Explicit infiltration equations and the Lambert W-function

The Green and Ampl infiltration formula. as well as the T,llsmll and Parlangc formula. arc two-parameter equations that arc both expressible in h::rms of Lambert IV-functions. These representations are used to derive explicit. simple and accurate approximations for each CllSl.'. The IWO infiltmlion fonnulas are limiting caSt-os that can be deduced from an existing three.par.lmeter in· filtmtion equation. the third parameter allowing for intcrpolation between the limiting cases. Besides the limiting cases. therc is another case for .... hich the three.parametcr infiltration equation yields an cxact solution. The three-parametcr equation can be sol\'ed by fi.'ted-point iterdtion. a scheme .....hich C-dn 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 practK:-.I1 circumstances. e 2002 Elsevier Science Ltd. All rightS rcservcd.