Estimating the universal scaling of gas diffusion in coarse-textured soils

Abstract

Gas diffusion, D, in partially saturated soils, constitutes a critical topic in soil sciences. However, it is a complex process and this limits its characterization and estimation. In this study, we analyzed and parameterized the soil gas diffusion using a combination of percolation theory (PT) and the effective-medium approximation (EMA). Here, we selected 126 coarse-textured soils with measurements including sand, silt, and clay content, bulk density, organic matter, porosity, soil water content measured at different pressure heads and saturation-dependent gas diffusion. First, we adopted the van Genuchten model, fit it to the soil water retention curve (SWRC), optimized its parameters, and determined the water content at the inflection point. Second, the parameters of the universal scaling law from PT and EMA were optimized by directly fitting the model to the saturation-dependent gas diffusion data. Those parameters are (1) the critical air-filled porosity, εc, (2) the crossover air-filled porosity, εx, at which the gas movement behavior changes from the percolation theory domain to the EMA domain; and (3) the average pore coordination number, z. Next, a multiple linear regression analysis (MLRA) was applied to link εc, εx and z to other soil parameters, such as soil textural and/or hydraulic properties. Uncertainties in our results were evaluated using a jack-knife resampling technique, which involved applying the MLRA more than 7000 times. Results revealed that the most accurate estimations were obtained when both soil textural and hydraulic properties were used simultaneously. However, the use of only soil textural parameters presents practical advantages, as it provides excellent estimations for εx and z, although not for εc. The latter is a critical parameter in the application of the PT and EMA to gas diffusion that requires both the soil basic properties and water saturation curve properties to be correctly estimated.