Air Pollution, the Automobile, and Public Health (1988)

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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

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.

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

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.

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,

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

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

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

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

170 concentrations. These models are based on solving the atmospheric di£usion/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 di£usivity 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<ci) = V ^<Ci) fit + Ri((cl), (C2), · · · (Cn)) + (Si(x, I)) i = 1, 2, 3, . . ., n (5) where the braces ( ) indicate an ensemble average, and K is the turbulent (eddy) di£usivity tensor. Pollutant dry deposition and ground level emissions enter the sys- tem as boundary conditions. Except for the simplest source distributions and chemical reaction mechanisms, (Si) 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 (ci) and uncoupled, then equation 5 forms a set of linear, uncoupled differential equations for determining the pollutant concentrations. This is the basis Mathematical Modeling of Effect of Emission Sources of the transport only and transport with linear chemistry models (which, for brev- ity, will be called transport models). Trans- port models are suitable for studying the e£ects of CO sources and primary particu- late 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 vol-  ume) and will be discussed here only briefly. Lagrangian Models. There are two dis- tinct 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 succes- sion 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 e£ect 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 evo- lution 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 veloc- ity, while diffusion about that center of mass is simulated by an additional random translation corresponding to the atmo- spheric diffusion rate (Lamb and Neiburger 1971; Cass 1981~. Lagrangian trajectory models can be viewed as following a column of air as it is adverted in the air basin at the local wind velocity. Simultaneously, the model de- scribes 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: SCi ~ BCi ~ = ~ Kzz ~ + Sift) + Ray, t) (~6) Trajectory models require spatially and temporally resolved wind fields, mixing

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).

172 Mathematical Modeling of Effect of Emission Sources Solar flux Transport U in C background Photochemistry ' (R) it, . . . . ·;' Emission Top of modeling region (val ia e in time) Mixed layer sources (S) ..., U Deposition Transport out C Figure 5. Schematic representation of a box model based on the conservation-of- mass equation. The stationary box allows pollutants to be adverted into and out of the modeled region. The height of the modeling region can increase, accounting for an increase in the height of the mixed layer. require relatively few input data, and are computationally intensive. Grid models at very quick computationally. Multiple tempt to solve a finite approximation to equation 5, including temporal and spatial variation of the meteorological parameters, emission sources, and surface characteris tics. Grid models divide the modeling re gion into a large number of cells, horizon tallv and vertically. that interact with each 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 frame- work. For chemically more complex situ- ations, however, the Gaussian plume model simply fails to provide an acceptable  solution. Because of its simplicity and be- cause 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 mod- els, 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 conser- vation-of-mass principles including emis- sions, deposition, chemical reactions, and a changing mixing (or inversion-base) height (figure 5~. Eulerian "grid" models are the most complex, but potentially the most power- ful, air quality models, involving the least- restrictive assumptions, and are the most , . . . other by simulating diffusion, advection, and sedimentation (for particles) of pollut- ant species. Input data requirements for grid models are similar to those for La- grangian trajectory models but, in addi- tion, require data on background concen- trations (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 Com- pounds. A number of compounds, regu- lated 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 pol

Armistead G. Russell 173 lutant transport, but also complex chemical transformation, R(c,t) in equation 4. Exam- ples of secondary pollutants are 03, 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 intercon- nected chemical reactions greatly increases the computational requirements for com- puter 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 en- countered when numerically calculating the change of pollutant concentrations due to chemical reaction is that the characteristic lifetimes of the different pollutants are dis- tributed over many orders of magnitude. Such systems are said to be computation- ally "stir' and are generally time-con- suming to solve. A suitable numerical so- lution scheme must be chosen when confronted by a stiff system. Some simpli- fications and procedures, described below, have been devised to help reduce the com- putational time, but the required computa- tional time is still a deterrent to the wide- spread 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 inven- tories have been developed for only a few geographic areas, most notably Los Angeles, California (figure 6), and a chem- ically detailed regional inventory for the eastern United States. Box, Lagrangian trajectory, and Eulerian grid models can be developed to include nonlinear chemical reactions. Box models, the first candidate, assume that the pollut- ants 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 ~BoUNDARY OF\RSBO^U~ \ US... ~7 . ..  f i Lm If_ Figure 6. Emissions of NH3, NOx, HCs, and CO in the Los Angeles area during 1982. A spatially "ridded, time-resolved, and speciated emissions in- ventory is necessary for conducting air quality mod- eling studies involving chemically reacting com- pounds. (Based on data from McRae 1981.) 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 deposi- tion. They will also provide the key to predicting (and hence controlling) the for- mation 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

