acid rain control strategies

O~tions exist desvite scientific

pollutant transport and transformation therefore are essential for determining what levels of emission reduction would achieve an acceptable policy in terms of economic efficiency, equity,

J. Hugh Elk R e Johns Hopkins Universily

Baltimore, MD 21218

The major sticking point in the public policy debate over acid rain remains whether we have enough reliable information to implement abatement strategies. This question certainly is not new. In 1984, for example, an Office. of Technology Assessment report (1) stated: "One of the most difficult ques- tions facing Congress, therefore, is whether to act now to control acid dep osition or wait for results from ongoing multimillion-dollar research programs. Both involve risks. Delaying action for 5 or 10 years will allow emissions to remain high for at least a decade or two, with the risk of further ecological damage. . . . Acting now involves the risk that the control program will be less cost effective or efficient than one designed 5 or 10 years from now." This complex issue involves identify-

ing the pollutants responsible for acid rain and their transport and transformation, as well as delineating policy op tions. Reliable estimates of long-range

and protection of the environment. Many long-range transport (LRT) simulation models are available (2. 3, but knowledge of the processes of atmospheric transport and transformation of pollutants remains incomplete.

Because all of the simulation models use different but plausible assumptions and procedures that provide a range of solutions, it has been argued that we do not yet know enough a b u t the relevant processes to act confidently using currently available abatement measures. The stakes are high. By underestimat- ing, we risk causing potentidy irrepa- rable damage to the environment. By overestimating, w e risk implementing too stringent abatement measures at a substantial cost (4).

Methods are available that can nar- row the range of risk and provide an improved basis for informed decision making. Instead of using only one of the existing transport models, ow pro- posed method uses several. They are imbdded in a mathematical optimization scheme that makes it possible to identify cost-effective abatement strate-

gies while remaining aware of the impact of potential errors.

Depositionamtrained strategies Because the acid rain control strate-

gies (5-7, most common in the litera- ture completely eliminate transfer coefficients, they are no longer deposition-constrained but are instead source- based (I). They render moot the argu- ment that we do not know enough about atmospheric transport and transformation to develop abatement strategies that depend on such information. This is essentially the position taken in the Office of khnology Assessment report (I), which concludes: ". . . a source-based program which regulates emissions directly is the only approach available now for controlling acid dep osition."

In contrast to this position, I suggest a different approach based on my view that abandoning deposition limitations (environmental quality standards) re- moves, or at least obscures, an essential part of the problem. Results of a series of analyses indicate whether the case for the imposition of controls can be strengthened by pulling together and setting in a new perspective the information now available on the long-range transport and transformation of acid

1248 Environ. Sci.Technol..Vol. 22. No. 11, lsaS 0013936W88/0922-1248$01.50/0 0 1988 American Chemical SocieN

rain precursors. 1 will examine ways in which existing and future knowledge of pollutant transport and transformation processes might be used, based on the following three assumptions.

Deposition-constrained approaches are potentially useful because they relate the cost of controlling acid rain to some measure of the ensuing environmental benefits. Useful information is available in existing transfer coefficients. A lack of consensus regarding which transfer coefficients are better, let alone best, need not preclude their use. First, 1 will demonstrate the effects of

differing LRT models on abatement strategy characteristics; then 1 will ex- plore procedures to combine the information from multiple models. Note that this approach differs substantially from that of optimization models that explic- itly treat transfer coefficients as random variables (8-13). The procedures described here involve optimization for- mulations that minimize average deposition violations of a standard, minimize maximum violations, and, finally, minimize maximum deposition violation-based “regret.” Regrer is de- fined as the difference between what we plan for and what actually occurs (in terms of deposition and aggregate emission removal). This difference results from our inability to know in advance which LRT model is correct.

