Source: S. Rathbun, Classnotes Environmental Statistics, Univ. of Georgia, Athens, July 1994
Ordinary kriging is used for spatial prediction when there is no trend in the data. When there is a trend in the data, we use universal kriging.
Assume that the variable of interest, Z, at site s, is a linear function of explanatory variables x1,...., xp :
NOTE that for universal kriging the explanatory variables x_1,...., x_p have to be known at each "s_0", that is, at each location for which the value of Z is to be predicted!
The lambda-i's are obtained by solving the universal kriging equations: