Advances in modeling of water in the unsaturated zone

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.