Non-stationary variogram models for geostatistical sampling optimisation: an empirical investigation using elevation data

Atkinson, P.M. and LLoyd, C.D. (2007) Non-stationary variogram models for geostatistical sampling optimisation: an empirical investigation using elevation data. Computers & Geosciences, 33 (10), 1285-1300. (doi:10.1016/j.cageo.2007.05.011).

Abstract

A problem with use of the geostatistical Kriging error for optimal sampling design is that the design does not adapt locally to the character of spatial variation. This is because a stationary variogram or covariance function is a parameter of the geostatistical model. The objective of this paper was to investigate the utility of non-stationary geostatistics for optimal sampling design. First, a contour data set of Wiltshire was split into 25 equal sub-regions and a local variogram was predicted for each. These variograms were fitted with models and the coefficients used in Kriging to select optimal sample spacings for each sub-region. Large differences existed between the designs for the whole region (based on the global variogram) and for the sub-regions (based on the local variograms). Second, a segmentation approach was used to divide a digital terrain model into separate segments. Segment-based variograms were predicted and fitted with models. Optimal sample spacings were then determined for the whole region and for the sub-regions. It was demonstrated that the global design was inadequate, grossly over-sampling some segments while under-sampling others.

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Contributors

Author: P.M. Atkinson

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