A Bayesian approach for estimating bacterial nonpoint source loading in an estuary with limited observations.

Large uncertainty in the estimation of bacterial nonpoint sources often results in the poor simulation of bacteria concentration in estuaries using a deterministic model. To better quantify the uncertainty in bacterial modeling, a Bayesian approach was incorporated into a tidally averaged estuarine model for estimating bacterial loading using in-stream observations. This was accomplished by using Bayes' theorem to develop a joint probability distribution for nonpoint source loadings based on the bacteria observations in the estuary. To overcome the geometry variation along the estuary for a non-linear transport problem with no analytical solution, the approach was implemented on a finite difference model. The approach was applied to Holdens Creek, a tidal river of the Pocomoke Sound of the Chesapeake Bay, to explore the feasibility of estimating bacteria sources and to develop an allowable load for the Creek to attain water quality standards. Further experiments were conducted to investigate the convergence for loading estimation, and the errors and uncertainties associated with load estimation using different data sets with varied sample sizes. With the use of limited observations, the nonpoint source loads can be estimated within an acceptable error range by selecting appropriate prior loading distributions. Because of the high spatial correlations among observations in the estuary, the errors in loading estimation at adjacent watersheds compensated each other, resulting in a good estimation of loads for the entire watershed. The approach not only provides an efficient methodology to assess the nonpoint source contribution for watershed management, but also has the additional advantage of addressing the problems of the uncertainty and error associated with bacterial simulation in the estuary.