Equivalent Parallel and Perpendicular Unsaturated Hydraulic Conductivities: Arithmetic Mean or Harmonic Mean?

Abstract

For saturated flows, it is well known that the equivalent parallel hydraulic conductivity is equal to the arithmetic mean of all individual hydraulic conductivities of the layers parallel to flows, and the equivalent perpendicular hydraulic conductivity is equal to the harmonic mean of all individual hydraulic conductivities of the layers perpendicular to flows. Due to the nonlinear relationship between the unsaturated hydraulic conductivity and the saturation, the validity of the same schemes for unsaturated flows needs to be examined. This study investigated equivalent hydraulic conductivities for unsaturated vertical flows under two distinct soil layering scenarios, layers parallel to flows (i.e., parallel vertical slabs or columns) and layers perpendicular to flows (i.e., horizontal layers). The two scenarios are referred to as the horizontal heterogeneity scenario and vertical heterogeneity scenario, respectively. The main objectives of this study were to: (i) examine the appropriateness of using simple arithmetic and harmonic means of hydraulic conductivity for unsaturated flows for the horizontal and vertical heterogeneity scenarios; and (ii) investigate the equivalent unsaturated hydraulic conductivities that are applicable to large‐scale hydrologic process modeling. The considered domain is typical for unsaturated flow that lies between the ground surface at the top and the groundwater table at the bottom. Results demonstrate that the arithmetic mean for the horizontal heterogeneity scenario and the harmonic mean for the vertical heterogeneity scenario, extended from the saturated flow situations, would introduce large relative errors in simulating the actual flux for coarser textured soils and for heterogeneous soils with large hydraulic parameter variances.