Three Principles of Water Flow in Real-World Structured Soils and a Mosaic Theory.

Water flow in real-world soils is fundamental to a number of environmental and ecological issues, but our ability to realistically model and predict water flow in real-world soils remains limited. Soil physics/hydrology has traditionally applied findings from fluid mechanics, together with necessary constitutive relations, to develop sets of governing equations. However, heterogeneities, structures, interfaces, roughness, and organisms in multiphase soil systems make the real-world soil deviated significantly from the continuum assumption. This paper synthesizes three principles of water flow in soils and suggests a mosaic theory that explains evolving flow networks embedded in the land surface and subsurface. The first principle came to light in the 19^th century, known as the Darcy’s law, which was later modified by E. Buckingham to describe unsaturated water flow in soils. This principle is essentially a macroscopic view of steady-state water flux being linearly proportional to hydraulic gradient and hydraulic conductivity. The second principle, proposed by L.A. Richards in the 20^th century, describes the minimum pressure gradient needed to initiate water flow through the soil-air interface. This principle is extended here to provide a more cohesive explanation to a number of soil hydrologic phenomena related to various interfaces and microscopic features (such as hysteresis, hydrophobicity, and flow through layered soils). The third principle is emerging in the 21^st century, where a combined macroscopic and microscopic view that portrays mosaic-like complex flow regimes in heterogeneous soils. This principle is tentatively summarized as: Water seldom moves uniformly in natural soils but always displays a dual-flow regime, i.e., it follows the least-resistant or preferred paths when “pushed” (e.g., by storms) or “attracted” (e.g., by plants), and moves diffusively into the matrix when “relaxed” (e.g., at rest) or “touched” (e.g., adsorption). The dynamic interaction between preferential flow and matrix flow domains under changing conditions results in complex and evolving flow networks that are embedded in the matrix of land surface and subsurface.  This leads to a mosaic theory that can be further tested and refined across scales and geographic regions from a growing number of observatories in the world. The implications of these principles and the mosaic theory will be discussed, including flow measurements and modeling.  Further quantification and integration of these flow principles and the mosaic theory in real-world soils and landscapes can lead to improved prediction and enhanced management of soil and water resources.