The offset correlation, a novel quality measure for planning geochemical surveys of the soil by kriging

This paper presents a quality measure to plan geostatistical soil surveys when measures based on the kriging variance are not applicable. The criterion is the consistency of estimates made from two non-coincident instantiations of a proposed sample design. We consider square sample grids, one instantiation is offset from the second by half the grid spacing along the rows and along the columns. If a sample grid is coarse relative to the important scales of variation in the target property then the consistency of predictions from two instantiations is expected to be small, and can be increased by reducing the grid spacing. The measure of consistency is the correlation between estimates from the two instantiations of the sample grid, averaged over a grid cell. We call this the offset correlation, it can be calculated from the variogram. This quality measure is illustrated for some hypothetical examples, considering both ordinary kriging and factorial kriging of the variable of interest. The factorial kriging case is considered since, when planning a small-scale synoptic geochemical survey we may wish only to map components of the variation of the target variable at certain spatial scales. The quality measure is then computed for ordinary and factorial kriging with variograms estimated from data on nickel, chromium and cobalt content of soil in the north-east of England. Our results show how the offset correlation responds to sample density and the form of the variogram, and how larger correlations can be achieved for factorial kriging than ordinary kriging at a given density. The results for data on soil metals showed that an offset correlation of 0.8 could not be achieved (ordinary kriging) by sampling at 5-km intervals, the density at which all of England and Wales is sampled. However, if the objective were to map by factorial kriging the coarser-scale components of variation, driven primarily by parent material, then for two of the metals (Co and Cr) the 5-km grid was adequate, and the sample effort of the survey from which the data were taken (0.44 samples km− 2) was excessive.

► Kriging predictions should be robust to a shift in the sample grid.
► A correlation-based quality measure is based on this proposal.
► The measure can be applied to ordinary kriging and factorial kriging predictions.
► The measure is illustrated for soil geochemical variables in eastern England.