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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
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.
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
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
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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66 as a constant-level (isobaric) trajectory (Heffter and Ferber 1977). The vertical component of the wind is ignored in this approach, so the method does not give true trajectories in many circumstances, such as near frontal zones or over a mountain range. A more sophisticated, but not necessarily better, approach is to assume an isentropic trajectory. In essence this method takes account of the fact that an air parcel will not in all cases follow a horizontal pressure surface but will remain on a surface of constant potential temperature. Calculations of isentropic trajectories therefore incorporate some large-scale vertical motions. However, the isentropic model still does not account for vertical motions in clouds or when isentropic surfaces intersect the terrain. The more complicated the single- trajectory models become, the less application they have in day-to-day operational use because of increased requirements for computer time and power. Single forward trajectories are rarely used to investigate precipitation chemistry because many sources usually contribute acidic precursors along the path of flow. An alternative approach is to compare the single backward trajectory to a given precipitation event. In back-trajectory analysis a parcel is traced back in time from a given precipitation event, allowing evaluation of the contributions of possible sources along the path of the parcel. In the absence of multiple sources along a path, single-trajectory analysis can be useful. For example, the episodic data on precipitation chemistry collected in Bermuda have been analyzed with the technique by Jickells et al. (1982). They found that when airflow was from the North American continent the acidity of the precipitation was an order of magnitude higher than when the rains were associated with flows from other directions. The North American continent evidently is the major source of acidic precursors in Bermuda, which is more than 1,000 km from the mainland. Limitations of single-trajectory analysis in describ- ing transport have caused meteorologists to develop multiple-trajectory Lagrangian models and models based on calculations at fixed points in space. In the latter (Eulerian) model, concentrations of atmospheric constitu- ents at fixed points are calculated for successive intervals of time based on concentrations calculated for previous intervals. Because the fixed points in space
67 are usually arranged in a grid pattern, the model is also known as a grid model. Single-trajectory calculations directed backward from receptors are sometimes helpful for identifying source areas frequently contributing to deposition at selected receptor sites. Grid models are most efficiently used for weighting the contributions of many sources to several receptors. Early work comparing back trajectories to limited event data on precipitation chemistry indicated that in the Northeast the more acidic precipitation came with flows from the Southwest (Kurtz and Schneider 1981, Miller et al. 1978). More recent studies using an improved data base show that single-trajectory analysis at a site in the Northeast suggests a regional acid precipitation phenomenon (Wilson et al. 1982). Compared with the interior of the United States, a much larger portion of the average annual precipitation in the Northeast is associated with cyclonic disturbances (low-pressure systems). The main tracks of cyclonic storms tend to converge in the northeastern United States and southeastern Canada (see Figure 4.7, Chapter 4). Thus the areas of eastern North America regarded as being particularly sensitive to acid deposition receive precipitation from storm systems with origins at almost any latitude in the interior or the West. Additional evidence that the air shed of the sensitive area is of synoptic scale is presented in Chapter 4. To date, acid-deposition models treat transport and mixing in terms of trajectories and diffusion. Episode models in current use take account of air pollution embedded in synoptic-scale weather systems, but they require great detail in inputs on wind, temperature, and moisture fields. Verification of any model is critical to its acceptance both as a description of scientific understanding and as a tool for analyzing policy choices. Methods are avail- able for testing the validity of trajectory calculations. Among the first was the use of special balloons, called tetroons, that maintain a constant altitude (Pack et al. 1978). Tetroons were released and tracked on the assump- tion that they behave like an idealized air parcel, despite the fact that they are confined to a surface of constant density. Because of logistic and other problems, however, this method has all but been abandoned, except in short-range experiments. A more effective method of
68 verifying trajectory calculations is to release an inert tracer, such as perfluorocarbon or an isotonically rare methane (such as CD4), that can be measured 1,000 km downwind or more. Plans are now being made to release tracers under a number of meteorological conditions to evaluate trajectory calculations. While techniques for computing trajectories have advanced markedly over the past decade, they still are plagued by a host of uncertainties. _ _ One difficulty that all such techniques share is the sparsity of meteoro- logical data. Upper-air soundings are made only twice daily at widely separated stations in the United States. More fundamentally, trajectory models incorporate simplifying assumptions, such as isobaric or isentropic behavior, that only approximate the true behavior of air masses. Consequently, in situations in which the assump- tions are not valid, model calculations may be unreliable. An example is the vicinity of storm systems, in which complex flows and thermodynamic processes limit severely the validity of the single-layered approach. Two different calculations of a trajectory in the vicinity of a frontal storm system appear in Figure 2.3, Chapter 2. One uses a constant-pressure (isobaric) surface and the other a constant-entropy (isentropic) surface (Davis and Wendell 1977). The trajectories were calculated for the same conditions and start from the same point (near St. Louis). The calculated positions of the two theoretical air parcels after 24 hours of transport are several hundred kilometers apart. Although the isentropic trajectory is expected to be closer to reality, Figure 2.3 contains no information about the location of the "reals trajectory in this case. The plot provides a graphic illustration of the level of uncer- tainty in current capabilities for predicting trajectories. The weaknesses in trajectory models are of particular concern because it is precisely in storm environments-- for which current models are weakest--that it is most important to trace pollutants with accuracy. Although transport theory suggests that errors in estimates of cra~eccorzes in clear air will tend to cancel if averages are taken over multiple events, large systematic biases may be expected in storm situations. Such uncertainties make attribution of specific deposition events to specific sources particularly difficult. _ _ _ . . . · . .