174 Mathematical Modeling of Effect of Emission Sources to lower concentrations can affect health, and the effects can be different. The choice of air quality models to be used for assess- ing health risks should reflect the temporal scale over which the health effects are ex- pected to occur. The temporal and spatial resolution of models can vary from min- utes 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 resolu- tion 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 meteorologi- cal 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 appropri- ate, 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 ap- proximations, and building up to more sophisticated model formulations when greater precision is needed. Modeling Approaches for Indiviclual Processes In general, models described in the previ- ous section simply provide a framework for combining theoretical descriptions of individual physical and chemical processes. The model's ability to correctly predict pollutant dynamics and to apportion source contributions depends on the accuracy of the individual process descriptions, the ac- curacy of the input data, and the fidelity with which the framework reflects the true interactions of the processes. Analytical models are composed of mod- ules describing (depending on model type) pollutant transport, diffusion, chemical re-  actions, deposition and emissions, aerosol dynamics, and heterogeneous (for exam- ple, gas/aerosol) interactions. Problem areas in each of these process descriptions are discussed below. Transport-related processes, advection and diffusion, are de- scribed by Samson (this volume), and will be discussed here briefly from a computa . . . tlona vlewpolnt. Turbulent Transport and Diffusion Numerical schemes developed to calculate the rate of transport of pollutants super from numerical diffusion and dispersion (Roache 1976~. Numerical diffusion and dispersion result from using a discrete ap- proximation to the governing system of equations, and are manifested by the com- puted solution being artificially spread out and ripples being formed. Numerous nu- merical schemes have been developed to minimize the errors induced, including higher-order finite-difference, finite-ele- ment, particle-in-cell, filtered, and spectral methods. In reviewing the use of different advection routines for solving the atmo- spheric diffusion equation 5, McRae et al. (1982c), Chock and Dunker (1983), and Schere (1983) compare accuracy and com . . putatlona. . requirements. Closure of the atmospheric diffusion equation 5, can be accomplished by utiliz- ing 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 in- volved in turbulent diffusion. An obvious need when applying this theoretical treat

Armistead G. Russell 175 ment 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 parame- terize 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 at- mospheric 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 . . ~ . . . prec actions ot c aspersion increases. Complex Terrain: Street Canyons Complex terrain represents an obstacle to modeling the transport of pollutants be- cause 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 can- yons 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 trans- port in street canyons is discussed by Sam- son (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 distribu- tion of O3 and the impact of automotive NOx emissions in street canyons needs to be addressed for two reasons: to determine population exposure to these pollutants, and to explain the difference between pre- dicted pollutant concentrations calculated when using a grid size much larger than the size of a street canyon and observed con- centrations 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 interac- tions, especially of reactive pollutants, need  to be included in street canyon models. Removal Processes Removal processes, particularly dry depo- sition 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 en- vironmental 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 me- chanical process, the second is primarily a chemical process, and neither is completely characterized at the present time. The prob- lem is confounded by the interaction be- tween the pollutants and biogenic surfaces where pollutant uptake is enhanced or re- tarded 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. Accu- rate mathematical description of the depo- sitional process has, as a result, been ad- vancing 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, A, to pre- scribe the deposition rate. The deposition velocity is defined such that the flux Fi of species i to the ground is Fi = Va`Ci(Zr) (9)

176 where cider) is the concentration of species i at some reference height Or' typically one to several meters. For a number of pollutants, v,~ has been measured under various mete- orological conditions and for a number of surface types. A basic problem with this parameterization is that it does not explic- itly 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 vat 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 stomata! activity increases (Whelpdale and Shaw 1974; Wesely and Hicks 1977; Wesely et al. 1985~. More recent models take this variation of v`' into account. In one ap- proach, the first step is to estimate the upper limit for Vat 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 re- ferred to as the resistance model (Wesely and Hicks 1977; Fowler 1978) that repre- sents v`' as the analog of an electrical conductance v,~= (ra+rb+rS) (10) where ra is the aerodynamic resistance con- trolled primarily by atmospheric turbu- lence, rb is the resistance to transport in the fluid sublayer very near the plant surface, and rS is the surface (or canopy) resistance (figure 7~. Of the three resistances, ra is essentially the same for all species, rb is the same for gaseous species with the same diffusivities, though it can be considerably greater for aerosols, and rS 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 rS. More recent models account for the variation of surface Mathematical Modeling of Effect of Emission Sources t Reference height (z,) Turbulent < fluid > Boundary > rb  its layer Surface effects Flux = C(z,) ra + rb + rs Analogous to I V Figure 7. The resistance model of deposition show- ing 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. resistance and diurnal change in fluid me- chanical transport. These parameterizations have been used to quantify the deposition flux of various compounds (McRae and Russell 1983; Walcek et al. 1986~. Less attention has been devoted to study- ing 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 grav- itational 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 spe- cies, leading to parameterization of deposi- tion velocities (Liu and Ilori 1974; Sehmel and Hodgson 1974; Hicks 1977; Slinn and Slinn 1981; Wesely et al. 1985~. More fun- damental 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 at- mospheric aerosols, so that the concentra- tions of these aerosols can be properly estimated and the related health effects as- sessed. Research in this area should follow two paths: experimental measurements of aerosol deposition in the environment, es- pecially actual aerosol velocities near sur

Armistead G. Russell 177 faces; and modeling and parameterization of the fundamental physical processes. Re- sults 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 character- ization of the processes leading to dry dep- osition 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 Carmi- chael 1982; Chameides and Davis 1982; Levine and Schwartz 1982; Munger et al. 1983; Graedel 1984; Kumar 1985~. Current research into these processes is concentrat- ing 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; Ja- cob and Hoffmann 1983; Jacob 1985~. Pre- CipitatiOn 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~; how- ever, no attempt has been made to model the relationship between pollutant emis- sions 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 ef- fects 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. At- kinson (this volume) gives an account of  the number and complexity of the interac- tions 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 or- ganic compounds, and reactions, that it is infeasible to incorporate an explicit state- ment 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 rep- resentation 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 re- active compounds such as 03, NO2, hy- droxy 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 hun- dreds of species present, chemical mecha- nisms use on the order of 50 species and about 100 reactions to accurately describe the principal features of atmospheric chem- ~stry. Three different types of chemical mech- anisms have evolved in an attempt to sim- plify 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

