Database Reference
In-Depth Information
1.
the risk α(u) (of a false positive or of over-
estimation), that is to say the probability of
declaring erroneously a location u “poten-
tially contaminated” is given by:
probability is absolutely subjective and variable
according to the specificity of the case study.
Source representative
concentration (crS): ucl Method
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(
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a() Pr
u
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k
k
k
The Source Representative Concentration, to-
gether with the data coming from the characteriza-
tion, constitutes the input for a site specific risk
assessment. Being its value directly proportional
to the calculated risk, it can be easily inferred
how its estimation accuracy is fundamental for
the correct execution of the whole Risk Assess-
ment procedure.
The Upper Confidential Limit UCL 95% of
the mean value provides a representative estima-
tion of the Source Representative Concentration;
statistically the UCL 95% of a mean is defined
as a value that, when calculated repeatedly for
randomly drawn subsets of site data, equals or
exceeds the true mean 95% of the times (U.S.EPA,
2001). This value is used for calculating the Source
Representative Concentration as it represents a
highly conservative estimation of the true mean
value, moreover it takes into account the uncer-
tainty linked the estimation of the mean, due to
limited sampling data.
(15)
For all the locations u such that the kriging
estimation z*(u)>z
k
. The symbol (n) means
conditional to the n sampling survey data.
In other words α(u) measures the probability
that the effective value Z(u) is lower than
the critical threshold z
k
, whereas the kriging
estimated value z*(u) exceeds it;
2.
the risk β(u) (of a false negative or of under-
estimation), that is to say the probability of
declaring erroneously a location u “clean”
is given by:
{
}
=-
(
( )
()
>
()
£
()
b() Pr
u
=
obZu
z
zu zn
*
1
Fuzn
;
k
k
k
(16)
For all the locations u for which the kriging
estimation z*(u)≤z
k
. More explicitly, β(u)
measures the probability that the effective
value is higher than the critical threshold,
while the kriging estimation is lower.A logi-
cal deduction defines the risk β(u) where the
risk α(u) is zero and conversely.
Calculation of UCL for Normal
Distribution: Student' s T Method
The calculation of UCL of the mean varies ac-
cording to the type of data distribution. If the data
distribution can be approximated as normal, the
most used method for the calculation of the UCL95
is the Student's T method, according to which:
By means of the maps of probability of ex-
ceeding a threshold fixed by the legislation it is
possible to govern the acceptable risk level. The
major difficulty found in this approach consists
in choosing an appropriate level of probability for
each type of risk such to initialize any intervention
on the area (Goovaerts, 1999). The decision proves
to be easy in the areas where the probability is
high or low, while it gets more complicated in the
other areas where it assumes intermediate values
variable from 0.3 to 0.7. The threshold value of
UCLCt
m
95
=+´e
(17)
Cm represents the mean concentration and t
the Student' s T value, tabulated in function of the
level of approximation required (in case of UCL
95% the level of approximation is 0.05).
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