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Risk Assessment for the Prevention of Grounc~water Contamination 14 INTRODUCTION Overview YACOV Y. HAIMES Case Western Reserve University AB STRACT Groundwater, which is a major source of water supply in the United States, is facing severe quantity and quality problems. Once contaminated, the options available for its use are both limited and costly. The immense risks and costs to the public associated with groundwater contamination necessitate the formulation of public policy that is conducive to the prevention of this contamination. This chapter addresses the prevention of groundwater contamination through the use of risk assessment, which embraces both the determination of costs, benefits, and levels of risks and the process of their social evaluation. Since the U. S. Environmental Protection Agency (EPA), mandated by present laws, will eventually promulgate national effluent guidelines that should be scientifically and technologically sound, economically efficient, and socially equitable, the adoption of risk assessment for this purpose seems imperative. Several recently developed risk-assessment methodologies that integrate multiobjective trade-off analysis are eval- uated in terms of their effective use in the formulation of public policies leading to the prevention of groundwater contamination. Two r~sk-assessment methodologies the multiobjective statistical method (MSM) and the partitioned multiobjective risk method (PMRM)- are also evaluated in terms of their specific usefulness to the EPA's ongoing effort in promulgating national effluent guidelines to limit toxic pollutants. Finally, the applicability of"economic incentives" discussed in the report by the NRC Committee on Ground- Water Resources in Relation to Coal Mining (1981) is also evaluated within the framework of risk assessment. Groundwater contamination is a major nationwide socioeco- nomic problem that has its roots in technological development. Its solution requires a scientifically sound and well-formulated public policy grounded in broad-based public participation that includes the private sector as well as the government. The lack of any one element of the above is likely to impede viable progress toward the prevention or reduction of groundwater contamination. In considering the many different sources and causes of groundwater contamination it becomes imperative that no sim- ple solution can address this problem adequately and compre- ]66 hensively. A comprehensive public policy that is cognizant of the multiplicity of causes and sources of groundwater contam- ination, that deals well with the inherent trade-offs associated with risk aversion or reduction, and that coordinates the needs of the involved multiple decision makers and constituencies can only be formulated through a lengthy process involving all concerned parties. To prevent groundwater contamination one must be aware of the sources of contamination, understand the movement of contaminants through porous media, and understand the tech- nical socioeconomic reasons that permit, encourage, and, in- deed, make groundwater contamination the widespread phe- nomenon that it is today. Central to the President's Commission on the Accident at Three Mile Island (1979) is that a group that set out to inves-

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Risk Assessment and Groundwater Contamination tigate a technology ended up talking about people. The Com- mission states: ". . . but as the evidence accumulated, it be- came clear that the fundamental problems are people-related problems and not equipment problems." What clearly emerges from the Commission's report an important theme of this chapter- is the recognition of the strong interplay that exists between man and technology and a commitment to the belief that, in the decision-making pro- cess, science and technology should be more fully integrated with social considerations. The efficacy of the risk-assessment process for the ultimate prevention or reduction of groundwater contamination relies on the formulation of policies that are scientifically and tech- nologically sound, economically and financially feasible, socially equitable, politically acceptable, environmentally safe, and le- gally compliant. People from many disciplines, constituencies, and interests must contribute to the formulation of such poli- cies. In this process potential risks risks of many classifica- tions as well as trade-offs associated with various alternative policy options are, to the extent possible, quantified and eval- uated, so that the detrimental impacts of these risks will be reduced or mitigated. It is constructive at this point to have a more specific defi- nition of risk. Two common definitions are presented here, one of which is adopted for this chapter. The U. S. Water Resources Council (1973) defines risk and the related concept of uncer- tainty as follows: Risk situations those in which the potential outcomes can be described by reasonably well-known probability distribu- tions. Uncertainty situations those in which potential outcomes cannot be described in objectively known probability distri- butions. A different definition of risk is offered by Kaplan and Garrick (19817. The notion of risk involves both uncertainty and some kind of loss or damage that might be received. They also make a distinction between risk (the possibility of loss or injury and the degree of probability of such loss) and hazard (a source of danger) and offer the following symbolic equation: risk= hazard/safeguards. They state that, "This equation also brings out the thought that we may make risk as small as we like by increasing the safe- guards but may never, as a matter of principle, bring it to zero. Risk is never zero, but it can be small." Because the notion of trade-offs within a framework of mul- tiple objectives (e. g., risk, safety, cost) is central to this chapter, we will adopt the U.S. Water Resources Council's definitions of risk and uncertainty. The risk-assessment process constitutes two major phases that partially overlap: (a) the quantitative processing and eval- uation of information through well-developed procedures and methodologies, including the quantification of risk and the de- velopment of alternative policy options, and (b) the introduc- tion of value judgment concerning what risks and their asso- ciated trade-offs are acceptable, what selections are preferred, 167 what policies are desirable, and what constitutes the ultimate decision (the "best compromise solutions. In evaluating alternative policy options concerning the pre- vention or reduction of groundwater contamination one should also inquire whether sufficient knowledge concerning the im- pact of contamination is available, so that the benefits from such prevention can be assessed and the additional cost in- curred in the prevention of contaminated discharges can be justified. The dilemma is whether to (a) wait for additional information and thus avoid potentially unnecessary cost while risking possible negative outcomes that might even be irre- versible or (b) take costly affirmative actions that might prove at a later time to have been unnecessary. Scope and Objectives The intended objectives of this chapter are the following: 1. Identify and articulate the risk and uncertainty aspects of groundwater contamination. 2. Identify the major sources of and causes for groundwater contamination. 3. Identify and articulate appropriate measures for the pre- vention of such contamination within the framework of risk assessment and trade-off analysis. 4. Formulate a hierarchical multiobjective framework that accounts for the legislative and regulatory statutory aspects at the higher level of the hierarchy and for the user/polluter as- pects at the lower level. The proposed framework is intended to advance one step forward the formulation of an urgently needed, sound, effective, and credible public policy for the prevention or reduction of groundwater contamination. 