Upscaling the Unsaturated Hydraulic Conductivities of Isotropic Soils

Accurate simulation and prediction of flow and transport of solutes in a heterogeneous vadose zone requires the appropriate hydraulic properties corresponding to the spatial scale of interest. Upscaling techniques provide effective properties to describe the vadose zone system's behavior with information collected at a much smaller scale. Realizing that a saturated system can be considered as a special state of the unsaturated system, the methodologies for upscaling the saturated hydraulic conductivity of heterogeneous isotropic porous media under steady-state flow conditions can be extended for upscaling the unsaturated hydraulic conductivity. An advantage of this approach is that the extended upscaling methods are independent of the choice of hydraulic function models. The Matheron, small-perturbation, and self- consistent upscaling methods were used to demonstrate the approach. The extended upscaling methods were tested using multi-step numerical experiments of gravity-induced flow into Miller-similar synthetic soils with different levels of heterogeneity. Results show that, under 3-D flow conditions in isotropic soils, the self- consistent method applies to all the soil heterogeneity conditions considered while the Matheron and small- perturbation methods are acceptable for soil of relatively low variability.