Statistical Sampling Strategies for Survey of Soil Contamination - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 167

less detail compared to Section 4.4 : a map depicting the mean values for several
blocks suffices. A typical example is estimating the means for spatial remediation
units to be used for decisions on remediation of the soil in these spatial units.
This difference in spatial resolution of the survey result determines the most
appropriate statistical approach for sampling. For estimating (parameters of) the
spatial cumulative distribution function (SCDF), generally a design-based approach
is most appropriate. This implies that sampling locations are selected by probability
sampling (random sampling), and that in estimating (parameters of) the SCDF the
selection probabilities of the sampling locations are taken into account.
For mapping purposes, a model-based approach is the best and only option. This
implies that sampling locations need not be selected randomly, but typically are
selected by purposive (targeted) sampling. In estimation (spatial interpolation) a
probabilistic model of spatial variation is used.
For estimating the mean of several delineated blocks, both statistical approaches
are possible. The most appropriate approach depends amongst others on the number
of blocks and the affordable number of sampling locations. To estimate the means
for a few blocks only, a design-based approach in which several sampling locations
are randomly selected from each block may be advantageous. However, if there are
many blocks, for instance more blocks than the total number of sampling locations,
then a model-based approach is suggested. For more details on the choice between
a design-based or a model-based sampling approach, I refer to Brus and de Gruijter
( 1997 ).
The choice between a design-based or a model-based sampling approach is only
one, be it a very important decision in designing a sampling scheme. Other choices
are the size and geometry (support) of the sampling units, the measurement (obser-
vation) method, the sampling design type (in the design-based approach), the spatial
interpolation method (in the model-based approach), the number of sampling loca-
tions, whether or not to take composite samples et cetera . All these choices should
be based on a thorough analysis of the aims and constraints (requirements) and on
the available prior information. This is not an easy task. The development of statis-
tically defensible environmental sampling designs that provide the right quality and
quantity of data for making decisions requires a systematic planning process. This
was the main motivation of the US-EPA to design a framework for this (EPA 2006 ).
A similar approach for survey and monitoring of natural resources is described by
de Gruijter et al. ( 2006 , Part I). These frameworks can be of great help in the design
process, and may prevent us from taking wrong or suboptimal decisions.
This chapter is largely based on de Gruijter et al. ( 2006 ).
4.2 Estimating (Parameters of) the Spatial Cumulative
Distribution Function
This section is about how to sample if we want to estimate the spatial cumulative
distribution function (SCDF) of the concentrations of one or several contaminants
in the soil of an area, or parameters of this distribution function, such as the