5. Develop foundations for internalizing the externalities of groundwater contamination through economic incentives and disincentives along with regulatory and public education mea- sures. 6. Explore the applicability of several risk-assessment meth- odologies to the proposed hierarchical multiobjective frame- work. Groundwater Contamination: Sources, Reasons, and Impacts The literature on groundwater contamination is relatively re- cent and dates on a significant level to the early 1950s, at which time saltwater intrusion was considered to be the dominant contaminant (Todd, 1959~. The discussion in the literature has intensified only during the last decade, when the contamination of aquifers reached epidemic proportions not only in the United States but worldwide. The "Brown Book" (Office of Science and Technology, 1966) offered the first serious call for an improved research program on groundwater contamination. In the Second National Water Assessment, by the U. S. Water Resources Council (1978), pol- lution of groundwater resources was identified as one of the critical problems facing the United States. The Holcomb Research Institute (1977) published an im- portant document on the utilization of numerical groundwater models for water-resource management. This report, which

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168 addressed the modeling aspects of groundwater contamination, was later revised (Bachmat et al., 19801. During the second session of the 95th Congress, the Committee on Science and Technology (1978) conducted congressional hearings and in- troduced a bill concerning groundwater-quality research and development. The committee then recognized that "severe quantity and quality problems are facing ground-water systems throughout the country as ground-water resources are being contaminated and wells are being closed or depleted. There is also inadequate information about the ground-water resource, leading to increased importance of the socioeconomic impacts resulting from contamination and closing of wells." The UNESCO International Hydrological Programme (1980) published a comprehensive report on the subject addressing the theoretical and practical aspects of groundwater contami- nation as well as numerous case histories from over a dozen countries. These and numerous other documents highlight the critical dimension and scope of groundwater contamination. The sources of groundwater contaminants are numerous (U. S. Environmental Protection Agency, 1977~. Among these are surface impoundments, landfills, leaks and spills, agricultural activities, land disposal of wastewaters, river infiltration, pe- troleum development activities, highway de-icing salt, septic tanks, saltwater intrusion, underground storage, and artificial recharge of wastewater. The reasons for the practices leading to contamination from the above sources can be classified into five major generic categories: economics, lack of education, technology, regula- tion problems, and accidents. Economics Often users/polluters avoid the additional costs required for safe discharge of hazardous wastes from their fa- cilities. In some cases, the present legal penalties imposed by courts on the practices that may lead to contamination are less than the cost that would have accrued to the user/polluter for safe and prudent practices. Furthermore, the present socio- economic and legal-institutional system does not induce users/ polluters to internalize the external cost of pollution control. Lack of Education A large, maybe even a dominant, portion of the population is not aware ofthe groundwater contamination problem or of the impacts of hazardous-waste disposal. This may be attributed to the fact that changes in groundwater quality (unlike those in surface water) are relatively slow and hidden, and their detection may only draw the attention of limited parties. Information is inadequate about groundwater resources and the socioeconomic impacts resulting from their contamination. Technology Technology for adequate and safe disposal of cer- tain hazardous wastes may either be unavailable or insuffi- ciently advanced and economically impractical. This aspect is one of the most difficult to address nuclear-waste disposal is a case in point. Regulation Adequate regulatory measures and standards for the prevention of groundwater contamination are not available. YACOV Y. HAIMES Often the lack of regulations is interpreted as implied permis- sion. A later section of this chapter focuses on this. Accidents Although accidents that may cause contamination cannot be completely prevented, measures can be taken to reduce their frequency and scope. In many cases contaminants in high concentrations are spilled within a short time. Analysis of accidents should provide a basis for a better understanding of their causes and ultimately should provide for more viable control mechanisms. Table 14.1 suggests a framework that relates the sources and reasons for groundwater contamination, thus providing a more systematic mechanism for the risk-assessment process and pol- icy formulation. The impacts associated with Table 14.1 can be classified, for the purpose of risk assessment, into four generic categories (1) human health hazards (known and unknown), (2) environmental degradation, (3) economic hardship, and (4) social dislocation. The quantification of these impacts consti- tutes a critical basis for the risk-assessment process. Groundwater-Quality Modeling A brief introduction to groundwater-quality modeling is pre- sensed in Anderson (1981~. Three primary types of models are in use today: advection, advection-dispersion, and geochemical models. In advection models, contaminants are carried along by water flow. Advection-dispersion includes the effect of mi- croscopic dispersion (which is negligible in comparison with macroscopic dispersion). Geochemical models normally sim- ulate the evolution of groundwater quality considering reac- tions involving calcium, magnesium, and sulfate. The two-dimensional advection-dispersion model for mass transport developed by Konikow and Bredehoeft (1978) is one of the most useful models available today. The aquifer is per- mitted to be isotropic or anisotropic, as well as heterogeneous. This model was successfully incorporated in a risk analysis study of groundwater contamination (Kaunas, 1982; Kaunas and Haimes, 19831. Fractures in rocks can greatly speed the transport of con- taminants underground. Tang et al. (1981) developed an ana- lytical solution for pollutant transport along a thin discrete fracture located in a saturated porous rock. Numerical results for various conditions closely match those generated by the fracture simulation model of Grisak and Pickens (1980~. Groundwater-management models generally combine a transport simulation model with an optimization technique to find optimal well locations, pumping rates, or other objectives. An aquifer behaves linearly in the steady-state case, so that an efficient linear program can be formulated with the discretized governing equations as constraints (Willis, 1979~. The same method can be applied to the nonlinear case, but this gives a large constraint matrix. Gorelick et al. (1979) used a recursive scheme to increase the efficiency of this method. Moosburner and Wood (1980) developed a land-use man- agement model and applied it to Jackson Township of the New Jersey Pine Barrens. Charbeneau (1981) developed a model for

