Otherwise, in this study, disjunctive kriging was applied (Liu et al.,
2006). The disjunctive kriging is the principal technical tool to estimate
the probability that the true values at the target points exceed some
threshold. It is based on the assumption that the data are a realization
of a process with a second order stationary bivariate distribution. The
assumption of second order stationary means that the covariance function
exists and that the variogram is therefore bounded. It is assumed
that the concentration of a heavy metal is a realization of a randomvariable
Z(x), where x denotes the spatial coordinates in two dimensions. If
a threshold concentration Z
is defined, marking the limit of what is acceptable,
then the scale is dissected into two classes which is less and
more than Z
c
c
, respectively. The value 0 and 1 can be assigned to two
classes. A new binary variable, or indicator, is denoted by Ω[Z(x) ≥ Z
].
At the sampling points the values of Z are known, and so the values 0
and 1 can be assigned with certainty. Elsewhere, one can at best estimate
Ω[Z(x) ≥ Z
]. In fact, it is necessary to do this in such a way that
the estimate at any place x
c
approximates the conditional probability,
given the data, that Z(x) equals or exceeds Z
0
(Liu et al., 2006; Zhao et
al., 2015).
c
c