A framework for uncertainty and risk analysis in Total Maximum Daily Load applications

In the United States, the computation of Total Maximum Daily Loads (TMDL) must include a Margin of Safety (MOS) to account for different sources of uncertainty. In practice however, TMDL studies rarely include an explicit uncertainty analysis and the estimation of the MOS is often subjective and even arbitrary. Such approaches are difficult to replicate and preclude the comparison of results between studies. To overcome these limitations, a Bayesian framework to compute TMDLs and MOSs including an explicit evaluation of uncertainty and risk is proposed in this investigation. The proposed framework uses the concept of Predictive Uncertainty to calculate a TMDL from an equation of allowable risk of non-compliance of a target water quality standard. The framework is illustrated in a synthetic example and in a real TMDL study for nutrients in Sawgrass Lake, Florida.