69 Treatment of Transformation Chemistry The extent to which realistic chemistry is incorporated into current regional models varies significantly. Most models used recently (see Table 3.2) employ absolutely no chemistry but include instead only a fixed SO2 transfor- mation rate (usually 1 to 4 percent/in). Results from such models should not be relied on in the development of control strategies for regional air-quality problems in which chemical phenomena play a central role. Attempts have been made by Rodhe et al. (1981) to include some chemistry (19 reactions) in their trans- formation-transport model. However, this work includes only a rudimentary scheme of gas-phase reactions involving only molecules of 03, CO, CH4, C2H4, CH2O, H~O2, NOR NO2, HNO3, and H2SO4 with intermediates of HO, O( D), O( P), and HO2. One aqueous-phase reaction was included super- ficially as SO2 + H2O2 + "CLOUDS ~ H2SO4. It is interesting, however, that Rodhe et al. con- cluded (p. 139) that "when dealing with a coupled chemical system like the one we have studied one may not assume a proportional dependence of concentrations on c`~'v`` ~ Acts. ~ -~-ney suggest, as we do, that models must include the essential chemistry that controls the oxidation of SO2, NO, NO2, and hydrocarbons in the atmosphere. It is almost certainly true that the scheme of Rodhe et al. fails to do this properly. Other chemical reaction schemes have been adapted for regional-scale models. Mueller and Hidy (1982b) have reported the application of a homogeneous gas-phase reaction scheme in the SURADS model. This calculation is run to generate a diurnally varying oxidation rate for sulfate that accounts for hydrocarbon vapor/nitrogen oxide emissions and their atmospheric distribution. This flaw en currently Is being extended to incorporate cloud chemistry in the chemical processing. It has been used in an integrated stepwise manner in the ELSTAR trajectory model (e.g., Lloyd et al. 1979). The STEM series of con; ~ an_ __~_ B~ mom models (e.g., Carmichael et al. 1983) and the air shed model reported by Stewart et al. (1983) incorporate a significant number of gas-phase reactions and cloud processes into an Eulerian grid calculation. The performance of the chemistry in these very complex numerical simulation schemes has not yet been compared with simpler schemes or with each other.
