An approximate solution to one-dimensional upward infiltration in soils for a rapid estimation of soil hydraulic properties

Soil hydraulic properties quantify soil pore structure and are essential input parameters for simulating soil hydrological processes in the vadose zone. Although methods have been proposed to estimate soil hydraulic properties, efficient and applicable ones are still scarce. In this study, we derived an approximate solution for a one-dimensional upward infiltration process with initially uniform soil water content distribution. Founded on our solution, a nonlinearly constrained optimization method was developed to simultaneously estimate the parameters Ks and n, hd of the Brooks-Corey model by measuring the upward infiltration process in a 5-cm high soil column. Numerical experiments simulated with Hydrus-1D were performed on six theoretical soils to evaluate the accuracy of the new method. The results indicate that the approximate solution can accurately simulate the upward infiltration process at the low initial soil water content range, with a relative error (Re) of 2.85% to 5.47% for soil water content distribution in space and time. For the cumulative infiltration curve, the Re ranges from 0.2% to 1.01%. The estimated parameters Ks and n, hd of the Brooks-Corey model are close to the actual parameter values, with a Re of 0.59% to 4.68% for n, 0.00% to 7.91% for hd, and 0.50% to 8.83% for Ks, respectively. It is concluded that the new method provides a simple and valuable tool for the accurate estimation of soil hydraulic properties.