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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| Vydáno v: | Water resources research Ročník 36; číslo 4; s. 891 - 910 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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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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(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. 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