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

Dib, Alain; Kavvas, M. L.

doi:10.5194/hess-2017-393

Cited by 1 publication

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References 41 publications

(62 reference statements)

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“…This study applied the proposed FPE methodology derived in the companion paper by Dib and Kavvas (2017) with an uncertainty in the roughness coefficient. In fact, the FPE methodology was found to replicate the ensemble average 5 discharge of the MC simulations quite well in both space and time.…”

Section: Discussionmentioning

confidence: 99%

“…The result is shown in Eq. (5), while its detailed derivation can be found in the companion paper by Dib and Kavvas (2017).…”

Section: Saint-venant Equations: Characteristic Form and Ensemble-avementioning

confidence: 99%

“…Therefore, in the wake of the preceding discussions, the first objective of this study is to apply the proposed FPE methodology derived in the companion paper (Dib and Kavvas, 2017) to a representative stochastic unsteady open-channel flow problem in order to solve for the probability density of the state variables of the flow process, and to provide a 5 quantitative description of the expected behavior and variability of the system in one single simulation. The second objective is to evaluate the performance of the proposed methodology and to validate its results by comparing the statistical properties of the flow variables computed by the FPE methodology against those calculated by the MC approach.…”

mentioning

confidence: 99%

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Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: numerical application

Dib¹,

Kavvas²

2017

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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 10 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 15 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.

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Section: Discussionmentioning

confidence: 99%

“…The result is shown in Eq. (5), while its detailed derivation can be found in the companion paper by Dib and Kavvas (2017).…”

Section: Saint-venant Equations: Characteristic Form and Ensemble-avementioning

confidence: 99%

mentioning

confidence: 99%

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Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: numerical application

Dib¹,

Kavvas²

2017

Preprint

Self Cite

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show abstract

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

Cited by 1 publication

References 41 publications

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: numerical application

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: numerical application

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