A quasi-solution of Richards' Equation for the downward infiltration of water into soil

A new equation is presented that expresses depth Z of soil water content θ at time t as an explicit function of θ and t and holds for all t ≥ 0. The new Z(θ, t) includes the classical J. R. Philip (1957b, c) solution for asymptotically large times. At moderate times, the new Z(θ, t) is matched to the classical Philip solution expressed as ϕt½ + χt + ψt⅔ + ω;t2 + …, where ϕ, χ, ϕ, ω,… are different functions of θ alone. The matching process enables the characterizing functions (or parameters) within Z(θ, t) to be evaluated in straightforward fashion from the moderate-time Philip functions (ϕ, χ, ψ, ω,…). When evaluated for either Philip's data or the Green and Ampt step-function solution, the new Z(θ, t) in each case describes the water content profiles with excellent accuracy for all times. Also, for all t ≥ 0, the new Z(θ, t) can be directly integrated to provide a new equation for cumulative quantity of water infiltrated or flux, both as explicit functions of time.