Geostatistics : Modelling spatial variation

Geostatistics, which was developed originally for mining, is now widely used for prediction of soil conditions at unvisited sites and for mapping from sample survey data. The technique is based on models of spatial variation. Soil properties are treated as the outcomes of random spatially correlated processes, to which may be added fixed effects of geographic trend or correlation with other environmental
variables. Prediction proceeds from sample data in two stages, namely (1) estimation of spatial covariances or semivariances to which are fitted plausible variogram models,
and (2) kriged predictions based on the variogram models. A figure shows how comparisons between data can be binned to estimate semivariances; others show popular variogram models. The techniques for stage 1 are illustrated with examples
from soil survey; equations define the kriging systems to predict without bias and minimize the prediction error variances for stage 2. Residual maximum likelihood (reml) is now best practice for estimating simultaneously coefficients of fixed effects and parameters of the variograms of random residuals for universal kriging and kriging with external drift. Thousands of published accounts attest to the merits of geostatistics for spatial prediction and mapping of soil properties.