178 Mathematical Modeling of Effect of Emission Sources Table 1. Example of Lumping Alkane-OH Reactions Explicit Reactions of Alkanes with OH: C2H6 + OH ~ C2Hs + H2O C3Hs + OH ~ C3H; + H2O CnH2n+2 + OH ~ CnH2n+ ~ + H2O C2H5 + O2 ' C2H5O2 C3H; + O2 ~ C3H7O2 CnH2n+, + O2 ~ CnH2n+ DOG J Lumped Representation: Initial Reaction with OH Alkyl Radical Oxidation Reaction Alkane + OH ~ RO2 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 prod- ucts are based on a weighted average of the properties of all the alkanes present. Only the dominant chemical features and reac- tions of each lumped class are used to describe reaction steps. By taking advan- tage of the common features of the organics and free radicals, lumping allows one to greatly reduce the number of required spe- cies and steps needed to accurately describe the prevailing pollutant chemistry. For ex- ample, as illustrated in table 1, the various alkanes (CnH2n+2) react with OH in a sim- ilar manner to form alkyl radicals (CnH2n+~. The alkyl radical then reacts rapidly with O2 to form an alkyl peroxy radical (CnH2n+~02~. (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 mecha- nism, a variation of a lumped mechanism, splits each organic molecule into functional groups using the assumption that the reac- tivity of the molecule is dominated by the chemistry of each functional group. Leone and Seinfeld (1985) analyzed the performance of six chemical mechanisms by comparing, quantitatively, why they behave differently under identical condi- tions. 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 test- ing new chemical mechanisms. Given the importance of the chemical mechanism to the outcome of model eval- uation, source apportionment, and control strategy studies, it is bothersome that the predictions of different chemical mecha- nisms do not always agree. Shafer and Seinfeld (1986) compared NOX/HC/O3 re- lationships, and the sensitivity of six chem- ical mechanisms to initial and boundary conditions. They found that the predicted

Armistead G. Russell 179 HC control needed to reduce O3 concen- trations 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 predic- tions, particularly the NOX/HC/O3 rela- tionship, should be studied further. Dif- ferent 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 knowl- edge of atmospheric chemistry increases and as attention is turned toward less abun- dant, 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 nitroa- renes, which are strong mutagens (Pitts and Winer 1984) and other organic com- pounds. · Recommendation 5. Research into the development of new chemical mecha- nisms 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 Indusion of a description of aerosol dynam- ics within air quality models is of primary importance because of the health effects associated with fine particles in the atmo- sphere (Schlesinger, as well as Sun, Bond, and Dahl, this volume), visibility deterio- ration, 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 dis- tribution of sizes and can coagulate, evap- orate, grow in size by condensation, be formed by nucleation, or sediment out. Furthermore, the species mass concentra tion alone does not fully characterize the aerosol. The particle size distribution (which changes with time) and composi- tion determine the fate of particulate air pollutants and their environmental and health effects. Particles of about 1 ,um 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 conden- sation in the atmosphere (figure 8~. Simulation of aerosol processes within an air quality model begins with the funda- mental equation of aerosol dynamics which describes aerosol transport (term 2), growth (term 3), coagulation (terms 4 and 5), and sedimentation (Friedlander 1977~: an SI +V On+ = TV rv 1/2 J pi v v~n~v~n~v--Ada o , | ,(3(v, v~n(-v~n~v~dv-V On (11) where n is the particle size distribution function; U is the fluid velocity; I is the droplet current that describes particle growth and nucleation due to gas-to-par- ticle conversion; v is the particle volume; ,`3 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) pre- sent a framework for modeling the forma- tion 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 simula- tion of the formation, growth, and trans- port 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 com

180 Mathematical Modeling of Effect of Emission Sources Chemical conversion | Hot | of gases to low vapor volatility vapors | 1 ~ Condensation Primary particles Co~.~l~sion 1 Low- l volatility l vapor 1 Homogeneous I nucleation | _ _ _= / Chain aggregates ~ Condensat on Growth Coagulation \ \` ~ Coagulation of nuclei \ Coagulation Windblown dust Emissions + Sea spray + Volcanoes 1 1 1 ~ ! \ Plant particles \ I ~ \ \ 1 / Rainout \ I / and \_ - \ washout Sedimentation \ 1 , 1 I 1 1 ~1 0.002 0.01 0.1 1 2 10 100 PARTICLE DIAMETER (~m)  Transient nuclei or .1. Aitken nuclei range I Accumulation ~ . Mechanically generated range aerosol range - Fineparticles · · Coarse particles 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 of smaller aerosols and condensation of gases on preexisting particles. The largest aerosols are usually generated mechanically. The various processes leading to the different sizes ensure that aerosol composition will change with size. (Adapted with permission from Whitby and Cantrell 1976, and the Institute of Electrical and Electronic Engineers.) pleted. Instead, as a first step, investigators have chosen to model the major individual aerosol components such as sulfates (sass 1981; Carmichael et al. 1986), nitrates (Rus- sell et al. 1983; Russell and Cass 1986), and carbonaceous aerosol (Gray 1986~. These studies predicted aerosol mass and chemical composition, not the aerosol size distribu- tion (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, Colo- rado, using as input a parameterized rate of condensable aerosol formation along with an inventory for primary aerosol emis- sions. They concluded that part of the

