We solve a versatile nonlinear convection-diffusion model for nonhysteretic redistribution of liquid in a finite vertical unsaturated porous column. With zero-flux boundary conditions, the nonlinear boundary-value problem may be transformed to a linear problem which is exactly solvable by the method of Laplace transforms. In principle, this technique applies to arbitrary initial conditions.

The analytic solution for drainage in an initially saturated semi-finite column is compared to previously available approximate analytic solutions, obtained by assuming constant diffusivity, as in the Burgers equation, or by neglecting diffusivity, as in the hyperbolic model. Contrary to popular opinion, the hyperbolic model has more than one shock-free solution in a semi-infinite medium z ⩾ 0, as opposed to an infinite medium z ∈ ℝ. However, both the Burgers equation and an improved hyperbolic model underestimate diffusivity at high liquid contents and consequently overestimate the curvature of the soil liquid content profile.