Components of Exposure

Human exposure to a pollutant, and its consequent impact on health, results from the simultaneous occurrence of two events—a pollutant concentration c(x,t) at point x and time t, and the presence of people:

Exposure=f[P(x,t), c(x,t)]

where P(x,t) represents the number of people at point x and time t inhaling a pollutant at concentration c(x,t). Sexton and Ryan (this volume) explain in detail the three components of personal exposure: magnitude of the concentration, duration, and (if the exposure is a discrete event that recurs) frequency; or, more generally, the magnitude c(x,t) of the concentration as a function of the path of the subject characterized by his or her position x at all times t for the duration of the time interval in which exposure takes place. This chapter discusses how air quality models can be used to determine how c(x,t) depends on emission sources.

Source/Receptor Relationships

The most direct method for observing the effect of a single air pollution source is to eliminate it completely, but complete elimination is usually impractical or impossible. A more feasible method is needed to predict the impacts of emission sources on air quality. Two distinctly different methods have been developed for making such predictions: mathematical models and physical models. A mathematical air quality model simulates pollutant evolution by interrelating symbolic descriptions of the important physical and chemical processes occurring in the atmosphere within a computational framework. A physical model simulates atmospheric processes with a scaled-down representation of the atmosphere in a laboratory setting. The most common example of a physical model is a smog chamber used to study atmospheric chemistry. Another example is wind tunnel testing using scale models of buildings to observe the transport of pollutants in city street canyons.

Mathematical models have a number of advantages over physical models when the question is to find out how much of each air pollutant at a given location is due to each particular emission source—a process called source apportionment. For example, smog chambers can only be used to study atmospheric chemical reactions in a fixed location and are not suited to simulate the effects of diffusion, changing spatial and temporal emission patterns, pollutant deposition at the ground, and varying meteorological conditions. On the other hand, by accurately describing the dynamics of pollutants as they travel from the many emission sites in a city to a sampling, or receptor, site, a mathematical model can keep track of the separate contributions of the sources of pollutants that influence air quality at a given location. The inputs to the calculation are the pollutant emission rates, and the output is the expected concentrations of the several atmospheric pollutants (figure 2).

Figure 2.

Inputs, outputs, and types of models commonly used in air quality modeling studies.

Mathematical models used in air pollution analysis fall into two types: empirical/ statistical and analytical/deterministic. In the former, the model statistically relates observed air quality data to the accompanying emission patterns, whereas chemistry and meteorology are included only implicitly (Seinfeld 1975). In the latter, analytical expressions describe the complex transport and chemical processes involving air pollutants. The pollutant concentrations are determined as explicit functions of the meteorology, topography, chemical transformation, and source characteristics, which are inputs to the calculation.

The subject matter of this chapter necessarily overlaps that of other chapters of this book. To minimize duplication, this chapter focuses on how mathematical models are used to predict pollutant concentrations as a function of emissions. Greatest attention is given to pollutants that are either known to be or suspected of being harmful to human health and to modeling on a scale appropriate to urban areas where pollutant concentrations and population densities are highest.

Our discussion begins with a section devoted to understanding the physical and chemical nature of the emissions, for these, in part, determine important characteristics that should be described by a mathematical model. Because of chemical reactions in the atmosphere, the dynamics of some automotive emissions and reaction products depend on the presence of other anthropogenic and natural sources, and it is often insufficient to consider one without the other. After the important emission source types have been identified, it is necessary to choose an appropriate model for each application. The different types of air quality models that are available are reviewed in the next section along with possible advances that could be made in their structure and application.

The section on modeling approaches presents our current understanding of the various individual physical and chemical processes (for example, transport, chemical reaction, dry deposition) that affect pollutant concentration in the atmosphere. A model's capabilities are determined by the level of detail at which each of the processes is described within the modeling framework. Many future advances in air quality modeling will come from better quantitative descriptions of individual processes, so a number of topics for fruitful research evolve from this section. The theoretical basis and accuracy of the complete model, each of its components, and the structure interrelating the components must be evaluated, as described in the succeeding section.

After a model has been evaluated, it is ready for use in conducting source apportionment, population exposure, and control strategy studies, as discussed in the next section. Studies of this type are of great interest, but few comprehensive control strategy studies have been conducted using state-of-the-art air quality models. Finally, a section addressing special topics and emerging issues in air quality modeling is followed by a summary of research recommendations.

Historical Perspective

The driving force behind the development of mathematical air quality models has been the Clean Air Act (American Meteorological Society 1981). Models have been used to demonstrate compliance with regulatory standards and to guide regulatory agencies toward possible emission control strategies for improving air quality. Air quality models motivated by the Clean Air Act are designed primarily to predict the concentrations of pollutants such as carbon monoxide (CO), nitrogen dioxide (NO₂), and ozone (O₃) that have been regulated by the federal government for many years, but not those of many trace toxic pollutants that are already of growing interest to health effects researchers and are likely to be subject to regulation in the future.

By the early 1970s, analytical models had been developed to the point that it was possible to predict the concentrations of pollutants such as CO that are largely determined by transport but not by atmospheric chemical reaction. The next step was to incorporate atmospheric chemistry into the model to describe the dynamics of pollutants, such as O₃ and NO₂ that are chemically active in the atmosphere (see, for example, Transportation Research Board 1976). By the early 1980s, photochemical airshed models had been developed that could accurately predict O₃ and NO₂ concentrations as a function of emissions. At present, a limiting factor in our ability to describe the dynamics of these two pollutants in an urban area is the availability of high-quality input data, not the model itself.

On the near horizon are models that describe aerosol processes in the atmosphere. So far, modeling studies have concentrated on specific aspects of the many different processes that control the size and composition of particulate matter in the atmosphere. Advances in this area are vital for providing better assessments of health impacts of emission sources.

The past decade has seen rapid development of empirical/statistical air quality models. Most models of the early 1970s assumed that basinwide air quality changed in direct proportion to total basinwide emissions. These “rollback” models were applied to basinwide emissions to predict concentrations of chemically inert as well as chemically reactive pollutants. Rollback models are limited in application because they ignore important effects due to the spatial distribution of emission source changes and atmospheric chemistry. Empirical receptor-oriented models that use the chemical composition of ambient pollution samples as a tracer for pollutant origin were introduced in the 1970s, but were initially applied in only a few cases. Because they accurately resolve source contributions to particulate matter concentrations, receptor models are now widely accepted as a replacement for rollback models.

Although there are still critical aspects of present models that could be improved, it is clearly time for more extensive use of models for explaining relationships between sources and health effects. A particularly pressing issue that can be studied using present models is the relationship between the nitrogen oxide emissions (NO and NO₂ and the sum is commonly symbolized schematically as NO _x ) and organic gas emissions in the formation of O₃ (the O₃-precursor relationship—see Pitts et al. 1976; Chock et al. 1983; Pitts et al. 1983). If resources are provided, the next decade should see models that are able to describe the dynamics of aerosols and currently unregulated toxic gases and to resolve many current questions about sources and air quality.

An important but historically underused facet of mathematical models is that they collect and codify what is understood about the constituent processes in a large system such as the atmosphere. In cases where models fail to perform well, they then reveal what is not understood. In this way, evaluation of model performance directs our attention to fruitful problems and topics for further research.

Empirical/Statistical Models

Mathematical air quality models are of one of two types: empirical/statistical or deterministic (figure 2). Empirical/statistical models, such as receptor-oriented and rollback models, are based on establishing a relationship between historically observed air quality and the corresponding emissions. The linear rollback model is simple to use and requires few data, and for those reasons has been widely used (see, for example, Barth 1970; South Coast Air Quality Management District and Southern California Association of Governments 1982). Linear rollback models assume that the highest measured pollutant concentration is proportional to the basinwide emission rate, plus the background value; that is,

c _max = aE + c _b (1)

where c _max is the maximum measured pollutant concentration, E is the emission rate, c _b is the background concentration due to sources outside the modeling region, and a is the constant of proportionality. The constant a accounts for the dispersion, transport, deposition, and chemical reactions of the pollutant. Thus, the allowable emission rate, E _a , necessary to reach a desired ambient air quality goal, c _d , using the linear rollback model can be calculated from

(2)

where E _o is the emission rate that prevailed at the time that c _max was observed. Presumably, pollutant concentrations at other times would also decrease toward background levels as emissions are reduced, and similar expressions can be written for relating annual mean concentrations to emission rates. Obviously this is a very simplified approach, and its application is limited. Nonlinear processes such as chemical reactions and spatial or temporal changes in the emission patterns are not accounted for explicitly in the rollback model formulation.

A second class of empirical/statistical models of continuing interest is the receptor-oriented model, used extensively for estimating source contributions to particulate matter concentrations in a number of geographic areas (Friedlander 1973; Heisler et al. 1973; Gartrell and Friedlander 1975; Gatz 1975, 1978; Gordon 1980; Watson et al. 1981; Cass and McRae 1983; Watson 1984; Hopke 1985). Nonreacting gases have also been tracked by receptor modeling methods (Yamartino 1983). Receptor models compare the measured chemical composition of particulate matter concentrations at a receptor site with the chemical composition of emissions from the major sources to identify the source contributions at ambient monitoring sites.

There are three major categories of receptor models: chemical mass balance, multivariate, and microscopic. Hybrid analytical and receptor (or combined source/ receptor) models have been proposed and used, but further investigation into their capabilities is required.

