Barry, D. A.Parlange, J.-Y.Li, L.Jeng, D.-S.Crapper, M.2005-12-092005-12-09200510.1016/j.advwatres.2005.03.010https://infoscience.epfl.ch/handle/20.500.14299/221201WOS:0002323285000027472The 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.Lambert W-1 function approximationsAsymptotic expansionsBranch pointIteration schemeLambert W functionSoil-water diffusivityInfiltration rateRichards' equationReal valuesVertical infiltrationHorizontal infiltrationExplicit expressionsNumerical evaluationCumulative storageCulumative infltrationSorptivitytext::journal::journal article::research article