Theoretical Appraisal of Field-Capacity Based Infiltration Models and their Scale Parameters

Abstract

In many hydrological applications, the modelling of water infiltration in soil is based either on Richards' equation or on the empirical concept of field-capacity utilized by capacity-type models. These two approaches feature different integration scales, and are often presented as antagonistic, with the former being physically correct and the latter a practical surrogate, however flawed by uncertain parameters. Here, we conducted a theoretical appraisal of a generic capacity model by comparing its predictions of water content in a macroscopic layer subjected to a constant surface infiltration flux with a length-averaged analytical solution of Richards' equation. We show that the choices of the time and spatial scales for the empirical model are not arbitrary, and discuss the cases in which they lead to an agreement with the mechanistic description, for a range of initial and boundary conditions, and for three soil types (sandy, loamy, and clayey). The concept of field-capacity hardly applies for the sandy soil because of its high hydraulic conductivity, but yields good results for finer textured soils. Provided that layer thickness exceeds 15 cm, capacity-type predictions had a 50 probability of being within 20 of mechanistic solutions, without requiring the hydrodynamic characterisation of the soil.