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

Abstract

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.

Momentum and Energy Predict the Backwater Rise Generated by a Large Wood Jam

“… C A could be used to characterize physical properties of preexisting LW jams (Dixon, 2016; Wohl et al., 2010) and compare LW jams across river systems through collaborative LW data collection (Scott et al., 2019). C A may also be predicted from LW jam length, solid volume fraction, and log diameter, allowing representation of engineered logjam designs in a flood model or network analysis (Hankin et al., 2020; Leakey et al., 2020; Persi et al., 2019; Ruiz Villanueva et al., 2014) as a composite structure (Equations and ). This may improve the design and long‐term assessment of engineered logjams used in river restoration and natural flood management.…”

“…This approach becomes unwieldy for complex jams composed of many logs and for naturally occurring jams with unknown material properties (Manners et al., 2007). The lack of a predictive method for describing a jam's generation of backwater rise has been identified as a significant research gap preventing quantitative comparison of jams across river systems, standardized reporting of jam physical properties (Dixon, 2016; Scott et al., 2019; Wohl et al., 2010), and jam representation in numerical models (Hankin et al., 2020; Leakey et al., 2020; Persi et al., 2019; Ruiz Villanueva et al., 2014).…”

Logjams With a Lower Gap: Backwater Rise and Flow Distribution Beneath and Through Logjam Predicted by Two‐Box Momentum Balance

“…This study provided a prediction of upstream backwater rise and velocity beneath the jam as a function of total discharge and jam geometric features, providing a way to represent jams in numerical flood models and to improve the design and assessment of river restoration and natural flood management projects. This approach allows representation of logjams with a lower gap in a flood model or network analysis (Hankin et al., 2020; Leakey et al., 2020; Persi et al., 2019; Ruiz Villanueva et al., 2014). Prediction of flow distribution and backwater rise due to logjams with a lower gap allows improved design of river restoration interventions that enable river continuity at base flow and achieve varying management goals including fish passage, flood risk, upstream sediment retention, and generation of pools suitable for fish refuge in summer months.…”

“…The increase in upstream water depth, or backwater rise, generated by channel‐spanning logjams has recently been described using a combination of momentum and energy constraints (Follett et al., 2020). Jams with a gap at the bed have been previously modeled as sluices with an empirically determined permeability coefficient (Hankin et al., 2020; Leakey et al., 2020). In this paper we consider flow through the gap using established sluice gate models (Chow, 1959; Henderson, 1966; Malcherek, 2018), together with drag generated by the group of logs in the jam region, which is represented by an adaptation of the law for drag in canopies (Follett et al., 2020).…”

Quantifying the hydrological implications of pre- and post-installation willowed engineered log jams in the Pennine Uplands, NW England

“…Future research is urgently needed for further catchment outlet monitoring, particularly as joined-up catchment-scale restoration projects like this are uncommon. The data and findings on WELJ level induced reach changes will contribute to 1 and 2 dimensional hydraulic models, in particular unit development and structural representation, which are used to predict flood benefits that often underpin flood scheme prefeasibility and options assessment (see Hewett et al, 2020;Leakey et al,2020).…”