Abstract
New formulae giving the position of the wetting front and the surface water content during horizontal infiltration when the surface flux is specified are presented. The flux can be any smoothly-varying function of time, though only nonhysteretic flow is modeled. The approximation is in excellent agreement with an exact analytical solution existing for constant boundary flux and a nonlinear Fujita diffusivity. It is also successfully compared with a further exact solution existing for a particular time-varying flux.
Similar content being viewed by others
References
Ames, W. F. 1965,Nonlinear Partial Differential Equations in Engineering, Academic Press.
Bond, W. J., Gardiner, B. N. and Smiles, D. E. 1982, Constant-flux absorption of a tritiated calcium chloride solution by a clay soil with anion exclusion,Soil Sci. Soc. Am. J. 46, 1133–1137.
Bond, W. J. and Phillips, I. R. 1990, Approximate solutions for cation transport during unsteady, unsaturated soil water flow,Water Resour. Res. 26, 2195–2205.
Smiles, D. E., Perroux, K. M., Zegelin, S. J. and Raats, P. A. C. 1981, Hydrodynamic dispersion during constant rate absorption of water by soil,Soil Sci. Soc. Am. J. 45, 453–458.
Boulier, J. F., Parlange, J.-Y., Vauclin, M., Lockington, D. A. and Haverkamp, R. 1987, Upper and lower bounds of the ponding time for near constant surface flux,Soil Sci. Soc. Am. J. 51, 1424–1428.
Broadbridge, P. and White, I. 1988, Constant rate rainfall infiltration: A versatile nonlinear model, 1, Analytical solutions,Water Resour. Res. 24, 145–154.
Elrick, D. E. and Robin, M. J. 1981, Estimating the sorptivity of soils,Soil Sci. 132, 127–133.
Gilding, B. H. 1991, Qualitative mathematical analysis of the Richards equation,Transportin Porous Media 5, 651–666.
Hogarth, W. L., Sardana, V., Watson, K. K., Sander, G. C., Parlange, J.-Y. and Haverkamp, R. 1991, Testing of approximate expressions for soil water status at the surface during infiltration,Water Resour. Res. 27, 1957–1961.
Kutilek, M. and Valentova, J. 1986, Sorptivity approximations,Transport in Porous Media 1, 57–62.
Lockington, D., Parslow, J. and Parlange, J.-Y. 1988, Integral estimates of the sorptivity,Soil Sci. Soc. Am. J. 52, 903–908.
Parlange, J.-Y. 1972, Theory of water movement in soils: 8. One-dimensional infiltration with constant flux at the surface,Soil Sci. 114, 1–4.
Parlange, J.-Y. 1975, On solving the flow equation in unsaturated soils by optimization,Soil Sci. Soc. Am. Proc. 39, 415–418.
Parlange, J.-Y., Hogarth, W. L. and Parlange, M. B. 1984, Optimal analysis of the effect of a surface crust,Soil Sci. Soc. Am. J. 48, 494–497.
Parlange, J.-Y, Hogarth, W. L., Boulier, J. F., Touma, J., Haverkamp, R. and Vachaud, G. 1985, Flux and water content relation at the soil surface,Soil Sci. Soc. Am. J. 49, 285–288.
Parlange, M. B., Prasad, S. N., Parlange, J.-Y. and Römkens, M. J. M. 1992, Extension of the Heaslet-Alksne Technique to Arbitrary Soil Water Diffusivities,Water Resour. Res. 28, 2793–2797.
Perroux, K. M., Smiles, D. E. and White, I. 1981, Water movement in uniform soils during constantflux infiltration,Soil Sci. Soc. Am. J. 45, 237–240.
Rogers, C. and Shadwick, W. F. 1982,Backlund Transformations and their Applications, Academic Press, New York.
Storm, M. L. 1950, Heat conduction in simple metals,J. Appl. Phys. 22, 940–951.
Watson, K. K., Sander, G. C., Sardana, V., Hogarth, W. L., Cunning, I. F. and Parlange, J.-Y. 1990, A comparative study of analytical and numerical solutions of water movement in unsaturated porous materials, in Hogarth, W. L. and Noye, B. J. (eds.),Computational Techniques and Applications: CTAC-89, Hemisphere Publishing, New York, pp. 269–276.
White, I., Smiles, D. E. and Perroux, K. M. 1979, Absorption of water by soil: The constant flux boundary condition,Soil Sci. Soc. Am. J. 43, 659–664.
White, I. and Broadbridge, P. 1988, Constant rate rainfall infiltration: A versatile nonlinear model, 2, Applications of solutions,Water Resour. Res. 24, 155–162.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lockington, D.A., Parlange, J.Y. Approximate formulae for the wetting front position and boundary water-content during horizontal infiltration. Transp Porous Med 18, 95–105 (1995). https://doi.org/10.1007/BF01064673
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01064673