Revisiting the Douglas–Jones method for modelling unsaturated flow in a cultivated soil

Abstract

Unsaturated flow in cultivated or uncultivated soils can be described by the ψ-based, θ-based or mixed form of the Richards equation. It is well known that the θ-based form is the most accurate one with the smallest mass balance errors. However, this form has the drawback that it is not suitable for saturated–unsaturated or near saturated flows. The ψ-based equation can be applied to any kind of flow but it is generally considered not so accurate as the θ-based equation. It has been shown in the literature that for short time computations, the mixed form of the Richards equation overcomes the mass conservation problems of the ψ-based form, while retaining the advantages of the ψ-based formulation. It is shown in this paper that the ψ-based formulation is more accurate and faster than the mixed form, if the Douglas–Jones predictor–corrector method is used for its solution. This superiority is more obvious in long time simulations, as is the case when the water dynamics of cultivated soils for a whole irrigation period is simulated. The model SWBACROS, which solves the ψ-based form of the Richards equation by the Douglas–Jones and alternatively by the implicit method, is used to prove this point. Also the mixed form of the Richards equation is solved by the implicit method. All the solutions are tested against solutions obtained from the literature. They are also tested against experimental results obtained in a field cultivated with cotton for a period of 5 months.