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Risk Assessment and Groundwater Contamination TABLE 14.1 Possible Framework Relating Sources and Reasons for Groundwater Contamination, Which Can Be Site or Regional Specific 169 Reasons for Contamination Sources of Contamination Economics Education Technology Regulations Accidents River infiltration Runoff Natural recharge Herbicides, insecticides, fertilizers Irrigation return water Land spreading of sludges Well development Septic tanks Municipal and industrial sewer systems Landfills Waste disposal Storage of minerals Recharge of wastewater Shallow wells Well injections into saline aquifers Underground storage (waste, heat) Surface and subsurface mining Acid mine drainage Disposal of feedlot waste Gas and oil field activities Pipelines Highway de-icing salt Saltwater intrusion contaminant transport in groundwater with adsorption and ion- exchange reactions using the method of characteristics. Go- relick and Remson (1982) and Gorelick (1982) developed a groundwater-quality management model that uses a linear pro- gramming formulation. Other management models have used specific discretized versions of the governing equations as a set of constraints in linear and nonlinear programs. THE MULTIOBJECTIVE FRAMEWORK Determining the acceptability of risk is undoubtedly one of the most complex and difficult decision-making problems facing public officials. Lowrance (1976) posed this all-encompassing problem in one sentence: "Who should decide on acceptability of what risks for whom, and in what terms, and why?" Starr (1969) distinguished between voluntary and involuntary risk as a basis for determining the acceptability of risk. Slovic et al. (1979) focused on the perception of risk and its dominant in- fluence on the acceptability of risk. Rowe (1977) provided some methodological approaches for risk assessment. Schwing and Albers (1980), in the book they edited, set as their objective a thorough discussion of social risk assessment and how safe is safe enough. Fischhoff et al. (1980) stated: "Acceptable-risk decisions are an essential step in the management of techno- logical hazards. In many situations, they constitute the weak (or missing) link in the management process. The absence of an adequate decision-making methodology often produces in- decision, inconsistency, and dissatisfaction. The result is nei- ther good for hazard management nor good for society." Common and central to the above-cited writings is the fun- damental premise that determining the acceptability of risk (within the risk-assessment process) is grounded in determining and evaluating trade-offs among the various objectives and/or attributes (Haimes, 19811. These multiple objectives are often noncommensurable, in conflict, and in competition. A spe- cialized field multiple criteria decision making (MCDM)- has emerged during the last decade, focusing on decision mak- ing with multiple objectives. Although the concept of Pareto optimality dates back to the nineteenth century, the intensive development and use of quantitative approaches for optimizing multiple objectives is a relatively recent phenomenon. Heur- istically, a Pareto-optimal solution for a multiobjective opti- mization problem, also known as an efficient and noninferior solution, is any solution for which one objective function can be improved only at the expense of degrading another. In addition, the notion of best is interpreted here as the preferred solution selected by a decision makerts) from within a Pareto- optimal set of solutions. The following is a more formal defi- nition of this concept for the problem: minimize ffi~x), f2(x), . . . foxy. A decision x* is said to be a noninferior solution to the above-posed problem if and only if there does not exist another x so that foxy ~ fj~x*y j = 1 2, . . . n, with strict inequality holding for at least one j Germane to MCDM and to risk assessment is the dominant role of the decision makerts) in selecting preferred policy options.

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170 Example Problem An oversimplified problem concerning groundwater contami- nation with trihalomethanes (THMs) is presented as an example of the overlap between risk assessment and multiobjective op- timization. The contamination is caused by landfills used as dump sites for hazardous chemical wastes under the jurisdiction of and controlled by City Z. Given that the U. S. Environmental Protection Agency (EPA) has not as yet promulgated regula- tions in compliance with the Resource Conservation and Re- covery Act (RCE{A) a fact that is causing a significant delay in issuing permits—City Z. to a large extent, must make its own risk assessment. About 50 percent of the city's water sup- ply is pumped from the aquifer contaminated by THMs. The simplified version of this problem can be posed as fol- lows. Let x denote the vector of decision variables (options) available to City Z. The city has a set of feasible disposal options, X. Thus, x ~ X (the decision vector x belongs to the feasible set X). Associated with each policy x are a cost function, foxy, and a risk function, f2(x). The most common unit for measuring cost is the dollar. The risk, on the other hand, may be measured in a number of ways, the simplest being the concentration of THMs in parts per billion (ppb). This surrogate indicator can in turn be used to determine a more direct measure of risk to health involving perhaps the probability of death and sickness. The risk-assessment/multiobjective optimization problem can be posed as minemxize a(X) f2(X)] (14. 1) or find the "best" policy x that would simultaneously minimize the cost and the risk. A noninferior solution of this multiobjective problem is one in which any reduction of the cost of pollution control can be achieved only at the expense of increasing the risk of contam- ination. The surrogate-worth trade-off (SLIT) a method for analyzing and optimizing multiple, noncommensurable, and FIGURE 14.1 Pareto-optimal solutions and trade-o~s. YACOV Y. HAI M E S conflicting objectives constitutes the backbone of the risk analysis in the multiobjective framework presented here. The trade-off values between the ith and jth objective func- tionsf~x) end fix), respectively, are denoted by Aij. These he's are generated by the SWT method and have been shown to satisfy the following relationships: Aij = —~f; ), i ~ j; i, j = 1, 2, . . . n, (14.2) where Aij ~ O is a sufficient condition ford noninferior solutions. Note that it is sufficient to generate only one row vector of the trade-off matrix, e.g., A~2, Air, . . . A~n, and to derive all other trade-offs from this vector. Figure 14.1 depicts the plotting of cost versus risk in the functional space. In comparing the three policies, XA, XB, and xc, chosen to lie on the Pareto-optimal frontier, it is evident that policy XA results in much lower levels of THMs concentration than do either XB or xc t.f2(XA) < f2(XB) (xc)~; however, it also results in much higher costs [f~(x^) > foxy > f,~xc)~. Thus the reduction of an additional amount of THMs (which is equivalent to reduction of risk to public health) translates into an increase in cost. Models, such as the mass-transport model of Konikow and Bredehoeft (1978), can relate a concentration response in a well to a spill input. Such models are most valuable for the quantification of the functions /;(x) (Kaunas, 19821. The most critical phase (in MCDM and risk assessment) is, of course, determining the "best" solution, namely, determin- ing exactly what level of risk is acceptable. There are several available methodologies that are capable of generating as many Pareto-optimal solutions as deemed necessary, and they pro- vide systematic procedures for the decision makerts) to reach that best solution. The SWT method is such a methodology, and it generates in addition all the respective trade-offs asso- ciated with the Pareto-optimal solutions (see Haimes and Hall, 19741. These trade-offs are essential for determining the ac- ceptability of risk by the decision makers. The slope of the Cost Function ISI fix) 1 fl(xa) f I (xb) f l (xc) 1 ~ % ~ Feasible Set / Mob Pareto (Opti mat Frontier - / ) 1 ~ _ &, _ Surrogate Risk Function [PPbl

