The vadose zone, i.e., the porous earth material below the land surface whose water saturation fluctuates, is spatially heterogeneous to a degree difficult to capture in routine measurements, and there is a need to reduce this complexity for purposes of prediction and management.
Scale invariance offers a way to do that.
One imagines a heterogeneous field soil to be the union of approximately homogeneous spatial domains, each of which can be associated with a small number of characteristic length scales that are related to the equilibrium properties and movement of water. Heterogeneity then simplifies into the spatial variability of these local length scales, while the generic functional relationships that describe soil water properties remain uniform. Roth et al. Techniques for measuring the hydrologic properties of soils were reviewed extensively in a conference proceedings volume edited by van Genuchten et al. The present report will focus instead upon the significance of scale invariance for the prediction of water movement in unsaturated soil based on analytical solutions of the Richards equation.