â€‹Bayesian Inference of Manning's n coefficient in a Storm Surge
Model Framework: comparison between Kalman lter and
polynomial based method
Adil Siripatana
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 de ned 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 of 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 in
ation factor on the filter performance.
To study the limitation of the Guassian restricted assumption on the SEIK lter,
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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 coe cient. 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 di erent 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.

DOI: 10.25781/KAUST-UY76S