Receptor models are powerful tools for source apportionment because of the vast amount of particulate species characterization data routinely collected at many sampling sites within the United States. Most of the information available is for elemental concentrations (for example, lead, nickel, aluminum) although recent measurements are leading to increased data on concentrations of compounds such as ionic species and carbon compounds. At a sampling (or receptor) site, the aerosol mass concentration of each species i is

(3)

where c _i is the mass concentration of species i at the receptor site; S _j is the total mass concentration of all species emitted by source category j as found at the receptor site; a _ij is the fraction of the total mass from source j emitted as species i arriving at the sampling site; m is the total number of species measured; and n is the total number of sources. The mass concentration c _i measured at the receptor site of interest and the coefficients a _ij that describe the chemical composition for the major sources are the inputs from which S _j , the mass apportioned to source j, is determined. Because a _ij characterizes the source, it is referred to as the source fingerprint and should be unique to the source. When the chemical composition of the emissions from two source categories are similar, it is extremely difficult for receptor models to distinguish between the sources. The categories of receptor models are differentiated by the techniques used to determine S _j .

Chemical Mass Balance Methods. Given that the source fingerprints a _ij for each of n sources are known, and that the number of sources is less than or equal to the number of measured species (n≤m), an estimate for the solution to the system of equations in equation 3 can be obtained. If m>n, then the set of equations is overdetermined, and least-squares or linear programming techniques are used to solve for S _j . This is the basis of the chemical mass balance (CMB) method (Miller et al. 1972; Cooper and Watson 1980). If each source emits a particular species unique to it (commonly called a tracer species), then a very simple tracer technique can be used (Friedlander 1977). Examples of tracers commonly used are lead and bromine from mobile sources, nickel from fuel oil, and sodium from sea salt. Often the necessary condition to use the latter method—that each source have a tracer species unique to itself—is not met in practice.

Microscopic identification models are similar to the CMB methods except that more information is included that distinguishes the source of the aerosol. Such chemical or morphological data include particle size and individual particle composition and are often obtained by electron or optical microscopy.

Multivariate Models. Multivariate models, including factor analysis models (Henry and Hidy 1979, 1982; Hopke 1981, 1985), rely on finding the underlying structure of large sets of particulate air quality data in order to determine the sources of the aerosol. Models based on factor analysis are the most widely used. Multivariate models operate by identifying bundles of elements whose concentrations fluctuate together from day to day, implying that these bundles come from a single “source.” When the composition of the hypothetical source is compared to the known composition of specific sources, it often becomes obvious what the group of cofluctuating chemical elements stand for. For example, lead and bromine concentrations are usually highly correlated because they are emitted primarily by the same sources (automobiles burning leaded gasoline). Thus, multivariate techniques identify groups of pollutants whose concentrations are correlated, and thus suggest the nature of the source. They do not rely on a detailed knowledge of the source fingerprint, a _ij, and can be used to refine estimates of the fingerprint.

Research intended to extend the power of receptor models for source apportionment is continuing, including development of methods to integrate measurement uncertainties into the analysis, incorporation of aerosol properties other than elemental composition, and inclusion of the effect of chemical reactions on secondary aerosol formation. Friedlander (1981) has proposed a method that includes a decay factor in the formulation of equation 3 to take into account the chemical transformation of aerosols such as PAHs. This method is limited to first-order decay and assumes a knowledge of the average pollutant residence time in the atmosphere. A more general technique that can be used to estimate the source contributions to secondary aerosol mass loadings using receptor modeling techniques would be of use.

Attempts to circumvent some of the limitations of receptor models include hybridization with source-oriented models that rely on mass emission rate data from the pollutant sources. Applications of this sort have met with varying success (Gartrell and Friedlander 1975; Pace 1979; Yamartino and Lamich 1979). Yamartino and Lamich used a hybrid model to identify areas with noninventoried emissions of CO. In theory, the source strengths of noninventoried or unknown emitters could be estimated using a hybrid technique, although uncertainty and sensitivity analyses need to be conducted on this type of model. Pace used a microinventory approach, assuming that most of the aerosol mass at a receptor is derived from nearby emitters, and was able to account for total suspended particulate concentrations (TSP) with a standard error of 17 percent. Note that hybrid models require additional data (that is, source strengths and meteorological data), but the prospects of added accuracy can justify the added effort. Hybrid models potentially could account for the secondary aerosols present in source apportionment studies. Further development and use of hybrid models is clearly warranted, since they potentially retain the strength of receptor-oriented as well as source-oriented (analytical) models.

■ Recommendation 1. Research should continue on the development of receptor models, especially on the hybridization of these models with other types of models. The inclusion of aerosol properties and formation should also be pursued.

Deterministic Models

Deterministic air quality models describe in a fundamental manner the individual processes that affect the evolution of pollutant concentrations. These models are based on solving the atmospheric diffusion/reaction equation, which is in essence the conservation-of-mass principle for each pollutant species (Lamb and Seinfeld 1973):

(4)

where c _i is the concentration of species i; U ¯ is the wind velocity vector; D _i is the molecular diffusivity of species i; R _i is the net production (depletion if negative) of species i by chemical reaction; S _i is the emission rate of i from sources; and n is the number of species. R can also be a function of the meteorological variables. In essence, this equation states that the time rate of change of a pollutant (term 1) depends on convective transport (2), diffusion (3), chemical reactions (4), and emissions (5). As discussed in the chapter on pollutant transport (Samson, this volume), the closure problem makes it necessary to approximate this equation, usually by K-theory (Lamb 1973):

(5)

where the braces 〈 〉 indicate an ensemble average, and K is the turbulent (eddy) diffusivity tensor. Pollutant dry deposition and ground level emissions enter the system as boundary conditions. Except for the simplest source distributions and chemical reaction mechanisms, 〈S _i 〉 and R, there are no analytical solutions to equation 5. If equation 5 can be simplified for a particular application, it is usually advantageous to do so.

An examination of equation 5 shows that if there are no chemical reactions, (R=0), or if R is linear in (c _i ) and uncoupled, then equation 5 forms a set of linear, uncoupled differential equations for determining the pollutant concentrations. This is the basis of the transport only and transport with linear chemistry models (which, for brevity, will be called transport models). Transport models are suitable for studying the effects of CO sources and primary particulate emissions sources on air quality, but not for studying reactive pollutants such as O₃, NO₂, HNO₃, and secondary organic species. Transport of nonreactive pollutants is described in detail by Samson (this volume) and will be discussed here only briefly.

Lagrangian Models. There are two distinct reference frames from which to view pollutant dynamics. The most natural is the Eulerian coordinate system which is fixed at the earth's surface. In that case, a succession of different air parcels are viewed as being carried by the wind past an observer who is fixed to the earth's surface. The second is the Lagrangian reference frame in which the frame of reference moves with the flow of air, in effect maintaining the observer in contact with the same air parcel over extended periods of time. Because pollutants are carried by the wind, it is often convenient to follow pollutant evolution in a Lagrangian reference frame, and this perspective forms the basis of

Lagrangian trajectory and Lagrangian marked-particle or particle-in-cell models. In a Lagrangian marked-particle model, the center of mass of parcels of emissions are followed, traveling at the local wind velocity, while diffusion about that center of mass is simulated by an additional random translation corresponding to the atmospheric diffusion rate (Lamb and Neiburger 1971; Cass 1981).

Lagrangian trajectory models can be viewed as following a column of air as it is advected in the air basin at the local wind velocity. Simultaneously, the model describes the vertical diffusion of pollutants, deposition, and emissions into the air parcel (figure 3). The underlying equation being solved is a simplification of equation 5:

Figure 3.

Schematic diagram of a Lagrangian trajectory model: (A) The column of air being modeled is advected at the local wind velocity along a trajectory path across the modeling region. Within the moving air parcel, the model describes the important processes (more...)

(6)

Trajectory models require spatially and temporally resolved wind fields, mixingheight fields, deposition parameters, and data on the spatial distribution of emissions. Lagrangian trajectory models assume that vertical wind shear and horizontal diffusion are negligible. Other limitations of trajectory and Eulerian models are discussed by Liu and Seinfeld (1975).

Gaussian Plume Model. One of the basic and more widely used transport models based on equation 5 is the Gaussian plume model (figure 4). Gaussian plume models for continuous sources can be obtained from statistical arguments or can be derived by solving:

Figure 4.

Diffusion of pollutants from a point source. Pollutant concentrations have separate Gaussian distributions in both the horizontal (y) and vertical (z) directions. The spread is parameterized by the standard deviations (σ) which are related to (more...)

(7)

where Ū is the temporally and vertically averaged wind velocity; x, y, and z are the distances in the downwind, crosswind, and vertical directions, respectively; and K _yy and K _zz are the horizontal and vertical turbulent diffusivities, respectively. For a source with an effective height H, with emission rate Q, and a reflecting (nonabsorbing) boundary at the ground, the solution is:

This solution describes a plume with a Gaussian distribution of pollutant concentrations, where σ _γ (x) and σ _z (x) are the standard deviations of the mean concentration in the y and z directions (figure 3). The standard deviations are the directional diffusion parameters, and are assumed to be related simply to the turbulent diffusivities, K _yy and K _zz . In practice, σγ(x) and σ _z (x) are functions of x, Ū, and the atmospheric stability as discussed by Samson (this volume), Gifford (1961), and Turner (1964, 1967).

Gaussian plume models are easy to use, require relatively few input data, and are very quick computationally. Multiple sources are treated by superimposing the calculated contributions of individual sources to ambient concentrations at a given receptor site. It is possible to include the first-order chemical decay of pollutant species within the Gaussian plume framework. For chemically more complex situations, however, the Gaussian plume model simply fails to provide an acceptable solution. Because of its simplicity and because of its use by regulatory agents, the search for improvements to Gaussian plume models is still an active area of research.

Eulerian Models. Of the Eulerian models, the box model is the easiest to envision conceptually. Simply, the atmosphere over the modeling region is perceived as a well-mixed box, and the evolution of pollutants in the box is calculated following conservation-of-mass principles including emissions, deposition, chemical reactions, and a changing mixing (or inversion-base) height (figure 5).

Figure 5.

