Inspectional Analysis in the Theory of Water Flow through Unsaturated Soil

Abstract Conventional inspectional analysis is applied to the one‐dimensional Richards equation to provide a unified classification scheme for three macroscopic scaling approaches which have been used to describe soil water flow phenomena under laboratory or field conditions. It is shown that the scaling parameters and similarity groups developed in an inspectional analysis of the Richards equation depend on the boundary and initial conditions imposed as well as on the special physical hypotheses invoked. Nielsen similarity analysis is based on a zero‐flux boundary condition and the assumption that the hydraulic conductivity, soil water diffusivity, and matric potential are exponentional functions of water content. Warrick similarity analysis, on the other hand, is formulated independently of the boundary and initial conditions while adopting three scaling parameters to define reduced forms of the water content, hydraulic conductivity, and matric potential. Field experiments have shown that two of these parameters often are correlated. Macroscopic Miller similarity analysis is based on the physical postulate that water transport through unsaturated soil is governed by viscous flow and capillary forces. It differs from the classical Miller similar media concept in that it requires a scaling parameter for the volumetric water content and makes no direct reference to the geometric structure of a soil at the pore scale.