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OCR for page 169
6
Models
INS RODUCTION
Mathematical models use systems of equations, based on a conceptual
framework, to describe interactions among components of physical, chemical,
or biological systems. The conceptual component of a model consists of the
assumptions and approximations that reduce a complex problem to a simpli-
fied, more manageable one. Models are used because they are an efficient
way to examine the cause-effect relationships among components (or vari-
ables) in a system.
The bases of mathematical models are the fundamental physical and chemi-
cal laws, such as the laws of conservation of mass, energy, and momentum.
Modelers must choose the level of detail in which components of a system are
described. Clearly, an extremely rigorous model that includes every phenome-
non in microscopic detail would be so complex that it would take a long time
to develop and might be impossible to use. A compromise is always required
between a rigorous description and getting an answer that is meaningful for
a specific application with limited resources. This compromise involves mak-
ing many simplifying assumptions, which should be carefully considered and
listed. They impose limitations on the model that should always be kept in
mind when evaluating the model's results.
Models are useful tools for quantifying the relationship between air-pollu-
tant exposure and important variables, as well as for estimating exposures In
situations where measurements are unavailable. Exposure models may obviate
extensive environmental or personal measurement programs by providing
estimates of population exposures that are based on small numbers of repre-
sentative measurements. The challenge is to develop appropriate models that
allow for extrapolation from relatively few exposure measurements to a much
larger population (Sexton and Ryan, 1988~.
A practical approach to assessing exposure through modeling requires
169
OCR for page 170
170 ASSESSING HUMAN EXPOSURE
decisions as to how precise and accurate the assessments need to be. The
ultimate focus is on the biological effects of exposure, so decisions on accuracy
and precision require some quantitative knowledge of the biological effects.
Limitations on resources require the exposure analyst to choose the most
economical methods to answer the question, How accurately must the e~o-
sure or exposure potential estimate be to provide the needed information for
risk estimation, risk management, or epidemiology?" For risk-related prob-
lems, the analyst seeks a magnitude of exposure that defines the threshold of
Significant risk.- In some cases, the threshold has already been set with the
establishment of an exposure limit (e.g., by ACGIH, OSHA, or EPA). In
other cases, the threshold needs to be ascribed on the basis of available infor-
mation on possible health effects of the contaminant of interest or a structural
analogue. The judgment of those assigning limits should be driven by the
quality of the data.
For risk assessment and management, health-effects data bases with a high
degree of uncertainty should result in concomitantly high levels of attributed
risk/(unit exposure)-that is, a low exposure limit as a prudent safeguard
against underestimating the health-effects potential of the agent. Thus, ex-
tremely meager information on contaminants and biological effects will result
in low exposure limits until the data base can be improved to justify a higher
limit.
For epidemiological studies, the modeler must understand the study design
sufficiently to recognize the trade-offs between levels of uncertainty in expo-
sure estimates and the ultimate risk evaluation that also depends on the level
of uncertainty in the health-effects data.
Given an exposure limit, the analyst needs to determine whether any
particular exposure scenario constitutes a significant fraction of that limit.
However, the analyst needs only to use models with ~enough" sophistication to
do the job with the least cost. Simple models can be used first to explore an
exposure scenario, because they require relatively few data and are thus less
expensive to implement than the more sophisticated techniques. Simple mod-
els generally yield biased estimates of exposure. It is recommended that only
models known to be conservative be used in screening calculations so that any
bias that exists is protective of the individual exposed. Consider a contami-
nant with a vapor pressure of 0.1 torr, a molecular weight of 100, and a daily
exposure limit of 8,000 (mg/m3) hr (an 8-hour time-weighted average of
1,000 mg/m3~. A simple model that assumes complete saturation of the air
with this compound will render an estimated exposure of 4,300 (mg/m3) hr.
or about 50% of the exposure limit. Assuming further that this compound is
not present in particulate form (which would increase the amount of contami-
nant inhaled) allows one to estimate a lack of significant risk vis-a-vis the
OCR for page 171
MODELS 171
exposure limit. The true exposure will most likely be below this very conser-
vative estimate, but greater quality of assessment is not needed, because this
is a worst-case scenario.
Exposure models can be used to identify major exposure parameters (e.g.,
sources, emotion rates, etc*) =d to assist epidemiolog~cal studies and risk
assessments. Although the input required for exposure models depends upon
the nature of the model, all exposure models require information on who is
exposed, to what contaminant, for how long, and under what circumstances
(Davis and Gusman, 1982~. Many models also require information on the
sources' transport, transformation and fate of the contaminants of interest.
Models generally red on assumptions and approximations to quantitatively
describe cause and effect relationships that are otherwise difficult to deter-
mine. In this way models are used to estimate exposures when it is impracti-
cal or impossible to measure exposures of an individual or population to a
contaminant. Despite the simplifications inherent in models, they provide
insights and information about the relationships between exposure and inde-
pendent variables that determine exposure.
Models discussed in this chapter are classified into two broad categories:
those which predict exposure (in units of concentration multiplied by time)
and those which predict concentration (in units of mass per volume). Al-
though concentration models are not truly exposure models, their output can
be used to estimate exposures when combined with information on human
time-activity patterns (see Figure 6.1~. Since exposure occurs when humans
are in contact u ith contaminantts), exposure models generally combine infor-
mation on the concentrations in microenvironments with information on activi-
ty patterns. The output of such models is a prediction or description of expo-
sure for individuals or populations.
Exposure models can be used to estimate individual exposures or the distri-
bution of individual exposures in a population. Activity patterns and micro-
environmental contaminant concentrations inputs to exposure prediction
models~:an be measured or modeled. The microenvironmental concentra-
tions and the activity pattern can vary from individual to individual, and from
time period to time period. Three types of models have been developed to
estimate population exposures: (a) simulation models such as SHAPE (Ott,
1981, 19843 and NEM (Johnson, 1984; Johnson and Paul, 1984), (b) the con-
volution model by Duan (1981, 1982, 1985, 1989), and (c) the variance compo-
nents model by Duan (1989~.
