Three-Porosity Model for Predicting the Gas Diffusion Coefficient in Undisturbed Soil

Abstract

The soil gas diffusion coefficient (DP) and its dependency on air-filled porosity (ε) govern most gas diffusion-reaction processes in soil. Accurate DP(ε) prediction models for undisturbed soils are needed in vadose zone transport and fate models. The objective of this paper was to develop a DP(ε) model with lower input parameter requirement and similar prediction accuracy as recent soil-type dependent models. Combining three gas diffusivity models: (i) a general power-law DP(ε) model, (ii) the classical Buckingham (1904) model for DP at air saturation, and (iii) a recent macroporosity dependent model for DP at −100 cm H2O of soil–water matric potential (ψ), yielded a single equation to predict DP as a function of the actual ε, the total porosity (Φ), and the macroporosity (ε100; defined as the air-filled porosity at ψ = −100 cm H2O). The new model, termed the three-porosity model (TPM), requires only one point (at −100 cm H2O) on the soil–water characteristic curve (SWC), compared with recent DP(ε) models that require knowledge of the entire SWC. The DP(ε) was measured at different ψ on undisturbed soil samples from dark-red Latosols (Brazil) and Yellow soils (Japan), representing different tillage intensities. The TPM and five other DP(ε) models were tested against the new data (17 soils) and data from the literature for additional 43 undisturbed soils. The new TPM performed equally well (root mean square error [RMSE] in relative gas diffusivity <0.027) as recent SWC-dependent DP(ε) models and better than typically used soil type independent models.