Abstract
We consider infiltration into a soil that is assumed to have hydraulic conductivity of the form K = K Seαh and water content of the form θ = (βK − θ r. Here h denotes capillary pressure head while KS, α, β and θ r represent soil specific parameters. These assumptions linearize the flow equation and permit a closed form solution that displays the roles of all the parameters appearing in the hydraulic function K and θ. We assume KS and θ r to be known. A measurement of diffusivity fixes the product of α and β resulting in a parameter identification problem for one parameter. We show that this parameter identification problem, in some cases, has a unique solution. We also show that, in some cases, this parameter identification problem can have multiple solutions, or no solution. In addition it is shown that solutions to the parameter identification problem can be very sensitive to small changes in the problem data.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cannon, J.R. and D.W. Zachamnn Parameter determination in parabolic partial differential equations from over-specified boundary data. International Journal of Engineering Science. 20 (6), 779–788, 1982.
Clothier, B.E. and I. White. Water diffusivity of a field soil. Soil Sci. Soc. Am. 46, 155–158, 1982.
Hornung,U. Identification of nonlinear soil physical parameters from an input-output experiment. In: P.Deuflhardt and E Harier(Editors), Workshop on Numerical Treatment of Inverse Problems in Differential and Integral Equations. Birkhauser, Boston, Mass, pp. 227–237, 1983.
Kool,J.B., J.C. Parker and M.Th.van Genuchten. Determining soil hydraulic properties from one-step outflow experiments by parameter estimation. I. Theory and numerical studies. Soil Sci. Soc. Am. J., 49, 1348–1354, 1985
Lomen,D.O. and A.W. Warrick. Linearized moisture flow with loss at the soil surface. Soil Sci. Soc. Amer. J. 42: 396–400, 1974.
Milly, P.C.D. Estimation of Brooks-Corey parameters from water retention data. Water Resour. Res., 23 (6), 1085–1089, 1987
Perroux, K.M., P.A.C. Raats and D.E. Smiles. Wetting moisture characteristics curves derived from constant-rate infiltration into this soil samples. Soil Sci Soc. Am., 46, 231–234, 1982
Philip, J.R. Steady Infiltration from buried point sources and spherical cavitities. Water Resour. Res. 4: 1039–1047, 1968.
Philip, J.R. The Theory Infiltration. Advances in Hydrosciences 5: 215–296, 1969.
Philip, J.R. General theorem on steady infiltration from surface sources, with application to point and line sources. Soil Sci. Soc. Amer. Proc. 35: 399–401, 1971.
Poulovassilis,A., M. Polychronides and P. Kerkides. Evaluation of various computational schemes in calculating unsaturated hydraulic conductivity. Agric. Water Management, 13, 317–327, 1988.
Raats, P.A.C. Steady infiltration from line sources and furrows. Soil Sci Soc. Amer. Proc. 35: 709–714, 1970.
Towner G.D. Analyzing one-step outflow experiments to calculate soil-water diffusivities using Gardner’s equation. J. Soil Sci., 33, 351–364, 1982.
Warrick, A.W. Time dependent linearized infiltration. Soil Sci. Soc. Amer. Proc. 38: 383–386, 1974.
White, I. Measured and approximate flux-concentration for absorption of water by soil. Soil Sci. Soc. Am. J., 43, 1074–1080, 1979.
PARAMETER IDENTIFICATION IN A SOL WITH CONSTANT DIFFUSIVITY 769
White, I, D.E. Smiles and K.M. Perroux. Absorption of water by soil: The constant flux boundary condtion.
Zachmann, D.W. A mathematical treatment of infiltration from a line source into an inclined porous medium. Soil Sci. Soc. Amer. J. 42: 685–688, 1978.
Zachmann, D.W. and A.W. Thomas. A mathematical investigation of steady infiltration from line sources. Soil Sci. Soc. Amer. Proc. 37: 495–500, 1973.
Zachmann D.W., P.C.Duchateau and A. Klute. The calibration of the Richards flow equation for a draining colum by parameter identification. Soil Sci. Soc. Am. J. 45, 1012–1015, 1981.
Zachmann D.W., P.C.Duchateau and A. Klute. Simultaneous approximation of water capacity and soil hydraulic conductivity by parameter identification. Soil Sci. 134, 157–163, 1982.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Zachmann, D., White, I. (1991). Parameter Identification in a Soil with Constant Diffusivity. In: Dagan, G., Hornung, U., Knabner, P. (eds) Mathematical Modeling for Flow and Transport Through Porous Media. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2199-8_16
Download citation
DOI: https://doi.org/10.1007/978-94-017-2199-8_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4127-2
Online ISBN: 978-94-017-2199-8
eBook Packages: Springer Book Archive