Bayesian Inference of Spatially-Varying Manning’s n Coefficients in the Coastal Ocean Using Ensemble Kalman Filter and Polynomial Chaos-Based MCMC
Bayesian inference is commonly used to reduce modeling uncertainties in coastal ocean model, especially for parameter estimation. Based on Bayes rule, the posterior can be sampled either directly, using a Markov chain Monte Carlo (MCMC) approach, or by sequentially processing the data following a data assimilation approach. In this contribution, both a deterministic EnKF and MCMC are used to estimate spatially-varying Manning’s n coefficients given synthetic water elevation data. For an EnKF inference, it is found that with reasonable ensemble size, the filter’s estimate converges to the reference Manning’s field. The parameter search space of the EnKF was enhanced through a Karhunen-Loeve (KL) expansion. We have also iterated on the filter update step to better account for the nonlinearity of the parameter estimation problem. In the second part of this work, a generalized KL expansion, which incorporates the covariance hyper-parameters uncertainty, is applied. A Polynomial Chaos (PC) expansion with similar coordinate transformation is exploited to build a cheap surrogate of the large-scale numerical model ADCIRC to accelerate the MCMC sampling algorithm. Our results demonstrate the efficiency of the proposed approach and suggest that including the hyper-parameters uncertainty greatly enhance the inferred posterior compared to the case with fixed hyper-parameters.
Mr. Adil Siripatana KAUST