Multiple deterministic models In this study, a linear programming

(LP) model is used to minimize indirectly the cost of SO, removal for eastern North America (Le., by mimimiz- ing required emissions reductions) subject to standards for maximum allowable deposition at selected sensitive receptor locations. Existing S a emission levels in units of tons of S a emit- ted per year are denoted as E*, where the subscript k (k = 1,2, . . . ,32) iden- tifies each of the 32 source regions. The decision variables in the model are the source-specific SO, removal levels shown as R,; again, k = 1, 2, . . ., 32. The bounds of Rk are zero and an arbi- trary upper limit of 0.99. The performance criterion or objective function then can be formulated as

32

MINIMIZE Ek’Rx (1) k= I

This summation represents the aggregate annual SO, emission reduction over all source regions.

The pollutant deposition at receptor j that results from a net emission, Ek(1- Rk), at source region k is described by the transfer coefficient, $k. We obtain these from LRT models. Given a total

of 32 source regions f$ = 1, 2, . . ., 32) and nine receptors (i = 1, 2, . . ., 9), then 32.9 = 288 transfer coefficients are required. The pollutant deposition rate resulting from a single net emission therefore is Er(l-R&. Depo- sition contributions are assumed to be additive; hence, the total deposition rate at receptor j attributable to net emissions from all source regions is:

The uncontrolled or nonanthropogenic pollutant deposition rate is shown as BG, (BG denotes background). User- specified maximum allowable deposition rates are represented as Dj. In total, then, user-supplied input to the LP

.ong-range transport model icronyms and descriptions IES Atmospheric Environment

Model (Lagrangian-bo is monthly concentrati and wet depositions 0

4ST Advanced Statistic

Output is monthly SO2 and S concentrations, dry depositio and bulk wet depositions of s

iNA Eastern North America Model of Air Pollution (puff- trajectory). Output is month and concentrations a wet and dry deposition.

WCA Center for Air Pollution Impact and Trends Analysis- Monte Carlo Model (Monte Carl ‘ Output is monthly SO2 and SO, concentrations and drv and we1 depositions.

MEP Meteoroloaical and Environmental Planning Ltd. Transport of Regional Anthropogenic Nitrogen and Sulfur Model (Lagrangian). Output is monthly concentratio and wet and dry deposition of sulfur.

MOE Ontario Ministry of the Environment Long-Range Transport Model (statistical). Output is long-term SO2 and S042- concentrations and ann wet and dry sulfur deposition.

UMA University of Michigan Atmospheric Contributions to Interregional Deposition Model (puff-trajectory). Output is estimates of source contributions to downwind concentrations and contributions of uowind sources

model consists of 32 emission levels, Ek; 288 transfer coefficients, tJk; nine background deposition rates, BG,; nine maximum allowable deposition rates, D,; and 32 upper bounds on the SO, removal levels, R,. These decision variables and input parameters can now be assembled to form a set of constraints or restrictions on permissible values for the SO, removal levels:

32

E Ek(l-R,)tJk + BG, 5 D, (3)

Again, there are a total of nine such constraints, one per receptor. The objective function (Equation l), the deposition constraints (Equation 3). and bounds on the removal levels completely define the LP model. The out- puts of the model are 32 values of the R, that minimize Equation 1 subject to Equation 3 and the bounds on the R,.

It is important to note that the assign- ment of maximum deposition rates currently is much debated. Rates previously considered appropriate generally were about 20 kg wet SO,/ha-year. More recent recommendations call for deposition rates of 9-14 kg wet S04/ha- year (14). The initial analyses here en- compass a broad range of deposition rates-12-22 kg S04/ha-year-fol- lowed by analyses using a rate of 20 kg wet S041ha-year.

The first set of analyses is divided into seven subsets. Each subset em- ploys transfer coefficients from one of seven different linear chemistry long- range transport models. The models (see box) are described in the US.- Canada Memorandum of Intent (Mol) studies (2). All models use the same configuration of 32 aggregated source regions and nine sensitive receptor areas. With minor modifications, emission levels for the aggregated source regions are similar to the emissions described in the MOI reports (2,15). The uncontrolled or nonanthropogenic background deposition rate is 6 kg wet SOJha-year and is constant for all receptors (2, 3, 14). Each of the seven LRT-specific LP models is solved in succession for each of six maximum deposition limits (i.e,, D, = 12, 14, . . ., 22) for a total of 42 computer

It is apparent from Figure 1 that even a broad-brush comparison of the trade- off between total SO, emissions removed and maximum deposition limit shows large differences, depending on which LRT model is employed. Given a maximum deposition l i t of 20 kg wet S04/ha-year, for example, the required aggregate S a removal varies between 6.60 million and 15.96 million tonslyear. These extremes correspond to the use of the transfer coefficients

k=l

mns.

