Environmental Modeling & Assessment

, Volume 20, Issue 4, pp 343–353 | Cite as

Roughness and Discharge Uncertainty in 1D Water Level Calculations

  • Silvia Bozzi
  • Giuseppe Passoni
  • Pietro Bernardara
  • Nicole Goutal
  • Aurélie Arnaud


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 uniform flow 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.


Uncertainty analysis Flood risk assessment Hydraulic models Monte Carlo 



This work is part of the research project Incertitudes conceived within the framework agreement between EDF and Politecnico di Milano. The authors would like to acknowledge Giulia Galli for the Monte Carlo simulations and Federico Malgarini for his preliminary analysis. We are also grateful to Ivo Fresia for his valuable advice on hydraulic modelling of the Po River, Diego Noja for fruitful discussions on the analytical methods and Etienne de Rocquigny for his contribution in the project set up. The hydrological and topographical data of the Po River and Garonne River have been provided respectively by the Interregional Agency for the Po River (AIPO) and the Direction Départementale de l’Equipement du Lot et Garonne.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Silvia Bozzi
    • 1
  • Giuseppe Passoni
    • 1
  • Pietro Bernardara
    • 2
  • Nicole Goutal
    • 2
  • Aurélie Arnaud
    • 3
  1. 1.Department of Electronics, Information Science, and BioengineeringPolitecnico di MilanoMilanItaly
  2. 2.Laboratory for Hydraulics Saint-Venant (LHSV)EDF R&DChatouFrance
  3. 3.EDF R&DChatouFrance

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