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Total maximum daily load (TMDL) modeling is typically used to link the allowable load (the TMDL) to the criterion in a water quality standard, while pollutant allocation modeling is applied to apportion the TMDL among sources in the watershed. An essential element of the TMDL modeling is the margin of safety (MOS), which is intended to reflect the uncertainty in the TMDL forecast to meet the criterion. Thus, in principle, when the TMDL modeling is conducted according to EPA requirements, an error analysis is to be undertaken to estimate the uncertainty in the forecast of the criterion.

However, the recent NRC report (NRC 2001) noted that the basis for the TMDL is attainment of the designated use. With that perspective, the true uncertainty in the forecast TMDL is not simply the uncertainty between the pollutant load and the criterion; rather, it is the forecast uncertainty between the pollutant load and the designated use. The criterion is a surrogate for the designated use, and the NRC observed that it is attainment of the designated use that is the ultimate goal of the TMDL. Thus, the MOS ignores the uncertainty between the criterion and the designated use.

What are the implications of this underestimated or hidden error? Clearly, this is a function of the adequacy of the criterion as a surrogate for the designated use. If the criterion is essentially a perfect indicator of designated use, then hidden error is inconsequential. However, if the criterion is an imperfect surrogate, or more likely, the adequacy of the criterion as a surrogate for designated use is poorly known, then the hidden uncertainty is also poorly known.

In this paper, we propose Bayesian (probability) network models linking the criterion to the designated use as a flexible, probabilistic approach for representing both the statistical expressions and the judgmental assessments necessary to relate criterion to use. As an example to illustrate concepts, the Bayesian modeling strategy is considered for the problem of eutrophication. Designated uses related to fish propagation, shellfish habitat, public water supply, and aesthetics are examined associated with nutrient, chlorophyll, and dissolved oxygen criteria. The outcomes of this study will be measures of the magnitude and consequence of the hidden error, leading to guidance on sensible choices and recommendations for water quality criteria and TMDL margin of safety assessments.

Document Type: Research Article


Publication date: January 1, 2002

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  • Proceedings of the Water Environment Federation is an archive of papers published in the proceedings of the annual Water Environment Federation® Technical Exhibition and Conference (WEFTEC® ) and specialty conferences held since the year 2000. These proceedings are not peer reviewed.

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