A Geostatistically Based Probabilistic Risk Assessment Approach - Evolving Application Domains of Data Warehousing and Mining - page 298

Figure 13. a) experimental and theoretic variogram of the variable b) map of the error

lines at equal probability of exceeding the CSC,
each delimiting an area of specific geometry.
Starting from the values estimated by means of
polygonal kriging inside each area it has been
possible to determine the probability distribution
of the considered variable. It can be pointed out
that the acceptation of a finite probability of
exceeding implies admitting the presence of an
“overestimation” (α) or an “underestimation”
error (β): for the examined case, the map of the
α error is reported in Figure 13b.
In Figure 14 are shown the areas enclosed by
the different curves of probability of exceeding the
threshold value. In correspondence of a high prob-
ability (close to 1) the area is much more restricted
and circumscribed than in correspondence of a low
probability (0.3). For each of these source areas it
is possible to determine the Source Representative
Concentration value with the UCL method.
In table 3 is reported, for each probability, the
maximum width (S w ) in direction orthogonal to
flow, of the areas enclosed by the corresponding
isolines and the value of UCL determined by means
of a test carried out with data estimated applying
polygonal kriging inside those areas.
The tests show above all, for all the examined
probabilities of exceeding, that the probability

density curve referred to the values is not para-
metric.
The graph in Figure 15a proposes the polynomial
regression between UCL and probability of exceed-
ing; it is possible to point out that, in relation to the
latter the values of the former increase up to the
maximum value of 59.42 µg/l in correspondence
of a probability of exceeding the CSC of 90%. In
Figure 15b analogous regression is proposed be-
tween the width of the Potentially Contaminated
Area and the probability of exceeding.

Probabilistic Risk Assessment

Once having obtained through geostatistics the
probability distributions that characterized the
most significant variables, it is possible to proceed
with Monte Carlo Analysis to determine the risk
probability function and subsequently to define
the acceptable risk level. Once fixed a specific
scenario of exposure, the expression of the risk
depends on the transversal dimension of the source
of contamination (S w ) and on the concentration
in the point of exposure (CPOE) that, in turn,
depends on the value of Source Representative
Concentration.
Making explicit in the analytic expression of