Schematic representation of a box model based on the conservation-of-mass equation. The stationary box allows pollutants to be advected into and out of the modeled region. The height of the modeling region can increase, accounting for an increase in the (more...)

Eulerian “grid” models are the most complex, but potentially the most powerful, air quality models, involving the least-restrictive assumptions, and are the most computationally intensive. Grid models attempt to solve a finite approximation to equation 5, including temporal and spatial variation of the meteorological parameters, emission sources, and surface characteristics. Grid models divide the modeling region into a large number of cells, horizontally and vertically, that interact with each other by simulating diffusion, advection, and sedimentation (for particles) of pollutant species. Input data requirements for grid models are similar to those for Lagrangian trajectory models but, in addition, require data on background concentrations (boundary conditions) at the edges of the grid system used. Eulerian grid models produce pollutant concentration predictions throughout the entire airshed, which can be examined over successive time periods to observe the evolution of pollutant concentrations and how they are affected by transport and chemical reaction.

Modeling Chemically Reactive Compounds. A number of compounds, regulated as well as unregulated, are formed in the atmosphere by a series of complex, nonlinear chemical reactions. Often the compounds formed are more harmful than their precursors. In this case it is necessary to use models that not only describe pollutant transport, but also complex chemical transformation, R($\bar{c}$,t) in equation 4. Examples of secondary pollutants are O₃, PAN, HNO₃, and many aerosols. Such models are also required to study the dynamics of chemically reactive primary pollutants such as benzene, and pollutants that are primary as well as secondary in origin, for example, NO₂ and formaldehyde. Addition of the capability to describe a series of interconnected chemical reactions greatly increases the computational requirements for computer storage as well as for time, and also the input data requirements. The increased computational demands arise because the evolution of some species must be followed simultaneously. One major difficulty encountered when numerically calculating the change of pollutant concentrations due to chemical reaction is that the characteristic lifetimes of the different pollutants are distributed over many orders of magnitude. Such systems are said to be computationally “stiff” and are generally time-consuming to solve. A suitable numerical solution scheme must be chosen when confronted by a stiff system. Some simplifications and procedures, described below, have been devised to help reduce the computational time, but the required computational time is still a deterrent to the widespread use of photochemical air quality models. Another major difficulty is that accurate, speciated emissions inventories for each of the many reactive air pollutants are needed. Such detailed emission inventories have been developed for only a few geographic areas, most notably Los Angeles, California (figure 6), and a chemically detailed regional inventory for the eastern United States.

Figure 6.

Emissions of NH₃, NO _x , HCs, and CO in the Los Angeles area during 1982. A spatially gridded, time-resolved, and speciated emissions inventory is necessary for conducting air quality modeling studies involving chemically reacting compounds. (Based on (more...)

Box, Lagrangian trajectory, and Eulerian grid models can be developed to include nonlinear chemical reactions. Box models, the first candidate, assume that the pollutants are mixed homogeneously within the modeling region, an assumption that is often inappropriate. Trajectory and grid models resolve pollutant dynamics on a much finer scale and have been used widely and with considerable success (Reynolds et al. 1973; Lloyd et al. 1979; Reynolds et al. 1979; Seinfeld and McRae 1979; Chock et al. 1981; Carmichael et al. 1986; Russell and Cass 1986). Chemically reacting models have received much attention because they are being used to plan air quality control programs in areas with photochemical smog problems and to study acid deposition. They will also provide the key to predicting (and hence controlling) the formation and dynamics of secondary aerosols and trace, but potentially harmful, gases in the atmosphere, such as PAN, HNO₃, and nitrous acid (HNO₂).

Temporal and Spatial Resolution of Empirical and Analytical Models

Short-term contact with high pollutant concentrations as well as chronic exposure to lower concentrations can affect health, and the effects can be different. The choice of air quality models to be used for assessing health risks should reflect the temporal scale over which the health effects are expected to occur. The temporal and spatial resolution of models can vary from minutes to a year and from several meters to hundreds of kilometers. The minimum meaningful temporal and spatial resolution of a model is determined by the input data resolution and the structure of the model. Statistical models generally rely on several years' worth of measurements of hourly or daily pollutant concentrations. The resolution of the input data would represent the minimum resolution of a statistical model. Resolution of analytical models is limited by the spatial and temporal resolution of the emissions inventory, the meteorological fields, and the grid size chosen for model implementation. The grid size of the model often corresponds to the grid size of the inventory and meteorological fields. For modeling urban air basins, the size of individual grid cells is on the order of a few kilometers per side, whereas for modeling street canyons, the cell size must be reduced to a few meters on each edge. The temporal resolution of urban models ranges from about 15 minutes to a few hours or days. Multiple time intervals can be combined to form pollutant concentration predictions for longer periods of time.

More than one model may be appropriate, if not necessary, for the analysis of a given problem. Choice of models will be influenced by available resources (time, computational facilities, and funds). A stepped approach is suggested, starting with simpler models (that is, Gaussian plume, rollback, or box models) for approximations, and building up to more sophisticated model formulations when greater precision is needed.

Turbulent Transport and Diffusion

Numerical schemes developed to calculate the rate of transport of pollutants suffer from numerical diffusion and dispersion (Roache 1976). Numerical diffusion and dispersion result from using a discrete approximation to the governing system of equations, and are manifested by the computed solution being artificially spread out and ripples being formed. Numerous numerical schemes have been developed to minimize the errors induced, including higher-order finite-difference, finite-element, particle-in-cell, filtered, and spectral methods. In reviewing the use of different advection routines for solving the atmospheric diffusion equation 5, McRae et al. (1982c), Chock and Dunker (1983), and Schere (1983) compare accuracy and computational requirements.

Closure of the atmospheric diffusion equation 5, can be accomplished by utilizing the K-theory, or gradient/diffusion, hypothesis (see Samson, this volume). K-theory is used to describe pollutant fluxes on scales smaller than the size resolvable by conventional wind velocity measurements, thus representing the many processes involved in turbulent diffusion. An obvious need when applying this theoretical treatment within an air quality model is some algorithm for establishing the value of the eddy diffusivity tensor, K. As a result of the large variety of processes involved, there are also a number of methods to parameterize the horizontal and vertical diffusion coefficients (Yu 1977). The usual limitation to the accuracy of diffusion calculations in a practical application is determined by the extent of measurements on the atmospheric structure taken during the period to be simulated. For most model applications, such as source apportionment studies, the number of observed factors relating to atmospheric turbulence are few and include only ground-level winds and temperatures, surface roughness, and cloud cover. At a few locations and times the inversion base (or mixing height), wind speeds aloft, and vertical temperature gradient may also be known. As the amount and accuracy of information characterizing atmospheric structure increases, confidence in model predictions of dispersion increases.

Complex Terrain: Street Canyons

Complex terrain represents an obstacle to modeling the transport of pollutants because large variations in the wind velocity occur over distances smaller than can be resolved by the wind sampling network. Classic examples are valleys and street canyons where the buildup of pollutants can be substantial. In urban areas, build-up of CO in street canyons is of interest and has been addressed by a number of authors (for example, Johnson et al. 1973), and transport in street canyons is discussed by Samson (this volume). These studies did not address the effect of chemical reactions on pollutant concentrations.

In regions subject to photochemical smog, modeling the transport and distribution of O₃ and the impact of automotive NO _x emissions in street canyons needs to be addressed for two reasons: to determine population exposure to these pollutants, and to explain the difference between predicted pollutant concentrations calculated when using a grid size much larger than the size of a street canyon and observed concentrations measured by air monitoring stations that may be located within the influence of the street canyon (Nappo et al. 1982). As an example, air quality models now in use for studying the formation and transport of O₃ and NO₂ use grid sizes of about 5 km square, compared to a street canyon width of a few tens of meters.

■ Recommendation 2. Chemical interactions, especially of reactive pollutants, need to be included in street canyon models.

Removal Processes

Removal processes, particularly dry deposition and scavenging by rain and clouds, are a major factor in determining the dynamics and ultimate fate of pollutants in the atmosphere. (See also, Atkinson, this volume.) The potential for health and environmental impacts is thus closely tied to the physical processes removing pollutants from the atmosphere.

Dry Deposition. Dry deposition occurs in two steps: the transport of pollutants to the earth's surface, and the physical and chemical interaction between the surface and the pollutant. The first is a fluid mechanical process, the second is primarily a chemical process, and neither is completely characterized at the present time. The problem is confounded by the interaction between the pollutants and biogenic surfaces where pollutant uptake is enhanced or retarded by plant activity that varies with time (Hicks and Wesely 1981; Hicks et al. 1983). It is very difficult to measure the depositional flux of pollutants from the atmosphere, though significant advances have been made in the last 10 years. Accurate mathematical description of the depositional process has, as a result, been advancing rapidly over the same time span.

Many factors affect dry deposition, but for computational convenience air quality models resort to using a single quantity called the deposition velocity, v _d , to prescribe the deposition rate. The deposition velocity is defined such that the flux F _i of species i to the ground is

F _i = v _d c _i (z _r ) (9)

where c _i (z _r ) is the concentration of species i at some reference height z _r , typically one to several meters. For a number of pollutants, v _d has been measured under various meteorological conditions and for a number of surface types. A basic problem with this parameterization is that it does not explicitly represent dry deposition as a complex linkage between turbulent diffusion in the surface boundary layer, molecular diffusion very near the surface, chemical reaction, and plant activity.

