# 2.5.4 Long-Range and Periodic Heterogeneities

In the Gy paradigm, "long-range heterogeneity" refers to the same contamination pattern as the term "large-scale heterogeneity," as discussed in Section 2.2.3. This heterogeneity involves the nonrandom, nonperiodic distribution of contaminant across the site. Identifying this heterogeneity is often an objective of sampling programs, such as mapping site-specific concentration trends. The question is: what is the volume over which knowledge of this heterogeneity is desired vs. what is the volume over which such heterogeneity is a distraction because the mean is the parameter of interest? In Gy's theory, this heterogeneity is considered the cause of long-range heterogeneity fluctuation error (CE2). This Gy-defined error may or may not be a relevant error for a sampling design, depending on whether knowledge of contaminant distribution or mean is desired and the spatial dimensions of both have been defined. Gy theory assumes that the parameter of interest is the mean, not contaminant distribution.

In the same way, periodic heterogeneity and its corresponding periodic heterogeneity fluctuation error (CE3) is the result of cyclical changes in space or time over a site. An example of a cyclical change in time is measuring nitrogen concentration in agricultural fields over several growing seasons. If sampling were always performed at the start of the growing season when nitrogen levels were highest, a misleadingly high value would be obtained if the average over the entire year were desired. Just as for the long-range heterogeneity fluctuation error above, it is only a true error if it causes an inaccurate estimate of a mean for some defined area, and in this case, for a defined period of time.

The heterogeneities discussed above can lead to additional sampling errors. Four of Gy's seven sampling errors are described above; the last three are covered below.