Finite difference and finite element simulation of field water uptake by plants

The problem of non-steady flow of water in a soil-plant system can be described by adding a sink term to the continuity equation for soil water flow. In this paper the sink term is defined in two different ways. Firstly it is considered to be dependent on the hydraulic conductivity of the soil, on the difference in pressure head between the soil and the root-soil interface and some root effectiveness function. Secondly the sink is taken to be a prescribed function of the soil water content. The partial differential equation applying to the first problem is solved by both a finite difference (FD 1) and a finite element (FE 1) technique, that applying to the second problem by a finite difference approach (FD 2). The purpose of this paper is to verify the numerical models against field measurements, to compare the results obtained by the three numerical methods and to show how the finite element method can be applied to complex but realistic two-dimensional flow situations. Two examples are given. The first concerns one-dimensional flow and it compares numerical results with those obtained experimentally in the field from water balance studies on red cabbage (Brassica oleracea L. ‘Rode Herfst’) grown on a clay soil in the presence of a water table. The second example describes two-dimensional flow in a complex field situation in the Netherlands where flow takes place under cropped field conditions through five anisotropic layers. Water is supplied to the system by infiltration from two unlined ditches and is withdrawn from the system by evapotranspiration and by leakage to an underlying pumped aquifer.