# Understanding ordinary kriging

Ordinary kriging assumes the model

Z(s) = µ + ε(s),

where µ is an unknown constant. One of the main issues concerning ordinary kriging is whether the assumption of a constant mean is reasonable. Sometimes there are good scientific reasons to reject this assumption. However, as a simple prediction method, it has remarkable flexibility. The following figure is an example in one spatial dimension:

It looks like the data is elevation values collected from a line transect through a valley and over a mountain. It also looks like the data is more variable on the left and becomes smoother on the right. In fact, this data was simulated from the ordinary kriging model with a constant mean µ. The true but unknown mean is given by the dashed line. Thus, ordinary kriging can be used for data that seems to have a trend. There is no way to decide, based on the data alone, whether the observed pattern is the result of autocorrelation—among the errors ε(**s**) with µ constant—or trend, with µ(**s**) changing with **s**.

Ordinary kriging can use either semivariograms or covariances (which are the mathematical forms you use to express autocorrelation), use transformations and remove trends, and allow for measurement error.