As shown in Figure 6-1, concentration models are separated into several
types: models based on the principles of physics and chemistry, and models
that statistically relate measurements of concentrations to independent vari-
ables thought to be direct determinants of concentration (e.g., gas emission
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172 ASSESSING HUMAN EXPOSURE
| Models based on principles || Models based on statistical |
of physics and chemistry relationships
.
C ancentratlons In microenvlronmen ts ~
~TT~me-~tivt tY
Modeled or measured Pattern Information
I ndoor Ou tdoor
Ex posure
Modeled
FIGURE 6.1 Schematic diagram of models used in exposure assessment
rate from a cooking range) or indirect indicators (e.g., the presence of a gas
range). There are also many hybrids of these two basic approaches to model
contaminant concentrations.
Concentration models based on physical principles quantitatively estimate
emission source dispersion, deposition in the environment (indoor or out-
door), and transport to the receptor for a given contaminant. The transfer of
a contaminant from one medium to another can also be modeled in this way.
If a contaminant undergoes chemical reaction in the environment, then models
based on chemical reaction kinetics principles are used to predict the outdoor
concentrations of the secondary contaminants (products of reaction). Ozone
and sulfuric acid aerosols are examples of secondary contaminants formed by
chemical reactions of primary contaminants as they are dispersed and trans-
ported in the outdoor atmosphere. Models to describe and predict their
concentrations and, ultimately, human exposures must, therefore, incorporate
the rates and products of the chemical reactions.
The development of faster, larger, and less costly computers has greatly
enhanced our ability to model complex phenomena like the turbulent flow of
air in the outdoor and indoor environments. An approach to modeling the
dispersion of contaminants from sources is to approximate the random motion
of individual air parcels. However, random motion requires total indepen
OCR for page 173
MODELS 173
dence of one time interval from another and this requirement is not met for
diffusion in the atmospheric boundary layers. Instead, a correlation will exist
between one time interval and the next. This autocorrelation can be modeled
approximately and the motion of a large number of individual parcels can be
calculated.
~7
IMPORTANT MODEL CHARACTERISTICS
Limited information is available regarding the accuracy of most contami-
nant concentration models and less is known about exposure models because
most models have not been adequately validated. Model users should under-
stand that model outputs have uncertainties, not just those arising from the
uncertainties in the input data, and that actual exposure lies somewhere in the
range of that uncertainty. The results of models should be presented with
their estimated uncertainties. To the extent possible, the description of the
model results should distinguish between input and model uncertainty. A
major objective for improving models should be to reduce uncertainty due to
the model itself so that the estimated exposure is closer to the real exposure
and the uncertainties are primarily associated with the uncertainties in the
input data.
Concentration and exposure models do not always include sufficient docu-
mentation (fundamental equations, assumptions, whether parameters were
lumped, etc.) that enable new users to identify and adjust critical model pa-
rameters to fit new applications and or to compare their problems with previ-
ous applications. The inclusion in a model of particular complex terrain, of
specific contaminant source locations, unique source types, or other unusual
features of a particular air shed may result in a model of high specificity;
portions of such specific models may be applied to other air sheds only if the
models are well documented. For example, a model developed for the Los
Angeles urban atmosphere could not be used to estimate contaminant concen-
trations In Denver's atmosphere unless the model takes account of the change
in air density from sea level to Denver's 5,000 foot elevation along with other
geographical differences. Although of limited use, sophisticated models are
valuable research tools and provide valuable information on concentrations or
exposures. With greater computational power becoming increasingly available,
these models could be more widely applied in the future. It is important that
users fully understand the models they apply, because improper use of a
complicated model increases the likelihood of obtaining misleading results.
Computer models need to be transferable from one computer system to
another so that the validity of the model can be checked by others and the
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174 ASSESSING HUMAN EXPOSURE
model can be applied to other problems. Source codes for models (e.g., com-
puter language code) in general should be provided in a form complete
enough that programmers need not resort to any functions or subroutines
other than those commonly available in the compiler for the model's language.
In addition, as expert systems are developed to assist the application of mod-
els, attention must be paid to ensuring that these systems can be operated by
new users.
CONCENTRATION MODELS
Models are used extensively to estimate outdoor contaminant concentra-
tions at specific sites. These models use physical, chemical, and statistical
methods to address the contaminant source release, dispersion, reaction, and
deposition. Models are also used to estimate indoor contaminant concentra-
tions; most of these applications have occurred in occupational/industrial
settings. They generally focus on measuring the contaminant concentration
in a worker's breathing zone. The following discussion reviews outdoor con-
centration models (e.g., emission, dispersion, atmospheric chemistry) and
indoor concentration models (industrial and nonindustrial), including a review
of deposition and mixing within and between rooms. Variability is discussed
for both types. The section concludes with a discussion of recent advances In
outdoor and indoor concentration models.
Outdoor Models~ontaminant Source Emissions
Emission models based on the properties of the chemicals, design parame-
ters of the emission sources, the physics of mixtures, and the ambient weather
conditions can provide an alternative to source monitoring (Owens et al., 1964;
MacKay and Matsugu, 1973; Reinhardt, 1977; Tung et al., 1985~. The type
and structure of a model depend on the source and type of contaminant re-
leases; some sources are continuously replenished and can be considered to
be at steady state, while other releases change in temperature or concentra-
tion. Hanna and Drivas (1987) describe in detail various models available for
dynamic and steady-state sources.
Accurate estimation of emissions from point, area, and volume sources is
necessary for accurate quantification of downwind ambient concentrations.
