Incorporating reliability into the definition of the margin of safety in total maximum daily load calculations

In the calculation of the total maximum daily load (TMDL), the margin of safety (MOS) is an attempt to account for the uncertainties related to the conceptual representation of the system and the inherently random nature of the processes under study. In general, the MOS is often the result of arbitrary or poorly supported decisions that have little to do with the reliability of the system. To improve the current practice in TMDL calculations, an enhanced reliability-based MOS is proposed here. The Modified Rosenblueth point estimate method is proposed in this paper as a valuable means to assess the uncertainty of a system, and, thus, its probability of failure. The Modified Rosenblueth method is a less computationally demanding uncertainty analysis technique, and can be easily coupled with deterministic hydraulic and water quality numerical models. A case study on arsenic concentrations in the Niagara River is discussed in this paper. The results of the uncertainty analysis are used to compute the effective risk of exceeding a selected water quality standard. It is shown that use of the uncertainty analysis in assessing the effective risk goes beyond the purely qualitative evaluation of traditional pass-and-fail methods. Moreover, the probability of exceeding a selected water quality standard is applied here to the calculation of the MOS term. Selecting the MOS based on the probability of failure provides a scientifically based definition of the TMDL. A reliability-based MOS enhances the current application of the TMDL by providing more reliable estimates, and is a step forward in making TMDL calculations more practical and standardized.