Preferential flow prediction—present and future

The generally accepted theory of unsaturated flow, encapsulated in the hundred-year-old Richardson-Richards equation (RRE), has been successful in many situations, especially for diffuse flow through homogeneous granular media with grains and pores of sand-size or smaller. Since the late twentieth century, some version of it has also been the most commonly applied predictor of preferential flow, typically in combination with the RRE in a dual-domain framework in which the parameters take different values in the two domains. Current knowledge of preferential flow processes, however, shows that this extension of its original use is inappropriate. Various alternative formulations have been developed for preferential flow, many of them based on film and wave concepts, but these also have limits on their applicability. They also can be prohibitively awkward to combine with RRE to account for the totality of flow in an unsaturated medium.

Given the different dominant processes of diffuse and preferential flow, the widely used dual-domain framework is appropriate. The RRE is available for flow in the diffuse domain, but improved methods are needed for the other two fundamental components: flow in the preferential domain, and the exchange of water between domains.

For the preferential domain, I suggest these concepts and guiding principles: (1) A flow-velocity parameterization that is generalized, not specifically tied to a particular geometrical form such as films. (2) Variability of volumetric flux that is independent of flow velocity, not inextricably linked to velocity as in the gravity term of the RRE. (3) Gravity is the only significant driving force. (4) The essential constancy and uniformity of gravitational force is a tremendous advantage, and with the absence of pure diffusive flow, it reduces the required variables to just two, flux and water content, as opposed to the triply-coupled water-content/matric-potential/conductivity variables in the RRE. Further consequences are that (a) the basic continuity equation is the central component of a partial differential equation operative within the preferential domain, and (b) flux boundary conditions are the only type possible for this domain. 

Some guidelines for domain exchange are: (1) Flow can go in either direction, seepage as well as abstraction, depending on the diffuse-domain water content. (2) The exchange can be represented as a first-order diffusion process, from the domain interface to an internal position within the diffuse domain; this requires an additional parameter representing the effective lateral distance that this introduced water travels within the diffuse domain.

A formulation based on these principles would require much development and testing, but if implemented with a minimal number of parameters, each of them having a physically meaningful interpretation, it could lead to a more versatile and acceptable way to predict preferential flow than is presently available.