Quantification of point sources such as stack discharges from manufacturing
units can be accomplished by a number of methods, including monitoring of
the sources directly and standard chemical engineering design procedures
OCR for page 175
MODELS 175
based on material and heat balances. For example, boiler emissions can be
defied by knowledge of the composition of the fuel burned and the ash
produced by the fuel combustion. Estimating releases from other processing
equipment may require knowledge of the reaction kinetics, vapor-liquid behav-
ior of the reaction mixtures, and the operating temperatures and pressures.
Emissions from nonpoint sources are more difficult to monitor. A number
of attempts have been made over the past decade to develop monitoring
techniques for vapor and particulate emissions from pits, ponds, and lagoons
(Harrison and Hughes, 1976, 1981; GCA, 1982; Thibodeaux et al., 1982) and
fugitive emissions from chemical process equipment (EPA, 1988c). The
Chemical Manufacturers' Association (CMA, 1987, 1989) and the EPA (1988c)
have published extensive data and models for the quantification of fugitive
emissions from chemical process equipment. EPA and the American
Petroleum Institute have published models for quantifying the emissions from
large storage tanks (EPA, 198Sa). Emissions are estimated for working losses
(filling and draining the vessels) and breathing losses (losses caused by the
diurnal temperature change). The EPA estimation procedure is frequently
updated for use by federal and state regulators and the manufacturing organi-
zations in permit negotiations and development of state implementation plans
for compliance with federal regulations.
The development of empirical models for emission rate estimations has
focused mainly on issues related to fugitive emissions. The rate of fugitive
emissions at any process point (valve, pump, etc.) is assumed to characterize
all similar process points or similar equipment items. Although this assump-
tion is known to be incorrect, data are insufficient to provide better emission
preclictions. High emission rate predictions are obtained with these models
and thus the subsequent exposure predictions may be overly conservative.
Models for sudden releases of hazardous materials are generally based on
fundamental principles of physics. The mass and heat balances (Bird et al.,
1960) used by the modelers have used either a dynamic solution or a steady-
state solution of the system of equations which describe these episodes. For
spills on land, a model was developed for quantification of liquefied natural
gas releases (Straw and Briscoe, 1978~. For spills on land or water, a model
was developed for characterizing the emissions of chemicals in the workplace
(Wu and Schroy, 1979~. These and related models are discussed by Hanna
and Drivas (1987~.
Models are used to calculate emissions of carbon monoxide, NOx, and
organics from motor vehicles. Seitz (1989) contrasts the methods used by the
state of California with those used by the federal government for transporta-
tion and emission analysis.
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176 ASSESSING HUMAN EXPOSURE
Validation
To ensure that their concentration estimates are appropriate, it is necessary
to validate emission models with data from operating systems. The type of
validation depends on the type of model and the ability of monitoring proto-
cols to quantify actual emissions accurately. For fugitive emissions, the rate
of losses to the environment can be measured directly by enclosing individual
sources to quantify the emission rate. The accuracy of the emission rate
measurement depends on the size and type of equipment, operating condi-
tions, and the chemical and physical properties of the chemicals being han-
dled. For example, the petroleum refining industry commonly involves high-
temperature processing of chemicals in large equipment, but the chemical
industry commonly uses ambient temperatures and small equipment and has
substantially lower emission rates.
Losses from large open ponds and pits are more difficult to quantify and
have caused difficulty in validation of emission models. The evaporation of
water from large lakes, monitored for many years by the U.S. Weather Serv-
ice, provides the best validation data base. Spill tests with chemicals such as
ammonia and liquefied natural gas offer another data base for validation and
calibration of emission models. Validation of models for aerated basins,
tanks, and lagoons can use standard data from the chemical engineering trans-
port literature when no reactions or other removal mechanisms are involved.
When a biological oxidation-reduction process is providing a competitive
removal mechanism, the validation of emission models is much more difficult.
Kinetic information is needed for biological degradation as an event separate
from losses due to volatilization. Much of the literature of biological reaction
kinetics combines volatilization and degradation losses and attributes the total
loss to kinetic reactions. This procedure makes the resulting data bases diffi-
cult to apply to specific sources.
Contaminant Dispersion
Models using annual average emission rates that were either measured or
estimated have been available since the early 1930s (Sutton, 1932) for simulat-
ing the dispersion of emissions from point sources. However, it was only in
the late 1960s and the early 1970s that there was substantial development of
computer programs for air dispersion of contaminants. For example, EPA has
supported the continuing development of a variety of Gaussian plume models
in its Users Network for Applied Modeling in Air Pollution (UNAMAP)
· ~
series or programs.
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MODELS 177
The basic concept of Gaussian plume models is that the turbulent disper-
sion of contaminants in the air has a random character of large-scale eddy
motion that is analogous to the Brownian motion of molecules. Prom this
analogy, a differential equation based on Fiches law is obtained and the solu-
tions are Gaussian functions. For atmospheric dispersion, motion ~ the
direction of the wind (advection) is modeled as the average wind speed.
Honzontal and vertical dispersion perpendicular to the prevailing wind direc-
tion are modeled as Gaussian functions with the standard deviations functions
of atmospheric stability and distance from the source (Henna et al., 1982~. To
incorporate some of the source characteristics that affect dispersion, buoyant
plume rise was included in the dispersion models (Briggs, 1969, 1971~.
In 1978, EPA designated certain dispersion model computer codes as ~ap-
proved models. for developing state implementation plans to achieve compli-
ance with National Ambient Air Quality Standards (NAAQS) (EPA, 1978~.
With EPA's endorsement of these models, they have become the principal
tools In plans for controlling contaminant sources. In developing control
strategies for contaminants regulated by the NAAQS, EPA developed models
that combined source emission rates with atmospheric dispersion to predict
the concentrations of the contaminants at a receptor site and to test the effec-
tiveness of control strategies. Prediction of the concentration of ozone, a
contaminant regulated by the NAAQS, requires modeling of the photochemi-
cal transformation of its precursors, i.e., volatile organic compounds and NOX,
as well as their transport.
