Predicting the frequency of water quality standard violations: A probabilistic approach for TMDL development

To address the impaired condition of the water bodies listed under Section 303(d) of the Clean Water Act, over 40 000 total maximum daily loads (TMDLs)for pollutants must be developed during the next 10-15 years. Most of these will be based on the results of water quality simulation models. However, the failure of most models to incorporate residual variability and parameter uncertainty in their predictions makes them unsuitable for TMDL development. The percentile-based standards increasingly used by the EPA and the requirement for a margin of safety in TMDLs necessitate that model predictions include quantitative information on uncertainty. We describe a probabilistic approach to model-based TMDL assessment that addresses this issue and is suitable for use with any type of mathematical model. To demonstrate our approach, we employ a eutrophication model for the Neuse River Estuary, North Carolina, and evaluate compliance with the state chlorophyll a standard, Any observed variability in chlorophyll a that is not explained by the model is explicitly incorporated via a residual error term. This probabilistic term captures the effects of any processes that are not considered in the model and allows for direct assessment of the frequency of standard violations. Additionally, by estimating and propagating the effects of parameter uncertainty on model predictions, we are able to provide an explicit basis for choosing a TMDL that includes a margin of safety. We conclude by discussing the potential for models currently supported by the EPA to be adapted to provide the type of probabilistic information that is necessary to support TMDL decisions.