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

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Abstract

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-Loève (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.

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Funding

This work was supported by the Office of Sponsored Research (OSR) at King Abdullah University of Science and Technology (KAUSTl, Saudi Arabia (grant number CRG3-2016).

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Authors and Affiliations

  1. King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

    Adil Siripatana & Omar Knio

  2. Laboratoire d’Informatique pour la Mecanique et les Sciences de l’Ingénieur, Paris, France

    Olivier Le Maitre

  3. University of Texas at Austin, Austin, TX, USA

    Clint Dawson

  4. 4700 King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia

    Ibrahim Hoteit

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  1. Adil Siripatana
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  2. Olivier Le Maitre
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  3. Omar Knio
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Correspondence to Ibrahim Hoteit.

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Responsible Editor: Martin Verlaan

This article is part of the Topical Collection on the 19th Joint Numerical Sea Modelling Group Conference, Florence, Italy, 17-19 October 2018

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Siripatana, A., Le Maitre, O., Knio, O. et al. Bayesian inference of spatially varying Manning’s n coefficients in an idealized coastal ocean model using a generalized Karhunen-Loève expansion and polynomial chaos. Ocean Dynamics 70, 1103–1127 (2020). https://doi.org/10.1007/s10236-020-01382-4

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