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3 Theoretical Models of Regional Air Quality Analysis of the spatial and temporal behavior of atmc- spheric parameters and climatological patterns depends on ~ thorough theoretical understanding of the physical and chemical processes involved. That understanding, in turn, depends on observations of phenomena in the field and in the laboratory. One purpose of analyzing the relationships between emissions of precursor gases and deposition of acidic or acid-forming substances is to develop means for assessing the potential effectiveness of alternative proposals for mitigating the adverse effects of acid deposition. Uncertainties in the current understanding of the relevant physical and chemical processes are reflected in uncertainties in analytical models of these relationships. Construction of analytical models is a typical method by which scientists approach complex problems. For many years earth scientists have been developing knowledge about flows of substances in the environment (within and among the atmosphere, hydrosphere, biosphere, and lithosphere). All elements cycle naturally through the environment; sulfur and nitrogen are two prominent examples. Models have been developed--some conceptual, some empirical, some theoretical--to organize that knowledge in ways that allow predictions to be made that are subject to testing. In recent years, this analytical approach has taken on considerable practical importance, because of the need to assess the implications of anthro- pogenic disturbances on natural ecological processes. So it is with models of acid deposition. In this report we are concerned with only part of the phenomenon of acid deposition: the relationships between emissions and deposition. Models of the cycling of sub S5

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56 stances in the hydrosphere, biosphere, and lithosphere are beyond the scope of this report. Models of the distribution of emissions through the atmosphere and their subsequent deposition can be divided into two classes: theoretical and empirical. Empirical models consist of analyses of observations in the field; Chapter 4 deals with empirical approaches used to manipu- late data and test hypotheses. In the class of theo- retical models are both deterministic calculations and estimates of material balance (or budgets); the current state of the art in these approaches is described below. MATERIAL BALANCE The method of material balance or budgeting involves assessing the gross flows of a substance into and out of compartments of the environment. The compartments are defined for the purposes of analysis; they are generally large, so that detailed behavior of constituents is not considered. Leaving out the detail, of course, means that the results may provide only general guidance and understanding. The most straightforward approach to budgets for acid deposition is to segment processes into one or more compartments, allowing flow between the compartments (e.g., Charlson et al. 1978). Budgets for sulfur in the atmosphere have been constructed for the global atmo- sphere (Granat 1976) and for regions of Europe and eastern North America (e.g., Galloway and Whelpdale 1980, Granat et al. 1976, Shinn and Lynn 1979). A summary of two budgets for eastern North America is shown in Table 3.-1; these calculations were made for each category by somewhat different means. They present a qualitatively similar (but quantitatively different) picture of the sulfur oxide transport and deposition in the eastern United States as well as export to the Atlantic Ocean. Other than giving estimates for the average annual deposition over large areas, these types of calculations reveal little about the consequences of changing anthro- pogenic emissions of sulfur or nitrogen. They also provide no guidance about the deposition of acid-producing material on specific regions that are ecologically sensitive. They do, however, provide a sense of the scale of exports of atmospheric pollutants from one region to another.

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57 TABLE 3.1 Companson of Atmospheric Sulfur Budget Estimates for the Eastern United Statesa and Northeastern United Statesb in teragrams (million metric tonnes) per year Galloway and Whelpdale (1980)a Shinn and Lynn ( 1 979)b Input Man-made emissions 14 7.5 Natural emissions 0.5 0.6 Inflow from oceans 0.2 Inflow from west 0.4 Transboundary flow 0.7 15.8 8.1 Output Transboundary flow 2.0 (1.1) Wet deposition 2.5 1.5 Dry deposition 3.3 2.5 Outflow to oceans 3.9 3.0 11.7 8.1 aArea east of 92 W (Mississippi River). Connecticut, Delaware, Illinois, Indiana, Kentucky, Maryland, Massachusetts, Michigan, New Jersey, New York, Ohio, Pennsylvania, Rhode Island, Virginia, and West Virginia. One application of the method has been to assess the transport of pollutants across international boundaries. Because certain pollutants, particularly sulfates and nitrates, may be transported large distances from the sources of their precursor gases, air pollution is an interstate and even an international issue. Not all the sulfur and nitrogen emitted from sources in the United States comes to the ground in the United States, and not all the sulfur and nitrogen that comes to the ground in the United States is emitted from sources in the United States. The same, of course, can be said for states and regions within the United States. It has been estimated that, of the total sulfur emitted to the atmosphere in the eastern part of the United States, about one third is transported to the western Atlantic Ocean and beyond, while roughly one sixth is exported to Canada. The remainder, about one half, falls in the United States (Galloway and whelpdale 1980). The fraction of the exports of atmospheric sulfur from the United States to Canada that is deposited in Canada is unknown. It has been hypothesized that the fraction of Canadian emissions of sulfur that falls in Canada is larger than the fraction of U.S. exports to Canada that

