Approximate analytical solution to equation for two-dimensional soil-water movement in ponding infiltration based on numerical simulation

Abstract

A simple analytical solution to two-dimensional (2D) ponding infiltration is essential for designing line-source or drip irrigation. We propose a new and simple approximate analytical method for calculating the 2D distribution of soil water with a 1-cm radius of ponding and uniform initial conditions and for estimating the horizontal and vertical distances of wetting fronts based on soil hydraulic parameters. The method assumes a semi-elliptical soil-wetting pattern and a one-dimensional profile of soil water at an arbitrary infiltration angle to solve the equation for the 2D movement of soil water and cumulative infiltration. We applied the numerical data simulated using HYDRUS-3D to validate the proposed method's parameters and evaluate the relationship between the wetting front and hydraulic parameters. The simulated results indicated that the assumptions were propitious to the fine-texture soils with air-entry suction larger than 10 cm. The ratio between the distances of the horizontal and vertical wetting fronts could be approximately predicted using the air-entry suction by analyzing the numerical results. The fitted results indicated that the parameters of the power function of the relationship between the distances of the horizontal and vertical wetting fronts and infiltration time could be described as polynomial and power functions of the diffusivity of saturated soil water. The approximate analytical solutions for the distance of the horizontal wetting front, depth of the vertical wetting front, and cumulative infiltration agreed well with other numerical simulations.