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Risk Assessment and Groundwater Contamination tangent to the Pareto-optimal frontier at Xs iS the trade-off associated with f2(xB) end f2(xB), as is depicted in Figure 14.1. Note that the units of Ale are the ratio of the units off, and f2(x), namely $/ppb. The SWT method assists the? deci.cion makers, by means of the surrogate-worth function, to arrive at the best-compromise solution, also known as the preferred solution. Because the scope of this chapter must be limited, the interested reader should explore the literature for further elaboration on the SWT method and its extensions and on MCDM in general (see, for example, Chankong and Haimes, 1983~. INTERNALIZING THE EXTERNALITIES OF POLLUTION The exponential growth of the chemical industry manifested in the development and manufacture of thousands of new prod- ucts annually has inundated the government bureaucracy. In- deed, the EPA and the National Cancer Institute are capable of testing only a small portion of new products with respect to their environmental and/or health hazards. This is because of the exceedingly high cost of testing and the time involved. A fundamental question remains unanswered: is it the re- sponsibility of the manufacturer-producer to ensure the public safety and the integrity of the environment from the adverse effects of new products; or is it the role of government, as the representative and protector of the public, to do so; or is it both? The issue is particularly critical and urgent with respect to the disposal of residual wastes. The national experience accumulated over the last decade in the control and abatement of surface-water pollution and air pollution should not be overlooked when considering the pol- lution of groundwater resources. Public Law 92-500, which was enacted in 1972 and called for a "zero discharge," ignored, in principle, the economic realities of the marketplace. Following the recommendations made by the National Commission on Water Quality in 1976, Congress enacted the Clean Water Act of 1977 (Public Law 95-217~. The Commission stated (National Commission on Water Quality, 1976~: Wise use of total national resources would support the imposition of only those levels of control or treatment that actually produce the intended results. Additional investment with only marginal identifiable benefits or improvements could operate to the detriment of competing demands of other worthwhile national programs, such as energy con- servation and air pollution control. Therefore, measures that are aimed at preventing ground- water contamination should be based not only on sound sci- entific, technological, and environmental considerations but also on sober socioeconomic realities. In this respect, a viable system of economic incentives and disincentives should be an integral part of and constitute firm foundations upon which regulations for contaminant/pollutant discharge standards are formulated. A recent report issued by the National Research Council stresses these points (NRC Committee on Ground- Water Resources in Relation to Coal Mining, 19811. The report stated, "The problem of institutional design and implementa- 171 tion is the final step necessary to ensure that ground-water conflicts, present and future, are resolved in an environmen- tally responsible, economically efficient, and socially equitable manner. On the economic incentives, the report stated, ``Economic incentives, either rewards or penalties, may be used to 'inter- nalize' externalities (both spatial and temporal) and thus to induce voluntary compliance with social goals." Economic in- centives may be created in two ways: (1) through the estab- lishment of liability rules that define the rights and duties of private individuals or organizations and (2) by involving gov- ernment more directly either as an imposer of taxes, charges, or fines to discourage inappropriate behavior or as a source of tax credits, loan guarantees, or other forms of positive incen- tives to encourage appropriate behavior. It is worth noting that a system of effluent charges for surface water has been implemented successfully in Germany, where the Ruhr and Emscher Genossenschaften have administered a program of environmental control for almost a century (Federal Water Pollution Control Administration, 1970, pp. 143-160~. Thus, in order to prevent groundwater contamination it is worth investigating the efficacy of effluent charges and a system of economic incentives and disincentives concepts well suited to the management of surface-water pollution (see Kneese and Bower, 1968; Hass, 1970; Kneese et al., 1970; Haimes, 1971, 1977; and Maddock and Haimes, 1975~. The process of risk assessment facilitates juxtaposing the risk of an event and the cost associated with the prevention of that risk. Hence a system of economic incentives and disincentives, when adequately and appropriately backed up by legislation, can serve as a potent measure for the prevention or reduction of such a risk. The socially equitable level of these economic measures can be determined (as will be discussed in more detail in subsequent sections) via trade-off analysis as part of the multiobjective optimization procedure and the risk-assessment process. Q UANTITATIVE ANALYS E S Introduction For pedagogical purposes, it is constructive to digress, dividing the risk-assessment process into three major, though overlap- ping, elements. 1. Information management: including data collection, re- trieval, and processing through active public participation. 2. Model quantification and analysis: including the quanti- f~cation of risk and other objectives, the generation of Pareto- optimal policies with their associated trade-offs, and the con- duct of impact and sensitivity analysis. 3. Decision making: the interaction between analysts and decision makers and the exercise of subjective value judgment for the selection of preferred policies policies for which the risks are deemed to be acceptable to the decision makers within the overall trade-off analysis. Although these elements are easily identified, the state of the art in risk assessment is still in its infancy concerning the

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172 many uncertainties associated with each element, in particular, the lack of knowledge in quantifying the causal relationship between the sources and reasons of groundwater contamination and the contamination's impacts. These uncertainties further complicate the third element the decision making and ex- ercising of subjective value judgment. These impediments, nevertheless, should not, in any way, prevent the use of risk assessment for policy decision, particularly for public-policy decisions such as those concerning the prevention of ground- water contamination. The information-management element is discussed else- where in this volume (Chapter 13) and thus will not be ad- dressed here. This section will be devoted to generic model quantification and analysis, keeping rigorous mathematical de- velopments to a minimum, though these will be supplemented with proper references for readers whose interests and ori- entation are more mathematical. Generic Model Formulation This section addresses the generic quantification of the causal input-output relationships between sources of contamination (What can happen?) and the impacts and damages of such con- tamination (If it does happen, what are the consequences?) in a framework that couples these causalities with the probabilities of occurrence (How likely is it that that will happen?) (see Kaplan and Garrick, 1981~. In the formulation of models, five groups of variables need to be defined. 1. Decision variables (x). These are measures controllable by the decision makers, such as legislation, promulgation of regulations, zoning, public education, and economic incentives and disincentives. The symbol x denotes a vector of such de- cision variables, x = (hi, x2, A). 