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 x 10(-5)%. This error is orders of magnitude lower than any existing analytical approximations.
Keywords: Lambert W-1 function approximations ; Asymptotic expansions ; Branch point ; Iteration scheme ; Lambert W function ; Soil-water diffusivity ; Infiltration rate ; Richards' equation ; Real values ; Vertical infiltration ; Horizontal infiltration ; Explicit expressions ; Numerical evaluation ; Cumulative storage ; Culumative infltration ; Sorptivity
Record created on 2005-12-09, modified on 2016-08-08