Multiscale contextual spatial modelling with the Gaussian scale space

We present a contextual spatial modelling (CSM) framework, as a methodology for multiscale, hierarchical mapping and analysis. The aim is to propose and evaluate a practical method that can account for the complex interactions of environmental covariates across multiple scales and their influence on soil formation. Here we derived common terrain attributes from multiscale versions of a DEM based on up-sampled octaves of the Gaussian pyramid. Because the CSM approach is based on a relatively small set of scales and terrain attributes it is efficient, and depending on the regression algorithm and the covariates used in the modelling, the results can be interpreted in terms of soil formation. Cross-validation coefficient of determination modelling (R-2), for predictions of clay and silt increased from 0.38 and 0.16 when using the covariates derived at the original DEM resolution to 0.68 and 0.63, respectively, when using CSM. These results are similar to those achieved with the hyperscale covariates of ConMap and ConStat. As with these hyperscale covariates, the multiscale covariates derived from the Gaussian scale space in CSM capture the observed spatial dependencies and interactions of the landscape and soil. However, some advantages of CSM approach compared to ConMap and ConStat are i) a reduced set of scales that still manage to represent the entire extent of the range of scales, ii) a reduced set of attributes at each scale, iii) more efficient computation, and iv) better interpretability of the important covariates used in the modelling and thus of the factors that affect soil formation.