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

摘要

Bayesian Inference of Manning's n coefficient in a Storm SurgeModel Framework: comparison between Kalman lter andpolynomial based methodAdil SiripatanaConventional coastal ocean models solve the shallow water equations, which describethe conservation of mass and momentum when the horizontal length scale ismuch greater than the vertical length scale. In this case vertical pressure gradientsin the momentum equations are nearly hydrostatic. The outputs of coastal oceanmodels are thus sensitive to the bottom stress terms de ned through the formulationof Manning's n coefficients. This thesis considers the Bayesian inference problem ofthe Manning's n coefficient in the context of storm surge based on the coastal oceanADCIRC model.In the first part of the thesis, we apply an ensemble-based Kalman filter, thesingular evolutive interpolated Kalman (SEIK) filter to estimate both a constantManning's n coefficient and a 2-D parameterized Manning's coefficient on one idealand one of more realistic domain using observation system simulation experiments(OSSEs). We study the sensitivity of the system to the ensemble size. we also accessthe benefits from using an ination factor on the filter performance.To study the limitation of the Guassian restricted assumption on the SEIK lter,5we 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 theestimation of the 1-D and 2-D Mannning's n coe cient. The gPc is used to build asurrogate model that imitate the ADCIRC model in order to make the computationalcost of implementing the MCMC with the ADCIRC model reasonable.We evaluate the performance of the MCMC-gPc approach and study its robustnessto di erent OSSEs scenario. we also compare its estimates with those resulting fromSEIK in term of parameter estimates and full distributions. we present a full analysisof the solution of these two methods, of the contexts of their algorithms, and makerecommendation for fully realistic application.