Estimation of TMDLs and Margin of Safety under Conditions of Uncertainty

In TMDL development, an adequate margin of safety (MOS) is required in the calculation process to provide a cushion needed because of uncertainties in the data and analysis. Current practices, however, rarely factor analysis' uncertainty in TMDL development and the MOS is largely arbitrarily selected. This paper presents a formal methodology for the estimation of TMDL and MOS as a function of analysis uncertainty, degree of protection provided, and fuzziness in water-quality standards. The probabilistic methodology is demonstrated through a hypothetical lake-sediment phosphorus model and eutrophication problem. Impacts of parametric uncertainty on the TMDL distribution and MOS are discussed. The performance of the widely used first-order approximation (FOA), with Gaussian and log-normal assumptions, is tested against the Monte Carlo (MC) method. The dependence of the MOS on the degree of protection provided against violating water quality standard is computed.