Appendix C
Source Identification and Apportionment Models

SPECIATED ROLLBACK MODELS

The speciated rollback model is a simple, spatially averaged mathematical model that disaggregates the major airborne particle components into chemically distinct groups that are contributed by different types of sources (Trijonis et al., 1975, 1988).

A linear rollback model is based on the assumption that ambient concentrations C above background are directly proportional to total emissions E in the region of interest. Stated as a formula, C-Cb = kE, where Cb is the background concentration due to emissions other than E (i.e., to emissions outside the region of interest; natural sources, even inside the region, are usually included in this background term). The constant of proportionality, k, is determined over a historical time period when both concentrations, C and Cb, and regional emissions, E, are known. With that information, new concentration estimates can be derived for proposed changes in emission levels. For an inert pollutant, the only assumption required for the model to be exactly correct at all points in the region is that the relative spatial distribution of emissions remains fixed despite the changes in emissions. 1 That assumption be-

1  

As with all models, there is an assumption that the concentrations apply to some given meteorology and given averaging time. In a temporal sense, the rollback model has the requirement that the temporal (e.g., diurnal) pattern of emissions remains fixed.



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Protecting Visibility in National Parks and Wilderness Areas Appendix C Source Identification and Apportionment Models SPECIATED ROLLBACK MODELS The speciated rollback model is a simple, spatially averaged mathematical model that disaggregates the major airborne particle components into chemically distinct groups that are contributed by different types of sources (Trijonis et al., 1975, 1988). A linear rollback model is based on the assumption that ambient concentrations C above background are directly proportional to total emissions E in the region of interest. Stated as a formula, C-Cb = kE, where Cb is the background concentration due to emissions other than E (i.e., to emissions outside the region of interest; natural sources, even inside the region, are usually included in this background term). The constant of proportionality, k, is determined over a historical time period when both concentrations, C and Cb, and regional emissions, E, are known. With that information, new concentration estimates can be derived for proposed changes in emission levels. For an inert pollutant, the only assumption required for the model to be exactly correct at all points in the region is that the relative spatial distribution of emissions remains fixed despite the changes in emissions. 1 That assumption be- 1   As with all models, there is an assumption that the concentrations apply to some given meteorology and given averaging time. In a temporal sense, the rollback model has the requirement that the temporal (e.g., diurnal) pattern of emissions remains fixed.

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Protecting Visibility in National Parks and Wilderness Areas comes less restrictive when the model is applied to larger, three-dimensional, and spatially averaged concentrations rather than to concentrations at individual points in a geographic region. Thus, the model is especially useful for spatially averaged problems, such as regional haze. A speciated rollback model for airborne particles is an aggregation of several separate rollback models for each individual chemical component of the atmospheric particle complex. In almost all cases, the anthropogenic materials in the dry particle mass almost entirely consist of five components: sulfates, organics, elemental carbon, nitrates, and crustal material (e.g., soil dust and road dust). Organics can be further subdivided into primary organic and secondary organic particles. In the simplest case, it is assumed that linear rollback models can relate each primary particle component (elemental carbon, crustal material, and primary organics) to its regionwide emission level and each secondary aerosol component (sulfates, nitrates, and secondary organics) to the emission level of its controlling gas phase precursor (e.g., SO2, NOx, NH3, and VOC). In considering the ambient nature of airborne particles (not only the measured dry fine-particle mass), particle-bound water is an additional important component. Certain chemical constituents of anthropogenic particles—such as sulfates, nitrates, and some organics—have an affinity for water. The constituents acquire water vapor from the atmosphere and form a liquid phase at relative humidities well below the 100% level normally associated with condensation. If the concentration of hygroscopic particles (i.e., those that retain water) is reduced, there is a corresponding reduction in the particle-bound water. Accordingly, water retention is usually incorporated into the rollback models for the hygroscopic airborne particles (i.e., sulfate-bound water is assumed to change in proportion to sulfate concentrations at a particular relative humidity, nitrate-bound water in proportion to nitrate concentrations, etc.). For example, if one is considering a rollback model for visibility effects, the total light-extinction contribution from nonbackground sulfate particles plus sulfate-associated water is assumed to change in proportion to SOx emissions. The speciated rollback model incorporates a very restrictive assumption in addition to the assumption about the spatial homogeneity of emission changes. The restrictive assumption is that there is only one controlling precursor for each secondary airborne particle component and that transformation and deposition processes are completely linear with

