Deterministic and probabilistic approaches to the development of pH total maximum daily loads: a comparative analysis

The most commonly used deterministic approach to the development of total maximum daily loads (TMDLs) fails to explicitly address issues related to a margin of safety and inherent variability of streamflows in the process of TMDL development. In this paper, the deterministic approach to pH TMDL development for Beech Creek watershed, Muhlenberg County, Kentucky, proposed by Ormsbee, Elshorbagy and Zechman is discussed. The shortcomings and the limitations of the assumptions associated with the deterministic approach are highlighted. An alternative probabilistic approach, to cope with the percentile-based water quality standards based on Monte Carlo simulation, is presented and compared to the deterministic approach. The proposed probabilistic approach provides a deeper insight into the issue of uncertainty and emphasizes the importance of handling the water quality standards and TMDLs in terms of magnitude and frequency rather than a single-valued approach. Expected exceedances and the confidence of compliance with percentile-based standards are estimated. Accordingly, an objective method of estimating the margin of safety for pH TMDLs is proposed.