Bayesian model for flow-class dependent distributions of fecal-indicator bacterial concentration in surface waters

A Bayesian statistical water quality model is demonstrated to predict fecal-indicator bacterial concentrations for waterbodies without sufficient monitoring data for data-intensive modeling techniques. Using a truncated bivariate normal likelihood function and the readily available observations of flow and bacterial concentration, the Bayesian approach propagates the uncertainty in the model parameterization to the final predictions of in-stream bacterial concentration. The proposed model captures the variation in the magnitude of bacterial loading between dry and wet conditions by estimating separate sets of model parameters for different flow conditions, but also has the capability to pool the data among flow conditions. The model can be used in two ways: first, the model specifies the percent of time that the recreational season in-stream concentration is not in compliance with the relevant water quality standard, and second, the model estimates the necessary bacterial load reduction for multiple flow conditions to meet the relevant water quality standard. Using an eleven year monitoring record for a site sampled at a monthly frequency on the Youghiogheny River in southwestern Pennsylvania, USA, the model parameters are updated and posterior predictions are generated for each 2-year increment. After six years of sampling, the predicted percent of time that the recreational season in-stream bacterial concentration is not in compliance with the relevant water quality is 82% with 95% CI(80,85), and the bacterial load reductions required to meet the standard are 14.7 CI(14.6,14.8), 14.5 CI(14.3, 14.6), and 14.0 CI(13.9, 14.2) log(10)(cfu/day) for the high, normal, and dry flow conditions, respectively. The change in estimated load reduction and percent exceedance resulting from additional monitoring for this site becomes small after six years of sampling, indicating that a decision does not need to be postponed for additional monitoring.