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Protecting Visibility in National Parks and Wilderness Areas respect to the precursor (i.e., that transformation rates and deposition velocities are independent of pollutant concentrations). Various complexities can be added to the speciated rollback model. First, rollback models can be disaggregated by particle-size fraction (e.g., coarse versus fine particles) as well as by chemical composition. Second, additional distinctions can be made between primary and secondary particles (e.g., separate rollback models can be formulated for primary versus secondary sulfate particles). Third, rather than using proportional relationships, nonlinearities in transformation processes can be approximately accounted for by assuming nonlinear functional relationships between emitted precursors and their atmospheric reaction products. Finally, the model can be disaggregated spatially by including separate transfer coefficients for different source areas or stack heights. The latter two modifications are ways of relaxing some of the restrictive assumptions of the rollback technique. Four types of information are needed to implement a speciated rollback model: Data on airborne particle concentrations disaggregated by components of the particles; Knowledge or assumptions regarding the controlling precursor for each secondary airborne particle component; Emission inventories for the important source categories of each airborne particle component and each gaseous precursor substance; Knowledge or assumptions regarding background concentrations (due to sources other than those that are in the inventory) for each component of the airborne particles and each gaseous precursor substance. One of the advantages of the rollback model is that this type of information is often obtained as a first step in any reasonable and practical control plan; therefore, rollback models often can be formulated and applied at an early stage in the source attribution process. RECEPTOR-ORIENTED MODELS BASED ON CHEMICAL SIGNATURES Receptor modeling is an active and developing field of research that has given rise to many different approaches and techniques. The follow-

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Protecting Visibility in National Parks and Wilderness Areas ing discussion provides a taxonomical overview, identifying some recurrent themes and attempting to clarify the relationships among various models. We then focus on two models (i.e., chemical mass balance and regression analysis) that are used so often that a more detailed discussion of their formulation is warranted. A variety of techniques extract information on the types of sources contributing to a given airborne particle sample on the basis of the particles' chemical composition. All the techniques are conceptually based on the same underlying model (Friedlander, 1977; Henry et al., 1984; Hopke, 1985; Gordon, 1988): In Equation C-1, the subscripts i,j, and t index ambient aerosol characteristics, emissions sources, and sampling intervals, respectively. The terms ci, Sj, and fij are defined as follows: ci is the ith characteristic of the airborne particles at the receptor site. That characteristic is typically the mass concentration (particle mass per unit air volume) of the particles or particle component. The characteristic also can be an air pollutant effect, such as the light-extinction coefficient (extinction cross-section per unit air volume) (Pitchford and Allison, 1984) or mutagenicity (revertants per unit air volume) (Lewis et al., 1988). For simplicity, our discussion will take the ci to be the mass concentration of the ith particle component. Sj is the ambient mass concentration (effluent mass per unit air volume) of the total effluent contributed by the jth emissions source at the receptor site. This contribution often is referred to as the source strength. A source can be defined as a specific industrial facility, such as the Navajo Generating Station (NGS) at Page, Arizona (NPS, 1989; NRC, 1990), a generic category, such as soil dust (Friedlander, 1973), or a geographic area, such as the midwestern United States (Rahn and Lowenthal, 1985). fij is the mass fraction (particle mass per effluent mass) as measured at the receptor site, of particle component i in the effluent of the jth source. The sequence f1j, f2j, fnj is referred to as the jth source's profile, or its chemical signature or fingerprint. For conserved chemicals, it may be possible to measure fij at the source (Core, 1989a). For

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Protecting Visibility in National Parks and Wilderness Areas substances produced or destroyed in the atmosphere, measurements at the source may have limited value (NRC, 1990). All the techniques have as their objective the estimation of the source contributions, fij Sij. A class of methods referred to as chemical mass balances (CMB) can be applied to the solution of Equation C-1 when the source characteristics fij are known. The simplest case involves a conserved substance i, which is emitted by a unique source j. Such a tracer can be endemic, such as lead in Los Angeles automobile exhaust during the early 1970s (Miller et al., 1972), or inoculated, such as deuterated methane (CD4) that was injected into the effluent of the Navajo Generating Station during the Winter Haze Intensive Tracer Experiment (WHITEX) (NPS, 1989; NRC, 1990). For the unique tracer, Equation C-1 simplifies to cit = fijt Sjt, which can be solved directly for the source strength in terms of the measured ambient concentration of the tracer and the mass fraction of the tracer in the source's effluent: Sjt = Cit /fijt. The jth source's contribution to another conserved substance, one that may be emitted by multiple sources, then can be calculated from the mass ratio measured at the jth source: In most cases sources are distinguished by overall chemical profiles rather than by unique individual substances. Such situations are typically modeled in terms of n conserved substances that are wholly accounted for by the emissions of m ≤ n sources. If the chemical profiles are linearly independent, then the system given by Equation C-1 (i = 1, n) can be solved for source strengths Sj (j = 1, m) in terms of the measured ambient concentrations ci and the source characteristics fij. To minimize the effects of measurement error, the number of substances is usually taken to exceed the number of sources (n > m), in which case an overdetermined solution is estimated by weighted least-squares fitting procedures (Watson et al., 1984). Useful information sometimes can be obtained even when there are more sources than substances (White and Macias, 1991). Given an estimate of source strengths, source contributions can be derived for any conserved substance, whether it is one of the n markers used in the solution or one with additional sources. If there are many more measured chemical