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58 falls in Canada. This supposition can be explained by the differences in the deposition processes for SO2 and sulfates and the fact that U.S. exports of atmospheric sulfur to Canada are likely to be richer in sulfates than Canadian emissions. Nevertheless, more sulfur is deposited than emitted in eastern Canada (Galloway and Whelpdale 1980), so U.S. exports can account for substantial quantities of the sulfur deposited there. DETERMINI STIC MODELS Most of the effort to develop models of acid deposition during the past decade has been devoted to deterministic descriptions of the distribution of sulfur oxides in plumes. The work has grown from efforts to develop plume models for studying effects of emissions on ambient concentrations of pollutants at relatively small distances from sources. Current models used to analyze regional pollution problems such as acid deposition apply to areas of the order of 106 km2 and focus on long-term "annual) average behavior, taking into account emissions, airflow, mixing, chemical transformations, and both wet and dry deposition. Generally, chemical transformations and deposition processes are treated parametrically, whereas transport is calculated using available data on wind fields, for example. The models are based on sets of continuity equations for concentrations of the species of interest; the continuity equations are coupled through terms representing the production and destruction of species in chemical reactions. The equations are solved using computers. In effect, deterministic models represent detailed material balance calculations analogous to the compart- mentalization approach mentioned earlier, but in this case the compartments in the atmosphere are much smaller, so detailed behavior must be included. Once confidence in deterministic models has been achieved, through testing and verifying, it should be possible to use them to assess the potential consequences of alternative proposals for mitigating acid deposition, since sensitivity tests would be feasible with this type of model. There is a variety of regional models for average deposition rates of sulfur oxides over eastern North America (e.g., U.S./Canada Work Group #2 1982). The models use different approximations to characterize

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so atmospheric processes (Table 3.2). They have not been verified systematically because of a lack of observa- tional data. However, testing and initial comparisons of several models for annual averages indicate that their accuracy in estimating either ambient SOx concentrations or wet-deposition rates is inadequate for quantitative assessment of the effects of emissions from specific sources (U.S./Canada Work Group #2 1982). Initial comparisons show no preference by performance for a specific model for application to the situation in eastern North America, although from the limited number of comparisons currently available, it appears as if models that treat meteorological parameters in a gross statistical sense appear to perform as well as the more sophisticated models (U.S./Canada Work Group #2 1982). At least three models (SURADS, ATM-II, and STEM) are capable of simulating regional sulfate pollution episodes over eastern North America (Table 3.2). These models use added sophistication in treating atmospheric processes, including incorporating multilevel winds and mixing, diurnally varying chemistry according to photochemical modeling, and variable dry-deposition rates. However, the SURADS model has not incorporated cloud processes and wet deposition in published applications. Tests of the SURADS model against the data from the Sulfate Regional Experiment yielded promising results for ambient sulfate conditions but less satisfactory results for sulfur dioxide concentrations "Mueller and Hidy 1982a). The other two models, RTM-II and STEM, incorporate cloud processes and other aspects of precipitation chemistry, but their performance in comparison with observations has not been reported. Treatment of Transport and Mixing Because long-range transport is at the heart of the controversies surrounding acid deposition, we review here the ways in which regional-scale models typically treat trajectory analysis. Meteorologists have approached the transport problem in a number of ways. The simplest method is to use observed values of horizontal winds at specified altitudes to calculate by interpolation where the winds would carry a given air parcel containing the material of interest (i.e., Lagrangian or trajectory model). This type of trajectory model has been widely used and is referred to

