Chapter 80: The VARIOGRAM Procedure

Overview

The VARIOGRAM procedure computes sample or empirical measures of spatial continuity for two-dimensional spatial data. These continuity measures are the regular semivariogram, a robust version of the semivariogram, and the covariance. The continuity measures are written to an output data set, allowing plotting or parameter estimation for theoretical semivariogram or covariance models. Both isotropic and anisotropic measures are available.

The VARIOGRAM procedure produces two additional output data sets that are useful in the analysis of pairwise distances in the original data. The OUTPAIR= data set contains one observation for each pair of points. The coordinates, distance, angle, and values of the analysis variables are written to this data set. The OUTDISTANCE= data set contains histogram information on the count of pairs within distance intervals, which is useful for determining unit lag distances.

Introduction to Spatial Prediction

Spatial prediction, in general, is any prediction method that incorporates spatial dependence. A simple and popular spatial prediction method is ordinary kriging.

Ordinary kriging requires a model of the spatial continuity, or dependence. This is typically in the form of a covariance or semivariogram.

Spatial prediction, then, involves two steps. First, you model the covariance or semivariogram of the spatial process. This involves choosing both a mathematical form and the values of the associated parameters. Second, you use this dependence model in solving the kriging system at a specified set of spatial points, resulting in predicted values and associated standard errors.

SAS/STAT software has two procedures corresponding to these steps for spatial prediction of two-dimensional data. The VARIOGRAM procedure is used in the first step. By computing a sample estimate of the variogram or covariance, you can choose a theoretical model based on graphical or other means.