Armistead G. Russell 181 disagreement between predictions and ob- servations was due to errors in the aerosol emissions inventory. This problem is uni- versal and will hinder any attempt to per- form a full simulation of atmospheric aero- sol dynamics. Construction of an accurate inventory of aerosol emissions will be an arduous task, although adoption of standards for particulate matter less than 10 ,um in diameter (PM-10) should has- ten inventory development, making it pos- sible to conduct more accurate modeling studies. The chemistry leading to the formation of some secondary organic aerosols has been clarified recently (Grosjean and Fried- lander 1980; Grosjean 1984, 1985; Hatake- yama et al. 1985) to the point that it is now feasible to conduct preliminary modeling studies of secondary organic aerosol forma- tion in the atmosphere. More research is required before it is possible to predict the formation of all the secondary organic par- ticulates. Once procedures for modeling secondary organic aerosol formation have been developed and accurate field data be- come available, it should be possible to construct size-resolved and chemically re- solved modeling programs for use in health effects, control strategy, and source appor- tionment work. The development of aero- sol 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 for- mation of very mutagenic, and possibly carcinogenic, nitro-PAHs (see also Atkin- son, this volume). Study of gas/aerosol reaction rates under controlled laboratory conditions has been attempted in a few cases (Baldwin and Golden 1979; tech et al. 1982~. Model calculations by Chameides and Davis (1982) indicate that the presence of aerosols can affect concentrations of cas eous 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 occur- ring between gases and aerosols that result in reaction. Additional research into meth- ods 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 reac- tions, and particle growth is perhaps the most critical research area for advancing air quality models to clarify relationships be- tween sources and health effects. Given in- creased field data, our current understanding of processes governing the production and growth of aerosols is such that major ad- vances in the use of aerosol process models should be realized in the next few years. Recommendation 6. Size-resolved and chemically resolved measurements of atmo- spheric aerosols are needed to test and further develop aerosol process models. Mode! Evaluation An air quality model must be tested before it can be used confidently for a specific application, such as control strategy design or source apportionment. Confidence in model predictions is vital because of the large cost of implementing policy decisions based on them and because of the impor- tance of the health and other effects that are influenced by the implementation of those policies. Model evaluation studies should determine the range of circumstances over which the model will perform adequately along with the accuracy of the inputs re- quired to implement the model and, if possible, should identify and quantify the reasons for differences between predictions and observations, although this is often impractical, or impossible, because of un . . . . certainties In input c .ata. There are three reasons why model pre- dictions may not agree with observations:

182 Mathematical Modeling of Effect of Emission Sources modeling error, measurement error, and uncertainty inherent in model formulation (Fox 1984~. Modeling error arises from incorrectly specifying input data or from model formulation problems due either to lack of a detailed understanding of the basic chemistry and physics or to the simplifica- tions required to make the problem com- putationally tractable. Inherent uncertain- ties exist because concentration values measured at a single point in space are in part determined by a stochastic process (turbulent diffusion) and are being com- pared to a value predicted in a deterministic fashion for a large averaging volume. This will remain even if model predictions and measurements are error free. Approachesfor 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 ex- ample, 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 So- ciety 1981; Fox 1981~. Fox (1981) identified three classes of performance measures: 1. Analysis of paired predicted versus observed concentrations for particular loca . . lions ant times. 2. Ability of the model to predict ob- served peak concentrations. 3. Comparison of the cumulative fre- quency distributions of the unpaired pre- dicted and observed concentrations. Bencala and Seinfeld (1979) developed a computer program for performing statisti- cal analyses. Table 2 lists some of the performance measures applied to the results of four photochemical models. Each model's adherence to fundamental principles should be scientifically evaluated (Fox 1981~. For models based on the atmo- spheric 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 evalua- tion 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 effec- tive 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-dimen s~ona~ w~no t~e~us tor every hour of simu lation; 2. An hourly emissions inventory for every species in each cell of the modeling region; 3. Hourly temperature, relative humid- ity, and mixing depth data for each cell; 4. Land use or surface roughness; 5. Vertically resolved initial concentra- tion 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.

Armistead G. Russell 183 Table 2. Performance Statistics for the Caltech, SAI, LIRAQ, and ELSTAR Models Model Performance Measure Caltecha SAIa LIRAQb ELSTARC Predicted peak ration O3 0.80 0.71 0 94e NO2 0.80 0.77 Correlation coefficient between predicted and observed concentrations O3 0.89 0.87 0.80 0.84 NO2 0.67 0.64 0.49 Biasf o3 NO2 Timing of peak prediction (hr)h o3 NO2 0.002 (3%) 0.078 (11%) -2 0.0728 -0.090g 0.024g 2 o 0.017 0.027 a Statistics are for a July 1974 evaluation period in the Los Angeles area. SAI = System Application, Inc. b The Livermore Regional Air Quality (LIRAQ) model was not evaluated for NO2 predictions. c The Environmental Lagrangian Simulation of Transport and Atmospheric Reactions (ELSTAR) is a trajectory model that was tested using various trajectories for various days, each with different peak predicted concentra- tions. Hence, no single number for statistics involving peak predictions is included. (Maximum concentration predicted)/(Maximum observed). e Average peak ratio. 1 N f ~ Pi- Oi N i=1 where Pi is the ith predicted concentration and Oi is the corresponding observed concentration. Values in parentheses are percent of mean. g Normalized bias is - N i= ~ Oi h Time of the predicted maximum minus the time of the observed maximum. This list is not exhaustive, nor does every model application require all this informa- tion 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 ac- quisition 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 upper- level 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 exe- cuted specifically to collect the data re- quired. Examples of field experiments con- ducted 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 de- signed to measure particulate carbon con- centrations 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 interpo