Dispersion modeling also can be done statistically. The air can be consid-
ered as a number of parcels or particles' which move in a random fashion
(Taylor, 1921~. The path of a single parcel can be described by a statistical
function. If the parcel is assumed to have independent motion at any step
during transport, it can be modeled as a Random walk,~ in analogy to Brownian
motion of molecules. That concept was extensively developed in the l950s,
but the methods became so complicated by the need for empirical factors that
they were replaced with the simpler Gaussian plume methods (Henna et al.,
1982).
In recent years, stochastic modeling of atmospheric dispersion has in-
creased in popularity, because it is relatively simple, it can be applied to com-
plicated problems, and it has been made more practical by improvements in
computer capability and costs. Probabilistic models can easily incorporate
physical phenomena, such as buoyancy, droplet evaporation, polydispersity of
released particles, and dry deposition.
Stochastic modeling is typically implemented as a numerical Monte Carlo
model. Boughton et al. (1987) describe a Monte Carlo simulation of atmo-
spheric dispersion in which parcel displacement or velocity is treated as a
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178 ASSESSING HUMAN EXPOSURE
continuous-time Markov process. They restrict the model to crosswind-inte-
grated point sources and assume that dispersion in the mean wind direction
is negligible. That reduces the analysis to one dimension. Liljegren (1989)
has extended the model to incorporate horizontal and vertical dispersion
perpendicular to the mean upend direction. The results of the latter model
agree well with published concentration data ~lilliam E. Dunn, University of
Illinois, Urbana, personal communication, 1988~. It appears that three-dimen-
sional stochastic models will offer considerable predictive improvement (in-
clucting predictions of concentration change with time) over conventional
Gaussian plume models.
Most of the studies to calibrate and validate plume dispersion models have:
involved the release of inert tracer gases from near the ground in nonbuoyant
plumes-conditions very different from real stack plumes. In general, the
studies have not covered a sufficient distance downwind to test the models
beyond a few kilometers, so the results might not be reliable. Tracer pro-
grams and in-plume aircraft flights do not provide sufficient data to permit
evaluation of the models' ability to predict short-term peak concentrations.
Long-term average values have been estimated with data from sparse net-
works of continuous monitors, but their spatial resolution might be too low for
estimation of impacts of peak concentrations. Thus, validation is still inade-
quate.
With support of the Electric Power Research Institute, a major study to
validate plume models was mounted in the early 1980s. The first study was
of a large coal-fired power plant situated in relatively simple terrain, to mini-
mme topographical uncertainties. The study compared three Gaussian plume
models and three stochastic models with ground-level concentrations obtained
with both routine and intensive measurements programs (Bowne and Londer-
gan, 1983). The results indicated serious deficiencies in the particular disper-
sion models tested; they do not address complicating effects~uch as complex
terrain, surface roughness, atmospheric chemistry, and large sources of heat
that cause localized climatic change-and therefore are of uncertain validity.
Little is known about how a plume is affected by the objects it passes over.
For instance, a large manufacturing plant may emit much heat that creates
localized climate changes that directly affect the plume. In what is called the
heat-island effect, large masses of hot air rise and change the local climate.
This can change weather patterns over large cities.
The behavior of buoyancy, neutral buoyancy, and dense clouds in regions
of complex terrain constitutes a problem for the dispersion modeler. The
buoyancy and neutral-buoyancy plume models developed to date provide little
encouragement that the problems can be solved to permit reasonable predic
OCR for page 179
MODELS 179
lions of exposure. Little research has been done on the behavior of dense
clouds.
The dense and neutral-buoyancy models use mixing factors to represent the
surface under a plume. For example, the factors used for rural terrain are
equivalent to flat, low-friction surfaces, which cause a minimum of plume
turbulence. For urban terrain, the impacts of homes, businesses, and factories
have been quantified by calibration experiments. Rural factors are usually
used to ensure that results do not underestimate contaminant concentrations.
However, surface roughness and the interaction of a plume with a building
can have substantial effects. If the plume is spread sideways by such an inter-
action, the results might well be catastrophic for a plant poorly designed for
the community setting.
Atmospheric Chemistry
It is now possible to describe in detail many of the individual reactions
occurring in photochemical smog (Niki et al., 1972; Demerjian et al., 1974;
Seinfeld, 1988~. Use of explicit and detailed mechanisms in air-shed or long-
range transport models, however, is not always practical, and detailed informa-
tion on the rate constants of the precursors, intermediates, and products is not
complete. The limitations on the understanding and quantitations of the
complex chemical reactions can severely limit the accuracy of the output
prediction. In addition, the computer time required for the integration of the
rate equations associated with the hundreds of individual compounds involved
is prohibitive using current computer systems.
For urban air-shed models, condensed or (lumped) chemical mechanisms
are generally used (Finlayson-Pitts and Pitts, 1986; Seinfeld, 1988~; i.e., reac-
tions or chemical species are grouped and an overall rate constant is used for
each group (Falls and Seinfeld, 1978; Whitten et al., 1980; McRae et al.,
1982~. This approach can affect the spatial and temporal accuracy and preci-
sion of a model. In addition, the lumping process limits the fundamental
understanding of the specific pathways and interesting chemistry may be hid-
den by the lumping process. To estimate ozone concentrations with a model,
for example, it is necessary to estimate the concentrations of reactive interme-
diates. The resulting concentrations of these other substances reflect many of
the simplifying assumptions and may lead to erroneous results, even if the
specific concentration sought i.e., ozone is accurately predicted.
