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Mathematical Modeling of the Effect of Emission Sources on Atmospheric Pollutant Concentrations ARMISTEAD G. RUSSELL Carnegie Mellon University Development of Air Quality Models / 162 Components of Exposure / 163 Source/Receptor Relationships / 163 Historical Perspective / 165 Emission Source Characteristics / 165 Categories of Air Quality Models / 167 Empirical/Statistical Models / 167 Deterministic Models / 169 Temporal and Spatial Resolution of Empirical and Analytical Models / 173 Modeling Approaches for Individual Processes / 174 Turbulent Transport and Diffusion / 174 Complex Terrain: Street Canyons / 175 Removal Processes / 175 Representation of Atmospheric Chemistry Through Chemical Mechanisms / 177 Aerosol Dynamics / 179 Model Evaluation / 181 Approaches for Testing Model Performance / 182 Data Requirements / 182 Analysis of Model Performance / 184 Application of Air Quality Models / 187 Population Exposure Calculations / 187 Source Apportionment and Control Strategies / 188 Future Uses / 192 Special Topics and Emerging Issues in Air Quality Modeling / 192 Modeling Large-Scale Processes / 192 Modeling Small-Scale Processes / 193 Indoor/Outdoor Pollutant Relationships / 193 Conclusion / 195 Summary of Research Recommendations / 196 ~ . , Air Pollution, the Automobile, and Public Health. @) 1988 by the Health Effects Institute. National Academy Press, Washington, D.C. 161

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162 Mathematical Modeling of Effect of Emission Sources Development of Air knowledge of the chemical and physical Quality Models When air pollution began to have a signif icant deleterious effect on human life, it became necessary to discover and under stand the links between emission sources and the air quality deterioration and health effects they cause. Only after the impacts of sources have been assessed correctly will it be possible to devise and implement ratio nal, convincing, and effective policies to improve air quality. Over $29 billion were spent in the United States in 1983 on air pollution abatement and control (Council on Environmental Quality 1984~. If a frac tion of that expense can be saved by better understanding the relation of air quality and health effects to emission sources, the monetary benefits will be tremendous. Knowledge of the relation between emis sions by a source and pollutant concentra tions in the air at later times and other places (that is, the source/receptor relation ship) is essential to calculating the exposure of humans to these pollutants and hence to predicting the health impacts resulting from these source emissions. Mathematical models have evolved as the most practical means to relate source emissions to the subsequent air pollution concentrations. Mathematical models integrate our Emissions (Johnson) ~~ Atmospheric chemistry (Atkinson) . ~ _ ~ 1 ===== Mathematical . air quality . model(s) (This chapter) . Transport . (Samson) _ =~ . Indoor and outdoor pollutant concentrations (Graedel) Figure 1. Steps required to link source emissions to health effects. processes ot pollutant dynamics Into a structured framework that can be used to explain the relationship between sources such as motor vehicle exhaust and the resulting impact on human health (figure 1~. The multistep process begins with char- acterizing the emissions. The second step is to accurately determine the effects that at- mospheric transport and chemical reactions have on pollutant concentrations. Mathe- matical models are ideally suited to this task. The next step is to correlate people's activities with pollutant concentrations and determine personal exposure. Exposure is related, through deposition in and absorp- tion by the respiratory tract tissues, to dose. Finally, dose is related to health ef- fects. Central to this process is the ability to accurately calculate the air quality contri- butions due to specific emission sources. This chapter reviews the development and current status of air quality models. It differs from previous reviews in emphasiz- ing the use of models in health-related studies. It also assesses the current state of air quality modeling technology. As a log- ical outcome, gaps in our current under- standing are highlighted and research op- portunities identified. Chemically reacting pollutant systems receive extra attention for two reasons: first, many of the signifi . .4, ~ , , Personal exposure and dose (*) *Sexton and Ryan Schlesinger Sun, Bond and Dahl Ultman Overton and Miller 'L it' 1 _ Health effects Relevant chapters in this volume are given in parentheses. Central to the process is a mathematical model to predict pollutant concentrations as a function of emissions. Depending on the study, more than one model may be required, for example, to predict indoor pollutant concentrations. Up to this point, mathematical modeling studies have been limited almost exclusively to the steps within the boxed area.

