Spatial variability of Australian soil texture: A multiscale analysis

- Empirical variograms are calculated for different spatial scales.
- Grid-based declustering reduces lumpy artefacts in variograms across scales.
- D Values (a unitless measure of roughness) are calculated from each variogram.
- We propose a method to estimate D values continuously across all spatial scales.

Understanding how soil variability changes with spatial scale is critical to our ability to understand and model soil processes at scales relevant to decision makers. The compilation of large legacy data sets has opened up new possibilities to model spatial variability at the continental or even global scale. Using the National Soil Site Collation (NSSC) dataset of Australia we created empirical variograms for sand and clay fraction at extents from 1 km to continental. The NSSC dataset is highly spatially clustered; a typical feature of legacy datasets. This leads to lumpy artefacts in the variograms. To reduce this lumpiness we employed grid based declustering. We used the declustered empirical variograms to calculate the Hausdorff Besicovitch Dimension - a unitless measure of spatial roughness. We first fit a power model to each declustered variogram and calculated the Hausdorff Besicovitch dimension at each modelled scale. This allowed us to assess the roughness or variability at each modelled extent, however this assessment was somewhat arbitrary and showed that roughness depends on the extent. We have proposed a new model that allows us to calculate the Hausdorff Besicovitch dimension continuously across all extents. The conceptual basis of this model moves away from a multi-fractal framework typically used by soil scientists. It allows us to describe spatial variability or stochasticity as a continuous function of spatial separation. Both our new model and the continental scale variograms of texture emphasise the high degree of short range variability in soil texture. Empirical variograms indicate that around 50% of spatial variability occurs at < 10 km, and 30% at < 1 km. Spatial variability of soil texture increases with depth consistently across all modelled extents. Beyond extents of around 100 km, the Hausdorff Besicovitch Dimension remains relatively stable. Soil spatial variability is highly stochastic at fine scales however it changes gradually with extent and scale rather than abruptly.