Pseudospectral methods provide fast and accurate solutions for the horizontal infiltration equation

Abstract

An extremely fast and accurate pseudospectral numerical method is presented, which can be used in inverse methods for estimating soil hydraulic parameters from horizontal infiltration or desorption experiments. Chebyshev polynomial differentiation in conjunction with the flux concentration formulation of Philip (1973) results in a numerical solution of high order accuracy that is directly dependent on the number of Chebyshev nodes used. The level of accuracy (<0.01% for 100 nodes) is confirmed through a comparison with two different, but numerically demanding, exact closed-form solutions where an infinite derivative occurs at either the wetting front or the soil surface. Application of our computationally efficient method to estimate soil hydraulic parameters is found to take less than one second using modest laptop computer resources. The pseudospectral method can also be applied to evaluate analytical approximations, and in particular, those of Parlange and Braddock (1980) and Parlange et al. (1994) are chosen. It is shown that both these approximations produce excellent estimates of both the sorptivity and moisture content profile across a wide range of initial and boundary conditions and numerous physically realistic diffusivity functions.