spatial pattern as contrasted with estimating a total were discussed by Eberhardt

and Gilbert (1976) at the lst ERDA Statistical Symposium held at Los Alamos,
November 2-5, 1975. The topic was presented as a "problem" for discussion,
and many valuable suggestions were offered by the statisticians in attendance,
particularly Dr. John W. Tukey of Princeton University and Bell Laboratories.
We hope to continue working on this design problem in conjunction with continuing
experimentation with computer contouring algorithms.

In preparation for the IAEA/ERDA and the ERDA symposia, we estimated 239Pu

concentration contours in surface soil of the GMX site using algorithms QUAD
Since most of these could not be published
and TREND available on SURFACE II.
in the Proceedings of the IAEA/ERDA symposium due to space limitations, we
All of the contours shown here are
include them here as Figures 9 through 14.

in units of nCi (of 2739Pu) per gram (dry) of surface soil. Figure 8 shows
questionable contours west of GZ obtained using NEAR as mentioned above.

Figure 9 was obtained using NEAR on the logarithms of the data.

As mentioned

above, the use of logarithms eliminated some of the doubtful contours obtained
on the untransformed data (Figure 8).

More samples must be collected just

west of GZ, however, to obtain accurate contours for that region.
The algorithm
QUAD, which searches for a minimum number of data points in each quadrate
within a specified distance! 3 of the point to be estimated, was also applied
to the logarithms of the data (Figure 10).
Note that contours are not estimated

west of ground zero. This occurred because of too few data points in this
area. Hence, QUAD can indicate when insufficient data are a problem. Figures 11
and 12 show contours resulting from fitting 4th and 6th degree polynomials to
the logarithms of these GMX soil data using the algorithm TREND.
These contours
show considerably less detail than those obtained above using NEAR or QUAD.
The 6th degree fit to the data is somewhat better than that provided by the
4th degree equation.
However, the black line along the left margin of the 6th

degree fit (Figure 12) indicates severe edge effects.

That is, the regression

equation is giving grossly inaccurate estimates in this area where no data

were collected.

Figure 13 shows contours obtained by using TREND to fit a 6th

degree polynomial to the untransformed data.

Note that the area included

within the 0.5 nCi/g contour is much larger for the original scale (Figure 13)

than for the log-transformed scale (Figure 12).
Serious edge effects are also
present in Figure 13.
These are plotted in Figure 14 to illustrate the wild
Pu estimates obtainable using polynomial fits in regions of the study site
where few data have been collected.
Of the contour methods applied thus far to the soil Pu data collected via
simple random sampling within strata, it appears that QUAD or NEAR applied to

the logarithms of the data are the most promising (see Gilbert et al., 1976,

Table IIT for a statistical evaluation).

Improved estimates appear to result

if an iterative fitting procedure is applied to the residuals of previous
(log) fits.

This iterative approach was suggested by Tukey (see discussion

after paper by Eberhardt and Gilbert (1976)) and has been investigated in part

by Gilbert (1976) using NEAR on SURFACE II.

13For Figure 8, we specified (a) maximum distance to nearest data point must

be < 100 feet, (b) maximum search radius = 200 feet.

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