An overview of uncertainty quantification techniques with application to oceanic and oil‐spill simulations

Iskandarani, Mohamed; Wang, Shitao; Srinivasan, Ashwanth; Thacker, W. C.; Winokur, Justin; Knio, Omar M.

doi:10.1002/2015jc011366

Cited by 32 publications

(25 citation statements)

References 47 publications

(86 reference statements)

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“…[]; Iskandarani et al . [] for more discussion on these issues. Another benefit of PC methods is the ability to perform analysis in the uncertain space: statistical moments can be computed by integration of the basis functions, and gradients by differentiation; for example:

E [M] = \int ρ (ξ) Ψ_{n} (ξ) d ξ \approx \sum_{n = 0}^{P} {\overset{M}{true}}_{n} \int ρ (ξ) Ψ_{n} (ξ) d ξ

\frac{\partial M}{\partial ξ} \approx \sum_{n = 0}^{P} {\overset{M}{true}}_{n} \frac{\partial Ψ_{n}}{\partial ξ}

where the operator

E []

denotes expectation.…”

Section: Eof Analysis and Pc Perturbationsmentioning

confidence: 99%

“…Different flavors of polynomial chaos methods can be derived depending on the choice of basis functions, and on the method used to determine the coefficients; an overview of these different techniques is presented in Iskandarani et al . []. Here we rely on the Galerkin projection approach [ Le Maître and Knio , ; Iskandarani et al ., ]: the basis functions are orthogonal polynomials with respect to the probability density function (pdf)

ρ (ξ)

of the uncertain variable:

true〈 Ψ_{m}, Ψ_{n} true〉 = \int Ψ_{m} (ξ) Ψ_{n} (ξ) ρ (ξ) d ξ = δ_{m, n} | | Ψ_{m} | |^{2};

and the series coefficients are determined by Galerkin projection with the integrals evaluated using numerical quadrature:

{\overset{M}{true}}_{n} (x, t) = \frac{true〈 M, Ψ_{n} true〉}{| | Ψ_{n} | |^{2}} \approx \frac{{〈 M, Ψ_{n} 〉}_{Q}}{| | Ψ_{n} | |^{2}} = \frac{1}{| | Ψ_{n} | |^{2}} \sum_{q = 1}^{Q} M (x, t, ξ_{q}) ω_{q} .

…”

Section: Introductionmentioning

confidence: 99%

“…We focus primarily on the implementation of the uncertainty analysis and refer the reader to Iskandarani et al . [] for the description of the PC methodology. Section 2 describes the construction of EOF perturbations designed to target uncertainties associated with Loop Current frontal dynamics; it also describes the PC‐ensemble used to compute the series coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…Mðx; t; nÞ M P ðx; t; nÞ5 X P n50 b M n ðx; tÞ W n ðnÞ (1) chosen basis functions. Different flavors of polynomial chaos methods can be derived depending on the choice of basis functions, and on the method used to determine the coefficients; an overview of these different techniques is presented in Iskandarani et al [2016]. Here we rely on the Galerkin projection approach [Le Maître and Knio, 2010;Iskandarani et al, 2016]: the basis functions are orthogonal polynomials with respect to the probability density function (pdf) qðnÞ of the uncertain variable:…”

Section: Introductionmentioning

confidence: 99%

“…In the following sections, we illustrate the application of the PC approach to quantify the uncertainties in the HYCOM forecast caused by uncertainties in the initial conditions. We focus primarily on the implementation of the uncertainty analysis and refer the reader to Iskandarani et al [2016] for the description of the PC methodology. Section 2 describes the construction of EOF perturbations designed to target uncertainties associated with Loop Current frontal dynamics; it also describes the PC-ensemble used to compute the series coefficients.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Quantifying uncertainty in Gulf of Mexico forecasts stemming from uncertain initial conditions

Iskandarani

Hénaff

Thacker³

et al. 2016

JGR Oceans

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Polynomial Chaos were used to quantify uncertainties in oceanic forecasts caused by initial conditions uncertainties.• Uncertainty in the strength of a frontal eddy controls uncertainty in the forecast.• Variance analysis suggests a loss of predictability in SSH in the Loop Current pinch-off region after day 20. Abstract.Polynomial Chaos (PC) methods are used to quantify initial conditions uncertainties in oceanic forecasts of the Gulf of Mexico circulation. Empirical Orthogonal Functions are used as initial conditions perturbations with their modal amplitudes considered as uniformly distributed uncertain random variAtmospheric Science, ables. These perturbations impact primarily the Loop Current system and several frontal eddies located in its vicinity. A small ensemble is used to sample the space of the modal amplitudes and to construct a surrogate for the evolution of the model predictions via a non-intrusive Galerkin projection. The analysis of the surrogate yields verification measures for the surrogate's reliability and statistical information for the model output. A variance analysis indicates that the sea surface height predictability in the vicinity of the Loop Current is limited to about 20 days.

