Environmental Engineering Reference
In-Depth Information
Double Sampling
In double sampling, also referred to as two-phase sampling or collaborative sam-
pling, two methods for measuring the contaminant concentrations are combined,
i.e., a cheap and relatively imprecise method, and an expensive, relatively precise
method. In many cases the cheap measurements are collected in the field, whereas
the expensive ones are obtained by laboratory analysis. In double sampling, a large
probability sample is selected where the contaminant concentration is measured
with the cheap method. From this large “first-phase” sample a random subsample is
selected where the contaminant concentration is also measured with the expensive
method. If the concentrations measured with both methods are strongly correlated,
then the efficiency of the sampling method can be increased. The optimal ratio of
the two numbers of sampling locations is
c z
c y
2
m
n =
1
ρ
,
(4.1)
2
ρ
with m and n the numbers of sampling locations with expensive and cheap mea-
surements, respectively, and c y and c z the measurement costs per location for the
expensive and cheap method, respectively. Chang and Yeh ( 2007 ) illustrate this
sampling method for estimating mean heavy metal concentrations, using relatively
cheap, field portable x-ray fluorescence measurements besides standard laboratory
measurements. Double sampling is cost-effective compared to measuring with the
precise method only if (Cochran 1977 , p. 341)
1
2 2
1
+
ρ
c y
c z >
.
(4.2)
ρ
2
Cheap measurements of the contaminant concentration can also be replaced by
measurements on a continuous covariate correlated with the contaminant concen-
tration, such as hand estimates of the clay percentage or the organic matter content.
This covariate can also be a categorical variable, for instance classes of contamina-
tion level (e.g. not contaminated, moderately contaminated, strongly contaminated)
based on organoleptic observations.
The mean concentration can be estimated by the regression estimator (continuous
covariate) or post-stratification estimator (categorical covariate), see Section 4.2.3
In this case, the known spatial mean for the covariate in Eq. ( 4.24 ) must be replaced
by the mean estimated from the large “first-phase” sample, and the relative area in
Eq. 4.22 by the ratio of the number of sampling locations in a given category and
the total number of locations of the “first-phase” sample, n .
Adaptive Cluster Sampling
Adaptive cluster sampling is a type of sequential sampling where additional
sampling locations are selected in the neighbourhood of sampling locations that
 
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