184 Mathematical Modeling of Effect of Emission Sources late pollutant concentration and meteoro- logical data that are collected at a few discrete locations and times to develop con- tinuous concentration and meteorological fields for model use. Some interpolation methods have been suggested for this pur- pose (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. Ob- jective analysis procedures are used to re- duce the divergence of interpolated wind fields (Endlich 1967; Dickerson 1978; Go- odin 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 predic- tions. Upper-level variables such as tem- perature structure (mixing depths), wind fields, and concentration data are particu- larly susceptible to this uncertainty (Russell and Cass 1986~. Upper-level pollutant con- centration 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, up- per-level initial conditions must be esti- mated 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 emis- sions 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 uncer- tainties in the inputs and reaction mecha- nisms have on model predictions (Falls et al. 1979; Dunker 1980, 1981; Seigneur et al. 1981; McRae et al. 1982b; Tilden and Sein- feld 1982~. Tilden and Seinfeld (1982) pre- sent the sensitivity of O3 and NO2 predic- tions 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 de- scribe model response to scaling initial con- ditions, boundary conditions, and ground- level emissions. For small perturbations of input parameters, the model responded lin-  early, although nonlinearities were present for larger changes. Model sensitivity to initial conditions decreases with time, sug- gestina that multiday simulations should be conducted. Multiday simulations are necessary if control strategy or source ap- portionment calculations are planned. Oth- erwise, the initial conditions will dominate the results. However, for grid models, long simulations can become sensitive to uncer- tainties 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 bound- ary conditions (McRae 1981~. Sensitivity analysis should also be used to direct exper- imental 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 predic- tions were within 30 ,ug/m3 of the obser- vations, and the root mean square (RMS) error was 95 ,ug/m3. During the period, concentrations ranged from near zero to about 600 ,ug/m3. The correlation coeff~- cient between predictions and observations was 0.54. As evidence of the advancement in air quality modeling capabilities, com- pare this to the evaluation statistics of pres- ent-day photochemical models (table 2) that describe transport as well as reaction.

Armistead G. Russell 185 Gaussian plume models have also been used to estimate CO, NOx, and particulate mat- ter 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 conser- vation model based on the numerical solu- tion 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 descrip- tion of the chemistry, although present knowledge of emission levels and atmo- spheric chemistry would indicate that at- mospheric 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 trajec- tory 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 Pro- cesses. Other improvements include more accurate descriptions of pollutant dry dep- osition, vertical transport, and more de- tailed input data. Examples of Lagrangian photochemical trajectory models include Environmental Lagrangian Muon or Transport and Atmospheric Reactions (EL- STAR) (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 de- veloped 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 La- grangian models, to evaluate the model. Statistical comparison of predicted and ob- served 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 forma- tion of aerosol NO3, PAN, and HNO3 (Russell et al. 1983; Russell and Cass 1986~. In order to reduce the effect of initial con- ditions, 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 NOT concentrations using the SURE data base. Predicted NO3 loadings agreed in magnitude with observations, but PAN predictions were generally high. Lagrangian trajectory models can accu- rately 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 pol- lutant concentration predictions only along a single air parcel trajectory. It is often desirable to study the areawide dynamics of pollutants, especially for population expo- sure calculations, and to present a more complete picture of the effects of source controls (for example, NOx 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 (Car- michael 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

186 Mathematical Modeling of Effect of Emission Sources 40 E Q 30 - z o G He LO An o Cal 20 10 40 Q 30 - z o z of o c' O3 Los Angeles downtown o: I: HI... I>. ..,.~.,...1 0:00 4:00 8:00 12:00 16:00 20:00 24:00 4:00 8:00 12:00 16:00 20:00 24:00 26 June TIME (PST) 27 June 20 10 NO2 Los Angeles downtown _ · O . . . ~ . . . 1 . . \~! . . . ~ . . . . . . ~ . . . 1 . . . 1 it. . . 1 . . . 0:00 4:00 8:00 12:00 16:00 20:00 24:00 4:00 8:00 12:00 16:00 20:00 24:00 26 June TIME (PST) 27 June Figure 9. Plot of predicted ( ) and observed (I) O3 and NOx concentrations (in parts per hundred million, pphm) at downtown Los Angeles during the June 2~27, 1974, modeling study showing the accuracy of model predictions. (Adapted with permission from McRae 1981.) 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, SOD. LIRAQ II, using a lumped chemical mechanism similar to that of Hecht et al. (1974), is used for computing photochemically reactive pol- lutant concentrations such as O3. Extensive statistical evaluations of the SAI and Caltech models were conducted using data for the dune 26-27, 1974, smog episode in Los Angeles. McRae and Sein- feld (1983) calculated the uncertainty in the Los Angeles basin emissions data for the 1974 period to be +20 percent for CO, + 15 percent for NOR, 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 Sein- feld (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 concentra- tions (table 2~. Part of the disagreement between predicted and observed NO2 con- centrations can be ascribed to interference of HNO3 and PAN with the measurement devices. Given the uncertainties in the me- teorological and emissions data, the agree- ment is quite good. Input data quality is a definite limitation to model performance. Russell and coworkers (1986) updated the chemical mechanism and added the capa- bility to predict ammonium nitrate aerosol concentrations within the Caltech model. They showed the model's ability to predict