Ozone models have been critically reviewed by Seinfeld (1988~. Improved
ozone models incorporate wind fields, chemical reaction mechanisms, turbu-
lent dispersion, and removal processes. The newer, more sophisticated mod
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196 ASSESSING HUMAN EXPOSURE
house and the characteristics of the soil, such as permeability, are important
factors influencing pressure-driven flows of soil gases. Efforts to model radon
entry from soil and the consequent indoor radon concentrations are only
beginning. Mowris and Fisk (1988) have developed an analytical (closed-
form) model of soil-gas flow based on its analogy to heat transfer. The model
was used to evaluate the impact of exhaust ventilation on indoor radon con-
centrations In two houses. It underpredicted radon concentrations by 23%
and 13% for two different periods In one house and overpreclicted by 22% in
a second house, but the authors noted that comparison with measured concen-
trations was encouraging. Loureiro (1987) has developed a theoretical model
to predict indoor radon concentrations.- It simulates rates of generation and
decay of radon In soil, its transport through the soil due to diffusion and
convection induced by a pressure disturbance at a crack in the basement, and
its entrance into the house through the crack. Two computer programs were
developed to calculate the pressure distribution in the soil and the resulting
velocity distribution of the soil gas and to solve the radon mass-transport
equation, calculate radon entry rates, and calculate the indoor radon concen-
tration. Indoor radon concentrations were found to be directly, although not
linearly, related to the ~ndoor-outdoor pressure difference.
Domestic water contaminated with gases, such as radon and volatile organic
compounds (VOCs), is a source of exposure that has only recently been recog-
nized as important. Dissolved gases in contaminated water are released in-
doors during such residential uses as showering and dish-washing (Andelman,
1985; Gesell and Prichard, 1975; McKone, 1987; Jo et al., in pressa). McKone
has developed a mass-transfer model to estimate human exposures to VOCs
due to their transfer from tap water to indoor air. It estimates the release of
VOCs from water and uses a three-compartment model to simulate the 21
hour concentration profile in the shower, the bathroom, and the rest of the
house. A preliminary data base on household characteristics and time-activity
patterns has been used to calculate a range of concentrations and human
exposures to seven VOCs. Nazaroff et al. (1987) used a single-compartment
mass-balance model with a long averaging time to calculate the distribution
of indoor-air Revlon in U.S. homes from tap water.
In another recent advance in modeling indoor concentrations of contami-
nants in homes, Traynor et al. (1988) developed a single-compartment mass-
balance model for combustion emissions, specifically CO, NO2 and respirable
particles. Input data for the model include distributions of housing stock
characteristics (e.g., volumes and air-exchange rates), use of combustion appli-
ances and sources (e.g., cigarettes), distribution of source emission rates, and
source use. The model uses deterministic and Monte Carlo simulation tech-
niques to generate distributions of average weekly concentrations of CO, NO2,
OCR for page 197
MODELS 197
and respirable particles for four regions of the country. The modeled distribu-
tions have generally compared well with available field measurements. The
model can also be used to rank indoor pollutant sources, identify high-risk
populations, identify key factors for attempts at control and mitigation, and
estimate exposures for epidemiolog~cal studies.
N~roff and Cass (1986) recently developed the first model for chemically
reactive pollutants in indoor air. It combines the multibox ventilation mode!
of Shair and Heitner (1974) with a modified version of the Falls and Seinfeld
photochemical kinetic mode} (Falls and Seinfel~ 1978; Russell et al., 1985~.
The mode] accounts for the effects of ventilation, filtration, heterogeneous
removal of gaseous pollutants, direct emissions, and homogeneous gas-phase
reactions and predicts concentrations of such chemically reactive contaminants
as HNO2, HNO3, NO3 and N205. Nazaroff and Cass (1986) tested the model
in a museum gallery, predicted and measured concentrations of several pollu-
tants were in reasonably good agreement. They also compared their modeled
steady-state ratio of HNO2 to NO2 due to homogeneous gas-phase reactions
with that measured by Pitts et al. (1985a) in an indoor environment; the ex-
penmental ratio was about 35 times the modeled ratio. Heterogeneous reac-
tions appear to play an important role in indoor production of HNO2 and
models for indoor atmospheric chemistry probably will eventually have to
incorporate heterogeneous chemical reactions. However, very little is known
about such reactions today.
EXPOSURE-ASSESSMEN] MODELS
Current exposure models are based on relatively general assumptions about
the distribution of contaminant concentrations in microenv~ronments, the
activity patterns that determine how much time people spend in each micro-
environment, and the representativeness of a sample to the population that
might be exposed to a contaminant.
Individual Exposures
In a model of individual exposure, contaminant concentrations in each
microenvironment are measured or modeled and time-activity patterns are
used to estimate the time spent in each microenvironment. (Exposure is the
product of time and contaminant concentration.) An individual's overall e~o-
sure can be separated into the sum of products of concentration and time in
OCR for page 198
198 ASSESSING HUMAN EXPOSURE
each microenvironment; this is termed a microenvironment decomposition
(Duan, 1981~.
Microenvironment decomposition can be extended to other summary expo-
sure measures, such as peak concentrations. If we are interested in total
exposure, microenvironmental decomposition is assumed to include all possi-
ble locales and activities. Duan (1981, 1985) developed a criterion for stratify-
ing microenvironments to improve the precision of estimated average eypo-
sures and applied it to identify the important microenvironments for CO
exposures.
Some models for predicting exposures make assumptions regarding the
independence between contaminant concentrations and time spent and activity
in a microenvironment. Such assumptions should be validated for specific
applications. Duan (1985) has suggested that there is no correlation between
CO concentrations and time on the basis of data from the Washington, D.C.,
CO study (Akland et al., 1985~. However, there will be problems in the exist-
ing models if correlations between occupancy periods and concentrations exist
for other contaminants, because the independent variables, time and concen-
tration, would not be truly independent. If the correlation is very high, the
predictions based on models might not be valid because of an inappropriate
assumption of independence. The committee is unaware of any empirical data
quantizing the extent of problems caused by the correlations. It is likely that
for contaminants such as particles, the presence of a person might change the
particle concentration of a previously unoccupied microenvironment. Further
study of the problems such correlation would produce is needed.
