The relevant range of scales for multi-scale contextual spatial modelling

Spatial autocorrelation in the residuals of spatial environmental models can be due to missing covariate information. In many cases, this spatial autocorrelation can be accounted for by using covariates from multiple scales. Here, we propose a data-driven, objective and systematic method for deriving the relevant range of scales, with distinct upper and lower scale limits, for spatial modelling with machine learning and evaluated its effect on modelling accuracy. We also tested an approach that uses the variogram to see whether such an effective scale space can be approximated a priori and at smaller computational cost. Results showed that modelling with an effective scale space can improve spatial modelling with machine learning and that there is a strong correlation between properties of the variogram and the relevant range of scales. Hence, the variogram of a soil property can be used for a priori approximations of the effective scale space for contextual spatial modelling and is therefore an important analytical tool not only in geostatistics, but also for analyzing structural dependencies in contextual spatial modelling.