Estimation of unsaturated hydraulic conductivity from morphological analysis of Xray-CT images

Water flow in the vadose zone is strongly non-linear due to the feedback of water flow, saturation, and the associated hydraulic conductivity. Therefore, the simulation of unsaturated flow at the continuum scale is notoriously complicated. Yet, not only the solution of the non-linear partial differential equation itself is difficult, also the appropriate parameterization of the unsaturated hydraulic conductivity function poses a challenge. Frequently, hydraulic conductivity is estimated from the water retention curve using capillary bundle models such as the well-established Mualem model or from pedotransfer functions that hardly include information on the actual pore space morphology. Here, a novel approach is presented to estimate the full unsaturated hydraulic conductivity function from a morphological analysis of Xray-CT images in the following way. First, the local pore space morphology is evaluated to obtain pore radius, Euclidean distances to the pore wall, and connectivity measures. Then, a local hydraulic conductivity and capillary forces are calculated for individual voxels of the images. This already permits to estimate the water retention curve and the water distribution inside the pore space at different levels of saturation. These configurations are then used to calculate an associated continuum scale hydraulic conductivity from dry to fully saturated conditions. This approach can be implemented in image analysis software, e.g. ImageJ, in a straight-forward way and may provide much better and specific estimates of the unsaturated hydraulic conductivity that sensitively affects the simulation of fluid flow in soils and the vadose zone provided satisfactory pore space acquisition with Xray-CT is possible.