Environ. Sci. Technol.. Voi. 22, NO. 11. 1988 1249

FIGURE 1 Trade-off between maximum allowable depositic limit and

20

’ ~’ SO2 removeda

from two LRT models, the Meteoro- logical and Environmental Planning Ltd. Transport of Regional Anthropo- genic Nitrogen and Sulfur (MEP) model and the Atmospheric Environ- ment Service Long-Range Transport (AES) model.

How, then, might we identify an abatement strategy from this information? If a decision maker wishes to act conservatively, that is, to avoid violat- ing the maximum allowable deposition limits by requiring higher levels of SO, removal, then the Advanced Statistical Trajectory Regional Air Pollution (ASP model or the AES model would be the best choice, independent of which maximum deposition limit is selected. Alternatively, a risk-taker might select the Eastern North America Model of Air Pollution (ENA) or the MEP model, both of which imply less stringent removal requirements (and lower costs) but a greater likelihood that the target deposition rate will be exceeded, possibly by a wide margin. Between these extremes lies the 01- tario Ministry of the Environment Long-Range Transport (MOE) model strategy. AU such choices, however, are implicitly risky because we have no as- surance that the possibilities shown in Figure 1 are all-inclusive, nor do we know their associated probabilities of occurrence.

Regret analyses An intuitively appealing choice for

attempting to extract useful information from the multiple model results uses a simple set of regret analyses, as shown in Table 1. This type of analysis enables us to determine the relative magnitudes of excessive or insufficient pollutant re-

moval that would result from Optimiz- ing an abatement strategy using transfer coefficients that prove to be inaccurate. Along the vertical axis are acronyms of the models that identify the transfer coefficients that can be used to optimize an abatement strategy. The horizontal axis shows the seven sets of transfer coefficients (i.e., possible futures), one of which we assume will occur. Each of the seven sets of transfer coefficients therefore represents a possible “future.” We assume that one of the LRT models will prove correct in its depic- tion of pollutant transport and transformation, but ex ante, that model is un- Imown.

Four types of outcomes can result and are reflected in the numerical en- tries in Table 1. For example, if we select the AES model transfer coefficients as our candidate choice (i.e., if the AES model is thought to be correct) and they actually are correct, then our measure of regret is zero. In other words, an abatement strategy that uses pollutant flux data from the AES model

would prove optimal because the condi- tions dwribed by that model are realized.

Alternatively, if AES model condi- tions are chosen and the accompanying removal levels are achieved, but reality is actually described using the Univer- sity of Michigan Atmospheric Contri- butions to Interregional Deposition (UMA) model transfer coefficients, then a regret of 6.07 million tons of exces SO, removal results. This figure shows that for a given maximum deposition limit, AES model removal levels are higher than those for the UMA model. With respect to environmental protection, this number indicates conservative regret. If, however, MOE model removal levels are adopted and AES model transfer coefficients are actually realized, then insufficient SO, removal will occur and the prescribed maximum allowable deposition limit will be violated at four receptors. Fi- nally, it is possible to have both excess removal and deposition violations, as is the case with the MOWUMA, MOE/ ENA, and ENAIMEP pairings.

Aggregate regret The next step in the regret analysis

involves aggregation of the LRT model-specific results. In one approach we aggregate regret by postulating that each of the seven sets of transfer coefficients is equally likely. Expected values of our regret measures thus are the arithmetic averages shown in Table 2.

Aggregation across possible futures in this manner permits the generation of certain trade-offs that may be useful in decision making. Notably, we see a quantification of the trade-off between expected excess removal and measures of deposition violation for various LRT model selections. Furthermore, the models amear to fall into three identifi- able groups.