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76 Nonlinearity in the SO2 transformation of the Rodhe et al. model was also observed in subsequent studies by Sampson (1982). He employed a somewhat improved hydro- carbon reaction scheme, but in other respects the mechanism was identical to that employed by Rodhe and his co-workers. Some of Sampson's results are reproduced in The solid lines in the figure Rive Samoson's Figure 3.1. _ _ results for the percentage change in ambient sulfate concentration after 24, 48, and 96 hours of transport from the source region as a function of changes in SO2 emissions. The results of the model suggest that a relatively small reduction in sulfate levels (roughly 15 percent) may result for long transport times (96 hours) from a 50 percent reduction in SO2 emissions. The results of Rodhe et al. and Sampson should be treated with caution. The so-called Rodhe-Crutzen- Vanderpol model used in both studies employed specific sequences of chemical reactions and assumed uniform additions of polluted background air throughout the period of transport and transformation. Different choices of oxidation pathways and changes in the strong background source may alter the results significantly. For example, the dashed lines of Figure 3.1 are the result of running Sampson's computer program without continuous dilution of the product mixture with background air containing sulfate (P.J. Sampson, University of Michigan, personal communication, 1982). The shift toward the linear curve (from the solid to the dashed curves in Figure 3.1) is the result of eliminating the trivial source of nonlinearity arising from the background source, term B in the equation, c = kS + B. considered earlier. The dashed lines of Figure 3.2 are the result of both deleting the background source of sulfate and selecting an alternative pathway for the homogeneous gas phase oxidation of SO2. Note that the alternative assumptions give a result that is essentially linear (with proportionality constants less than unity). The original Rodhe-Crutzen-Vanderpol model employed reaction (3.1) for oxidation of S02, HO + SO2 ~ H2SO4, (3.1) whereas the modification that produced the dashed curves of Figure 3.2 used HO + SO2 (+ O2, H2O) ~ H2SO4 ~ HO2. (3.2)

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77 Reaction (3.1) is a single, simplified reaction in which an attempt is made to condense the chemistry that occurs in and following the primary hydroxy radical attack on so2 HO + SO2(+M) ~ HOS02(+M) [Equation (A.56) in Appendix A]. See Appendix A for a more complete discussion of the reaction. The use of reaction (3.1) is equivalent to assuming that the addition of the hydroxy radical to SO2 ter- minates the chain reactions of the HO radical, and by some undefined process the initial product of reaction (3.3) leads to H2SO4 without regenerating a chain- carrying species. The assumption of reaction (3.1) perturbs the atmospheric reaction cycles involving HO2 and HO radicals, which result in the oxidation of hydrocarbons, aldehydes, CO, SO2, NO, NC2, and other impurity species. For example, the oxidation of CO occurs in reactions (3.4) through (3.6) by way of HO-radical attack on CO: HO + CO ~ H + CO2' H + O2(+M) ~ HO2(+M), HO2 + NO ~ HO + NO2. (3.3) (3.4) (3.5) (3.6) Note that although an HO radical is lost in reaction (3.4), another is regenerated in reaction (3.6). Similar cycles occur involving CH2O and the hydrocarbons, for example. Now if a reaction such as (3.1) occurs, an HO radical is removed; no further regeneration of the HO radical occurs. In writing reaction (3.2), we assume in accordance with experience in other atmospheric reaction cycles that a chain-carrying radical (HO2) is developed following the occurrence of reaction (3.3). For example, reaction (3.2) summarizes the net result of the sequence (3.3), (3.7), and (3.8): HO + SO2(+M) ~ HOSO2(+M), HOSO2 + O2 ~ HO2 + SO3, SO3 + H2O ~ H2SO4. (3.3) (3.7) (3.8) Presumably, reaction (3.7) would often be followed by regeneration of the HO radical through reaction (3.6), at least in NO-rich polluted atmospheres.

