TY - JOUR

T1 - Non-stationary variogram models for geostatistical sampling optimisation

T2 - an empirical investigation using elevation data

AU - Atkinson, Peter M.

AU - LLoyd, Christopher D.

N1 - M1 - 10

PY - 2007/10

Y1 - 2007/10

N2 - 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.

AB - 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.

KW - Kriging

KW - Spatial structure

KW - DEM

U2 - 10.1016/j.cageo.2007.05.011

DO - 10.1016/j.cageo.2007.05.011

M3 - Journal article

VL - 33

SP - 1285

EP - 1300

JO - Computers and Geosciences

JF - Computers and Geosciences

SN - 0098-3004

IS - 10

ER -