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neither sufficiently known nor applied either in
scientific or in operative contexts (Castrignanò
et al., 2002). Even this approach may be defined
probabilistic, as it recognizes explicitly the
uncertainty associated to the estimation of any
environmental variable and permits to evaluate
this uncertainty from the analysis of a series of
stochastic simulations carried out on the area.
Each of these simulations provides a map of the
pollutant concentration in the study area and is
consistent with the set of data and their structures
of spatial continuity: each map consequently can
be considered as an equally probable description
of the unknown reality.
é
ë ê
()
ù
û ú
VarDu
uissampled if CV u
()
=
is l
arg
e
é ë ê
ù û ú
EDu
()
(24)
This type of coefficient of variation CV is large
if the denominator is small, that is if the simulated
pollutant concentrations and threshold values are
close and so the uncertainty about the exceedence
of that threshold becomes large. For the same
average difference, the CV will be larger if the
variance of the distribution of differences is large
(Van Meirvenne & Goovaerts, 2001).
StochAStIc SIMulAtIonS
cASe StudIeS
The explained geostatistical approach bases itself
on the estimation of the kriging variances that are
independent from the calculated values, depend-
ing uniquely on the geometric disposition of the
samples and the adopted variogram model. In most
studies on polluted areas, the observed variances
show a proportional effect on the measured values,
therefore their utilization in the calculation of
confidence intervals can result somewhat fishy
(Castrignanò et al., 2002). A development on geo-
statistics that represents an alternative technique
of spatial modeling, is the stochastic simulation,
particularly adapt in those applications in which
more importance is attached to global statistics
rather than to local accuracy. In fact the simula-
tion attempts at reproducing the basic statistical
characteristics of the data, such as the histogram
and the spatial continuity, calculating a series of
alternative stochastic images (equiprobable) of the
random process (simulations) and thus carrying
out a statistical analysis on them for the evaluation
of the uncertainty.
These techniques were developed on purpose
in order to give an answer to the inadequacy of
the measures of spatial uncertainty according to
the traditional statistic methods, unluckily are still
case Study I: combination
of Indicator kriging and
land use Information
This example is taken from a study of Castrignanò
et al. (2004). An application of the indicator vari-
able approach is made to a pollution case study,
regarding a derelict manufacturing factory located
in Apulia Region (South- East of Italy).
Arsenic and Land use Indicator Coding
The following information available over the
study area has been combined:
z(u
α ) = Values of arsenic concentration in
groundwater (expressed in μg/l) at n loca-
tion u α , α=1,2,…,n;
l(u
α ) = Land use information, at all loca-
tions within the area.
The z-values represent hard information in the
sense that they are direct measurements of arsenic
content. On the contrary, land use information
provides only indirect (soft) information about
the values of the variable Z. Using both hard and
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