Approximate analytical solution of a soil water movement equation under different ponding radii on the basis of numerical simulation

This study addresses the problem of 2D soil water movement under ponding radii of 1, 2, and 3 cm. The soil water movement characteristics (shape parameters of the water content profile, ratio of horizontal wetting front to vertical wetting front, relationship between infiltration time and horizontal wetting front, and relationship between infiltration time and cumulative infiltration) under the above three kinds of water ponding radius were analyzed. On the basis of the assumption that the soil wetting body is a semi-ellipse and the analytical solution of the 1D soil water movement equation at any angle, the approximate analytical solution of the 2D soil water movement equation under ponding conditions is optimized. The function relationships between infiltration time, wetting front, and cumulative infiltration are established. We applied the numerical data simulated by HYDRUS-3D to validate the parameters in proposed analytical solutions and evaluated the relationships between the wetting front and hydraulic parameters. The results indicate that as the water ponding radius increases, the wetting body and 2D water content distribution becomes larger. When the water ponding radius was 2 cm, the numerical and analytical solution of 1D soil water distribution showed the best comparison results, and the model error was the smallest. The ratio of wetting fronts was linearly increased with the increase of air-entry suction with R² = 0.9969.