Spatial prediction of soil properties using EBLUP with the Matérn covariance function

Spatial prediction with the presence of spatially dense ancillary variables has attracted research in pedometrics. While soil survey and analysis of soil properties are still expensive and time consuming, the secondary data can be made available on a dense grid for the whole area of interest. The main aim of using the ancillary data is to enhance prediction of soil properties by making use of the ancillary variables as covariates. Methods that can be used for this purpose are kriging with external drift, cokriging, regression kriging, and REML-EBLUP (Residual Maximum Likelihood-Empirical Best Linear Unbiased Predictor). Regression kriging is a sub-optimal method that has been utilised extensively because it is easy to use and has been shown empirically to perform as well as other methods. A statically sound method is REML-EBLUP. This paper examines the use of REML-EBLUP in combination with the Matérn covariance function for spatial prediction of soil properties. Methods for estimating parameters of the Matérn variogram using REML, and prediction with EBLUP are described. The prediction capability of REML-EBLUP, regression kriging, and ordinary kriging is compared for four datasets. Results show that although REML-EBLUP generally improves the prediction, the improvement is small compared with regression kriging. Thus, for practical applications regression kriging appears to be a robust method. REML-EBLUP is useful when the trend is strong, and the number of observations is small (< 200). We concluded that improvement in the prediction of soil properties does not rely on more sophisticated statistical methods, but rather on gathering more useful and higher quality data.