1. Explicit infiltration equations and the Lambert W-function
- Author
-
R. Haverkamp, David Andrew Barry, J-Y Parlange, Miller, C. T., Parlange, M. B., and Hassanizadeh, S. M.
- Subjects
Green-Ampt formula ,Mathematical model ,Ponded conditions ,Water flow ,FLOW ,Quantitative Biology::Tissues and Organs ,Mathematical analysis ,Approximations ,Limiting ,Physics::Geophysics ,Real values ,Talsma-Parlange formula ,Infiltration (hydrology) ,symbols.namesake ,Exact solutions in general relativity ,Lambert W function ,symbols ,Sorptivity ,Water Science and Technology ,Mathematics - Abstract
The Green and Ampt infiltration formula, as well as the Talsma and Parlange formula, are two-parameter equations that are both expressible in terms of Lambert W-functions. These representations are used to derive explicit, simple and accurate approximations for each case. The two infiltration formulas are limiting cases that can be deduced from an existing three-parameter infiltration equation, the third parameter allowing for interpolation between the limiting cases. Besides the limiting cases, there is another case for which the three-parameter infiltration equation yields an exact solution. The three- parameter equation can be solved by fixed-point iteration, a scheme which can be exploited to obtain a sequence of increasingly complex explicit infiltration equations. For routine use, a simple, explicit approximation to the three- parameter infiltration equation is derived. This approximation eliminates the need to iterate for most practical circumstances.
- Published
- 2002