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78 -50 -30 -10 24h 24h' ~/ 48h ~/ +50- _ ~ t 1 0 ~ :48h ~1 1 1 1~ +50 96h, ~ ~I +10 +30 _ _ _ -50 - _ -30 ASO2(percent) with reaction (3.1 ) and sulfate background with reaction (3.1 ) but without su If ate backgrou nd FIGURE 3.1 Effect of the assumption of background sulfate on the Rodhe-Crutzen- Vanderpol model for chemical transformation. SOURCE: Sampson (1982) and P.J. Sampson, University of Michigan, personal communication (19823. The participation of reaction (3.1) results in a direct nonlinear feedback into the SC2 oxidation mechanism, while reaction (3.2) does not seriously perturb the concentration of the hydroxy radical. The best available experimental evidence today supports the contention that the HO level in reacting mixtures of hydrocarbons, NOx' and SO2 is relatively insensitive to SO2 concentrations and that the sequence (3.3), (3.7), (3.8), or some similar chain-propagating reactions, is important (Stockwell and Calvert 1983). In the experiment, Stockwell and Calvert varied the amount of

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79 +50 ~ - a, Q +30~ 11 ~ o u' a +10 -50 -30 - 1 0 _ _ / / '' /~' /~' 1 1 l I r I I - +10 +30 +50 96h A' ~ 48h 24h 96h~D 48h ~ ',;~/ 24h ''''/ ~ ~ / 24h '''',/ 48h ~ / 96h ~ i\SO2 (percent) ,~,7 -30~ -50 ~ with reaction (3.1 ) and sulfate background with reaction (3.2) but without sulfate background FIGURE 3.2 Effect of the assumptions of background sulfate and chain termination on the Rodhe-Crutzen-Vanderpol model for chemical transformation. SOURCE: Sampson (1982) and P.J. Sampson, University of Michigan, personal communication (1 982). SO2 in dilute, irradiated mixtures of CO, MONO, and NOx in air (at 1 atm), monitored the concentration of HO radicals by measuring the rate of formation of CO2, and observed the ultimate formation of H2SO4 aerosol as identified by its infrared spectrum. Within the limits of experimental error, the concentration of HO radical was found to be insensitive to the concentration of SO2 even when as much as one half of the HO radicals in the system reacted with SC2 leading ultimately to

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80 the formation of sulfuric acid aerosol. Chain termina- tion as implied in reaction (3.1) was found not to be important. The main point to recognize from this discussion is that either an apparent near linearity or a nonlinearity in the model may result from different, rather subtle, simplifying assumptions related to the choice of chemical mechanism. We conclude from these results that deviations of SO2 conversion rates from linearity with respect to SO2 concentration may be much smaller than has been implied recently from the results of simulations employing the seemingly realistic yet simplified reaction schemes. Generation of nitric acid in gas-phase reactions does involve termination of an HO-radical chain directly via HO + NO2(+M) ~ HNO3(+M), (3.9) and in this case we must expect the concentration of the reactant HO to be a function of the NO2 concentration. The concentration of the HO radical in an air mass is determined by the rates of reaction that generate it and those that destroy it. That is, at any time t the steady-state concentration of HO is given by [HO] = 7(Ri)t/ki[Ai]t, where [(Ri)t is the sum of the rates of all HO- radical generating reactions at time t, ki is the rate constant for the ith removal reaction of HO with reactant Al, and the summation [ki[Ai]t extends over all HO-loss reactions. It should be noted that reaction (3.9) is only one of several HO-HC2-radical chain termination reactions that occur in the troposphere. Thus in theory the effect of small changes in the concentration of NO2 on the concentration of HO is not expected to be dramatic. For example, computer simulations of the chemistry of the polluted atmosphere (see the mechanisms of Calvert and Stockwell 1983) show that only about 10 percent of the HO-HO2-radical termination occurs through the HO-NO2 reaction (3.9) for a tropospheric air mass typical of an urban, polluted area with an ambient concentration of NOX of 100 pph at sunrise. Air masses containing one tenth and one one-hundredth of this concentration of NOX at sunrise, but the same levels of other pollutants as before, give about 0.1 and 0.01 percent of the total HO-HO2-radical chain termination through reaction (3.9). The time dependence of the concentrations of

