A practical two‐step approach for mixed model‐based kriging,with an application to the prediction of soil organic carbon concentration

Soil scientists often use prediction models to obtain values at unsampled locations. The spatial variation in the soil is best captured by using the empirical best linear unbiased predictor (EBLUP) based on a restricted maximum likelihood (REML) approach that efficiently exploits available data on both mean trends and correlation structures. We proposed a practical two‐step implementation of the REML approach for model‐based kriging, exemplified by predicting soil organic carbon (SOC) concentrations in mineral soils in Estonia from the large‐scale digital soil map information and a previously established prediction model. The prediction model was a linear mixed model with soil type, physical clay content (particle size < 0.01 mm) and A‐horizon thickness as fixed effects and site, transect, plot, year, year‐transect random intercepts and site‐specific random slopes for clay content. We used only the site‐specific intercept EBLUPs for estimating spatial correlation parameters as they described most of the variation in the random effects (86.8%). Fitting an exponential correlation model to these EBLUPs resulted in an estimated range of 10.5 km and the estimated proportion of the variance from the nugget effect was 0.23. The results of a simulation study showed a downwards bias that decreased with sample size. The results were validated through an external dataset, resulting in root mean square errors (RMSE) of 1.06 and 1.07% for the two‐step approach for kriging and the model with only fixed effects (no kriging), respectively. These results indicate that using the two‐step approach for kriging may improve prediction.