Representing channel uncertainty in regional scale inundation models

Flood hazard is typically simulated using hydraulic models that are parameterised with observed river and floodplain bathymetry. However, this approach is fundamentally limited by the lack of observed river bathymetry for most of the world's rivers along with model structures that are inflexible and not designed for large scale application. Therefore, simulating inundation across large areas requires a different approach where bathymetry and friction are estimated as reach averaged components of the hydraulic model from observable variables such as water level and channel width. Where reach averaging means that local variability in width and depth, such as that due to meandering, is ignored or parameterised as a sub-grid process by the model. Here, we present a hydraulic model where the river channel is described by four physically meaningful parameters, which for the first time allows sensitivity to model structure, in terms of geometry, to be assessed. The first two parameters and an explanatory variable (e.g. catchment area) control the channel bank full depth, and a third describes the channel friction. The final parameter describes the channel shape using a power term s, which is used to calculate the flow width for any flow depth given the bank full width and depth. This approach allows the flow width to vary with depth in a flexible manner, but required a novel and computationally efficient regression method for estimating the wetted perimeter to be developed. s can take any value above 0 and produce a real geometry. However, in physical terms, values below 1 result in convex shaped banks, while values above 1 result in concave channels that tend towards rectangular. The river channel model was coupled with a 2D inundation model using a simple to set-up sub-grid scale channel approach. The research questions we then investigated were: 1) How accurately can wetted perimeter be estimated? 2) Can the geometry parameters be clearly identified from water level fluctuations and what other constraining data is valuable? 3) Does the additional geometric flexibility give more accurate simulations than a rectangular channel and what are the main sources of uncertainty? A computationally expensive trapezium method was used to demonstrate that the wetted perimeter estimates were accurate to within 2% during dynamic simulation. The minimum spatiotemporal coverage and number of observations needed to identify the channel parameters was assessed using a twinned modelling approach and a Gauss-Marquardt-Levenberg parameter optimiser. This established that it is possible to identify the channel parameters from moderate to low flow water level fluctuations, given at least two locations and times, although more observations will be needed for real test cases due to model and observation uncertainty. Next the approach was implemented on the River Severn UK using real level data. Channel geometry estimates agreed well with field observations and showed that the power shaped channel geometry obtained via calibration was more realistic than using a rectangular channel. Finally the model was used to simulate a large flood event in 2007, where the sensitivity of the inundation predictions to parameter uncertainty was quantified.