Statistical Sampling Strategies for Survey of Soil Contamination - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 200

with high concentrations of natural geochemical elements. The threshold concen-
tration may be a constant value that does not vary in space, or a spatially varying
concentration. An example of the latter is a soil standard defined in terms of
soil organic-matter content, clay percentage and pH, thus taking into account the
bio-availability of the contaminant.
In detecting hot spots, the aim of the survey is to find out whether at any point
in the study area the critical threshold concentration is exceeded. Finding the exact
location is not part of the aim (Section 4.5.1 ). Once we know that there are locations
where the threshold concentration is exceeded, in general the reconnaissance survey
is followed by a survey with the aim of delineating hot spots, i.e., making a map
depicting where the threshold is exceeded, see Section 4.5.2 .
A different aim, related to detection of hot spots, is the estimation of the frac-
tion of the area with values exceeding the threshold concentration. For this aim
the design-based adaptive cluster sampling strategy can be a good choice (Section
4.2.1.4 ). An unbiased estimate of the sampling variance of the estimated areal
fraction can then be obtained from the sample.

4.5.1 Detecting Hot Spots

The detection of hot spots can be achieved better with purposive sampling than with
probability sampling. If one has no prior information on the location of the hot spots,
samples are typically taken on a purposively selected, regular grid. Gilbert ( 1987 )
worked out a method for calculating the required grid spacing from the consumer's
risk,

, i.e., the probability of not hitting a hot spot if it exists , and the geometry
(size and shape) of the hot spot. This method is implemented in the Visual Sample
Plan software (Matzke et al. 2007 ). The probability of hitting a hot spot if it exists is
calculated by summing the zones of coverage for the sampling locations, excluding
overlaps. The zone of coverage for any sampling location can be obtained by draw-
ing the contour of a hot spot with its centre at the sampling location. If the centre of
the hot spot is in the zone of coverage, it will be detected from the sampling loca-
tion. In practice, either an elliptical or a circular shape is assumed, and a decision
is being made on the minimum size (length of semi-major axis) of any hot spot that
we want to detect with a specified probability (Matzke et al. 2007 ).
So far, it has been assumed that a hot spot exists. In other words, it is assumed that
the probability that a hot spot exists is 1. If the existence of a hot spot is uncertain,
the probability that a hot spot exists and is detected can be estimated by

β

P ( A , B ) = P ( B | A ) P ( A ), (4.41)

where P ( B A ) is the probability that the hot spot is hit, conditional on its existence,

and P ( A ) is the probability that the hot spot exists. Given the grid spacing and geom-
etry of the hot spot one can calculate P ( B

|

| A ) and simply multiply this by the a priori