Analytical model of infiltration under constant surface ponding

TL;DR

This paper presents an exact analytical solution to the nonlinear Richards equation for one-dimensional infiltration under constant ponding, providing a versatile model for various soil types and validating previous approximate solutions.

Contribution

It introduces a convergent power series solution for the nonlinear Richards equation applicable to different soils and compares it with existing approximate methods.

Findings

Exact infiltration coefficients are tabulated with higher-order corrections.

The power series solution converges for both small and large times.

Previously published approximate solutions are validated against the exact solution.

Abstract

An analytical solution of the nonlinear Richards equation is presented, for one-dimensional infiltration into a soil of uniform initial moisture content subject to a constant depth of surface ponded water. Adopted mathematical forms of the soil water diffusivity and conductivity are flexible enough to model a range of real soils. The solution takes the form of a power series in $\sqrt t$, but is observed to converge not only for small times but also for relatively large times at which travelling-wave-like behavior is evident. The solution is used to tabulate exact infiltration coefficients with higher-order corrections as the natural nonlinear limit of soil properties is approached. Previously published approximate solutions that apply for a wide range of soil properties are tested against the exact solution and found to be sufficiently accurate.