Environmental Engineering Reference
In-Depth Information
4.5.2 Delineating Hot Spots
When no prior measurements on the target variable are available, and the locations
of the hot spots are unknown, the best option is purposive grid sampling, or alter-
natively according to some spatial coverage or geostatistical sample (Section
4.3.2
).
There are two ways to increase the efficiency of these samples in order to delineate
hot spots: sampling in two or more phases (Section
4.5.2.1
) and composite sampling
(Section
4.5.2.2
).
4.5.2.1 Phased Sampling
The efficiency of sampling can be increased by sampling in two, or even more
phases (batches). For instance, the first phase could involve sampling the area on
a purposively selected square grid. The sample data are then used to design an
additional sample of
n
locations, by estimating the concentration at the nodes of
a fine interpolation grid and the kriging variance of these interpolations. Englund
and Heravi (
1994
) proposed to select additional locations by assuming a triangular
probability distribution on the interval [
Y
3
V
K
(
Y
)] . This probability
distribution is used to calculate for each grid node the probability of decision errors
and the expected loss. The node with the highest expected loss is selected as the first
additional sampling location. This procedure is repeated (the kriging variances must
be updated in each iteration) until the predetermined number of additional sampling
locations has been selected.
If the costs of sampling and measurement per sampling location are substantial
compared to the costs of decision errors, then the optimal number of sampling loca-
tions can be calculated by including this cost component in the loss function. To
profit from phased sampling, the number of sampling locations in the first phase
must be approximately 75% of the total number of sampling locations (Englund
and Heravi
1994
).
3
V
K
(
Y
),
Y
−
+
4.5.2.2 Composite Sampling
Composite sampling is recommended when the laboratory measurement costs are
high. Figure
4.15
shows an example where the four aliquots at the corners of square
cells are combined to form a composite sample. Analysing the composite sample
instead of the individual aliquots reduces the measurement costs, so that more loca-
tions can be sampled for the same budget. Due to the larger number of sampling
locations, the sample has a better spatial coverage, so that the probability of hit-
ting a hot spot is higher. The problem is that mixing the aliquots implies a loss
of information on the concentration in the individual aliquots. The concentration
of an individual aliquot may exceed the threshold concentration, while that of the
composite sample does not.
Several methods have been developed to identify the individual aliquots (further
briefly referred to as “individuals”) with the highest values or with values above
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