Early models used a value for v _d that remained constant throughout the day. However, measurements show that the deposition velocity increases during the day as the surface heating increases atmospheric turbulence and hence diffusion, and plant stomatal activity increases (Whelpdale and Shaw 1974; Wesely and Hicks 1977; Wesely et al. 1985). More recent models take this variation of v _d into account. In one approach, the first step is to estimate the upper limit for v _d in terms of the transport processes alone. This value is then modified to account for surface interaction, since the earth's surface is not a perfect sink for all pollutants. This has led to what is referred to as the resistance model (Wesely and Hicks 1977; Fowler 1978) that represents v _d as the analog of an electrical conductance

v _d (r _a +r _b +r _s )⁻¹ (10)

where r _a is the aerodynamic resistance controlled primarily by atmospheric turbulence, r _b is the resistance to transport in the fluid sublayer very near the plant surface, and r _s is the surface (or canopy) resistance (figure 7). Of the three resistances, r _a is essentially the same for all species, r _b is the same for gaseous species with the same diffusivities, though it can be considerably greater for aerosols, and r _s depends greatly on the surface affinity for the diffusing species. For example, HNO₃, which reacts rapidly with most surfaces, has a very low surface resistance, usually taken as zero (Huebert 1983; Huebert and Robert 1985; Walcek et al. 1986), whereas CO is not very reactive and has a high r _s . More recent models account for the variation of surface resistance and diurnal change in fluid mechanical transport. These parameterizations have been used to quantify the deposition flux of various compounds (McRae and Russell 1983; Walcek et al. 1986).

Figure 7.

The resistance model of deposition showing the three regions over which deposition is depicted to take place. The total resistance to deposition is the sum of the three and is analogous to an electrical system of series resistors.

Less attention has been devoted to studying the deposition of aerosols and how to effectively model their rate of deposition. Major differences between the deposition of gases and aerosols are that aerosols have a much lower diffusivity, the rate of gravitational settling can be significant for larger particles, and the surface resistance for aerosols is not determined by species reactivity. Particulate deposition velocities have been measured for a number of species, leading to parameterization of deposition velocities (Liu and Ilori 1974; Sehmel and Hodgson 1974; Hicks 1977; Slinn and Slinn 1981; Wesely et al. 1985). More fundamental work has been conducted for deposition to smooth surfaces (Sehmel 1971, 1980; Reeks and Skyrme 1976), and should be expanded to nonideal surfaces.

It is important to better understand the processes leading to the deposition of atmospheric aerosols, so that the concentrations of these aerosols can be properly estimated and the related health effects assessed. Research in this area should follow two paths: experimental measurements of aerosol deposition in the environment, especially actual aerosol velocities near surfaces; and modeling and parameterization of the fundamental physical processes. Results from these studies can be used in refining models for the apportionment of aerosol contributions between different source types and may aid the improvement of models for aerosol deposition in human lungs.

■ Recommendation 3. Better characterization of the processes leading to dry deposition of chemically reactive pollutants and aerosols is needed.

Scavenging by Rain, Fog, and Clouds. Wet removal, or precipitation scavenging, can be effective in cleansing the atmosphere of pollutants, and depends on the intensity and size of the raindrops (Martin 1984). Fog and cloud droplets can also absorb gases, capture particles, and promote chemical reactions (Adewuyi and Carmichael 1982; Chameides and Davis 1982; Levine and Schwartz 1982; Munger et al. 1983; Graedel 1984; Kumar 1985). Current research into these processes is concentrating on more fundamental descriptions of the absorption of pollutants by droplets and chemical dynamics, taking into account the species solubility, reactivity, and the fluid mechanics of a falling drop (Schwartz and Frieberg 1981; Drewes and Hale 1982; Jacob and Hoffmann 1983; Jacob 1985). Precipitation scavenging is not as important on an urban scale as on a regional scale and is not included in most urban-scale models. Fog chemistry can be important to human health on an urban scale, as evidenced in London in 1952 when thousands of persons died during an episode of excess industrial air pollution and fog. (Seinfeld 1986); however, no attempt has been made to model the relationship between pollutant emissions and fog chemical dynamics in an urban area.

■ Recommendation 4. Research into the development of “emissions-to-fog chemistry” models is needed and would be valuable for determining source/health effects relationships in the instances where fog in urban areas may lead to compounds harmful to human health.

Representation of Atmospheric Chemistry Through Chemical Mechanisms

A complete description of atmospheric chemistry within an air quality model would require tracking the dynamics of many hundreds of compounds through thousands of chemical reactions. Many of these compounds affect human health. Atkinson (this volume) gives an account of the number and complexity of the interactions taking place and provides insight into how much is known (and unknown) about the rate and products of these reactions (see also Atkinson and Lloyd 1984). There are so many reactive species, particularly organic compounds, and reactions, that it is infeasible to incorporate an explicit statement of all reactions for each species within the chemical mechanism used by urban air pollution models, even if atmospheric chemistry were completely understood. Fortunately it is not necessary to follow every compound. Instead, a compact representation of the atmospheric chemistry, commonly called a chemical mechanism, is used. The chemical mechanism represents a compromise between using an exhaustive description of the chemistry and being computationally tractable. It is the principal method for modeling the dynamics of reactive compounds such as O₃, NO₂, hydroxy radicals, and PAN in air quality models. The level of chemical detail is balanced against the computational time that increases as the number of species and reactions increase. Instead of the hundreds of species present, chemical mechanisms use on the order of 50 species and about 100 reactions to accurately describe the principal features of atmospheric chemistry.

Three different types of chemical mechanisms have evolved in an attempt to simplify the HC (organic) chemistry: surrogate (Graedel et al. 1976; Dodge 1977), lumped (Falls and Seinfeld 1978; Atkinson et al. 1982), and carbon bond (Whitten et al. 1979; Killus and Whitten 1982). These mechanisms were developed primarily to study the formation of O₃ and NO₂ in photochemical smog but can be extended to compute the concentrations of other pollutants believed to be noxious.

Surrogate mechanisms use the chemistry of one or two compounds in each class of organics to represent the chemistry of all the species in that class; for example, the explicit chemistry of butane might be used to describe the chemistry for all the alkanes.

Lumped mechanisms are based on the grouping of chemical compounds into classes of similar structure and reactivity; for example, all alkanes are lumped into a single class whose reaction rates and products are based on a weighted average of the properties of all the alkanes present. Only the dominant chemical features and reactions of each lumped class are used to describe reaction steps. By taking advantage of the common features of the organics and free radicals, lumping allows one to greatly reduce the number of required species and steps needed to accurately describe the prevailing pollutant chemistry. For example, as illustrated in table 1, the various alkanes (C _n H_{2 n} + ₂) react with OH in a similar manner to form alkyl radicals (C _n H_{2 n +1}). The alkyl radical then reacts rapidly with O₂ to form an alkyl peroxy radical (C _n H_{2 n + 1}O^· ₂). (See Atkinson, this volume.) When expressed explicitly, this involves over 30 species and 20 reactions. This would lead to a mechanism too large to be used in an air quality model. By lumping, the series of reactions can be reduced to one, and the number of required organic compounds is reduced to two. This is a tremendous savings in computational time while maintaining the necessary chemical detail. The carbon bond mechanism, a variation of a lumped mechanism, splits each organic molecule into functional groups using the assumption that the reactivity of the molecule is dominated by the chemistry of each functional group.

Table 1.

Example of Lumping Alkane-OH Reactions.

Leone and Seinfeld (1985) analyzed the performance of six chemical mechanisms by comparing, quantitatively, why they behave differently under identical conditions. They were able to identify critical areas that, when improved, would bring the predictions of each mechanism into much closer agreement. This analytical technique is suited to developing and testing new chemical mechanisms.

Given the importance of the chemical mechanism to the outcome of model evaluation, source apportionment, and control strategy studies, it is bothersome that the predictions of different chemical mechanisms do not always agree. Shafer and Seinfeld (1986) compared NO _x /HC/O₃ relationships, and the sensitivity of six chemical mechanisms to initial and boundary conditions. They found that the predicted HC control needed to reduce O₃ concentrations from 0.4 to 0.12 parts per million (ppm) varied among the six mechanisms as did the sensitivities to perturbations in boundary and initial conditions. The effect of chemical mechanisms on model predictions, particularly the NO _x /HC/O₃ relationship, should be studied further. Different mechanisms should be embedded within a complete airshed model and the results compared.

New, or at least modified, reaction mechanisms will be required as the knowledge of atmospheric chemistry increases and as attention is turned toward less abundant, but potentially harmful, trace gases. For example, the chemistry of dinitrogen pentoxide (N₂O₅) and the NO₃ radical is just unfolding (Graham and Johnston 1978; Atkinson et al. 1984; Winer et al. 1984; Russell et al. 1985; Johnston et al. 1986), as are the reactions leading to nitroarenes, which are strong mutagens (Pitts and Winer 1984) and other organic compounds.

■ Recommendation 5. Research into the development of new chemical mechanisms is essential to advancing the accuracy and scope of air quality model predictions, especially as interest grows in the effects of noncriteria pollutants.

Aerosol Dynamics

Inclusion of a description of aerosol dynamics within air quality models is of primary importance because of the health effects associated with fine particles in the atmosphere (Schlesinger, as well as Sun, Bond, and Dahl, this volume), visibility deterioration, and the acid deposition problem. Although the effects of aerosols on health are not fully understood, it is known that aerosols can contain strongly mutagenic and toxic compounds such as PAHs, nitro-PAHs, and lead. Aerosol dynamics differ markedly from gaseous pollutant dynamics in that particles come in a continuous distribution of sizes and can coagulate, evaporate, grow in size by condensation, be formed by nucleation, or sediment out. Furthermore, the species mass concentration alone does not fully characterize the aerosol. The particle size distribution (which changes with time) and composition determine the fate of particulate air pollutants and their environmental and health effects. Particles of about 1 µm or smaller in diameter penetrate the lung most deeply and represent a substantial fraction of the total aerosol mass. The origin of these fine particles is difficult to identify because much of that fine particle mass is formed by gas-phase reaction and condensation in the atmosphere (figure 8).

Figure 8.