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Armistead G. Russell 163 cant components of automotive exhaust are very reactive and contribute to the forma- tion of secondary products that are of as much, or more, concern as the original components; and second, air quality mod- els that include descriptions of atmospheric chemistry are the most thorough and com- plete and will be the basis for future ad- vanced models. By comparing our present knowledge with current needs, we can identify what these advances are likely to be. This chapter is intended for researchers interested in relating automotive emissions to the resulting health effects, not primarily for specialists in air quality modeling, and is organized to show how mathematical models are useful for providing critical information needed by the health effects community. 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,tJ at point x and time t, and the presence of people: Exposure = f[P(x, t), crux, t)] where P(x,tJ represents the number of peo- ple at point x and time t inhaling a pollutant at concentration c~x,tJ. Sexton and Ryan (this volume) explain in detail the three components of personal exposure: magni- tude of the concentration, duration, and (if the exposure is a discrete event that recurs) frequency; or, more generally, the magni- tude c~x,tJ of the concentration as a func- tion 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 ex- posure takes place. This chapter discusses how air quality models can be used to determine how c~x,tJ 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 elim- ination is usually impractical or impossible. A more feasible method is needed to pre- dict the impacts of emission sources on air quality. Two distinctly different methods have been developed for making such pre- dictions: mathematical models and physical models. A mathematical air quality model simulates pollutant evolution by interrelat- ing 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 labo- ratory 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 trans- port 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 dep- osition at the ground, and varying meteo- rological conditions. On the other hand, by accurately describing the dynamics of pol- lutants as they travel from the many emis . . sion sites in a City to a samp ing, or recep- tor, site, a mathematical model can keep track of the separate contributions of the sources of pollutants that influence air qual- ity at a given location. The inputs to the calculation are the pollutant emission rates, and the output is the expected concentra- tions of the several atmospheric pollutants (figure 2~. Mathematical models used in air pollu- tion analysis fall into two types: empirical/ statistical and analytical/deterministic. In the former, the model statistically relates observed air quality data to the accompa- nying emission patterns, whereas chemis- try and meteorology are included only im- plicitly (Seinfeld 19751. In the latter, analytical expressions describe the complex transport and chemical processes involving air pollutants. The pollutant concentrations

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164 Mathematical Modeling of Effect of Emission Sources ~,~j~ i, ~ INPUTS Emissions Land use Topography Initial concentrations Background concentrations Meteorology Windfields Turbulence Temperature Humidity Mixing depth Precipitation Fog concentration Mathematical Model MODEL TYPES Empirical statistical Rollback Receptor models Analytical deterministic Transport Gaussian plume Lagrangian trajectory Marked particle Eulerian Photochemical Box model Lagrangian trajectory Eulerian grid OUTPUTS ~ Pollutant concentrations Source impacts Figure 2. Inputs, outputs, and types of models commonly used in air quality modeling studies. are determined as explicit functions of the meteorology, topography, chemical trans- formation, and source characteristics, which are inputs to the calculation. The subject matter of this chapter neces- sarily overlaps that of other chapters of this book. To minimize duplication, this chap- ter focuses on how mathematical models are used to predict pollutant concentrations as a function of emissions. Greatest atten- tion 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 auto . . . . motive emissions anc . reaction proc ucts depend on the presence of other anthrono- genic 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 ap- plication. The different types of air quality models that are available are reviewed in the next section along with possible ad vances 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 pollut- ant 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 frame- work. Many future advances in air quality modeling will come from better quantita- tive 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 eval- uated, as described in the succeeding sec- t~on. After a model has been evaluated, it is ready for use in conducting source appor- tionment, population exposure, and con- trol strategy studies, as discussed in the next section. Studies of this type are of great interest, but few comprehensive con- trol 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 rec- ommendations.

