Theoretical Semivariogram Models

The VARIOGRAM Procedure

Theoretical Semivariogram Models

The VARIOGRAM procedure computes the sample, or experimental semivariogram. Prediction of the spatial process at unsampled locations by techniques such as ordinary kriging requires a theoretical semivariogram or covariance.

It is necessary, then, to decide on a theoretical variogram based on the sample variogram. While there are methods of fitting semivariogram models, such as least squares, maximum likelihood, and robust methods (Cressie 1993, section 2.6), these techniques are not appropriate for data sets resulting in a small number of variogram points. Instead, a visual fit of the variogram points to a few standard models is often satisfactory. Even when there are sufficient variogram points, a visual check against a fitted theoretical model is appropriate (Hohn 1988, p. 25ff).

In some cases, a plot of the experimental semivariogram suggests that a single theoretical model is inadequate. Nested models, anisotropic models, and the nugget effect increase the scope of theoretical models available. All of these concepts are discussed in this section. The specification of the final theoretical model is provided by the syntax of PROC KRIGE2D.

Note the general flow of investigation. After a suitable choice is made of the LAGDIST= and MAXLAGS= options and, possibly, the NDIR= option (or a DIRECTIONS statement), the experimental semivariogram is computed. Potential theoretical models, possibly incorporating nesting, anisotropy, and the nugget effect, are computed by a DATA step, then they are plotted against the experimental semivariogram and evaluated. A suitable theoretical model is thus found visually, and the specification of the model is used in PROC KRIGE2D. This flow is illustrated in Figure 34.3; also see the "Getting Started" section for an illustration in a simple case.

Figure 70.10: Flowchart for Variogram Selection

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