Statistical Sampling Strategies for Survey of Soil Contamination - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 191

that in estimation (spatial interpolation) a probabilistic model of spatial variation is
used. Section 4.4.1 describes various sampling patterns that can be used for spa-
tial interpolation. The next Section 4.4.2 shortly describes how, once the data at the
sampling locations are collected, a map of the contaminant concentration can be
obtained. The final Section 4.4.3 is about how to determine the required number of
sampling locations.
4.4.1 Sampling Patterns
As sampling locations are not selected randomly, we may search for the pattern of
sampling locations, i.e. the x - and y -coordinates, that gives the most precise map.
Hereafter I will first describe regular sampling patterns (grids). Next, the constraint
of sampling on a grid will be relaxed, generally resulting in irregular patterns. These
patterns can be optimized with a criterion defined in terms of distances (between
sampling points and the nodes of a fine interpolation grid) leading to spatial cover-
age and spatial infill samples, or in terms of the estimation error variance, leading
to geostatistical samples.
4.4.1.1 Purposive Grid Sampling
Sampling on a regular grid is attractive because of its simplicity. The sampling
locations can be positioned in the field easily, especially the nodes of square grids.
Contrary to grid sampling in a design-based approach, in a model-based approach
the grid need not be placed randomly on the study area. The grid typically is located
such that the grid nodes optimally cover the study area. Commonly used grid pat-
terns are square, triangular and hexagonal. Which pattern is optimal depends on
the variogram, amongst others. If the contaminant shows moderate to strong spatial
autocorrelation, the triangular pattern gives the best result.
Grid sampling is suboptimal when the shape of study area is irregular and when
the study area contains enclosures that are inaccessible for sampling, think, for
instance, of built-up areas. Shifting the nodes to nearby locations, results in an irreg-
ular pattern. Sampling on a grid may also be suboptimal if we want to add new
sampling locations to existing ones. The new sampling locations should fill in the
empty spaces in between the existing sampling locations.
4.4.1.2 Spatial Coverage and Spatial Infill Sampling
Relaxing the constraint of sampling on a grid, leads to spatial coverage samples, or
in case of an additional sample, to spatial infill samples. For such samples, a pattern
is calculated that covers the area or fills in the space as uniformly as possible. This
is achieved by minimizing a quality measure that is defined in terms of the distances
between the nodes of a fine interpolation-grid and the sampling locations. Many
distance measures can be selected, see Royle and Nychka ( 1998 ). Brus et al. ( 2007 )