Quantification of uncertain bed roughness under design conditions and propagation to the design water levels, a case study for the river Rhine

Hydrodynamic river models are applied to design and evaluate measures for purposes such as safety against flooding. The modeling of river processes involves numerous uncertainties, resulting in uncertain model results. Knowledge of the type and magnitude of these uncertainties is crucial for a meaningful interpretation of the model results. The aim of this study is to quantify the uncertainty due to the hydraulic roughness predictor for the river bed in the main channel and assess its effect on the uncertainty in the modelled water levels under design discharge conditions. This uncertainty in the main channel roughness predictor consists of the uncertainty between different roughness predictors and the uncertainty within each roughness predictor. To assess the uncertainty between the selected roughness predictors, we compared five roughness predictors that computed the hydraulic resistance of the river bed in the Dutch river Rhine, based on measurements of bed forms characteristics and water levels for different discharges. The propagation of this uncertainty to the water levels is carried out using a two dimensional hydrodynamic river model with dimensions similar to the river Rhine in The Netherlands. It is shown that different roughness predictors result in significantly different roughness values for the same measurements of bed form and flow characteristics. To determine the uncertainty between the different roughness predictors under design conditions, the Generalized Extreme Value distribution is used to extrapolate the predicted roughness values for each roughness predictor to design conditions. The uncertainty between and within the roughness predictors are combined to show that with 95% confidence the Nikuradse roughness for the main channel of the river Rhine under design conditions lies between 0.32 m to 1.03 m. The uncertain roughness results in a large uncertainty range in the design water levels of 71 cm.