Bayesian Load Duration Curves for Bacterial Total Maximum Daily Loads: Urban Case Study

A Bayesian load duration curve approach is developed to estimate indicator bacterial load reductions for a small, urban watershed with stormwater and animal inputs. The Bayesian load duration curve approach uses the truncated bivariate normal probability distribution to predict flow, in-stream bacterial concentration, and the resulting load for a specified number of flow conditions. Using non-informative priors, the Bayesian approach propagates the uncertainty resulting from the natural variability in observed concentrations through to the predicted in-stream indicator bacterial concentration and load. Using the best estimate 90^th percentile in-stream loads, the Bayesian method predicts indicator bacterial load reductions ranging between 68% for low flows and 99.9% for high flows. The predicted distributions of in-stream bacterial concentration are then compared pre- and post-implementation of stormwater filtration. The pre-implementation distribution of in-stream indicator bacterial concentration demonstrates that the stream exceeds the standard of 235 cfu/100ml E. coli 76.1% of the time during the recreational season with a 95% credible interval CI(74.6, 78.0). The post-implementation distribution of indicator bacterial concentration predicts that the concentration of indicator bacteria exceeds the limit set by the water quality standard 72.4% CI(70.6, 74.3). Alternatively, the Bayesian model is then used to predict in-stream concentration post-implementation of an aggressive ultra-violet disinfection process.