70 Treatment of Dry and Wet Deposition Dry deposition is usually treated parametrically in models rather than in terms of the fundamental physics of the processes. For example, simple treatments assume that the rate at which gaseous SO2 or sulfate aerosol particles reach the ground is directly proportional to the atmospheric concentrations of the respective pol- lutants near the ground. The constant of proportional- ity, called the deposition velocity, is often assumed for simplicity to be independent of spatial coordinates and time. Because dry-deposition processes depend on char- acteristics of ground cover, surface roughness, and stability of the air layer immediately above the surface, more sophisticated treatments use variable deposition velocities according to the spatial dependence of these conditions. The deposition velocity may also be taken to vary diurnally or can be estimated from aerodynamic param- eters, such as surface winds. Resistance to gas-phase transfers associated with the stomata of leaves or the assimilation capacity of underlying surfaces can also be incorporated in theoretical treatments. The dry- deposition velocities for sulfate aerosol particles are usually assumed to be somewhat less (between 10 and 50 percent) than those for gaseous SO2. More generally, the rate of particle deposition is dependent on size, but currently available models have not yet taken this dependence into account. Dry deposition of NO2 differs somewhat from that of SO2 and is sometimes taken to be as little as one half that of SO2. There are no regionally representative measurements of dry deposition. Therefore the parameterizations adopted in models have not been tested extensively. are based on limited experiments in the field or in wind tunnels. Thus the limitations of the parameterizations have not been established quantitatively. On the basis of comparison of model outputs with measurements, parameterization of dry deposition should be known within a factor of 2, but the range of measurements is much larger than this (e.g., Sehmel 1980). The parameterization of wet deposition is extremely difficult for episode calculations because of the variability in time and space of cloud cover, cloud depth, and precipitation. Over a long period of time, such as a year, averaged wet deposition is assumed to be proportional to the total quantity of precipitation or Instead they
71 the precipitation rate. The parameterization of wet deposition typically is one of two types, both of which should be considered as being in rudimentary stages of development. The first class of parameterization involves the scavenging coefficient, which is defined as the rate at which an air pollutant is incorporated into precipitation per unit volume divided by the local concentration of the pollutant. If the scavenging coefficient is known, then wet removal can be calculated in a relatively straight torward manner on the basis of airborne pollutant con- centrations. _ _ _ ~_ ~ Although in principle the scavenging ~err~czenc varies in space and time, the usual practice is to use ~storm-average" values. The second class of parameterization involves the scavenging ratio, which is the ratio of the concentration of the pollutant in precipitation at ground level to the concentration of the pollutant in air at ground level. The scavenging ratio is somewhat easier to apply in practice than the scavenging coefficient because the former does not require a vertical integration of pollutant concentration to obtain the deposition rate. Both the scavenging coefficient and the scavenging ratio have well-established theoretical bases. Consid- erable theoretical work has been applied to their physical evaluation. The parameterizations suffer from the difficulty, however, that they consolidate the effects of a large number of complex physical processes. As a consequence the parameters conceal a great deal of uncertainty, particularly when aqueous-ohase transfor- mac~on processes are involved. used in regional models tend to be based more on empirical data than on analysis of actual mechanistic fine proporc~ona.~ry coefficients are often deduced from comparison of ambient air concentrations and precipitation chemistry or from semiempirical models (e.g., Scott 1978, 1981). The parameters actually behavior. - ~ Recent diagnostic models of scavenging appear to be moderately successful in resolving some of these individual mechanisms, and these techniques can be expected to be applied to regional models in the future. Considering the crudeness of parameterization of wet and dry deposition, it is surprising that the linear models perform better in estimating the long-term average wet deposition of sulfate than in estimating the ambient concentrations.
72 Linearity or Nonlinearity in Theoretical Models ~- Physical Processes A deterministic source-receptor model generally provides the solutions (or approximations to the solutions) of a set of conservation equations for each species of the form aCi ~ - at = -V.Civ - Wi + ri. The relationship, called the continuity equation, simply expresses a material balance for pollutant species i in terms of the time rate of change of its time-averaged concentration (ci), the flow and diffusion field (V.c~vi), its rate of removal by deposition processes (wi), and its net rate of production by chemical reaction (ri). Each of the parameters in the equation in general varies as a function of position x and time. This equation, together with suitable boundary and initial conditions, is considered to be a complete mathematical description of any constituent in the air. A profusion of methods has been applied for solving equations of this type, and a correspondingly large number of ~models" for solutions exists. The character- istics of a number of models are given in Table 3.2. A comprehensive discussion of the methods of solution used in these models is beyond the scope of this report; it is important, however, to recognize that, whatever the class to which a particular model belongs, the model still may be described in terms of the continuity equation or its derivatives and may be viewed as a solution to these equations with appropriate initial and boundary conditions. Recently, in connection with proposals for mitigating acid deposition, the question has arisen as to whether deposition rates are linear functions of emissions. It is therefore appropriate to discriminate between linear and nonlinear models and to indicate their significant differences. The continuity equation and its boundary conditions can be mathematically linear or nonlinear, depending on whether nonlinear operators act on the dependent variable ci, the concentration of species i. A linear operator L is one that satisfies the relationship
