Modeling Saturated‐Unsaturated Water Flow in Soils
Publication: Journal of Irrigation and Drainage Engineering
Volume 113, Issue 2
Abstract
A model for the transient one‐dimensional water movement in the saturated‐unsaturated zone using a finite difference method with stochastic inputs is developed. Hysteresis in the soil water retention and hydraulic conductivity‐ versus‐moisture content relationship is incorporated. The model considers layered geologic formations with each layer having different parameters. Monte Carlo simulation, together with the nearest neighbor model, is used to incorporate the stochastic nature of hydraulic conductivity into the flow model. Outputs of the flow model include pressure head, water content, and the watertable elevation. Two Monte Carlo simulations of 100 realizations each are made for a 12‐day simulation period. Input standard deviations of the log saturated hydraulic conductivity are assumed to be 20% and 40% of the mean of log saturated conductivity for the two Monte Carlo runs, respectively. The standard deviations of the water‐table elevation and pressure head increase with an increase in the standard deviation of log saturated hydraulic conductivity. The model is applied to predict a long‐term water‐table fluctuation, and the predicted water table agrees well with the observed one.
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References
1.
Baker, F. G., and Bouma, J. (1976). “Variability of hydraulic conductivity in two subsurface horizons of two silt loam soils.” Soil Sci. Soc. Am. Proc., 40, 219–222.
2.
Chung, S. O. (1985). “Stochastic modeling of water movement in the saturated‐unsaturated zone,” thesis presented to Iowa State University, at Ames, Iowa, in partial fulfillment of the requirements for the degree of Doctor of Philosophy (University Microfilm International Order No. 85‐14383, Ann Arbor, Mich.).
3.
Dagan, G. (1979). “Models of groundwater flow in statistically homogeneous porous formations.” Water Resour. Res., 15(1), 47–63.
4.
Douglas, J., and Jones, B. F. (1963). “On predictor‐corrector methods for nonlinear parabolic differential equations.” J. Soc. Ind. and Appl. Math., 11(1), 195–204.
5.
Freeze, R. A. (1969). “The mechanism of natural groundwater recharge and discharge: 1. One‐dimensional, vertical, unsteady, unsaturated flow above a recharging or discharging groundwater flow system.” Water Resour. Res. 5(1), 153–171.
6.
Freeze, R. A. (1975). “A stochastic‐conceptual analysis of one‐dimensional groundwater flow in nonuniform homogeneous media.” Water Resour. Res., 11(5), 725–741.
7.
Fritton, D. D., Kirkham, D., and Shaw, R. H. (1970). “Soil water evaporation, isothermal diffusion, and heat and water transfer.” Soil Sci. Soc. Am. Proc., 34(2), 183–189.
8.
Fujioka, Y., and Kitamura, T. (1964). “Approximate solution of a vertical drainage problem.” J. Geophys. Res., 69(24), 5249–5255.
9.
Gilding, B. H. (1983). “The soil‐moisture zone in a physically‐based hydrologic model.” Adv. in Water Resour. 6, 36–43.
10.
Huggins, L. F., and Monke, E. J. (1968). “A mathematical model for simulating the hydrologic response of a watershed.” Water Resour. Res., 4(3), 529–539.
11.
Molz, F. G., and Remson, I. (1970). “Extraction term models of soil moisture use by transpiring plants.” Water Resour. Res., 6(5), 1346–1356.
12.
Mualem, Y. (1973). “Modified approach to capillary hysteresis based on a similarity hypothesis.” Water Resour. Res., 9(5), 1324–1331.
13.
Mualem, Y. (1974). “A conceptual model of hysteresis.” Water Resour. Res. 10(3), 514–520.
14.
Mualem, Y. (1976). “A new model for predicting the hydraulic conductivity of unsaturated porous media.” Water Resour. Res., 12(3), 513–522.
15.
Mualem, Y. (1977). “Extension of similarity hypothesis used for modeling the soil water characteristics.” Water Resour. Res., 13(4), 773–780.
16.
Mualem, Y., and Dagan, G. (1975). “A dependent domain model of capillary hysteresis.” Water Resour. Res., 11(3), 452–460.
17.
Neuman, S. P. (1973). “Saturated‐unsaturated seepage by finite elements.” J. Hydraul. Div., ASCE, 99(12), 2233–2250.
18.
Neuman, S. P., Feddes, R. A., and Bresler, E. (1974). “Finite element simulation of flow in saturated‐unsaturated soils considering water uptake by plants.” Israel Inst. of Tech., Hydrodyn. & Hydraul. Engrg. Lab., Haifa, Israel.
19.
Nielsen, D. R., Biggar, J. W., and Erh, K. T. (1973). “Spatial variability of fieldmeasured soil‐water properties.” Hilgardia, 42(7), 215–259.
20.
National Oceanic and Atmospheric Administration (NOAA). (1985). Climatological data. NOAA, Iowa City, Iowa.
21.
Saxton, K. E., Johnson, H. P., and Shaw, R. H. (1974). “Watershed evapotranspiration estimated by the combination method.” Trans. ASAE, 17(4), 668–672.
22.
Smith, L. (1978). “A stochastic analysis of steady‐state groundwater flow in a bounded domain,” thesis presented to the University of British Columbia, at Vancover, B.C., Canada, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
23.
Smith, L., and Freeze, R. A. (1979a). “Stochastic analysis of steady state groundwater flow in a bounded domain: 1. One‐dimensional simulations.” Water Resour. Res., 15(3), 521–528.
24.
Smith, L., and Freeze, R. A. (1979b). “Stochastic analysis of steady state groundwater flow in a bounded domain: 2. Two‐dimensional simulations.” Water Resour. Res., 15(6), 1543–1559.
25.
Smith, L., and Schwartz, F. W. (1980). “Mass transport: 1. A stochastic analysis of macroscopic dispersion.” Water Resour. Res., 16(2), 303–313.
26.
Soil Conservation Service. (1975). Soil Survey: Webster County, Iowa, U.S. Department of Agriculture, SCS, Washington, D.C.
27.
Van Genuchten, M. T. (1980). “A closed‐form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J., 44, 892–898.
28.
Van Genuchten, M. T. (1982). “A comparison of numerical solutions of the one‐dimensional unsaturated‐saturated flow and mass transport equations.” Adv. in Water Resour., 5, 47–55.
29.
Willardson, L. S., and Hurst, R. L. (1965). “Sample size estimates in permeability studies.” J. Irrig. Drain. Div., ASCE, 91(1), 1–9.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 113 • Issue 2 • May 1987
Pages: 233 - 250
Copyright
Copyright © 1987 ASCE.
History
Published online: May 1, 1987
Published in print: May 1987
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