Estimation of Moisture-Dependent Anisotropy in Effective Unsaturated Hydraulic Conductivity and Moisture-Retention Curve Using Spatial Moments of Moisture Plumes.

We have developed a new approach that uses spatial moments of three-dimensional snapshots of a moisture plume under transient flow conditions to estimate the three-dimensional effective unsaturated hydraulic conductivity tensor. The evolution of the spatial first moment in the vertical (z) direction of a moisture plume is used to determine the vertical velocity (Vz) of the center of the plume. This velocity is then related to the gravity term, dKz(theta)/d(theta), of the moisture-based Richards' equation and thus, the vertical unsaturated hydraulic conductivity can be derived. Afterwards, the rate of changes of the second spatial moments in the x, y, and z directions of the plume are related to the water diffusivity tensor (Dx, Dy, and Dz). Assuming that Dx=Kx/C, Dy=Ky/C, and Dz=Kz/C relations, where C is the moisture capacity term, we solve for Kx, Ky, Kz, and C. Application of the new approach to a field experiment yields an effective unsaturated hydraulic conductivity tensor that exhibits moisture-dependent anisotropy. The effective hydraulic conductivities appear to be consistent with laboratory-measured unsaturated hydraulic conductivity data from small core samples; they also reproduce general behavior of observed moisture plume at the site. Finally, potential applications of the approach to laboratory- and field-scale problems, in conjunction with recently advanced geophysical survey tools, are discussed.