73 L(aci + Dcj) = aL(ci) + DL(cj), where ~ and ~ are arbitrary constants. Thus, for example, if the net rate of production (ri) of species i through chemical reactions is proportional to the first power of ci, such as ri= Delhi, If, however, ri = Tacit, ri is linearly related to cf. the relationship is nonlinear. While detailed discussion of the continuity equation and its solutions is beyond our current purpose, we note that solutions to linear and nonlinear forms of the continuity equation have characteristics that are of practical importance in formulating control strategies. An important feature of linear systems of this type is that the results satisfy the principle of superposition. From the characteristics of linear operations we can find the combined consequences of, say, two sources simply by summing the contributions of each calculated without regard for the other. This practice is central to Lagrangian trajectory modeling and is not applicable if nonlinear processes predominate. Let us suppose, for example, that a simple form provides the following relationship between the magnitude of the pollution source Sij at location x and a resulting ambient concentration at a specified location x: ci(x,t) = kijSij(xj,t). The coefficient kij depends on the separation of the source and receptor locations (x - x;) and is assumed to be constant. The concentration ci is proportional to the first power of Sij, which is to say that ci is linearly related to Sij. For the linear form of this type, a change in Sij would result. in a proportionate change in cf. For example, a 50 percent reduction in Sij would result in a 50 percent reduction in cf. Simple linearity does not, however, guarantee propor- tionate (one-for-one) reductions. Suppose, for example, that there are a number of sources (N. for example) influencing ci and that a substantial background concentration Bi (due to natural sources) is present. In this more general case, Ci has the form W Ci(X't) = .E ki jSij + Bi(X,t),
74 where the symbol): indicates a sum of the contributions from each of the N sources. This result is still linear in the jth source strength, Sij, but if Bi and the contributions from the other N - 1 sources are not very small compared with kijSij, a decrease in Sij would produce a less than proportionate change in cf. Although noted here in a rather simplistic sense, the linear relationship is the underlying basis for the so-called linear-rollback strategy of emission reduction. Because of the complexity of atmospheric processes, it is unreasonable to expect that a simple linear equation with constant coefficients would provide an accurate description of source-receptor relationships. A more useful expression has the form N cij(X,t) = ~ Pi jail + Bi(x,t), 3=1 where the parameter p depends on atmospheric variables, such as wind speed and rainfall rate, and changes in time and space appropriately to reflect the dependence of the atmospheric variables on time and space. Most regional source-receptor models in current use yield results of this type. Although p is functional in form, this expression is still a linear equation and necessarily stems from a linear form of the continuity equation. The implications regarding superposition and rollback discussed in the context of the simpler linear result apply here as well, provided that the functional dependence of p does not inadvertently include S. It is in fact more realistic to expect that the function p depends explicitly or implicitly on S. for example, through the concentrations of other atmospheric species. In this case, we can write the solution to the continuity equation in the same form but with a new factor of proportionality q that depends explicitly on S: N cij(x~t) = Eqij(sii)sii + Bi(x,t), j-1 where again the variables in the argument of q are functions of time and space. This result is nonlinear since Sij appears both functionally in the argument of qij and as a first-order multiplier. The dependent variable ci no longer depends on the first power of Sij (the independent variable).
75 Because a number of atmospheric processes are nonlinear, the most accurate and complete model of the atmosphere must be nonlinear. There are computational advantages to linear mathematical systems, however, and a corresponding tendency to approximate physical processes in a manner such that linearity is obtained. Such "lin- earization~ is a common practice in science and engineer- ing; its success depends on the degree of deviation from linearity of the phenomenon being studied as well as on the intended application. Linearized models may do well in simulating observed regional deposition patterns, for example, whereas their capability to predict responses to specific changes in emissions may be comparatively poor. Chemical Processes Most researchers who have analyzed regional air-quality data have assumed a linear mechanism for transforming SO2 into sulfate with a rate between 0.1 and 4.0 percent/in (Table 3.2). More complex reaction schemes generally have not been used to rationalize results from observations. By their nature, linear models predict a form of proportional response to emission reductions. In some cases this has previously been demonstrated to be an extremely poor assumption (e.g., in the control of photo- chemical oxidants in urban areas). Linearity may also be a poor assumption for circumstances involving acid pre- cipitation. There is substantial support, however, for the argument that currently we simply do not understand the atmospheric interactions sufficiently well to supply the mathematical detail required by nonlinear concepts. Some attempts have recently been made to incorporate chemical nonlinearities into models of acid precipitation. Most of these schemes concentrate on the production of acid sulfate as an aerosol rather than on aqueous-phase processes in clouds. As described earlier in the section on the treatment of transformation chemistry, Rodhe et al. (1981) employed a highly simplified but seemingly realistic chemical scheme for SO2 and NOx oxidation and found some very nonlinear effects. For example, their results indicated that a 10 percent increase in NOx emissions would lead to a 5 percent reduction in sulfate concentration downwind from the source region, and a 10 percent decrease in SO2 emission would result in only a 3 to 4 percent decrease in sulfate production.
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)
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.
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
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
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
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 H2°k 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)
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.
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.
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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