An analytical solution to Richards' equation for a draining soil profile


  • A. W. Warrick,

  • D. O. Lomen,

  • A. Islas


Analytical solutions are developed for the Richards' equation following the analysis of Broadbridge and White. Included here is the solution for drainage and redistribution of a partially or deeply wetted profile. Additionally, infiltration for various initial conditions is examined as well as evaporation at the upper boundary. In all cases the surface flux is constant, whether it be zero for drainage, positive for infiltration, or negative for evaporation. The solutions assume specific forms for the soil water diffusivity and hydraulic conductivity functions: a(b − θ)−2 and β + γ(b − θ) + λ/[2(b − θ)], respectively. Here θ is the water content and a, b, β, γ, and λ are constants.