Roughness and Discharge Uncertainty in 1D Water Level Calculations

In this study, we investigate the effect of two key uncertainty sources in one-dimensional (1D) water level calculations: the roughness coefficient and the upstream discharge. The work shows how these two uncertainties, separately and together, propagate through the hydraulic model and result in the uncertainty of water levels. The analysis is conducted for the case of uniformflow in rectangular channels and for steady gradually varied flow in real rivers. In the first case, the exact probability density functions (PDFs) of water levels are obtained analytically through the derived distribution method, while in the second case, the output PDFs are heuristically obtained via Monte Carlo simulations. The results show that (1) the water level PDFs have a lower coefficient of variation than the input PDFs due to the mathematical nature of the relationship between input and output; (2) the propagation of symmetric input distributions through the uniform and steady flow equations determines asymmetric output distributions, due to model nonlinearities. In particular, discharge uncertainty leads to left skewed water level PDFs while roughness uncertainty is responsible for output distributions with heavier right tails. Therefore, in the case of roughness uncertainty, the adoption of symmetrical PDFs would lead to underestimation of high quantiles; (3) water level calculations are more sensitive to uncertainty in the Strickler coefficient rather than in upstream discharge, when the two variables are characterised by the same level of uncertainty, and (4) roughness and discharge uncertainties have a significant effect on the predicted water levels, and they should not be neglected in the practical applications, such as flood forecasting, floodplain mapping and design of flood protection solutions.