Fast and Accurate Approximation to Kriging Using Common Data Neighborhoods

Abstract

Unknown values of a random field can be predicted from observed data using kriging. As data sets grow in size, the computation times become large. To facilitate kriging with large data sets, an approximation where the kriging is performed in sub-segments with common data neighborhoods has been developed. It is shown how the accuracy of the approximation can be controlled by increasing the common data neighborhood. For four different variograms, it is shown how large the data neighborhoods must be to get an accuracy below a chosen threshold, and how much faster these calculations are compared to the kriging where all data are used. Provided that variogram ranges are small compared to the domain of interest, kriging with common data neighborhoods provides excellent speed-ups (2–40) while maintaining high numerical accuracy. Results are presented both for data neighborhoods where the neighborhoods are the same for all sub-segments, and data neighborhoods where the neighborhoods are adapted to fit the data densities around the sub-segments. Kriging in sub-segments with common data neighborhoods is well suited for parallelization and the speed-up is almost linear in the number of threads. A comparison is made to the widely used moving neighborhood approach. It is demonstrated that the accuracy of the moving neighborhood approach can be poor and that computational speed can be slow compared to kriging with common data neighborhoods.