Spatial Prediction
Spatial prediction, in general, is any prediction method that incorporates
spatial dependence. In fields such as petroleum exploration, mining, and water pollution analysis, data are available at
specific spatial locations (such as experimental stations positioned above the ground or at certain distances in the air),
and the goal is to predict unsampled locations. The unsampled locations are often mapped on a regular grid, and the
predictions are used to produce surface plots or contour maps. 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.
In this framework, you can perform spatial prediction with SAS/STAT software using two steps. First, you model the covariance or semivariogram of the spatial process using the VARIOGRAM procedure. 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. The KRIGE2D procedure performs the second of these steps using ordinary kriging of two-dimensional data. Both procedures are provided in SAS/STAT software.
The VARIOGRAM Procedure
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 KRIGE2D Procedure
The KRIGE2D procedure performs ordinary kriging in two dimensions. PROC KRIGE2D can handle anisotropic and nested semivariogram models. Four semivariogram models are supported: the Gaussian, exponential, spherical, and power models. A single nugget effect is also supported.
Local kriging is supported through the specification of a radius around a grid point or the specification of the number of nearest neighbors to use in the kriging system. When you perform local kriging, a separate kriging system is solved at each grid point using a neighborhood of the data point established by the radius or number specification. You can specify the locations of kriging estimates in a GRID statement, or they can be read from a SAS data set. The grid specification is most suitable for a regular grid; the data set specification can handle any irregular pattern of points.
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