How to Optimally Represent Riverbed Geometry with a Simplified Cross-Section Shape in Shallow Water Models

Riverbed geometry is crucial information of water flow models. Despite precise digital terrain models (DTM) are more widely available at rather reduced costs via RADAR or LIDAR surveys, the river bathymetry remains barely invisible. The only way to precisely measure riverbed geometry would be to carry out field surveys all along the river, which is too costly in reality. The use of physically-based models to simulate flood inundation extend is often hampered by a lack of data regarding the geometry of the riverbed. The bathymetry used is generally highly simplified and interpolated from very few measurement cross-sections. This study investigates how a river cross-section can be simplified into a trapezoidal cross-section shape, based on classically available data. The equivalent cross-section shape is defined by two parameters: the bottom elevation and the bank slope (assumed identical on both sides). The methodology is set up on a 19 km length river (Alzette—Luxembourg) for which the river bed and the floodplain have been measured over 144 cross-sections. A one-dimensional hydraulic model designed using the HEC-RAS software and validated in a previous study is considered here as the reference. For each cross-section, the two parameters are calibrated, by minimising the root mean square error between the real and simplified sections. Three different cost functions are tested, based on: flow area, wet perimeter and hydraulic radius. The “real” and “simplified” hydraulic models are run under steady-state configuration with several discharge values. First results show a relatively small influence of the simplified cross-section shape on water elevation, especially for higher discharge. Next step will be to infer this optimal shape from the partial information given by the DTM.