Simplifying The Practice Of Kriging In Presence Of Trends

The Universal Kriging (UK) and the Ordinary Kriging (OK) systems of equations are variations of the well-known system of Normal Equations. They differ only by the number of constraints present in the system. The dual version of these sytems enables one to interpret kriging as the fitting, of an interpolation surface, whose components are a series of variogram functions plus a polynomial trend model. This trend model should account for any systematic decrease or increase of the variable over the study area. It is shown that modeling the trend is useful only when the locations being estimated are beyond the range of influence of neighboring data (extrapolation cases). A case study based on a public-domain coal data set is presented. The variable described (seam thickness) shows an actual trend of increasing data values towards the NW corner of the region considered. UK and OK are used to estimate coal thickness at locations within sample data range (interpolation cases). The UK algorithm that includes a model for the trend does not improve the estimation when compared to the simpler OK algorithm with no trend model. Thus, in interpolation situations, the simpler OK algorithm is recommended.