Stochastic analysis of transient flow in unsaturated heterogeneous soils
A stochastic unsaturated water flow model is developed for heterogeneous soils subject to a transient flow regime. Equations are developed for a fully three‐dimensional soil profile, and results are presented for an example one‐dimensional problem. The model predicts the mean and covariance of the s...
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| Published in: | Water resources research Vol. 36; no. 4; pp. 891 - 910 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Blackwell Publishing Ltd
01.04.2000
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| ISSN: | 0043-1397, 1944-7973 |
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| Abstract | A stochastic unsaturated water flow model is developed for heterogeneous soils subject to a transient flow regime. Equations are developed for a fully three‐dimensional soil profile, and results are presented for an example one‐dimensional problem. The model predicts the mean and covariance of the soil water content, Darcy's flux, and pore water velocity as a function of the boundary flux and saturated hydraulic conductivity statistics. The statistics of the pore water velocity can be used to predict solute transport in soils, as shown by Foussereau et al. [this issue]. Approximate flow‐related moment equations are solved analytically in the Laplace domain. Then, the analytical results are numerically inverted using a modified fast Fourier transform algorithm. The model predictions are compared to results obtained from Monte Carlo simulations for two different boundary flux patterns characteristic of humid climates and two different soil types (a fine sand and a sandy loam). Comparing the approximate solutions of the statistical moments to the outputs of the Monte Carlo simulations shows (1) the dominance of the boundary flux variability over that of the saturated conductivity on the overall prediction uncertainty, particularly at shallow depths, and (2) the good performance of the stochastic unsaturated flow model, particularly for fine‐textured soils subject to boundary fluxes with coefficients of variation up to ∼1.5. As the boundary flux coefficient of variation increases and the soil becomes coarser, the model performance deteriorates because the flow system becomes significantly more nonlinear. |
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| AbstractList | A stochastic unsaturated water flow model is developed for heterogeneous soils subject to a transient flow regime. Equations are developed for a fully three‐dimensional soil profile, and results are presented for an example one‐dimensional problem. The model predicts the mean and covariance of the soil water content, Darcy's flux, and pore water velocity as a function of the boundary flux and saturated hydraulic conductivity statistics. The statistics of the pore water velocity can be used to predict solute transport in soils, as shown by
Foussereau et al.
[this issue]. Approximate flow‐related moment equations are solved analytically in the Laplace domain. Then, the analytical results are numerically inverted using a modified fast Fourier transform algorithm. The model predictions are compared to results obtained from Monte Carlo simulations for two different boundary flux patterns characteristic of humid climates and two different soil types (a fine sand and a sandy loam). Comparing the approximate solutions of the statistical moments to the outputs of the Monte Carlo simulations shows (1) the dominance of the boundary flux variability over that of the saturated conductivity on the overall prediction uncertainty, particularly at shallow depths, and (2) the good performance of the stochastic unsaturated flow model, particularly for fine‐textured soils subject to boundary fluxes with coefficients of variation up to ∼1.5. As the boundary flux coefficient of variation increases and the soil becomes coarser, the model performance deteriorates because the flow system becomes significantly