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Protecting Visibility in National Parks and Wilderness Areas substances than sources, then the comparison of modeled concentrations with observed ambient concentrations of all chemical substances can provide a valuable internal check on model consistency (Friedlander, 1973; Kowalczyk et al., 1978). The CMB model possesses some attractive properties as a tool for apportioning conserved characteristics of the ambient airborne particles. Unlike the statistical approaches discussed below (e.g., factor analysis), the CMB model can be applied to individual ambient samples. More critically, it is an easily understood and easily scrutinized model that is straightforwardly derived from physical principles, and it contains no unmeasured quantities. The CMB's deterministic character carries a cost, however; it requires comprehensive prior information on the identities and chemical characteristics of all important sources that contribute to the ambient aerosol. When multiple ambient samples are available, a class of methods referred to as factor analysis offers empirical insights into the identities and characteristics of major sources. The basic idea behind factor analysis is that the ambient concentrations of various conserved chemical substances should correlate with each other if they have a common source. That idea can be seen in the simplest case, where j is the only source of substances i and i', and the source characteristics fijt = fij and fi'jt = fi'j are stable from one sample to the next. According to Equation C-1, the only source of variability in the ambient concentrations cit, = fijSjt and ci' = fi'jSjt is then the common source strength Sjt. The two concentrations should therefore correlate, both being high when source j is present and both being low when source j is absent; moreover, their standard deviations should be proportional to the substances' abundance at the source. Inverting that logic, one can hypothesize that substances that are highly correlated in ambient air have a common source, and one can infer the chemical signature of the source from ambient measurements alone. Factor analysis provides a framework for partially extending the simple reasoning outlined above to situations with multiple sources. A sequence of p ambient measurements, each characterizing n substances, can be represented as a cloud of p points in n-dimensional space ("Q-mode analysis") or n points in p-dimensional space ("R-mode analysis") (Hwang et al., 1984). In either representation all points should, according to Equation C-1, lie within model and measurement error of the m-

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Protecting Visibility in National Parks and Wilderness Areas dimensional hyperplane determined by the chemical profiles of the m distinct emissions sources. The algebra of factor analysis allows the dimensionality and orientation of this hyperplane to be estimated from the data. The source profiles themselves can be recovered in the special case where each substance has a unique source (via "VARIMAX rotation") or when the profiles are approximately known already (via "target transformation") (Hopke, 1985). Factor analysis thus serves to validate and refine the source information used in the CMB model. The set of source profiles cannot be recovered uniquely without some such prior knowledge, because the set constitutes only one of an infinite number of possible coordinate systems (Henry, 1987). In the context of visibility studies, the models of CMB and factor analysis are critically limited by their restriction to airborne particle characteristics that are conserved during transport from source to receptor. As discussed in Chapter 4 of this report, the extinction cross-section of the ambient aerosol is contributed largely by secondary particulate matter, which is not directly emitted by any source, and is inflated by liquid water whose abundance is determined by ambient relative humidity conditions. The optical characteristics of source emissions are thus a function of atmospheric transport and transformation, and are highly variable relative to the tracer substances used in CMB and factor analysis. The optically relevant portion of a source's profile at the receptor site consequently cannot be determined by direct measurements of its emissions but must be estimated by source-oriented modeling or by regression analysis of ambient data. Linear regression analysis is a well-established (Seber, 1977; Draper and Smith, 1981) and well-studied (Belsley et al., 1980; Fuller, 1987) class of procedures for estimating unknown coefficients in linear relationships from multiple observations of the dependent and independent variables. Equation C-1, adapted to account for the sulfate concentration, adapted to, for example, is a linear relationship in which the source-specific ratios of sulfate to effluent are unknown parameters. Given measured ambient sulfate concentrations cit, and ambient effluent concentrations Sjt derived from CMB analyses of conserved substances, regression analysis can generate estimates of the average sulfate-to-effluent ratios fij at the receptor. The regression estimates are determined by optimizing the agreement between measured and modeled sulfate values. All the foregoing analyses require the existence of chemical signatures

