Articles | Volume 22, issue 3
https://doi.org/10.5194/hess-22-1993-2018
https://doi.org/10.5194/hess-22-1993-2018
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

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Cited articles

Abbott, M. B.: An introduction to the method of characteristics, American Elsevier, New York, 243 pp., 1966.
Abbott, M. B. and Ionescu, F.: On the numerical computation of nearly horizontal flows, J. Hydraul. Res., 5, 97–117, https://doi.org/10.1080/00221686709500195, 1967.
Amein, M.: Streamflow routing on computer by characteristics, Water Resour. Res., 2, 123–130, https://doi.org/10.1029/WR002i001p00123, 1966.
Barré de Saint-Venant, A.-J.-C.: Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leur lit, C. R. Acad. Sci., 73, 147–154, 1871.
Beam, R. M. and Warming, R. F.: Implicit finite-difference algorithm for hyperbolic systems in conservation-law form, J. Comput. Phys., 22, 87–110, https://doi.org/10.1016/0021-9991(76)90110-8, 1976.
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.