MODEL Statement

The KRIGE2D Procedure

MODEL Statement

MODEL model-options ;

You can use the following options to specify a semivariogram or covariance model. The specified model is used in the kriging system defined by the most previous PREDICT statement.

There are two ways to specify a semivariogram or covariance model. In the first method, you specify the required parameters SCALE, RANGE, and FORM, and possibly the optional parameters NUGGET, ANGLE, and RATIO, explicitly in the MODEL statement.

In the second method, you specify an MDATA= data set. This data set contains variables corresponding to the required SCALE, RANGE, and FORM parameters, and, optionally, variables for the NUGGET, ANGLE, and RATIO parameters.

The two methods are exclusive; either you specify all parameters explicitly, or they all are read from the MDATA= data set.

ANGLE=angle

ANGLE=(angle₁,...,angle_k)

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.

FORM=SPHERICAL | EXPONENTIAL | GAUSSIAN | POWER

FORM=SPH | EXP | GAUSS | PW

specifies the functional form of the semivariogram model. All the supported models are two-parameter models (SCALE= and RANGE=). A FORM= value is required; in the case of a nested semivariogram model, you must specify a form for each nesting.

See the section "Theoretical Semivariogram Models" for details on how the FORM= forms are determined.

MDATA=SAS-data-set

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 variables NUGGET, ANGLE, and RATIO.

The FORM variable must be a character variable, assuming only the 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 semivariogram model. For example, to specify a nonnested model using a spherical covariance, an MDATA= data set might look like

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

The PROC KRIGE2D statement to use the MDATA= specification is of the form

   proc krige2d data=...;
      pred var=....;
      model mdata=md1;
   run;

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

   proc krige2d data=...;
      pred var=....;
      model scale=25 range=10 form=sph;
   run;

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

   data md1;
      input scale range form $ nugget angle ratio;
      datalines;
      20 8 S  5 35 0.7
      12 3 G  5 0  0.8
      4  1 G  5 45 0.5
      ;

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

   proc krige2d data=...;
      pred var=....;
      model scale=(20,12,4) range=(8,3,1) form=(S,G,G)
            angle=(35,0,45) ratio=(0.7,0.8,0.5) nugget=5;
   run;

This example is somewhat artificial in that it is usually hard to detect different anisotropy directions and ratios for different nestings 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, see the section "Theoretical and Computational Details of the Semivariogram" in the chapter on the VARIOGRAM procedure.

NUGGET=number

specifies the nugget effect for the model. The nugget effect is due to a discontinuity in the semivariogram as determined by plotting the sample semivariogram (see the chapter on the VARIOGRAM procedure for details). For models without any nugget effect, this option is left out; the default is NUGGET=0.

RANGE=range

RANGE=(range₁,...,range_k)

specifies the range parameter in 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 except the power model. 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. See the section "Theoretical Semivariogram Models" for details on how the RANGE= values are determined.

RATIO=ratio

RATIO=(ratio₁,...,ratio_k)

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.

SCALE=scale

SCALE=(scale₁,...,scale_k)

specifies the scale 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 in the preceding PREDICT statement. See the section "Theoretical Semivariogram Models" for details on how the SCALE= values are determined.

SINGULAR=number

gives the singularity criteria for solving kriging systems. The larger the value of the SINGULAR= option, the easier it is for a kriging system to be declared singular. The default is SINGULAR=1E-7. See the section "Details of Ordinary Kriging" for more detailed information.

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