Understanding simple kriging
Simple kriging assumes the model
Z(s) = µ + ε(s),
The known constant—solid line—is µ. This can be compared to ordinary kriging. For simple kriging, because you assume that you know µ exactly, you also know ε(s) exactly at the data locations. For ordinary kriging, you estimated µ, so you also estimated ε(s). If you know ε(s), you can do a better job of estimating the autocorrelation than if you are estimating ε(s). The assumption of exactly knowing the mean µ is often unrealistic. However, sometimes it makes sense to assume that a physically based model gives a known trend. Then you can take the difference between that model and the observations, called residuals, and use simple kriging on the residuals, assuming the trend in the residuals is known to be zero.