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Protecting Visibility in National Parks and Wilderness Areas for at least some of the sources of interest in a given application. To be broadly useful, such signatures must be distinctive, stable, and measurable. Because they minimize collinearity problems in the solution of the system described by Equation C-1, the most helpful signatures involve substances predominantly attributable to a single major source or source category. Table 5-2 lists examples of substances that have been used as endemic markers and the sources to which they are usually attributed. Endemic tags also have been identified for some airsheds that are rich in a distinctive source type (Rahn, 1981; Miller et al., 1990). Unique signatures can be created by inoculating targeted sources with substances that are otherwise scarce in the atmosphere (e.g., unusual perfluorocarbons, deuterated methane, or sulfur hexafluoride). Such artificial tags have been applied to specific sources (Shum et al., 1975; Georgi et al., 1987; NPS, 1989) and to airsheds (Reible et al., 1982; Haagenson et al., 1987). Artificial tracers often are used to elucidate airflow patterns. In such studies, the tracer is typically released in discrete puffs. In contrast, tracers used to support receptor modeling should be released over a sustained period to avoid ambient samples that contain an unknown proportion of tagged and untagged effluent. To study particle fluxes, it is necessary that (1) the ratio of tracer injected into the stack to stack gas-particle loading is constant, and (2) the dispersive and depositional characteristics of the tracer and primary particles emitted from the stack are similar. The distinctiveness of an endemic source signature depends in general on its context. Several of the tracer-substances' source attributions in Table 5-2, for example, must be considered unreliable in the southwestern United States, where copper smelters are important sources of vanadium, arsenic, sellenium, and lead (Small et al., 1981). In actual applications, it can be difficult to verify the attribution of a signature to a specific source. At the large distances over which sources can contribute to regional haze, there may be many sources for any endemic tracer. A useful multi-substance signature based on characteristic substance ratios rather than characteristic substances per se, must preserve its distinctiveness over all combinations of all potential sources of any of the signature's constituents. Fluctuations in source signatures can produce significant uncertainty in source apportionment. There is some variability, often undocumented, in the composition of emissions from any individual source. The SO 2-to-NOx ratio in the Navajo Generating Station's emissions varies by

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Protecting Visibility in National Parks and Wilderness Areas about 20% (Richards et al., 1981), for example, and the sulfur-to-selenium ratios in two samples taken during WHITEX differed by a similar amount (NPS, 1989). Additional variability is introduced by the diversity in the chemical composition of emissions from the individual sources that make up a given source category, especially at the large distances relevant to regional haze. The selenium-to-aluminum ratios in fine-particle emissions from coal-fired power plants can vary by 70% (Sheffield and Gordon, 1986), for example, even for facilities located in the same geographic region and using similar particle control technology. Figure 5-1 shows copper smelters within the same geographic region to have widely varied chemical signatures. Even suspended soil dust varies significantly in composition from site to site (Cahill et al., 1981). No chemical signature is of value unless it can be identified at ambient concentrations. In many national parks and wilderness areas, this requirement places heavy demands on measurement technology. For example, Table 5-1 shows that most of the tracers identified in Table 5-2, including vanadium, manganese, nickel, arsenic, selenium, bromine, and lead, were not quantified routinely by the trace-element monitoring network operated by the National Park Service between 1979 and 1986. The main problem is that a source's impact on visibility through the atmospheric formation of secondary particle components does not lessen with distance in proportion to the dilution of its primary emissions. Moreover, the detectability of chemical signatures does not necessarily improve with the progress of technology, because analytical advances complete with improved emissions controls. As one example, the decrease in automotive lead emissions since the mid-1970s has clearly outpaced increases in analytical sensitivity, making it difficult to use lead as a tracer for automotive aerosol emissions. Recent use of CMB calculations and regression analysis as part of the visibility impairment study contained in the National Park Service's WHITEX report (NPS, 1989) has focused particular attention on those two source apportionment methods. For this reason, an extended discussion of both models follows. CMB Models The CMB model was first proposed by Winchester and Nifong