2. Input variables (u). These are materials discharged and/ or entering the groundwater system. These input variables are not necessarily controllable by the public decision makers but rather are controllable by the individual parties involved in the contamination of aquifers. Input variables include, for example, the discharge of THMs, synthetic organic contaminants (SOCs), trichloroethylene (TCE), and saltwater intrusion due to pump- ing. For a more parsimonious notation and without loss of generality, the system's inputs and outputs are lumped into u. For example, water pumpage and artificial recharge can both be conveniently considered as part of the vector u in the context of modeling groundwater contamination. The symbol u denotes a vector of such input variables, u = fun, us, . . . up). 3. Exogenous variables (a). These are variables related to external factors, albeit affecting the system either directly or indirectly. Theoretically, these exogenous variables could en- compass the entire universe excluding x and u. For practical purposes, however, exogenous variables such as the physical characteristics of an aquifer; water demand for industrial, ur- ban, and agricultural development; technology assessment; and economic market forces may be considered. The symbol a denotes a vector of such exogenous variables, a = god, as, . . . (xp). YACOV Y. HAIMES 4. Random variables (v). A probability-distribution function (Pdf) may or may not be known for each random variable. For example, knowledge of probability distributions for random events such as precipitation and streamflow (and thus for nat- ural recharge of aquifers) can be assumed. On the other hand, Pdfs for random events such as accidental spills may not be known, and uncertainty analysis rather than risk analysis should be conducted. The symbol v denotes a vector of such random variables, v = Ivy, v2, . . . A). 5. State variables (s). These are variables that may represent the quantity and quality level (state) of the groundwater system at any time. Examples of such state variables include the water- table level, concentration of salinity, and THMs or biological contamination. The symbol s denotes a vector of such state variables, s = ask, so, sk). The next step constitutes defining all objective functions (including risk functions) and constraints. Here, a critical dis- tinction must be made between the objectives of the polluter and those of the public and its representatives. The risks and costs of dumping hazardous chemical wastes, for example, are certainly different for the polluter than for the user of the contaminated groundwater. To maintain realism in generic model development, here, a simple two-level hierarchy is introduced (Haimes, 1977~. The aquifer system can be decomposed into N subsystems, each of which may be affected by a different party. In a de- generate and extreme case, all N subsystems can collapse into one system the entire aquifer. The first (lower) level of the hierarchy consists of the various subsystems/users. The second (higher) level of the hierarchy consists of an overall coordinator with powers to promulgate regulations for discharge standards and impose economic incentives and disincentives. A similar two-level hierarchical model for the planning and management of groundwater is discussed in detail by Maddock and Haimes (1975~. From the above definitions, it is clear that the five variables (vectors) are not all independent of each other. For example, the state of the groundwater system (s) depends on the quantity of contaminants (u) disposed of, what measures (x) are taken to prevent contamination, the frequency at which such con- tamination occurs (v), and the physical characteristics (~) of the aquifer. Thus, s = six, u, v, a). Therefore, the various objectives and constraints of the sub- systems/users can be written as functions of the state vector (s), whereby dependence on x, u, v, and a is implicit. Letups) represent the ith ohiective function ofthe subsystem/ it. O=~O ~ — ~ ~ eve i,, a, _, . . . J. For example, let J~(s) = cost in dollars of contamination prevention, f2(s) = "risk" of contamination with THMs, f3(s) = "risk" of contamination with saltwater intrusion. The risk functions can be represented in numerous ways. For example, their representation can be in terms of probability a\nd consequence, expected value, utility function, or other functions. In subsequent discussion in this chapter more than one rep- resentation will be used. Often no knowledge of the probability-

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Risk Assessment and Groundwater Contamination distribution function for a specific random variable may be available, in which situation one of the methodologies for un- certainty analysis, such as the uncertainty/sensitivity index method (USIM) (Haimes and Hall, 1977), may be used. Similarly, all the system's constraints (e.g., physical, eco- nomic, institutional) can be defined as gigs) ~ 0, i = 1, 2, . . . I. The set of all feasible solutions/policies (X) that satisfy all the constraints can be defined as X = fx~gits) ~ 0, i = 1, 2, . . . 11. The overall mathematical formulation of the groundwater contamination-prevention problem seeks to minimize all ob- jective functions (in a multiobjective sense) via selection of the best feasible decision variables/measures, x. Mathematically this can be represented by minemxize flash f2`Sy fj~sy~ where s = six, u, v, e). Before discussing various methodologies for the quantifica- tion of risks associated with groundwater contamination, the institutional framework must be further discussed in a form compatible with the mathematical model. For this purpose, the hierarchical multiobjective framework introduced in the next section is intended to act as a bridge among the quanti- tative aspects of (1) risk assessment, (2) the determination of the acceptability of risk through decision making and the ex- ercise of value judgment, and (3) the desired institutional and other socioeconomic measures that would provide a basis for implementation of contamination-prevention policies. A Hierarchical Multiobjective Framework Of the numerous problems and issues related to water-re- sources planning and management, those associated with groundwater are undoubtedly the least studied, yet the most complex. In particular, the planning and management of groundwater resources is plagued by legal and institutional impediments (Haimes, 1980~. In the eastern and midwestern portions of the United States, for example, groundwater law is judge-made law, deriving from the English common-law rule of absolute ownership, whereby each landowner was allowed to pump water from wells on overlying land without restriction (Corker, 1971~. The central question that should be raised is: What is the efficacy of risk assessment in the prevention of groundwater contamination in light of present institutional and legal realities? The principal answer is grounded in the Re- source Conservation and Recovery Act (RCRA) of 1976 (Public Law 94-580) and the Clean Water Act (Public Law 95-217) and, to a lesser degree, in the Toxic Substances Control Act (Public Law 94-469~. The fourth objective of the RCRA is "regulating the treatment, storage, transportation, and disposal of hazard- ous wastes which have adverse effects on health and the en- vironment." The EPA, charged by Congress to promulgate regulations and standards for toxic discharges, is currently working on issuing new permits for the control of toxic pol- lutants. The EPA is concentrating on 129 priority toxic pol- lutants selected on the basis of the frequency of their occur- rence in water, their chemical stability and structure, the amount 173 of the chemical produced, the availability of the chemical pro- duced, and the availability of applicable chemical standards and measurements (Silva, 1981~. This National Pollutant Dis- charge Elimination System (NPDES) permit program, which was established by Congress when it passed the 1972 Federal Water