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tions were found in many samples of water drawn
from other zones of the region, even not close to
the study area. These probability distributions
have allowed to estimate the risk α, or of a false
positive, and the risk β, or of a false negative.
Deciding on the balance of the two risks α and
β is a clearly political decision, which falls well
beyond the realm of geostatistics. Nevertheless,
geostatistics can assist in decision-making man-
agement by ranking the potentially polluted areas
on the basis of the assessed impact (Castrignanò
et al., 2004).
The next phase of the analysis has concerned
the drawing up of concentration maps applying
kriging (or co-kriging) for each contaminant in
those areas in which the probability of exceed-
ing the detection limit proves to be higher than
90%.
In Figg. 7-8 are reported, respectively, the
krigged maps in the mean, in the best and in the
worst scenario of potential contamination obtained
using confidence interval limits, for VC and cDCE.
The confidence interval maps, that represent the
variation range for the contamination values with
an error of 5%, show a spot area to the south for
both pollutants.
As far as TCE and PCE are concerned, the areas
in which the values are higher than the detection
limit prove to be wider than for VC and cDCE.
Moreover, from the visualization of the maps, a
high similarity between the spatial distributions of
the contaminants TCE and PCE can be detected.
The existence of a high correlation between TCE
and PCE, confirmed by their values being jointly
low in some zones and high in others (Figure 6)
has allowed to carry out a multivariate analysis
on the two variables.
The cokrigged maps of TCE and PCE look
coherent with the maps of the indicator variables,
showing similar spatial structures. In Figure 9 are
shown the TCE concentration maps, obtained
through co-kriging, in the mean, in the best and the
worst scenario of potential contamination, drawn
up by making use of 95% confidence interval
limits. The confidence maps show large differ-
ences between the maximum and the minimum
values, nevertheless, they identify a spot area of
higher values down south.
In Figure 10 are shown the same concentration
maps obtained for PCE, in the mean, in the best
and the worst scenario of potential contamination.
The last two maps show very different PCE values,
but they detect two common spot areas, one more
southern and the other one more northern, with
an error ≤ 5%. In this way it has been possible to
case Study II: Indicator cokriging
in Presence of censored data
This example is taken from a study of Castrignanò
et al (2007). In the case study, the examined vari-
ables are the concentrations of Vinyl Chloride
(VC), cis-1,2-Dichloroethylene (cDCE), Trichlo-
roethylene (TCE) and Tetrachloroethylene (PCE),
expressed in μg/l, detected in a wide industrial
district located in Apulia. These pollutants are
characterized by some values below the detection
limit of the instrument. Their elaboration has been
carried out by means of cokriging of the indicator
variables and for each single pollutant the map of
probability of exceeding the detection limit has
been drawn up. From the analysis of these maps
(Figure 6) it is possible to make some consider-
ations on the spatial variability of the data:
•
VC concentrates much of the values below
the detection limit (0.05 μg/l) in the north-
ern part;
cDCE shows a low number of values be-
•
low the detection limit (0.005 μg/l) con-
centrated in a more central area;
TCE and PCE show values below the de-
•
tection limit (0.02 and 0.05 μg/l, respec-
tively), mostly concentrated in a central
area.
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