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Protecting Visibility in National Parks and Wilderness Areas (1971), Hidy and Friedlander (1972), Kneip et al. (1972), and Friedlander (1973). It has been applied widely to apportionment of sources of primary particulate emissions on local and regional scales, to groundwater problems, and to apportionment of sources of VOCs and air toxics and of sources contributing to light extinction (Cooper and Watson, 1980; Hopke and Dattner, 1982; Hopke, 1985; Pace, 1986; Gordon, 1980, 1988; Watson et al., 1989). The CMB model has been used widely in the regulatory community (EPA, 1987c), and many validation studies have been completed with the model (Stevens and Pace, 1984). The current state of the art limits the model's regulatory application to particulate matter that is directly emitted to the atmosphere. The ability of the CMB model to apportion airborne particle concentration or light extinction to sources is limited to categories of sources with dissimilar source profiles, because of the assumptions inherent in the model and because of its inability to resolve sources of secondary particles. The first-order principles of the CMB model have been described (Watson et al., 1991), and assumptions implicit in its application have been documented in the literature (Watson et al., 1991). The sensitivity of the model to deviations from modeling assumptions has been examined in two studies, both of which were designed to determine if the CMB model could be used in regulatory settings (Stevens and Pace, 1984; Javitz et al., 1988a,b). CMB source apportionment was first used as a basis for regulatory action by the state of Oregon, when in 1977, it sponsored the Portland Aerosol Characterization Study (PACS). PACS was the first large-scale, successful receptor modeling study specifically designed to support State Implementation Plan revisions to attain EPA's Total Suspended Particulate NAAQS (National Ambient Air Quality Standard). The study spawned much of the receptor modeling technology that is in use today (Watson, 1979). The source apportionment results developed during PACS were applied by the staff of the Oregon Department of Environmental Quality in the first joint applications of receptor and dispersion modeling (Hanrahan, 1981; Core et al., 1982). Concurrent with the revision of the NAAQS for particulate matter, EPA released several guidance documents to state regulatory agencies that supported the use of the CMB model as a technical basis for PM10 control strategies (Pace and Watson, 1987; EPA, 1987c). (PM10 refers

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Protecting Visibility in National Parks and Wilderness Areas to particles less than 10 µm in diameter.) EPA has continued to support state air regulatory agencies' application of the CMB model by continued development of software (Watson et al., 1991). Source profile information also is being gathered (Core et al., 1984; Shareef et al., 1988; Core, 1989a; Houck et al., 1989). Theory of the CMB Model Watson et al. (1990a,b) have described the theoretical basis of the CMB model in several publications. The CMB model consists of a least-squares estimate of the solution to a set of linear equations that expresses each concentration of a chemical species at a receptor air-monitoring station as a linear sum of the products of source-profile species at the receptor site multiplied by source contributions. The source profile (i.e., the fractional amount of each chemical species in the emissions from each source type) and the ambient concentrations of each species measured at the receptor site with appropriate uncertainty estimates serve as input data to the model. The output consists of the ambient airborne particle mass increment and the amount of each chemical substance contributed by each source type. The model calculates values for the contributions from each source and the uncertainties associated with those source contributions. Input data on uncertainties are used both to weight the importance of input data on chemical species concentrations when computing the solution and to calculate the uncertainties associated with the source contributions. Derivation and Solutions The concentration of a conserved pollutant measured at a receptor air-monitoring site during a sampling period of length T due to a source j with a constant emission rate Ej is where Dj is a dispersion factor depending on wind velocity u, atmospheric stability, and location of source j with respect to a receptor (x).

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Protecting Visibility in National Parks and Wilderness Areas distributions, has been carried out for zero-dimensional "boxlike" models-, those studies can provide guidelines for quantifying aerosol dynamics that could be used in regional scale three-dimensional models (Middleton and Brock, 1977; Gelbard et al., 1980). A summary of three-dimensional mechanistic models by Seigneur and Saxena (1990) is presented in Table C-1. The summary lists all the current models that are being (or could be) used as the basis for visibility modeling of the type discussed in this section. Mechanistic visibility models are intended to calculate from first principles the impact of gases and particles on atmospheric optical properties. Such models are being developed, but many years might pass before they are available for routine regulatory purposes. In principle, these models use information on emissions, meteorology, and chemical transformations to calculate gaseous pollutant concentrations and particle concentrations or size distributions in a three-dimensional spatial domain. The results could be used to calculate the optical effects of the airborne particles. Mechanistic modeling that incorporates comprehensive calculations of particle concentrations but not size distributions is the current state of the art. This modeling can be achieved by extending acid deposition models or certain regional photochemical smog models to calculate concentrations of primary particulate substances as well as products of gas-to-particle conversion (Russell et al., 1988a; Middleton and Burns, 1991). To use this approach, however, to determine optical characteristics requires assumptions about particle size distributions. Size distributions are required in visibility studies because the optical properties of particles strongly depend on particle sizes. To produce a comprehensive mechanistic model for visibility impairment, direct calculations of chemically resolved airborne particle size distributions are needed in conjunction with a theoretical treatment of scattering and absorption of light by particles to calculate the optical properties of aerosols. The current understanding of atmospheric aerosol processes requires considerable refinement before such models can be used with confidence. The construction of such models is under way, but many years will be required for model evaluation. Traditionally, mechanistic models are classified as Lagrangian or Eulerian, the distinction being based on the reference frame used for the description of fluid motion. Lagrangian trajectory models quantify the

