larger after iterating.

This behavior results, most likely,

from the

difficulty of fitting a surface to the very large concentration observed

near GZ without distorting grid estimates in nearby areas.

Residuals in antilog form at sample collection points are usually smaller
on the average than those from fits in the wuntransformed scale.
Also,
distortions in the antilog concentration surface due to the extreme data
point near GZ appear to be minor.
However, the correlation between
observed data and residuals tends to be somewhat larger for the log and
antilog fits than for untransformed data fits.
Moreover, fitting in log
scale does not, of course, eliminate fitting problems due to a lack of
data in certain regions of the study site.
Recall, for example, the
apparently spurious contours south of GZ for both the untransformed and
antilog fits due to insufficient number and placement of samples in that

area (Figures 6-9).

The plotting of observed data and residuals on estimated contour maps
has proved useful in subjectively evaluating the estimated surface at
other than data points.
Efforts should be made, however, to try kriging
techniques to estimate these concentration surfaces,* since this approach
yields an estimation variance for each grid node estimate.
Furthermore,
if the underlying assumptions of kriging are satisfied, this method
yields best linear unbiased estimates of concentration at grid nodes.

ACKNOWLEDGMENTS

I wish to thank Ms. Barbara Vinson of Battelle-Northwest for her excellent
assistance in writing computer programs and performing so well a variety
of other computing tasks associated with this paper.
Special recognition
is also due Ms. Mary Lou Lomon, who did such an excellent job in typing
the manuscript.

*See Delfiner and Gilbert (1978),

this volume.

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