Advances in modeling of water in the unsaturated zone

Abstract

This paper reviews recent advances in analytical and numerical solution of problems of water flow through rigid soils in the unsaturated zone. The Richards model remains the most widely accepted and fertile framework for water flow analyses. More general formulations are reserved for the analysis of problems involving macroporosity, thermal effects, and air pressure effects. Many exact and approximate solutions have been derived for particular boundary value problems of homogeneous soils using methods such as quasi-linear analysis, Green-Ampt analysis, perturbation, and the kinematic wave approximation. Numerical simulators have become bigger and more accurate due to improvements in the areas of nonlinear solution procedures, mass conservation, computational efficiency, and computer hardware. Problems of natural heterogeneity have been addressed primarily through application of various stochastic methods to the Richards model. The stochastic formulations generally refute the concept of simple 'equivalent' homogeneous properties, but do themselves offer a certain limited potential for a predictive capability.

Modeling and field evidence of finger formation and finger recurrence in a water repellent sandy soil

“…Mathematical solutions to Richards' equation are inherently stable (in a physical sense) [Milly, 1988], but when hysteresis in the water retention function is incorporated, the mathematical solutions may yield unstable flow as a natural outcome [Nieber, 1996]. This means that not incorporating hysteresis in a model for water repellent or coarse-textured soils may be seriously misleading, especially for solute transport prediction.…”

Infiltration into soils: Conceptual approaches and solutions

“…Because of a series of issues intrinsically related to the nature of the infiltration process, accurate numerical simulation of infiltration remains a challenge, and convergence and stability are continuing problems. Among these issues, we can list the presence of steep wetting fronts; the elliptic form of Richards' equation in saturated domains; the non-mass-conserving of algorithms solving for ; and the fact that -based algorithms cannot be applied to situations where parts of the domain are saturated [Milly, 1985[Milly, , 1988Hills et al, 1989;Kirkland et al, 1992]. Different finite difference algorithms were developed that deal with these issues [Klute, 1952;Hanks and Bowers, 1962;Rubin, 1968;Brandt et al, 1971;Neuman, 1972;Vauclin et al, 1979].…”

Physics of water repellent soils

“…In hydrophilic soils, water can infiltrate as a flat horizontal stable Richards' typewetting front. According to Milly (1988), the wetting front in a hydrophobic soil is unconditionally stable when Richards' equation is used without hysteresis in the soil moisture characteristic curve (Nieber et al, 2000). This paper is divided into several parts.…”