Geoscience Reference
In-Depth Information
10.4 Spatial Designs
The main part of the remainder of this chapter consists of two sections. The
research designs section relates four common designs that are generally more
appropriate for research studies than monitoring studies, although the designs
in this section can be applied to monitoring studies under certain circumstances
(e.g., when there are only a few monitored variables). These designs, listed in
Table 10.2, consist of simple random sampling, two-stage sampling, stratified
sampling, and cluster sampling. The monitoring designs section describes
three designs that are generally more appropriate for monitoring studies. These
designs are the two-dimensional systematic sample, the one-dimensional gen-
eral random sample (GRS), and
d
-dimensional balanced acceptance sample
(BAS). An important characteristic of these designs is that they ensure a high
degree of spatial coverage. R code to draw the more complex samples (i.e., GRS
and BAS) is available on the topic's web site (https://sites.google.com/a/west-
inc.com/introduction-to-ecological-sampling-supplementary-materials/).
10.4.1 Research Designs
This section contains brief descriptions of four common spatial sampling
designs that are generally appropriate for research studies. As noted, a long-
term study's interest may lie in a single variable, and in this case, the designs
of this section could be applied in a monitoring setting. Also, certain of the
sampling plans (i.e., simple random, systematic, and GRS) can be applied at
different stages of a larger design. For example, it is possible to draw a sys-
tematic sample of large collections of sampling units at one level, followed
by a simple random sample of units from within the large collections. There
is more about these inite-population designs in Chapter 2 of this topic, and
they are covered extensively in the topics by Cochran (1977), Scheaffer et al
.
(1979), Särndal et al
.
(1992), Lohr (2010), and Müller (2007).
Except for simple random sampling, a significant amount of a priori infor-
mation is required about the target variables and the study area before a sam-
ple can be drawn. For instance, to implement a stratified design, regions of
the study area must be classified into categories. This categorization requires
knowing or estimating an auxiliary variable on which strata are defined. If a
maximum entropy design is to be implemented, some information about the
magnitude and structure of spatial covariance must be known. If a cluster
design is to be implemented, the size and configuration of clusters must be
known throughout the study area.
10.4.1.1 Simple Random Sampling
Simple random samples of a geographic study area are drawn by first bound-
ing the study area with a rectangular box to delineate the horizontal
x
and