The first Q ~ U D consists of the AES and AST mheL and is characterized by solutions with sparse violations and relatively large expected excess removals. This is seen in the extreme right

1250 Environ. Sci. Technol., MI. 22, No. 11. 1988

column of Table 2. The product of expected size of violation and expected number of violations is markedly lower for these models.

The second group at the other extreme consists of the MEP and ENA models. Their solutions have negligible expected excess removals but relatively large expected violations.

Finally, in group three, we see that the MCA, UMA, and MOE models yield solutions with less extreme trade- offs between excess removal and deposition violations. There remains, however, the critical and difficult value judgment involving excess removal (i.e., additional cost that yields environmental benefits) versus violation (i.e., cost savings that result in environmental degradation).

A cnmpromise approach A more robust compromise approach

optimizes source removal levels subject to deposition constraints for all seven LRT models sidtaneously. Thus we do not optimize a strategy with respect to any particular LRT model's transfer coefficients; rather, we attempt to find a strategy that is optimal with respect to all seven sets of coefficients. We h o w that such a strategy will be less efficient (i.e., more required emissions will be removed or deposition results will be less desirable) than a strategy optimized for a particular LRT model. Our uncertainty regarding which m s f e r coefficients are correct results in less efficient solutions. The gain associated with a compromise approach lies in minimizing the undesirable consequences of implementing a strategy based upon the use of an incorrect LRT model.

An important reformulation is neces- sary in this approach. A model that minimizes emissions removed (mvolv- ing a total of 32 decision variables) subject to 63 deposition constraints (Le., Seven sets of nine receptors) will yield results virtually identical to the AES or AST model solutions, because the 32 removal levels, which appear seven times in the constraint set, will be de- termined solely by those constraints at which the prescribed deposition l i t s are most difficult to attain. We have seen previously that these "most difficult" constraints are associated with the AES and AST model transfer coefficients. Satisfaction of these constraints guarantees satisfaction of the deposition limitations for all other LRT models. But we seek solutions that permit not only oversatisfaction of deposition limits l i e those above, but deposition violations as well.

Minimizing aversge violations A new LP has been constructed to

obtain solutions that minimize aggre-

gate deposition violations for all seven possible transfer coefficient futures. Our previous constraints (Equation 3) are reformulated as 32

E Ek(l-&)tjkm +BGj + q'"-V/'=Dj (4) k = l

Equation 4 differs in two important ways from the prior constraints in Equation 3: First, the transfer coefficients now possess a superscript m, which denotes model type (i.e., for AES m=l; for AST m=2, . . .; for ENA m=7). The model thus contains seven sets of nine deposition constraints needing 288 x 7 = 2016 transfer coefficients. Second, the original inequality has been replaced by an equality, and two new sets of decision variables, U,'" and v/", have been added. There are 63 of each, and they represent deviations about the "target" deposition l i t , D,,.

The LP solution procedure (16) IS such that in any given constraint one of these cases will result: both U,'" and 5'" = 0; U,'" > Oand V,'" = 0; or U,'" = 0 and V,m > 0. The first case corresponds

gate violations therefore are expected value or simply average violations.

A constraint also has been added to tix aggregate emission removal to a predetermined value. It is written:

32

E EkRk = S (6) k = l

where S is the stipulated aggregate SO2 emission reduction level. Without this constraint (or equivalently, a second objective function to minimize aggregate emission removal), emission removal will increase as much as needed to eliminate all deposition violations, con- trary to our goal of indirectly minimizing the cost of pollution control.

The first set of analyses has been conducted for aggregate emission reductions of 2-18 million tonslyear, in increments of 2 million tondyear. This range encompasses the reductions considered likely to protect "all but the most sensitive aquatic resources" (8-10 million tons) (1); it also includes those reductions (2-5 million tons of SO2 per year) that would "at a minimum, offset

to mkting the deposition target e&tly. The second represents deposition overachievement (Le., the resulting deposition rate is less than the target rate): the

expected emissions increases with util- ity and indusmal growth.''

