USE OF RATIOS IN TRANSURANIC FIELD STUDIES
Ratios play a prominent role in environmental transuranic studies.
A major application is to ecosystem models where a ratio is used to
express the relationship between transuranic concentrations in
various ecosystem components.
Two examples are found in the Proceedings of the Workshop on Environmental Research for Transuranic
Elements (1976, pp. 23-24): the concentration ratio (CR), defined as
activity per weight of plant part
:
activity per weight of substrate or reference material
and the inventory ratio (IR), defined as
activity per unit area in product ,
activity per unit area in source
Other uses of ratios in environmental transuranic studies include
detecting whether differential movement between two elements, say
Pu and Am, is occurring in the soil profile, and as a means of
detecting local contamination by some transuranic element by noting
a change in its ratio to another element (or isotope) from their
background level ratio.
This paper deals mainly with the use of average ratios.
It is important to realize, however, that there are situations where an average
ratio is not appropriate, e.g. when there is a systematic change in
the ratio over space or time.
An illustration of this is the detection of local contamination mentioned above.
Suppose we have the
situation in Figure 1: a ??9Pu source and sampling sites located
downwind from it.
Rather than calculate an average ratio of 239Pu
to 238py over all sites, it would seem more appropriate to know how
the ratios change with increasing distance from ground zero.
Ratio data have been presented in a variety of ways in the environmental transuranic literature.
A simple List of ratios or average
ratios from different sites is sometimes given.
This is appropriate
when the data come from different study sites and there is no
justification for pooling the data or for performing any further
statistical treatment.
Ratios have also been presented in histogram
form.
This was done, for example, by Emery et al. (1976), to compare
the distribution of ratios in various ecosystem components in their
study of U-pond at Hanford. One can also plot the numerator versus
the denominator or the logarithms of the numerator versus logarithms
of the denominator and view the estimation of a ratio as a regression
602
239 Py
CONTAMINATION
SOURCE
Figure 1.
AREA
Change in Ratio 23%Pu/235Pu over Space
through the origin. Alternatively, ratio data are often presented as
an average ratio, sometimes with an estimated standard error, but
often without any indication as to how the average or its standard
error were calculated.
There are certain problems associated with estimating an average ratio.
The statistical properties of ratios have not been fully developed and
the properties of average ratios that are known do not appear to be
widely understood.
It is known, e.g. that the estimated average ratio
is often statistically biased and in most cases the variance of the
estimate is only an approximation (Cochran, 1963, p. 160~163).
The
problem is further compounded by the many ways an average ratio can
be estimated.
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