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Armistead G. Russell 165 Historical Perspective The driving force behind the development of mathematical air quality models has been the Clean Air Act (American Meteorolog- ical 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 mod- els motivated by the Clean Air Act are designed primarily to predict the concen- trations of pollutants such as carbon mon- oxide (CO), nitrogen dioxide (NO2), and ozone (03) 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 de- termined by transport but not by atmo- spheric 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 con- centrations 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 atmo- sphere. So far, modeling studies have con- centrated 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 ot emission sources. The past decade has seen rapid develop- ment 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. Em- pirical receptor-oriented models that use the chemical composition of ambient pol- lution samples as a tracer for pollutant ori- gin were introduced in the 1970s, but were initially applied in only a few cases. Because they accurately resolve source contribu . . . . tons 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 mo- dels for explaining relationships between sources and health effects. A particularly pressing issue that can be studied using pres- ent models is the relationship between the nitrogen oxide emissions (NO and NO2 and the sum is commonly symbolized schemat- ically as NOX) and organic gas emissions in the formation of O3 (the O3-precursor re- lationship-see Pitts et al. 1976; Chock et al. 1983; Pitts et al. 1983~. If resources are provided, the next decade should see mod- els that are able to describe the dynamics of aerosols and currently unregulated toxic gases and to resolve many current ques- tions 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 top- ics for further research. Emission Source Characteristics The composition of emissions from mobile sources is discussed in detail by Johnson,

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166 Mathematical Modeling of Effect of Emission Sources and atmospheric chemical transformations and transport are covered in chapters by Atkinson and Samson, respectively (all in this volume). It is important to realize that if the air quality model is to be an effective tool for predicting pollutant concentrations and health effects and devising strategies for controlling them, the essential characteris- tics of the sources must be retained within the model. For example, the dynamic be- havior of power plant plumes is very dif- ferent from that of automotive tail pipe emissions in that plumes are not immedi- ately dispersed by the motion of and tur- bulence surrounding the source, but rise hundreds of meters because of thermal buoyancy. Likewise, the chemical compo . . . . . . . . SltlOn 01 automotive emlSSlOnS IS quite C .11 ferent from that of power plant emissions. Consequently, it is useful to divide all sources into two categories: mobile and stationary. Most of the total mass of emis- sions from mobile sources comes from automobiles and trucks, but rail vehicles, ships, aircraft, motorcycles and off-the- road vehicles also make a contribution. Stationary sources are divided further into two classes: anthropogenic and natural emitters. It is imprudent to neglect stationary sources when characterizing the impact of mobile source emissions. Chemical com- pounds emitted from stationary sources react extensively with automotive emis- sions to form various substances in the air. A classic example is the formation of O3 in urban areas. NOx emissions (primarily from automobiles, trucks, and stationary source combustion) react with hydrocar- bons (HCs) from mobile and stationary sources to form O3 and other photochem- ical oxidants (Atkinson, this volume). Most mobile source emissions are gener- ated by combustion, but other noncom- bustion releases occur. Significant quanti- ties of HCs come from fuel evaporation, and particulate matter originates from tire wear, brake wear, and road dust. Auto exhaust contains NO, NO2, CO, organics (commonly referred to as HCs), NH3, and a variety of particulate species such as aero- sol carbon, lead (especially in older vehi cles), and bromine. Near the source, the pollutants are rapidly mixed by turbulence generated mechanically from the move- ment of the automobiles. After initial mix- ing, the pollutants move away from the road by convection, and are further dis- persed by atmospheric turbulence and transport. Stationary sources, such as power plants and industrial complexes, and natural sources such as forest canopies, emit HCs, NOx, sulfur oxides (SO2 and SO3, com- monly called SOx), NH3, particulate mat- ter, and CO. Large point sources often emit from tall stacks, and the momentum and buoyancy of the emitted gas can carry the pollutants above the mixed layer, re- ducing their local impact, but increasing their persistence in the atmosphere over long distances. Organic compounds and NOx emissions are both involved in reactions leading to the formation of 03, NO2, nitric aclct (HNO3), particulate nitrate (NOT ), peroxy- acetyl nitrate (PAN), and other