Stock et al. (1985) used personal-activity profiles and household characteris-
tics to partition the locations into seven broad microenvironments: three
indoor, two outdoor, and two transportation modes. From measured concen-
trations of the criteria pollutant gases (ozone, NO2, SO2, CO), aeroallergens,
aldehydes, TSP, and inhalable particles and the time in each partition, eypo-
sure estimates were calculated. The results will ultimately be combined with
epidemiological data to determine the health effects of exposure to specific
pollutants in a community environment.
More or less sophisticated versions of partitioning are used in the work-
place, where they are referred to as job exposure profiling (JEP). JEP some-
times consists of grouping and compiling work tasks with durations of expo-
sure at breathing-zone concentrations (Austin and Phillips, 1983~. The prod-
uct of such analysis is a prediction of exposure of any employee involved in
the tasks covered by the JEP. Hansen and Whitehead (1988) recently moni-
tored the activities and breathing-zone concentrations of printing-press opera-
tors and modeled time-weighted average exposures as a function of location
and the number of times a "hazardous task" was performed.
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MODELS 199
Population Exposures
Modeling exposure of populations requires the combining of microenviron-
ment concentrations with individual activity patterns and extrapolation of the
results to a population. Data on human activity patterns have been combined
with measured outdoor concentrations in the NAAQS exposure model (NEM)
to estimate exposures to CO (Biller et al., 1981; Johnson and Paul, 1983~.
The NEM was modified to include indoor exposures by incorporation of the
indoor-air quality model (LAQM) (Hayes and Lundberg, 1985~. The IAQM,
based on the interactive solution of a one-compartment mass-balance model,
incorporates three basic indoor microenvironments: home, office or school,
and transportation vehicle. It has been used to estimate distributions of ozone
exposures (Hayes and Lundberg, 1985) and to evaluate strategies for mitigat-
ing indoor exposures to selected pollutants in five situations, e.g., CO exposure
from a gas boiler in a school (Eisinger and Austin, 1987~.
As mentioned in the introduction to this chapter, three types of models
have been developed to estimate population exposures: (a) simulation models
such as SHAPE, (b) the convolution model, and (c) the variance-component
model. The simulation of human air pollution exposure model (SHAPE) (Ott,
1981) is a computer model that generates synthetic exposure profiles for a
hypothetical sample of human subjects; the profiles can be summed into com-
partments or integrated exposures to estimate the distribution of a contami-
nant of interest. The bulk of the model estimates the exposure profile of
contaminants attributable to local sources; the contribution of remote sources
is assumed to be the same as the background. The total exposure is therefore
estimated as the sum of exposure due to local sources and the ambient back-
ground.
For each individual in the hypothetical sample, the model generates a pro-
file of activities and contaminant concentrations attributable to local sources
over a given period, say, 24 hours. Activity profiles are generated or accepted
as input. At the beginning of the profile, the model generates an initial mi-
croenvironment and duration of exposure according to a probability distribu-
tion. At the end of that duration, the model uses transition probabilities to
simulate later periods and other microenvironments. The procedure is repeat-
ed until the end of a selected long period. For each time unit, say, 1 minute,
in a given microenvironment, the model generates a contaminant concentra-
tion according to a microenv~ronment-specific probability distribution: each
microenvironment has a specific probability distribution for each contaminant
concentration. Such models obviously require validation with measured expo-
sure data for a subset of microenvironments and patterns.
Duan (1981, 1985, 1989) developed the convolution model for integrated
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200 ASSESSING HUAL4N EXPOSURE
exposures. It calculates distributions of exposure from distributions of concen-
trations observed in defined microenvironments and the distribution of time
spent in those microenv~ronments.
The variance-component model (Duan, 1989) assumes that short-term
contaminant concentrations can be decomposed Into components that vary In
time and those that do not. SHAPE deals mainly with the t~me-varying com-
ponent; the convolution model deals mainly with the time-invariant exposure.
The two components can be summed or multiplied to yield an estimated
concentration value. It is necessary to determine the distributions of the two
concentration components. If continuous personal-monitoring data are avail-
able, it is possible to estimate the. distributions of the two components directly.
If integrated personal-monitoring data are available, the methods described
by Duan (1989) can be applied. Once the concentration distributions are
available, exposure distributions can be estimated with a computer simulation
similar to SHAPE. Instead of generating a contaminant concentration for
each time unit independently, as in SHAPE, a time-invariant concentration
and a time-va~ng concentration are generated for each unit and combined
to determine 1-minute concentrations. The remainder of the simulation is
identical to that in SHAPE.
All three types of models (SHAPE, convolution, and variance-component)
need to make assumptions about independence. The critical difference among
the three types is in those assumptions. SHAPE assumes that the short-term
pollutant concentrations (e.g., 1-minute averages) within the same microenvi-
ronment are stochastically independent and independent of activity patterns.
It follows that the microenvironmental concentration is not correlated with
activity time in that microenvironment. Furthermore, the variance of concen-
tration decreases in inverse proportion to activity time. For longer activities
in the same microenvironment, the concentration is averaged over more time
units. Similar assumptions were made in an earlier version of NEM; a more
recent version of NEM incorporates serial correlation in the 1-minute aver-
ages (Johnson et al., 1990~.
The convolution model assumes that microenvironmental concentrations
are statistically independent of activity pattern. That implies that they are not
correlated with activity time and that the variance of the concentration also
stays constant, irrespective of time. That needs to be validated. Switzer
(Stanford University) noted in a private communication with Duan in 1982
that the forms of the variance functions used in both models might be unreal-
istic and that some compromise between the two might be desirable.
