On the three‐parameter infiltration equation of Parlange et al. (1982): Numerical solution, experimental design, and parameter estimation

Soil water infiltration is central to hydrologic studies and lends itself for detailed experimentation mathematical–physical modeling. The most rigorous of these approaches numerically solve Richards’ equation, possibly coupled through a heterogeneous soil surface routine groundwater model. This approach computationally expensive prone mass balance errors overparameterization. Analytic solutions the process obviate need specification hydraulic functions simplify computation inverse determination properties. paper investigates usefulness Parlange's three-parameter equation forward modeling vertical experiments. quasi-exact implicit solution also credited Haverkamp coworkers in recent literature, valid entire event, matches cumulative data from different soils its (super-)parameters, S, Ks, β, exhibit solid underpinning. Nonetheless, has not entered mainstream use simulation analysis absence robust, exact efficient numerical solution. builds upon work Jaiswal et al. presents theory, algorithms, source codes two procedures equation. We illustrate using measured Water Infiltration Global (SWIG) database. Our findings highlight potential characterization sorptivity, S [L T−1/2], saturated conductivity, Ks T−1], unitless coefficient, β. provides powerful alternative mathematically more convenient explicit equations that suffer physical underpinning and/or limited time validity.