Polynomial Chaos–Based Bayesian Inference of K-Profile Parameterization in a General Circulation Model of the Tropical Pacific

Abstract
The authors present a polynomial chaos (PC)-based Bayesian inference method for quantifying the uncertainties of the K-profile parameterization (KPP) within the MIT general circulation model (MITgcm) of the tropical Pacific. The inference of the uncertain parameters is based on a Markov chain Monte Carlo (MCMC) scheme that utilizes a newly formulated test statistic taking into account the different components representing the structures of turbulent mixing on both daily and seasonal time scales in addition to the data quality, and filters for the effects of parameter perturbations over those as a result of changes in the wind. To avoid the prohibitive computational cost of integrating the MITgcm model at each MCMC iteration, a surrogate model for the test statistic using the PC method is built. Because of the noise in the model predictions, a basis-pursuit-denoising (BPDN) compressed sensing approach is employed to determine the PC coefficients of a representative surrogate model. The PC surrogate is then used to evaluate the test statistic in the MCMC step for sampling the posterior of the uncertain parameters. Results of the posteriors indicate good agreement with the default values for two parameters of the KPP model, namely the critical bulk and gradient Richardson numbers; while the posteriors of the remaining parameters were barely informative. © 2016 American Meteorological Society.

Citation
Sraj I, Zedler SE, Knio OM, Jackson CS, Hoteit I (2016) Polynomial Chaos–Based Bayesian Inference of K-Profile Parameterization in a General Circulation Model of the Tropical Pacific. Monthly Weather Review 144: 4621–4640. Available: http://dx.doi.org/10.1175/MWR-D-15-0394.1.

Acknowledgements
This research made use of the resources of the Supercomputing Laboratory and computer clusters at King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. IS, SZ, CJ, and IH are supported in part by KAUST Award CRG-1-560 2012-HOT-007; SZ and OK are supported in part by the Office of Advance Scientific Computing Research, U.S. Department of Energy, under Award DE-SC0008789.

Publisher
American Meteorological Society

Journal
Monthly Weather Review

DOI
10.1175/MWR-D-15-0394.1

arXiv
1510.07476

Additional Links
http://journals.ametsoc.org/doi/10.1175/MWR-D-15-0394.1

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