Example of size distribution of an urban aerosol showing the three modes containing much of the aerosol mass. The fine mode contains particles produced by condensation of low-volatility gases. The mid-range, or accumulation mode, results from coagulation (more...)

Simulation of aerosol processes within an air quality model begins with the fundamental equation of aerosol dynamics which describes aerosol transport (term 2), growth (term 3), coagulation (terms 4 and 5), and sedimentation (Friedlander 1977):

(11)

where n is the particle size distribution function; $\bar{U}$ is the fluid velocity; I is the droplet current that describes particle growth and nucleation due to gas-to-particle conversion; v is the particle volume; β is the rate of particle coagulation; and C is the sedimentation velocity. The chemical composition of the aerosol also changes with size. Gelbard and Seinfeld (1980) present a framework for modeling the formation and growth of aerosols by sectioning the size distribution, n, into discrete ranges. Their sectional model can then follow the size and chemical composition of an aerosol as it evolves by condensation, coagulation, sedimentation, and nucleation. However, application of these methods to a simulation of the formation, growth, and transport of all the components of an urban aerosol from their emission sources using a fundamental description of the aerosol dynamics and chemistry has yet to be completed. Instead, as a first step, investigators have chosen to model the major individual aerosol components such as sulfates (Cass 1981; Carmichael et al. 1986), nitrates (Russell et al. 1983; Russell and Cass 1986), and carbonaceous aerosol (Gray 1986). These studies predicted aerosol mass and chemical composition, not the aerosol size distribution (that is, how the aerosol is distributed over specific size ranges). A primary reason for not proceeding with the size-resolved calculation is the lack of adequate data for input and verification.

Middleton and Brock (1977) attempted to model the evolution of the aerosol size distribution and mass in Denver, Colorado, using as input a parameterized rate of condensable aerosol formation along with an inventory for primary aerosol emissions. They concluded that part of the disagreement between predictions and observations was due to errors in the aerosol emissions inventory. This problem is universal and will hinder any attempt to perform a full simulation of atmospheric aerosol dynamics. Construction of an accurate inventory of aerosol emissions will be an arduous task, although adoption of standards for particulate matter less than 10 µm in diameter (PM-10) should hasten inventory development, making it possible to conduct more accurate modeling studies.

The chemistry leading to the formation of some secondary organic aerosols has been clarified recently (Grosjean and Friedlander 1980; Grosjean 1984, 1985; Hatakeyama et al. 1985) to the point that it is now feasible to conduct preliminary modeling studies of secondary organic aerosol formation in the atmosphere. More research is required before it is possible to predict the formation of all the secondary organic particulates. Once procedures for modeling secondary organic aerosol formation have been developed and accurate field data become available, it should be possible to construct size-resolved and chemically resolved modeling programs for use in health effects, control strategy, and source apportionment work. The development of aerosol process models will be a very important area of research over the next decade.

Heterogeneous gas/aerosol interactions, such as the reaction between HNO₃ and sea salt (Duce 1969),

HNO₃(gas) + NaCl(solid or aqueous) → HCl(gas) + NaNO₃(solid or aqueous)

have been included in very few modeling studies to date (Russell and Cass 1986). Pitts and Winer (1984) present evidence for heterogeneous reactions leading to the formation of very mutagenic, and possibly carcinogenic, nitro-PAHs (see also Atkinson, this volume). Study of gas/aerosol reaction rates under controlled laboratory conditions has been attempted in a few cases (Baldwin and Golden 1979; Jech et al. 1982). Model calculations by Chameides and Davis (1982) indicate that the presence of aerosols can affect concentrations of gaseous species. Dahneke (1983) presents an expression that can be used to estimate the reaction rate between aerosols and gases, given experimental measurements that characterize the fraction of collisions occurring between gases and aerosols that result in reaction. Additional research into methods for incorporating chemical reactions at aerosol surfaces into chemical mechanisms is warranted.

Development of aerosol process models incorporating gas-to-particle conversion of harmful compounds, heterogeneous reactions, and particle growth is perhaps the most critical research area for advancing air quality models to clarify relationships between sources and health effects. Given increased field data, our current understanding of processes governing the production and growth of aerosols is such that major advances in the use of aerosol process models should be realized in the next few years.

■ Recommendation 6. Size-resolved and chemically resolved measurements of atmospheric aerosols are needed to test and further develop aerosol process models.

Approaches for Testing Model Performance

At present, there are no formal standards or universally accepted tests used to validate model performance. One reason for this is that there are a wide variety of models developed for different purposes. For example, a model designed to predict annual average pollutant concentrations may not be easily compared to a model designed to predict hour-to-hour pollutant variations. Model evaluation procedures must account for the intended model application and formulation.

Some criteria have been suggested for measuring model performance (Brier 1975; Bowne 1980; American Meteorological Society 1981; Fox 1981). Fox (1981) identified three classes of performance measures:

1.

Analysis of paired predicted versus observed concentrations for particular locations and times.

2.

Ability of the model to predict observed peak concentrations.

3.

Comparison of the cumulative frequency distributions of the unpaired predicted and observed concentrations.

Bencala and Seinfeld (1979) developed a computer program for performing statistical analyses. Table 2 lists some of the performance measures applied to the results of four photochemical models.

Table 2.

Performance Statistics for the Caltech, SAI, LIRAQ, and ELSTAR Models.

Each model's adherence to fundamental principles should be scientifically evaluated (Fox 1981). For models based on the atmospheric diffusion equation 5, this means that mass should be conserved and that physically unrealistic predictions such as negative concentrations do not occur. Graphic comparison of the predicted and observed concentrations together can be helpful in diagnosing the nature of the differences between observed and predicted pollutant levels. A final method for model evaluation involves comparing the results of one model against those of another, or to a particular case for which an analytical solution is available.

Data Requirements

The data requirements for conducting model evaluation studies differ greatly among model types. In many cases, lack of data is the major barrier to model evaluation and successful source impact studies. Acquiring the data can be an arduous task. For a Gaussian plume model, the required data could include as little as the mean wind velocity, source emission rate, atmospheric stability (and hence diffusivity), and effective source height (Weber 1982). At the other extreme, a large grid model that incorporates chemical kinetics requires considerably more information before it can be tested—millions of pieces of input data including (McRae and Seinfeld 1983):

1.

Vertically resolved, three-dimensional wind fields for every hour of simulation;

2.

An hourly emissions inventory for every species in each cell of the modeling region;

3.

Hourly temperature, relative humidity, and mixing depth data for each cell;

4.

Land use or surface roughness;

5.

Vertically resolved initial concentration for every species in each cell;

6.

Boundary conditions (concentrations) for each species;

7.

Solar radiation data and cloud cover; and

8.

Measured hourly ground level data for comparison against model predictions.

This list is not exhaustive, nor does every model application require all this information in the detail prescribed. Acquisition of the necessary data can be the major obstacle to a successful evaluation and application program. Nevertheless, the input data acquisition process is vital because the quality of the data ultimately limits the maximum possible quality of the model evaluation study results.

Meteorological data such as surface wind velocity, temperature, relative humidity, and cloud cover are more widely available than emissions inventories, though upperlevel wind and temperature data are scarce. It is necessary to collect ambient air quality data, for specifying initial and boundary conditions as well as for comparison with model predictions. Often, the experimental data necessary for model evaluation are not available, and field studies must be executed specifically to collect the data required. Examples of field experiments conducted for such a purpose include the Los Angeles Reactive Pollutant Program (LARPP) (Zak 1982); a study to acquire regional HNO₃, aerosol NO₃ ^– and PAN concentrations (Russell and Cass 1984); the Sulfate Regional Experiment (SURE) (Electric Power Research Institute 1981); Regional Air Pollutant Study (RAPS) (Schiermeier 1978); and a program designed to measure particulate carbon concentrations for use in an air quality model evaluation study (Gray 1986). Studies such as these are costly, time-consuming, and significantly increase the effort required to confirm model performance.

Data must be in a form compatible with the model. It may be necessary to interpolate pollutant concentration and meteorological data that are collected at a few discrete locations and times to develop continuous concentration and meteorological fields for model use. Some interpolation methods have been suggested for this purpose (see for example Goodin et al. 1979a). Particular care must be taken in developing wind fields from sparse data because the wind field should be mass consistent. Objective analysis procedures are used to reduce the divergence of interpolated wind fields (Endlich 1967; Dickerson 1978; Goodin et al. 1979b).

A field of input values generated by interpolation over a large geographic area from sparse data is intrinsically uncertain and leads to uncertainty in model predictions. Upper-level variables such as temperature structure (mixing depths), wind fields, and concentration data are particularly susceptible to this uncertainty (Russell and Cass 1986). Upper-level pollutant concentration data are also seldom available except from a few intensive measurement programs—for example, LARPP (Zak 1982) and RAPS (Schiermeier 1978) (see also Edinger 1973; Blumenthal et al. 1978). In the absence of measurements aloft, upper-level initial conditions must be estimated in a way that is consistent with the ground-level measurements and known chemical principles (Russell et al. 1986). Chemically reacting models also require that HC measurements, usually measured as total hydrocarbon concentration (THC), be split into the organic gas classes used by the model (Reynolds et al. 1979; McRae and Seinfeld 1983; Russell and Cass 1986). HC splitting factors either can be based on relative abundance of HCs in the emissions inventory or on detailed atmospheric chemical measurements (see, for example, Graedel 1978; Lamb et al. 1980; Grosjean and Fung 1984).

