Soil Water Content Variability in the 3D ‘Support-Spacing-Extent' Space of Scale Metrics.

Knowledge of soil water content variability provides important insight into soil functioning, and is essential in many applications. We undertook a systematic review to see how the definition of scale can affect conclusions about the scale-dependence in soil water content (SWC) variability. Support, spacing, and extent were three scale metrics.  We found six types of experiments in which scale was changed. With data obtained without a change in extent, the scale change in some cases consisted in the simultaneous change of support and spacing, and the power law decrease in variance with support increase was found.  Datasets that were collected with different support or sample volumes for the same extent and spacing showed the decrease of variance as the sample size increased. A variance increase was common when the scale change consisted in change in spacing without the change in supports and extents. An increase in variance with the extent of the study area was demonstrated with data an evolution of variability with increasing size of the area under investigation (extent) without modification of support.  The variance generally increased with the extent when the spacing was simultaneously changed. Finally, the decrease in variability was noted for changes in extent for a given support without modification of spacing.  All above trends were holding up to some threshold scale metric value. We noted that  set of hyperplanes can be used to depict the scale dependencies in the space of scale metrics. Slopes, thresholds, or both, appear to be preserved as SWC changes. Overall, published information on the effect of scale on soil water content variability in the 3D space of scale metrics did not contain controversies in qualitative terms. However, there were substantial differences in quantitative terms, that might reflect site-specific differences in soil water content controls and scale change methods.