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-2017-394
© 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: numerical application
Alain Dib and M. Levent Kavvas Department of Civil and Environmental Engineering, University of California, Davis, 95616, USA
Abstract. The characteristic form of the Saint–Venant equations was solved in a stochastic setting by using a newly proposed Fokker–Planck Equation (FPE) methodology. This methodology computes the ensemble behavior and variability of a system by directly solving for its time-space evolutionary probability distribution. The new methodology was tested on a stochastic unsteady open-channel flow problem, with an uncertainty arising from the channel’s roughness coefficient. The computed statistical descriptions of the flow variables were compared to the results obtained through Monte Carlo (MC) simulations in order to evaluate the performance of the FPE methodology. The comparisons showed that the proposed methodology can adequately predict the results of the considered stochastic flow problem, including the ensemble averages, variances, and probability density functions in time and space. However, unlike the large number of simulations performed by the MC approach, only one simulation was required by the FPE methodology. Moreover, the total simulation period of the FPE methodology was significantly smaller than that of the MC approach. As such, the results obtained in this study indicate that the proposed FPE methodology is a powerful and time-efficient approach for predicting the ensemble average and variance behavior, in both space and time, for an open-channel flow process under an uncertain roughness coefficient.

Citation: Dib, A. and Kavvas, M. L.: Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: numerical application, Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-394, in review, 2017.
Alain Dib and M. Levent Kavvas
Alain Dib and M. Levent Kavvas
Alain Dib and M. Levent Kavvas

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Short summary
A newly proposed method is applied to solve the stochastic unsteady open-channel flow system (with an uncertain roughness coefficient) in only one simulation. After comparing its results to those of the Monte Carlo simulations, the new method was found to adequately predict the temporal and spatial evolution of the probability density of the flow variables of the system. This revealed the effectiveness, strength, and time-efficiency of this new method as compared to other popular approaches.
A newly proposed method is applied to solve the stochastic unsteady open-channel flow system...
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