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Protecting Visibility in National Parks and Wilderness Areas TABLE C-1 Overview of Three-Dimensional Air Quality Model Model Area of Application References for Model Formulation References for Model Performance Evaluation RADM-II (Regional Acid Deposition and Oxidant Model) Eastern North America Chang et al., 1987 Middleton et al., 1988 ADOM (Regional Acid Deposition and Oxidant Model) Eastern North America and northern Europe Venkatram et al., 1988 Venkatram et al., 1988 STEM-II (Regional Acid Deposition and Oxidant Model) Philadelphia, Central Japan, Kentucky, and northeastern United States Carmichael et al., 1986 Carmichael and Peters, 1987; Chang, 1987 ROM (Regional Oxidant Model) Northeastern United States, and southeastern United States Lamb, 1983 Schere, 1986 RTM-III (Regional Oxidant Model) Northeastern United States, Minnesota, northern Europe, and San Joaquin Valley Liu et al., 1984 Liu et al., 1984; Morris et al., 1987 UAPM (Urban Oxidant and Particulate Matter Model) Los Angeles Basin McRae et al., 1982; Pilinis and Seinfeld, 1988a,b McRae and Seinfeld, 1983; Russell et al., 1988b

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Protecting Visibility in National Parks and Wilderness Areas Model Area of Application References for Model Formulation References for Model Performance Evaluation UAM/PARIS (Urban Oxidant and Particulate Matter Model) More than 10 urban and nonurban areas in the United States and Europe Reynolds et al., 1973, 1979; Seigneur et al., 1983 Roth et al., 1983; Seigneur et al., 1983 LIRAQ (Urban Oxidant Model) San Francisco Bay Area, Monterey, St. Louis MacCracken et al., 1978; Penner and Connell, 1987 Penner and Connell, 1987   Source: Seigneur and Saxena, 1990. Copyright ©1990. Electric Power Research Institute. EPRI EN-6649, Status of Subregional and Geoscale Models, Vol. 1. Air Quality Models. Reprinted with permission.

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Protecting Visibility in National Parks and Wilderness Areas complex transport of trace chemicals by assuming that all the substances are uniformly mixed within a chemically isolated parcel of air that moves through the atmosphere following the mean motion of the air. In contrast, Eulerian models adopt a fixed two-or three-dimensional grid system, and continuity equations for chemical substances are solved at each grid point to calculate time-varying concentrations of several substances over a specified domain. The Eulerian modeling approach provides the framework for most of the complex atmospheric photochemical models that represent the coupling and feedback among multiple physical and chemical phenomena. Within the Eulerian framework, it is possible to incorporate mathematical descriptions of numerous physical and chemical processes that are difficult to consider in the models with Lagrangian approaches, especially when the interaction of multiple sources with different spatial, temporal, and chemical characteristics must be considered and when model outputs are to represent concentration gradients over large geographical regions. Processes that are included in mechanistic visibility models are outlined in Figure C-2. The modeled airshed is divided into grids of a size that depends on the terrain characteristics. The grids are initialized with a set of chemical concentrations. For each grid cell, hourly meteorological and gas and particle emissions data are specified for typical computational periods of 3–5 days. The models that use this information to calculate the time-dependent three-dimensional distributions of gases and particle size distributions. Mechanistic models generally solve the following chemical conservation equation for each of the transported gas phase chemicals: where C is the species volume mixing ratio, V is the three-dimensional velocity vector at each grid point in the model domain, Ke is the eddy diffusivity used to quantify the subgrid-scale fluxes due to subgrid-scale turbulence, Pchm and Lchm are gas-phase chemical production and loss terms, E is the emission rate, (C/t)clouds is the time rate of change due

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Protecting Visibility in National Parks and Wilderness Areas FIGURE C-2 Mechanistic visibility modeling system.

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Protecting Visibility in National Parks and Wilderness Areas to cloud effects (including subgrid-scale vertical redistribution, aqueous chemical interactions, various nucleation and other droplet-related processes, and scavenging), and (C/t)dry represents the rate of change due to dry deposition. A general equation for calculating Qi, the concentration of the total aerosol mass in size category i, is given as: The term on the left represents the change in the total concentration of the airborne particle mass in size category i over time. The first term on the right refers to advection and the second to turbulent diffusion of the airborne particles. The growth term represents the change in concentration due to changes in thermodynamic equilibrium and nucleation of new airborne particles and condensation of vapor onto existing particles due to production of new material via gas-phase chemical reactions. The coagulation term represents the change in concentration due to coagulation of particles. The removal term represents the concentration change due to sedimentation, particle scavenging, and wet and dry deposition as well as the effect of cloud processing on the size distributions. Finally, Ei represents the change in aerosol concentration due to direct particulate emissions. For the proper treatment of visibility issues, it is essential that the models include appropriate descriptions of the aerosol processes. Mechanistic visibility models should involve two separate components. First, chemically resolved airborne particle size distributions need to be calculated at specified grid points. Information is required on the characteristics of primary particle emissions as well as on atmospheric aerosol processes that affect further evolution of particle size distributions. Processes that must be considered include advection, diffusion, coagulation, evaporative shrinkage or condensational growth of particles, gas-particle chemical reactions, cloud processing, and wet or dry deposition. There is a close coupling between the formation of secondary particles,

