Journal cover Journal topic
Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
https://doi.org/10.5194/hess-2017-393
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
09 Aug 2017
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).
Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: theoretical development
Alain Dib and M. Levent Kavvas Department of Civil and Environmental Engineering, University of California, Davis, 95616, USA
Abstract. The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian–Eulerian Fokker–Planck Equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.

Citation: Dib, A. and Kavvas, M. L.: Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: theoretical development, Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-393, in review, 2017.
Alain Dib and M. Levent Kavvas
Alain Dib and M. Levent Kavvas
Alain Dib and M. Levent Kavvas

Viewed

Total article views: 256 (including HTML, PDF, and XML)

HTML PDF XML Total BibTeX EndNote
219 36 1 256 3 3

Views and downloads (calculated since 09 Aug 2017)

Cumulative views and downloads (calculated since 09 Aug 2017)

Viewed (geographical distribution)

Total article views: 256 (including HTML, PDF, and XML)

Thereof 253 with geography defined and 3 with unknown origin.

Country # Views %
  • 1

Saved

Discussed

Latest update: 18 Oct 2017
Publications Copernicus
Download
Short summary
A new method is proposed to solve the stochastic unsteady open-channel flow system in only one single simulation, as opposed to the many simulations usually done in the popular Monte Carlo approach. The derivation of this new method gave a deterministic and linear Fokker–Planck equation whose solution provided a powerful and more efficient approach for quantifying the ensemble behavior and variability of such a stochastic system, regardless of the number of parameters causing its uncertainty.
A new method is proposed to solve the stochastic unsteady open-channel flow system in only one...
Share