Spatiotemporal Stochastic Open-Channel Flow. I: Model and Its Parameter Data

Gates, Timothy K.; Al-Zahrani, Muhammad A.

doi:10.1061/(asce)0733-9429(1996)122:11(641)

Cited by 29 publications

(22 citation statements)

References 25 publications

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“…However, some studies have provided median and range values, while others have attempted to fit different probability distributions to the data (Gates and AlZahrani, 1996). Using such information, Manning's n was assumed for this study to be a random variable with a normal distribution having a mean of 0.035 and a standard deviation of 0.005.…”

Section: Estimating the Statistical Characteristics Of Manning's Rougmentioning

confidence: 99%

“…Using such information, Manning's n was assumed for this study to be a random variable with a normal distribution having a mean of 0.035 and a standard deviation of 0.005. The mean and standard deviation were chosen in a way that provides realistic values and distributions of n that fall within the ranges and 25 statistics provided by Gates and AlZahrani (1996) and that conform to the table of typical values in Chow (1959). Moreover, the generated n values from the assumed statistics never fell below 0.01, thus complying with the fact that the roughness coefficients for flows in natural streams and excavated channels are always greater than 0.01 (Chow, 1959).…”

Section: Estimating the Statistical Characteristics Of Manning's Rougmentioning

confidence: 99%

“…While it may be possible to assume that the flow and channel parameters are deterministic so as to obtain a deterministic solution to the Saint-Venant equations, such parameters usually exhibit high uncertainty in the real world (Gates and AlZahrani, 1996;Ercan and Kavvas, 2012a). In fact, uncertainties in these parameters may originate from several factors, including a channel's physical conditions and geometric parameters, its upstream boundary and initial conditions, as well as any lateral inflows (Chow, 1959;Sturm, 2001;Liang and Kavvas, 2008;Ercan and Kavvas, 2012a).…”

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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

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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: Estimating the Statistical Characteristics Of Manning's Rougmentioning

confidence: 99%

Section: Estimating the Statistical Characteristics Of Manning's Rougmentioning

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

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“…MCS is simple to implement; however, it requires considerable computational e ort due to large number of realizations needed. Application of MCS in open channel ow has been reported by Gates and Alzahrani [17,18] for Colombia River in US. The uncertainties in geometrical properties and bed slope are investigated via their distribution functions and, consequently, statistical moments are evaluated for the ow eld.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty analysis of open channel flow: stochastic approach to Advection–Diffusion equation

2017

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Abstract. In uid mechanics applications, transport occurs through the combination of advection and di usion. This paper presents a stochastic approach to describe uncertainty and its propagation based on Advection-Di usion Equation. To assess the uncertainty in initial water depth, random initial condition is imposed on the framework of 1D open cannel ow. Karhunen-Loeve Expansion is adopted to decompose the uncertain parameter in terms of in nite series containing a set of orthogonal Gaussian random variables. Eigenstructures of covariance function associated with the random parameter, which play a key role in computing coe cients of the series, are extracted from Fredhulm's equation. The ow depth is also represented as an in nite series of its moments, obtained via polynomial expansion decomposition in terms of the products of random variables. Coe cients of these series are obtained by a set of recursive equations derived from the ADE. Results highlight the e ect of various statistical properties of initial water depth. The mean value and variance for the ow depth are compared with Monte Carlo Simulation as a reliable stochastic approach. It is found that when higher-order approximations are used, KLE results would be as accurate as the results of MCS, however, with much less computational time and e ort.

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“…Various uncertainties may add to the complexity of solving the Saint-Venant equations (Gates and AlZahrani, 1996a;Ercan and Kavvas, 2012a) and these may correspond to several factors. Physical conditions of open channels may be uncertain due to their high degree of variability (Sturm, 2001).…”

Section: Introductionmentioning

confidence: 99%

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

Dib¹,

Kavvas²

2018

Hydrol. Earth Syst. Sci.

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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 FokkerPlanck 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.

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Spatiotemporal Stochastic Open-Channel Flow. I: Model and Its Parameter Data

Cited by 29 publications

References 25 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

Uncertainty analysis of open channel flow: stochastic approach to Advection–Diffusion equation

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

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