Pollution Control Act Amendments (Public Law 92-500), constitutes the basis for the following proposed hierarchical multiobjective framework. In principle, a region (system) having boundaries that can be determined on the basis of political-geographical or hy- drological considerations may be subdivided into N subregions (subsystems). In any region all potential contaminant dis- charges (which may contaminate groundwater, for example) are controlled by the EPA,s NPDES permit program. The policy decisions at the higher level of the hierarchy are controlled by the EPA. The users/polluters (whether industry, farms, or mu- nicipalities) constitute the various lower-level subsystems. Clearly, the parties at both the lower and higher levels aspire to multiple noncommensurable goals and objectives that are likely to be in conflict and in competition. Furthermore, the elements of risk manifested in these objectives and the ac- ceptability of these risks are perceived, evaluated, and traded offdifferently by the lower-level and higher-level parties. How- ever, since the parties at each level have considerable degrees of freedom in selecting the most appropriate measures (within the permitted set of feasible options) that lead toward achieving their objectives, a coordination mechanism for the entire sys- tem is most desirable. Tractable mathematical coordination schemes of hierarchical multiobjective models have recently been developed (see Haimes and Tarvainen, 1981, and Tarvainen and Haimes, 19821. In these models, each subsystem is allowed to optimize (in a mul- tiobjective Pareto-optimal sense) its own set of objectives sub- ject to specified constraints and limitations, and the preferred solutions generated by each subsystem are coordinated within the objectives of the higher-level subsystem (the EPA in this case). The latter generates its own modified preferred policy, and, through the use of economic incentives and disincentives (in the form of Lagrange multipliers, trade-offs, and shadow prices) along with other measures (regulatory standards and educational programs), the higher level induces the lower-level subsystem to perform acceptably. Because the scope and level of the mathematical presentation must obviously be limited, there will be no further discussion here of the coordination scheme. However, the implications of such a scheme should not be overlooked. Through risk as- sessment, the EPA can evaluate the trade-offs associated with promulgating specific pollution-discharge standards in terms of the following questions (Kaplan and Garrick, 19811: 1. What can happen (i.e., what can go wrong)? 2. How likely is it that that will happen? 3. If it does happen, what are the consequences? In addition, the EPA can incorporate additional questions con- cerning socioeconomic impacts, the cost to industry, and other political-geographical considerations. The user/polluter can in turn conduct his own risk assess- ment, posing the same three basic questions, albeit from an

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174 entirely different (and more parochial) perspective. The con- sequences brought up in the third question may include the cost of potential lawsuits in addition to the more obvious civic responsibility of the user/polluter to the protection of public health and the integrity of the environment. RISK-ASSESSMENT METHODOLOGIES The purpose of this section is to consider the efficacy of two recently developed risk-assessment methodologies (that inte- grate multiobjective trade-off analysis) and to evaluate them in terms of their effective use in the formulation of public policies leading to the prevention of groundwater contamination. These are (1) the multiobjective statistical method (MSM) and (2) the partitioned multiobjective risk method (PMRM). Two other multiobjective risk-assessment methods the uncertainty/sen- sitivity index method (USIM) and the risk/dispersion index method (RDIM) described, respectively, by Haimes and Hall (1977) and Rarig and Haimes (1983) while applicable here, will not be discussed. The Multiobjective Statistical Method The multiobjective statistical method (MSM) was developed for the U.S. Army Corps of Engineers to account for the risk of floodings in the design of interior drainage systems (Haimes et al., 19801. The method is an integration of a multiobjective scheme (the surrogate-worth trade-off (SOOT) method] and a statistical procedure to assess the probability of a risk event and its consequences. Problem Definition To better understand the MSM, consider the risk of ground- water contamination due to a polluted river that traverses the aquifer, where recharge is induced by stream infiltration. The following variables can be defined: (1) Random variables, v: Van, storm event that is associated with a storm hyetograph characterized by a sequence of given rainfall intensities and durations, m ~ t1, 2, . . . M]; v2, river stage, i ~ t1, 2, . . . I]; vet, contaminant (THMs) event, 1~ t1, 2, . . . L]. (2) Input variables, u: us, discharge of polluted effluents into the river by in- dustry 1; dustry 2; us, discharge of polluted effluents into the river by in- U3, pumpage rate. (3) Exogenous variables, ~x: oh, water withdrawals (demand); CX2, nominal aquifer transmissivity coefficient; (X3, nominal aquifer storage coefficient. (4) Decision variables, x: x,, effluent charges; charges; YACOV Y. HAIMES x2, standards promulgated by EPA for effluent dis- X3, construction of advanced wastewater treatment plants. (5) State variables, s: so, groundwater table; so, concentration of contaminant k in the groundwater. Other random, input, decision, exogenous, and state variables can be introduced as appropriate. The following sample of objectives and constraints can be defined: f, (s), cost of contamination prevention; f2(s), expected value of THM concentration; f3(s), expected value of number of cancer patients due to carcinogenic groundwater contaminants. The quantification of these objective (risk) functions in terms of expected values, which account for the probability distri- bution functions of the random variables v, is the essence of the MSM. The construction off; )'s is discussed in the next section. The constraints are grist, total budget available; g2(s), effluent standard limitations; g3(S), upper limit on pumpage rate. Thus, the set of all feasible solutions, X, is defined as X = ~x~gi~s) ~ O. i - 1, 2, 3~. The overall mathematical formulation of the risk-assessment problem is given by minimize l first, f2(s), f3(s)~. Construction of Risk Functions Often the most convenient way to construct risk (as well as other objective) functions is in terms of the state variables rather than the decision variables. For example, a risk function associated with health hazards can be more easily constructed in terms of the level of contaminant concentrations (state vector s) than in terms of the measures taken to prevent such a con- tamination (decision vector x). On the other hand, in the mul- tiobjective optimization and trade-off analysis part of risk as- sessment, it is much more convenient to have these functions expressed explicitly in terms of the decision vector x rather than the state vector s. The MSM resolves this dilemma by constructing these risk and other functions in terms of the state variables, and, through simulation and regression analysis, re- generates these functions in terms of the decision variables (specific steps will be discussed subsequently). The other problem that needs to be resolved is incorporating the effects of the random variables into the model. This is accomplished by dividing the range of each random variable into a sequence of disjoint intervals. The events defined by this partitioning are mutually exclusive and collectively ex- haustive. This partitioning is indicated by the sets l1, 2, . . . M), {1, 2, . . . 1), and {1, 2, . . . L} for the random variables vat, v2, and v', respectively.

