A Bayesian network incorporating observation error to predict phosphorus and chlorophyll a in Saginaw Bay

Empirical relationships between lake chlorophyll a and total phosphorus concentrations are widely used to develop predictive models. These models are often estimated using sample averages as implicit surrogates for unknown lake-wide means, a practice than can result in biased parameter estimation and inaccurate predictive uncertainty. We develop a Bayesian network model based on empirical chlorophyll-phosphorus relationships for Saginaw Bay, an embayment on Lake Huron. The model treats the means as unknown parameters, and includes structure to accommodate the observation error associated with estimating those means. Compared with results from an analogous simple model using sample averages, the observation error model has a lower predictive uncertainty and predicts lower chlorophyll and phosphorus concentrations under contemporary lake conditions. These models will be useful to guide pending decision-making pursuant to the 2012 Great Lakes Water Quality Agreement.