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

Abstract

Bayesian inference with coordinate transformations and polynomial chaos for a Gaussian process with a parametrized prior covariance model was introduced in [61] 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 [61], 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 to using a covariance with fixed hyper-parameters.

Surrogate recycling for structures with spatially uncertain stiffness

“…Sraj et al [10] propose a procedure that eliminates the requirement of having a priori knowledge of the covariance hyper-parameters using this established Bayesian inference framework in conjunction with the Karhunen-Loève expansion and generalized polynomial chaos expansion. Siripatana et al [11] accelerate this procedure by adding a second, nested generalized polynomial chaos surrogate. However, these studies assume that the covariance hyperparameters of the unknown spatially varying quantity are notoriously intangible.…”

A non‐Gaussian Bayesian filter for sequential data assimilation with non‐intrusive polynomial chaos expansion

“…Nevertheless, the intrusive DO scheme makes widespread adoption time consuming. While there have been several papers on Bayesian inference of parameters from PCE models, [22][23][24][25][26] the advantages posed by PCE in quantifying uncertainty and the availability of non-intrusive numerical schemes and packages 18,27 have only been rarely utilized in sequential non-Gaussian data assimilation. 28 The present article aims to fill this gap.…”