With either the additive or multiplicative form of the variance component
model, the time-invariant components are assumed to be stochastically inde-
pendent of the time-varying components. It is further assumed that for differ
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MODELS 201
ent time units, the time-vary~ng components are independent from one interval
to the next. Alternatively, it can be assumed that the time-vary~ng components
have an autocorrelation structure.
Duan (1985) examined data from EPA's Washington, D.C., CO study and
found that concentrations and internal were unrelated. Ott et al. (19~) used
data from EPA's CO study in Denver to emmine the validity of SHAPE,
comparing exposure distributions of CO estimated with SHAPE and with the
direct approach (personal monitoring). They found the estimated average
exposures to be similar and the estimated exposure distributions to be cliffer-
ent at the extremes of the distributions. That result might be due to failure
to account for autocorrelation and the time-invariant component. Duan
(1989) examined several statistical parameters for microenvironments In data
from the Washington, D.C., CO study and found the time-invariant
component to be dominant.
Temporal Aspects
One cause of inaccuracy in exposure modeling is failure to obtain measure-
ment data on an appropriate time scale. Outdoor air is often sampled in the
summer, and concentrations for an entire year are then estimated on the basis
of a single season. But sampling and analysis programs must cover enough
time for concentrations to be reasonably estimated for a fuD year, if they are
to serve as reliable inputs to exposure models. Very few sampling studies have
extended over a long enough period to revead seasonal and year-to-year varia-
tions.
An example of good sampling design was that of the Portland Aerosol
Characterization Study (Cooper and Watson, 1979~. The researchers attempt-
ed to learn the representative composition of airborne particulate matter and
its sources without having to sample every day and analyze every sample.
They stratified the year into eight defined meteorological regimes and took
samples when conditions and time of year were appropriate. Although many
samples were taken, only enough were analyzed to yield useful average values
for each regime. The regime averages were then combined in proportion to
their probability of occurrence during the year. Representative annual con-
centration averages were obtained at a reasonable level of effort for both
sampling and analysis. However, because of the variability of occupancy
times, it may be that different averaging times are appropriate in estimating
average exposures as compared with average concentration.
Many estimates of annual average concentrations of indoor radon are based
on measurements taken over periods of a few days under conditions that are
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202 ASSESSING HUMAN EXPOSURE
quite unrepresentative of those existing ~ a house over a whole year. The
estimates so derived can easily differ from true annual averages by a factor of
2 or more, because, for example, the conditions that give rise to indoor radon
change from season to season (Nero et al., 1986~.
Modeling of very long exposures, as is required in assessing risk associated
with exposure to carcinogens, presents several major difficulties. The typical
practice is to measure or model the concentration of a contaminant at one
time and determine lifetime exposure by multiplying that concentration by a
long period, e.g., the lifetime of a person. However, both exposures and
activity patterns change substantially over a lifetime. Industrial processes also
change over time. Sources (such as wood-burn~ng stoves) are introduced, and
sources (such as catalytic converters in motor vehicles) are eliminated or
modified. Large facilities typically have a design life of 30 years, so consider-
able uncertainty can be anticipated in a typical calculation of 70-year lifetime
exposure.
Time-activity patterns and locations of people also vary substantially over
long periods. In the United States, people change their place of residence
frequently and rarely live in the same place over a lifetime. For agents such
as radon, such mobility can have a substantial impact on exposure and thus
on the use of exposure estimates in an epidemiological study.
A person's activity patterns shift from childhood through early adulthood
and middle age to old age. There have been some efforts to address differ-
ences in exposure associated with aging, but this aspect of variability in e~o-
sure over long periods has generally not been addressed in exposure modeling.
The modeling of short-duration peak exposures is also attended by tempo-
ral problems. Typical steady-state airborne-concentration models are not able
to provide estimates for periods shorter than 1 hour and have difficulty In
modeling time-varying concentrations, which can lead to high short-term
exposures. If an exposure model is to estimate the effects of peak exposures
on sensitive populations, the concentration model must provide reliable esti-
mates on biologically relevant time scales. Some important developments in
stochastic models that might be able to provide such estimates have not yet
been incorporated into exposure-estimation procedures.
SUMMARY
Models are useful tools for quantifying the relationship between air-pollu-
tant exposure and important variables, as well as for estimating exposures in
situations where measurements are unavailable. Models may obviate extensive
environmental or personal measurement programs by providing estimates of
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MODELS 203
population exposures that are based on small numbers of representative meas-
urements. They can be used to identify major exposure parameters and to
assist epidemiological studies and risk assessments. Models generally rely on
assumptions and approximations to describe quantitatively cause-and-effect
relationships that are otherwise difficult to determine. Despite the simplifica-
tions inherent in models, they provide insights and information about the
relationships between exposure and independent variables that determine
exposure.
Models discussed In this chapter are classified into two broad categories:
those that predict exposure (in units of concentration multiplied by time) and
those that predict concentration (in units of mass per volume). Although
concentration models are not truly exposure models, their output can be used
to estimate exposures when combined with information on human activity
patterns. Exposure models can be used to estimate individual exposures or
the distribution of individual exposures in a population. Activity patterns and
microenvironmentalcontaminant concentrations inputstoexposure-prediction
models~an be measured or modeled.
Concentration models are separated into several types within two catego-
ries: models based on the principles of physics and chemistry and models that
statistically relate measurements of concentrations to independent variables
thought to be direct determinants of concentration. Many hybrids of these
two basic approaches to model contaminant concentrations also exist.
Concentration Models
These models are used extensively to estimate outdoor contaminant con-
centrations at specific sites. These models use physical, chemical, and statisti-
cat methods to address the contaminant source release, dispersion, reaction,
and deposition. Models are also used to estimate indoor contaminant concen-
trations; most of these applications have occurred in occupational or industrial
settings. They generally focus on measuring the contaminant concentration
in a worker's breathing zone.