oxidized and nitrated organic compounds, and can increase the oxidation rate of sulfur dioxide (SOT. Some of the compounds formed in the atmosphere by gas-phase reactions in- volving automotive exhaust compounds are mutagenic and potentially carcinogenic, for example nitroarenes (Pitts and Winer 1984), nitro-polycyclic aromatic hydrocar- bons (nitro-PAHs) (Grosjean et al. 1983), and nitroxyperoxyalkyl nitrates and dini- trates (Bandow et al. 1980; Atkinson et al. 1984~. Less effort has been devoted to de- veloping mathematical models that will . . . estimate concentrations anc . source contrl- butions to the formation of these toxic trace species for a number of reasons: these spe- cies are not regulated, few data exist to quantify their ambient concentrations, and the chemistry leading to their formation is not completely understood. The necessary data are beginning to be assembled, and the use of mathematical models to study the formation and transport of trace, muta . . . . genlc, anc . caranogenlc organic com- pounds will become an important activity in the future. Primary organic particulates, soot (also _ _ 7

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Armistead G. Russell 167 called elemental carbon or graphitic car- bon), lead, and bromine compounds do not participate extensively in the photochemi- cal reactions but can be affected by gas- phase pollutants. Studies are beginning to elucidate the extent of formation of second- ary atmospheric organic particulates and the conversion of compounds from one type to another while in the aerosol phase. For modeling purposes, there are two distinct types of emissions: unreactive and reactive. Unreactive emissions include CO, lead, soot, and some fraction of the organic particulates. (CO participates in photo- chemical reactions, but its concentration is determined predominantly by direct CO emissions. Pollutants are referred to as un- reactive if reactions do not appreciably af- fect their concentrations over the time scales being modeled.) Reactive pollutants include HCs, NOX, and SO2, which can react to form secondary pollutants such as 03, PAN, and aerosol sulfates. As will be discussed in the next section, it is often more efficient and sometimes necessary to use different types of mathematical models to describe the dynamics of these two cat- egories of pollutants. Categories of Air Quality Models Health effects can arise from exposure to a single pollutant species or from combined actions and interactions of a mixture of compounds the subject is exposed to. The health effects of short-term exposure to high concentrations may not be equivalent to those from longer contact with moderate levels of the pollutant of interest. These alternatives must be reflected in the choice of models used to establish connections between sources and ultimate health effects. First, the pollutants and the time and spatial scales of interest are defined, and then an appropriate Codeless is chosen. Models have been formulated in a number of ways. Each formulation involves certain approx- imations and has certain strengths and lim- itations. This chapter shows how models can be used for relating health effects to sources. Consequently, limitations and strengths are stressed to assist in choosing the most effective models to best utilize the available resources. If care is not exercised In Choosing a model, one of two undesirable outcomes may ensue: a model may be chosen that by its formulation is incapable of doing the job (such as using a nonchemically reactive model to estimate the concentrations of 03, PAN, and even NO2), or a model is chosen that is more complex and time-consuming than is necessary (such as a photochemical airshed model to estimate elemental carbon or CO levels in an area heavily impacted by mobile source emissions). Empirical/Statistical Models Mathematical air quality models are of one of two types: empirical/statistical or deter- ministic (figure 2~. Empirical/statistical models, such as receptor-oriented and roll- back models, are based on establishing a relationship between historically observed air quality and the corresponding emis- sions. 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 South- ern California Association of Governments 1982~. Linear rollback models assume that the highest measured pollutant concentra- tion is proportional to the basinwide emis- sion rate, plus the background value; that Is, Cmax = aE + Cb (1) where cmax is the maximum measured pol- lutant concentration, E is the emission rate, cb is the background concentration due to sources outside the modeling region, and a is the constant of proportionality. The con- stant a accounts for the dispersion, trans- port, deposition, and chemical reactions of the pollutant. Thus, the allowable emission rate, Ea' necessary to reach a desired ambi- ent air quality goal, c,t, using the linear rollback model can be calculated from

