Modelling the Impact of Leaky Barriers with a 1D Godunov-Type Scheme for the Shallow Water Equations

There is increasing interest in distributing small-scale interventions across the landscape as an alternative means of reducing flood risk. One such intervention, the leaky barrier, is introduced in channels to slow down high flows and encourage temporary storage on the floodplain. While these barriers have been implemented widely, there is still resistance to their use at the scales required to impact significantly on flood risk, at least partially due to an evidence gap. In particular, there is no standard method for representing leaky barriers in hydraulic models. This study sets out a methodology for developing mathematical models which capture the hydraulics of leaky barriers accurately, allowing key questions about their combined behaviour in catchments to be answered. A 1D Godunov-type scheme is set up and leaky barriers incorporated with internal boundary conditions. This model is tested against benchmarks from the literature and new steady-state data, and then run predictively on transient cases. The method will help to answer key questions about the optimal leakiness of small-scale interventions, the limits to their usefulness, and how combinations of barriers may or may not cause synchronisation problems when the effect of multiple barriers is aggregated.