Isotropic variogram models are produced by specifying terms for three model parameters – nugget variance, sill, and range. GS+ will initially specify these terms automatically, but you should examine this fit and make changes based on your own understanding of your data.
After GS+ fits a model, you can change the model in the Variogram Model Window:
Choose one of four isotropic models (Linear, Spherical, Exponential, and Gaussian). As a model is chosen the variogram graphs will be updated to denote the change.
Any of the three parameters for each model may be changed within the ranges allowed for individual parameters. To change a value either move the slider beneath it or type a new value directly into the text box:
• Nugget Variance or Co – the y-intercept of the model; the nugget variance can never be greater than the sill.
• Sill or Co+C – the model asymptote; the sill can never be less than the nugget variance.
• Range (A) – the separation distance over which spatial dependence is apparent. Sometimes this is called the effective range in order to distinguish range A from a modelrange parameter A0. In GS+ the Range A is calculated from A0 as described in the formulas for the different models: Spherical, Exponential, Gaussian, and Linear.
GS+ provides three statistics to aid the interpretation of model output:
• Residual Sums of Squares – provides an exact measure of how well the model fits the variogram data; the lower the reduced sums of squares, the better the model fits. When GS+ autofits the model, it uses RSS to choose parameters for each of the variogram models by determining the combination of parameter values that minimizes RSS for any given model. The Residual SS displayed in the This Fit box is calculated for the currently defined model.
• r2 – provides an indication of how well the model fits the variogram data; this value is not as sensitive or robust as the Residual SS value for best-fit calculations; use RSS to judge the effect of changes in model parameters.
• Proportion C/(Co+C) -- this statistic provides a measure of the proportion of sample variance (Co+C) that is explained by spatially structured variance C. This value will be 1.0 for a variogram with no nugget variance (where the curve passes through the origin); conversely, it will be 0 where there is no spatially dependent variation at the range specified.
Statistics for the Autofit model (the model most recently calculated by GS+) appear in this box. In this way you can compare your changes to model terms against that calculated automatically.
Automatically refit the model using as starting conditions the parameters in this dialog window. Model fitting in GS+ is somewhat dependent on starting conditions (assumed model parameters prior to iterations). Sometimes you can fit a better model by hand, in which case Refitting will further refine parameters to minimize RSS. To return to the original model parameters you may need to exit this Model definition window and recalculate the variogram.
Press OK to close the dialog window and apply any changes made to individual models. Press Cancel to exit the dialog without applying changes.