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Bimodal Probability Law Model for Unified Description of Water Retention, Air and Water Permeability, and Gas Diffusivity in Variably Saturated Soil

^a Section for Environmental Engineering, Dep. of Life Sciences, Aalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
^b Dep. of Hilly Land Agriculture, National Agricultural Research Center for Western Region, Ikano 2575, Zentsuji, Kagawa, 765-0053, Japan
^c Dep. of Biological and Environmental Sciences, Graduate School of Science and Engineering, Saitama University, 255, Shimo-okubo, Sakura-ku, Saitama, 338-8570 Japan. T.G. Poulsen, currently: Section for Environmental Engineering, Dep. of Life Sciences, Aalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark

View larger version (29K): [in a new window]   Fig. 1. Sampling locations for the 14 soils used in the study.

View larger version (25K): [in a new window]   Fig. 2. Soil properties: (a, b) soil water retention, (c, d) hydraulic conductivity, (e, f) air permeability, and (g, h) gas diffusivity as functions of fluid phase (air or water) content for the Tsumagoi 3 and 7 soils. Also shown are Campbell (1974)–type power function models used to predict these parameters. Curves in Fig. 2c and 2d indicate the Campbell model using saturated hydraulic conductivity and hydraulic conductivity at –10 cm H2O soil water potential as reference point, respectively.

View larger version (30K): [in a new window]   Fig. 3. Campbell constitutive model slope for (a) soil water retention, (b) hydraulic conductivity, (c) air permeability and relative gas diffusivity, and (d) values of constitutive Campbell model slopes for the Tsumagoi 3, 4, 6, and 7 soils for hydraulic conductivity, air permeability and relative gas diffusivity. Also shown in Fig. (d) are the corresponding Campbell slopes proposed in literature (solid and dotted curves).

View larger version (33K): [in a new window]   Fig. 4. Measured and bimodal probability law (BPL) model (Eq. [2]) fitted values of soil water content as a function of minimum soil water potential given as pF (pFmax = 6.9) minus actual soil water potential measured as pF for nine volcanic ash soils. Curves indicate fitted BPL model (Eq. [2]) and Terms 1 and 2 in the BPL model, respectively.

View larger version (25K): [in a new window]   Fig. 5. Measured and bimodal probability law (BPL) model (Eq. [2]) fitted values of hydraulic conductivity as a function of soil water content for four volcanic ash soils. Curves indicate fitted BPL model (Eq. [2]) and Terms 1 and 2 in the BPL model, respectively.

View larger version (31K): [in a new window]   Fig. 6. Measured and bimodal probability law (BPL) model (Eq. [2]) fitted values of air permeability as a function of air-filled porosity for eight volcanic ash soils. Curves indicate fitted BPL model (Eq. [2]) and Terms 1 and 2 in the BPL model, respectively.

View larger version (31K): [in a new window]   Fig. 7. Measured and bimodal probability law (BPL) model (Eq. [2]) fitted values of relative gas diffusivity as a function of air-filled porosity for nine volcanic ash soils. Curves indicate fitted BPL model (Eq. [2]) and Terms 1 and 2 in the BPL model, respectively.

View larger version (28K): [in a new window]   Fig. 8. Rate of change in hydraulic conductivity, air permeability, and relative gas diffusivity with volumetric phase (air or water) content for the Tsumagoi 3 soil calculated by the fitted bimodal probability law (BPL) model as a function of volumetric phase content.

View larger version (23K): [in a new window]   Fig. 9. The bimodal probability law (BPL) model constant B1 for hydraulic conductivity, air permeability and relative gas diffusivity as a function of B1 for soil water retention for the Tsumagoi 3, 4, 6, 7; Miura 1; Tsukuba; Alakawa; and Toyohashi soils.

View larger version (26K): [in a new window]   Fig. 10. Saturated hydraulic conductivity for 10 soils as a function of air permeability at –100 cm soil water potential. Indicated also is the empirical model for predicting KS from ka100 by Loll et al. (1999). Also shown are measurements of relative gas diffusivity for eight soils as a function of ka100.