Analysis of Model Performance

Sensitivity/uncertainty analysis has been applied to estimating the effect that uncertainties in the inputs and reaction mechanisms have on model predictions (Falls et al. 1979; Dunker 1980, 1981; Seigneur et al. 1981; McRae et al. 1982b; Tilden and Seinfeld 1982). Tilden and Seinfeld (1982) present the sensitivity of O₃ and NO₂ predictions to variations in inputs of up to 50 percent, showing the complex relationship of the response. Dunker (1980, 1981) uses analysis of the partial derivatives to describe model response to scaling initial conditions, boundary conditions, and ground-level emissions. For small perturbations of input parameters, the model responded linearly, although nonlinearities were present for larger changes. Model sensitivity to initial conditions decreases with time, suggesting that multiday simulations should be conducted. Multiday simulations are necessary if control strategy or source apportionment calculations are planned. Otherwise, the initial conditions will dominate the results. However, for grid models, long simulations can become sensitive to uncertainties in boundary conditions. Modeling regions should be designed to minimize this effect over the area of most interest and also to capture the effect of inflow boundary conditions (McRae 1981). Sensitivity analysis should also be used to direct experimental research by identifying the model components, such as rate constants and physical parameterizations, that are major causes of uncertainties in predictions.

Extensive model evaluation studies have been conducted for a number of models beginning with the Gaussian plume models and continuing to the state-of-the-art urban and regional photochemical, air quality models. Turner (1964) used a multiple-source Gaussian model to predict 24-hr averaged concentrations of SO₂ in the Nashville, Tennessee, area. He included a first-order chemical decay of SO₂ to form sulfates. Fifty-eight percent of the predictions were within 30 µg/m³ of the observations, and the root mean square (RMS) error was 95 µg/m³. During the period, concentrations ranged from near zero to about 600 µg/m³. The correlation coefficient between predictions and observations was 0.54. As evidence of the advancement in air quality modeling capabilities, compare this to the evaluation statistics of present-day photochemical models (table 2) that describe transport as well as reaction. Gaussian plume models have also been used to estimate CO, NO _x , and particulate matter concentrations. More recent evaluations of Gaussian plume model performance have been made by Smith (1984) and Irwin and Smith (1984).

In an early application of a mass conservation model based on the numerical solution of equation 3 with simple chemical kinetics, Lamb (1968) calculated CO values in Los Angeles for September 23, 1968. The RMS error was 6.8 ppm, or 50 percent of the mean. Disagreement was ascribed to the lack of a vertically resolved wind field and the need for a more complete description of the chemistry, although present knowledge of emission levels and atmospheric chemistry would indicate that atmospheric production of CO is of lesser importance. Sklarew and coworkers (1972) used a particle-in-a-cell, Lagrangian model to examine the same set of data, reducing the RMS error to 2.7 ppm. They also compared model results to observations for NO₂. Agreement was disappointing for NO₂, presumably because of the need for a more accurate description of atmospheric chemistry.

Recently developed photochemical air quality models, in the Lagrangian trajectory as well as the Eulerian grid form, use more complete descriptions of atmospheric chemistry based on the condensed chemical mechanisms described in the section on Modeling Approaches for Individual Processes. Other improvements include more accurate descriptions of pollutant dry deposition, vertical transport, and more detailed input data. Examples of Lagrangian photochemical trajectory models include Environmental Lagrangian Simulation of Transport and Atmospheric Reactions (ELSTAR) (Lloyd et al. 1979), and the Caltech model (Seinfeld and McRae 1979; McRae et al. 1982a; Russell et al. 1983), which are vertically resolved, the kinetic model developed by Whitten and Hogo (1978), and Empirical Kinetic Modeling Approach (EKMA) developed for the EPA. Each of these models has been used to estimate the effect of emission controls on air quality.

Lloyd et al. (1979) tested the chemical mechanism of the ELSTAR model against smog chamber data. Then they used the data from the LARPP field study, which was specifically designed for testing Lagrangian models, to evaluate the model. Statistical comparison of predicted and observed O₃ and NO₂ concentrations is given in table 2. Seinfeld and McRae (1979) first tested the Caltech photochemical trajectory model in Los Angeles using data from a very smoggy (episode) day—June 27, 1974. Further evolution of the model included testing its capability to predict the formation of aerosol NO₃, PAN, and HNO₃ (Russell et al. 1983; Russell and Cass 1986). In order to reduce the effect of initial conditions, multiday simulations were used in the latter evaluation study.

A model for the long-range transport of nitrogen compounds (Bottenheim et al. 1984) also was developed to predict PAN and NO_$\bar{3}$ concentrations using the SURE data base. Predicted NO_$\bar{3}$ loadings agreed in magnitude with observations, but PAN predictions were generally high.

Lagrangian trajectory models can accurately predict pollutant concentrations and test emission control alternatives. They take relatively little time to execute on a computer (up to 500 or more times faster than grid models), but they produce pollutant concentration predictions only along a single air parcel trajectory. It is often desirable to study the areawide dynamics of pollutants, especially for population exposure calculations, and to present a more complete picture of the effects of source controls (for example, NO _x controls can have a very different effect on O₃ near the source than far away). Rather than run thousands of trajectory simulations, it is more efficient to use Eulerian grid models such as the System Applications, Inc. (SAI) Urban Airshed Model (Reynolds et al. 1973; Seigneur et al. 1983), the regional sulfate transport and reaction model (Carmichael and Peters 1984a,b), the Livermore Regional Air Quality (LIRAQ) model (MacCracken et al. 1978), and the Caltech Airshed Model (McRae et al. 1982a; McRae and Seinfeld 1983). Also, Eulerian grid models are subject to fewer fundamental constraints.

Both the Caltech and the SAI urban air quality models are vertically resolved, as opposed to the vertically integrated LIRAQ model (Duewer et al. 1978; MacCracken et al. 1978) that has been used in San Francisco in two forms. LIRAQ I is used to model relatively nonreactive pollutant transport (for example, CO, SO₂). LIRAQ II, using a lumped chemical mechanism similar to that of Hecht et al. (1974), is used for computing photochemically reactive pollutant concentrations such as O₃.

Extensive statistical evaluations of the SAI and Caltech models were conducted using data for the June 26–27, 1974, smog episode in Los Angeles. McRae and Seinfeld (1983) calculated the uncertainty in the Los Angeles basin emissions data for the 1974 period to be±20 percent for CO, ±15 percent for NO _x , and ±25 percent for reactive hydrocarbons (RHCs). Results of the statistical analysis for these models is given in table 2. They applied the Fortran program developed by Bencala and Seinfeld (1979). Graphic results are shown in figure 9. For the June 26–27 period, both the Caltech and the SAI models tended to underpredict peak O₃ and NO₂ concentrations (table 2). Part of the disagreement between predicted and observed NO₂ concentrations can be ascribed to interference of HNO₃ and PAN with the measurement devices. Given the uncertainties in the meteorological and emissions data, the agreement is quite good. Input data quality is a definite limitation to model performance. Russell and coworkers (1986) updated the chemical mechanism and added the capability to predict ammonium nitrate aerosol concentrations within the Caltech model. They showed the model's ability to predict inorganic NO₃ and PAN, as well as O₃ and NO₂ concentrations. Extensive summaries of many recent model evaluation studies have been made by Dennis and Downton (1984) and Wagner and Ranzieri (1984).

Figure 9.

Plot of predicted (——) and observed (●) O3 and NO _x concentrations (in parts per hundred million, pphm) at downtown Los Angeles during the June 26–27, 1974, modeling study showing the accuracy of model predictions. (Adapted (more...)

Model evaluation is a vital part of any air quality modeling study. A major limitation is accurate input data, especially on unobserved, upper-level initial and boundary conditions, as well as meteorological parameters. Testing of the more advanced models has shown that they are capable of predicting O₃, NO₂, HNO₃, and PAN as well as nonreactive pollutant concentrations directly from data on meteorological conditions and pollutant emissions.

■ Recommendation 7. The most advanced air quality models should be compared against each other and against field experimental observations using a detailed and accurate set of input and verification data. Reasons for any discrepancies should be identified and conflicting findings reconciled.

Population Exposure Calculations

Advanced air quality models are powerful tools for use in exposure studies that seek to relate health effects to individual pollutant emission sources. These models can also provide a framework for predicting future exposures resulting from changing emissions. Advanced air quality models, however, have not yet been used widely for population exposure calculations. A preliminary demonstration of the potential for such use is contained in the 1982 Air Quality Management Plan (AQMP) for Los Angeles. Here the SAI urban airshed model was used to estimate the change in population exposure to O₃ that would result from a set of planned emissions reductions (South Coast Air Quality Management District 1982). That study presents a spatially resolved map of the change in population “dosage,” defined as

(12)

where P(x,y) is related to the local population density; F is a function that equals 1 if c(x,y,t) —the concentration at (x,y) —is greater than or equal to a threshold concentration K; and T is the number of hours in the simulation. Note that this is not the usual definition of dosage but is the definition used in that particular study. Thus dosage has units of ppm-person-hours and measures the cumulative amount of air pollutant to which a population is exposed above a threshold value, K. Likewise, they calculated “exposure,” where exposure (E) is defined by

(13)

Again, this is not the usual definition of exposure, but is a measure of how long people are exposed to pollutant concentrations over a threshold value K. Units of exposure are typically person-hours. A finding of this study was that although emission reductions should decrease O₃ exposure in most portions of the basin, some locations would be adversely affected. The above calculation is a first step toward the development of integrated source/exposure studies.

Source Apportionment and Control Strategies

Receptor Models. Receptor models, by their formulation, are effective in determining the source contributions to particulate matter concentrations. The sources contributing to airborne particle loadings have been identified in Washington, D.C. (Gordon et al. 1981), St. Louis (Gatz 1978; Hopke 1981), Los Angeles (Gartrell and Friedlander 1975; Cass and McRae 1983), Portland, Oregon (Watson 1979), and Boston (Hopke et al. 1976; Alpert and Hopke 1980, 1981), as well as other areas, such as the desert (Gaarenstroom et al. 1977). In one effort, a number of researchers were convened to use various receptor models to examine the sources of the Houston aerosol (Stevens and Pace 1984).

