1. Bayesian modelling of Enterococcus Exceedences at Boston Harbor Beaches Ann Michelle Morrison OMSAP June 10, 2008

2. Beach Management Two PrioritiesTwo Priorities –Protect Public Health –Maintain Recreational Beach Access Fecal Indicator Bacteria – EnterococcusFecal Indicator Bacteria – Enterococcus –Exceed: >104 CFU/100 mL –No Exceed:  104 CFU/100 mL

3. Bayesian Networks Bayesian networks are models that relate possible states of reality by probabilityBayesian networks are models that relate possible states of reality by probability Bayes Rule, developed byBayes Rule, developed by Revered Thomas Bayes Revered Thomas Bayes For any two events, A and B, p(B|A) = p(A|B) x p(B) / p(A) Conditional Probability – everything is related!

4. Basic Bayesian Network Design Bayesian networks are generally designed to follow causal linkagesBayesian networks are generally designed to follow causal linkages Netica Tutorial, Norsys, Inc. 2007

5. Constitution Beach Bayesian Network

6. Boston Harbor Beaches

7. Management Model Comparison – Constitution Beach Management Model TPRTNR Green Flag Red Flag Bayesian (1996 – 2004) 0.760.820.970.32 48 Hour Rain 0.21 in. threshold 0.650.800.960.23 Previous Day’s Enterococcus 0.170.930.930.17

8. Management Model Comparison – Wollaston Beach Management Model TPRTNR Green Flag Red Flag Bayesian (1996 – 2004) 0.690.800.950.35 48 Hour Rain 0.21 in. threshold 0.560.790.920.30 Previous Day’s Enterococcus 0.240.890.890.24

9. Management Model Comparison – Tenean Beach Management Model TPRTNR Green Flag Red Flag Bayesian (1996 – 2004) 0.570.880.930.44 48 Hour Rain 0.21 in. threshold 0.600.790.930.30 Previous Day’s Enterococcus 0.340.900.910.30

10. Management Model Comparison – Carson Beach Management Model TPRTNR Green Flag Red Flag Bayesian (1996 – 2004) 0.280.920.950.20 48 Hour Rain 0.21 in. threshold 0.520.760.960.12 Previous Day’s Enterococcus 0.160.950.950.16

11. Conclusions Bayesian networks are powerful tools to visually model an environmentBayesian networks are powerful tools to visually model an environment The Bayesian networks for Constitution, Wollaston, and Tenean Beaches perform as well or better than a rainfall alone management modelThe Bayesian networks for Constitution, Wollaston, and Tenean Beaches perform as well or better than a rainfall alone management model Carson Beach has a very low probability of an Enterococcus exceedence. 48 Hour Rainfall thresholds are the most protective, but often close a clean beachCarson Beach has a very low probability of an Enterococcus exceedence. 48 Hour Rainfall thresholds are the most protective, but often close a clean beach

12. Rain is IMPORTANT Beach 1996 – 2004 Local gauges TPR 1996 – 2007 Logan Only TPR Constitution0.760.21 Carson0.280 Tenean0.570.56 Wollaston0.690.56