal, 44,
892-898.
Weaver, J.W., 2004, Characteristics of Spilled Oils, Fuels, and Petroleum Products: 3a.
Simulation of Oil Spills and Dispersants Under Conditions of Uncertainty, US
EPA, EPA 600/R-04/120.
Zheng, C. and G.D. Bennett, 1995, Applied Contaminant Transport Modeling: Theory
and Practice, Van Nostrand Reinhold, New York, 440pp.
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9 Appendix
The uncertainty analysis for the Johnson and Ettinger (JEM) model was
performed using a subset of the model input parameters that were presumed uncertain.
These parameters were described by their range only. This approach was based on two
assumptions. First is that the parameters were uniformly distributed. For many of the
parameters very little data exist on their values, so that distributions and correlations are
similarly unknown. The second assumption is that the extremes (maximum and
minimum) of the simulations occur at the endpoints. This was likely to be the case as
the a function is composed of exponentials. The result was shown empirically when
simulations with intermediate parameter values always showed their extremes to lie at the
endpoints of the parameter ranges. Further, this observation agrees with figures
presented in Johnson (2002) over a range of A, B and C values.
The A, B, and C variables encapsulate the basic JEM input parameters into three
dimensionless groups. These dimensionless groups could possibly form the basis for an
uncertainty analysis. Such an analysis would require far fewer simulations (8 versus 512
or more, see Table 1) because there would be only three variable parameters.
Use of the dimensionless parameters has the promise of allowing simple
definition of generic worst cases. If one could be assured that the extreme values of
model output always occurred with extreme values of the inputs (A, B, and C), then case-
specific uncertainty analysis is unnecessary. Because of linkages between the
parameters, however, a consistent choice of the minimum and maximum of A and B can
not be made. Table 14 shows the required maximum or minimum values of the basic
parameter values required to give maximum A, B and C values. Two inconsistencies
exist for selecting the maximum parameters:
maximizing A requires maximum AB; maximum B requires minimum AB
maximizing A requires maximum Dxeff; maximum B requires minimum Dceff
The converses apply for selecting the minimums of A and B. In all cases the
dependencies are somewhat arbitrary and could be broken if the area of the crack was
made independent of the foundation area, and if the diffusion coefficients were not
arbitrarily set equal to each other. At some level the parameters would necessarily
remain linked: the area of the cracks cannot approach the area of the foundation, and
some basic parameter values (i.e., the air and water phase diffusion coefficients) are the
same for either subsurface or crack diffusion coefficients. Relaxing these assumptions to
the maximum allowable, would enable the search for extreme values of the JEM, using
the using the maximum and minimum of the parameter values given in Table 14.
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Table 14 Relationships between basic input parameters and the maximum values of the
dimensionless groups A, B, and C. (The minimum values of these parameters occur with the opposite
choices of the basic input parameters.)
Maximum
value of the
dimensionless
parameter:
A
B
C
occurs with
maximum
value of:
DTe"
AB
Qs
Lc
Qs
and Minimum
value of:
QB
LT
Dce"
11
AB
QB
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