Armistead G. Russell 187 inorganic NO3 and PAN, as well as O3 and NO2 concentrations. Extensive summar- ies of many recent model evaluation stu- dies have been made by Dennis and Down- ton (1984) and Wagner and Ranzieri (1984~. Model evaluation is a vital part of any air quality modeling study. A major limi- tation is accurate input data, especially on unobserved, upper-level initial and bound- ary conditions, as well as meteorological parameters. Testing of the more advanced models has shown that they are capable of predicting 03, NO2, HNO3, and PAN as well as nonreactive pollutant concentra- tions directly from data on meteorological conditions and pollutant emissions. · Recommendation 7. The most ad- vanced air quality models should be com- pared 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 recon- ciled. Application of Air Quality Moclels Analytical and receptor models are power- ful tools for use in source apportionment, emission control strategy, and population exposure calculations. There is no doubt, however, that the full potential of the newer models has yet to be realized. The ultimate goal is their use in emission con- trol strategy and health impact studies, of which exposure and source apportionment calculations are vital components. 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 emis- sions. Advanced air quality models, how- ever, have not yet been used widely for population exposure calculations. A pre- liminary 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  D(x, y, K) = T ~ P(x, y~c~x, y, t) Fitch, y, t), K] (12) t=1 where P(x,y) is related to the local popula- tion 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 concen- tration K; and T is the number of hours in the simulation. Note that this is not the usual definition of dosage but is the defini- tion 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 E(x, y, K) = T ~ P(x, y) Finch, y, t), K] t=1 (13) Again, this is not the usual definition of exposure, but is a measure of how long people are exposed to pollutant concentra- tions 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 af- fected. The above calculation is a first step toward the development of integrated source/exposure studies.

188 Mathematical Modeling of Effect of Emission Sources Source Apportionment and Control Strategies Receptor Models. Receptor models, by their formulation, are effective in determin- ing the source contributions to particulate matter concentrations. The sources con- tributing 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 Bos- ton (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 atmo- sphere. On the basis of data taken at a receptor station on the Washington Uni- versity campus, he found that 15 percent of the fine particulate matter was from motor vehicles, although little of the coarse parti- cle fraction was derived from mobile sources. An unusually high contribution from paint was attributable to a paint pig- ment 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 care- fully 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 (ACHED) (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 ni- trates and secondary organics. According to the 1974 emissions inventory for the Los Ane;eles area (McRae and Seinfeld 1983), mobile sources are responsible for 62.3 percent of the NOX emissions (precursor to NO3 aerosols). If one apportioned the measured NO3 to sources in proportion to their contribution to the basin-wide NOX  inventory, then the mobile source contri- bution in the study by Gartrell and Fried- lander (1975) increases to 35 percent of the total aerosol mass. In addition, part of the unidentified organic compounds, ammo- nium, and water may be attributable to mobile sources. This is a rough calculation, indicating that source attribution of sec- ondary 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. Us- ing 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 emis- sions 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 arbi- trary perturbations in some sources but not others. They are, however, good for deter- mining the sources of particulate matter . . . . w Len 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 to- tally on an input emissions inventory, which may be uncertain or difficult to obtain. Figure 10 shows the mass appor- tionment of the aerosol in Portland, Ore- gon, and the aerosol emissions inventory

Armistead G. Russell 189 / I/ndustrial point sources ~,371 t/yr BEFORE CMB ADJUSTMENT 14,563 t/yr Other area sources 913 Vyr Open burning 461 Vyr Oil and gas space heating 493 tar Motor vehicle exhaust 2,180 t/yr Road dust 3,145 t/yr - Other area sources 913 t/yr Open burning 461 ttyr / Industrial / point ~ sources / :5 Vyr Road dust 22,508 t/yr I; /:  - AFTER CMB ADJUSTMENT 38,827 tlyr -Oil and gas space heating 493 Vyr Wood space heating 4,600 Vyr Motor vehicle exhaust 2,187 Vyr 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.) before and after adjustment using the CMB receptor modeling study. Major deficien- cies were identified and improved in the emission inventory for wood burning and road dust. An extension of the simultaneous use of receptor and source models that merits investigation follows the above methodol- ogy except that a chemically reactive trans- port model is used to estimate the forma- tion of secondary aerosols such as sulfate, NO3-, 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 Andy. Source-Oriented Modeling Studies. Non- reactive, 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 esti- mate 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 (sass 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 appor- tionment has a much more complex mean- ing when discussing secondary pollutants that are formed by series of complex atmo- spheric reactions, rather than being directly emitted from sources. These pollutants in- clude 03, PAN, and secondary aerosols. The reason is that an incremental change in the emissions of precursors to the forma- tion of a secondary pollutant need not lead to a proportional change in the pollutant concentration, if any change at all results. For example, NOx and HCs are precursors to the formation of 03, but increasing the emissions of one precursor can have a very different result than increasing the other. In fact, decreasing NOx emissions may in- crease local O3 concentrations while at the same time decreasing O3 concentrations downwind. A common graphic representation of the relationship of maximum O3 concentra . . . . . lions to 1nltla precursor concentrations ot NOx and HCs is the O3 isopleth diagram (figure 11).

