Statistical Sampling Strategies for Survey of Soil Contamination - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 172

Geographical Stratification

If we have no prior information on the spatial distribution of the soil contaminant
that can be used for stratification, then we may use geographical strata to spread
the sampling locations as uniformly as possible over the study area. Spreading the
sampling locations over the area generally enhances the precision of the estimated
parameters. The best spatial coverage will be obtained when the geographical strata
have maximum compactness. A simple, straightforward method for computing such
compact geographical strata is k-means clustering of small grid cells, using the x-
and y-coordinates of their centres as classification variables, see Brus et al. ( 1999 )
for more details. Compact geographical strata can be designed by the R-package
spcosa (Walvoort et al. 2009 , 2010 ).
Figure 4.2 shows an area of 836 ha with peat soils near Mijdrecht, south of
Amsterdam in the Netherlands, planned for development of nature. Since the recla-
mation of the peat areas in the Middle Ages, a mixture of garbage from the nearby
cities, farmyard manure, dune-sand and dredged sediments, has been dumped on the
weak peat soils. As a result, the topsoils are contaminated with Pb, Cu and Zn. The
study area was divided into 15 compact geographical strata of equal surface area. In
each stratum, two sampling locations were selected by simple random sampling.

4.2.1.3 Random Grid Sampling

A simple way of drawing random samples with good spatial coverage, i.e. samples
whose locations are spread uniformly over the study area, is random grid sampling
(SY). Possible shapes for the grid cells are square, triangular, and hexagonal. The
triangular shape was shown to be most efficient in general. Besides the shape of
the grid cells, we must decide on their size (grid spacing) and on the orientation
of the grid. The grid spacing determines the number of sampling locations in the
study area. So, if we have decided on the required (allowed) number of sampling
locations, then we may use this number to calculate the grid spacing. For square

grids, the grid spacing (m) can be calculated with √ A

n , where A istheareainm 2 ,
and n is the number of sampling locations. The grid is randomly placed over the
study area as follows. One location is selected by simple random sampling from
the study area. Given the chosen orientation of the grid, the grid is extended in
all directions using the selected location as a starting node. Finally, all nodes are
selected that fall within the study area. There is no need for random selection of the
orientation of the grid, random selection of the first node suffices for design-based
statistical inference (estimation).
In general, the spatial coverage of an area by a random grid is better than by
a geographically stratified random sample, even with one location per stratum.
Consequently, in general, random grid sampling will give more precise estimates
of the (parameters of) the SCDF. There are two disadvantages of random grid sam-
pling compared to geographically stratified random samples. First, estimation of
the sampling variance is cumbersome. This is because we do not have independent
replicates of the sample: the grid can be considered as one 'cluster' of sampling
locations, see Section 4.2.2.1 Second, in general the number of sampling locations

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