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

^a Environmental Engineering Section, Dep. of Life Sciences, Aalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
^b City and Environment Section, Aalborg Municipality, Vesterbro 14, DK-9000 Aalborg, Denmark
^c Dep. of Hilly Land Agriculture, National Agricultural Research Center for Western Region, Ikano 2575, Zentsuji, Kagawa, 765-0053 Japan
^d Graduate School of Science and Engineering, Saitama University, 255 Shimo-okubo, Saitama, 338-8570 Japan
^e Soils and Biogeochemistry, Dep. of Land, Air and Water Resources, University of California, Davis, CA 95616

View larger version (23K): [in a new window]   Fig. 1. Value of the three-porosity model (TPM) tortuosity–connectivity parameter, X (Eq. [14]), as a function of soil macroporosity (100) and total porosity ().

View larger version (28K): [in a new window]   Fig. 2. The Campbell SWC model (Eq. [1]; solid lines) fitted to measured data for five Yellow soils. The pF equals log(– in cm H2O) where is the soil–water matric potential. UDP: Ultra-deep plowed, NP: Normal plowed.

View larger version (44K): [in a new window]   Fig. 3. Comparison of the Buckingham–Burdine–Campbell (Eq. [5]) and the three-porosity model (Eq. [12] and [14]) gas diffusivity models with measured data for (a–g) seven Yellow soil layers from Japan, (h–m) 10 Latosol layers from Brazil, and (n–p) three Dutch soils (Freijer, 1994). Values of Campbell b for each soil are given. Values of 100 are given or can be found from Table 1 (as total porosity minus soil–water content at pF 2). In (h–m) the open triangles denote compost-amended soil. UDP: Ultra-deep plowed, NP: Normal plowed.

View larger version (58K): [in a new window]   Fig. 4. Scatter-plot comparison of predicted and measured, relative gas diffusivities in 21 differently textured soils from Europe (first column), 17 Latosols and Yellow soils (Brazil and Japan) (second column), and 22 Andisols and Gray-lowland soils from Japan (third column). Model predictions are (top to bottom): (a–c) the Millington and Quirk (1961) model (MQ [1961]), Eq. [4], (d–f) the Millington and Quirk (1960) model (MQ [160]), Eq. [3], (g–i) the Buckingham–Burdine–Campbell (BBC) model, Eq. [5], (j–l) the macroporosity (100) based Eq. [6], and (m–o) the three-porosity model (TPM) gas diffusivity model, Eq. [12] and [14]. RMSE, root mean square error; AIC, Akaike's information criterion.

View larger version (22K): [in a new window]   Fig. 5. Relation between the Campbell pore-size distribution parameter, b, and the Three-Porosity Model tortuosity–connectivity parameter, X (Eq. [14]), for the 60 soils considered in Fig. 4.