Inverting the Friction Coefficient of Heterogeneous Riverbeds Using 2D Hydraulic Simulations and Fluvial Topo-Bathymetric LiDAR Data

Forecasting the magnitude and frequency of floods has become progressively important under climate change. Flood inundation, determined by flow depth and velocity, results from the interplay between gravitational and frictional forces. Flow resistance, a critical factor in determining velocity, is often parameterized using the roughness coefficient Manning’s n. Despite its importance in geomorphology and hydrology, constraining n in natural rivers remains challenging, as synoptic data on riverbed geometry and roughness are sparse. Topo-Bathymetric LiDAR (TBL) data open up new opportunities to constrain the spatial variation of n in rivers by providing detailed and accurate measurements of riverbed and water surface geometry. This study presents a novel, iterative approach to estimate spatially variable n values across a Digital Elevation Model (DEM), given that the channel bed, water surface, and total discharge are independently constrained. The method adjusts n iteratively until the best agreement between predicted and measured water depth is achieved. The model is first validated on artificial, homogeneous reference surfaces to establish statistical criteria for convergence to an optimal solution. We demonstrate the model's ability to resolve complex n distributions by introducing different n patches with varying patch sizes and testing how backwater effects influence model accuracy across varying channel slopes, n patch sizes, and river discharges. Finally, we apply our approach to a 1 m resolution DEM created from a high-resolution TBL dataset covering the 25 km-long Ardèche Gorge, France. This application highlights the method's effectiveness in natural environments, emphasizing its potential to enhance flow resistance parameterization linked to morphological characteristics when channel bed, water surface, and discharge data are available.