Green–Ampt approximations

Barry, Andrew, Parlange, J.-Y., Li, L., Jeng, D.-S. and Crapper, Martin (2005) Green–Ampt approximations. Advances in Water Resources, 28 (10). pp. 1003-1009. ISSN 0309 1708

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Official URL: http://dx.doi.org/10.1016/j.advwatres.2005.03.010

Abstract

The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W−1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W−1 function and vice versa. An infinite family of asymptotic expansions to W−1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green–Ampt infiltration with immediate ponding), a method is presented for approximating W−1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green–Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10−5%. This error is orders of magnitude lower than any existing analytical approximations.

Item Type: Article
Uncontrolled Keywords: Lambert W−1 function approximations; Asymptotic expansions; Branch point; Iteration scheme
Subjects: H200 Civil Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Becky Skoyles
Date Deposited: 08 Jun 2016 08:46
Last Modified: 08 Jun 2016 08:46
URI: http://nrl.northumbria.ac.uk/id/eprint/27052

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