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81 reactants that form HO or react to destroy it are complex functions of the initial pollutant concentrations, so that the quantitative effect of the concentration of HO on NOX initial concentration can be obtained only through detailed calculations. However, the net effect of lowering the initial NOX concentration by a factor of 10 (from 100 to 10 ppb) while keeping all other impurities at the same fixed level of the highly polluted air mass is to lower the maximum HO concentration from 1.6 x 10 7 to 0.96 x 10-7 ppm, only a factor of about 1.7. Clearly the dependence of HO concentration is not so sensitive to NCX concentration as one might have expected at first consideration. Thus a more detailed analysis of the complex homogeneous chemistry of the troposphere predicts that the relationship between changes in ambient concentrations of SO2 and changes in gas-phase formation of sulfate should exhibit only small deviations from linearity. The simple theoretical considerations of Oppenheimer (1983) lead to the same conclusion. Nonlinear conversion of SO2 to sulfate can in theory result from the liquid-phase oxidation of SO2 (HSOi) by hydrogen peroxide (H2O2). For certain atmospheric conditions a limited supply of H2C2 may exist in the atmosphere through gas-phase reactions (3.10) to (3.12): 2HO2 ~ H2O2 + O2, HO2 ~ H2O ~ HO2eH2O' HO2. H2O + H2O ~ H2O2 + H2O + O2. The rate of hydrogen peroxide generation in reactions (3.10) and (3.12) depends on the square of the HO2 radical concentration. In NO-rich polluted atmospheres, however, reaction (3.6), the rate of which is proportional to the first power of the HC: concentration, competes favorably for HO2 radicals. Reaction (3.6) is very fast in NO-rich atmospheres, with the result that the generation of H2O2 in reactions (3.10) and (3.12) is suppressed. Although the uptake of the limited H2k into cloud water and rain will take place efficiently, for these circumstances the amounts of H2O2 may be significantly less than those of HSo] in the water. Obviously, the oxidation of only a fraction of the HSO3 can occur for these con- ditions, and the reaction becomes oxidant limited. SO2 in cloud water cannot be oxidized faster than the oxidant is provided to the droplet. (3.10) (3.11) (3.12)

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82 Note that for the case of an oxidant-limited reaction, a nonlinear response in sulfuric acid deposition will result from emission reductions. Only when Sal emissions are reduced so that ambient concentrations of SO2 approach the level of the oxidant present in cloud water will a decrease in the sulfuric acid formation and deposition result. For example, if the H2O2 available in cloud water were consistently only 40 percent of the SO2 that is dissolved in the cloud water at a given location, and if oxidation occurred largely through the H2Oz-HSO3 reac- tion, then a 60 percent reduction of the SON would result in no reduction in the sulfuric acid in cloud water at this location, but subsequent reductions would lead to proportionally lower acid formation and deposition. It is also possible that even with sufficient oxidant in cloud water, other substances that may also be present, such as formaldehyde, may inhibit the H2O2-HSO3 reaction. Existing analytical data for H2O2 in clouds do not allow an unambiguous conclusion to be reached today on the possible importance of these nonlinear effects. Limitation of oxidant for HSO3 or SO2 may arise because of physical processes as well as the chemical influence described. For example, we have noted pre- viously that it is likely that H2O2 vapor present in dry air dissolves in cloud droplets to provide oxidant for the conversion of SO2. Hydrogen peroxide is a very soluble gas and may be rained out early in some storm systems, leaving a significant fraction of SO2 vapor unreacted. Several types of nonlinear effects may be expected from factors not immediately related to oxidant levels. For example, as described in Chapter 2 and Appendix A, there is some evidence that SC2 is oxidized more readily in the aqueous phase than in the gas phase. Also, increased concentrations of alkaline soil dust in the air due to drought or changing wind patterns can result in the neutralization of precipitation acidity. In the absence of extensive measurements, we judge that nonlinear effects of SO2 emission control on acid deposition that arise from chemical conversion mechanisms are probably small for the gas-phase conversion steps, but significant nonlinearity is anticipated for certain special conditions such as an oxidant-limited H2O2-HSO3 reaction in cloud water. However, these conditions cannot be tested from the existing data base.

