Environmental Engineering Reference
In-Depth Information
14
A: Subarea with
small fraction
C: Subarea with
large fraction
12
10
8
B: Subarea with
medium fraction
Regulatory
level
6
D: Subarea with no
data on fraction
4
2
0
0
0.2
0.4 0.6
h (Fraction of contaminated soil)
0.8
1
Figure 13.38 Prior probability distributions for fraction of contaminated soil based on historical land-use in
subareas of oil refinery (see Figure 13.37 for subareas).
above the regulatory limit) in a set of samples followed a binomial distribution. Therefore,
the updated distribution for the fraction of contaminated samples in a subarea would also
follow a β-distribution ( Table 13.1).
A framework to make decisions on whether or not to remediate a subarea was then for-
mulated. Guidance on the relative cost of failing to remediate a subarea that was contami-
nated was established for remediation based on input from the regulators. If an area was
suspected to have benzene contamination, the regulators would generally require that 20
samples be taken and support a decision to not remediate the area if all 20 samples were
clean. Mathematically, if there is nothing known about an area (i.e., the prior probability
distribution of the fraction exceeding 50 mg/kg is uniform between 0 and 1), then obtaining
20 clean samples is equivalent to achieving a probability of 66% that the fraction is <1/20.
Therefore, the relative cost of failing to remediate a contaminated site was set to be three
times greater than the cost of remediation, meaning that the decision to remediate would
be preferred if the probability that the contaminated fraction was <1/20 was smaller than
66% ( Figure 13.39). On the basis of prior information, the probability was assessed for each
subarea that the contaminated fraction was smaller than 0.05 ( Figure 13.40). The decision
to remediate a subarea could be made if there was a large probability of high benzene con-
centrations in the soil or if little was known about it based on the prior information.
Finally, an assessment of the value of information from additional soil samples was con-
ducted to design a remedial investigation program. An example of the preposterior decision
tree for this assessment in one particular subarea is shown in Figure 13.41. Results from
Cost
Remediation
C R
Subarea i:
H ~ Beta(a i , b i )
P ( H < 1/20) = p i
No future problem
$ 0
No
remediation
P ( H £ 1/20) = p i
Future problem
C R : $ Cost of
remediation
3 × C R
P ( H > 1/20) = 1- p i
Figure 13.39 Prior decistion tree to analyze the remediation decision.
 
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