Explicit infiltration equations and the Lambert W-function

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.

Miller, C. T.
Parlange, M. B.
Hassanizadeh, S. M.
Published in:
25 Years of Advances in Water Resources, 259-264
Amsterdam, The Netherlands, Elsevier Science B. V.
Reprinted from Advances in Water Resources 25(8-12): 1119- 1124.

 Record created 2005-12-09, last modified 2018-01-27

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