MODELING SOURCE/LINKAGE ANALYSIS UNCERTAINTY USING SIMULATION AND BAYESIAN NETWORKS FOR A MERCURY TMDL IN NORTHERN CALIFORNIA
Abstract:In many cases, “knowing how little you know” is an important part of decision-making under uncertainty. In the case of mercury TMDLs in mercury/gold mine impacted watersheds, it is well understood that large uncertainties exist in estimates of the various mercury source loadings, predictions of methyl mercury formation and bioaccumulation in fish, and other predictions made in the TMDL linkage analysis. Current linkage analysis practice often involves the use of deterministic models in series, with the outputs from one model being used as inputs into another deterministic model. Uncertainty is often “handled” through the use of safety factors in environmental targets and/or the use of ad hoc uncertainty estimates. In practice, these ad hoc uncertainty estimates may have little influence in the actual decision-making process. The work reported here is part of a larger effort to demonstrate a probabilistic approach that treats uncertainty as risk to be managed in the decision-making process (Labiosa et al., 2005; Labiosa et al., 2003).
We explore in detail the importance of the consideration of uncertainty for a particular situation, a mercury TMDL case study involving a small, mercury mine-impacted watershed with high background mercury loadings in Northern California. To explicitly model uncertainty, we used stochastic empirical models, bootstrapping, Monte Carlo simulations, and elicited expert judgment to generate conditional probability distributions over the environmental variables of interest. We use the resulting conditional probability distributions to build a Bayesian network (BN) model of the causal relationships between potentially controllable variables (e.g., mine total mercury loadings) and environmental target variables (e.g., methylmercury loading at a compliance point). The BN can then be used to make fast probabilistic forecasts about the response of the system to potential future mitigation efforts and other predictions and inferences. By integrating the source and linkage analyses in a Bayesian network, BN algorithms can be used to efficiently and quickly approximate the propagation of uncertainty through the various steps in the source/linkage analysis. This computational speed allows mitigation/allocation scenarios to be probabilistically explored in real time in a workgroup meeting setting.
Our results demonstrate that the consideration of uncertainty in this mercury source/linkage analysis provides significant decision insights. These insights include information relevant to designing and prioritizing future monitoring activities, ranking potential mitigation strategies by probability of compliance with multiple environmental targets, and exploring the trade-offs between mitigation costs and compliance uncertainty for various strategies and scenarios. Most importantly, the “best load allocation/mitigation strategy” that emerges from deterministic source/linkage modeling may significantly differ from that supported by a probabilistic analysis.
Document Type: Research Article
Publication date: January 1, 2005
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