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prove soil and groundwater sampling campaigns,
in terms of lower costs both for sampling and for
laboratory analyses. Moreover the application
of geostatistical techniques makes it possible to
design a sampling scheme making reference to
optimization criteria in function of the pursued
aim. The geostatistical criterion can allow to
insert new points where the knowledge is more
approximate and to eliminate others where the
information is redundant.
Uncertainty assessment is a preliminary step in
decision-making processes, such as delineation of
hazardous areas. In the process of characterization
and remediation, multistage sampling involves an
interruption of the sampling process until the data
are available for estimating contaminant concen-
trations at unsampled locations, which will guide
the selection of locations where additional data are
needed (Castrignanò, 2008). This can improve the
cost-effectiveness of a sampling campaign.
(u) of the domain, a “gain in precision” P can
be defined as the ratio:
=
()
-
()
é
ë
ê
ù
û
ú
2
2
s
u
s
u
1
2
P
()
2
s
u
(22)
1
where σ
1
²(u) represents the Kriging variance in
the point (u) calculated on the basis of a number
of measurements and σ
2
²(u) the one after adding
the fictitious point.
It is then possible to trace curves of isoprofit
of precision to define, in correspondence of the
maximum values, the preferential localization
of the new measurement points.
The procedure of eliminating the redundant
measurement points has been applied in Tuscany
(Beretta et al., 1995) by means of an inverse
procedure to the one proposed by Delhomme
(1978). This method consists in removing points
from the network estimating the value of the vari-
able in the single eliminated points on the basis
of the values of the variable assumed in nearby
points; consequently the isoloss of information
is evaluated by means of the relation:
Optimal Sampling Design
for Characterization
In the field of optimizing the efficiency of sam-
pling, the pursued aim is that of minimizing the
estimation error; a typical optimal sampling
problem consists in searching for a set of samples
which satisfies the criterion of optimization
based on the minimization of the estimation
variance (Castrignanò, 2008). The expression
of the Kriging variance depends uniquely on
the semivariogram of the variable, and not on its
punctual values. Therefore if the semivariogram
has been identified, the kriging variances can be
determined independently from the knowledge
of the values that the variable assumes in corre-
spondence of different points. This is an important
property on which the “fictitious-point method”
(Delhomme, 1978) is based. This method consists
in adding a fictitious point, with a value of the
variable arbitrarily fixed, calculating the Krig-
ing variance and comparing it with the previous
one. Once added a fictitious point in a position
I
=-
Z Z
i
*
(23)
i
where Z*
i
represents the value of the estimated
variable after suppressing the value Zi.
i
. One fixed
the maximum number of measurable points, on
the basis of technical-economical evaluations,
this procedure is applied by means of a “trial
and error” method up to the achievement of a
configuration that gives the minimum loss of
information.
Sampling design has to be considered there-
fore as a multi-stage procedure. This means that
in order to optimize sampling the variogram has
to be known, but the variogram itself must be
obtained by sampling. It is necessary therefore
to split the sampling resources between those
required for establishing the variogram and those
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