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168 Mathematical Modeling of Effect of Emission Sources Ea ca,- Cb _= (2) Eo CmaX - Cb where Eo is the emission rate that prevailed at the time that cmax was observed. Presum- ably, pollutant concentrations at other times would also decrease toward back- ground levels as emissions are reduced, and similar expressions can be written for relat- ing annual mean concentrations to emission rates. Obviously this is a very simplified approach, and its application is limited. Nonlinear processes such as chemical reac- tions and spatial or temporal changes in the emission patterns are not accounted for explicitly in the rollback model formula- tion. A second class of empirical/statistical models of continuing interest is the recep- tor-oriented model, used extensively for estimating source contributions to particu- late matter concentrations in a number of geographic areas (Friedlander 1973; Heis- ler et al. 1973; Gartrell and Friedlander 1975; Gatz 1975, 1978; Gordon 1980; Wat- son et al. 1981; Cass and McRae 1983; Watson 1984; Hopke 1985~. Nonreacting gases have also been tracked by receptor modeling methods (Yamartino 1983~. Re- ceptor models compare the measured chemical composition of particulate mat- ter concentrations at a receptor site with the chemical composition of emissions from the major sources to identify the source contributions at ambient monitor . . ng sites. There are three major categories of re- ceptor models: chemical mass balance, multivariate, and microscopic. Hybrid an- alytical 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 characteriza- tion data routinely collected at many sam- pling 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 concentra tions of compounds such as ionic species and carbon compounds. At a sampling (or receptor) site, the aerosol mass concentra- tion of each species i is n ~ aijS; i= 1, 2, . . . m (3) j=1 where ci is the mass concentration of species i at the receptor site; Sj is the total mass concentration of all species emitted by source category j as found at the receptor site; aij 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 ci mea- sured at the receptor site of interest and the coefficients aij that describe the chemical composition for the major sources are the inputs from which Sj, the mass apportioned to sourcej, is determined. Because aid char- acterizes 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 catego- ries 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 Sj. Chemical Mass Balance Methods. Given that the source fingerprints aid 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 tech- niques are used to solve for Sj. 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

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Armistead G. Russell 169 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 distin- guishes the source of the aerosol. Such chemical or morphological data include particle size and individual particle compo- sition and are often obtained by electron or optical microscopy. Multivariate Models. Multivariate mod- els, including factor analysis models (Henry and Hidy 1979, 1982; Hopke 1981, 1985), rely on finding the underlying struc- ture 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 compo- sition of specific sources, it often becomes obvious what the group of cofluctuating chemical elements stand for. For example, lead and bromine concentrations are usu- ally highly correlated because they are emitted primarily by the same sources (au- tomobiles burning leaded gasoline). Thus, multivariate techniques identify groups of pollutants whose concentrations are corre- lated, and thus suggest the nature of the source. They do not rely on a detailed knowledge of the source fingerprint, aid, and can be used to refine estimates of the fingerprint. Research intended to extend the power of receptor models for source apportion- ment is continuing, including development of methods to integrate measurement un- certainties 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 resi- dence time in the atmosphere. A more general technique that can be used to esti- mate the source contributions to secondary aerosol mass loadings using receptor mod- eling techniques would be of use. Attempts to circumvent some of the limitations of receptor models include hy- bridization with source-oriented models that rely on mass emission rate data from the pollutant sources. Applications of this sort have met with varying success (Gar- trell and Friedlander 1975; Pace 1979; Ya- martino 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, al- though uncertainty and sensitivity analyses need to be conducted on this type of model. Pace used a microinventory approach, as- suming 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 re- ceptor-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 pro- cesses that affect the evolution of pollutant

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170 concentrations. These models are based on solving the atmospheric diusion/reaction equation, which is in essence the conserva- tion-of-mass principle for each pollutant species (Lamb and Seinfeld 19731: dci -+ U Vci = V D`Vc at + Ri(Cl, C2, C3, en) + Si(x, t) i= 1, 2, 3, . . ., n (4) where ci is the concentration of species i; U is the wind velocity vector; Di is the mo- lecular diusivity of species i; Ri is the net production (depletion if negative) of species i by chemical reaction; Si 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 convec- tive transport (2), diffusion (3), chemical reactions (4), and emissions (5). As dis- cussed in the chapter on pollutant transport (Samson, this volume), the closure prob- lem makes it necessary to approximate this equation, usually by K-theory (Lamb 1973): foci) + (O . V OCR for page 161