Over the past decade, research in air quality in nonindustrial indoor envi-
ronments has dramatically changed the understanding of human exposures to
many airborne contaminants. Many critical factors involved in residential
exposures differ from those in industrial exposures. For example, the indoor
exposed population includes members who are very young, very old, or infirm.
The potential indoor exposure duration in residences is much longer com-
pared with a typical working career. The concentrations of contaminants and
ventilation rates are often much lower in residences than in industrial environ
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204 ASSESSING HUMAN EXPOSURE
meets. Most advances in indoor-air modeling have come from increasing the
sophistication and complexity of the models.
Outdoor
New developments In stochastic dispersion models offer improvements in
the prediction of the average and time-varyLng concentrations to which individ-
uals are exposed. Receptor models can be used to cross-validate dispersion
models. They also can be used to identify sources of exposure.
In many cases, the data describing the source characteristics are not avail-
able on the time scale at which the model predictions are needed. Such
mismatches In the time scale of the measurements with the time scale of the
models preclude adequate model development, validation, and application to
new biologically relevant exposure situations. Because of the changing nature
of sources and source emissions with changes in production and control tech-
nology and in the economic conditions, it is necessary to measure periodically
the amounts and chemical characteristics of sources of airborne contaminants.
Improvements In photochemical models now permit far more accurate
predictions of the spatial and temporal variability of ozone and some other
atmospheric constituents than were previously possible. However, it is still not
possible to incorporate the complete, explicit mechanisms into air-shed or
long-range transport models.
Indoor
Current models used to predict worker exposures to airborne toxicants are
relatively simple, undeveloped, and unvalidated. This deficiency has caused
practitioners to use models-instead of estimation techniques as though they
were conservative screening techniques.
Little work has been done to model very short-term exposures (peak expo-
sures) and gradients relative to dispersion, deposition, and ventilation in in-
door environments. The sources of indoor-air pollution need to be character-
ized. Measuring and modeling the temporal patterns of source strength as a
function of readily identifiable or measurable source characteristics are critical
steps in that process. In addition, more work is needed to model the relation-
ship of indoor-air quality to the composition of the ambient atmosphere.
Furthermore, the chemistry of the indoor atmosphere remains to be investi-
gated.
The variability of concentrations in indoor
Industrial air over short time
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MODELS 205
frames needs to be measured for emergency situations. The validation of the
models to predict concentrations is linked to appropriate sampling time
frames and methods with adequate sensitivity to specific chemical species.
Indoor-Air Chemistry
Indoor-air chemistry needs substantial research, including surface reactions
on various materials, sorption, deposition, and rates for these processes rela-
tive to ventilation or other loss mechanisms.
Exposure Models
Current exposure models are based on relatively general assumptions about
distribution of contaminant concentrations in microenvironments, the activity
patterns that determine how much time people spend in each microenv~ron-
ment, and the representativeness of a sample to the population that might be
exposed to a contaminant. In a model of individual exposure, contaminant
concentrations in each microenvironment are measured or modeled, and time-
activ~ty patterns are used to estimate the time spent in each microenv~ron-
mcut. Modclir~g closure of populations requires the combining of microenv~-
ronmental concentrations with individual activity patterns and extrapolation of
the results to a population.
Models for predicting exposures to populations have been developed re-
cently. They have not, however, been adequately validated. Limited validation
studies of the SHAPE exposure model, for example, have shown that the
average values are well predicted but show substantial discrepancies in the
tails of the distribution. Further development and validation of the models
are warranted. One cause of inaccuracy in exposure modeling is failure to
obtain measurement data on an appropriate time scale. Sampling and analysis
must cover sufficient time for concentrations to be reasonably estimated for
a full year, if they are to serve as reliable inputs to exposure models.
Source Models
Source emission models are available to predict mass emission rates for a
variety of dynamic and steady-state emission problems. The available emis-
sion models allow the estimation of downwind exposure for continuous or
catastrophic releases of pure compounds or binary mixtures. These models
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206 ASSESSING HUMAN EXPOSURE
have not been validated. Dense-cloud dispersion models are available to
estimate downwind exposure for heavier-than-air vapor releases; they also
have not been validated.
Emission-rate estimation protocols are available for defining losses from
chemical-processing equipment. Emission modeling coupled with dispersion
modeling and time-activity estimates allow estimation of exposures for work-
place-population exposure concerns before construction of new production
facilities.
Validation
Further validation studies are needed for virtually all existing models, in-
cluding concentration prediction and exposure models. In particular, immedi-
ate efforts are needed to validate the NEM model and modify the model to
more accurately reflect the actual situations that can result in high population
exposures. Valid emission-rate models are needed to provide precise estimates
for multicomponent mixtures. Validated dispersion models are needed to
predict downwind concentration for complex terrain to provide accurate e~o-
sure estimates for down- and up-gradient terrain conditions. The same data
set cannot be used to refine and validate a model; new, independent data are
required to validate any refined model. All assumptions used in developing
a model should be documented explicitly. Care should be taken by investiga-
tors in any field-monitoring program to integrate their measurements pith the
modeling community needs so that the requisite model input data are ob-
tained, and the measurement results can be used to test, refine, or validate
appropriate models.
Measurements are needed of the concentrations of airborne pollutants In
workplaces and homes along with the critical independent variables, such as
source-emission rate distributions and the indoor general ventilation fields.
Concentration gradients u ithin physically defined microenvironments also need
to be measured accurately. When planning measurement campaigns, consid-
eration should be given to the sampling strategies that would permit the ex-
trapolation of the results to biological time frames other than those of the
measurement program.
Representative terms from entire chapter:
exposure models
