Modeling Infiltration with Approximate Solutions to Richard’s Equation
Publication: Journal of Hydrologic Engineering
Volume 9, Issue 5
Abstract
Using approximate analytical solutions of the nonlinear Richard’s equation, simple models for the simulation of water content, pressure head, hydraulic head, and infiltration rate profiles, subject to either constant conditions, time-variable rainfall, or redistribution, are developed. New practical expressions for the time to ponding and infiltration rate at the ground surface for a variable rainfall rate are proposed. These physically based expressions preserve the nonlinearity inherent in the differential equation, may be easily incorporated into storm-water management models, and do not require the concept of infiltration rate capacity. The results are obtained by adopting well-known expressions for the soil-water physical relationships and the simultaneous solution of the Richard’s and pressure gradient at the ground equations. To verify the analytical procedure, a new solution of the water-content-based Richard’s equation was developed and tested with respect to experimental values, Philip’s solution, and Parlange’s solution, with excellent agreement. In fact, the present model better predicted the location and shape of the wetting front and the tails after that, than did the classical solutions. The models were also compared with a limited finite-difference solution, with reasonable agreement, and with a solution to the linearized Richard’s equation, with poor agreement. Nonlinearity in the differential equation appears to be an important system feature.
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Published In
Journal of Hydrologic Engineering
Volume 9 • Issue 5 • September 2004
Pages: 421 - 432
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Aug 27, 2002
Accepted: Jan 16, 2004
Published online: Aug 16, 2004
Published in print: Sep 2004
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