Armistead G. Russell A Air parcel moving t , 4( x t) Lagrangian along trajectory_ ~ = - (( x t) coordinates A< T Column i ,~ -~ height , it(c) "` z H t) ,' l i ~ ' , LED '71 z(t) Mixing height ANY ~__ ~ . variation along ~x ~ JO ~ . trajectory path Euterian ~1 coordinates / V9C - K d Trajectory path do B 2 ~deli+ 2 zj R(c,)-i T i-2 zz~l. 1 Liz 1 2 Figure 3. Schematic diagram of a Lagrangian trajec- tory model: (A) The column of air being modeled is adverted at the local wind velocity along a trajectory path across the modeling region. Within the moving air parcel, the model describes the important processes affecting the pollutant (i) evolution and concentration (c) such as chemical reactions (R), deposition (VR)' emissions (E), and vertical diffusion (Knot). (B) Verti- cal resolution is gained by dividing the column into a number of cells in the vertical direction. height fields, deposition parameters, and data on the spatial distribution of emis- sions. Lagrangian trajectory models assume that vertical wind shear and horizontal dif- fusion are negligible. Other limitations of trajectory and Eulerian models are dis- cussed 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: - Bc 62c 62c U ~ = Kyy ~ 2 + Kzz ,~z2 (7) where U is the temporally and vertically averaged wind velocity; x, y, and z are the 171 distances in the downwind, crosswind, and vertical directions, respectively; and Ky and Kzz are the horizontal and vertical turbulent difFusivities, respectively. For a source with an effective height H. with emission rate Q. and a reflecting (nonab- sorbing) boundary at the ground, the solu- tion is: Y ~27,U(,y~x~az~x) P fx1 o ~ 2trzZ~x) xp 2(1i~:X' 1 (8) LIZ' This solution describes a plume with a Gaussian distribution of pollutant concen trations, where tTy(X) and Mix) are the standard deviations of the mean concentra tion in the y and z directions (figure 3~. The standard deviations are the directional dif fusion parameters, and are assumed to be related simply to the turbulent diffusivities, Kyy and K=z. In practice, crux) and a=(x) are functions of x, U. and the atmospheric stability as discussed by Samson (this vol ume), Gifford (1961), and Turner (1964, 1967~. Gaussian plume models are easy to use, // no''\ ~ \ X Figure 4. Diffusion of pollutants from a point source. Pollutant concentrations have separate Gaus- sian distributions in both the horizontal (y) and verti- cal (z) directions. The spread is parameterized by the standard deviations (a) which are related to the diffu- sivity (K).

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196 Mathematical Modeling of Effect of Emission Sources actual physical phenomena involved. Dep- osition processes and some aspects of aero- sol dynamics fall in this category. On the other hand, development of advanced chemical mechanisms is quite possible us- ing our present knowledge of atmospheric chemistry. Inclusion of aerosol processes within fu- ture air quality models was identified as a key area for future research, particularly because of the suspected health effects of small particles. The ability to relate particle size and composition to the original sources will be critical in future exposure and impact studies. By advancing air qual- ity modeling methods now, we will be able to answer questions that now face us and be situated to address, in a timely manner, questions that arise in the future. It is clear that models now can predict the dynamics of the regulated pollutants such as CO, NO2, 03, and some components of particulate matter directly from data on emissions and thus are well suited for defining source-air quality relationships for those pollutants. However, it is also clear that this capability has been extended to only a few of the many nonreguiateu pollutants that may be of interest to the health effects research community in the future. Inasmuch as regulation has been the principal driving force for model develop- ment, this is understandable. However, progress in expanding model capabilities could be encouraged if toxicologists and epidemiologists collaborated with physical scientists to specify the additional pollu . . . tents, concentrations, anc . averaging times of interest, so that air quality scientists could develop or modify models to suit the specific needs of the health effects research community and anticipate the demands likely to arise from future regulation. Clearly the research proposed here would involve a variety of disciplines. This coop- eration would lead to a better understand- ing of the sources of the pollutants that impact human health. ~. Summary of Research Recommendations Evaluating the present state of mathematical modeling as a means to relate emissions to air quality and consequently health effects points to a number of areas for promising research. How- ever, advances in mathematical air quality models are ultimately limited by our understanding of the basic physics and chemistry being described within the