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Risk Assessment and Groundwater Contamination The major steps of the MSM are the following: 1. Determine the feasible set of decisions/measures, X, for the prevention of groundwater contamination. 2. Determine relevant historical records associated with the random variables, v, and from these data determine the prob- ability-distribution functions. 3. Construct the risk and other objective functions in terms of contamination levels as fiats), j = 1, 2, 3. 4. Construct the state variable vector (groundwater table and concentration of contaminants) in terms of the input vector, u, decision vector, x, and random-variables vector, v. In gen- eral u is dependent on x fi.e., up. 5. Specify the levels of rainfall events, M, river stage inter- vals, 1, and levels of contaminant events, L. 6. Generate, for example, via simulation, M x I x L values of the state vector s for each set of decisions, Xk, k = 1, 2, . . . K. Also, generate all joint and/or conditional probabilities as- sociated with the random variables, v. 7. For predetermined values of the exogenous variables, ax, substitute for each set of decisions Xk, k = 1, . . . K, the values of the state vector, s, in the risk and other objective functions. The result is f USA, Al, V2, v')], j = 1, 2, 3; m = 1, 2, . . . M; i = 1, 2, . . . 1; 1 = 1, 2, . . . L; k= 1,2,...K. 8. Based on the multiplication theorem of probability, gen- erate for each xk the expected value off; ), denoted by foxy), using the joint and/or conditional probabilities (as appropriate). 9. Given the set of ordered pairs, |xk, f~xk)l, k = 1, 2, . . . K; j = 1, 2, 3, use a regression-analysis technique (such as least-squares) to determine the functional relationship fat-): x > fax); j = 1, 2, 3. At the completion of this stage, the expected values of all risk and other objective functions are expressed in terms of the decision vector x. 10. Use the surrogate-worth trade-offmethod to (a) generate Pareto-optimal solutions, (b) generate corresponding trade-off values, and (c) determine the decision maker's preferred so- lution and levels of acceptability of risk. The use of expected value, while a sound approximation of the frequency-versus-damage risk distribution in many circum- stances, falters when extreme events are considered. High- damage/low-frequency events and low-damage/high-frequency events appear mathematically equivalent in the expected value context. The partitioned multiobjective risk method, through a partitioning scheme, circumvents the drawback of the ex- pected-value approach by constructing risk functions that can be evaluated in a multiobjective framework (Asbeck and Haimes, 19837. The Partitioned Multiobjective Risk Method Two seemingly unrelated problems—the multiobjective op- timization problem and the quantification of probabilistic dam- 175 ages have been over the years addressed in a similar, albeit somehow deficient, way. Until the early 1970s the weighting approach was the dominant solution for multiobjective (vector) optimization problems, converting multiple noncommensura- ble objectives, through a set of normalized weights, into a scalar objective (utility) function. These weights have been purport- edly held to represent the decision makers' preferences among the various objectives. These preferences, moreover, are im- plicitly assumed to be constants and, thus, independent of the relative levels of each objective function. Methodologies de- veloped in the early 1970s, such as the SWT method, avoid these precommensuration impediments, and through the use of Pareto-optimal solutions (policy options) and their associated trade-offs, the decision makers are assisted in determining a preferred/compromise solution. A similar situation has prevailed in the quantification of prob- abilistic damages, or risk functions, through the use of the expected-value concept. In the classical expected-value ap- proach, extreme events with low probability of occurrence are given the same proportional weight/importance (in the mul- tiobjective commensurate process) regardless of their potential catastrophic and irreversible impact. Yet it is a commonly ac- knowledged fact that the outcome of a catastrophic accident that may cause 10,000 deaths with a low frequency of 1O-5 is neither perceived nor accepted to be in the same category of more common accidents that occur with a much higher fre- quency of, say, 10 - ~ but that may cause the death of one person each time. It is argued here that the mathematical artifice— weighting coefficients in the form of probabilities used in the expected-value approach is basically the same as that used in the conversion of a multiobjective optimization problem into a scalar single-objective problem. Thus, in this sense, the ex- pected-value concept is as deficient and has the same flaws as the multiobjective weighting method. A common way of describing the risk associated with an event has been through its cumulative probability distribution func- tion. The random variable may be, for example, the spillage of a contaminant. A conventional means of dealing with this randomness has been to employ mathematical expectation or expected value to the random variable. Much information about extreme events is concealed in the expectation process. The PMRM seeks to reduce this information loss by modifying the expectation procedure (Asbeck and Haimes, 1983~. In essence, the probability distribution function is divided into several seg- ments, e. g., three segments, according to the exceedence prob- ability of an event. A modified expectation (a conditional ex- pectation) is taken over each of these segments, resulting in functional relationships between spillage and groundwater con- tamination. The central motivation in developing the PMRM is to provide a description of risk that is fuller than that of expected value. The particular aim here is to separate, for scrutiny by the decision makers, low-probability/high-damage events from high-probability/low-damage events. Another way of viewing this motivation is in terms of optimistic and pessi- mistic attitudes. One may relate assigning high importance to low-probability/high-damage events as a pessimistic attitude or assign less importance to these events as an optimistic attitude (Haimes, 19827.

