Application of Bayesian Monte Carlo Analysis to Determine the Uncertainty in the Lake Okeechobee Water Quality Model

A Bayesian Monte Carlo (BMC) analysis was used to quantify the uncertainty in predictions of the Lake Okeechobee Water Quality Model (LOWQM). The LOWQM is a time-variable eutrophication model simulating sixteen state variables and requiring over 100 input parameters. BMC estimates model uncertainty by combining prior information regarding the uncertainty of model inputs with the ability of different parameter input sets to describe available data on state variables. Prior uncertainties for model inputs relating to rate coefficients were determined via literature review, while the uncertainty in boundary conditions were defined through analysis of site-specific data. The degree to which a given model simulation was capable of describing observed data (i.e. the likelihood function) was defined as the percent of time that a simulation's results fell within the 95% confidence interval of the observed total phosphorus data.The overall uncertainty in model inputs was determined by conducting 5500 Monte Carlo iterations, selecting each input from their pre-specified prior distributions, and weighting each result by the calculated likelihood. Of these 5500 iterations, 1521 had total phosphorus likelihood functions greater than 50 percent. These 1521 iterations were then used to project the uncertainty in LOWQM predictions for a series of future load reduction scenarios. This type of analysis can provide two types of management benefit: 1) It identifies which input parameters are most uncertain, and can be used to target additional monitoring to optimally reduce uncertainty, and 2) It identifies the uncertainty surrounding predictions for future scenarios, allowing better support for management decisions than predictions of expected values alone.