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It is recognized (e.g. NRC, 2001; EPA, 2002) that the TMDL Margin of Safety component is not currently being addressed in a rigorous manner. Research recently conducted for the Water Environment Research Foundation (WERF) (Dilks, 2002) identified the root causes related to difficulties in rigorously defining the TMDL Margin of Safety, and provided a range of options for defining the MOS. Limited practical experience in defining TMDL uncertainty was found to be a primary problem inhibiting rigorous determination of the Margin of Safety. A modified implicit approach was identified as an interim method to allow improved estimation of the MOS until more rigorous explicit methods could be adapted for widespread use. Implicit methods for determining the MOS have traditionally had two weaknesses: 1) They do not explicitly define how large the MOS is, and 2) They provide no quantitative information on the degree of protection provided. The WERF research provided guidance on quantifying the MOS for explicit approaches, but provided little information regarding the degree of protection provided. This paper extends that work to provide insight on estimating the degree of protection provided by implicit approaches.

Monte Carlo analysis was conducted using dissolved oxygen and fecal coliform bacteria models for typical TMDL applications to determine the uncertainty in model prediction caused by uncertain inputs, and to explicitly define the level of protection provided by different implicit MOS approaches. Results show that the implicit Margin of Safety ranged from 0 to 59% of the TMDL, with a corresponding probability of attaining standards ranging from 50 to 96%. This wide range of protection makes it essential that caution be taken in using implicit approaches to ensure that meaningful results are obtained.

The degree of protection provided by implicit approaches cannot be determined a priori for most TMDL applications without conducting more rigorous uncertainty analyses. However, results of this work identify some guiding principles that will constrain the variability in level of protection provided by implicit MOS approaches in some cases. In general, implicit approaches provide a more certain level of protection when: 1) A relatively small number of uncertain parameters are involved, 2) The parameters treated as conservative play a significant role in defining allowable loads, and 3) The uncertainty in these parameters is relatively well quantified. Implicit approaches cannot be used to credibly estimate the level of protection provided by the MOS as the above assumptions become violated, and should not be used in those situations.

Document Type: Research Article


Publication date: 2003-01-01

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