190 Mathematical Modeling of Effect of Emission Sources 0.28 0.24 0.20 0.16 Q - O 0.12 of 0.04 / jet nL : / l o3 - , contours / ~ /\ ~0.30 : T-~0.25 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 NONMETHANE HYDROCARBONS (ppm C) Figure 11. O3 isopleth diagram showing the re sponse of O3 concentrations to changes in initial NOx and nonmethane hydrocarbon concentrations (meth ane is not included because of its low reactivity). The varying response to NOx reductions is dependent upon the particular initial concentrations. Initial NOx concentration is given in parts per million by volume (ppmV) and HC as parts per million of carbon atoms (ppmC). Note that at one position on a curve, such as point C, a decrease in the NOx concentration results in a much larger decrease in O3 concentrations than a similar decrease at another position on the same isopleth, such as B. At point A, the graph indicates that decreasing NOx would increase O3 formation. 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 im provement from controlling the other source separately. This clouds the issue of definitively assessing the impact that a sin gle source has on air quality in that its impact dynamically responds to changes in other sources and to varying meteorologi cal conditions. Mathematical modeling of photochemi cal air pollution can delineate the relation  ship that a source has on air quality. For example, a model that has undergone suc cessful evaluation using the actual emis- controls; signs 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 concen- trations of the reactive as well as unreactive species would have been without that source. In this fashion, researchers can as- sess 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 implemen- tation 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 trajec- tory model to study the impact of automo- tive emissions in Los Angeles, and Tesche et al. (1984), who used the SAI airshed model to evaluate emission controls pro- posed for the Los Angeles area. The trajectory study of Chock and col- leagues used the ELSTAR model described previously, in this case examining air qual- ity changes in Los Angeles due to reduc- tions in automotive emissions of HCs, NOX, and CO. Two trajectories were modeled, each 8 or 10 hr long. Results indicate that drastic improvement (O3 re- duced 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 NOX emissions from 3.8 to 2.45 g/mile and HCs from 9.67 to 1.94 g/mile. Further NOX reduction was found to be ineffective for controlling O3. Pitts et al. (1983) commented on the conclusion that further NOX reductions would not be beneficial, noting that short trajectories (of a few hours) are extremely sensitive to initial conditions, many of which are un- certa~n. Tesche and colleagues present the results of a number of model calculations, depict- ing the result of 18 emission control possi- bilities in the Los Angeles basin. Among the conditions modeled were: 1. 1987 (AQMP) emissions inventory expected in the absence of further emission . 2. All elevated emissions removed from

Armistead G. Russell 191 case 1, above (that is, power plant emis- sions 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 inven- tory, run 1 (South Coast Air Quality Man- agement District and Southern California Association of Governments 1982~. Of the three cases where a source type was re- moved, removing mobile sources (run 4) showed the greatest decrease in Or (low a ered from 0.194 to 0.138 ppm). That study also provides a classic example of the non- linearity of the photochemical system. The net improvement in O3 for cases 2, 3, and 4 added together is 0.04 ppm. The reduction in NOX 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), NOX 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 NOX controls will reduce 03, NO2, PAN, and inorganic NO3- formation in the east- ern portion of the Los Angeles basin. The debate on the effectiveness of NOX controls is, perhaps, at present the most critical question to be answered by urban air qual- ity 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 reac- tion 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 (sass and McRae 1981~: Find x such that C(xJ is minimized, subject to QiE(x,t)M(x,tJ] ' S  where 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 ,ug/m3 sul- fate level as contrasted with about $40 million for a least-cost strategy, or a sav- ings of about half. Other studies have shown similar results. Kyan and Seinfeld (1974), following the work of Trijonis (1974), illustrate an economically opti- mized control strategy for photochemical pollutants. The large data requirements and compu- tational 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 NOX, least-cost control strategies can be estimated by identifying the least-cost ap- proach to achieving various levels of HC and NOX 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.

192 Mathematical Modeling of Effect of Emission Sources 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 emis- sions 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 en- larging 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 develop- ment 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. Typi- cally, 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 cur- rent policy problem now awaiting comple- tion 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 iden- tifying gaps in our knowledge. Also, mod- els can predict concentrations of trace gases that would be difficult to observe experi- mentally, thus alerting researchers to pos- sible undetected problems. It is clear that much time has been de- voted to developing and evaluating ad- vanced photochemical models (see earlier sections on Modeling Approaches for Indi- vidual 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 (sass 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 con- ducting those studies, there is often no mechanism to pay for this necessary effort.  Special Topics and Emerging Issues in Air Quality Modeling Previous sections of this chapter addressed the formulation and use of air quality mod- els as they have generally been viewed in the past. As our knowledge of air pollutant transport and chemical reaction processes increases, new types of air quality models are being constructed. In many cases, prob- lems that were computationally intractable can now be handled by faster computers. These areas that are undergoing rapid de- velopment present numerous opportunities for research. Aerosol process modeling that includes combined smog/fog cycles (as dis- cussed in the section on Modeling Ap- proaches for Individual Processes) is, per- haps, the most important emerging topic in modeling for health effects purposes. Other emerging issues and special topics are dis- cussed below. 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 be- cause of increasing industrial and mobile source activity. Such models can help an- swer questions surrounding the increased emissions of novel substances such as fluo- rocarbons or long-term impacts of more

