Environmental Sampling Design - Fundamentals of Environmental Sampling and Analysis - page 59

collect samples around midnight time for (c), but it will better represent the data than (b) if
SO 2 discharge peaks at a certain time of the day. Option (d) would generate better precision if
SO 2 discharge present a clear difference between day and evening. As the project goal is to
estimate the weekly average mean concentration, this appears to be too costly. Overall, option
(c) may least likely to give the unbiased estimate.

EXAMPLE 3.2. Simple random sampling from two waste tanks. A manufacturing
plant had been generating a liquid waste over a period of years and storing it in a large
open-top tank. As this tank approached its capacity, some of the waste was allowed to
overflow to a nearby small tank (Fig. 3.6). Prior to sampling the following information is
available:

(a) The large tank had a diameter of 50 ft, a height of 20 ft, and an approximate volume
of 295,000 gal. It was encircled and traversed by catwalks to allow access to the
entire waste surface. Contaminant concentration appears to be heterogeneous due to
the long time of operation, but it was determined that vertical composite samples
(not the vertical strata) are sufficient.
(b) The small tank had a diameter of 10 ft, a height of 10 ft, and an approximate volume
of 6000 gal. There is only a small inspection port on the top allowing a limited
access. A decision was made to use two tank trucks and to sample the waste
randomly over time as it drains from the tank into the tank trucks. It was estimated
that it would take 300 min to drain the tank at a rate of 20 gal/min.

If financial constrains allow for a total of 15 samples to be collected from each tank, design a
sampling strategy using simple random sampling approach.

Inspection
port

6000 Gallon
overflow tank

295,000 Gallon
storage tank

Catwalks

Figure 3.6 A bird's eye view of a waste tank and an overflow tank (U.S. EPA, 1986)

SOLUTION: This example was excerpted and slightly modified from a guideline by the U.S.
EPA. Here a simple random sampling over a two-dimensional space is used for the large waste
tank because the operators are interested in the average composition and variability of the
waste, and not interested in determining if different vertical strata existed. For the small
overflow tank, a random sampling over time was used since sampling over space is impossible
due to the limited access from the only inspection port on the top. We are also given that the
total number of samples is 15 for each tank, so the question remains is fairly easy, that is, how
to generate the random numbers to represent those locations in space (large tank) and time
points (small tank).
There are many ways to acquire random numbers. For instance, we can just simply use the
page number of a topic to obtain them while we are in the field. One can also use a random