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

• Published in: Ocean dynamics 2020-08, Vol.70 (8), p.1103-1127
• Main Authors: Siripatana, Adil, Le Maitre, Olivier, Knio, Omar, Dawson, Clint, Hoteit, Ibrahim
• Format: Article
• Language: English
• Subjects: 17-19 October 2018; Algorithms; Applications; Atmospheric Sciences; Bayesian analysis; Chaos; Coefficients; Computer simulation; Coordinate transformations; Covariance; Earth and Environmental Science; Earth Sciences; Engineering Sciences; Feasibility studies; Florence; Fluid- and Aerodynamics; Fluids mechanics; Gaussian process; Geophysics/Geodesy; Italy; Markov analysis; Markov chains; Mathematical models; Mechanics; Monitoring/Environmental Analysis; Numerical models; Ocean models; Ocean, Atmosphere; Oceanography; Oceans; Parameter uncertainty; Parameterization; Parameters; Polynomials; Probability theory; Sciences of the Universe; Statistical inference; Statistical methods; Statistics; Topical Collection on the 19th Joint Numerical Sea Modelling Group Conference; Transformations (mathematics); Two dimensional models
• ISSN: 1616-7341; 1616-7228
• DOI: 10.1007/s10236-020-01382-4

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.