Contextual spatial modelling in the horizontal and vertical domains.

Multi-scale contextual modelling is an important toolset for environmental mapping. It accounts for spatial dependence by using covariates on multiple spatial scales and incorporates spatial context and structural dependence to environmental properties into machine learning models. For spatial soil modelling, three relevant scales or ranges of scale exist: quasi-local soil formation processes that are independent of the spatial context, short-range catenary processes, and long-range processes related to climate and large-scale terrain settings. Recent studies investigated the spatial dependence of topsoil properties only. We hypothesize that soil properties within a soil profile were formed due to specific interactions between different features and scales of the spatial context, and that there are depth gradients in spatial and structural dependencies. The results showed that for topsoil, features at small to intermediate scales do not increase model accuracy, whereas large scales increase model accuracy. In contrast, subsoil models benefit from all scales-small, intermediate, and large. Based on the differences in relevance, we conclude that the relevant ranges of scales do not only differ in the horizontal domain, but also in the vertical domain across the soil profile. This clearly demonstrates the impact of contextual spatial modelling on 3D soil mapping.