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Protecting Visibility in National Parks and Wilderness Areas which plays a major role in visibility impairment, and gas and in-cloud chemistry. Also, aerosol transport and removal by wet or dry deposition are dependent on local meteorology. Therefore, models that are used to determine airborne particle size distributions must be linked with meteorology and gas-phase chemistry models. Lorentz-Mie theory is used to calculate the optical characteristics of airborne particles by integrating over calculated particle size distributions. The particle-concentration prediction and the optical aspects of these computations involve mathematical approximations (introduced to speed up the calculations) and assumptions about the physical and chemical characteristics of atmospheric particles. These simplifications will affect the validity of calculated results. Therefore, the uncertainties associated with such model predictions need to be determined. The phenomena that need to be considered in developing the aerosol models vary among the different chemical species. For example, although some sulfate particles are emitted directly by sources, most sulfate particles are formed in the atmosphere by the chemical transformation of SO2 gas. Reactions that lead to sulfate particle formation can take place either in the gas phase or in liquid particles or cloud droplets. The size distribution and therefore, the optical properties of the secondary sulfate particles depend on the chemical transformation mechanism. Organic particles can be either primary (directly emitted as particles) or secondary (formed from gas-phase organic substances), although the relative contributions of both remain poorly understood. The particulate nitrate, ammonium, and water content are determined primarily by thermodynamic equilibrium between particles and gas-phase species. All particles are influenced by removal processes, although the extent of wet removal processes will depend on hygroscopicity and particle size. An important practical issue in developing mechanistic visibility models is the assessment of the detail and accuracy with which such processes need to be described to achieve satisfactory results. A variety of approaches has been developed for calculating the evolution of atmospheric particle size distributions. Several have been compared by Seigneur et al. (1986). The approaches differ in accuracy, computational speed, and ability to describe the behavior of multicomponent aerosol systems and internally and externally mixed particles. Each of these factors needs to be weighed in selecting the optimal model for a given application.

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Protecting Visibility in National Parks and Wilderness Areas Proper characterization of the relationship between aerosol concentrations, the properties of the visual environment, and the effect on the public of changes in visual air quality is central to correct prediction of the effects of visibility protection programs. The relationship between aerosol concentrations as determined by models and human perception generally is based on optical principles. Most work to date is based on the assumption that particles are spherical and that particles consist of homogeneous mixtures. Lorentz-Mie theory is then used to calculate the scattering and absorption of light by individual particles. The total extent of particle scattering and absorption is determined by integrating over calculated particle size distributions that are chemically resolved. Although the assumption is often reasonable for submicron particles, little experimental work has been done to examine its validity. The effect of nonspherical particles on light extinction needs to be considered in areas where coarse dust and fly ash are important contributors to visibility reduction. The scattering and absorption of light by air and NO2, respectively, are straightforward calculations. The optics calculations described above can be made for each of the grid points at which composition-dependent particle size distributions are calculated explicitly or implicitly by an air quality model. The calculations provide information on variations of atmospheric optical properties over the three-dimensional grid. Thus, for model calculations where particle size distributions are estimated, it is possible to use radiative transfer theory (Chandrasekhar, 1960) to calculate visibility indexes that depend on sight path, cloud cover and ground reflectance, color and texture of distant objects, and the angle between the observer and the sun, which requires data on the surrounding terrain and cloud cover. When composition-dependent size distributions are not calculated explicitly in the model, alternative approaches must be developed to link the aerosol composition information to optical factors. For example, in many field studies it has been observed that the atmospheric extinction coefficient per unit mass for certain airborne particle components (e.g., sulfate and elemental carbon particles) typically lies within a characteristic range of values. Those empirically determined extinction efficiency values could be multiplied by model predictions of aerosol species chemical concentrations to estimate the light-extinction coefficient that corresponds to a particular situation being modeled.

