specifies the angle of the major axis for anisotropic models, measured in degrees clockwise from the N–S axis. In the case of a nested semivariogram model, you can specify an angle for each nesting. The default is ANGLE=0.

specifies the functional form or forms of the semivariogram model, where form_spec can take only the values SPHERICAL, EXPONENTIAL, and GAUSSIAN. The two ways of specifying the FORM= parameter allow specification of both nested and non-nested models.

The following abbreviations are permitted. For the spherical model, you can specify the form_spec as FORM=SPHERICAL, FORM=SPH, or FORM=S. For the exponential model, you can specify the form_spec as FORM=EXPONENTIAL, FORM=EXP, or FORM=E. For the Gaussian model, you can specify the form_spec as FORM=GAUSSIAN, FORM=GAUSS, or FORM=G.

specifies the input data set that contains parameter values for the covariance or semivariogram model. The MDATA= data set must contain variables named SCALE, RANGE, and FORM, and it can optionally contain the variables NUGGET, ANGLE, and RATIO.

The FORM variables must be character, and they can assume the same values allowed in the explicit FORM= syntax described previously. The RANGE and SCALE variables must be numeric. The optional variables ANGLE, RATIO, and NUGGET must also be numeric if present.

The number of observations present in the MDATA= data set corresponds to the level of nesting of the covariance or semivariogram model. For example, to specify a non-nested model that uses a spherical covariance, an MDATA= data set might contain the following statements:

   data md1;
      input scale range form $;
      datalines;
      25 10 SPH
   run;

The PROC SIM2D statement to use the MDATA= specification is of the form shown in the following:

   proc sim2d data=...;
      sim var=.... mdata=md1;
   run;

This is equivalent to the following explicit specification of the covariance model parameters:

   proc sim2d data=...;
      sim var=.... scale=25 range=10 form=sph;
   run;

The following MDATA= data set is an example of an anisotropic nested model:

   data md2;
      input scale range form $ nugget angle ratio;
      datalines;
      20 8 S  5 35 .7
      12 3 G  5 0  .8
      4  1 G  5 45 .5
      ;

   proc sim2d data=...;
      sim var=.... mdata=md2;
   run;

This is equivalent to the following explicit specification of the covariance model parameters:

   proc sim2d data=...;
      sim var=.... scale=(20,12,4) range=(8,3,1) form=(S,G,G)
                   angle=(35,0,45) ratio=(.7,.8,.5) nugget=5;
   run;

This example is somewhat artificial in that it is usually hard to detect different anisotropy directions and ratios for different nestings by using an experimental semivariogram. Note that the NUGGET value is the same for all nestings. This is always the case; the nugget effect is a single additive term for all models. For further details, refer to the section The Nugget Effect in the KRIGE2D procedure.

The SIMULATE statement can be given a label. This is useful for identification in the OUTSIM= data set when multiple SIMULATE statements are specified. For example:

   proc sim2d data=...;
      gauss1: sim var=.... form=gauss;
      mean ....;
      gauss2: sim var=.... form gauss;
      mean ....;
      exp1: sim var=.... form=exp;
      mean ....;
      exp2: sim var=.... form=exp;
      mean ....;
   run;

In the OUTSIM= data set, the values "GAUSS1," "GAUSS2," "EXP1," and "EXP2" for the LABEL variable help to identify the realizations corresponding to the four SIMULATE statements. If you do not provide a label for a SIMULATE statement, a default label of SIM is given, where is the number of unlabeled SIMULATE statements seen so far.

specifies the nugget effect for the model. This effect is due to a discontinuity in the semivariogram as determined by plotting the sample semivariogram (refer to the section The Nugget Effect in the KRIGE2D procedure for details). For models without any nugget effect, the NUGGET= option is left out. The default is NUGGET=0.

specifies the range parameter in the semivariogram models. In the case of a nested semivariogram model, you must specify a range for each nesting.

The range parameter is the divisor in the exponent in all supported models. It has the units of distance or distance squared for these models, and it is related to the correlation scale for the underlying spatial process.

Refer to the section Theoretical Semivariogram Models in the KRIGE2D procedure for details on how the RANGE= values are determined.

specifies the ratio of the length of the minor axis to the length of the major axis for anisotropic models. The value of the RATIO= option must be between 0 and 1. In the case of a nested semivariogram model, you can specify a ratio for each nesting. The default is RATIO=1.

specifies the scale (or sill) parameter in semivariogram models. In the case of a nested semivariogram model, you must specify a scale for each nesting. The scale parameter is the multiplicative factor in all supported models; it has the same units as the variance of the VAR= variable.

Refer to the section Theoretical Semivariogram Models in the KRIGE2D procedure for details on how the SCALE= values are determined.

specifies the seed to use for the random number generator. The SEED= value has to be an integer.

gives the singularity criteria for solving the set of linear equations involved in the computation of the mean and covariance of the conditional distribution associated with a given SIMULATE statement. The larger the value of the SINGULAR= option, the easier it is for the covariance matrix system to be declared singular. The default is SINGULAR=1E–8.

For more details on the use of the SINGULAR= option, see the section Computational and Theoretical Details of Spatial Simulation.