Hopke (1981) used size-resolved data and factor analysis to analyze coarse and fine particle fractions in the St. Louis atmosphere. On the basis of data taken at a receptor station on the Washington University campus, he found that 15 percent of the fine particulate matter was from motor vehicles, although little of the coarse particle fraction was derived from mobile sources. An unusually high contribution from paint was attributable to a paint pigment factory in the city, thus showing how a receptor model can be used to identify unusual sources.

Gordon and coworkers (1981) used a chemical mass balance (CMB) technique and varied the number of elements used in the balance to test the sensitivity of the model's results to the choice of marker elements. They found that using nine carefully chosen chemical elements for their calculations gave results comparable to a similar analysis using data on 28 or more chemical components.

In one of the earlier applications of the CMB technique, Gartrell and Friedlander (1975) estimated the sources of particulate mass in Los Angeles atmosphere during the Aerosol Characterization Experiment (ACHEX) (Hidy 1975). In this case, mobile sources accounted for at least 6 percent of the aerosol mass at the Pomona receptor site. As noted previously, receptor models are not directly suited for determining the source of secondary aerosols such as nitrates and secondary organics. According to the 1974 emissions inventory for the Los Angeles area (McRae and Seinfeld 1983), mobile sources are responsible for 62.3 percent of the NO _x emissions (precursor to NO_$\bar{3}$ aerosols). If one apportioned the measured NO$\bar{3}$ to sources in proportion to their contribution to the basin-wide NO _x inventory, then the mobile source contribution in the study by Gartrell and Friedlander (1975) increases to 35 percent of the total aerosol mass. In addition, part of the unidentified organic compounds, ammonium, and water may be attributable to mobile sources. This is a rough calculation, indicating that source attribution of secondary aerosol species poses a problem for receptor models and a challenge for future research.

Core and coworkers (1981) combined the use of a receptor model developed by Watson (1979) and a source-oriented model as part of a particulate air quality control strategy analysis in Portland, Oregon. Using CMB techniques, they identified source contributions to the ambient aerosol and then used dispersion modeling to confirm those source contributions. Then, they compared the results obtained with the two models and revised the particulate emission inventory input into the source/dispersion model. Then, they used the revised emissions inventory in dispersion modeling of emission control strategy alternatives. This approach utilized the strengths of the two types of models. Receptor models are not suitable for predicting the outcome of arbitrary perturbations in some sources but not others. They are, however, good for determining the sources of particulate matter when an accurate emissions inventory is not available. Dispersion models, on the other hand, are well suited for modeling the impact of a wide variety of emissions changes that would result from changed emission control regulations but rely totally on an input emissions inventory, which may be uncertain or difficult to obtain. Figure 10 shows the mass apportionment of the aerosol in Portland, Oregon, and the aerosol emissions inventory before and after adjustment using the CMB receptor modeling study. Major deficiencies were identified and improved in the emission inventory for wood burning and road dust.

Figure 10.

Emissions inventory of aerosol before and after using chemical mass balance modeling to improve the estimates of emission rates. (Adapted with permission from Core et al. 1981, and the American Chemical Society.)

An extension of the simultaneous use of receptor and source models that merits investigation follows the above methodology except that a chemically reactive transport model is used to estimate the formation of secondary aerosols such as sulfate, NO_$\bar{3}$, ammonium, and secondary organic carbon. Products of this research would include estimates of source contributions to secondary aerosols, improved emissions-estimates for the aerosol precursors, and determination of the gross conversion rates of gases to aerosols (see Recommendations 1 and 4).

Source-Oriented Modeling Studies. Nonreactive, mass conservation models based on solving equation 3, including Gaussian plume models, have been used extensively for source apportionment, control strategy analysis, and source impact modeling of nonreactive pollutants such as CO, and of carbonaceous aerosol. Recently, Gray (1986) used a particle-in-cell model to estimate the sources that contribute to primary carbonaceous aerosol concentrations and further used the model to define optimal strategies for controlling aerosol carbon. Models of this type have been used to study the sources that contribute to secondary aerosol sulfate formation (Cass 1981).

Source apportionment, when applied to nonreactive pollutants, has a very clear meaning; that is, source apportionment means determining what proportion of pollutant measured at a receptor site was emitted from a given source. Source apportionment has a much more complex meaning when discussing secondary pollutants that are formed by series of complex atmospheric reactions, rather than being directly emitted from sources. These pollutants include O₃, PAN, and secondary aerosols. The reason is that an incremental change in the emissions of precursors to the formation of a secondary pollutant need not lead to a proportional change in the pollutant concentration, if any change at all results. For example, NO _x and HCs are precursors to the formation of O₃, but increasing the emissions of one precursor can have a very different result than increasing the other. In fact, decreasing NO _x emissions may increase local O₃ concentrations while at the same time decreasing O₃ concentrations downwind.

A common graphic representation of the relationship of maximum O₃ concentrations to initial precursor concentrations of-NO _x and HCs is the O₃ isopleth diagram (figure 11).

Figure 11.

O₃ isopleth diagram showing the response of O₃ concentrations to changes in initial NO _x and nonmethane hydrocarbon concentrations (methane is not included because of its low reactivity). The varying response to NO _x reductions is dependent upon the (more...)

Analysis of the effect of emission control on the improvement in O₃ air quality is further complicated by the fact that the effect of controlling two emission sources together is not necessarily equal to the incremental improvement from controlling one source added to the incremental improvement from controlling the other source separately. This clouds the issue of definitively assessing the impact that a single source has on air quality in that its impact dynamically responds to changes in other sources and to varying meteorological conditions.

Mathematical modeling of photochemical air pollution can delineate the relationship that a source has on air quality. For example, a model that has undergone successful evaluation using the actual emissions inventory for the period studied can have the inventory revised to exclude all emissions from a source. The second set of calculations using this perturbed inventory should simulate what the pollutant concentrations of the reactive as well as unreactive species would have been without that source. In this fashion, researchers can assess the impact individual sources have on air quality. A similar procedure is followed to estimate the improvement that can be expected from controlling source emissions to varying degrees, simulating implementation of control options or strategies.

Photochemical modeling studies that have examined the effect of specific sources on air quality are scarce. Notable examples are Chock et al. (1981), who used a trajectory model to study the impact of automotive emissions in Los Angeles, and Tesche et al. (1984), who used the SAI airshed model to evaluate emission controls proposed for the Los Angeles area.

The trajectory study of Chock and colleagues used the ELSTAR model described previously, in this case examining air quality changes in Los Angeles due to reductions in automotive emissions of HCs, NO _x , and CO. Two trajectories were modeled, each 8 or 10 hr long. Results indicate that drastic improvement (O₃ reduced from 0.20 to 0.04 ppm and NO₂ from 0.17 to 0.10 ppm for one of the trajectories) would result from reducing automotive NO _x emissions from 3.8 to 2.45 g/mile and HCs from 9.67 to 1.94 g/mile. Further NO _x reduction was found to be ineffective for controlling O₃. Pitts et al. (1983) commented on the conclusion that further NO _x reductions would not be beneficial, noting that short trajectories (of a few hours) are extremely sensitive to initial conditions, many of which are uncertain.

Tesche and colleagues present the results of a number of model calculations, depicting the result of 18 emission control possibilities in the Los Angeles basin. Among the conditions modeled were:

1.

1987 (AQMP) emissions inventory expected in the absence of further emission controls;

2.

All elevated emissions removed from case 1, above (that is, power plant emissions removed);

3.

Refinery emissions removed from case 1, above;

4.

Mobile source emissions removed from case 1, above;

5.

No emissions at all.

In each of these calculations, the base case inventory used was the 1987 AQMP inventory, run 1 (South Coast Air Quality Management District and Southern California Association of Governments 1982). Of the three cases where a source type was removed, removing mobile sources (run 4) showed the greatest decrease in O₃ (lowered from 0.194 to 0.138 ppm). That study also provides a classic example of the nonlinearity of the photochemical system. The net improvement in O₃ for cases 2, 3, and 4 added together is 0.04 ppm. The reduction in NO _x and RHC emissions, when the three cases are combined, is 93 percent and 71 percent, respectively. However, model calculations indicate that a 100 percent emissions reduction should improve O₃ by 0.13 ppm, three times more than would be expected by addition of the effect of individual cases that add up to nearly a complete elimination of the emission sources.

In many of the simulations conducted by Tesche et al. (1984), NO _x control appears to be a relatively ineffective approach to controlling O₃. This is a point that is being debated in the scientific literature at present (Pitts et al. 1983). Trajectory simulations by Russell and Cass (1986) indicate that NO _x controls will reduce O₃, NO₂, PAN, and inorganic NO_$\bar{3}$ formation in the eastern portion of the Los Angeles basin. The debate on the effectiveness of NO _x controls is, perhaps, at present the most critical question to be answered by urban air quality models, and further research into the issue is critical for understanding how to control O₃ and related photochemically generated species. (See Recommendation 7.)

A motivation for developing advanced transport models and transport and reaction models is to create an ability to guide decisions regarding the most cost-effective set of control techniques to obtain a desired air quality (that is, optimal control strategy development). In general, least-cost control strategy development attempts to solve the mathematical programming problem (Cass and McRae 1981):

Find $\bar{x}$ such that C($\bar{x}$) is minimized, subject to Q[E(x,t)M(x,t)]≤S

where $\bar{x}$ is a set of control measures that can be applied to the sources E, minimizing the cost C, such that the air quality Q, is less than or equal to a prescribed level S. M represents the changing meteorology, and t is time. Q and S may include a number of species.

