Unsaturated flow in heterogeneous soils with spatially distributed uncertain hydraulic parameters

Journal of Hydrology

Volumn 275, Issue 3-4, 2003, Pages 182-193

  Tartakovsky, Daniel M ^a   Lu, Zhiming ^b   Guadagnini, Alberto ^c   Tartakovsky, Alexandre M ^d  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c POLITECNICO DI MILANO   (Italy)

^d IDAHO NATIONAL LABORATORY   (United States)

Author keywords

Moment equations; Nonlinear; Porous media; Random; Stochastic

Indexed keywords

APPROXIMATION THEORY; FILTRATION; FLOW OF FLUIDS; RANDOM PROCESSES; SOIL MECHANICS;

HETEROGENEOUS SOILS;

HYDRODYNAMICS;

CONFERENCE PROCEEDING; HYDRAULIC CONDUCTIVITY; MATHEMATICAL MODELING; UNSATURATED FLOW; UNSATURATED MEDIUM;

CONFERENCE PROCEEDING; HYDRAULIC PROPERTY; NUMERICAL MODEL; STOCHASTICITY; UNSATURATED FLOW; VADOSE ZONE;

EID: 0037407457     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1694(03)00042-8     Document Type: Conference Paper

References (39)

1. Amir, O., Neuman, S.P., 2001. Gaussian closure of one-dimensional unsaturated flow in randomly heterogeneous soils. Transport in Porous Media 44, 355-383.
2. Clothier, B.E., Scotter, D.R., 1982. Constant flux infiltration from a hemispherical cavity. Soil Science Society of America Journal 46, 696-700.
3. Foussereau, X., Graham, W., Rao, P., 2000. Stochastic analysis of transient flow in unsaturated heterogeneous soils. Water Resources Research 36, 891-910.
4. Gómez-Hernández, J.J., 1991. PhD Thesis, Stanford University.
5. Guadagnini, A., Neuman, S.P., 1999a. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains, 1. Theory and computational approach. Water Resources Research 35, 2999-3018.
6. Guadagnini, A., Neuman, S.P., 1999b. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains, 1. Computational examples. Water Resources Research 35, 3019-3040.
7. Guadagnini, A., Neuman, S.P., 2001. Recursive conditional moment equations for advective transport in randomly heterogeneous velocity fields. Transport in Porous Media 42, 37-67.
8. Indelman, P., Or, D., Rubin, Y., 1993. Stochastic analysis of unsaturated steady-state flow through bounded heterogeneous formations. Water Resources Research 29, 1141-1148.
9. Khaleel, R., Relyea, J.F., 2001. Variability of Gardner's alpha for coarse textured sediments. Water Resources Research 37, 1567-1575.
10. Li, B., Yeh, T.-C.J., 1998. Sensitivity and moment analyses of head in variably saturated regimes. Advances in Water Research 21, 477-485.
11. Lu, Z., Neuman, S.P., Guadagnini, A., Tartakovsky, D.M., 2000. Direct solution of unsaturated flow in randomly heterogeneous soils. In: Bentley, L.R., Sykes, J.F., Brebbia, C.A., Grey, W.G., Pinder, G.F. (Eds.), Proceedings of the XIII International Conference on Computational Methods in Water Resources, vol. 2. Balkema, Rotterdam, pp. 785-792.
12. Mood, M.A., Graybill, F.A., 1963. Introduction to the Theory of Statistics, McGraw-Hill, New York.
13. Neuman, S.P., 1993. Eulerian-Lagrangian theory of transport in space-time nonstationary velocity-fields: exact nonlocal formalism by conditional moments and weak approximation. Water Resources Research 29, 633-645.
14. Neuman, S.P., Orr, S., 1993. Prediction of steady state flow in nonuniform geologic media by conditional moments: exact nonlocal formalism, effective conductivities, and weak approximation. Water Resources Research 29, 341-364.
15. Neuman, S.P., Tartakovsky, D.M., Wallstrom, T.C., Winter, C.L., 1996. Correction to the Neuman and Orr 'Nonlocal theory of steady state flow in randomly heterogeneous media'. Water Resources Research 32, 1479-1480.
16. Phillip, J.R., 1985. Approximate analysis of the borehole permeameter in unsaturated soil. Water Resources Research 21, 1025-1033.
17. Raats, P.A.C., 1976. Analytical solutions of a simplified flow equation. Transactions of the ASAE 19, 683-689.