more nonlinear. A stochastic unsaturated water flow model is developed for heterogeneous soils subject to a transient flow regime. Equations are developed for a fully three-dimensional soil profile, and results are presented for an example one-dimensional problem. The model predicts the mean and covariance of the soil water content, Darcy's flux, and pore water velocity as a function of the boundary flux and saturated hydraulic conductivity statistics. The statistics of the pore water velocity can be used to predict solute transport in soils, as shown by Foussereau et al. [this issue]. Approximate flow-related moment equations are solved analytically in the Laplace domain. Then, the analytical results are numerically inverted using a modified fast Fourier transform algorithm. The model predictions are compared to results obtained from Monte Carlo simulations for two different boundary flux patterns characteristic of humid climates and two different soil types (a fine sand and a sandy loam). Comparing the approximate solutions of the statistical moments to the outputs of the Monte Carlo simulations shows (1) the dominance of the boundary flux variability over that of the saturated conductivity on the overall prediction uncertainty, particularly at shallow depths, and (2) the good performance of the stochastic unsaturated flow model, particularly for fine-textured soils subject to boundary fluxes with coefficients of variation up to similar to 1.5. As the boundary flux coefficient of variation increases and the soil becomes coarser, the model performance deteriorates because the flow system becomes significantly more nonlinear. A stochastic unsaturated water flow model is developed for heterogeneous soils subject to a transient flow regime. Equations are developed for a fully three‐dimensional soil profile, and results are presented for an example one‐dimensional problem. The model predicts the mean and covariance of the soil water content, Darcy's flux, and pore water velocity as a function of the boundary flux and saturated hydraulic conductivity statistics. The statistics of the pore water velocity can be used to predict solute transport in soils, as shown by Foussereau et al. [this issue]. Approximate flow‐related moment equations are solved analytically in the Laplace domain. Then, the analytical results are numerically inverted using a modified fast Fourier transform algorithm. The model predictions are compared to results obtained from Monte Carlo simulations for two different boundary flux patterns characteristic of humid climates and two different soil types (a fine sand and a sandy loam). Comparing the approximate solutions of the statistical moments to the outputs of the Monte Carlo simulations shows (1) the dominance of the boundary flux variability over that of the saturated conductivity on the overall prediction uncertainty, particularly at shallow depths, and (2) the good performance of the stochastic unsaturated flow model, particularly for fine‐textured soils subject to boundary fluxes with coefficients of variation up to ∼1.5. As the boundary flux coefficient of variation increases and the soil becomes coarser, the model performance deteriorates because the flow system becomes significantly more nonlinear. |
| Author | Foussereau, X. Graham, W. D. Rao, P. S. C. |
| Author_xml | – sequence: 1 givenname: X. surname: Foussereau fullname: Foussereau, X. – sequence: 2 givenname: W. D. surname: Graham fullname: Graham, W. D. – sequence: 3 givenname: P. S. C. surname: Rao fullname: Rao, P. S. C. |
