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Gas Transport Parameters in the Vadose Zone: Development and Tests of Power-Law Models for Air Permeability

^a Graduate School of Science and Engineering, Saitama Univ., 225 Shimo-okubo, Sakura-ku, Saitama, 338-8570, Japan
^b Environmental Engineering Section, Dep. of Biotechnology, Chemistry, and Environmental Engineering, Aalborg Univ., Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
^c Dep. of Agroecology, Danish Inst. of Agricultural Sciences, Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark
^d Dep. of Land, Air, and Water Resources, Univ. of California, Davis, CA 95616

View larger version (33K): [in a new window]   Fig. 1. Log-transformed air permeability, log (ka), and gas diffusivity, log (Dp/D0), as a function of air-filled porosity, , for (a and c) field soils (Gjorslev and Mammen) and for (b and d) lysimeter soils (Rønhave, Foulum, and Jyndevad). The Dp/D0 data are from Kawamoto et al. (2006).

View larger version (14K): [in a new window]   Fig. 2. Comparison of log-transformed air permeability, log(ka), and gas diffusivity, log(Dp/D0), as a function of log-transformed air-filled porosity, log (), for differently textured soils. The tortuosity–connectivity parameter () values for air permeability and gas diffusivity are given; b = Campbell (1974) pore-size distribution parameter.

View larger version (14K): [in a new window]   Fig. 3. The tortuosity–connectivity parameter () values as a function of the Campbell (1974) b for lysimeter soils (Rønhave, Foulum, and Jyndevad). Three expressions for (b), = 2 + 3/b (Burdine, 1953), = 2 + 5/2b (Mualem, 1976), and = 1 + 3/b (Alexander and Skaggs, 1986) are given by solid curves. The = 1 + 0.25b (Moldrup et al., 1998) and = 1 + 0.05b (Moldrup et al., 2001) are given by broken lines.

View larger version (19K): [in a new window]   Fig. 4. Equivalent pore diameter for gas flow (estimated by Eq. [10]) at matric potential of –100 cm H2O (dg,100) as a function of air-filled porosity at matric potential of –100 cm H2O (100) for lysimeter soils and field soils (shallow and deep soil layers).

View larger version (21K): [in a new window]   Fig. 5. Log-transformed air permeability at matric potential of –100 cm H2O [log(ka,100)] as a function of air-filled porosity at matric potential of –100 cm H2O (100) for lysimeter soils and field soils (shallow and deep soil layers). Estimated and regression curves for ka,100 (Eq. [12] with equivalent pore diameter for gas flow estimated by Eq. [10] = 150 µm and Eq. [13]) are given.

View larger version (23K): [in a new window]   Fig. 6. Scatterplot comparison of predicted and measured log-transformed air permeability, log(ka), for lysimeter soils and field soils (shallow and deep soil layers). Predictive models for ka as a function of air-filled porosity [ka()]: (a) ka = ka,100(/100)1+3/b (Eq. [14]); (b) ka = ka,100(/100)X–1 (Eq. [15]); and (c) ka = 700(21003 + 0.04100)(/100)X–1 (Eq. [15] with Eq. [12]); where ka,100 and 100 are the values at matric potential of –100 cm H2O. Calculated RMSE values by Eq. [2] using log(ka) data are given.

View larger version (25K): [in a new window]   Fig. 7. Depth distribution of log-transformed air permeability, log(ka), for (a, b, and c) Gjorslev and (d, e, and f) Mammen at three different soil-water matric potentials of –20, –50, and –160 cm H2O. Averaged measured data and standard deviation of log(ka) are shown. Predicted log(ka) by three different models for ka as a function of air-filled porosity [ka()], ka = ka,100(/100)1+3/b, ka = (8901002.5)(/100)X–1, and ka = 700(21003 + 0.04100)(/100)X–1, are given, where ka,100 and 100 are the values at matric potential of –100 cm H2O.

View larger version (15K): [in a new window]   Fig. 8. Independent test of new models of air permeability as a function of air-filled porosity, ka(), for Hjørring subsurface soils (12 samples from 4–5-m depth and 12 samples from 6–7-m depth): (a) log-transformed air permeability at matric potential of –100 cm H2O, log(ka,100), as a function of air-filled porosity, 100 [estimated and regression curves for ka,100 (Eq. [12] with equivalent pore diameter for gas flow = 150 µm and Eq. [13]) are given]; (b) scatterplot comparison of predicted and measured log(ka). Calculated RMSE values by Eq. [2] using log(ka) data are given.