DECISION SUPPORT FOR WATER-QUALITY ANALYSIS

Decision-Analytical Approach [ Justification ]

Managing mercury is quite complex as a result of physical (sediment dynamics), chemical net (methyl-mercury formation), and biologic (food-web dynamics and bioaccumulation) uncertainties. Although mercury research has made great strides, the complexity of mercury biogeochemistry and its associated environmental impacts still challenge the scientific community. The scientific understanding of mercury biochemical cycling and transport within California is still incompletely understood and contains significant uncertainties that should be incorporated into the decisionmaking process.

Although decision analysis for water-quality management can be done by using a wide variety of approaches to water-quality/natural-system forecasting, the USGS WGSC has been researching the use of Bayesian network models to forecast water-quality and ecologic responses to mitigation strategies. Bayesian decision analysis can be described as a unified framework for coherent decisionmaking. A Bayesian probability network (BPN), which integrates information of varying rigor and detail into a simple model of a complex system, consists of the set of variables of interest, along with a representation of the causal relations among the variables.

These relations are identified and quantified by using historical data, physical-process-based models, conceptual models, and expert judgment. Conditional probabilities—the probabilities of an event, given that another event has occurred—are assigned to each link, and probabilistic predictions of model endpoints are then made on the basis of the entire set of conditional probabilities assigned for each system variable. The grand appeal of the Bayesian approach for environmental decisionmaking is its explicit treatment of uncertainty, including expert judgment, which allows easy updating of prediction and inference when new data observations become available (Labiosa et al., 2005a).

Probability networks provide a methodology for combining expert knowledge of causal structures and aggregate ecosystem response with conceptual models that are identifiable from available data. Thus, they are conceptual rather than deterministic models, intended to represent a coherent set of beliefs about a system rather than simulate or reproduce the actual physical processes themselves. Those beliefs may incorporate some detailed knowledge of the physical processes but generally are simply convictions based on experiences of the interaction between certain variables. The use of expert opinion is common in Bayesian modeling, and well-developed protocols exist for eliciting opinions in probabilistic form (Labiosa et al., 2005b).

A BPN approach is selected for use in this research because estimates of water-quality parameters can easily be presented in probabilistic terms, doing so allows new information to be integrated as it becomes available, BPNs are useful in many aspects of environmental management, and the graphical representation of a BPN that shows the causal relations may ease communication of the approach to potential users/stakeholders. In addition, the “conceptual” nature of Bayesian networks makes it a worthy tool because the physical processes of mercury are not well understood.

A BPN approach links scientific assessments to stakeholder objectives through four steps:
    1) Stakeholder Concerns: Elicit stakeholder concerns and desired “endpoints” (for example, methyl-mercury contents in water and fish tissue). These concerns can be addressed through public meetings and surveys.
    2) Bayesian Probabilistic Network: Construct a probabilistic-network model to link attributes corresponding to stakeholder interests with proposed management actions (for example, best management practices). Graphical models can be constructed that depict the probabilistic relations among uncertain variables (influence diagrams), to be used to perform both prediction and inference.
    3) Model Network: Validate with existing data and use to provide scientific guidance for water-quality management decisions. Determine causality in the system, using the model to “predict” past observation. Perform sensitivity analyses.
    4) Model and Data Evaluation: Evaluate the models and data needed to improve the statistical and deterministic relations between management options and meeting the desired endpoint. Update the model as new information becomes available.

A BPN contrasts with commonly used deterministic approaches that model system behavior on the basis of mathematical representations of the underlying mechanisms and on deterministic approaches that ignore uncertainty. A Bayesian network decision-analytical tool (or any other type of approach that uses decision analysis with decision trees) has distinct advantages over other non-probabilistic decision frameworks, including (Shachter, 1988):

     • Representation and proliferation of uncertainty in a computationally efficient manner;
     • Integration of diverse information, including the results from, for example, science-and-engineering models, cost-benefit analyses, data analyses, and decisionmaker preferences;
     • Integration of predictions of mitigation consequences into a model that evaluates the various possible consequences; and
     • Inclusion of sensitivity analysis.

A BPN approach may reduce the impacts of time, money, and data constraints on analysis and decisionmaking by (1) integrating various data types, including narrative information, and therefore providing a larger database; (2) reducing initial data-collection needs, given the ability to update probabilities with new information without redoing analysis; and (3) requiring fewer site-specific inputs, given the simplicity of the Bayesian network approach (Nielson, 2001).

Because the uncertainties involved in estimating total mercury loading and predicting the environmental impacts of load-reduction projects are significant, an approach that explicitly treats uncertainty is useful for decision-support activities. For decisions that involve perturbations to complex natural systems, BPNs that are built from the best available scientific models, data, and expert judgments can be used to predict the probabilities of the various outcomes of those decisions (Reckhow, 1999; Borsuk et al., 2002; Stow et al., 2003).


A more specific decision-influence diagram for assessing mitigation strategies for meeting a mercury water quality standard. Since compliance is predicted probabilistically, the procedure of using arbitrary safety factors to hedge against uncertainty can be replaced by the explicit consideration of uncertainty and its consequences for mitigation decisions (Wood, 2005).

A BPN approach estimates best decisions, given the decisionmakers’ consensus on information, alternatives, and preferences, and allows the modeler to focus on predictive accuracy over the temporal and spatial scales desired for the variables of interest to decisionmakers, removing details that are determined to be extraneous to the decisionmaking problem. This approach can incorporate beliefs and preferences explicitly, as opposed to producing results from mechanistic models, and uses them in ways implicitly affected by those preferences. We assert that this approach is a fairer, more transparent way to handle the uncertainties.

All decisionmaking is subjective, and so any decision-analytical tool must be modified to reflect the beliefs and preferences of decisionmakers before use. From a decision-analytical perspective, the tradeoff between mitigation costs and the probability of compliance (a measure of decision uncertainty) with various environmental/ecologic targets can be explicitly modeled, with no need for safety factors or other arbitrary hedges against risk (Labiosa, 2003). This concept, a basic economic preference, may prove useful for evaluating mitigation strategies because strategies that yield higher probabilities of success would naturally be more appealing at a given cost.

A BPN approach recognizes that the uncertainties in model inputs and their propagation through the relations between system variables may result in large uncertainties in the relations between mitigation efforts and effects on the environmental endpoints of interest, for example, total mercury loadings and methyl-mercury contents in water and fish tissue. A decision-analytical approach is used so that these large uncertainties can be meaningfully interpreted within the decisionmaking context.

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