ETL 1110-1-175
30 Jun 97
environmental conditions throughout the specified
(1) One of the most common applications for
study area. The evaluations may require either
kriging techniques in the final phases of HTRW
point or block estimates. Often, design factors are
site investigations is evaluating compliance. For
addressed in the analytical phase as well.
instance, a question such as "Is the mean concen-
tration of constituent x within compliance limits?"
(2) A common application for kriging tech-
is ubiquitous to HTRW site investigations. Mak-
niques in HTRW site investigations is estimating
ing determinations concerning compliance is very
real means. More common, however, is estimating
similar to estimating areal extent as part of the
the extent of areal contamination. Usually these
analysis. Investigators and managers have much
estimates involve chemicals in air, water, and soil;
to gain from the confidence information available
however, if sufficient information is available,
from kriging techniques as to the reliability of
such estimates could include a wide range of
estimates as well as in optimizing monitoring
environmental factors that involve many issues
networks.
other than contaminants. Perhaps the most com-
mon examples concern geologic and hydrologic
(2) Kriging can also be very useful if man-
factors, such as depth to bedrock and groundwater-
agers are interested in making decisions based on
level elevations. Investigators need to realize that
the probability of certain conditions existing. If a
almost any set of measurements can be distributed
condition can be defined by the manager, then, pro-
using kriging techniques, providing there is a
viding there are adequate data, indicator kriging
sufficient amount and distribution of measured
can provide an estimate for the probability of
information.
existence. A common example of this kind of
application is making areal determinations for
(3) The investigator also needs to realize that
probabilities that concentrations for a constituent
the resultant kriging estimates can be gridded.
do or do not exceed, for example, an action level.
This gridding affords investigators opportunities to
perform mathematical or logical operations, or
(3) There are many operational remediation
both, on the kriging estimates, provided that
issues that kriging techniques may address as well.
investigators are comfortable with kriging esti-
Remedial activities at HTRW sites often need esti-
mates. Saturated thickness could, for example, be
mates for amounts in general. For instance, there
calculated from kriging estimates for groundwater
could be a need for information regarding volumes
elevations and base of aquifer elevations.
of contaminants to be treated, volumes of soil to be
excavated, volumes of soil to be stored, and so on.
(4) Often, after preparing estimates for areal
By combining estimates for different geologic,
properties, the investigator may appreciate the
hydrologic, and chemical factors, estimates for
opportunity afforded by kriging techniques to eval-
these volumes can be obtained from kriging tech-
uate the confidence associated with the estimates.
niques in much the same way as saturated thick-
Maps of kriging standard deviations can provide
nesses can be calculated.
the investigator with information concerning the
confidence associated with the kriging estimates.
1-5. An Overview of Some Technical
Although the areas of lowest confidence may be
Aspects of Geostatistics
well-known intuitively, maps of the kriging stan-
dard deviation are an important step toward quan-
tification. More often than not, even the most
The purpose of this section is to provide an
experienced investigator will benefit from careful
overview of some of the procedures and concepts
study of maps of kriging standard deviations.
to be treated in detail in this ETL. Some of the
technical ideas and terminology will be introduced
d. Implementation of remediation.
in very general terms, with the goal of orienting the
1-4
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