Average and maximum violations arc exoressed in units of kdwet S)/ha-year,

magnitude of the overachievement is given by the value of q'". The last case represents exceeding the target limit; the magnitude of the violation is given by the value assigned to y'".

The previous objective function (Equation 1) is reformulated to minimize deposition violations:

and the number of dep%ition violaitions can be plotted graphically against aggregate emission reduction. These violations, as expected, decrease with in- creasing removal effort. The average violations represent a simple arithmetic average across all models and all recep tors; that is, the sum of all violations divided bv 63. The number of elements

32 in the summations varies with emis- MINIMIZE E wjmbm sions removed and can be shown as

j, m "number of violations." where W." is an optional, user-specified weight that can be used to increase or decrease violations Dreferentiallv at

Miwing maximum violation The notion of smallest average viola-

selected receptors. It is importani to note that in simply summing deposition violations across all models and all receptors, we implicitly make the important distributional assumption that all model htures are. equally likely. Aggre-

tion across ~II seven LRT modi1 possibilities is intuitively appealing, but it involves the undesirable distributional assumption of equal likelihood. The recent International Sulfur Deposition Model Evaluation report (3) evaluated

Environ. Sci. Technol., Val. 22. NO. 11. 1988 1251

11 LRT models and categorized them into three groups according to their sea- sonal and annual prediction performance. Clearly, not all models perform equally well and do not represent equally likely model futures. Attaching relative probabilities of occurrence to these models, however, is currently beyond our grasp for several reasons. Perhaps most important is the lack of deposition measurements that are suffi- ciently complete to permit LRT model- specific verification.

F~r tu~ te ly , it is possible to eliminate this underlying distributional assump tion and simultaneously yield solutions of practical value. Rather than minimize average violations, we instead minimize the maximum deposition vi* lation. Violations are not summed across models or receptors, so the im- plication of equal model likelihood is removed. This formulation uses the deposition constraints of the previous model (Equation 4) and an additional set of definitional constraints:

(7) These constitute 63 new inequalities and one new decision variable, MAX- MOL, which represents the largest dep osition violation across all deposition constraints for all seven LRT model types. The new objective function is

MINIMIZE: MAXVIOL (8) A series of runs were again con-

ducted for S@ emission reductions of 2-18 million tons/year; the results are ploned in Figure 2a. Compared with the solutions that minimized average violations, the minmax approach yields consisteutly smaller maximum violations, as shown in the direct comparison of Figure 2b. Thus the adverse dep- ositional consequences of selecting the “wrong” LRT model are lessened. These smaller values are achieved at the expense of modest increases in the number of locations at which violations

Another way to evaluate the minmax solutions is to construct new minmax models individually for each of the seven LRT model types. Recall that the original minmax approach involves a single optimization model containing deposition constraints from all seven LRT models. The new minmax models also act to minimize the maximum d e p osition violation, but only with respect to individual sets of deposition constraints-again, nine per LRT model. The seven new models therefore yield solutions that m i n i the maximum violation, given that the LRT model type is known.

The LRT model-specific minmax results are shown in Figure 3. The

1252 Envimn. Sci. Technol.. Vol. 22, No. 11, isas

MAxvIoL - y m 2 o

simply:

OCCUI.

Minimizing maximum viohtiop 40

A Average wolation Maximum violation Number of violations

Comparison of maximum violation@

A Max (min(avg)) violation Max (min(max)) violation

“cost” of comparing these seven solutions with those of the compromise minmax approach is not knowing in advance which LRT model is correct. The compromise minmax solutions al- ways yield larger maximum violations than any of the seven LRT model-specific minmax solutions. In the case of AES and AST model results, the differences are very small. Differences in maximum violations are of course larger for other LRT model-spi6c results, as ex-.

(20 kg wet S04/ha-year for all models and all receptors) with deposition tar- gets that are obtained from the LRT model-specific minmax analyses. Thus a violation in the minmax-regret model represents an excess of the smallest violation possible for each receptor, if we know in advance which LRT model is c o m t . The objective of this formulation also is to minimize the maximum excess (i.e., minimize maximum regret) across all model types and recep tors. Results are shown in Firmre 4.