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83 FINDINGS AND CONCLUSION S Application of current air-quality models to regional- scale processes has provided guidance on the significance of dynamic processes influencing sulfur deposition. Theoretical models have provided results that are qualitatively consistent with empirical observations, thus demonstrating important temporal and spatial scales of source-receptor relationships. Qualitatively the models have pointed to the importance of certain geo- graphical groupings of SCAN sources and the potential influence of the sources on certain receptor areas. However, current models have not provided results that give confidence in their ability to translate SO2 emissions from specific sources or localized groupings of sources to specific sensitive receptors. Little has been done in models to translate NOx emissions into nitrate deposition or to link sulfate and nitrate to acid (H+) deposition. These capabilitities are considered assent tial for models to be used to study the consequences of alternative control strategies in circumstances in which long-range transport processes are involved. Because of the simplifying assumptions that are made in order to develop practical, economical regional-scale models of air quality and because data are not available to validate or verify them, researchers in the field gent orally have only limited confidence in current results. The models and their results are useful research tools. However, because of deficiencies in the base of meteoro- logical data required as input and because of the sen- sitivity of their output to simplifying assumptions regarding both the physical and chemical processes, we do not regard currently available models as sufficiently developed to be used with confidence in predicting responses of the atmospheric system to alternative control strategies. Despite these limitations, theoretical models are and probably will continue to be used in industrial and urban planning, for which spatial scales are smaller than those of interest in acid deposition. Given the state of knowledge of the physics and chemistry of the atmosphere in the context of long-range transport of air pollution, and given the state of the art of techniques for making quantitative estimates, we advise caution in projecting changes in deposition patterns that result from changes in emissions of precursor gases.

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84 On the basis of laboratory evidence, we conclude that an alternative to the model of Rodhe et al. (1981), which has been widely used to represent the chemical processes involved in acid deposition, more correctly employs gas- phase reactions leading to oxidation of SO2 that results in HO-HO2-radical chain propagation. Laboratory evidence suggests that chain-terminating reactions involving SO2 probably play only a minor role in atmospheres polluted with SCt. When the Rodhe-Crutzen-Vanderpol model is modified so that SC2 oxidation does not terminate chains, the nonlinearity in the relationship between changes in ambient SO2 concentrations and changes in ambient sulfate concentrations (i.e., the commonly reported result of the Rodhe model) is greatly reduced. Laboratory and field studies as well as theory suggest that oxidation of SO2 in cloud water is rapid and come plete, provided that concentrations of oxidants (H2O2, O3) are sufficient (see Chapter 2). Measurements of oxidant concentrations in cloud water, although limited, suggest that concentrations may be sufficient in eastern North America for complete oxidation of SC2, except perhaps in winter. If this is the case, then strong deviations from linearity in the relationship between changes in annual average ambient SO2 concentrations and changes in the net production of sulfate in clouds would not be expected. The relationships between emissions of so2 and NOX and the deposition of sulfuric and nitric acids are complex. Models to predict patterns of the deposition of hydrogen ion will have to account for neutralizing substances as well as sulfuric and nitric acids. Assuming that the ambient molar concentrations of NOx and basic substances (such as ammonia and calcium carbonate) remain unchanged, we conclude that a reduction in sulfate deposition will result in at least as great a reduction in the deposition of hydrogen ion. REFERENCES Calvert, J.G., and W.R. Stockwell. 1983. Deviations from the O3-NO-NO2 photostationary state in tropospheric chemistry. Can. J. Chem. (in press). Carmichael, G.R., and L.K. Peters. 1983. An Eulerian transport chemistry removal model for SO2 and sulfate. Atmos. Environ. (in press).

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