model. In this regard, Samson and Atkinson (both this volume) have identified research that would enhance mathematical modeling of air quality by improving the understanding of the underlying physical and chemical processes on which such models are based. We are currently able to describe mathematically the dynamics of unreactive pollutants in urban areas with a great deal of confidence. In addition, our ability to model NO2 and O3 is well advanced, though the issues that surround the effect of NOx controls on O3 air quality still should be resolved. Recommendations 5 and 7 (detailed below) would result in greatly increased confidence in model predictions and lead to answering major questions. Much of the limitation to developing a greater capability for defining source/air quality relationships is not due to the model itself, but rather to a lack of accurate data for use in the models. Processes affecting the formation and growth of aerosols are not nearly as well understood as processes involving the gas-phase alone. The ability to model aerosol dynamics is, likewise, relatively undeveloped. This is understandable. It was necessary to develop

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Armistead G. Russell 197 gas-phase models before attempting a complete description of aerosol processes, because the formation and growth of aerosols is directly affected by gas-phase compounds, whereas the gas-phase is only slightly affected by aerosols. Presently, photochemical air quality models are able to provide the basis for an aerosol processes model. Because of the importance of inhalation of aerosols to human health, an aerosol process model is essential in determining source/health effects relationships. Recommendation 6, below, would lead to rapid development of a comprehensive aerosol process air quality model. The final step in constructing a system for determining source/ air quality relationships for use in exposure studies involves devel- oping a comprehensive indoor air quality model, as described by Recommendation 9. The model envisioned would include gas- phase chemistry as well as aerosol dynamics, and hence relies on completing the first three projects. Completion of the four high-priority research recommendations listed below is essential to an improved understanding of relation- ships between sources and health effects. A number of moderate- and lower-priority research recommendations arising from consid- erations in the text are listed next. Undoubtedly there are others whose urgency and importance will command attention as the field evolves. The following recommendations emphasize research efforts that will rapidly increase the capability to apply air qua- lity models to describe the dynamics of air pollutants believed to be harmful to health, and to identify the sources of those pollutants. HIGH PRIORITY Recommendations Development of an accurate, condensed chemical mechanism Construction of an would increase the confidence in using models to assess source Advanced Chemical impacts on air quality and could be used to examine the dynamics Mechanism of compounds suspected of causing health problems. The mecha nism should accurately reproduce smog chamber experiments , , ~ , when the expected wall radical source is included and agree with a large explicit "master" mechanism that includes a detailed descrip tion of atmospheric chemistry as it is now understood. As discussed by Leone and Seinfeld (1985), the concentration predictions from that condensed mechanism (including trace radical species) as well as the relative production routes of various species such as O3 should be close to the predictions of an explicit mechanism over a variety of initial conditions and emission rates during the simula tion. The condensed mechanism must be small enough to be used in an urban air quality model. The mechanism should then be incorporated into one of the advanced air quality models, and research Recommendation 7 then should be pursued. Recommendation 7 The most advanced air quality models should be compared Model Comparison against each other and against field experimental observations, and Evaluation using a detailed and accurate set of input and verification data. Collection of the needed data is vital to air quality model develop ment. Reasons for any discrepancies should be identified. Input

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198 Mathematical Modeling of Effect of Emission Sources data preparation would need to be well documented and open to review. A major issue to be addressed as part of this study concerns the effect of NOx emissions on the formation of O3 (Pitts et al. 1983~. Previous modeling studies of the problem have been con- ducted with differing conclusions. It is very important to reconcile these conflicting findings, and this type of project is the most direct method to do so. Recommendations The scientific knowledge currently exists that would permit Aerosol Process development of models for basic atmospheric aerosol processes, Model Development but the atmospheric data needed to conduct preliminary tests of such a model are not available. What is required are size-resolved and chemically resolved aerosol measurements collected in a man ner