The models estimated by the krige package assume a powered exponential covariance structure. Each parametric covariance function for kriging models corresponds to a related semivariance function, given that highly correlated values will have a small variance in differences while uncorrelated values will vary widely. More specifically, semivariance is equal to half of the variance of the difference in a variable's values at a given distance. That is, the semivariance is defined as: \(\gamma(h)=0.5*E[X(s+h)-X(s)]^2\), where \(X\) is the variable of interest, s is a location, and h is the distance from s to another location.
The powered exponential covariance structure implies that the semivariance follows the specific functional form of \(\gamma(d)=\tau^2+\sigma^2(1-\exp(-|\phi d|^p))\) (Banerjee, Carlin, and Gelfand 2015, 27). A perk of this structure is that the special case of p=1 implies the commonly-used exponential semivariogram, and the special case of p=2 implies the commonly-used Gaussian semivariogram. Upon estimating a model, it is advisable to graph the functional form of the implied parametric semivariance structure. By substituting estimated values of the nugget, decay, and partial.sill terms, as well as specifying the correct power argument, it is possible to compute the implied semivariance from the model. The distance argument easily can be a vector of observed distance values.