Analytical solution for one-dimensional water infiltration in rooted soils before and after ponding

Accurately predicting the time to ponding and the infiltration rate after rainfall begins is crucial for runoff prediction, erosion control, agricultural irrigation planning, and slope stability. Previous analytical solutions for ponding prediction have primarily focused on bare soil. This study presents, for the first time, an exact analytical solution for one-dimensional water infiltration in rooted soil both before and after ponding. The advantage of this analytical solution lies in its ability to simulate changes in moisture content distribution both before and after ponding and predict the ponding time and infiltration rate afterward. The solution is derived through a new solution strategy, i.e., the combined use of separation of variables and Duhamel's theorem. Its accuracy has been validated by comparing it with existing analytical solutions for simple cases and numerical solutions for flow in rooted soils. This analytical solution provides a straightforward means to analyze the impacts of key model parameters, including the effects of root water uptake, hydraulic properties, rainfall intensity, and variations in rainfall on moisture content distribution, ponding time, and infiltration rate. New findings indicate that root water uptake delays the ponding time, with the delay effect becoming more pronounced as root water uptake capacity increases. Furthermore, there exists a critical α value that determines the maximum ponding time, for k_s = 1.0 cm hr^-1, this critical α value appears around 0.02 cm⁻¹. Additionally, root water uptake increases the critical rainfall intensity q_cr necessary for ponding to occur. For α = 0.01 cm⁻¹, when root water uptake is 0.0025 hr^-1, the q_cr for rooted soil increases from 1.0 cm hr^-1 in bare soil to 1.072 cm hr^-1.