Increment-averaged kriging for 3-D modelling and mapping soil properties: Combining machine learning and geostatistical methods

Prediction and mapping of soil properties for different soil depths can provide important information for effective land management. Such predictions and maps are often built based on soil data from multiple soil surveys, and the sampled depths will rarely align with depths for which the predictions and maps are required. A recently proposed approach to deal with such datasets, termed increment-averaged kriging (IAK), fits a single model using data from all profiles and all soil depths. The approach considered several potential stumbling blocks: the effect that different widths of the sampled depth intervals has on the variances (sample support); potential non-stationarity in the covariances, depending on soil depth; the need to account for interactions between depth and the effect of covariates. In this work, we present some extensions to the original work that (i) extend the covariance model, (ii) integrate the use of a machine learning algorithm, Cubist, into the framework so that its regression parameters can be fitted while accounting for the correlation and sample support of the data, and (iii) apply a composite likelihood approximation to enable estimation and prediction with large datasets. Code to implement the method in R is also made available so that practitioners can test IAK on their own datasets.