Strange results

Very strange values

When two (or more) of the observations are at very close distant but not at the same location, the kriging system may become ill conditioned (i.e. unstable). Ill conditioned kriging systems may lead to exceptional answers (unrealistically high or low values) or to error messages. The solution to this is to replace the close observations with one new observation (e.g. their average) or to relocate them on the same location (so that gstat will, by default, replace them by their average).

Checking the kriging matrices for their condition number can be done by setting cn_max to an appropriate value. If the estimated condition number of a matrix exceeds this value, a warning message is printed and a missing value is generated.

Negative cokriging prediction variances

If arbitrary coregionalizations are defined (and the command set nocheck=1; is set to allow this), than you will probably have encountered the warning:

Warning: No Intrinsic Correlation or Linear Model of
Coregionalization

or

Warning: Cauchy-Schwartz violation: ...

After the first warning, positive definiteness of the cokriging system cannot be guaranteed anymore and thus cokriging variances may become anything--positive or negative, even if the variograms pass the Cauchy-Schwartz check.

Unrecognised IC or LMC

IC (intrinsic correlation) or LMC (linear model of coregionalization) [13,10] are two models for a set of variograms and cross variograms that guarantee non-negative prediction variance. Gstat only recognises them when the order in which basic variogram models appear in the variogram definition are identical. E.g.,

variogram(a):   1   nug() + 1   sph(2);
variogram(b):   2   nug() + 1   sph(2);
variogram(a,b): 0.5 nug() + 0.8 sph(2);

will be recognised as LMC, but

variogram(a):   1   nug() + 1  sph(2);
variogram(b):   1   sph(2)+ 2  nug(); # <- changed order
variogram(a,b): 0.5 nug() + 0.8sph(2);

will not be recognised by gstat as LMC, although it is one. Both definitions will produce identical output.

Simulation speed

Simulation may be slow. Speeding up simulations can be done by (1) a faster machine, or (2) tuning (reduce) the neighbourhood size, especially the radius, or (3) choosing another simulation program, or (4) modifying the source (let me know!).