Averaging or adding domain conductivities to calculate the unsaturated soil hydraulic conductivity

Recent models of the unsaturated hydraulic conductivity curve (UHCC) are the sum of separate UHCCs for domains of capillary water, film water, and water vapor. This requires parallel, noninteracting domains. A theoretical framework for aggregating domain conductivities to a bulk soil UHCC is presented to identify and possibly relax implicit assumptions about domain configuration. The paper develops arithmetic, harmonic, and geometric averages of the liquid-water conductivities that can be arithmetically averaged with the vapor conductivity. However, current models for capillary and film conductivities are intrinsic, that is, valid within their respective domain. The vapor conductivity is a bulk conductivity, that is, it gives the conductivity of the gaseous domain as it manifests itself in the soil. Conversion relationships use the domain volume fractions as approximations of the as-yet unknown weighting factors to convert between intrinsic and bulk conductivities. This facilitates consistent averaging of domain conductivities. Even with consistent averaging, a truly physically accurate model of the UHCC based on domain conductivities is fundamentally elusive. Nevertheless, models based on the three averages and the unweighted sum of the domain conductivities produce good fits to data for two soils but diverge in the dry range. The fitted curves for the capillary and film water depend on the averaging (or adding) method. Hence, they are not strictly characteristic of their respective domains. The true intrinsic domain conductivity functions may be impossible to determine.