A BAYESIAN OBSERVATION ERROR MODEL TO PREDICT CYANOBACTERIAL BIOVOLUME FROM SPRING TOTAL PHOSPHORUS IN LAKE MENDOTA, WISCONSIN

We developed a logistic model for predicting summer blue-green biovolu me from mean (log metric) spring total phosphorus concentration in Lak e Mendota, Wisconsin. The model incorporates uncertainty in the sample estimates of the ''true'' mean total phosphorus values. We used Bayes Theorem to assess model parameters and predictive uncertainty from 19 years of data. When compared with a ''naive'' model that does not acc ommodate phosphorus uncertainty, the observation error model has a hig her parameter variance, but lower prediction uncertainty. Lower predic tion uncertainty occurs because some of the noise in the data is resol ved as phosphorus uncertainty, thus reducing the variance of the model disturbance term. The observation error model results in less stringe nt phosphorus targets to meet acceptable blue-green levels than does t he naive model because of this lower prediction uncertainty.