Articles | Volume 22, issue 3
Hydrol. Earth Syst. Sci., 22, 1993–2005, 2018
Hydrol. Earth Syst. Sci., 22, 1993–2005, 2018

Research article 28 Mar 2018

Research article | 28 Mar 2018

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development

Alain Dib and M. Levent Kavvas 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.

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 effective approach for quantifying the ensemble behavior and variability of such a stochastic system, regardless of the number of parameters causing its uncertainty.