A Bayesian hierarchical model to guide development and evaluation of substance objectives under the 2012 Great Lakes Water Quality Agreement

Under the 2012 Great Lakes Water Quality Agreement Canada and the United States are obliged to develop target concentrations for water quality constituents of particular concern. These "substance objectives" are closely analogous to numerical criteria under the US Clean Water Act. To develop effective substance objectives, it is important to consider how compliance with these objectives will be evaluated. Total phosphorus concentrations, for example, vary temporally and spatially, thus sample-based statistics will always be uncertain measures of the "true" underlying population characteristic. Using data from Saginaw Bay in Lake Huron, we develop a Bayesian hierarchical model that can be used to evaluate compliance with target concentrations on a temporally and spatially explicit basis. The "confidence of compliance" with targets can be assessed from the variance of the model parameter posterior distributions. This approach allows data to be grouped to represent spatial and temporal domains of particular interest, such as spring mean conditions in a certain area, and facilitates "partial pooling" of information so that regions with sparse data and high uncertainty can "borrow information" from more data-rich areas.