A Geostatistically Based Probabilistic Risk Assessment Approach - Evolving Application Domains of Data Warehousing and Mining - page 297

Figure 12. a) experimental and theoretic variogram b) map of the estimated values for arsenic (in µg/l)
with isoline of threshold value 10µg/l

elaboration. The original variable has been pre-
emptively normalized and standardized at mean
zero and unitary variance by means of Gaussian
anamorphosis. The analysis of the variogram map
of arsenic didn't reveal particular anisotropies,
therefore the process has been assumed as isotro-
pic. The experimental variogram of the normalized
standard variable has been calculated and a theo-
retic model has been adapted to it, characterized
by nugget effect and a spherical structure with
range = 422.09 m (Figure 12a).
The compatibility between the amount of
data and the structural model has been verified
by means of a cross-validation test. The map of
arsenic concentration has been obtained after
back transforming the values of the standard
Gaussian variable interpolated by means of Or-
dinary Kriging and is reported in Figure 12b. In
the same figure the black line evidences the area
of the Source of Contamination included in the
isochon 10 µg/l.
The Source Representative Concentration for
this area can be obtained by means of the UCL
method: considering the values of the variable
estimated by means of polygonal kriging inside

the study area, tests with ProUCL software are
carried out in order to determine the correspond-
ing value of UCL. Considering the source area in
Figure 12b, and carrying out tests (with ProUCL
software) on the data estimated by means of
polygonal kriging inside the area, the obtained
Source Representative Concentration value is
equal to UCL = 40.58 µg/l.

Approach 3: Geostatistical
Approach: Indicator Kriging

The application of Indicator Kriging has implied
the codification of the variable arsenic into a
binary indicator variable, that assumes either
the value 1 or 0 according as it exceeds or not
the CSC of 10µg/l. After the codification the
variogram of the indicator variable has been
constructed and it has been modelled by means
of a set of authorized theoretic functions (Figure
13a).A theoretic variogram has been determined,
made up of three structures: 1) nugget effect; 2)
spherical model with range=209.17m; 3) spheri-
cal model with range=567.13m. The application
of Indicator Kriging has permitted to represent the