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Protecting Visibility in National Parks and Wilderness Areas HYBRID MODELS Hybrid models have been developed in the belief that no single mechanistic or receptor-oriented model can represent reality accurately under all circumstances and that each modeling approach has its own specific strengths and weaknesses. Hybrid (or composite) models offer the possibility of better resolution of source contributions by combining two or more receptor, trajectory, deterministic, or atmospheric chemistry models. For example, the multiscale source-receptor model suggested by Chow (1985) combines a regional scale trajectory model, a principal component analysis receptor model, a CMB receptor model, and an urban scale Gaussian dispersion model into a single composite modeling approach. Linear-Chemistry—CMB Hybrid Models Composite model research has been pursued because the current state of the art limits regulatory applications of conventional CMB receptor modeling to particulate matter that is directly emitted to the atmosphere. The remaining sulfate, nitrate, and organic compounds that are not attributed to primary emissions are classified as secondary substances and cannot be attributed to specific sources, thereby severely limiting conventional use of the CMB model in visibility studies. If additional assumptions are made, hybrid CMB-atmospheric chemistry models can be used to extend conventional CMB modeling beyond the limits outlined in EPA's regulatory guidance. If one accepts the assumption that conversion of reactive gases (e.g., SO2) to secondary particles (e.g., SO42-) is complete and that the secondary substances have not been preferentially deposited en route to the receptor, secondary particles can be apportioned among contributing source types. In real-world applications where conversion is not complete or the secondary particles are deposited during transport, CMB has been used only in research settings to quantitatively estimate secondary aerosol source contributions. Several investigators have proposed secondary aerosol hybrid receptor models that include SO2-to-sulfate transformation and deposition terms, but none of the models has undergone thorough validation study (Stevens and Lewis, 1987; Dzubay et al., 1988).

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Protecting Visibility in National Parks and Wilderness Areas Lewis and Stevens (1985) proposed a hybrid model that typifies the current state of hybrid models developed as a direct extension of the chemical element tracer approach that forms the basis of CMB receptor modeling methods. In that model, the secondary sulfate concentration from a specific source is estimated as where Mp is the mass concentration at the receptor of primary fine particles from the source, A is the ratio of the source mass emission rate for SO2 and fine particles, and T describes both the transformation of SO2 to sulfate in the atmosphere and its loss due to deposition at the earth's surface. A chemical reaction model is needed to specify the extent of conversion, T, of SO2 to form sulfate. Mp can be estimated by CMB receptor model applications or by use of multiple linear regression analysis. Mp also can be estimated using source tracers such as deuterated methane (CD4) when the assumption is made that the tracer is associated uniquely with a specific source. Tracer applications are discussed below. Lewis and Stevens theorize that these hybrid models are limited to distances of less than 200 km because of the following factors: (1) the concentration of source tracer elements used to estimate Mp must be above measurement detection limits; (2) particle fractionation effects during transport due to the differing size distributions of the chemical species must not occur; and (3) the estimate of plume age required to calculate T becomes less certain as the distance from the source increases. Given those limitations, the principal assumptions inherent in the application of the hybrid model of Lewis and Stevens for secondary aerosol apportionment are as follows: (1) dispersion, deposition, and transformation processes are linear or pseudo-first-order processes in nature; (2) dispersion affects all three pollutants (SO2, sulfate, and Mp) identically; (3) dry deposition is the only form of deposition that occurs (wet deposition, and oxidation by aqueous phase and heterogeneous processes are excluded); (4) deposition affects all the fine particles in the same way, but the rate of deposition of SO2 might be different; (5) secondary sulfate is produced only by homogeneous gas-phase oxidation of SO2; and (6) plume age can be estimated from available wind data.

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Protecting Visibility in National Parks and Wilderness Areas If the path of the air parcel can be computed by trajectory analysis, then plume age can be estimated more exactly. Many real physical situations of interest may occur outside the bounds of the above assumptions (e.g., heterogeneous SO2 oxidation in clouds often is important). A second type of composite model has been developed that employs CMB receptor modeling for attribution of primary airborne particles to their sources, accompanied by a separate deterministic model for sulfate formation and transport that is driven by atmospheric transport, reaction, and dilution calculations rather than by tracer concentration data (Harley et al., 1989). This approach employs the sulfate formation model of Cass (1981), which is based on gridded SO2 and primary sulfate emissions, hourly wind speed, wind direction, mixing height, dry deposition rates, and measured or computed atmospheric pseudo-first-order rates for conversion of SO2 to sulfates. The composite model has been applied to study the least-cost solution to the aerosol control problem in the Los Angeles basin (Harley et al., 1989). Additional hybrid modeling can be envisioned in which tracer or CMB models are used for elements of the source attribution problem that are difficult to determine with a deterministic model (e.g., predictions of airborne soil-dust concentrations). More complete deterministic models for secondary airborne particle formation would then be used to compute sulfate, nitrate, and secondary organic particle concentrations along with those primary particle concentrations that are due to ducted emission sources.