Statistics - Field Sampling: Principles and Practices in Environmental Analysis - page 168

6.12.5. Block Kriging
Analytical results from point sources are used in calculating kriging estimates; however,
the values from an area can also be averaged and these values used to produce a map of
that characteristic. For example, the data in the sample areas in Figure 6.1 can be
averaged, as shown in Table 6.7, and this average can be used in block kriging. A map
produced by block kriging is generally smoother than the map made from point values.
(See Figure 6.10.)
6.13. COREGIONALIZATION
Sometimes two different properties are related to each other. For example, plant wilting
point and soil organic matter are closely related. When such a relationship exists, a
procedure called cokriging can be carried out. When two characteristics are closely
related additional information for predicting one characteristic based on measurements of
the second is possible. In some situations this is exactly what is done in modeling; that is,
a component related to or dependent on already known characteristics is used to estimate
the concentration and movement of the unknown component.
The whole area of geostatistics is mathematically intense, involving a great number of
variables and mathematical operations. The calculations themselves are not difficult, but
they do involve discrete mathematics and calculus. A number of computer programs are
available to carry out geostatistical calculations and can be purchased at reasonable cost
from firms such as RockWare. (Information for contacting this company is given in
Appendix B.)
6.14. GEOSTATISTICAL PROBLEMS
It would be nice if applying geostatistical methods could solve all environmental
problems. Unfortunately this is not the case. Geostatistics works best in areas that are
relatively homogeneous and the variables well known or studied. Applying kriging to a
field without knowing anything about it can be expected to lead to inaccurate estimations.
A 100-ha field uniformly made up of a sandy soil so that all the horizons and their
characteristics are the same or are well defined will be amenable to kriging. If the field
contains a compacted area, however, this area may not be amenable to kriging applied to
a transect line trough that area. This is particularly true in two instances.
The first instance would be where a compacted area smaller than the range is
encountered. If this range is used to identify sampling intervals, the compacted area may
be missed. In this case two problems can develop. First, if the compacted area is missed
its effects on the component of interest will not be taken into consideration in making a
management decision, such as a remediation plan. Second, the area on one side of the
compacted area may react very differently to the component of interest, and this
difference may be missed.
The second instance occurs where the subsurface changes dramatically, although the