Bayesian inference of spatially varying Manning’s n coefficients in an idealized coastal ocean model using a generalized Karhunen-Loève expansion and polynomial chaos

Autor: Omar M. Knio, Olivier Le Maitre, Clint Dawson, Adil Siripatana, Ibrahim Hoteit
Přispěvatelé: King Abdullah University of Science and Technology (KAUST), Uncertainty Quantification in Scientific Computing and Engineering (PLATON), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas at Austin [Austin]
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Ocean Dynamics
Ocean Dynamics, Springer Verlag, 2020, 70 (8), pp.1103-1127. ⟨10.1007/s10236-020-01382-4⟩
Ocean Dynamics, 2020, 70 (8), pp.1103-1127. ⟨10.1007/s10236-020-01382-4⟩
ISSN: 1616-7341
1616-7228
DOI: 10.1007/s10236-020-01382-4⟩
Popis: Bayesian inference with coordinate transformations and polynomial chaos for a Gaussian process with a parametrized prior covariance model was introduced in Sraj et al. (Comput Methods Appl Mech Eng 298:205–228, 2016a) to enable and infer uncertainties in a parameterized prior field. The feasibility of the method was successfully demonstrated on a simple transient diffusion equation. In this work, we adopt a similar approach to infer a spatially varying Manning’s n field in a coastal ocean model. The idea is to view the prior on the Manning’s n field as a stochastic Gaussian field, expressed through a covariance function with uncertain hyper-parameters. A generalized Karhunen-Loeve (KL) expansion, which incorporates the construction of a reference basis of spatial modes and a coordinate transformation, is then applied to the prior field. To improve the computational efficiency of the method proposed in Sraj et al. (Comput Methods Appl Mech Eng 298:205–228, 2016a), we propose to use two polynomial chaos expansions to (i) approximate the coordinate transformation and (ii) build a cheap surrogate of the large-scale advanced circulation (ADCIRC) numerical model. These two surrogates are used to accelerate the Bayesian inference process using a Markov chain Monte Carlo algorithm. Water elevation data are inverted within an observing system simulation experiment framework, based on a realistic ADCIRC model, to infer the KL coordinates and hyper-parameters of a reference 2D Manning’s field. Our results demonstrate the efficiency of the proposed approach and suggest that including the hyper-parameter uncertainties greatly enhances the inferred Manning’s n field, compared with using a covariance with fixed hyper-parameters.
Databáze: OpenAIRE
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