Mathematical modelling of water and solute movement in ridge plant systems with dynamic ponding

We present a mathematical model that describes the movement of water and solutes in a ridge and furrow geometry. We focus on the effects of two physical processes: root water uptake and pond formation in the furrows. Special attention is paid to the physical description of ponding as an effect of transient rain events. We focus on phenomena taking place in the furrow cross-section, not on the drainage along the furrow. The resulting model comprises a coupled system of partial and ordinary differential equations that describe the mathematical interplay between solute transport, water movement and furrow pond depth. The system of equations is solved numerically using finite element techniques. We conducted numerical simulations to determine how mobile solutes with low buffer powers penetrate into the soil. We considered two cases: low rainfall, in which pond formation does not occur, and high rainfall, in which significant ponding is observed in the furrows. We found, in the presence of roots, that mobile solutes collected into a concentrated spot adjacent to the root system independent of rainfall intensity. In the absence of roots, however, we observed that water infiltration from ponding acted as the dominant transport mechanism for mobile solutes. This resulted in deep solute penetration into the soil when compared with non-ponded furrows.