Fine-scale heterogeneous structure impact on the scale-dependency of the effective hydro-electrical relations of unsaturated soils

Abstract

Non-invasive geo-electrical tools are widely used to monitor vadose zone processes. At the core of these methods is the assumption that the obtained subsurface’s electrical conductivity maps can be translated to hydrological state-variables via site-specific hydro-electrical relations calibrated with laboratory or field data. However, the common practice that assumes spatially homogeneous hydro-electrical relations neglects the impact of soil heterogeneity on those relations and can cause significant errors in translating the electrical measurements to the hydraulic state variables. In this work, numerical simulations conducted on synthetic soil samples with different permeability structures were used to examine the fine-scale heterogeneous structure impact on the hydro-electrical relations calibrated at different measurement scales. Results have shown that the soil’s mm-scale heterogeneous structure significantly impacts the effective hydro-electrical relations scale-dependency, where even for a weakly heterogeneous structure, the calibrated hydro-electrical relations can vary by almost 20% between the 10 and 50 cm measurement scales. Such differences can highly influence the inferred saturation degree, where errors can extend to more than 5%. Furthermore, a stochastic inversion technique was developed based on Approximated Bayesian Computation, to confine the soil’s geostatistical parameters. The proposed approach was tested against two synthetic cases and one realistic case based on experimental data. Results have shown that the proposed approach could detect the actual permeability structure statistical parameters by calibrating the effective hydro-electrical properties at only three different measurement scales.