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.