Combined Bayesian statistics and load duration curve method for bacteria nonpoint source loading estimation

Nonpoint source load estimation is an essential part of the development of the bacterial total maximum daily load (TMDL) mandated by the Clean Water Act. However, the currently widely used watershed-receiving water modeling approach is usually associated with a high level of uncertainty and requires long-term observational data and intensive training effort. The load duration curve (LDC) method recommended by the EPA provides a simpler way to estimate bacteria loading. This method, however, does not take into consideration the specific fate and transport mechanisms of the pollutant and cannot address the uncertainty. In this study, a Bayesian statistical approach is applied to the Escherichia coli TMDL development of a stream on the Eastern Shore of Virginia to inversely estimate watershed bacteria loads from the in-stream monitoring data. The mechanism of bacteria transport is incorporated. The effects of temperature, bottom slope, and flow on allowable and existing load calculations are discussed. The uncertainties associated with load estimation are also fully described. Our method combines the merits of LDC, mechanistic modeling, and Bayesian statistics, while overcoming some of the shortcomings associated with these methods. It is a cost-effective tool for bacteria TMDL development and can be modified and applied to multi-segment streams as well.