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

Abstract

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