Environmental Engineering Reference
In-Depth Information
contaminant concentration. Contrary to the previous section, an estimate of the
mean for the study area as a whole (global mean) or of its SCDF, is not sufficient
for this purpose. For remediation purposes we need to know where the concen-
trations exceed threshold concentrations. As remediation measures are generally
applied on blocks with dimensions in the horizontal plane of tens to hundreds of
m
2
, the required spatial resolution of the map can be adapted to these dimensions,
and estimation at point locations (see Section
4.4
) is not needed.
To estimate the mean concentrations for the delineated blocks, either a design-
based or a model-based approach can be applied. The best sampling strategy
depends, amongst others, on the number of blocks and the affordable number of
sampling locations or, in case composite samples are taken, the affordable num-
ber of composite samples. If we can afford several sampling locations (composite
samples) in each block, say more than five, then a design-based approach can be a
good option, because the quality of the design-based estimates of the block-means
and their sampling variances are independent of model-assumptions on the spatial
variation. However, if the spatial variation within the blocks is considerable, then
the precision of the estimated block-means can be rather low. If a higher precision
is required, then a model-based approach can be considered. It requires quite a few
sampling locations, say more than 100-150, in order to obtain a reliable model of the
spatial variation (variogram) (Webster and Oliver
1992
). Using this model in block
kriging might give more precise estimates of the spatial means of the blocks. A
design-based alternative for situations where the number of sampling locations per
block is rather small, is the synthetic or regression estimator, see Section
4.3.1.1.
For more details on the choice between a design-based or model-based sampling
strategy, I refer to Brus and de Gruijter (
1997
).
4.3.1 Design-Based Approach
If a design-based approach is chosen, in each block several locations are selected by
probability sampling. If a map is available with units that are related to the contami-
nant concentrations, i.e. the mean concentration differs between the map units, then
we can increase the precision by using the map units as strata in random sampling,
see Section
4.2.1.2.
Otherwise, random grid sampling within the blocks (Section
4.2.1.3
), or stratified random sampling with compact geographical strata within the
blocks (Section
4.2.1.2
) is a good alternative.
To estimate the mean of a given block, only the data that originate from that block
are used. I refer to Section
4.2.2.1
for the estimators of the mean and their sampling
variance.
To save laboratory costs, the soil aliquots collected at the sampling locations
within a given block can be bulked, see Section
4.2.4
. If in decision-making we
want to account for uncertainty in the estimated block-means, at least two composite
samples must be collected from each block, and separately analyzed.
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