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Gutjahr, Stochastic analysis of unsaturated flow in heterogeneous soils, 3, Observation and applications, Water Resour. Res., 21, 465-471, 1985c. Zhang, D., T. C. Wallstrom, C. L. Winter, Stochastic analysis of steady state unsaturated flow in heterogeneous media: Comparison of the Brooks-Corey model and Gardner-Russo models, Water Resour. Res., 34, 1437-1449, 1998. Eagleson, P. S., Climate, soil, and vegetation, 3, A simplified model of soil moisture movement in the liquid phase, Water Resour. Res., 14, 722-730, 1978c. Wolfram, S., Mathematica, A System for Doing Mathematics by Computer2, Addison-Wesley-Longman, Reading, Mass., 1991. Eagleson, P. S., Climate, soil, and vegetation, 5, A derived distribution of storm surface runoff, Water Resour. Res., 14, 741-748, 1978e. Russo, D., J. Zaidel, A. Laufer, Stochastic analysis of solute transport in partially saturated heterogeneous soil, 2, Prediction of solute spreading and breakthrough, Water Resour. Res., 30, 781-790, 1994b. 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S., Climate, soil, and vegetation, 7, A derived distribution of annual water yield, Water Resour. Res., 14, 765-776, 1978g. Parlange, M. B., G. G. Katul, R. H. Cuenca, M. L. Kavvas, D. R. Nielsen, M. Mata, Physical basis for a time series model of soil water content, Water Resour. Res., 28, 2437-2446, 1992. 1966; 17 1993; 29 1982; 18 1964; 3 1997 1974 1995 1993 1978; 14 1991 1989; 25 1985; 21 1996; 32 1998; 22 1978 1999 1987; 23 1991; 27 1990 1997; 33 1986; 22 1992; 28 1999; 35 1977; 3 1984 1979; 43 1998; 34 1994; 30 e_1_2_1_20_1 e_1_2_1_41_1 Jury W. A. (e_1_2_1_26_1) 1986; 22 e_1_2_1_24_1 e_1_2_1_45_1 Foussereau X. (e_1_2_1_16_1) e_1_2_1_43_1 e_1_2_1_28_1 e_1_2_1_49_1 e_1_2_1_31_1 e_1_2_1_8_1 e_1_2_1_6_1 e_1_2_1_12_1 Mei C. C. (e_1_2_1_34_1) 1997 e_1_2_1_50_1 e_1_2_1_4_1 e_1_2_1_10_1 e_1_2_1_33_1 e_1_2_1_52_1 e_1_2_1_2_1 e_1_2_1_39_1 e_1_2_1_14_1 e_1_2_1_37_1 e_1_2_1_18_1 Jury W. A. (e_1_2_1_25_1) 1990 Mood A. M. (e_1_2_1_35_1) 1974 e_1_2_1_42_1 e_1_2_1_40_1 e_1_2_1_23_1 e_1_2_1_46_1 e_1_2_1_21_1 e_1_2_1_44_1 Gelhar L. W. (e_1_2_1_17_1) 1993 e_1_2_1_27_1 e_1_2_1_48_1 e_1_2_1_29_1 Journel A. G. (e_1_2_1_22_1) 1978 Wolfram S. (e_1_2_1_47_1) 1991 e_1_2_1_7_1 e_1_2_1_30_1 e_1_2_1_5_1 e_1_2_1_3_1 e_1_2_1_13_1 e_1_2_1_51_1 e_1_2_1_11_1 e_1_2_1_32_1 e_1_2_1_38_1 e_1_2_1_15_1 e_1_2_1_36_1 e_1_2_1_9_1 e_1_2_1_19_1 |
| References_xml | – reference: Mantoglou, A., L. W. Gelhar, Capillary tension head variance, mean soil moisture content, and effective specific soil moisture capacity of transient unsaturated flow in stratified soils, Water Resour. Res., 23, 47-56, 1987a. – reference: Zhang, D., Nonstationary stochastic analysis of transient unsaturated flow in heterogeneous media, Water Resour. Res., 35, 1127-1141, 1999. – reference: Eagleson, P. S., Climate, soil, and vegetation, 5, A derived distribution of storm surface runoff, Water Resour. Res., 14, 741-748, 1978e. – reference: Russo, D., J. Zaidel, A. Laufer, Numerical analysis of flow and transport in a three-dimensional partially saturated heterogeneous soil, Water Resour. Res., 34, 1451-1468, 1998. – reference: Eagleson, P. S., Climate, soil, and vegetation, 4, The expected value of annual evaporation, Water Resour. Res., 14, 731-739, 1978d. – reference: Foussereau, X., W. D. Graham, G. A. Akpoji, G. Destouni, andP. S. C. Rao, Stochastic analysis of transport in unsaturated heterogeneous soils under transient flow regimes,Water Resour. Res., 4. – reference: Wolfram, S., Mathematica, A System for Doing Mathematics by Computer2, Addison-Wesley-Longman, Reading, Mass., 1991. – reference: Polmann, D. J., D. McLaughlin, S. Luis, L. W. Gelhar, R. Abadou, Stochastic modeling of large-scale flow in heterogeneous unsaturated soils, Water Resour. Res., 27, 1447-1458, 1991. – reference: Eagleson, P. S., Climate, soil, and vegetation, 3, A simplified model of soil moisture movement in the liquid phase, Water Resour. Res., 14, 722-730, 1978c. – reference: Harter, T., T.-C. J. Yeh, Flow in unsaturated random porous media, nonlinear numerical analysis and comparison to analytical stochastic models, Adv. Water Resour., 22, 257-272, 1998. – reference: Dagan, G., E. Bresler, Solute dispersion in unsaturated heterogenous soil at field scale, 1, Theory, Soil Sci. Soc. Am. 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| Title | Stochastic analysis of transient flow in unsaturated heterogeneous soils |
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