Armistead G. Russell 193 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 radi- ation were to reach the earth's surface be- cause of stratospheric O3 depletion. The technical barriers facing the development of extremely large-scale models are essentially the same as for urban-scale models, mag- nified by problems of data collection on a global scale. Modeling Small-Scale Processes Often the information desired from mod- eling studies depends on processes that occur on spatial scales much smaller than the resolution of most urban air quality models. The modeling of NOx air quality in street canyons involves small-scale pro- cesses of this sort. Introduction of point- source emissions into grid-based air quality models likewise involves a mismatch be- tween 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 con- centrations, against which model predic- tions 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 frus- trate comparisons to model predictions of directly emitted pollutants such as CO and NO or rapidly reacting secondary pollut- ants 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 dif . ferences between large-grid, volume-aver- aged predictions and point measurements (see Nappo et al. 1982~. How can the treatment of small pro- cesses 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 at- mosphere outside the plume, while main- taining its integrity. In an evaluation of the SAI urban airshed model using both ap- proaches, 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 produc- tion platforms, may have to be treated in great detail. For reacting plumes those containing NOx, HCs, or possibly SOx- the large concentration gradients that exist make the macro- and the micro-scale mix- ing processes important to the overall dynamics of pollutant evolution. · Recommendation 8. Additional re- search 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 pol- lutant concentrations make a major contri- bution 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 out- door air quality, indoor emissions, ventila

194 Mathematical Modeling of Effect of Emission Sources lion 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 interac- tions?" As in outdoor situations, receptor-ori- ented 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 limita- tions on the two approaches indoors are similar to those discussed previously for outdoor applications. However, some un- usual 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, 03, and particulate matter). The usual approach to indoor air quality modeling has been to apply a mass balance equation, similar to equation 5. For a sin- gle-compartment model this becomes (Na- tional Research Council 1981) dC V d = qOCO(1-Fo) + q1C(l-F1) +q2CO- (qO+ q1 +q2) C + S-R where V is the volume of the structure (or room), q0 and q2 are the rates at which air is brought into the building from outdoors through a ventilation system or by infiltra- tion, respectively (figure 12), and qua is the air recirculation rate. Both the makeup air (qO) 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 effi- ciencies are Fn and F1 for the makeup air v filter and recirculated air filter, respec- tively. S represents indoor emission sources, and R is an indoor sink term. Multicompartment models involve a sys- tem of similar coupled differential equa- tions. Mass balance models have been used to successfully relate indoor air quality to outdoor pollutant levels, especially for nonreactive gases such as CO. However, Infiltrated air Make-up air lqOCO 1 ~,Fil ~A/ PI her// I Intake fowl _ ~ qOCO (1-Fo) ~ r q1cj (1-Fl) Building volume V Building surface area A = ~A Building source ^ J  Building sink Building concentration Outdoor concentration Recirculated air . s R Cj Co - 1 .,. Iq3Ci Exfiltrated air Iq4Ci Exhaust air Mass balance for air: qO + q2 = q3 + q4 Figure 12. Indoor air quality model, including mass balance on pollutants and air. (Adapted with permis- sion from Shair and Heitner 1974, and the American Chemical Society.) agreement for reactive gases such as O3 and SO2 has not been as close (National Re- search Council 1981~. Most indoor air qual (14) ity models have yet to use as sophisticated a description of the chemical kinetics as have their outdoor counterparts. 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, artifi- cial 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 diffu- sion rates. Input parameters for mass bal- ance models should be measured for each individual building used in a study. Differ

Armistead G. Russell 195 ences 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 per- sonal exposure, it is evident that attention should be focused on determining the sources of pollutants found indoors. Real- izing the critical role that outdoor pollut- ants play, indoor/outdoor air quality rela- tionships 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 reac- tive 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/out- door 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 ex posure. Conclusion Mathematical models, statistical as well as deterministic, have evolved to become powerful tools for apportioning the impact of sources on certain aspects of air quality. Models can be used to study human expo- sure to air pollutants and to identify cost- effective control strategies. Their use for designing optimal emission control strate- gies, alone, could lead to large savings in emission control costs. Given the appropri- ate input data, air quality models can accu rately predict the concentrations of the reg- ulated pollutants such as CO, 03, and NOSE as well as some of the noncriteria - . . pollutants. A primary limitation on the accuracy of model results at present is not the model formulation, but the accuracy of the available input data. Receptor-oriented (statistical) models use  the large volume of data available on pol- lutant concentrations and use the underly- ing structure of a data set to separate the contribution of different emission sources to observed air quality. The most common types of receptor models use chemical mass balance and multivariate analysis tech- niques and have been used in a number of locations to identify and apportion source contributions at receptor sites. However, the assumptions involved in formulating receptor models limit their use for source impact research to studying nonchemically reacting systems. For control strategy de- velopment, other limitations exist. One area for promising research is the hybridization of receptor-oriented models with source- oriented (or analytical) models, thereby capturing the power of both methods. Analytical models are composed of a number of modules each describing, math- ematically, a physical or chemical process, such as transport, diffusion, deposition, and chemical reaction. This is particularly true of the advanced photochemical air quality models. Some research areas have been identified where model capabilities can be improved or expanded: 1. Advancing and testing the chemical mechanisms used to model air quality; 2. Inclusion of models of aerosol pro- cesses, including the chemical reactions leading to aerosol formation and heteroge- neous reactions; 3. Models relating indoor and outdoor . . . air quality; 4. Further use of air quality models in source apportionment and control studies, and in personal exposure research; 5. Improved description of pollutant deposition, both wet and dry. In some of these areas, a better under- standing of the underlying physical process is needed, requiring basic research into the

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

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

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

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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