height variograms, respectively.

These variograms, computed using

Equation 17, follow the same pattern as the soil variogram (Figure 10)

with a peak at about 140 ft.

They are biased estimates of the true

underlying variograms due to the presence of "drift."

The two FIDLER

variograms diverge as the trend in concentrations becomes strong, with

the 1-ft readings showing more variability.
Since the spacing of the clusters for Line 1 was 20 ft, there is no
information on the relationship between concentrations 20 in. to 20 ft
apart.
The 100 adjacent FIDLER readings taken 10 ft south of the lines
cover 500 in. or 42 ft.
This corresponds to the distance covered by the
first two clusters from the original sampling plan.
These readings are
given in Figure 13, where each point plotted is the mean of two readings.
The lower line connects the surface height readings and the upper line
the 1-ft height readings.
The two lines tend to follow each other, with
1-ft readings being almost always higher and smoother because the instrument is integrating over a larger soil surface.
The estimated variograms for the two sets of FIDLER readings along
Line 1 are given in Figure 14.
Consistent with the observed FIDLER

readings, the 1-ft height variogram is lower and smoother than that of
the surface readings.

The 1-ft height variogram increases until the

distance between readings is about 350 in. or 29 ft and then decreases.

The number of data pairs for estimating the variogram at distances
greater than 29 ft are relatively few, so these points have relatively
poor precision.
These data suggest there is a correlation structure
among FIDLER readings at short distances.

The experimental variograms in Figure 14 were also computed using Equation 17.
These variograms are probably not badly biased since the
FIDLER data plotted in Figure 13 do not show evidence of strong systematic

"drift" over the 42-ft distance. Notice that the "nugget effect" is
greater for the surface than the 1~ft height, a reflection of the
smaller variability between adjacent readings at the l1-ft height.

Results for Line 2
The soil concentration data for Line 2 are given in Figure 15.

Note

that these concentrations are in the pCi/g range, as opposed to the

nCi/g range for Line 1.
In comparison to Line 1 Am data, the variability
between clusters along Line 2 accounts for a much smaller proportion of
the total variance; 55 rather than 82%.
The variability between adjacent
samples and that between aliquots within samples account for 25 and 21%,
respectively, of the total variability along Line 2.
This contrasts
with 15 and 3% for Line 1.
Along Line 2, there is almost as much
variability between aliquots as there is between adjacent samples.
We
note that this type of information can be used to estimate the optimum
allocation of sampling effort for estimating average concentrations,
i.e., for determining the optimum number of clusters, samples within
clusters, and aliquots per sample for estimating the mean concentration

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