For all the semivariogram models considered previously, the following property holds:

However, a plot of the experimental semivariogram might indicate a discontinuity at ; that is, as , while . The quantity is called the nugget effect; this term is from mining geostatistics where nuggets literally exist, and it represents variations at a much smaller scale than any of the measured pairwise distances—that is, at distances , where

There are conceptual and theoretical difficulties associated with a nonzero nugget effect; refer to Cressie (1993, Section 2.3.1) and Christakos (1992, Section 7.4.3) for details. There is no practical difficulty, however; you simply visually extrapolate the experimental semivariogram as . The importance of availability of data at small lag distances is again illustrated.

As an example, an exponential semivariogram with a nugget effect has the form

and

where the factor is called the partial sill, and the sill .

This is illustrated in Figure 46.11 for the parameters , , and nugget effect .

You can specify the nugget effect in PROC KRIGE2D with the NUGGET= option in the MODEL statement. It is a separate, additive term independent of direction; that is, it is isotropic. There is a way to approximate an anisotropic nugget effect; this is described in the following section.

Figure 46.11 Exponential Semivariogram Model with a Nugget Effect