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176 To explain the PMRM, the concept of triplets introduced by Kaplan and Garrick (1981) will be used as a vehicle for devel- oping risk distributions for each choice of the state vector, and it directly arrives at a means of constructing the multiobjective risk functions. A triplet begins with an outcome scenario, so, that describes a specific occurrence. Related to that scenario are a statistical frequency of the occurrence, ¢, and a resulting damage, d. Thus, a triplet (se, ¢, cl) has been created that describes the scenario. Notice that the three pertinent questions in a risk analysis have been answered: (se) answers what can happen, (~) answers how likely it is to happen, and (d) answers what detrimental consequences would ensue. Given any particular course of action, a variety of scenarios could be envisaged, each with an associated frequency and damage. For the example problem, each course of action is completely described by the components of the state vector s. By exhaustively listing all scenarios, frequencies, and damages for a specific s, the risk (R) associated with s will be enumerated. Mathematically, it(s) = Discos), Acts), dills)], j = 1, . . . I, where ~ scenarios have been listed. To bring reason to this list, reorder the subscripts, j, so that the damages obey dits) < ~(s) < . . . < dBase. Then a cumulative frequency may be defined as Ads) = ~ jokes), j = 1, . . . ]. k =j The cumulative frequency, Acts), describes the frequency of exceeding a particular damage level. The risk associated with the course of action s is now described by the set of damage and cumulative frequency pairs. Mathematically, it(s) = facts), dj~s)~. This enumeration process may be repeated for each specific s. Here, the digression begins to bear fruit. Each curve it(s) may now be approximated by a smooth curve similar to Figure 14.2, via some curve-fitting technique such as the least-squares used in the MSM. FIGURE 14.2 Risk distribution in terms of frequency versus damage for a particular choice of the state vector s. YACOV Y. HAIMES The PMRM extends this concept as follows. The risk distri- bution is separated into any number of distinct ranges k (k = 1, . . . K). Figure 14.2 shows high-, intermediate-, and low- frequency ranges. The frequency axis of the risk distributions for each specific state s may be segmented identically by choos- ing the same partitioning values 4?~ and ~2 for each. Associated with the frequency-axis segments will be segments on the risk curve (defined by Rat and R2) and on the damage axis (defined by do and d21. These Rae, R2, di, and d2 are not arbitrary: they are dictated by the choice of ~~ and ~2 as seen in Figure 14.2. A weighted average of the damage associated with each fre- quency-axis segment, k, may be computed and designated by His) for every k = 1, . . . K. Looking across all values for the state vector s reveals a set of point pairs is, chest; for each frequency segment k = 1, . . . K. In a manner similar to Figure 14.3, a smooth curves, k = 1, . . . K may be fitted through each of these point sets to reveal a set of damage functions corresponding to each of the frequency-axis segments. The example depicted in Figures 14.2 and 14.3 has three damage functions that describe high-, in- termediate-, and low-frequency levels. These may be ex- pressed in a multiobjective format as fuse, f2(s), f3(s)~. In the example developed in the section on the MSM, mul- tiobjective risk descriptions could be developed for the second and third objectives. The damage ordinate would take on the appropriate dimensions: the THM concentration and the num- ber of cancer patients due to carcinogenic groundwater con- taminants, respectively. EPILOGUE The underlying premise of this chapter is that risk assessment can provide the foundations upon which a successful program for the prevention of groundwater contamination can be built. This risk-assessment process is grounded on the use of systems modeling and improved decision-making processes based on quantitative as well as qualitative/subjective analysis. The findings of a recent study conducted by the Office of Technology Assessment (OTA) (1981) on the efficacy of mod- O1 A) dl(s) dl d2(s) d2 d3(s)

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Risk Assessment and Groundwater Contamination 0 (s ) , ~ t(s3) it, .~ \ AS \/ ._ \ X Wr2(5) - eling in water-resources management, planning, and policy are particularly pertinent here. The OTA study states: Mathematical models have significantly expanded the nation's ability to understand and manage its water resources. They are currently used to investigate virtually every type of water resource problem; for small- and large-scale studies and projects; and at all levels of deci- sionmaking. In some cases, they have increased the accuracy of esti- mates of future events to a level far beyond "best judgment" decisions. In other areas, they have made possible analyses that cannot be per- formed empirically or without computer assistance. Further, they have made it feasible to quantitatively compare the likely effects of different resource decisions. The above OTA findings, which are congruent with this chap- ter's premise, should be studied with respect to their impli- cations on research and development needs. On the subject of improving federal problem-solving capabilities, the OTA report states: Many of the analytic responsibilities mandated by federal and state water resources legislation cannot adequately be carried out without models. However, the analytic tools needed to fulfill many legislative requirements and decisionmaker information needs are currently un- available. The majority offederal agencies have no overall strategy for developing, using, disseminating, and maintaining these tools. And finally, Unless clear direction and priority-setting mechanisms are provided by Congress and the Executive Office of the President, the best analytic tools will not be available throughout the Federal Government, and many needed models will not be built. From the above it is evident that although risk assessment and the decision-making process associated with it can lead to the prevention or reduction of groundwater contamination, a 177 FIGURE 14.3 Weighted average of damages for each frequency axis segment viewed across choices of the state vector s. concerted research and development effort in this area is im- perative. ACKNOWLE DGM E NTS The author is grateful to John Bredehoeft for inspiring the writing of this chapter, Virginia Benade for her conscientious editorial work, Ken Loparo for his contribution to the section on MSM, and Eric Asbeck for his contribution to the section on PMRM. The reviews and many constructive comments made by Steven Gorelick, Leonard F. Konikow, Thomas Maddock III, W. Scott Nainis, Paula Stone, and Thomas Usselman are very much appreciated. Finally, special appreciation is due to Mary Ann Pelot for her capable typing and retyping of this chapter. Support for this research was provided in part by the National Science Foundation under Grant No. ENG-79-03605 and the U.S. Department of Energy under Grant No. DEACO-180- RA050256. REFERENCES Anderson, M. P. (1981). Groundwater quality models state of the art, in Proceedings and Recommendations of the Workshop on Ground Water Problems in the Ohio River Basin, Ohio River Basin Com- . . mlsslon. Asbeck, E. L., and Y. Y. Haimes (1983). The Partitioned Multiobjective Risk Method (PMRM), Tech. Rep. No. 83-7 (accepted in Large Scale Systems), Center for Large Scale Systems and Policy Analysis, Case Western Reserve U., Cleveland, Ohio. Bachmat, Y., J. Bredehoeft, B. Andrews, D. Hole, and S. Sebastian (1980). Ground-Water Management: The Use of Numerical Models,

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