Usually, blind application of the best available control technology to the largest sources, as is often proposed, is not the most cost-effective means for improving air quality. Cass and McRae (1981) showed that applying the best available technology to the largest sources first could cost about $70 million/yr to meet a 10 µg/m³ sulfate level as contrasted with about $40 million for a least-cost strategy, or a savings of about half. Other studies have shown similar results. Kyan and Seinfeld (1974), following the work of Trijonis (1974), illustrate an economically optimized control strategy for photochemical pollutants.

The large data requirements and computational times make it expensive to test a large number of emission control strategies using the most advanced photochemical airshed models. Instead, realizing that the precursors of O₃ and NO₂ are HC and NO _x , least-cost control strategies can be estimated by identifying the least-cost approach to achieving various levels of HC and NO _x emissions and then using the advanced air quality models to identify the perturbed emissions level that will meet the desired air quality standard. Cass and McRae (1981) summarize the techniques for devising least-cost control strategies. One question not adequately addressed in the literature is whether or not an optimal strategy for reducing O₃ on high-episode days will be as effective at reducing O₃ on typical days.

Future Uses

As new technologies change pollutants and emission patterns, it is important to be able to answer, in advance, the question “What will be the probable effects of future emissions of novel substances?” Photochemical models are ideally suited for predicting the changes, a priori. Specific applications for models would be to test the effect of enlarging the fleet of diesel-powered vehicles on particulate and gas-phase pollutants, changing fuel compositions, or converting the vehicle fleet to methanol fuel.

One reason for advancing the technology base built into mathematical models is to be able to answer questions that will arise in the future. Given the lag time of several years between initiation of model development and proof of model performance, it is necessary to work continually on extending model capabilities. Development periods of four or more years can be expected. Typically, once a particular air quality problem has reached the point of public debate, the time scale allowed for technical analysis of the problem is shorter than the time needed to develop new modeling tools from scratch. Yet, without the appropriate tools for conducting a competent engineering analysis, inefficient—or worse, ineffective —costly decisions will be made. One current policy problem now awaiting completion of an advanced air quality model is that of acid deposition control.

In addition to source apportionment studies, air quality models can be used to identify potential areas of research by identifying gaps in our knowledge. Also, models can predict concentrations of trace gases that would be difficult to observe experimentally, thus alerting researchers to possible undetected problems.

It is clear that much time has been devoted to developing and evaluating advanced photochemical models (see earlier sections on Modeling Approaches for Individual Processes and Model Evaluation) and that much can be gained if these models are put into effective use by government regulatory agencies. One barrier to such use is manpower problem; there are very few organizations capable of conducting a source apportionment study that involves chemically reacting pollutant emissions (Cass and McRae 1981). Although further use of advanced models for the design of optimal control strategies, alone, would appear capable of identifying economic savings well in excess of the cost of conducting those studies, there is often no mechanism to pay for this necessary effort.

Modeling Large-Scale Processes

The advance in very powerful computers has made it possible to start thinking about modeling extremely large-scale transport and reaction systems in some detail, such as the problem of acid deposition in eastern North America. On yet a larger scale are the global circulation models which include a description of atmospheric chemistry to estimate how the chemical composition of the atmosphere will change with time because of increasing industrial and mobile source activity. Such models can help answer questions surrounding the increased emissions of novel substances such as fluorocarbons or long-term impacts of more mundane substances such as CO and CO₂. The questions addressed in this case often involve global-scale health effects such as the increase in skin cancer that would occur if greater amounts of ultraviolet solar radiation were to reach the earth's surface because of stratospheric O₃ depletion. The technical barriers facing the development of extremely large-scale models are essentially the same as for urban-scale models, magnified by problems of data collection on a global scale.

Modeling Small-Scale Processes

Often the information desired from modeling studies depends on processes that occur on spatial scales much smaller than the resolution of most urban air quality models. The modeling of NO _x air quality in street canyons involves small-scale processes of this sort. Introduction of point-source emissions into grid-based air quality models likewise involves a mismatch between the high concentrations that in fact do exist near the source versus the lower concentrations computed by a model that immediately mixes those emissions throughout a grid cell of several kilometers on each side. Because of computational time constraints, it is often impractical to fully describe the processes that take place on a scale smaller than the main model grid (subgrid scale), but one must be able to ensure that answers obtained from large-scale calculations are correct over the spatial averaging scale adopted by the model.

In urban-scale modeling, the usual grid dimensions are on the order of 1 to 10 km, with ground-level cell heights of 10 to 100 or more meters. Measured pollutant concentrations, against which model predictions are compared, however, are point values, taken a few meters above the ground, and these can be directly affected by nearby sources. This situation can frustrate comparisons to model predictions of directly emitted pollutants such as CO and NO or rapidly reacting secondary pollutants such as O₃ and NO₂. Concentrations of slowly reacting secondary pollutants such as HNO₃ would be less affected. One needs better methods to reconcile the differences between large-grid, volume-averaged predictions and point measurements (see Nappo et al. 1982).

How can the treatment of small processes be improved? Treatment of large point sources (for example, power plants) in urban-scale photochemical models can be handled in two general ways: (1) much like area sources where the emissions are mixed instantaneously throughout a cell, or (2) by separately treating an expanding, reacting plume that interacts with the atmosphere outside the plume, while maintaining its integrity. In an evaluation of the SAI urban airshed model using both approaches, Seigneur et al. (1983) found little difference for the regional dynamics of O₃ in Los Angeles. This may not be the case in all situations, especially when viewing the impact of major point sources in other geographic areas or when the concern is for air quality very near the source.

Point sources that dominate emissions in a specific area, such as offshore oil production platforms, may have to be treated in great detail. For reacting plumes—those containing NO _x , HCs, or possibly SO _x — the large concentration gradients that exist make the macro- and the micro-scale mixing processes important to the overall dynamics of pollutant evolution.

■ Recommendation 8. Additional research is needed on near-source dispersion and reactions of pollutants for inclusion in plume models.

Indoor/Outdoor Pollutant Relationships

Air quality models have traditionally dealt with calculating the effect of pollutant sources on outdoor air quality. However, much of the time people are indoors, either at home, at work, or in a car (National Research Council 1981). Thus, indoor pollutant concentrations make a major contribution to personal time-weighted pollutant exposure (Sexton and Ryan, this volume). Indoor air quality models currently are being developed to bridge the gap, relating the pollutant concentrations indoors to outdoor air quality, indoor emissions, ventilation rates, indoor transport, and indoor chemistry. Key questions are, “To what extent do pollutants derived from outdoor sources interact with indoor emissions, and what are the products of those interactions?”

As in outdoor situations, receptor-oriented and transport (source) models can be used to estimate source impacts on indoor air quality (Turk 1963; Shair and Heitner 1974; Borazzo et al. 1987; Sexton and Hayward 1987). Constraints and limitations on the two approaches indoors are similar to those discussed previously for outdoor applications. However, some unusual chemical constituents can be found at high concentrations indoors (for example, formaldehyde, radon, and tobacco smoke), as well as the traditional outdoor pollutants (CO, NO₂, O₃, and particulars matter).

The usual approach to indoor air quality modeling has been to apply a mass balance equation, similar to equation 5. For a single-compartment model this becomes (National Research Council 1981)

(14)

where V is the volume of the structure (or room), q ₀ and q ₂ are the rates at which air is brought into the building from outdoors through a ventilation system or by infiltration, respectively (figure 12), and q ₁ is the air recirculation rate. Both the makeup air (q ₀ ) and the recirculated air may be filtered such that the pollutant concentration of the filtered air is (1−F) times that entering the unit. The characteristic filtration efficiencies are F ₀ and F ₁ for the makeup air filter and recirculated air filter, respectively. S represents indoor emission sources, and R is an indoor sink term. Multicompartment models involve a system of similar coupled differential equations. Mass balance models have been used to successfully relate indoor air quality to outdoor pollutant levels, especially for nonreactive gases such as CO. However, agreement for reactive gases such as O₃ and SO₂ has not been as close (National Research Council 1981). Most indoor air quality models have yet to use as sophisticated a description of the chemical kinetics as have their outdoor counterparts.

Figure 12.

Indoor air quality model, including mass balance on pollutants and air. (Adapted with permission from Shair and Heitner 1974, and the American Chemical Society.)

A potential area for research involves studying the effect that chemistry has on indoor pollutants. The concentrations of some pollutants indoors will behave much differently than those outdoors because of the magnitude of the concentrations, artificial lighting, and the large surface areas for deposition. Another interesting question is “How will the pollutants emitted indoors, such as formaldehyde, react with vehicle-related pollutants drawn from outside, such as O₃ and NO₂?”

One factor that will complicate the use of indoor air quality models arises from the fact that different buildings (and rooms) vary tremendously in surface reactivity, humidity, ventilation, filtration, and diffusion rates. Input parameters for mass balance models should be measured for each individual building used in a study. Differences among buildings pose a problem for receptor models, too. Source signatures must be identified for each building.

Given the significant contribution that indoor pollutant concentrations add to personal exposure, it is evident that attention should be focused on determining the sources of pollutants found indoors. Realizing the critical role that outdoor pollutants play, indoor/outdoor air quality relationships should be further defined, and the sources of the indoor pollutants identified. By linking the results from outdoor air quality source apportionment studies with similar studies using models that relate indoor air quality to that outdoors, it should be possible to identify the effect of outdoor sources on indoor air quality, and the related human exposure, even for reactive gases. Results of combined indoor/ outdoor studies can be used for setting outdoor air quality standards that consider the effect of outdoor air quality on indoor pollutant levels. Ultimately, indoor/outdoor air quality models can be used to devise optimal strategies for controlling emission sources in a way that is more directly related to human exposure.

■ Recommendation 9. Further research is needed into the use of models that relate indoor exposure to outdoor air quality. The procedures outlined by Sexton and Ryan (this volume) should be useful in guiding future studies of the relationship between emission sources and human exposure.