We see that the magnitude-of the ex- cesses is relatively small. Nevertheless, the minmax-regret model creates sig- nificantly different removal level as- signments than does either the minmax or the minimum average violation a p pmacb. To illustrate the differences, the removals for our three main ap-

Minimizimaximumregret Another method for developing com-

promise regret-based strategies in- volva a simple reformulation of the compromise minmax model. This reformulation, minmax-regret, @aces the maximum receptor deposition limit

proaches-minimize average violation, minimize maximum violation, and minimize maximum regret-corresponding between maximum dewsition violatior

given in Table 3. On a source-specific basis, it is clear

that the differences in assigned optimal removal levels from approach to a p proach can be very large. Assuming an aggregate emission reduction of 10 million tondyear, source region l provides a good example (see Table 3). If we minimize average violations, the removal level for region 7 is 0.99; for minmax violation, this value falls to 0.20; and for minmax regret, the removal level is 0.03. Conversely, for source region 20, the assigned removal level increases from the minimize average violation approach to the minmax regret approach.

The minmax approaches generally assign high removal levels to sources that have relatively large baseline depc- sition contributions to the receptors where the maximum violations eventu- ally ocm. This is not the case for region 7. Its baseline contributions across all receptors are sizable; hence it plays an important role (removal level = 0.99) when we attempt to minimize average violation. Conversely, region 20 has moderate baseline contributions to all receptors, but proportionately larger contributions to the receptors where the maximum violations occur.

The central question is which of the three approaches is preferable, and, more specifically, what advantages the minmax-regret approach has over our

I

A AES maximum violations AST maximum violations

0 MCA maximum violations * UMA maximum violations

MOE maximum violations ' MEP maximum violations ENA maximum violations

0 Compromise maximum violations

minmax violation strategies. Disaggre- gated comparisons such as those above are useful but diffise. The focus can be sharpened by taking optimal solutions from each of the three approaches and exposing them to our seven LRT model futures. For aggregate emission reductions of 2 million and 10 million tons of S@ per year, the performance of the three approaches in terms of number of

violations, average violation, and maximum violation is shown in Table 4.

Comparisons between solutions that minimize average violation and minimize maximum violation have been dis- cussed previously: Smaller maximum violations are achieved at the expense of larger average violations and more locations where violations occur. The minmax-regret strategies yield some new results. These strategies have slightly greater maximum Giolations, but lower average violations than the basic minmax approach. The minmax- regret strategies therefore fall between those obtained for the minimize average and minimize maximum violation aDDfOaCheS. Minmax reeret vields the

A A Average violation regret Maximum violation regret

&kt conservative res& in-terms of maximum violations.

Uniform cutbacks In the name of equity, uniform cut-

back strategies are frequently pro- posed. We have prepared a series of comparisons involving the minmax-regret strategies and uniform cutback strategies at removal levels of 30%, 50%, and 70%. The SO2 emission re- / \ ductions commensurate with these strategies are 6.95 million, 11.59 million, and 16.22 million tons of SOz per vear. resoectivelv. The uniform cutback &its il; terms 'bf average, maximum, and number of deposition violations are plotted in Figure 5.

The differences in maximum violations between the minmax-regret a p proach and the uniform cutback a p

Envimn. Sci. Technol., Vol. 22, No. 11. 1988 1253

proach are very large. If SO, emission reduction is 6.95 million tons/year (a uniform cutback of 30%), the minmax- regret approach yields a maximum violation that is 62% less than its uniform cutback counterpart. Similar maximum violation reductions for cutbacks of 50% and 70% are 74% and 97%, re- spectively. The minmax-regret approach also is superior in terms of average and number of deposition violations.

Choosing an appronch Four possible approaches to acid rain

control strategies have been set forth here: minimize average violation, minimize maximum violation, minimize maximum regret, and uniform cutbacks. Given the current knowledge about complex atmospheric processes and the presence of important multiple objenives (1 7, 18), there can be no un- equivocal conclusion as to which is best. Nevertheless, the results can be structured to identify those approaches best suited to certain rough categories of policy objectives.

