Bayesian Inference of Manning's n coefficient of a Storm Surge Model: an Ensemble Kalman filter vs. a polynomial chaos-based MCMC

Abstract

Conventional coastal ocean models solve the shallow water equations, which describe the conservation of mass and momentum when the horizontal length scale is much greater than the vertical length scale. In this case vertical pressure gradients in the momentum equations are nearly hydrostatic. The outputs of coastal ocean models are thus sensitive to the bottom stress terms defined through the formulation of Manning’s n coefficients. This thesis considers the Bayesian inference problem of the Manning’s n coefficient in the context of storm surge based on the coastal ocean ADCIRC model. In the first part if the thesis, we apply an ensemble-based Kalman filter, the singular evolutive interpolated Kalman (SEIK) filter to estimate both a constant Manning’s n coefficient and a 2-D parameterized Manning’s coefficient on one ideal and one of more realistic domain using observation system simulation experiments (OSSEs). We study the sensitivity of the system to the ensemble size. we also access the benefits from using an inflation factor on the filter performance. To study the limitation of the Guassian restricted assumption on the SEIK filter, we also implemented in the second part of this thesis a Markov Chain Monte Carlo (MCMC) method based on a Generalized Polynomial chaos (gPc) approach for the estimation of the 1-D and 2-D Mannning’s n coefficient. The gPc is used to build a surrogate model that imitate the ADCIRC model in order to make the computational cost of implementing the MCMC with the ADCIRC model reasonable. We evaluate the performance of the MCMC-gPc approach and study its robustness to different OSSEs scenario. we also compare its estimates with those resulting from SEIK in term of parameter estimates and full distributions. we present a full analysis of the solution of these two methods, of the contexts of their algorithms, and make recommendation for fully realistic application.