Sampling and bulking strategies for estimating soil properties in small regions

SUMMARY Estimates of mean values of soil properties within small rectangular blocks of land can be obtained by kriging provided the semi‐variogram is known. This paper describes optimal rectangular grid sampling configurations whereby estimation variances can be minimized. For linear semi‐variograms square blocks are best estimated by sampling at the nodes of a centrally placed grid with its interval equal to the block side divided by the square root of the sample size. For spherical semi‐variograms the same configuration is almost optimal. The estimation variance of a bulked sample can be identical with that of a kriged estimate where the semi‐variogram is linear and equal portions of soil are taken from each node on the optimally configured grid and provided the soil property is additive. For spherical semi‐variograms the above is approximately true. Comparisons with estimates that take no account of known spatial dependence show that the true variances can be much less than those apparent using classical theory, and the necessary sampling effort much less. Within block‐variances are often needed for planning, and an appendix gives two‐dimensional auxiliary functions from which they can be calculated for linear and spherical semi‐variograms.