We will deal first with the uniform cutback approach. According to our

notions of regret, it has little to offer. Its attraction is its simplicity, apparent equity, and its potential salability to the decision-making community. These ob- servations may dominate the decision- making pmcess, perhaps rightly so. If such an approach is the only politically viable one, then notions of regret, optimal method, and the like are moot. On the other hand, if costs, distribution of benefits, and efficiency are allowed to influence the decision-making process, then regret-based optimization metho- dologies could be useful.

If policy choices extend beyond simple uniformity, and the policy priority is to protect the environment and mitigate the environmental consequences of choosing a strategy based on an incorrect LRT model, then the minmax-regret approach appears to be a good choice. It achieves a reasonable balance between different environmental im- pacts: maximum deposition violation, average deposition violation, and the number of receptors at which violations

A part of this balance also involves equal concern for all of the receptors in the system. This is extremely impor-

OCCUI.

tant, because the characteristics of the solutions depend strongly on the models’ attempts to minimize deposition violations at the “most difficult” receptor locations (typically, the west- ern Pennsylvania and southern A w a - chia receptors). If deposition criteria are relaxed at these receptors, then deposition violations and number of violations at the remaining receptors will decrease dramatically (17) . This relaxation, however, essentially sacri- fices precisely those receptor locations that may be most in need of protection. To a limited extent, this type of behav- ior already occurs for the minimize average violation approach.

For a number of reasons then, the minmax-rept approach appears to be the most desirable for any level of expenditure. That expenditure, represented by the choice of appropriate aggregate removal level (e.g., from a minimum of 2 million tons S@ removed per year to a maximum of 18 million tons in our analyses), involves some difficult scientific assessments. The choice also is politically very sensitive. It will remain so as long as the environmental detriments of acid rain elude quantification-which may be forever. Perhaps we should accept the notion that the implementation of acid rain controls probably will precede our abiiity to quantify the detriments we hope to mitigate. “It is in the nature of the acid deposition problem, that actions have to be taken despite incomplete knowledge” (4).

Regret-- approaches also can be used to evaluate the results of new simulation models as they become available. From a decision-making view- point, a new generation (e.g., nonlinear chemistry) model could be viewed as an eighth possible LRT model in the future. If such an eighth predictive model is deemed more realistic than its predwessors, then it can be preferen- tially weighted and influence or even dominate the characteristics of the resulting regret-based strategy. Similarly, the role and influence of existing models can be re-examined if one proves more representative than the others upon future verification. Of particular concern in this context are the effects that systematic errors common to all models might have on strategy characteristics.

In the near term, the implementation of an acid rain control strategy is likely to precede our ability to characterize the physics and chemistry of long- range transport and transformation per- f d y . Significant levels of uncertainty are i n h e m in the data needed to cali- brate and verify transport predictions. The role of the approaches described here is to use the information we do

1254 Environ. Sci.Tachnol.. Vol. 22, No. 11,1988

A A Averaae violation

SO, emission reduction (million tonslyear)

have more fully in the hope of making better decisions.

Acknowledgments I am indebted to my colleagues in the De- partment of Geography and Environmental Engineering and to the ESdrTreviewers for their numerous contributions. Notably, stimulating discussions with C.S. ReVelle and S. Schwartz influenced much of the direction of the paper. M.G. Wolman, E. Schoenberger, and 1.L. Cohon reviewed the manuscript and provided many helpful suggestions. L. England cheerfully and ex- pertly did word processing of the manuscript. The support of the National Science Foundation, Environmental and Water Quality Program, Grant No. ECE8504582 is gratefully acknowledged. This research was conducted using the Cornell National Supercomputer Facility, a resource of the Center for Theory and Simulation in Sci- ence and Engineering at Cornell Univer- sity, which is funded in part by the Na- tional Science Foundation, New York State, and the EIM Corporation.

This article was reviewed for suitability as an ES&T fealure by Jon C. Liebman, University of Illinois, Urbana, IL 61801.

References ( I ) Acid Rain and Transported Air Pollu-

tants: Implications for Public Policy; OTA-0.205; Office of Technology As- sessment: Washington, DC, 1984.

