Chapter 65: The SIM2D Procedure


Overview

The SIM2D procedure produces a spatial simulation for a Gaussian random field with a specified mean and covariance structure in two dimensions using an LU decomposition technique.

The simulation can be conditional or unconditional. If it is conditional, a set of coordinates and associated field values are read from a SAS data set. The resulting simulation honors these data values.

You can specify the mean structure as a quadratic in the coordinates. You can specify the covariance by naming the form and supplying the associated parameters.

PROC SIM2D can handle anisotropic and nested semivariogram models. Three covariance models are supported: Gaussian, exponential, and spherical. A single nugget effect is also supported.

You can specify the locations of simulation points 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.

The SIM2D procedure writes the simulated values for each grid point to an output data set. The SIM2D procedure does not produce any displayed output.

Introduction to Spatial Simulation

The purpose of spatial simulation is to produce a set of partial realizations of a spatial random field (SRF) Z ( s ), s ˆˆ D R 2 in a way that preserves a specified mean µ ( s ) = E [ Z ( s )] and covariance structure C z ( s 1 ˆ’ s 2 ) = cov ( Z ( s 1 ) , Z ( s 2 )).

The realizations are partial in the sense that they occur only at a finite set of locations ( s 1 , s 2 , , s n ). These locations are typically on a regular grid, but they can be arbitrary locations in the plane.

There are a number of different types of spatial simulation and associated computational methods . PROC SIM2D produces simulations for continuous processes in two dimensions. This means that the possible values of the measured quantity Z ( s ) at location s = ( x , y ) can vary continuously over a certain range.

An additional assumption, needed for computational purposes, is that the spatial random field Z ( s ) is Gaussian.

Spatial simulation is different from spatial prediction, where the emphasis is on producing a point estimate at a given grid location. In this sense, spatial prediction is local. In contrast, spatial simulation is global; the emphasis is on the entire realization ( Z ( s 1 ) ,Z ( s 2 ) , ,Z ( s n )).

Given the correct mean µ ( s ) and covariance structure C z ( s 1 ˆ’ s 2 ), SRF quantities that are difficult or impossible to calculate in a spatial prediction context can easily be approximated by repeated simulations.




SAS.STAT 9.1 Users Guide (Vol. 6)
SAS.STAT 9.1 Users Guide (Vol. 6)
ISBN: N/A
EAN: N/A
Year: 2004
Pages: 127

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