that can be fully utilized for model development. A three-step procedure is suggested: a. Preliminary model calculations should be made using the limited data currently available to identify specific parameters that need to be well characterized during a large-scale aerosol measure ment experiment. b. A measurement program should be designed and conducted to obtain the data identified in step (a). c. The results of steps (a) and (b) could then be used for more detailed model development and more thorough model testing. The model should include reactions leading to highly toxic com pounds, such as PAH reactions with NOx. Recommendation 9 Indoor air quality models complementary to outdoor air quality Indoor Air Quality models are needed to relate indoor air quality and exposure to Modeling sources. Mathematical models are currently under development, along with characterization of important input parameters. Further work is needed, especially to advance model descriptions of gas-phase chemistry, deposition, and aerosol dynamics indoors. Receptor-oriented models have received less attention for indoor applications, although they could be a powerful tool for use in _ . ~ source apportionment studies. Results from indoor air quality studies that relate indoor pollutant concentrations to those out doors can be combined with similar studies on outdoor air to help develop air quality standards and conduct source-related health impact studies. MODERATE PRIORITY Recommendation 3 Dry deposition of chemically reactive air pollutants and aerosols Pollutant Deposition is an area of current research interest. Given the importance to the Modeling fate and impact of pollutants, and as a vital part of any modeling studies, better characterization of the process leading to deposition ~ ~ . would be valuable. This problem should be attacked using field experiments as well as laboratory analyses, complemented by derivation of new computer-based algorithms to be used for describing dry deposition processes based on fundamental physical principles. Laboratory analyses should focus on the mechanics of particle transport through boundary layers by making detailed

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Armistead G. Russell 199 particle velocity measurements near surfaces. Outdoor deposition measurements would benefit from improved instrumentation. Recommendation 1 Receptor models such as those using chemical mass balance Receptor Modeling techniques have proven to be very convenient tools for apportion ing the contributions of sources to atmospheric particulate matter concentrations. Combining receptor and source models appears to have great potential. Further studies using hybrid or combined models will benefit from the strengths of both types of models. Also, it may be possible to add the ability to identify the sources of secondary aerosols when using receptor models. Recommendation 2 Studies to date have concentrated on pollutant transport but not Pollutant Dynamics chemical interactions. Inclusion of chemical reactions within a in Street Canyons street canyon model is important to determine near-source effects on the concentrations of pollutants such as NO2 and O3. A field study in which reactive pollutants such as O3, NO, and NO2 and a tracer are closely monitored in and above a street canyon would provide the data required for testing a chemically reactive street canyon air quality model. LOWER PRIORITY Recommendation 4 Interactions between smog and fog droplets are known to Fog Chemistry increase fog acidity and acid deposition, although direct health effects are not well known. Smog/fog interactions will also affect the evolution of gas-phase pollutants. We should combine our knowledge of gas-phase and fog droplet chemistry into a single model to investigate how the interaction affects pollutant evolution in an urban atmosphere. Recommendation 8 Plumes may dominate pollutant concentrations in the near field, Reactive Plume and such as near a power plant or highway. Much of the work to date Subgrid Scale has considered chemically inert plumes, and the few reacting plume Modeling models have adopted extensive approximations. Given the reactiv ity of vehicular exhaust and the amount of time people spend on the road, it is important to gain a better understanding of the near source dispersion and reaction of pollutants. Acknowledgments I thank Drs. Glen Cass and Ken Sexton for their comments during the preparation of this manuscript and am grateful for the many helpful comments of the review- ers. Correspondence should be addressed to Armistead G. Russell, Department of Mechanical Engineering, Car negie Mellon University, Pittsburgh, PA 15213. References Adewuyi, Y. G., and Carmichael, G. R. 1982. A theoretical investigation of gaseous absorption by water droplets from SO2-HNO3-NH3-(:O2-HC1 mixtures, Atmos. Environ. 16:719-729. Alpert, D. J., and Hopke, P. K. 1980. A quantitative determination of sources in the Boston urban aero- sol, Atmos. Environ. 14:1137-1146. Alpert, D. J., and Hopke, P. K. 1981. A determina- tion of the sources of airborne particles collected during the regional air pollution study, Atmos. Environ. 15:675-687.

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