18. Ragab, R., Cooper, J.D., 1993a. Variability of unsaturated zone water transport parameters: implications for hydrological modeling, 1. In situ measurements. Journal of Hydrology 148, 109-131.
19. Ragab, R., Cooper, J.D., 1993b. Variability of unsaturated zone water transport parameters: implications for hydrological modeling, 2. Predicted vs. in situ measurements and evaluation methods. Journal of Hydrology 148, 133-147.
20. Reynolds, W.D., Elrick, D.E., 1985. In situ measurements of field-saturated hydraulic conductivity, sorptivity and the a-parameter using the Guelph permeameter. Soil Science 140, 292-302.
21. Reynolds, W.D., Elrick, D.E., 1987. A laboratory and numerical assessment of the Guelph permeameter method. Soil Science 144, 282-299.
22. Russo, D., 1983. A geostatistical approach to trickle irrigation design in heterogeneous soil, 1. Theory. Water Resources Research 19, 632-642.
23. Russo, D., 1984. A geostatistical approach to the solute transport in heterogeneous fields and its application to salinity management. Water Resources Research 20, 1260-1270.
24. Russo, D., 1988. Determining soil hydraulic properties by parameter estimation: on the selection of a model for the hydraulic properties. Water Resources Research 24, 453-459.
25. Russo, D., Bouton, M., 1992. Statistical analysis of spatial variability in unsaturated flow parameters. Water Resources Research 28, 1911-1925.
26. Russo, D., Russo, I., Laufer, A., 1997. On the spatial variability of parameters of the unsaturated hydraulic conductivity. Water Resources Research 33, 947-956.
27. Scotter, D.R., Clothier, B.E., Harper, R.E., 1982. Measuring saturated hydraulic conductivity and sorptivity using twin rings. Australian Journal of Soil Research 20, 295-304.
28. Talsma, T., 1987. Re-evaluation of the well permeameter as a field method for measuring hydraulic conductivity. Australian Journal of Soil Research 25, 361-368.
29. Tartakovsky, D.M., 1999. Prediction of steady-state flow of real gases in randomly heterogeneous porous media. Physica D 133, 463-468.
30. Tartakovsky, D.M., 2000. Real gas flow through heterogeneous porous media: theoretical aspects of upscaling. Stochastic Environmental Research and Risk Assessment (SERRA) 133 (2000), 109-122.
31. Tartakovsky, D.M., Guadagnini, A., 2001. Prior mapping for nonlinear flows in random environments. Physical Review E 64, 035302(R)-035302(R).
32. Tartakovsky, D.M., Neuman, S.P., 1998. Transient flow in bounded randomly heterogeneous domains, 1. Exact conditional moment equations and recursive approximations. Water Resources Research 34, 1-12.
33. Tartakovsky, D.M., Neuman, S.P., 1999. Extension of 'Transient flow in bounded randomly heterogeneous domains, 1. Exact conditional moment equations and recursive approximations'. Water Resources Research 35, 1921-1925.
34. Tartakovsky, D.M., Winter, C.L., 2001. Dynamics of free surfaces in random porous media. SIAM Journal on Applied Mathematics 61, 1857-1876.
35. Tartakovsky, D.M., Neuman, S.P., Lu, Z., 1999. Conditional stochastic averaging of steady state unsaturated flow by means of Kirchhoff transformation. Water Resources Research 35, 731-745.
36. Ünlü, K., Nielsen, D.R., Biggar, J.W., Morkoc, F., 1990. Statistical parameters characterizing the spatial variability of selected soil hydraulic properties. Soil Science Society of America Journal 54, 1537-1547.
37. White, I., Sully, M.J., 1992. On the variability and use of the hydraulic conductivity alpha parameter in stochastic treatment of unsaturated flow. Water Resources Research 28, 209-213.
38. Wierenga, P.J., Hills, R.G., Hudson, D.B., 1991. The Las Cruces Trench site: characterization, experimental results, and one-dimensional flow predictions. Water Resources Research 27, 2695-2705.
39. Yeh, T.-C.J., 1989. One-dimensional steady state infiltration in heterogeneous soils. Water Resources Research 25, 2149-2158.