(2) United States-Canada Memorandum of Intent on Transboundary Air Pollution, Final Report; Office of Environmental Processes and Effects Research, U.S. En- vironmental Protection Agency: Wash- ington, DC, 1982.

(3) International Sulfur Deposition Model Evaluation; EPA-600/3-87-008; U.S. En- vironmental Protection Agency: Wash- ington, DC, 1987.

(4) Nierenberg, W. A. Interim Report from OSTP's Acid Rain Peer Review Panel; Office of Science and Technology Policy, Executive Ofice of the President: Wash- ington, DC, 1983.

(5) Ellis, 1. H.; McBean, E. A; Farquhar, G. I. 3. Environ. Eng. Div. (Arne,: Soe.

CivilEn~.11985.111. 119. (6) Morrisoi,'M. B.: Rubi",~E. S. 1. Air Pol-

lut. Control Assoc. 1985,35, 1137. (7) Shaw, R. W. Atmos. Environ. 1986, 20.

201. Fortin, M.; McBean, E. A. Atmos. Envi- ron. 1983, 17. 2331. Fronza. G.; Melli, Atmos. Environ. 1984,18,53l, Ellis, 1. H.; McBean, E. A,; Farquhar, G. I. Amos. Environ. 1985,19, 925. Ellis, 1. H.; McBean, E. A,; Farquhar, G. 1. Amos. Environ. 1986, 20, 501. Ouldmann, 1. -M. Geographical Analysis 1986, 18, 198. Fuessle, R. W.; Brill, E. D; Liebman, I. C. 3. Environ. Eng. Div. (Amer. Soc. Civil Eng.) 1987, 113. 106. Schindler, D. W. Science 1988,237, 149. Young, I.W.S.; Shaw, R. W. A r m s . En- wiron. 1986,20, 189. Hadley, G. Linear Programming; Addi- son-Wesley: Reading, MA, 1963; p. 168. Ellis, 1. H. European Journal of Opera- rionnl Reseorch 1988,35, 365. Ellis, 1. H. Civil Engineering Systems 1987,4, 58.

J . Hugh Ellis has been an assistanr profes- sor in the Deparrmenr of Geography and Environmental Engineering ar the Johns Hopkins University since 1984. His research in environmental sysrems analysis includes stochasric optimization and system analytic approaches to acid rain and wafer quality control.

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Ius special rcpon explores the ranouc rcientllii topics of pubLC concern to T @are chemicals m the envuonmeni

Among the topics you'll fmd covered to help you manage the risk and communicatc the results of risk assessment are: * B e i i more realistie about chemical

-Exposure assessment *Cancer doseresponse eanpolations *Physiological pharmacolrinetic modeling .And m o m . . .

carcinogenesis

Wastewater Treatment iaPpl pdate your knowledge of the latest PICCKSCS for the meaunent of U wastewater with this in-depth repon.

You'll fmd topics such as these . . . *Removing particles in water and

* Removing dissolved organic contaminants

*Removing dissolved inorganic

*Anaerobic wastewater heahnent *To name a few. . .

wastewater

from water

contaminaots from water

Computer Usage in Engineering ii3w~

tilize the power of the computer to bridge the gap between engineers and U public decision-makers with this

report that briefs you on the computer basics and then discusses new trends and applications, such as artiJicd intehgence, and their potential impan on envimmenral enpineering. You'll also see.how WMMI computenmight change the praitice of enhnmental much more.

ALL S E W MUST BE PRE-PAID BY Wawc OR MOWY ORDER.

TO ORDER. send check or monev order with name, address, telephone nurhber, and quantify of each seria to: American Chemical Soeiety, Distribution Mice, 11% 16thSmeet, NW, Washington, D.C. 20036 (202) 8724363

with name, address, telephone nurhber, and quantify of each seria to: American Chemical Soeiety, Distribution Mice, 11% 16thSmeet, NW, Washington, D.C. 20036 (202) 8724363

Environ. Sci. Technol., Vol. 22, No. 11, 1988 1255

acid rain control strategies

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