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Scaling of Richards' Equation for Infiltration and Drainage

Dep. of Soil and Water Science, Univ. of Arizona, Tucson 85721

*Corresponding author.

ABSTRACT

Scaling techniques allow a single solution to Richards' equation to suffice for numerous specific cases of water flow in unsaturated soils. Here, such solutions are presented for the well-known hydraulic functions of Brooks and Corey. Infiltration for a constant water content or a constant flux at the soil surface is considered as well as drainage for a semi-infinite profile. Although limited to a single form of hydraulic properties, the results are otherwise more general than those previously available. Of particular interest is that the hydraulic conductivity and air-entry values are embedded within the reduced variables. This is an advantage for computational efficiency, such as when using parameter optimization techniques. Three examples are presented. In the first, a single solution is presented, valid for four combinations of saturated hydraulic conductivity and surface water content. A second example relates to drainage, also with one solution to describe four combinations of physical parameters. The final example is for constant flux infiltration.

Received for publication March 16, 1992.