Bayesian modelling of
Enterococcus
Exceedences at Boston
Harbor Beaches
Ann Michelle Morrison
OMSAP June 10, 2008
Beach Management
• Two Priorities
– Protect Public Health
– Maintain Recreational Beach Access
• Fecal Indicator Bacteria – Enterococcus
– Exceed: >104 CFU/100 mL
– No Exceed:  104 CFU/100 mL
Bayesian Networks
• Bayesian networks are models that relate
possible states of reality by probability
• Bayes Rule, developed by
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!
Basic Bayesian Network Design
• Bayesian networks are generally
designed to follow causal linkages
Netica Tutorial, Norsys, Inc. 2007
Constitution Beach Bayesian Network
72 Hour Rain
0 to 0.01
32.1
0.01 to 0.21 33.5
0.21 to 3.16 34.5
0.619 ± 0.92
pLogan 3 Day Rain
0
33.4
0 to 0.23
33.2
0.23 to 7.85 33.5
1.39 ± 2.3
1
2
3
4
48 Hour Rain
0
47.6
0 to 0.17
25.6
0.17 to 3.16 26.8
0.469 ± 0.85
pECOC
2 to 10
31.4
10 to 50
44.3
50 to 18300 24.3
2240 ± 4700
Phase Stage
34.0
23.2
8.38
34.4
2.43 ± 1.3
pLogan 2 Day Rain
0
48.1
0 to 0.22
28.1
0.22 to 3.36 23.9
0.458 ± 0.87
pLogan Rain
0
68.1
0 to 0.17
17.3
0.17 to 3.36 14.6
0.273 ± 0.71
Dry, Damp, Wet
Damp
30.9
Dry
33.3
Heavy
18.4
Light Rain 17.4
Exceed Enterococcus
No
91.7
Yes
8.28
Low Tide Height
-0.56 to 0.05 32.7
0.05 to 0.31
34.1
0.31 to 0.81
33.2
0.164 ± 0.36
pSunshine Percent
0 to 50
35.6
50 to 82
31.0
82 to 100 33.4
59.8 ± 30
Tide Height MLLW
-0.4 to 1.7 34.3
1.7 to 2.6
32.7
2.6 to 3.6
33.0
1.95 ± 1.1
Wind Direction
E
17.7
N
6.67
NE
6.76
NW
10.8
S
12.6
SE
5.27
SW
21.1
W
19.0
WNW
0.20
24 Hour Rain
0
66.4
0 to 0.11
16.3
0.11 to 2.44 17.3
0.229 ± 0.55
pWind Direction
E
17.0
N
7.14
NE
7.36
NW
10.2
S
12.8
SE
4.83
SW
20.9
W
19.7
pAvg_ Wind Speed
4.3 to 8.5 32.3
8.5 to 11
38.3
11 to 70
29.4
17.7 ± 17
pWind Speed Peak
11 to 20 27.0
20 to 25 39.0
25 to 74 34.0
29.8 ± 17
Salinity
19.1 to 29.4 29.3
29.4 to 30.2 36.1
30.2 to 37.4 34.7
29.6 ± 4.3
Water Temperature
-0.6 to 19
28.3
19 to 21
36.2
21 to 27.5 35.5
18.4 ± 6.9
Boston Harbor Beaches
Management Model Comparison –
Constitution Beach
Management
Model
TPR
TNR
Green Flag
Red Flag
Bayesian (1996 –
2004)
0.76
0.82
0.97
0.32
48 Hour Rain
0.21 in. threshold
0.65
0.80
0.96
0.23
Previous Day’s
Enterococcus
0.17
0.93
0.93
0.17
Management Model Comparison –
Wollaston Beach
Management
Model
TPR
TNR
Green Flag
Red Flag
Bayesian (1996 –
2004)
0.69
0.80
0.95
0.35
48 Hour Rain
0.21 in. threshold
0.56
0.79
0.92
0.30
Previous Day’s
Enterococcus
0.24
0.89
0.89
0.24
Management Model Comparison –
Tenean Beach
Management
Model
TPR
TNR
Green Flag
Red Flag
Bayesian (1996 –
2004)
0.57
0.88
0.93
0.44
48 Hour Rain
0.21 in. threshold
0.60
0.79
0.93
0.30
Previous Day’s
Enterococcus
0.34
0.90
0.91
0.30
Management Model Comparison –
Carson Beach
Management
Model
TPR
TNR
Green Flag
Red Flag
Bayesian (1996 –
2004)
0.28
0.92
0.95
0.20
48 Hour Rain
0.21 in. threshold
0.52
0.76
0.96
0.12
Previous Day’s
Enterococcus
0.16
0.95
0.95
0.16
Conclusions
• Bayesian 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
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 beach
Rain is IMPORTANT
1996 – 2004
Local gauges
TPR
0.76
1996 – 2007
Logan Only
TPR
0.21
Carson
0.28
0
Tenean
0.57
0.56
Wollaston
0.69
0.56
Beach
Constitution