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E [M] = \int ρ (ξ) Ψ_{n} (ξ) d ξ \approx \sum_{n = 0}^{P} {\overset{M}{true}}_{n} \int ρ (ξ) Ψ_{n} (ξ) d ξ

\frac{\partial M}{\partial ξ} \approx \sum_{n = 0}^{P} {\overset{M}{true}}_{n} \frac{\partial Ψ_{n}}{\partial ξ}

where the operator

E []

denotes expectation.…”

Section: Eof Analysis and Pc Perturbationsmentioning

confidence: 99%

ρ (ξ)

of the uncertain variable:

true〈 Ψ_{m}, Ψ_{n} true〉 = \int Ψ_{m} (ξ) Ψ_{n} (ξ) ρ (ξ) d ξ = δ_{m, n} | | Ψ_{m} | |^{2};

and the series coefficients are determined by Galerkin projection with the integrals evaluated using numerical quadrature:

{\overset{M}{true}}_{n} (x, t) = \frac{true〈 M, Ψ_{n} true〉}{| | Ψ_{n} | |^{2}} \approx \frac{{〈 M, Ψ_{n} 〉}_{Q}}{| | Ψ_{n} | |^{2}} = \frac{1}{| | Ψ_{n} | |^{2}} \sum_{q = 1}^{Q} M (x, t, ξ_{q}) ω_{q} .

…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantifying uncertainty in Gulf of Mexico forecasts stemming from uncertain initial conditions

Iskandarani

Hénaff

Thacker³

et al. 2016

JGR Oceans

Self Cite

View full text Add to dashboard Cite

show abstract

Propagation of uncertainty and sensitivity analysis in an integral oil‐gas plume model

Wang

Iskandarani

Srinivasan³

et al. 2016

JGR Oceans

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Polynomial Chaos expansions are used to analyze uncertainties in an integral oil‐gas plume model simulating the Deepwater Horizon oil spill. The study focuses on six uncertain input parameters—two entrainment parameters, the gas to oil ratio, two parameters associated with the droplet‐size distribution, and the flow rate—that impact the model's estimates of the plume's trap and peel heights, and of its various gas fluxes. The ranges of the uncertain inputs were determined by experimental data. Ensemble calculations were performed to construct polynomial chaos‐based surrogates that describe the variations in the outputs due to variations in the uncertain inputs. The surrogates were then used to estimate reliably the statistics of the model outputs, and to perform an analysis of variance. Two experiments were performed to study the impacts of high and low flow rate uncertainties. The analysis shows that in the former case the flow rate is the largest contributor to output uncertainties, whereas in the latter case, with the uncertainty range constrained by aposteriori analyses, the flow rate's contribution becomes negligible. The trap and peel heights uncertainties are then mainly due to uncertainties in the 95% percentile of the droplet size and in the entrainment parameters.

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Quantifying uncertainties in fault slip distribution during the Tōhoku tsunami using polynomial chaos

et al. 2017

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An efficient method for inferring Manning's n coefficients using water surface elevation data was presented in Sraj et al.[1] focusing on a test case based on data collected during the Tōhoku earthquake and tsunami. Polynomial chaos expansions were used to build an inexpensive surrogate for the numerical model GeoClaw, which were then used to perform a sensitivity analysis in addition to the inversion. In this paper, a new analysis is performed with the goal of inferring the fault slip distribution of the Tōhoku earthquake using a similar problem setup. The same approach to constructing the PC surrogate did not lead to a converging expansion, however an alternative approach based on Basis-Pursuit DeNoising was found to be suitable. Our result shows that the fault slip distribution can be inferred using water surface elevation data whereas the inferred values minimizes the error between observations and the numerical model. The numerical approach and the resulting inversion are presented in this work.

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An overview of uncertainty quantification techniques with application to oceanic and oil‐spill simulations

Cited by 32 publications

References 47 publications

Quantifying uncertainty in Gulf of Mexico forecasts stemming from uncertain initial conditions

Quantifying uncertainty in Gulf of Mexico forecasts stemming from uncertain initial conditions

Propagation of uncertainty and sensitivity analysis in an integral oil‐gas plume model

Quantifying uncertainties in fault slip distribution during the Tōhoku tsunami using polynomial chaos

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